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RAI Response: ISORAD-TC1, Docket No. 71-3099, 10/31/2021; SAR Test Report Package (Non-Proprietary)
	ML21330A020
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Site:	07103099
Issue date:	10/31/2021
From:	; Isoflex Radioactive
To:	; Division of Fuel Management
	Nishka Devaser, NMSS/DFM
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ISORAD-TC1 Type B Package Docket Number 71-3099 RAI Test Reports Certain Information Withheld Under 10 CFR 2.390 Security Related & Proprietary Information USNRC RAI Purposes Only

ISO-RAD Canada Inc Ottawa, ON, Canada By: Kevin J. Schehr, DBA and Wayne Pettipas, Eng.

T: +1-504-305-4320 Date: October 27, 2021 T: +1-504-717-7811 (m)

Subject:

Validation Report for ISORAD-TC1 Thermal Analysis Introduction The purpose of this report is to answer the United States Nuclear Regulatory Commission (USNRC)s Request for Additional Information (RAI) 3-3.

The RAI is as follows:

Provide adequate description and results on the type of analysis used to validate the thermal code used to perform the thermal evaluation of the ISORAD-TC1 transportation package during NCT and HAC. SAR Chapter 3 states that the finite element analysis (FEA) and the thermal model of the package were validated against thermal analysis of other similar transport containers.

However, the staff did not find any description or validation results that support this statement in the SAR. The staff needs this information to verify that the applicant used adequate analytical tools that would result in realistic or conservative estimate of thermal results.

This information is needed to determine compliance with SSR-6 Paragraphs 654, 656, 657, and 728 ISO-RAD Canada Inc. (ISO-RAD) used a four stage Thermal Analysis validation process for the ISORAD-TC1. The four stages consisted of the following:

1) Review of other similar Type B packages as shown in Table 1, Table 2, and Table 3.

2) Review of SolidWorks Flow Simulation 2019 Validation documents,

3) Review of the Thermal Analysis results as compared to other similar packages as shown in Tables, and

4) Hand calculations to verify some of the results.

Stage 1 The Stage 1 Validation Review was conducted by ISO-RAD. ISO-RAD reviewed other manufacturers SAR applications to use as a comparison for how other packages were constructed. The Thermal Analysis review examined the materials of construction, thermal coefficients used, model construction, the approaches to the Thermal Simulations, the software used, and other factors.

Table 1 shows the basic components and dimensional data used for the packages under comparison. The packages that were compared are very similar dimensionally and weight with the exception of the Revision 0

Validation Report October 27, 2021 Page 2 Component C)uter Dru m Dia meter 390m m 400m m 400m m 400mm 325m m C)uter Dru m Height 550m m 494mm 494mm 494mm 415mm In ner Cask Diameter 168 m m 181mm 178mm 178mm 230mm I nner Cask Hei ht 250mm 245mm 272mm 272 mm 325mm DU Shield Diameter 161.3 mm 174mm 171mm 171mm 173mm DU Shield Hei ht 216 mm 216.6 mm 240.6mm 240.6mm 267mm Drum/Keg/Other Drum Keg Keg Keg No ne Insulation Material Kaolite 1600 Poly Foam Poly Foam Poly Foam No ne Outer Drum Diameter 533.4mm 425mm 424mm 398.65 Outer Drum Height 508mm 540mm 585mm 593mm Inner Cask Diameter 190.5 mm 169mm 200mm 17().36 mn Inner Cask Height 270mm 248mm 302.5mrt 27S} mm DU Shield Diameter 178.0 mm 160.3mrl 161.6mrt lSS},s mn DU Shield Height 238.25 mm 214mm 217.9mrt 21.ci mm Drum/Keg/Other Pallet & Cage Drum Keg Insulation Material None Table 1: Summar')' of basic TyJ:)e B J:>acka e dimensions.

Table 2 shows the basic components and the materials of construction of the packages lmder comparison. The comparison reveals similarities that include depleted uranium shielding, steel outer casings, eutectic baniers, insulating materials, and an Outer Dnun/keg. Most of the packages lmder review used the approach of insulating the thennal load within the package. Two Packages reviewed

) did not contain insulating materials or outer dnllllslkegs. The last two packages used heat dissipation principles to meet the the1mal requirements.

-i---

Material Outer Drum( exterior) 300 ss 304SS 304SS 304SS No ne Outer Drum(interior) 300 ss 304SS 304SS 304SS No ne Inner Cask(exterior) 300SS 304SS 304S$ 304SS 304SS Inner Cask(interior) 300 ss 304 ss 304ss 304 S Shield Mat/ Thick DU(63m m) DU(51mm) U ( 46mm) DU( 6 mm)

Shield Plug (exterior) 300 ss 304 ss 304 S 304 ss Shield Plug (interior) DU(UNK) DU(UNK) DU(U K) DU(U_N)

Eutectic Barrier Brass/Copper Unknown Unkn wn Unkn0\11n Insulation Material Kaolite 1600 Poly Foam Poly Fo 1m Poly F am No ne

Validation Report October 27, 2 02 1 Page 3 Outer Drum (exterior) Ca e - Steel Outer Drum interior Carbon Steel 300SS 304SS 304SS Inner Cask exterior 300SS 300SS 304SS 304SS Inner Cask (interior) 300SS 300SS 304SS Titanium (GR 2)

Shield Mat/Thick DU (61.2mm) DU (63 mm) DU ( 49.5mm) DU (62 mm s

Eutectic Barrier Copper Brass Unknown Brass Insulation Material None Cork Pol Foam Cork Cork Table 2: Summary of basic materials of construction.

Table 3 compares the thermal analysis approach used for the packages lmder comparison. The thermal simulation analysis approach taken by other manufacturers was varied. - used the Dassault Systemes Abacus product and ISO-RAD chose another Dassault Systemes product, SolidWorks Flow Simulation.

Thermal Test Thermal Simulation ANSYS ANSYS ANSYS ANSYS Unknowt Fire Test No Yes Yes Yes Unknown Additional Analysis Scale model of Unknown Unknown Unknown Unknown Inner Container NCT Avg Surface T 45.2 °C Unknown Unknown Urknown Unknow n NCT Max Surface T 49.0°C Unknown Unknown urknown Unknown Test Wattage 58.1* 49.5 49.5 4 Thermal Test Thermal Simulation SolidWorks Unknown Abacus SolidWorks Flow Simul & Flow Simul .

ANSYS Fire Test No Unknown No No Additional Analysis Unknown Unknown Analysis to 3979 Hand Cale package NC::r Avg Surface T UnknoVl.n Unknown U nk nown 44.63° (

NCT Max Surface T 44.0°C** Unknown 41.S"C 48.8 2°C 3

u s*s.

Used incorrect watts per curie of lr-1 9 2 but did use a 5 8.1 watt heat load.

- Had higher temperatures but were deemed inaccessible by QSA Global.

Stage 2 The Stage 2 Validation Review was conducted by ISO-RAD. The review included review of Dassault Systemes SolidWorks Flow Simulation Software Validation documents. ISO-RAD also reviewed the validation docmnent for the ANSYS simulation software. The software validation processes are ve1y similar by conducting a series of prescribed models are running the simulation to achieve the result for

Validation Report October 27, 2021 Page 4 comparison. Thermal simulations conducted by SolidWorks Flow Simulation 2019 are extremely accurate with less than 1% error. SolidWorks has endorsed the approach of Verification first, then validation known as (V & V). SolidWorks Flow Simulation was validated through a process approved and accepted using the Guide de validation des progiciels de calcul de structures (Structural Analysis Software Validation Guide). This guide was published by AFNOR (Association Française de NORmalisation, French Standardization Association) and written and compiled by the SFM (Société Française des Mécaniciens). The SolidWorks Flow Simulation 2019 Validation document is attached.

ISO-RAD chose SolidWorks Flow Simulation because the package was designed using SolidWorks Engineering Software and the model was easily transferred into SolidWorks Flow Simulation. ISO-RAD chose Hawk Ridge Systems (HRS) to conduct the Thermal Analysis because they were rated number 1 in Canada and the USA for Engineering expertise with SolidWorks software. The ISORAD-TC1 BPIC Thermal Analysis was conducted by HRS using SolidWorks 2019 and SolidWorks Flow Simulation 2019 Service Pack 5.

ISO-RAD chose to run the simulation on the package with 65 Watts. The decision was based on the less than 1% error in the SolidWorks Flow Simulation software and to account for other variations between the simplified model and the actual design. The wattage limit for the approved package is 60.88 watts (10,125 curies of Ir-192). The actual wattage limit is 6.75% lower than the simulation tested wattage.

ISO-RAD believes the Thermal Simulation Model is a worst case because the air gaps, chamfers (also case small air gaps, and other features were removed making the heat transfer between components flow. The air gaps would create disruptions to heat transfer flow. Most of the packages reviewed made a similar approach for heat transfer.

Stage 3 The Stage 3 Validation Review was conducted by ISO-RAD and Hawk Ridge Systems (HRS). HRS reviewed and compared the thermal results from the Type B package before, during, and after the thermal simulation was conducted using the Dassault Systemes SolidWorks Flow Simulation software. ISO-RAD then reviewed other similar Type B package thermal results and compared to the ISORAD-TC1 results. The hand calculated results were within a margin of less than 1% (0.11%) of the ANSYS result 45.2°C versus 45.151 °C spreadsheet calculation (See spreadsheet comparison). During the review it was noted that the incorrect wattage value was used for Ir-192 but was tested to 58.1 watts. The error caused the package to be limited to 6250 curies of Ir-192 and was subsequently corrected and the curies were increased to 9450 curies. See Attached Spreadsheet comparison.

Stage 4 The Stage 4 Validation review was conducted using hand calculations as in attached report.

Conclusion A comparison was conducted based on the ANSYS results for the and verified by hand calculations. Another comparison was made of the ISORAD-TC1 package to the ANSYS package results, and the accuracy was essentially the same. In addition, the ISORAD-TC1 package simulation analysis was conducted at 65 watts versus the actual package limit of 60.88 watts. used the

Validation Report October 27, 2021 Page 5 SolidWorks Flow Simulation software to conduct thermal analysis on the package.

has used Abacus another product by the same company as SolidWorks for the package. Based on the review conducted by ISO-RAD the SolidWorks Flow Simulation software is as accurate as the ANSYS software and is valid.

Kevin J. Schehr, DBA Managing Director ISO-RAD Canada Inc.

Attachments:

1. SolidWorks Flow Simulation 2019 Validation

2. ANSYS Simulation Validation

3. ISORAD-TC1 / Comparison Spreadsheet

4. ISORAD-TC1 Hand Calculation Report

j;)..

-DASSAULT

.SLI.STEME.S SOLIDWORKS Simulation 2019 Validation BASED ON THE GUIDE DE VALIDATION DES PROGICIELS DE CALCULS DE STRUCTURES, by AFNOR ABSTRACT The purpose of this report is to present the accuracy of results given by SOLIDWORKS simulation 2019 using the Guide de validation des progiciels de calcul de structures (Structural Analysis Software Validation Guide) published by AFNOR (Association Franc,aise de NORmalisation, French Standardization Association).

101 validation examples (linear static analysis, vibration, dynamic response, thermal, nonlinear) from the guide are analyzed.

Results given by SOLIDWORKS Simulation generally fall within 1 % of the ideal solution. .... .,..,.. . .........

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zj5 SOLIDWORKS

INTRODUCTION The purpose of this report is to present the accuracy of results given by SOLIDWORKS Simulation 2019 using the Guide de validation des progiciels de ca/cul de structures (Structural Analysis Software Validation Guide).

This guide was published by AFNOR (Association Fran9aise de NORmalisation, French Standardization Association) and written and compiled by the SFM (Societe Fran9aise des Mecaniciens).

This report compares results It is a compilation of 143 validation examples for Finite Elements Analysis software. The given by SOLIDWORKS Simulation validation examples belong to a wide range of domains: linear static analysis, vibration, 2019 with 101 examples dynamic response, thermal, nonlinear, and fluid mechanics.

representative of the Guide de validation des progicie/s de Not all of them fit in the range of analysis capabilities of SOLIDWORKS Simulation. That's ca/cul de structures published by the case of the validation examples in fluid dynamics, for instance. Therefore, a set of 101 AFNOR (Association Fran9aise examples were selected. They are presented in this report using the evaluation form de NORmalisation, French template provided in the guide. In addition to the form, screen captures of the model and Standardization Association). results have been added when useful for a better understanding. However, information about each model's geometry, material properties, loads, and boundary conditions have not been copied into this report. To obtain all the above information, the reader should refer to the guide itself.

While modeling each problem in SOLIDWORKS Simulation, the intent has been to meticulously follow the modeling guidelines recommended for each example. When not possible, an equivalent approach was used. For instance, when it was not possible to perform a study with the recommended element type, an equivalent study was set up with another element type. Wherever applicable and meaningful, however, the validation examples have been run with more than one element type.

As you will see in this report, this year again, results given by SOLIDWORKS Simulation generally fall within 1 % of the reference solution.

Julien Boissat SOLIDWORKS Simulation Expert Technical Support Engineer

CONTENTS I. STRUCTURAL MECHANICS ............................................................................. 9

1. Linear static ...................................................................................................... 10 SLENDER BEAM WITH BOTH ENDS FIXED SSLL 01-89 ........................................................................................................................10 SLENDER BEAM ON THREE SIMPLE SUPPORTS SSLL 03-89 ........................................................................................................................11 BIMETALLIC STRIP FIXED ON BOTH ENDS CONNECTED WITH A RIGID BAR SSLL 05-89 ........................................................................................................................12 FIXED THIN ARC UNDER INPLANE BENDING SSLL 06-89 ........................................................................................................................13 FIXED THIN ARC UNDER OUT OF PLANE BENDING SSLL 07-89 ........................................................................................................................14 SIMPLY SUPPORTED THIN ARC UNDER INPLANE BENDING SSLL 08-89 ........................................................................................................................15 TWO BAR SYSTEM WITH THREE UNIVERSAL JOINTS SSLL 09-89 ........................................................................................................................16 FRAME WITH LATERAL CONNECTIONS SSLL 10-89 ........................................................................................................................17 FRAMEWORK OF ARTICULATED BASR UNDER CONCENTRATED LOAD SSLL 11-89 ........................................................................................................................18 PRE-STRESSED BAR SSLL 13-89 ........................................................................................................................19 SIMPLY SUPPORTED PLANAR FRAME SSLL 14-89 ........................................................................................................................20 PLATE UNDER BENDING AND SHEAR IN ITS OWN PLANE SSLP 01-89........................................................................................................................21 PERFORATED PLATE UNDER SIMPLE TRACTION SSLP 02-89........................................................................................................................23 CANTILEVER RECTANGULAR PLATE SSLS 01-89 ........................................................................................................................24 SIMPLY SUPPORTED SQUARE PLATE SSLS 02-89 ........................................................................................................................25 CIRCULAR PLATE UNDER UNIFORM PRESSURE LOAD SSLS 03-89 ........................................................................................................................26 RECTANGULAR HOLLOW BEAM UNDER TORSION SSLS 05-89 ........................................................................................................................27

CONTENTS THIN CYLINDER UNDER UNIFORM RADIAL PRESSURE SSLS 06-89 ........................................................................................................................28 THIN CYLINDER UNDER UNIFORM AXIAL PRESSURE SSLS 07-89 ........................................................................................................................29 THIN CYLINDER UNDER HYDROSTATIC PRESSURE SSLS 08-89 ........................................................................................................................30 THIN CYLINDER UNDER ITS OWN WEIGHT SSLS 09-89 ........................................................................................................................31 TORE UNDER INTERNAL UNIFORM PRESSURE SSLS 10-89 ........................................................................................................................32 SPHERICAL CAP UNDER INTERNAL PRESSURE SSLS 14-89 ........................................................................................................................33 SPHERICAL CAP UNDER RADIAL FORCE SSLS 15-89 ........................................................................................................................34 SPHERICAL CAP UNDER MOMENT SSLS 16-89 ........................................................................................................................35 SPHERICAL CAP UNDER ITS OWN WEIGHT SSLS 17-89 ........................................................................................................................36 SPHERICAL CAP UNDER IMPOSED DISPLACEMENT SSLS 18-89 ........................................................................................................................37 CYLINDRICAL SHELL UNDER ITS OWN WEIGHT SSLS 19-89 ........................................................................................................................38 PINCHED CYLINDRICAL SHELL SSLS 20-89 ........................................................................................................................39 SPHERICAL SHELL WITH HOLE SSLS 21-89 ........................................................................................................................40 SPHERICAL CAP UNDER EXTERNAL UNIFORM PRESSURE SSLS 22-89 ........................................................................................................................41 CYLINDRICAL MEMBRANE UNDER BENDING SSLS 23-89 ........................................................................................................................42 SIMPLY SUPPORTED RECTANGULAR PLATE UNDER UNIFORM PRESSURE SSLS 24-89 ........................................................................................................................43 SIMPLY SUPPORTED RHOMB PLATE UNDER BENDING SSLS 25-89 ........................................................................................................................44

PLATE UNDER NORMAL SHEAR SSLS 27-89 ........................................................................................................................45 FULL CYLINDER UNDER SIMPLE TRACTION SSLV 01-89 .......................................................................................................................46

CONTENTS FULL SPHERE UNDER UNIFORM PRESSURE SSLV 02-89 .......................................................................................................................47 THICK SPHERICAL TANK UNDER INTERNAL PRESSURE SSLV 03-89 .......................................................................................................................48 THICK INFINITE PIPE UNDER INTERNAL PRESSURE SSLV 04-89 .......................................................................................................................49 BEAM WITH ELLIPTIC CROSS SECTION UNDER TORSION SSLV 05-89 .......................................................................................................................50 RECTANGULAR SECTION SHAPE BEAM UNDER TORSION SSLV 06-89 .......................................................................................................................51 BLOCK STRETCHED UNDER ITS OWN WEIGHT SSLV 07-89 .......................................................................................................................52 PRISMATIC BEAM UNDER PURE BENDING SSLV 08-89 .......................................................................................................................53 THICK PLATE WITH ITS EDGES FIXED SSLV 09-89 .......................................................................................................................54

2. Non linear static ............................................................................................... 56 RECTANGLE UNDER PURE BENDING (PLANE STRESS, PERFECT PLASTICITY)

SSNP 11-89 .......................................................................................................................56 CYLINDER UNDER PRESSURE (PLANE STRAIN, PERFECT ELASTOPLASTICITY)

SSNP 13-89 .......................................................................................................................57

3. Linear dynamic ................................................................................................. 59 THIN CYLINDER FIXED ON BOTH ENDS SDLA 01-89 .......................................................................................................................59 SLENDER FOLDED BEAM, ONE END FIXED THE OTHER FREE SDLL 02-89 .......................................................................................................................61 SLENDER BEAM ON TWO SIMPLE SUPPORTS UNDER AXIAL FORCE SDLL 05-89 .......................................................................................................................62 PLANAR FRAME MADE OF I BEAMS SDLL 08-89 .......................................................................................................................63 SLENDER BEAM WITH VARIABLE RECTANGULAR SECTION, ONE END FIXED THE OTHER FREE SDLL 09-89 .......................................................................................................................64 SLENDER BEAM WITH VARIABLE RECTANGULAR SECTION, BOTH ENDS FIXED SDLL 10-89 .......................................................................................................................66 THIN CIRCULAR RING COMPLETELY FREE SDLL 11-89 .......................................................................................................................68 THIN CIRCULAR RING FIXED AT TWO POINTS SDLL 12-89 .......................................................................................................................70

CONTENTS THIN CIRCULAR RING FIXED BY AN ELASTIC LEG SDLL 13-89 .......................................................................................................................72 VIBRATION MODES OF AN ELBOWED PIPE SDLL 14-89 .......................................................................................................................74 THIN FREE RING WITH A PUNCTUAL MASS SDLL 16-89 .......................................................................................................................76 THIN SQUARE PLATE WITH 3 OR 4 FREE EDGES SDLS 01-89 .......................................................................................................................78 THIN RHOMBOID PLATE FIXED ON ONE EDGE SDLS 02-89 .......................................................................................................................80 THIN RECTANGULAR PLATE SIMPLY SUPPORTED ON EDGES SDLS 03-89 .......................................................................................................................81 THIN RING SHAPED PLATE FIXED ON INNER EDGE SDLS 04-89 .......................................................................................................................83 COMPRESSOR BLADE: THIN SHELL FIXED-FREE SDLS 05-89 .......................................................................................................................85 THIN WINGED CIRCULAR PLATE SDLS 06-89 .......................................................................................................................87 THIN SPHERE COMPLETELY IMMERSED IN A PERFECT AND INCOMPRESSIBLE FLUID SDLS 07-89 .......................................................................................................................89 BENDING OF SYMMETRICAL FRAME SDLX 01-89 .......................................................................................................................91 ASSEMBLY OF THIN RECTANGULAR SHAPED SHEETS SDLX 03-89 .......................................................................................................................93 II. THERMAL ...................................................................................................... 95

1. Linear steady state thermal............................................................................... 96 PIPE: PRESCRIBED TEMPERATURES TPLA 01-89 .......................................................................................................................96 PIPE : PRESCRIBED TEMPERATURE, CONVECTION TPLA 02-89 .......................................................................................................................98 PIPE : CONVECTION TPLA 03-89 .......................................................................................................................99 POWER OUTPUT IN A PIPE TPLA 04-89 .....................................................................................................................100 CYLINDRICAL BAR WITH FLUX DENSITY TPLA 05-89 .....................................................................................................................101 CYLINDRICAL BAR WITH CONVECTION TPLA 06-89 .....................................................................................................................102

CONTENTS ORTHOTROPIC PIPE TPLA 07-89 .....................................................................................................................103 TWO-MATERIAL PIPE : CONVECTION TPLA 08-89 .....................................................................................................................105 TWO-MATERIAL PIPE : CONVECTION, THERMAL CONTACT RESISTANCE TPLA 09-89 .....................................................................................................................106 SIMPLE WALL : PRESCRIBED TEMPERATURES TPLL 01-89......................................................................................................................107 SIMPLE WALL : PRESCRIBED TEMPERATURES, CONVECTION TPLL 02-89......................................................................................................................108 SIMPLE WALL : CONVECTION TPLL 03-89......................................................................................................................109 POWER OUTPUT IN A BAR TPLL 04-89......................................................................................................................110 TWO-MATERIAL WALL : CONVECTION TPLL 05-89......................................................................................................................111 TWO-MATERIAL WALL : CONVECTION, THERMAL CONTACT RESISTANCE TPLL 06-89......................................................................................................................112 L SHAPED PLATE WITH GEOMETRIC SINGULARITY TPLP 01-89 .....................................................................................................................113 ORTHOTROPIC SQUARE TPLP 02-89 .....................................................................................................................115 HOLLOW SPHERE: PRESCRIBED TEMPERATURES TPLV 01-89 .....................................................................................................................117 HOLLOW SPHERE: PRESCRIBED TEMPERATURES, CONVECTION TPLV 02-89 .....................................................................................................................118 HOLLOW SPHERE: CONVECTION TPLV 03-89 .....................................................................................................................119 TWO-MATERIAL HOLLOW SPHERE : CONVECTION TPLV 04-89 .....................................................................................................................120 TWO-MATERIAL HOLLOW SPHERE: CONVECTION, THERMAL CONTACT RESISTANCE TPLV 05-89 .....................................................................................................................121 POWER OUTPUT IN A HOLLOW SPHERE TPLV 06-89 .....................................................................................................................122 ORTHOTROPIC CUBE TPLV 07-89 .....................................................................................................................123

2. Non linear steady state thermal ...................................................................... 125

CONTENTS PIPE : CONVECTION, RADIATION TPNA 01-89 ....................................................................................................................125 SIMPLE WALL : CONVECTION, RADIATION TPNL 01-89 .....................................................................................................................126 RADIATION IN A SQUARE CAVITY TPNP 01-89 ....................................................................................................................127 HOLLOW SPHERE: CONVECTION, RADIATION TPNV 01-89 ....................................................................................................................128 RADIATION IN A CUBIC CAVITY TPNV 02-89 ....................................................................................................................129

3. Transient linear THERMAL .......................................................................... 130 CYLINDER : HEAT TRANSFER BY CONVECTION TTLA 01-89 .....................................................................................................................130 WALL UNDER THERMAL SHOCK TTLL 01-89 ......................................................................................................................132 PLATE : HEAT TRANSFER BY CONVECTION TTLL 02-89 ......................................................................................................................134 SPHERE : HEAT TRANSFER BY CONVECTION TTLV 01-89 .....................................................................................................................135 III. THERMOMECHANICS ............................................................................... 136

1. Linear static .................................................................................................... 137 THICK PIPE SUBMITTED TO A THERMAL GRADIENT HSLA 03-89 .....................................................................................................................137 IV. BIBLIOGRAPHY .......................................................................................... 138

I. STRUCTURAL MECHANICS

STRUCTURAL MECHANICS

1. Linear static EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo TuinkPad W540, Windows 10 x64, futel i7 vPro core, 16Gb RAM, Graphics Card Intel lID Graphics 4600.

Test name: SLENDER BEAM WITH BOTH ENDS FIXED Codification: SSLL 01-89 Test perfonned by: Julien BOISSAT Date : 3/25/2019 Model used Finite elements 0 Botmdary elements D Other Element type : BEAM Number of degrees of freedom or mesh density :

Nb of nodes = 135 Nb of elements = 130 Nb of DOF = 774 Results :

Physical quantity and Calculated Deviation Location reference unit value (%)

Shear force in G V(N) -540 -547 1. .29 Moment in G M(Nm) 2800 2800 0 Displacement in G v(m) - 4.92 X 10-2 - 4.92 X 10-2 0 Axial force in A H(N) -24000 -24000 0 Comments:

0---------------

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, futel i7 vPro core, 16Gb RAM, Graphics Card futel HD Graphics 4600.

Test name: SLENDER BEAM ON THREE SIMPLE SUPPORTS Codification: SSLL 03-89 Test e1fonned b : Julien BOISSAT Date : 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : BEAM Number of degrees of freedom or mesh density Nb of nodes = 132 Nb of elements = 126 Nb of DOF = 753 Results :

Physical quantity and Calculated Location Deviation(%)

reference unit value Moment inB M(Nm) +/- 63000 +/- 62960 .06 Displacement in B v(m) - 0.010 - 0.010 0 Reaction force in B V(N) 21010 21010 0 Comments :

The ve11ical beam was modeled in order to simulate the elastic suppo1t.

4P2019 08S08UI Al ri!,lls reseMICI. Confioenlill DoRII dotrilllle. 11

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation I Version: 2019 B3 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: BIMETALLIC STRIP FIXED ON BOTH ENDS CONNECTED WITH A RIGID BAR Codification: SSLL 05-89

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Test pe1fo1med by: Julien BOISSAT I Date: 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : BEAM Number ofdegrees of freedom or mesh density Nb of nodes =357 Nb of elements = 353 Nb ofDOF =2112 Results :

Physical quantity and Calculated Location Deviation(%)

reference unit value B V (m) -0.125 -0.123 1.6 D V (m) -0.125 -0.123 1.6 A V(N) 500 500 0 A M(Nm) 500 497.5 0.5 C V(N) 500 500 0 C M(Nm) 500 497.5 0.5 Comments:

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkPad W540, Windows l O x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: FIXED THIN ARC UNDER INPLANE BENDING Codification: SSLL 06-89 Test pe1fonned by: Julien BOISSAT Date: 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : BEAM Number of degrees of freedom or mesh density Nb of nodes = 1181 Nb of elements = 590 Nb of DOF = 3540 Results :

Physical quantity and Calculated Location Deviation(%)

referenee unit ,,aloe u ( m) 0.3791 0.3790 .03 B V (m) 0.2417 0.2417 0 0 (rad) 0.1654 0.1654 0 Comments:

e2019 Oassaul Systernes. Al li!,lls .....-.ed. Conli<letll!II Do rot clotrill.lle. 13

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: FIXED THIN ARC UNDER OUT OF PLANE BENDING Codification: SSLL 07-89 Test e1fonned b : Julien BOISSAT Date : 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : BEAMS Number ofdegrees offreedom or mesh density :

Nb ofnodes = 539 Nb ofelements = 269 Nb ofDOF = 1614 Results:

Physical quantity and Calculated Location Deviation(%)

reference unit value B llB (m) 0.13462 0.13449 0.1 For 0=15 ° M, (Nm) 74.1180 74.183* 0.09 MJ (Nm) - 96.5925 -96.405* 0.19 Comments :

: Obtained by averaging the nodal values oftwo neighboring elements e20190assaultSystemes. Al ii!,lls ...........,_ Confia<<itill Oorotdlsttibule. 14

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, futel i7 vPro core, 16Gb RAM, Graphics Card futel HD Graphics 4600.

Test name: SIMPLY SUPPORTED THIN ARC UNDER INPLANE BENDING Codification: SSLL 08-89 Test erfonned b : Julien BOIS SAT Date : 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : BEAM Number of degrees of freedom or mesh density Nb of nodes = 561 Nb of elements = 280 Nb ofDOF = 1683 Results:

Physical quantity and Location Calculated value Deviation(%)

reference unit A 0A (rad) -3.0774 X 10 2 -3.0774 X 10 2 0 B 0B(rad) 3.0774 X 10 2 3.0774 X 10 2 0 C vc(m) -1.9206 X 10- 2 -1.9218 X 10-2 0.05 B UB (m) 5.3912 X 10 2 5.3923 X 10 2 0.02 Colillilents :

e2019 Oassaul Systernes. Al ii!,lls reser.ed. Conli<letll!II Do rot clotrill.lle. 15

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: TWO BAR SYSTEM WITH THREE UNIVERSAL JOINTS Codification: SSLL 09-89 Test performed by : Julien BOISSAT Date : 3/25/2019 Model used Finite elements Boundary elements Other Element type : BAR Number of degrees of freedom or mesh density :

Nb of nodes =5 Nb of elements = 2 Nb of DOF =3 Results :

Physical quantity and Location Calculated value Deviation(%)

reference unit C vC (m) -3 x 10-3 -3 x 10-3 0 Bar AC (Pa) 7 x 107 7 x 107 0 Bar BC (Pa) 7 x 107 7 x 107 0 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer con figuration used: Lenovo ThinkPad W540, Windows 10 x64, futel i7 vPro core, 16Gb RAM, Graphics Card futel HD Graphics 4600.

Test name: FRAME WITH LATERAL CONNECTIONS Codification: SSLL 10-89 Test erfonned b : Julien B OIS SAT Date : 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : BEAM Number of degrees of freedom or mesh density Nb of nodes = 417 Nb of elements = 411 Nb ofDOF = 2451 Results :

Physical quantity and Location Calculated value Deviation (%)

reference unit A 0 (rad) 0.227118 0.2274 0.12 A MAB(Nlll) 11023.72 11021 0.02 A M.A.c(Nm) 113.559 113.7 0.12 A MAn(Nm) -12348.588 -12347 0.01 A M.A.E(Nlll) 1211.2994 1213 0.13 Comments:

e20190assaultSysternes. Alii!,llsreseMOd.ConliGenlill Oorotclotrill.lle. 17

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 1 6Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: F RAM EWORK OF ARTICULATED BAS R UND ER CONCENTRATED LOAD Codification: SSLL 11-89 Test e1fo1med b : Julien BOIS SAT Model used Finite elements 0 Bounda1y elements Other Element type : BAR Number of degrees offreedom or mesh density Nbofnodes =4 Nb of elements = 4 NbofDOF =6 Results :

Physical quantity and Location Calculated value Deviation(%)

reference unit C uc(m) 0.2651 7xl0 3 0.2652 X 10 J 0.01 C vc{m) 0.08839 X 10-J 0.08839 X 10-J 0 D llD (m) 3.47902 X 10 J 3.479 X 10 J 0 D vv(m) -5. 60084 X 10-J -5.6 X 10-J 0.02 Comments :

e20190assaulSysternes. Alii!,lls reseMOd. Conli<letllill Oorotclotrill.lle. 18

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configmation used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: PRE-S TRESSED BAR Codification: SS LL 13-89 Test 1fonned by: Julien BOISSAT I Date : 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : BEAMS N umber ofdegrees of freedom or mesh density :

Nb of nodes = 200 Nb of elements = 196 Nb ofDOF = 1164 Results:

Physical quantity and Calculated Location Deviation (%)

reference unit value CE N, traction force 584584 586279 0.29 (N)

H M, bending 49249.5 48233 2.06 moment(Nm)

D vv(m) --0.0005428 -0.0004901 10.75 Comments :

e2019DassaultSysternes. Al li!,lls reseMOd. ConliGenlill Oorotdlstril>ule. 19

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SilvIPL Y SUPPORTED PLANAR FRAME Codification: SSLL 14-89 Test erfonned b : Julien BOISSAT Date: 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : BEAM Number ofdegrees offreedom or mesh density Nb ofnodes = 285 Nb ofelements = 280 Nb ofDOF = 1680 Results :

Physical quantity an d reference Deviation(

Location Calculated value unit %)

A V, vertical 31500.0 31500.6 0.002 reaction (N)

A H, horizontal 20239.4 20239.6 0.001 reaction (N)

C vc(m) -0.03072 -0.03079 0.23 Comments : Typo conected in the guide: p=-30000N instead of3000N/m e2019DaosaulSystemes. Alii!,lls ..........,_ Confia<<itill Oorotclotti1111e. 20

STRUCTURAL MECHANICS EVALUATION FOR M Software: SOLIDWORKS Simulation I Version: 2019 B3 Computer configmation used: Lenovo TuinkPad W540, Windows 10 x64, Intel i 7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: PLATE UNDER BENDING AND SHEAR IN ITS OWN PLANE C edification: SSLP O 1-89 Test pe1fom1ed by: JulienBOISSAT I Date : 3/25/2019 Model used Finite elements 0 Boundaryelements Other E lement type : SHELL 6 Number ofdegrees offreedom or mesh density Nb of nodes = 5290 Nb ofelements = 2541 Nb ofDOF = 31530 Results :

Physical Reference Calcul ated Location Deviation (%)

Quantity value value (L,y) v1 0.3413 0.35607 4.328%

(L,v) V2 0.3573 0.35608 -0.341%

5 ................................................. ..... . . . ....... -

2 t- 1 o- -+- --+ 1-- ..._ - --+ ,_ -- --+- I 0.000 0.200 0.400 0.600 0.800 1.000 Distance parametiique T aw({ [N/mm"2 (MPa))

Distribution ofShear stress along Y e2019 Oaosaul Systemes. Al li!,lls ...........,_ Confia<<itill Do IOI clotti1111e. 21

STRUCTURAL MECHANICS Distribution of SX stress along top edge Distribution of SX stress along fixed edge Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: PERFORATED PLATE UNDER SIMPLE TRACTION Codification: SSLP 02-89 Test performed by : Julien BOISSAT Date : 3/25/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 7168 Nb of elements = 3424 Nb of DOF = 42444 Results :

Location Physical quantity Reference Calculated Deviation (%)

(Space-Time) (unit) value value (a,0) (N/mm2) 7.5 7.584 1.12 (a,/4) (N/mm2) 2.5 2.513 0.52 (a,/2) (N/mm ) 2

-2.5 -2.559 2.36 Comments :

The formulas of the analytical solution are solely applicable when the length and width of the sheet are large enough compared to the diameter of the hole. The stresses away from the hole should not be affected by its presence. With the given dimensions, the ratio between the diameter and the width is equal to 0.2 which is not enough. For the formulas to be applicable, the plate should be at least 4 times larger (ratio equal to 0.05). The values in the table above are given for such a modified geometry.

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: CANTILEVER RECTANGULAR PLATE Codification: SSLS 01-89 Test performed by : Julien BOISSAT Date : 3/25/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 10467 Nb of elements = 5058 Nb of DOF = 62604 Results :

Physical Location Reference value Calculated value Deviation (%)

quantity Side x = 1 w (m) -0.0973 -0.0958 1.57 Comments :

Do not perform Large Displacement calculations.

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SIMPLY SUPPORTED SQUARE PLATE Codification: SSLS 02-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 4505 Nb of elements = 2184 Nb of DOF = 27030 Results :

Physical Reference Calculated Location Deviation (%)

quantity value(1) value Center O wO (m) -0.1649 x 10-3 -0.1648x 10-3 0.01 Comments :

(1)

"Roarks Formulas for Stress & Strain" (6th ed. p.458) gives the following formula for a thin simply supported square plate :

qb 4 Max y = where b is the width, a is the length, t the thickness and = -0.0444 for Et 3 b

=1 which gives a maximum displacement ymax = -0.1649 x 10-3m.

a

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: CIRCULAR PLATE UNDER UNIFORM PRESSURE LOAD Codification: SSLS 03-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 and SHELLAX Number of degrees of freedom or mesh density :

SHELL 6: SHELLAX Nb of nodes = 10343 Nb of nodes = 1525 Nb of elements = 5082 Nb of elements = 510 Nb of DOF = 59922 Nb of DOF = 3040 Results :

Physical Reference Calculated value Deviation (%)

Location quantity value SHELL 6 SHELLAX SHELL 6 SHELLAX Center O wO (m) -0.0065 -0.0065 -0.0065 0 0 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configmation used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: RECTANGULAR HOLLOWBEAM UNDER TORSION Codification: SSLS 05-89 Test e1fonned b : JulienBOISSAT Date: 3/25/2019 Model used Finite elements 0 B01mda1y elements D Other D Element type : SHELL 6 Number ofdegrees offreedom or mesh density Nb ofnodes = 10292 Nb ofelements = 5114 Nb ofDOF = 61368 Results :

Location Physical Reference Calculated Deviation (Space-Time) quantity (1mit) value value (%)

Point A v(m) -0.617 X 10-(> -0.616 X 10"6 0.16 (0.5,0,0.05) 0x(rad) 0.123 X 10 -4 0.123 X 10-4 0

<1xy (Pa) -0.11 X 106 -0.1096 X 106 0.36 Point B w(m) -0.987 X 1o*6 -0.986 X 10*6 0.1 (0.8,-0.05,0) 0x(rad) 0.197 X 10 -4 0.}97 X 10-4 0

<1,;y (Pa) (I) -0.11 X 106 -0.1096 X 106 0.36 Collllllents :

(I) A typo was detected in the Guide: at point B, the table should read <lxz instead of <lxy.

e20190aosaulSystemes. Alii!,lls .....-.-ed. Confia<<itill Oorotclotti1111e. 27

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: THIN CYLINDER UNDER UNIFORM RADIAL PRESSURE Codification: SSLS 06-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : SHELL6T Number of degrees of freedom or mesh density :

Nb of nodes = 4296 Nb of elements = 2104 Nb of DOF = 25776 Results :

Physical Reference Calculated Location Deviation (%)

quantity value value 11 (Pa) 0.0 70 (1) -

All points 22 (Pa) 5.00 x 105 5.02 x 105 0.4 R (m) 2.38 x 10-6 2.38 x 10-6 0 L (m) -2.86 x 10-6 -2.86 x 10-6 0 Comments :

(1) 11 = 500 Pa should be compared to the load and/or to 22 . The result is acceptable (ratio equal to 1/1000).

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: THIN CYLINDER UNDER UNIFORM AXIAL PRESSURE Codification: SSLS 07-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : SHELL6 Number of degrees of freedom or mesh density :

Nb of nodes = 10368 Nb of elements = 5120 Nb of DOF = 62208 Results :

Physical Reference Calculated Location Deviation (%)

quantity value value 11 (Pa) 5.00 x 105 5.00 x 105 0 22 (Pa) 0.0 152 (1) -

All points L (m) 9.52 x 10-6 9.525 x 10-6 0.05 R (m) -7.14 x 10-7 -7.155 x 10-7 0.14 Comments :

(1) 22 = 106 Pa should be compared to the load and/or to 11 . The result is acceptable (ratio smaller than 1/1000).

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: THIN CYLINDER UNDER HYDROSTATIC PRESSURE Codification: SSLS 08-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 4600 Nb of elements = 2256 Nb of DOF = 27504 Results :

Physical Reference Calculated Location Deviation (%)

quantity value value x 11 (Pa) 0.0 90 (1) -

x = L/2 22 (Pa) 5.00 x 10 5 4.99 x 105 0.2 x = L/2 R (m) 2.38 x 10-6 2.37 x 10-6 0.42 x=L L (m) -2.86 x 10 -6

-2.86 x 10-6 0 (rad) (2) 1.19 x 10 -6 1.185 x 10 -6 0.42 Comments :

(1) 11 = 640 Pa should be compared to the load and/or to the calculated stress 22 . The result is acceptable (ratio around 1/1000).

(2) (rad) Derived from =arcsin R(l)/l = R(x = L/2)/(L/2)

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: THIN CYLINDER UNDER ITS OWN WEIGHT Codification: SSLS 09-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

SHELL 6:

Nb of nodes = 33040 Nb of elements = 16188 Nb of DOF = 198240 Results :

Physical Reference Location Calculated value Deviation (%)

quantity value x 22 (Pa) 0.0 48 (1) -

x=L 11 (Pa) 3.14 x 105 3.14 x 105 0 x (m) 2.99 x 10-6 2.99 x 10-6 0 R (m) -4.49 x 10-7 -4.49 x 10-7 0 (rad) -1.12 x 10-7 -1.15 x 10-7 2.68 Comments :

(1) 22 = value should be compared to the load and/or to 11. The result is acceptable (ratio equal to 1/1000).

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: TORE UNDER INTERNAL UNIFORM PRESSURE Codification: SSLS 10-89 127 Test erfonned b : Julien BOISSAT Date: 3 /25/2019 Model used Finite elements 0 Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density Nb of nodes = 813 Nb of elements = 37 4 Nb of DOF = 4866 Results:

Location Physical Reference Calculated Deviation (Space-Time) quantity (1mit) value value (%)

Any r <J22 (Pa) 2.5 X 105 2.51 X 105 0.40 r=a b an (Pa) 7.5 X 105 7.46 X 105 0.53 Jr(m) 1.19 x 10-1 1.11 x 10-1 -1.68 r = a+b <J11 (Pa) 4.17 X 105 4.16 X 105 0.24 Jr(m) 1.79 X 10-6 1.77 X 10-6 -1.12 Comments :

Any r corresponds to edge 1.

r = a - b corresponds to edge 2.

r = a + b con*esponds to edge 3.

e21119 Oaosaul 5Ystemes. Al li!,lls rese,vect Confioetllill Do rot clottibule. 32

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SPHERICAL CAP UNDER INTERNAL PRESSURE Codification: SSLS 14-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 2359 Nb of elements = 1134 Nb of DOF = 14145 Results :

Reference Calculated Deviation Location Physical quantity value value (%)

For every 11 = 22 (Pa) 2.50 x 105 2.50 x 105 0

= 90° R (m) 8.33 x 10-7 8.34 x 10-7 0.12 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SPHERICAL CAP UNDER RADIAL FORCE Codification: SSLS 15-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 4755 Nb of elements = 2244 Nb of DOF = 28527 Results :

Physical Calculated Deviation Location Reference value quantity value (%)

Mid-surface 11 (Pa) 0 8.7 -

22 (Pa) 9.09 x 105 9.07 x 105 0.22 On external plane R (m) 4.33 x 10-6 4.33 x 10-6 0 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SPHERICAL CAP UNDER MOMENT Codification: SSLS 16-89 Test pe1fonned by: Julien BOISSAT Date: 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density Nb of nodes = 3130 Nb of elements = 1459 Nb ofDOF = 18777 Results:

Physical Reference Calculated Location Deviation(%)

quantity value value a22 (Pa) 8.26 x IO' 8.18 x IO' -0.96 Outer edge JR(m) 3.93 X }0 6 3.93 X }0 6 0 Comments:

Outer edge con-esponds to 111embra11e stress 011 edge 1.

e2019DaosaulSystemes. Alii!,lls ..........,_ Confia<<itill Oorotclotti1111e. 35

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SPHERICAL CAP UNDER ITS O\VN WEIGHT Codification: SSLS 17-89 Test erfonned b : JulienBOISSAT Date: 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density Nb of nodes = 4607 Nb of elements = 2240 Nb of DOF = 27639 Results:

Physical Reference Calculated Location Deviation (%)

quantity value value 4

OH (Pa) 7.85 X 10 7.80 X 104 0.64 0=90 ° 0'22 (Pa) -7.85 X 10 4

-7.90 X 104 0.64 R(m) 4.86 X 10- 1 4.88 X 10-1 0.41 Comments :

0 = 90°c01re.s 011ds Toed e I.

e2019DassaultSystemes. Alli!,llsresetved.Confia<<itill Oorotclotti1111e. 36

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SPHERICAL CAP UNDER IMPOSED DISPLACEMENT Codification: SSLS 18-89 Test erfonned b Date: 3/25/2019 Model used Finite elements 0 Botmdary elements D Other D Element type : SHELL 6 Number ofdegrees of freedom or mesh density Nb ofnodes = 4607 Nb ofelements = 2240 Nb ofDOF = 27378 Results Physical Reference Calculated Location Deviation (%)

quantity value value Vi (N) per radian 4.62 X }0 4 4.64 X 104 0.4 Mid surface an (Pa) 0.0 6.9xI04 < 1> -

<122 (Pa) 2.1 X }07 2.IxI0 7 0 an (Pa) 3.81x IO' 3. 79xIO' 0.79 Extemal plane

<122 (Pa) 3.24 X 107 3.33 X 10 7 2.78 Collllllents

<1 > Compared to cm, au is negligible.

Mid smface corresponds to membrane stress 011 edge 1.

External lane co,res 011ds to bottom stress 011 ed e 1.

e2019DaosaulSystemes. Alii!,lls ..........,_ Confia<<itill Oorotclotti1111e. 37

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: CYLINDRICAL SHELL UNDER ITS OWN WEIGHT Codification: SSLS 19-89 Date: 3/25/2019 Finite elements 0 Boundary elements Other Element type: SHELL 6 Number ofdegrees offreedom or mesh density :

Nb ofnodes = 4565 Nb ofelements = 2214 Nb ofDOF = 27390 Results:

Physical Reference Calculated Location Deviation(%)

quantity value value B WB(m) -3.70 X 10 2 -3.6x 10 2 2.78 Collllllents:

In the Guide, the unit of y was interpreted as N/m3 instead ofkg/m3

e2019DaosaulSystemes. Alii!,lls ..........,_ Confia<<itill Oorotclotti1111e. 38

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, futel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: PINCHED CYLINDRICAL SHELL Codification: SSLS 20-89 Test erformed b : Julien BOISSAT Date: 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 4600 Nb of elements = 2240 Nb of DOF = 27600 Results:

Reference Calculated Location Physical quantity Deviation (%)

value value v(m),

A -113.9 X 10-J -113.7 X 10-J 0.18 displacement in y Collllllents:

e2019DaosaulSystemes. Alii!,lls ..........,_ Confia<<itill Oorotclotti1111e. 39

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, futel i7 vPro core, 16Gb RAM, Graphics Card futel HD Graphics 4600.

Test name: SPHERICAL SHELL WITH HOLE Codification: SSLS 21-89 G]

Test perfonned by : Julien BOIS SAT Date: 3/25/2019 Model used Finite elements 0 BOlmdary elements Other Element type : SHELL 6 Number ofdegrees offreedom or mesh density Nb ofnodes = 1188 Nb ofelements =564 Nb ofDOF = 7128 Results:

Physical Reference Calculated Lo cation Deviation(%)

quantity value value llA (m),

A(R,0,0) 94.0 X 10*3 96.8 X 10*3 2.89 displacement in x Comments :

e2019DaosaulSystemes. Alii!,lls ...........,_ Confia<<itill Oorotclotti1111e. 40

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W 540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SPHERICAL CAP UNDER EXTERNAL UNIFORM PRESSURE Codification: SSLS 22-89 Test e1fonned b : Julien BOISSAT Date: 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : SHELL 6 Number ofdegrees offreedom or mesh density :

Nbofnodes =10347 Nb ofelements = 4978 NbofDOF =61785 Results :

Reference Calculated Deviation Location Physical quantity value value (%)

° 1/f = 15 11 (m), -1.73 X 10-j -1.76x 10-j 1.73 1/1 =45

° horizontal -1.02 X 10- 3 -1.0l x 10- 3 0.99 1/f = 15

° a (Pa), external -0.74 X 108 -0.69 X 108 7.25 1/f = 45

° meridian -0.68 X 10 -0.69 X 108 1.47 Comments :

02019 Dassaul 5Ystemes. Al li!,lls "'"""""'- Conlioenlial Do rot clotri1111e. 41

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: CYLINDRICAL MEMBRANE UNDER BENDING Codification: SSLS 23-89 Test e1fonned b : Julien B OISSAT Date: 3/25/2019 Model used Finite elements 0 Boundary elements Other Element type : SHELL 6 Number ofdegrees offreedom or mesh density :

First and second load Nb ofnodes = 4473 Nb ofelements = 2168 Nb ofDOF = 26436 Results:

Reference Calculated Deviation Location Physical quantity value value (%)

circumferential stress 59.93 -0.12 Point E 60 on external skin (MPa) 59.80 -0.33 Comments :

e2019DaosaulSystemes. Alii!,lls ..........,_ Confia<<itill Oorotclotti1111e. 42

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation I Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SIMPLY SUPPORTED RECTANGULAR PLATE UNDER UNIFORM PRESSURE Codification: SSLS 24-89 L @1_ 1 _ J__ \

+rL_LJ __LL L i, j i_LJ_ J_ \

'i --

1 - -l---l-:'W-f--t-a

\__

... -t-+-1 - -fil Test pe1fo1med by : Julien BOISSAT I Date: 3/25/2019 Model used Finite elements 0 Boundaiy elements Other Element type : SHELL 6 Number ofdegrees offreedom or mesh density:

b/a = 1 bla=2 b/a=5 Nb ofnodes = 899 Nb ofnodes = 1798 Nb ofnodes = 4499 Nb ofelements = 418 Nb ofelements = 853 Nb ofelements = 2158 Nb ofDOF = 5391 NbofDOF = 10785 Nb ofDOF = 26991 Results:

Reference Calculated Location Physical quantity (I) Deviation(%)

value value a (deflection at A) 0.0443 0.0444 0.23 b/a = 1.0 Bending moment fJ 0.0479 0.0479 0 BendinK moment /h 0.0479 0.0479 0 a (deflection at A) 0.1106 0.1106 0 bla = 2.0 Bending moment fJ 0.1017 0.1017 0 Bending moment /J1 0.0464 0.0463 0.22 a (deflection at A) 0.1415 0.1415 0 b/a = 5.0 Bending moment fJ 0.1246 0.1245 0.08 Bending moment /J1 0.0375 0.0376 0.27 Comments :

Values a, /J and ,8J are calculated from the values ofWmax, O'x max, O'y max and the following

. apa 4 2 _ 6M

, Mxnmc. - /Jpa and Mymax = /Ji pa and <YFlex

_ 2 fo1mulas . wnmc --3 Practically, /J = SXBenciing (Point A) /0.06, /31 =SYBending (Point A) /0.06 and a = WmaxllO All in SI units.

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SIMPLY SUPPORTED RHOMB PLATE UNDER BENDING Codification: SSLS 25-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

= 80° = 60° = 40° = 30° N. of nodes = 4657 N. of nodes = 4617 N. of nodes = 4701 N. of nodes = 4729 N. of elements=2260 N. of elements=2236 N. of elements=2266 N. of elements = 2268 N. of DOF = 27942 N. of DOF = 27702 N. of DOF = 28206 N. of DOF = 28374 Results :

Physical Reference Calculated Location Deviation (%)

quantity value value

= 80° 1.409 x 10-3 1.408 x 10-3 -0.07

= 60° 0.9318 x 10-3 0.9320 x 10-3 0.021 wC (mm)

= 40° 0.3487 x 10-3 0.3506 x 10-3 0.545

= 30° 0.1485 x 10-3 0.1503 x 10-3 1.212 Comments :

A typo in the guide was corrected: E = 30 x 106 Pa instead of 36 x 106

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configtn*ation used: Lenovo TuinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Gra hies Card Intel HD Gra hies 4600.

Test name: PLATE UNDER NORMAL SHEAR Codification: SSLS 27 89 Test Date: 3/25/2019 Model used Finite elements 0 Botmdary elements Other Element type : SHELL 6 Nmnber ofdegrees offreedom or mesh density :

Nb ofnodes = 9663 Nb ofelements = 4650 Nb ofDOF = 57804 Results :

Reference Calculated Deviation Location Physical quantity value value (%)

Displacement w Point C 35.37 X 10* 3 35.30 X 10* 3 -0.23 (m) I Comments :

e2019DaosaulSystemes. Alii!,lls ..........,_ Confia<<itill Oorotclotti1111e. 45

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, futel i7 vPro core, 16Gb RAM, Graphics Card futel HD Graphics 4600.

Test name: FULL CYLINDER UNDER SIMPLE TRACTION Codification: SSLV 01-89 Model used Finite elements 0 Boundary elements Other Element type : TETRA 10 Number ofdegrees offreedom or mesh density :

Nb ofnodes = 3188 Nb ofelements = 1915 Nb ofDOF = 9561 Results:

Physical Reference Calculated Deviation Location quantity value value (%)

point A u,1 (m) J.5 X 10-3 1.5 X 10-3 0 point B lfB (m) 1.5 X 10"3 1.5 X 10-3 0 point C uc(m) 1.5 X 10-3 1.5 X 10"3 0 pointD lfD(m) 1 X 10"3 1 X 10"3 0 point E llE(lll) 0.5 X 10-3 0.5 X 10-3 0 point A W,t (m) -0.15 X 10-J -0.15 X 1 o-J 0 pointD WD(lll) -0.15 X 10"3 -0.15 X 10"3 0 point E W£(lll) -0.15 X 10-3 -0.15 X 10*3 0 point F wp(m) -0.15 X 10"3 -0.15 X 10"3 0 Comments:

e21119 Dassaul 5Ystemes. Al li!,lls .....,.,.,_ Confi<lential Do not dotrillule. 46

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: FULL SPHERE UNDER UNIFORM PRESSURE Codification: SSLV 02-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 24086 Nb of elements = 16357 Nb of DOF = 72255 Results :

Reference Calculated Deviation Location Physical quantity value value (%)

point A x (MPa) -100 -100.04 0.04 point B y (MPa) -100 -99.77 -0.230 point C z (MPa) -100 -100.09 0.090 point A uA (m) -0.2 x 10-3 -0.2 x 10-3 0

-3 point B vB (m) -0.2 x 10 -0.2 x 10-3 0 point C wC (m) -0.2 x 10-3 -0.2 x 10-3 0 point A x (MPa) -100 -99.973 -0.03 point B y (MPa) -100 -99.867 -0.133 point C z (MPa) -100 -99.901 -0.099 point A uA (m) -0.1 x 10 -3

-0.1 x 10-3 0 point B uB (m) -0.1 x 10-3 -0.1 x 10-3 0 point C uC (m) -0.1 x 10 -3

-0.1 x 10-3 0 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: THICK SPHERICAL TANK UNDER INTERNAL PRESSURE Codification: SSLV 03-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 or SHELLAX Number of degrees of freedom or mesh density :

TETRA 10 SHELLAX Nb of nodes = 11265 Nb of nodes = 2605 Nb of elements = 7439 Nb of elements = 1246 Nb of DOF = 33795 Nb of DOF = 5210 Results :

Physical Reference Calculated value Deviation (%)

Location quantity value SHELL 6 SHELLAX SHELL 6 SHELLAX Internal rr (MPa) -100 -99.082 -99.9 -0.92 -0.10 edge (MPa) 71.43 71.414 71.4 -0.02 -0.04 r=a u (m) 0.4 x 10-3 0.4 x 10-3 0.4 x 10-3 0 0 External rr (MPa) 0 0.029 0 - -

edge (MPa) 21.43 21.429 21.41 0 0.09 r=b u (m) 1.5 x 10-4 1.5 x 10-4 1.5 x 10-4 0 0 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: THICK INFINITE PIPE UNDER INTERNAL PRESSURE Codification: SSLV 04-89 Test performed by : Julien BOISSAT Date: 3/25/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 or SHELLAX Number of degrees of freedom or mesh density :

TETRA 10 SHELLAX Nb of nodes = 11865 Nb of nodes = 2505 Nb of elements = 7808 Nb of elements = 1202 Nb of DOF = 35595 Nb of DOF = 5010 Results :

Physical Reference Calculated value Deviation (%)

Location quantity value SHELL 6 SHELLAX SHELL 6 SHELLAX r (MPa) -60 -59.71 -59.966 -0.48 -0.06 Internal (MPa) 100 99.96 99.973 -0.04 -0.03 wall max (MPa) 80 80.28 79.96 0.35 -0.05 ur (m) 59 x 10-6 59 x 10-6 59 x 10-6 0 0 r (MPa) 0 0.02 0.005 - -

External (MPa) 40 40 39.996 0 -0.01 wall max (MPa) 20 20.04 19.996 0.2 -0.02 ur (m) 40 x 10-6 40 x 10-6 40 x 10-6 0 0 Comments :

STRUCTURAL MECHANICS E VALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card futel HD Graphics 4600.

Test name: BEAM WITH ELLIPTIC CROSS SECTION UNDER TORSION Codification: SSLV 05-89 Test pe1fonned by: Julien BOISSAT Date: 3/26/2019 Model used Finite elements 0 BOlmdary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density Nb of nodes = 10467 Nb of elements = 6604 Nb of DOF = 30930 Results:

Calculated Deviatio Location Physical quantity Reference value value n(%)

<Jxy (MPa) -39.5 -39.65 0.38 O {MPa) xz 0 0 ax9 (MPa) 39.5 39.65 0.38 Point A u(m) 0 0 v(m) -2.57 X 10- 3 -2.49 X 10-3 -3.11 Wm 0 0

<Jxy (MPa) 0 0 O (MPa) xz 19.8 19.73 -0.35 ax9 (MPa) 19.8 19.73 -0.35 Point B u(m) 0 0 v(m) 0 0 3 3 w(m) 4.97 X 10- (l) 4.98 X 10- 0.20 Point C u(!!!l -9.6 X 10- -9.64 X 10- 0.42 Collllllents:

In order to avoid singularities near the prescribed displacements, results have been obtained with a 16m beam and a measure of the results done at section x=8m. It implied the modification of the Reference values using the formulas given in the validation guide.

e20190aosaulSystemes. Alii!,lls-Confia<<itill Oorotdiotti1111e. 50

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019SP 2 Computer configuration used: Lenovo ThinkPad W 540, Windows 10 x64, Intel i7 vPro core, 16 Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name:RECTANGULAR SECTION SHAPE BEAM UNDER TORSION Codification: SSLV 06-89 Test erfonned b :JulienBOISSAT Date: 3/27/2019 Model used Finite elements 0 Boundary elements Other Element type : TETRA I 0 Number of degrees of freedom or mesh density :

l= 10m l=20m Nb of nodes = 1 2 1 37 Nb of nodes =2 3 284 Nb of elements = 76 28 Nb of elements = 1464 3 Nb of DOF = 3 595 2 Nb of DOF = 69393 Results:

Calculated Deviatio Location Physical quantity Reference value value n {%)

P oints A and B, middle of the long sides 0/L (rd/m) 2.78 X 10-3 2 7. 4 X 10-3 - 1 4. 4 l= 10m

<l xy I max {MPa) 202.6<1> 202.7 0.05 0/L (rd/m) 2 7. 8 X 10-3 2 7. 8 X 10-3 0 L=20m U xy I max {MPa) 203_7(1) 202.9 -0. 39 Comments:

Cl) The calculated <Jxy I max stress is the value fmmd on the lines of the long sides when far enough from the extremities in order to avoid the singularities . "Roark's Formulas foraStress

& Strain" (6 th ed. p. 348 ) gives the following formula for a rectangular beam with a "2 x 2b"

[

a (b)2 (b)' (b) 4 section ( b) 3T b ]

Max r = 1+0.6095 a+0.886 5 a -1 8. 023 a +0.9100 which gives the 8ab 2 ;

reference value of 203 .7 MPa. This value was used in place of the one prescribed by the validation guide which used one taken from an abacus (less accurate).

e2019Dassault5Ystemes. Al ii!,lls rese,vect Confia<<itill Dorotdisttibule. s1

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo TuinkPad W540, Windows 10 x64, futel i7 vPro core, 16Gb RAM, Graphics Card futel HD Graphics 4600.

Test name: BLOCK STRETCHED UNDER ITS OWN WEIGHT Codification: SSLV 07-89 Test erfonned by: Julien BOISSAT J Date: 3/27/2019 Model used Finite elements 0 Bmmdary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density Nb ofnodes = 9810 Nb of elements = 6380 Nb ofDOF = 29427 Results:

Calculated Deviati Location Physical quantity Referenee value value on(%)

Point B ws(m) 1.72 X 10 -6 1.72 X 10-6 0 Point Band C 6w(m) 0.014 X 10-6 0.014 X 10 -6 0

-6 Point A andD 6u(m) 0.17 X 10 0.17 X 10 -6 0 Point A Uzz(MPa) 0.229 0.229 0 Point£ u,,(MPa) 0.1145 0.1148 0.26 Comments :

ws (m) is measured in Z direction, and hence is ositive e20190aosaulSystemes. Alii!,lls ..........r. Confia<<itill Oorotdiotti1111e. S2

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: PRISMATIC BEAM UNDER PURE BENDING Codification: SSLV 08-89 Test performed by : Julien BOISSAT Date: 3/27/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 10221 Nb of elements = 6511 Nb of DOF = 30660 Results :

Calculated Deviatio Location Physical quantity Reference value value n (%)

Point B(1) zz (MPa) 10 10 0 Point A uA (m) -4 x 10-4 -4 x 10-4 0 Point B wB (m) 2 x 10-4 2 x 10-4 0 Point F or G vF = -vG (m) 0.15 x 10-4 0.15 x 10-4 0 Point D or E vD = -vE (m) -0.15 x 10-4 -0.15 x 10-4 0 Comments :

(1)

Supposed typographic error in the validation guide: it should read "Point B" instead of "Point A" on this location to calculate zz (MPa).

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinlcPad W540, Windows 10 x64, Intel i 7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: THICK PLATE WITH ITS EDGES FIXED Codification: SSLV 09-89 Test pe1fonned by: Julien BOISSAT Date: 3/27/2019 Model used Finite elements 0 Bounda1y elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density In both cases, meshing and calculating were done with the default Qarameters.

Results:

L oa d . P ressure p = lMPa Physical Reference Calculated Location Deviation (%)

quantity value value H20 0.76231 X 10-4 1.17

).,= 10 Q4 0.78661 X 10-4 0.7740 X 10-4 1.96 Ana. 0.6552 X 10-4 17.70 H20 0.53833 X 10-J 1.72

)., = 20 Q4 0.55574 X 10- J 0.5485 X 10-J 1.46 Ana. 0.52416 X 10-J 4.47 H20 0.80286 X 10-:z 2.43

)., = 50 Q4 wc(m) 0.8348 X 10-2 0.8234 X 10-2 1.49 Ana. Note: we (m) is 0.81900 X 10-2 0.42 H20 measured in z 0.26861 X 10-l 2.75

).,= 75 direction, and 0.28053 X 10-l 0.2766 X 10-l 1.61 04 Ana. hence is 0.27641 X 10-l 0.15 H20 positive 0.63389 X 10-l 0.53

')..= 100 Q4 0.66390 X 10-l 0.6534 X 10-l 5.03 Ana. 0.65520 X 10-l 3.77 e2019DaosaulSystemes. Alii!,lls ..........,_ Confia<<itill Oorotclotti1111e. S4

STRUCTURAL MECHANICS Load : Concentrated force F = 1 x 106 N Physical Reference Calculated Location Deviation (%)

quantity value value(1)

H20 0.42995 x 10-3 2.38

= 10 Q4 0.41087 x 10-3 0.4261 x 10-3 2.15 Ana. 0.29146 x 10-3 44.00 H20 0.25352 x 10-2 2.24

= 20 Q4 0.25946 x 10-2 0.2606 x 10-2 0.10 Ana. 0.23317 x 10-2 11.16 H20 0.35738 x 10-1 3.42

= 50 Q4 wC (m) 0.37454 x 10-1 0.3700 x 10-1 1.32 Ana. Note: wc (m) is 0.36433 x 10-1 1.45 H20 measured in -Z 0.11837 4.16

= 75 Q4 direction, and 0.12525 0.12326 1.56 Ana. hence is 0.12296 0.28 positive H20 0.27794 4.59

= 100 Q4 0.29579 0.2909 1.72 Ana. 0.29146 0.26 Comments :

(1)

The values in the above table are the average of the calculated values on the vertical edge (thickness) going through Point C because a concentrated force creates a singularity.

The test is clearly a success : it shows plainly the growing deviation between a calculated displacement with a thin PLATE type analytical solution and the displacement calculated with the SOLIDWORKS Simulation 3D model when the slenderness ratio decreases.

STRUCTURAL MECHANICS

2. Non linear static EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, futel i7 vPro core, 16Gb RAM, Graphics Card futel HD Graphics 4600.

Test name: RECTANGLE UNDER PURE BENDING (PLANE STRESS, PERFECT PLASTICITY)

Codification: SSNP 11-89 Test erfonned b : Julien BOIS SAT Date: 3/27/2019 Model used Finite elements 0 B01mda1y elements D Other D Element type :SHELL Number ofdegrees of freedom or mesh density :

Nb ofnodes = 100 Nb ofelements = 144 Nb ofDOF = 249 Results:

UA (mm) Value type Referenee value Calculated value Deviation(%)

a°xx(MPa) 483.0 466.3 -3.46 0.02875 Mo(N.m) 805.0 789 -2.04 0.05 M 1074 1059 -1.35 0.1 M 1174 1163 -9.78 0.15 M 1193 1182 -2.56 0.2 M 1199 1186 -1.07 0.3 M 1204 1192 -0.96 0.4 M 1205 1193 -1.00 0.5 M 1206 1193 -1.08 i cfxx 483 - (1) -

CX) Mr 1207.5 - -

Comments :

Cl) The software cannot create an infinite displacement. Moreover, in order to obtain convergence, a non-zero tangent modulus was used.

e2019 Oaosaul Systemes. Al rights rese<Ved. Confia<<itill Do IOI clotti1111e. 56

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: CYLINDER UNDER PRESSURE (PLANE STRAIN, PERFECT ELASTOPLASTICITY)

Codification: SSNP 13-89 Test performed by : Julien BOISSAT Date: 3/27/2019 Model used Finite elements Boundary elements Other Element type :PLANE 2D Number of degrees of freedom or mesh density :

Nb of nodes = 2706 Nb of elements = 1237 Nb of DOF = 7836 Results :

Pressure p Radius r Physical Reference Calculated Deviation (MPa) (mm) quantity (MPa) value value (%)

1 -100 -99.33 0.67 1.5 r -25.93 -25.96 0.11 100 2 0 0.03 -

(elasticity) 1 166.7 165.98 0.43 1.5 92.59 92.68 0.10 2 66.7 66.77 0.10 Starts py 129.68 131 1.02 yielding Complete plim 240.11 239.99 -0.39 yield

STRUCTURAL MECHANICS Fig1: Tube starts yielding on inner face Fig2: Tube finishes yielding on outer face Comments :

STRUCTURAL MECHANICS

[ 3. Linear dynamic EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: THIN CYLINDER FIXED ON BOTH ENDS Codification: SDLA 01-89 Test pe1fonned by : Julien BOISSAT Date: 3/27/2019 Model used Finite elements 0 Boundaiy elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density Nb of nodes = 4464 Nb of elements = 2190 Nb of DOF = 25776 Results : Reference values Frequency (Hz) 11 = 2 4 6 8 10 12 14 E - 700 525 720 1095 1559 2118 Ill =

1 C 1925.5 771.1 538.5 719.6 1081.8 1549.7 2108.5 s 2772 880 568 742 1104 1573 2132 E - 1620 980 900 1140 - -

2 C 3929.0 1775.8 1041.5 922.3 1165.6 1595.4 2140.9 s 5251 2088 1121 952 1189 1620 2167 E - - 1650 1350 1325 1711 2225 3 C 5892.7 2968.0 1764.9 1323.4 1361.3 1698.7 2207.5 s 6997 3441 1915 1368 1383 1720 2233 Calculated values (Hz) 11 =2 4 6 8 10 12 14 Result 1921.8 766.3 534.6 717.4 1079.4 1545 2099.1 Ill= 1 Deviation(%) 0.19 0.63 0.71 0.31 0.22 0.30 0.45 2 Result 3914.4 1760.5 1025.9 910.5 1157 1586.5 2127.4 Deviation(%) 0.38 0.87 1.50 1.30 0.74 0.57 0.63 Result 5859 2934 1730 1292.1 1336.7 1677.2 2185.2 3

Deviation% 0.58 1.16 2.00 2.41 1.84 1.28 1.02 e2019DaosaulSystemes. Alii!,lls ..........,_ Confia<<itill Oorotclotti1111e. 59

STRUCTURAL MECHANICS m = 1, n = 6 m = 2, n = 6 m = 3, n = 6 Comments :

The deviation was calculated checking the results of SOLIDWORKS Simulation against the results << average of the 2 codes >> (marked as C in the table).

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SLENDER FOLDED BEAM, ONE END FIXED THE OTHER FREE Codification: SDLL 02-89 Test performed by : Julien BOISSAT Date: 3/27/2019 Model used Finite elements Boundary elements Other Element type : BEAM Number of degrees of freedom or mesh density :

Nb of nodes = 151 Nb of elements = 150 Nb of DOF = 888 Results :

Nature of the Frequency (Hertz) vibration mode Deviation (%)

i Order Reference value Calculated value 1 1,2 11.76 11.725 2.73 2 3,4 105.88 103.98 1.53 3 5,6 294.10 294.41 -0.38 4 7,8 576.44 565.32 -2.96 Order 2 Order 4 Comments :

The model was made with an arbitrary angle of 1° for the fold as it wasnt specified in the test description.

Using respectively the average frequency of modes (1,2), (3,4), (5,6) and (7,8).

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: SLENDER BEAM ON TWO SIMPLE SUPPORTS UNDER AXIAL FORCE Codification: SDLL 05-89 Test performed by : Julien BOISSAT Date: 3/27/2019 Model used Finite elements Boundary elements Other Element type : BEAM Number of degrees of freedom or mesh density :

Nb of nodes = 119 Nb of elements = 117 Nb of DOF = 705 Results :

Nature of the vibration Frequency (Hertz)

Deviation (%)

mode Reference Calculated Bending 1 28.702 28.69 0.04 lFxl = 0 Bending 2 114.807 114.57 0.21 Bending 1 22.434 22.422 0.05 lFxl = 105N Bending 2 109.080 108.85 0.21 lFxl = 0 N, Bending 1 lFxl = 105 N, Bending 2 Comments :

STRUCTURAL MECHANICS EVALUATION FOR M Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkPad W540, Windows 10 x64, Intel i7 vPro core, 16Gb RAM, Graphics Card Intel HD Graphics 4600.

Test name: PLANAR FRAME MADE OF I BEAMS Codification: SDLL 08-89 Test pe1fonned by: Julien BOISSAT Date: 3/28/2019 Model used Finite elements 0 Boundary elements Other Element type : SHELL Number of degrees of freedom or mesh density Nb ofnodes = 54 73 Nb ofelements =2524 Nb ofDOF = 63486 32814 Results :

Order of Vibration mode Frequency (Hertz) Deviation(%)

the WBIWG vibration Reference Calculated Reference Calculated Frequency WBIWG mode 1 16.456 16.466 1.213 1.16 0.08 4.35 2 38.165 37.159 -0.412 -0.422 2.64 2.54 Mode 1 D1ynam1c resoonse :

Values Point Value type (m) Deviation (%)

Reference Calculated B,E WBmax -9.8 X 10-2 -1.02 X 10-I 3.92 G wamax -12.5 X 10- 2 -12.4 X 10-2 0.81 G WB+ WG max -2.27 X 10-l -2.26 X 10-I 0.44 Colillilents:

WB is the deflection of the lateral beam at its center.

wa is the deflection ofthe central beam at its center. Therefore wa =vertical displacement ofpoint G - WB e2019DaosaulSystemes. Alii!,lls ..........,_ Confia<<itill Oorotclotti1111e. 63

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: SLENDER BEAM WITH VARIABLE RECTANGULAR SECTION, ONE END FIXED THE OTHER FREE Codification: SDLL 09-89 Test performed by : Julien BOISSAT Date: 3/28/2019 Model used Finite elements Boundary elements Other Element type : TETRA10 and BEAM Number of degrees of freedom or mesh density :

TETRA10 BEAM

=4 Nb of nodes = 11686 Nb of nodes = 201 Nb of elements = 6691 Nb of elements = 100 Nb of DOF = 34743 Nb of DOF = 600

=5 Nb of nodes = 13362 Nb of nodes = 201 Nb of elements = 7980 Nb of elements = 100 Nb of DOF = 39717 Nb of DOF = 600 Results :

TETRA10 elements:

Nature of Frequency (Hertz) Frequency (Hertz)

Deviation (%)

the =4 =5 vibration Reference Calculated Reference Calculated =4 =5 mode 1 54.18 54.19 56.55 56.56 0.02 0.02 2 171.94 171.56 175.79 175.43 -0.22 -0.20 Bending 3 384.40 381.97 389.01 386.57 -0.63 -0.63 4 697.24 688.61 702.36 693.67 -1.24 -1.24 5 1112.28 1090.1 1117.63 1095.5 -1.99 -1.98 Mode 3 Mode 4

STRUCTURAL MECHANICS BEAM elements:

Nature of Frequency (Hertz) Frequency (Hertz)

Deviation (%)

the =4 =5 vibration Reference Calculated Reference Calculated =4 =5 mode 1 54.18 54.21 56.55 56.57 0.06 0.04 2 171.94 171.93 175.79 175.76 -0.01 -0.02 Bending 3 384.40 383.76 389.01 388.17 -0.17 -0.22 4 697.24 694.11 702.36 698.49 -0.45 -0.55 5 1112.28 1103.1 1117.63 1106.7 -0.83 -0.98 Mode 3 Mode 4 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 PR1 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: SLENDER BEAM WITH VARIABLE RECTANGULAR SECTION, BOTH ENDS FIXED Codification: SDLL 10-89 Test performed by : Julien BOISSAT Date: 3/29/2019 Model used Finite elements Boundary elements Other Element type : TETRA10 and BEAM Number of degrees of freedom or mesh density :

TETRA10 BEAM Nb of nodes = 15051 Nb of nodes = 541 Nb of elements = 8761 Nb of elements = 270 Nb of DOF = 44817 Nb of DOF = 1614 Results :

Frequency Frequency Calculated Vibration of (Hz) Deviation (%)

mode reference (Hz) TETRA10 BEAM TETRA10 BEAM 1 143.303 146.13 145.85 1.97 1.78 2 396.821 399.8 399.37 0.75 0.64 3 779.425 779.61 779.34 0.02 0.01 4 1289.577 1282.2 1282.5 0.57 0.55 Mode 1 Mode 2

STRUCTURAL MECHANICS Mode 3 Mode 4 Vibration mode i(x)

Order of the vibration mode x = 0. 0.1 0.2 0.3 0.4 0.5 0.6 Reference 0 0.237 0.703 1 0.859 0.354 0 TETRA10 0 0.236 0.703 1.000 0.861 0.356 0 1 Deviation(%) 0 0.27 0.03 0.00 0.21 0.60 0 BEAM 0 0.240 0.708 1.000 0.857 0.354 0 Deviation(%) - 1.24 0.67 0.00 0.24 0.01 -

Reference 0 -0.504 -0.818 0 1 0.752 0 TETRA10 0 -0.503 -0.822 -0.004 1.000 0.755 0 2 Deviation(%) 0 0.14 0.48 - 0.00 0.38 0 BEAM 0 -0.506 -0.814 0.012 1.000 0.748 0 Deviation(%) - 0.47 0.48 - 0.00 0.58 -

Reference 0 0.67 0.21 -0.831 0.257 1 0 TETRA10 0 0.669 0.214 -0.831 0.252 1.000 0 3 Deviation(%) 0 0.14 1.71 0.01 1.84 0.00 0 BEAM 0 0.674 0.194 -0.834 0.271 1.000 0 Deviation(%) - 0.65 7.57 0.33 5.42 0.00 -

Reference 0 -0.67 0.486 0 -0.594 1 0 TETRA10 0 -0.674 0.486 0.005 -0.598 1.000 0 4 Deviation(%) 0 0.52 0.02 - 0.61 0.00 0 BEAM 0 -0.668 0.502 -0.026 -0.579 1.000 0 Deviation(%) - 0.28 3.32 - 2.54 0.00 -

Comments :

i(x) is the value of the lateral displacement of the mode shape (normalized so that the value is 1 at the location of the max lateral displacement), at x. x is thedistance along the beam length taken from the large cross section.

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: THIN CIRCULAR RING COMPLETELY FREE Codification: SDLL 11-89 Test performed by : Julien BOISSAT Date: 3/29/2019 Model used Finite elements Boundary elements Other Element type : TETRA10 and BEAM Number of degrees of freedom or mesh density :

Solid elements: Beam elements Nb of nodes = 13955 Nb of nodes = 400 Nb of elements = 7401 Nb of elements = 200 Nb of DOF = 41865 Nb of DOF = 1200 Results :

In plane Nature of the Frequency (Hz) Deviation vibration mode

(%)

Calculated value i Order Reference value Solid Beam Solid Beam 0,1 1,2,3 0. 0 0 0 - -

2 4,5 318.38 319.15 317.99 319.15 0.12 0.24 3 6,7 900.46 900.49 897.7 900.49 0.31 0.00 4 8,9 1726.55 1720.4 1716.6 1720.4 0.58 0.36 5 10,11 2792.21 2769.6 2766.4 2769.6 0.92 0.81 i=1 i=2

STRUCTURAL MECHANICS i=3 i=4 i=5 Out of plane Nature of the Frequency (Hz) Deviation vibration mode

(%)

Calculated value i Order Reference value Solid Beam Solid Beam 0,1 1,2,3 0 0 0 0 - -

2 4,5 510 508.5 510 508.6 0.20 0.47 3 6,7 1572 1577.5 1572 1577.6 1.13 0.78 4 8,9 3116 3150.8 3116 3151 2.14 1.04 i=0 i=1 i=2 i=3 i=4 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: THIN CIRCULAR RING FIXED AT TWO POINTS Codification: SDLL 12-89 Test performed by : Julien BOISSAT Date: 3/29/2019 Model used Finite elements Boundary elements Other Element type : TETRA10 and BEAM Number of degrees of freedom or mesh density :

Solid elements Beam elements Nb of nodes = 14374 Nb of nodes = 432 Nb of elements = 7666 Nb of elements = 216 Nb of DOF = 43398 Nb of DOF = 1284 Results :

Order of the Frequency (Hz) vibration mode Deviation (%)

Calculated value j i Reference value Solid Beam Solid Beam 1 anti 1 235.3 235.6 235.9 0.13 0.25 2 sym 1 575.3 574.5 575.8 0.14 0.09 3 anti 2 1105.7 1101.5 1104.2 0.38 0.14 4 anti 3 1405.6 1400.8 1403.6 0.34 0.14 5 sym 2 1751.1 1737.5 1741.9 0.78 0.53 6 anti 4 2557.0 2529.3 2535 1.08 0.86 7 sym 3 2801.5 2726.5 2737.3 2.68 2.35 Antisymmetric modes Symmetric modes Mode 2 Mode 1

STRUCTURAL MECHANICS Mode 6 Mode 7 Mode 3 Mode 5 Mode 4 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: THIN CIRCULAR RING FIXED BY AN ELASTIC LEG Codification: SDLL 13-89 Test performed by : Julien BOISSAT Date: 3/29/2019 Model used Finite elements Boundary elements Other Element type : TETRA10 Number of degrees of freedom or mesh density :

Solid elements Shell elements Nb of nodes = 15149 Nb of nodes = 8672 Nb of elements =8174 Nb of elements = 3830 Nb of DOF = 45366 Nb of DOF = 51990 Results :

Frequency (Hz)

Nature of the Deviation (%)

vibration mode Calculated value Reference value Solid Shell Solid Shell 1 anti 28.8 30.0 29.9 4.00 3.82 2 sym 189.3 189.8 190.1 0.26 0.42 3 anti 268.8 268.7 269 0.04 0.07 4 anti 641.0 660.0 655.1 2.88 2.20 5 sym 682.0 681.8 683.2 0.03 0.18 6 anti 1063.0 1100 1092.2 3.48 2.75

STRUCTURAL MECHANICS Mode 2 Mode 1 Mode 4 Mode 3 Mode 6 Mode 5 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: VIBRATION MODES OF AN ELBOWED PIPE Codification: SDLL 14-89 Test performed by : Julien BOISSAT Date: 3/29/2019 Model used Finite elements Boundary elements Other Element type : BEAMS Number of degrees of freedom or mesh density :

l=0m l = 0.6 m l=2m Nb of nodes = 561 Nb of nodes = 659 Nb of nodes = 829 Nb of elements = 280 Nb of elements = 416 Nb of elements = 646 Nb of DOF = 1674 Nb of DOF = 2490 Nb of DOF = 3870 Results :

Nature of the vibration Frequency (Hz) Deviation mode Reference Calculated (%)

Out of plane 1 44.23 44.13 0.23 In plane 1 119 119.52 0.44 l=0m Out of plane 2 125 125.9 0.72 In plane 2 227 226.07 0.41 Out of plane 1 33.4 33.21 0.57 l = 0.6 m In plane 1 94 94.07 0.07 Out of plane 2 100 98.8 1.20 In plane 2 180 182.73 1.52 Out of plane 1 17.9 17.65 1.40 In plane 1 24.8 24.43 1.49 l=2m Out of plane 2 25.3 24.94 1.42 In plane 2 27 26.73 1.00

STRUCTURAL MECHANICS Modes for l = 2 m In plane Out of plane Mode 1 Mode 1 Mode 2 Mode 2 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: THIN FREE RING WITH A PUNCTUAL MASS Codification: SDLL 16-89 Test performed by : Julien BOISSAT Date: 3/29/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 13896 Nb of elements = 7360 Nb of DOF = 41829 Results :

Order of the Frequency (Hz)

Deviation (%)

vibration mode Reference Calculated In plane 1,2,3 0. 0 -

Sym 4 227.29 227.63 0.12 Anti 5 297.87 296.34 0.51 Sym 6 718.42 717.27 0.16 Anti 7 873.88 860.16 1.57 Transverse 1,2,3 0. 0 -

4 409.8 409.21 0.15 5 510.2 508.21 0.38

STRUCTURAL MECHANICS Vibration modes in plane Mode 4 Mode 5 Mode 6 Mode 7 Vibration modes out of plane Mode 4 Mode 5 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: THIN SQUARE PLATE WITH 3 OR 4 FREE EDGES Codification: SDLS 01-89 Test performed by : Julien BOISSAT Date: 4/2/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

1.Fixed edge 2.Free Nb of nodes = 4629 Nb of nodes = 4629 Nb of elements = 2246 Nb of elements = 2246 Nb of DOF = 27360 Nb of DOF = 27774 Results : 1.Fixed edge Order of the Frequency (Hertz) vibration mode Deviation (%)

i Reference value Calculated value 1 8.7266 8.6733 0.61 2 21.3042 21.252 0.25 3 53.5542 53.16 0.74 4 68.2984 67.913 0.57 5 77.7448 77.312 0.56 6 136.0471 135.27 0.57 Mode 1 Mode 2 Mode 3 Mode 4

STRUCTURAL MECHANICS Mode 5 Mode 6 2.Free Order of the Frequency (Hertz) vibration mode Deviation (%)

i Reference value Calculated value 7 33.7119 33.645 0.20 8 49.4558 48.922 1.09 9 61.0513 60.604 0.74 10 87.5160 86.864 0.75 11 87.5160 86.907 0.7 Mode 7 Mode 8 Mode 9 Mode 10 Mode 11 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: THIN RHOMBOID PLATE FIXED ON ONE EDGE Codification: SDLS 02-89 Test performed by : Julien BOISSAT Date: 4/2/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

= 0° = 15° Nb of nodes = 6561 Nb of nodes = 6381 Nb of elements = 3200 Nb of elements = 3110 Nb of DOF = 38880 Nb of DOF = 37800

= 30° = 45° Nb of nodes = 5701 Nb of nodes = 4737 Nb of elements = 2770 Nb of elements = 2288 Nb of DOF = 33720 Nb of DOF = 27936 Results :

Nature of the Frequency (Hertz) vibration mode Deviation (%)

i Reference value Calculated value 1 8.6734 8.6734 0

= 0° 2 21.253 21.253 0 1 8.9990 8.9538 2.04

= 15° 2 22.1714 21.728 0.84 1 9.8987 9.8159 0.84

= 30° 2 25.4651 23.513 8.30 1 11.15 11.264 -1.01

= 45° 2 27 28.103 -3.91 Vibration modes = 45° f1=11.26 Hz f2=28.1 Hz Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: THIN RECTANGULAR PLATE SIMPLY SUPPORTED ON EDGES Codification: SDLS 03-89 Test performed by : Julien BOISSAT Date: 4/2/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 4491 Nb of elements = 2176 Nb of DOF = 26940 Results :

Nature of the Frequency (Hertz) vibration mode Deviation (%)

i j Reference value Calculated value 1 1 35.63 35.62 0.03 2 1 68.51 68.49 0.03 1 2 109.62 109.58 0.04 3 1 123.32 123.25 0.06 2 2 142.51 142.41 0.07 3 2 197.32 197.11 0.11

STRUCTURAL MECHANICS 1,1 2,1 1,2 3,1 2,2 3,2 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: THIN RING SHAPED PLATE FIXED ON INNER EDGE Codification: SDLS 04-89 Test performed by : Julien BOISSAT Date: 4/2/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 4642 Nb of elements = 2218 Nb of DOF = 27024 Results :

Nature of the Frequency (Hertz) vibration mode Deviation (%)

i j Reference value Calculated value 0 0 79.26 79.34 0.10 0 1 518.85 516.37 0.48 1 0 81.09 80.95 0.17 1 1 528.61 526.68 0.37 2 0 89.63 89.56 0.08 2 1 559.09 556.98 0.38 3 0 112.79 113.04 0.22 3 1 609.70 607.96 0.29

STRUCTURAL MECHANICS 0,0 0,1 1,0 1,1 2,0 2,1 3,1 3,0 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: COMPRESSOR BLADE: THIN SHELL FIXED-FREE Codification: SDLS 05-89 Test performed by : Julien BOISSAT Date: 4/2/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 4629 Nb of elements = 2246 Nb of DOF = 27360 Results :

Nature of the Frequency (Hertz)

Deviation (%)

vibration mode Reference value Calculated value 1 85.6 85.9 0.35 2 134.5 138.4 2.82 3 259.0 246.9 4.90 4 351.0 342.4 2.51 5 395.0 386.4 2.23 6 531.0 528.2 0.53

STRUCTURAL MECHANICS Mode 2 Mode 1 Mode 4 Mode 3 Mode 5 Mode 6 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: THIN WINGED CIRCULAR PLATE Codification: SDLS 06-89 Test performed by : Julien BOISSAT Date: 4/2/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 8796 Nb of elements = 4164 Nb of DOF = 52104 Results :

Nature of the Frequency (Hertz) vibration mode Reference value Calculated value Deviation (%)

Torsion Bending D1 D2 D1 D2 ND (°)

0 0 267.2 902 280.49 948.92 4.74 4.94 1 45 264.7 901 279.8 954.76 5.40 5.63 2 90 295.1 971 304.8 1017.3 3.18 4.55 3 135 361.1 1210 365.09 1242.5 1.09 2.62 4 180 -- 1663 1679.4 0.98 4 180 390.5 1643 393.92 1670.8 0.87 1.66 135 -- 2189 2215.4 1.19 90 -- 2627 2681.9 2.05 45 -- 2783 2902.7 4.12 0 -- 2805 2932.6 4.35 D1 Family

STRUCTURAL MECHANICS ND 0 - 0° ND 1 - 45° ND 2 - 90° ND 3 - 135° ND 4 - 180° D2 Family ND 0 - 0° ND 1 - 45° ND 2 - 90° ND 3 - 135° ND 4 - 180° ND 4 - 180° 135° 90° 45° 0° Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: THIN SPHERE COMPLETELY IMMERSED IN A PERFECT AND INCOMPRESSIBLE FLUID Codification: SDLS 07-89 Test performed by : Julien BOISSAT Date: 4/2/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

In the void t/R = 0.04 t/R = 0.004 Nb of nodes = 4242 Nb of nodes = 10130 Nb of elements = 2120 Nb of elements = 5064 Nb of DOF = 25452 Nb of DOF = 60780 Results :

In vacuum Nature of Frequency (Hertz) the vibration Reference value Calculated value Deviation (%)

mode t/R = 0.04 t/R = 0.004 t/R = 0.04 t/R = 0.004 i j 2 0 237.25 236.71 237.41 236.93 0.07 0.09 3 0 282.85 280.49 283.15 280.56 0.11 0.03 4 0 305.24 297.65 305.39 297.8 0.05 0.05 5 0 324.17 306.16 324.16 306.44 0 0.09 6 0 346.76 311.10 346.52 311.41 0.07 0.1 7 0 376.68 314.35 376.55 314.71 0.03 0.11 8 0 416.0 316.77 415.17 317.28 0.20 0.16 9 0 465.75 318.80 463.85 319.26 0.41 0.14 10 0 526.20 320.71 522.84 321.41 0.64 0.22

STRUCTURAL MECHANICS i=2 i=3 i=4 Comments : The simulation of the immersed sphere is out of the softwares range.

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: BENDING OF SYMMETRICAL FRAME Codification: SDLX 01-89 Test performed by : Julien BOISSAT Date: 4/2/2019 Model used Finite elements Boundary elements Other Element type : BEAM Number of degrees of freedom or mesh density :

Nb of nodes = 389 Nb of elements = 385 Nb of DOF = 2292 Results :

Nature of the Frequency (Hertz) vibration mode Deviation (%)

i Reference value Calculated value 1 anti 8.8 8.8 0.00 2 anti 29.4 29.5 0.34 3 sym 43.8 43.8 0.00 4 sym 56.3 56.56 0.46 5 anti 96.2 95.97 0.24 6 sym 102.6 102.8 0.19 7 anti 147.1 146.6 0.34 8 sym 174.8 174.6 0.11 9 anti 178.8 178.8 0.00 10 anti 206 206.5 0.24 11 sym 266.4 264.7 0.64 12 anti 320 318.1 0.60 13 sym 335 333.1 0.57

STRUCTURAL MECHANICS Mode 2 Mode 5 Mode 8 Mode 13 Comments :

STRUCTURAL MECHANICS EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: ASSEMBLY OF THIN RECTANGULAR SHAPED SHEETS Codification: SDLX 03-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 4600 Nb of elements = 2260 Nb of DOF = 27600 Results :

Nature of the Frequency (Hertz) Deviation (%)

vibration mode Finite elements Calculated w.r.t. w.r.t.

i Experimental model value Exp. FEM 1 606 584 +/- 1% 585 3.59 0.17 2 760 826 +/- 1.5% 826 7.99 0 3 865 855 +/- 1.7% 852 1.53 0.35 4 944 911 +/- 2% 912 3.51 0.11 5 1113 1113 +/- 3.6% 1107 0.54 0.54 6 1144 1136 +/- 4% 1157 1.12 1.82

STRUCTURAL MECHANICS Mode 1 Mode 2 Mode 4 Mode 3 Mode 5 Mode 6 Comments :

II. THERMAL

THERMAL

1. Linear steady state thermal EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, *aphics card NVIDIA uadro 2000.

Test name: PIPE: PRESCRIBED TEMPERATURES Codification: TPLA 01-89 Test pe1fonned by: Julien BOISSAT Model used Finite elements 0 Bom1dary elements Other Element type : TRIANG Number ofdegrees of freedom or mesh density:

2D - Extruded 2D - Ax i-symmetric Nb of nodes = 2921 Nb of nodes = 6615 Nb of elements = 1370 Nb of elements = 3140 Nb ofDOF = 2599 Nb of DOF = 5985 Results :

2D - Extruded Refe rence values Calculated values r(m) Deviation(%)

Tee) (

,p W/m ) 2 Tee) ,p lW/m2) 0.3 100 1729.91 100 1729.94 0 0 0.31 82.98 1674.11 82.98 1674.07 0 0 0.32 66.51 1621.79 66.51 1621.73 0 0 0.33 50.54 1572.64 50.54 1572.61 0 0 0.34 35.04 1526.39 35.04 1526.27 0 0.01 0.35 20 1482.78 20 1482.67 0 0.01 Reference value of the output flux </>II= 3260.80 W/m Calculated value </>JI= 3260.23 W/m Deviation(%)= 0.02 Temperature plot________

e2019DaosaulSystemes. Alii!,lls ..........,_ Confia<<itill Oorotclotti1111e. 96

THERMAL 2D - Axi-symmetric Reference values Calculated values r (m) Deviation (%)

T (°C) (W/m²) T (°C) (W/m²)

0.3 100 1729.91 100 1729.83 0 0 0.31 82.98 1674.11 82.98 1674.04 0 0 0.32 66.51 1621.79 66.51 1621.73 0 0 0.33 50.54 1572.64 50.54 1572.59 0 0 0.34 35.04 1526.39 35.04 1526.34 0 0 0.35 20 1482.78 20 1482.73 0 0 Reference value of the output flux /l = 3260.80 W/m Calculated value /l = 3260.80 W/m Deviation (%) = 0 Comments :

The Reference value of the output flux /l is the heat flux for a 1m extrusion thicknes, and for the entire cross section.

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: PIPE : PRESCRIBED TEMPERATURE, CONVECTION Codification: TPLA 02-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : SHELL6 Number of degrees of freedom or mesh density :

Nb of nodes = 1180 Nb of elements = 533 Nb of DOF = 1069 Results :

Reference values Calculated values r (m) Deviation (%)

T (°C) (W/m²) T (°C) (W/m²)

0.3 66.49 1005.29 66.49 1005.2 0 0.01 0.31 56.60 972.89 56.60 972.83 0 0.01 0.32 47.03 942.46 47.03 942.43 0 0 0.33 37.75 913.90 37.75 913.87 0 0 0.34 28.74 887.02 28.74 887.00 0 0 0.35 20 861.6 20 861.57 0 0 Reference value of the output flux /l = 1894.94 W/m Calculated value /l = 1894.92 W/m Deviation (%) = 0 Comments :

The Reference value of the output flux /l is the heat flux for a 1m extrusion thicknes, and for the entire cross section.

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: PIPE : CONVECTION Codification: TPLA 03-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : SHELL6 Number of degrees of freedom or mesh density :

Nb of nodes = 2147 Nb of elements = 1008 Nb of DOF = 2147 Results :

Physical quantity Reference value Calculated value Deviation (%)

Ti (°C) 272.27 272.35 0.03 Te (°C) 205.05 204.51 0.27 i (W/m²) 34160.01 34146.32 0.04 e (W/m²) 26276.93 26198.90 0.30

/l (W/m) 64390.11 64364.26 0.04 Comments :

The Reference value of the output flux /l is the heat flux for a 1m extrusion thicknes, and for the entire cross section.

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: POWER OUTPUT IN A PIPE Codification: TPLA 04-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TRIANG Number of degrees of freedom or mesh density :

Nb of nodes = 2619 Nb of elements = 1252 Nb of DOF = 2461 Results :

Reference value Calculated values r (m) Deviation (%)

T (°C) (W/m²) T (°C) (W/m²)

1.0 20.00 -58.2 20.00 -58.16 0 0.07 1.2 28.73 -30.17 28.73 -30.17 0 0 1.5 32.62 2.87 32.62 2.878 0 0.28 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: CYLINDRICAL BAR WITH FLUX DENSITY Codification: TPLA 05-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 25788 Nb of elements = 15387 Nb of DOF = 25642 Results :

Reference value Calculated value z (m) Deviation (%)

T (°C) T (°C) 0.0 0.00 0.00 -

0.1 -4.00 -4.00 0 0.2 4.00 4.00 0 0.3 24.00 24.00 0 0.4 56.00 56.00 0 0.5 100.00 100.0 0 0.6 156.00 156.0 0 0.7 224.00 224.0 0 0.8 304.00 304.0 0 0.9 396.00 396.0 0 1.0 500.00 500.0 0 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: CYLINDRICAL BAR WITH CONVECTION Codification: TPLA 06-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 25788 Nb of elements = 15387 Nb of DOF = 25642 Results :

Reference value Calculated value z (m) Deviation (%)

T (°C) T (°C) 0.0 0.00 0.00 -

0.1 0.37 0.37 0 0.2 0.97 0.97 0 0.3 2.19 2.19 0 0.4 4.78 4.79 0.21 0.5 10.39 10.40 0.10 0.6 22.56 22.56 0 0.7 48.95 48.95 0 0.8 106.21 106.2 0.01 0.9 230.44 230.3 0.06 1.0 500.00 500.0 0 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: ORTHOTROPIC PIPE Codification: TPLA 07-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 40898 Nb of elements = 26460 Nb of DOF = 40898 Results :

z (m) r (m) Reference value T (°C) Calculated value T (°C) Deviation(%)

0.030 100.01 100.8 0.78 0.035 81.90 82.95 1.27 0 0.040 66.22 67.34 1.66 0.045 52.38 53.39 1.89 0.050 40.00 40.74 1.82 0.030 102.51 102.6 0.09 0.035 84.40 84.44 0.05 l/2 0.040 68.72 68.76 0.06 0.045 54.88 54.91 0.05 0.050 42.51 42.54 0.07 0.030 105.01 104.4 0.58 0.035 86.90 85.93 1.13 l 0.040 71.22 70.18 1.48 0.045 57.38 56.43 1.68 0.050 45.01 44.33 1.53

THERMAL r, z (W/m²) -500 - -

z, Ri (W/m²) 11310 11310 0 z, Re (W/m²) 6786 6778.8 -0.11 Comments :

In order to satisfy the boundary conditions, the face was split and the convection was applied separately to each strip because the software does not currently allow ambient temperature variation for convection as a boundary condition.

Because of this, the heat flux in Z is not uniform and the corresponding valuer, z (W/m²)

for is unavailable.

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: TWO-MATERIAL PIPE : CONVECTION Codification: TPLA 08-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Solid elements Axisymmetric shell elements Nb of nodes = 6500 Nb of nodes = 2623 Nb of elements = 4063 Nb of elements = 1260 Nb of DOF = 6500 Nb of DOF = 2623 Results :

Physical Deviation (%)

quantity Calculated value Reference value Solid Shell Solid Shell Ti (°C) 25.42 25.42 25.42 0 0 Tm (°C) 17.69 17.69 17.69 0 0 Te (°C) 12.11 12.11 12.11 0 0 i (W/m²) 6687.44 6686.2 6687.4 0.02 0 m (W/m²) 5732.09 5731.1 5732 0.02 0 e (W/m²) 5422.25 5421.4 5422.2 0.02 0

/l (W/m) 12605.52 12603.2 12605.5 0.02 0 Comments :

The Reference value of the output flux /l is the heat flux for a 1m extrusion thicknes, and for the entire cross section.

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: TWO-MATERIAL PIPE : CONVECTION, THERMAL CONTACT RESISTANCE Codification: TPLA 09-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 12061 Nb of elements = 7645 Nb of DOF = 12061 Results :

Physical Reference value Calculated value Deviation quantity Ti (°C) 25.11 25.11 0 1

T m (°C) 17.33 17.33 0 T2m (°C) 5.91 5.91 0 Te (°C) 0.3 0.3 0 i (W/m²) 6732.90 6732.7 0 m (W/m²) 5771.06 5770.9 0 e (W/m²) 5459.11 5459 0

/l (W/m) 12691.23 12691.08 0 Comments :

The Reference value of the output flux /l is the heat flux for a 1m extrusion thicknes, and for the entire cross section.

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: SIMPLE WALL : PRESCRIBED TEMPERATURES Codification: TPLL 01-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : SHELL Number of degrees of freedom or mesh density :

Nb of nodes = 5151 Nb of elements = 2500 Nb of DOF = 4949 Results :

Location Deviation Temperature T (°C) Calculated value x (m) (%)

0.00 100.0 100.0 0 0.01 84.0 84.0 0 0.02 68.0 68.0 0 0.03 52.0 52.0 0 0.04 36.0 36.0 0 0.05 20.0 20.0 0 Reference value of heat flux from face A to face B = 1200 W/m² Calculated value = 1200 W/m² Deviation (%) = 0 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: SIMPLE WALL : PRESCRIBED TEMPERATURES, CONVECTION Codification: TPLL 02-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : SHELL Number of degrees of freedom or mesh density :

Nb of nodes = 5151 Nb of elements = 2500 Nb of DOF = 5050 Results :

Location Temperature T (°C) Calculated value Deviation (%)

x (m) 0.00 73.33 73.33 0 0.01 62.67 62.67 0 0.02 52 52 0 0.03 41.33 41.33 0 0.04 30.67 30.67 0 0.05 20 20 0 Reference value of heat flux from face A to face B = 800 W/m² Calculated value = 800 W/m² Deviation (%) = 0 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: SIMPLE WALL: CONVECTION Codification: TPLL 03-89 Test erfonned b : Julien BOISSAT Date: 4/3/2019 Model used Finite elements 0 Boundary elements Other Element type: TRIANG Number ofdegrees of freedom or mesh density:

Nb ofnodes = 741 Nb of elements = 336 Nb ofDOF = 741 Results:

Location Reference value Calculated value Deviation(%)

TA (°C) 21.71 21.71 0 Ts (0C) 416.57 416.57 0 rp (W/m2) 834.2 834.27 0.01 Comments:

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THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: POWER OUTPUT IN A BAR Codification: TPLL 04-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : SHELL Number of degrees of freedom or mesh density :

Nb of nodes = 4221 Nb of elements = 2000 Nb of DOF = 4179 Results :

Location Calculated Reference value Deviation (%)

x (m) value 0.0 20.0 20.0 0 0.2 T (°C) 28.0 28.0 0 0.5 32.5 32.5 0 0.0 -50.0 -50.0 0 0.2 (W/m²) -30.0 -30.0 0 0.5 0.0 0.0 0 Comments :

THERMAL EV ALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000 Test name: TWO-MATERIAL WALL : CONVECTION Codification: TPLL 05-89 Test pe1fonned by : Julien BOISSAT I Date: 4/3/2019 Model used Finite elements 0 Boundary elements Other Element type : SHELL Number ofdegrees offreedom or mesh density Nb ofnodes = 4617 Nb ofelements = 2240 Nb ofDOF = 4617 Results:

Location Referenee value Calculated value Deviation(%)

TA.(°C) 25 25 0 TB(°C) 85 85 0 Tc(0C) 103 103 0 (f) (W/m2) -900 -900 0 Comments:

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THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 S P 2 Computer configuration used: Lenovo ThinkStation S 20, Windows 7 x64, Intel Xeon W 3565, 12Gb RAM, gra phics card NVIDIA Quadro 2000.

Test name: TWO-MATERIAL WALL : CONVECTION, THERMAL CONTACT RESISTANCE Codification: TPLL 06-89 Test}: :>erfom1ed b Model used Finite elements 0 Boundary elements Other Element type: TETRAl0 Number ofdegrees of freedom or mesh density :

Nb of nodes = 11633 Nb of elements = 6971 Nb ofDOF = 11633 Results :

Location Referenee value Calculated value Deviation(%)

TA (°C) 25 25 0 TB1 (°C) 85 85 0 Ti(°C) 118.75 118.75 0 Tc(0C) 136.75 136.75 0 (I) (W/m ) -900 -900 0 2

Comments :

02019 Dasaau* 5Ystemes. Al rigl\ts ..

-. O>nfldenlial Do ncl distn l>lte 112

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: L SHAPED PLATE WITH GEOMETRIC SINGULARITY Codification: TPLP 01-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : SHELL 6 Number of degrees of freedom or mesh density :

Nb of nodes = 3201 Nb of elements = 1536 Nb of DOF = 3103 Results :

Reference value T (°C) Calculated value T (°C) Deviation (%)

10 10 0 10 10 0 10 10 0 10 10 0 10 10 0 7.869 7.874 -0.06 8.018 8.018 0 8.514 8.516 -0.02 9.001 9.099 -1.09 9.316 9.306 0.11 5.495 5.496 -0.02 5.680 5.671 0.16 6.667 6.667 0 8.640 8.658 -0.21 9.009 9.007 0.02 2.816 2.819 -0.11 2.881 2.882 -0.03 2.972 2.968 0.13 0 0 0 0 0 0 0 0 0

THERMAL Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: ORTHOTROPIC SQUARE Codification: TPLP 02-89 Test e1fonned b : Julien BOISSAT Date: 4/3/2019 Model used Finite elements 0 Botmdary elements Other Element type: SHELL 6 Number of degrees of freedom or mesh density Nb of nodes = 4575 Nb of elements = 2206 Nb of DOF 4575 Results:

1185 *1, 0m, ---' NOde1151 (0.1,0.1,0 r,,

; t __._,.._.

9.98 Celsiusc

-1254 ( 0.1,1.49e 009.0 m Node1120(1.49e CIJ9,1 .49e 009, 0 m Nale 1257 [0.1,1 .49e 009,0 "'

27 Cetsm 22.S Cdsm *18 c.tsus ode 593(3.7:le-010,-0.1,0 ,r -------lNode !HO (0.1 ,-0.1 ,0 l.

30.5 Celsius 'l--

= 26 C.lsiu* J e2019 Oau&llt SVS!ffl>es. Al rigl\ts iesecved. conrlClenlial Do not disttlbute 115

THERMAL Reference value Calculated value Point Deviation (%)

T (°C) T (°C)

O 22.5 22.5 0 A 35.0 35.0 0 B 26.0 26.0 0 C 10.0 9.98 0.2 D 19.0 19.0 0 E 30.5 30.5 0 F 18.0 18.0 0 G 14.5 14.5 0 H 27.0 27.0 0 x (W/m²) 45.0 45.0 0 y (W/m²) 60.0 60.0 0 Comments :

In order to apply the convection boundary condition, the edges in short were split in many shorter edged. The convection boundary condition was then applied separately to each one.

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: HOLLOW SPHERE: PRESCRIBED TEMPERATURES Codification: TPLV 01-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 and TRIANG Number of degrees of freedom or mesh density :

TETRA10 TRIANG Nb of nodes = 7478 Nb of nodes = 770 Nb of elements = 4445 Nb of elements = 345 Nb of DOF = 6235 Nb of DOF = 630 Results :

TETRA 10 Reference value Calculated value r (m) Deviation (%)

T (°C) (W/m²) T (°C) (W/m²)

0.3 100.00 1866.67 100.00 1866.77 0 0.01 0.31 81.94 1748.18 81.94 1748.07 0 0.01 0.32 65.00 1640.63 65.00 1640.72 0 0.01 0.33 49.09 1542.70 49.09 1542.79 0 0.01 0.34 34.12 1453.29 34.12 1453.15 0 0.01 0.35 20.00 1371.43 20.00 1370.8 0 0.05 TRIANG Reference value Calculated value r (m) Deviation (%)

T (°C) (W/m²) T (°C) (W/m²)

0.3 100.00 1866.67 100.00 1867.46 0 0.04 0.31 81.94 1748.18 81.94 1748.21 0 0 0.32 65.00 1640.63 65.00 1640.67 0 0 0.33 49.09 1542.70 49.09 1542.74 0 0 0.34 34.12 1453.29 34.12 1453.34 0 0 0.35 20.00 1371.43 20.00 1370.63 0 0.06 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: HOLLOW SPHERE: PRESCRIBED TEMPERATURES, CONVECTION Codification: TPLV 02-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 7472 Nb of elements = 4441 Nb of DOF = 6765 Results :

Reference value Calculated value r (m) Deviation (%)

T (°C) (W/m²) T (°C) (W/m²)

0.3 65.00 1050 65.00 1050.08 0 0.01 0.31 54.84 983.35 54.84 983.26 0 0.01 0.32 45.31 922.85 45.31 922.86 0 0 0.33 36.36 867.77 36.36 867.75 0 0 0.34 27.94 817.47 27.94 817.45 0 0 0.35 20.00 771.43 20.00 771.31 0 0.02 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: HOLLOW SPHERE: CONVECTION Codification: TPLV 03-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 and TRIANG Number of degrees of freedom or mesh density :

Solid elements Axisymmetric shell elements Nb of nodes = 11372 Nb of nodes = 2697 Nb of elements = 7252 Nb of elements = 1276 Nb of DOF = 11372 Nb of DOF = 2697 Results :

Physical Deviation (%)

quantity Calculated value Reference value Solid Shell Solid Shell Ti (°C) 250.28 250.28 250.27 0 0 Te (°C) 184.34 184.34 184.34 0 0 i (W/m²) 37458.77 37421.75 37448.18 0.10 0.03 e (W/m²) 21939.36 21923.73 21935.36 0.07 0.02 (W) 42364.87 42364.8 42364 0 0 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: TWO-MATERIAL HOLLOW SPHERE : CONVECTION Codification: TPLV 04-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 8923 Nb of elements = 5498 Nb of DOF = 8923 Results :

Physical Calculated Reference value Deviation (%)

quantity value Ti (°C) 25.06 25.06 0 Tm (°C) 17.84 17.84 0 Te (°C) 13.16 13.16 0 i (W/m²) 6740.53 6729.3 -0.17 m (W/m²) 4952.23 4948.2 -0.08 e (W/m²) 4431.32 4430.9 -0.01 (W) 7623.36 7623.36 0 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: TWO-MATERIAL HOLLOW SPHERE: CONVECTION, THERMAL CONTACT RESISTANCE Codification: TPLV 05-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TETRA 4 Number of degrees of freedom or mesh density :

Nb of nodes = 10982 Nb of elements = 6973 Nb of DOF = 10982 Results :

Physical Calculated Reference value Deviation (%)

quantity value Ti (°C) 25.02 25.02 0 Tm1 (°C) 17.79 17.79 0 2

Tm (°C) 7.87 7.87 0 Te (°C) 3.18 3.18 0 i (W/m²) 6747.33 6746.8 0.01 m (W/m²) 4957.22 4956.9 0.01 e (W/m²) 4435.79 4435.5 0.01 (W) 7631.04 7630.45 0 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: POWER OUTPUT IN A HOLLOW SPHERE Codification: TPLV 06-89 Test performed by : Julien BOISSAT Date: 4/3/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 11231 Nb of elements = 7431 Nb of DOF = 9817 Results :

Reference value Calculated value r (m) Deviation (%)

T (°C) (W) T (°C) (W) 1.0 20.00 -837.8 20.00 -837.8 0 0 1.2 29.33 -532.8 29.33 -532.8 0 0 1.5 32.50 157.1 32.50 157.1 0 0 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: ORTHOTROPIC CUBE Codification: TPLV 07-89 Test performed by : Julien BOISSAT Date: 4/4/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 67289 Nb of elements = 46596 Nb of DOF = 67289

THERMAL Results :

Reference value Calculated value Point Deviation (%)

T (°C) T (°C)

O 22.5 22.5 0 A 35.0 35.0 0 B 26.0 26.0 0 C 10.0 10.0 0 D 19.0 19.0 0 E 30.5 30.5 0 F 18.0 18.0 0 G 14.5 14.5 0 H 27.0 27.0 0 I 29.0 29.0 0 J 20.0 20.0 0 K 4.0 4.0 0 L 13.0 13.0 0 M 16.5 16.5 0 N 41.0 41.0 0 P 32.0 32.0 0 Q 16.0 16.0 0 R 25.0 25.0 0 S 28.5 28.5 0 x (W/m²) 45.0 = Cte 45.0 0 y (W/m²) 60.0 = Cte 60.0 0 z (W/m²) 30.0 = Cte 30.0 0 Comments :

In order to satisfy the boundary conditions, we had to split the faces and apply the convection separately to each small face because the software does not allow ambient temperature variation for convection as a boundary condition.

THERMAL

2. Non linear steady state thermal EVALUATION FORM Software: SO LIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: PIPE : CONVECTION, RADIATION Codification: TPNA 01-89 Test e1fonned b : Julien BOISSAT Date: 4/4/2019 Model used Finite elements 0 Boundary elements Other Element type : TETRA 10 Number of degrees of freedom or mesh density :

Nb of nodes = 8413 Nb of elements = 5164 Nb ofDOF = 8413 Results:

Physical Reference Yalue Calculated Yalue Del'iation (%)

quantity T; (° C) 105.55 104.7 -0.81

r. c c) o 82.56 81.93 -0.76 rp; (W/m2) -11577.49 -11455.2 -1.06 rp,, (W/m2 ) -8822.98 -8790.55 -0.37

<1> (W) 21807.15 21605 -0.93 Collllilents :

The negative reference values for <p; and rp,, indicate that their direction con esponds to the negative radial direction. Hence reporting values opposite to those given b y the software for the radial direction.

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THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: SIMPLE WALL: CONVECTION, RADIATION Codification: TPNL O1-89 Test pe1formed by: Julien BOISSAT Date: 4/4/2019 Model used Finite elements 0 Boundary elements Other Element type : SHELL Number ofdegrees of freedom or mesh density :

Nb ofnodes = 4515 Nb ofelements = 2168 Nb ofDOF = 4515 Results:

Location Reference value Calculated value Deviation (%)

TA (°C) 28.56 28.55 0.04 Ts(°C) 488.27 488.15 0.02 rp (W/m2) 971.20 971.05 0.02 Comments:

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THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B3 Computer configuration used: Lenovo ThinlcStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: RADIATION IN A SQUARE CAVITY Codification: TPNP O 1-89 Test pe1fonned by : Julien BOISSAT I Date: 4/4/2019 Model used Finite elements 0 Boundary elements Other Element type : SHELL Number ofdegrees offreedom or mesh density Nb ofnodes = 608 Nb ofelements = 968 Nb ofDOF = 1272 Results :

Location Reference value T (K) Calculated value Deviation (%)

Lateral face (3) 1192 1208.5 1.38 Comments :

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THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: HOLLOW SPHERE: CONVECTION, RADIATION Codification: TPNV 01-89 Test performed by : Julien BOISSAT Date: 4/4/2019 Model used Finite elements Boundary elements Other Element type : TETRA10 Number of degrees of freedom or mesh density :

Nb of nodes = 11421 Nb of elements = 7298 Nb of DOF = 11421 Results :

Physical Calculated Reference value Deviation (%)

quantity value Ti (°C) 91.74 91.04 -0.76 Te (°C) 71.13 70.70 -0.60 i (W/m²) 11666.60 11545 -1.04 e (W/m²) 6825.85 (1) 6763.6 -0.91 (W) 13194.61 13069.6 -0.95 Comments :

(1)

Typo in the validation guide. Reference value e was checked with the formula e = he (Te - Tee)

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: RADIATION IN A CUBIC CAVITY Codification: TPNV 02-89

I ?'iOc.Otrl I 6S1e..00l 1503.<003 I SOO..Oll3

. 1333,,011)

I 25Qe,O)J I .1Sft.o)3 I ODe.Oll Test erfonned b : Julien BOISSAT Date: 4/4/2019 Model used Finite elements 0 Boundary elements D Other D Element type : SHELL 6 Number of degrees of freedom or mesh density Nb of nodes = 586 Nb of elements = 252 Nb of DOF = 628 Results:

Referenee value Calculated value Deviation Location T(K) T(.K1 (%)

Face (3) lateral 1223.4 1223.3 -0.008 Collllllents :

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THERMAL

3. Transient linear THERi'1AL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: CYLINDER : HEAT TR ANSFER BY CONVECTION Codification: TTLA 01-89 Test pe1fonned by : Julien BOISSAT Date: 4/4/2019 Model used Finite elements 0 Boundary elements D Other D Element type : SHELL Number ofdegrees offreedom or mesh density Nb ofnodes = 1325 Nb ofelements = 630 Nb ofDOF = 1325 Results :

Reference values Calculated value Deviation Time (s) T(°C) Tioc)

Outer face At center Outer face At center

(%)

600 461 314 459 326 0.35 3.96 800 550 412 539 424 1.97 2.91 1000 637 510 607 508 4.73 0.36 1200 686 588 665 580 3.13 1.32 1400 735 657 714 642 2.89 2.32 1600 774 706 756 694 2.36 1.66 1800 813 755 792 739 2.64 2.10 2200 873 828 848 810 2.84 2.17 2600 910 880 889 862 2.25 2.08 3000 936 917 920 899 1.76 1.93 3400 951 941 941 927 1.01 1.52 3800 970 959 957 947 1.30 1.29 02019 Dassawt Systtomes. Al rigl\ts ieseM!d. C<lnfidential Do not distllbute 130

THERMAL Temperature at center Temperature on outer face Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: WALL UNDER THERMAL SHOCK Codification: TTLL 01-89 Test performed by : Julien BOISSAT Date: 4/4/2019 Model used Finite elements Boundary elements Other Element type : SHELL Number of degrees of freedom or mesh density :

Nb of nodes = 1111 Nb of elements = 500 Nb of DOF = 1100 Results :

T (x,t) Reference values Calculated values Deviation (%)

n=45 x (m) x (m) x (m) t (s) 0.2 0.4 0.6 62.49 34.27 17.26 4.56 7.74 4.88 0.1 62.49 34.27 17.26 74.61 52.46 35.82 1.29 2.57 3.09 0.2 74.61 52.46 35.82 80.64 63.31 49.71 0.67 1.47 2.24 0.3 80.64 63.31 49.71 84.87 71.25 60.46 0.54 1.19 1.87 0.4 84.87 71.25 60.46 88.11 77.39 68.88 0.48 1.05 1.59 0.5 88.11 77.39 68.88 90.65 82.21 75.51 0.44 0.92 1.37 0.6 90.65 82.21 75.51 92.64 86.00 80.73 0.40 0.80 1.18 0.7 92.64 86.00 80.73 94.21 88.98 84.83 0.34 0.69 1.00 0.8 94.21 88.98 84.83 95.44 91.33 88.06 0.30 0.60 0.86 0.9 95.44 91.33 88.06 96.41 93.17 90.60 0.26 0.51 0.72 1 96.41 93.17 90.60 97.78 95.77 94.18 0.19 0.37 0.52 1.2 97.78 95.77 94.18 98.62 97.38 96.39 0.14 0.26 0.36

THERMAL 1.4 98.62 97.38 96.39 98.62 97.38 96.39 0.14 0.26 0.36 1.6 99.15 98.38 97.77 99.15 98.38 97.77 0.09 0.19 0.25 1.8 99.47 98.99 98.62 99.47 98.99 98.62 0.07 0.13 0.18 2 99.67 99.38 99.14 99.67 99.38 99.14 0.05 0.08 0.12 Reference Calculated T (x,t) values values Deviation (%)

n=45 x (m) x (m) x (m) t (s) 0.8 1 0.8 1 0.8 1 0.1 8.09 5.07 8.92 6.49 10.30 28.06 0.2 26.37 22.77 25.71 22.35 2.49 1.84 0.3 42.27 39.32 41.08 38.13 2.81 3.03 0.4 54.87 52.55 53.55 51.17 2.41 2.62 0.5 64.74 62.92 63.43 61.55 2.03 2.18 0.6 72.45 71.03 71.21 69.73 1.71 1.83 0.7 78.47 77.36 77.34 76.18 1.44 1.53 0.8 83.18 82.31 82.17 81.25 1.22 1.29 0.9 86.86 86.18 85.96 85.24 1.03 1.09 1 89.73 89.20 88.95 88.38 0.87 0.92 1.2 93.73 93.41 93.16 92.80 0.61 0.65 1.4 96.17 95.98 95.76 95.54 0.43 0.46 1.6 97.66 97.54 97.37 97.24 0.29 0.31 1.8 98.57 98.50 98.37 98.29 0.20 0.21 2 99.13 99.08 98.99 98.94 0.14 0.14 Comments :

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 B1 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: PLATE : HEAT TRANSFER BY CONVECTION Codification: TTLL 02-89 Test performed by : Julien BOISSAT Date: 4/4/2019 Model used Finite elements Boundary elements Other Element type : SHELL Number of degrees of freedom or mesh density :

Nb of nodes = 10251 Nb of elements = 5000 Nb of DOF = 10251 Results :

Reference Calculated Time (s) temperatures(°C) temperatures(°C) Deviations (%)

On surface At center On surface At center 800 412 264 394 245 4.45 7.33 1000 461 314 441 303 4.30 3.34 1500 559 451 544 432 2.68 4.31 2000 647 550 628 536 2.95 2.52 2500 711 637 696 621 2.06 2.44 3000 764 710 752 691 1.54 2.66 3500 814 765 798 748 1.99 2.23 4000 848 813 835 794 1.53 2.30 5000 902 877 890 863 1.32 1.59 6000 936 920 927 909 0.98 1.22 7000 958 948 951 939 0.70 0.92 8000 972 966 968 960 0.46 0.67 Comments:

THERMAL EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: SPHERE : HEAT TRANSFER BY CONVECTION Codification: TTLV 01-89 Test performed by : Julien BOISSAT Date: 4/4/2019 Model used Finite elements Boundary elements Other Element type : TETRA 10 and SHELLAX Number of degrees of freedom or mesh density :

TETRA 10 SHELLAX Nb of nodes = 23554 Nb of nodes = 1341 Nb of elements = 16004 Nb of elements = 634 Nb of DOF = 23554 Nb of DOF = 1341 Results :

Reference Calculated value temperature Deviations (%)

T (°C)

Time T (°C)

(s)

On At On surface At center On surface At center surface center 3D 2D 3D 2D 3D 2D 3D 2D 400 461 334 458 458 323 323 0.65 0.66 3.41 3.42 600 608 500 577 577 470 470 5.07 5.07 6.05 6.06 800 696 618 670 670 586 586 3.74 3.75 5.19 5.20 1000 774 706 742 742 677 677 4.09 4.10 4.15 4.16 1200 828 774 799 799 748 748 3.52 3.53 3.41 3.42 1400 868 828 843 843 803 803 2.88 2.89 3.02 3.03 1600 902 872 877 877 846 846 2.73 2.73 2.96 2.97 1800 923 902 904 904 880 880 2.02 2.03 2.45 2.45 2000 942 923 925 925 906 906 1.77 1.78 1.81 1.82 2200 956 942 942 942 927 927 1.50 1.50 1.61 1.62 2400 962 956 954 954 943 943 0.78 0.79 1.37 1.38 Comments :

III. THERMOMECHANICS

BIBLIOGRAPHY

4. Linear static EVALUATION FORM Software: SOLIDWORKS Simulation Version: 2019 SP2 Computer configuration used: Lenovo ThinkStation S20, Windows 7 x64, Intel Xeon W3565, 12Gb RAM, graphics card NVIDIA Quadro 2000.

Test name: THICK PIPE SUBMITTED TO A THERMAL GRADIENT Codification: HSLA 03-89 S.692e-001

, *2.31S.,.CO s.aooe.e01

., .o,ne+OJ1 Test pet onned by : Julien BOISSAT Model used Finite elements 0 Bmmdary elements D Other Element type : TETRA 10 Number ofdegrees offreedom or mesh density Nb ofnodes = 11361 Nb ofelements = 7238 Nb ofDOF = 34083 Results :

Physical quantity and Location Calculated value Deviation(%)

reference unit

<l(} (Pa) -100.86 X 106 -100.79 X 106 -0.07 r = Ri Uz (Pa) -130.26 X 106 -130.26 X 106 0.00 llr (m) 6 7.644 X 10 6 7.644 X 10 0.00

<l(} (Pa) 42.00 X 106 42.00 X 106 0.00 6

r =Re Uz (Pa) 12.6 X 10 12.608 X 106 0.06 llr(m) 30.6 X 10 6 30.508 X 10 6 0.30 Comments :

C,2019 Dasaawt 5Ysttmes. Al rigl\ts ,,,__ C<lnficlential Do not distllDe 137

BIBLIOGRAPHY IV. BIBLIOGRAPHY

BIBLIOGRAPHY Title : Guide de validation des progiciels de calcul de structures Author : Société Française des Mécaniciens Editor : Association Française de Normalisation (AFNOR)

Roark and Thimoshenko books Language : French are classic references used by many engineers. ISSN: 0297-4827 ISBN-10: 2124866117 ISBN-13: 978-2124866113 Title : ROARKs Formulas for Stress & Strain 6th edition Author : Warren C. Young Editor : McGRAW-HILL INTERNATIONAL EDITIONS Language : English ISBN-10: 0071003738 Title : Théorie des plaques et coques (Theory of plates and shells)

Author : S. Timoshenko, S. Woinowsky-Krieger Editor : DUNOD Language : French Library polytechnique Ch. Beranger N° 5768 - 2nd trimestre 1968

www.solidworks.com Dassault Systmes SOLIDWORKS Corp.

175 Wyman Street Waltham, MA 02451 Phone: 1 800 693 9000 Outside the US: +1 781 810 5011 Email: generalinfo@solidworks.com Europe Headquarters Japan Headquarters Phone: +33 4 13 10 80 20 Phone: +81 3 6270 8700 Email: infoeurope@solidworks.com Email: infojapan@solidworks.com Asia/Pacific Headquarters Latin America Headquarters Phone: +65 6511 9188 Phone: +55 11 3186 4150 Email: infoap@solidworks.com Email: infola@solidworks.com

Validation Methodology for Modern CAD-Embedded CFO Code: from Fundamental Tests to Industrial Benchmarks White Paper u:JUH Authors:

Dr. A.V. Ivanov, T.V. Trebunskikh, V.V. Platonovich Mentor Graphics Corporation, Russia Dr. A.V. Ivanov QA Test Manager

THEME Confidence in Results: Verification & Validation; Benchmarks & Test Cases

SUMMARY

SOLIDWORKS Flow Simulation is a new class of CFD (Computational Fluid Dynamics) analysis software (called Concurrent CFD) that is fully embedded in the mechanical design environment, for all general engineering applications.

As with all novel technologies, considerable attention is paid to Validation and Verification (V&V) of SOLIDWORKS Flow Simulation. As the end user of Concurrent CFD software is a professional engineer, this places strict requirements on calculation accuracy, reliability and robustness, as well as the usability of the software.

Validation aims to provide users with comprehensive information about software functionality and its ability to correctly simulate the main physical phenomena underlying fluid flow and heat transfer processes, which occur in equipment as designed and in situ (e.g. in process plant).

This paper will describe the methodologies used in the V&V of an immersed boundary CAD-embedded CFD code which involves four distinct levels of testing. The first level involves the fundamental tests which are simple enough in terms of geometry and problem formulation.

These tests are used to verify basic physical laws and algorithmic correctness. At the second level there are groups of tests that demonstrate how well a particular function of the product or physical model is working (e.g. conjugate heat transfer, cavitation, condensation, etc.).

The third level is comprised of applied industrial problems and benchmarks. At this level software validations for specific equipment with complex geometry are considered (cyclones, heat exchangers, engines, blowers, pumps, etc). The last level integrates validation tests and benchmarks from a certain industry (e.g. aerospace & defence, electronics, HVAC, process, etc.)

as a prerequisite for certification or accreditation. In general the categorization of cases within these levels depends on geometric and flow complexity, availability of reference data and its accuracy, and so on. For each level a small selection of SOLIDWORKS Flow Simulation validation examples are given in this paper.

Example cases from the first and second levels are provided with the software as CAD geometry plus boundary conditions and other numerical settings needed to mesh and solve the problem, so user can replicate validation cases on their own hardware, and use these to augment the tutorial examples provided with the software.

Keywords Validation, Verification, Benchmarks, Testing, SOLIDWORKS Flow Simulation, CFD, CAD-embedded, Engineering Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 1

1. INTRODUCTION Nowadays it is impossible to produce competitive, high-quality products without computer-aided engineering (CAE) software. The increasing role of CFD calculations within CAE has been observed in recent years.

The largest efficiency in using CAE systems (and CFD in particular) is achieved by inserting them directly into the product design process by the utilization of CAE/CFD not only by dedicated departments, but also by mechanical engineers engaged directly in design, particularly when used upfront in early design, i.e. design-concurrent CFD (Concurrent CFD). This process, which was initially initiated in aerospace, automotive, electronics and other high-technology industries, now covers practically all engineering fields.

The immersed-boundary CAD-embedded CFD code SOLIDWORKS Flow Simulation represents a new class of CFD analysis software that was initially intended for mechanical engineers to use during the design process as an integral part of a product lifecycle management (PLM) concept.

To develop such a class of CFD software the following question should be answered: what are the specific characteristics of a mechanical design engineer as a CFD user?

1. Using 3D CAD system as a main design tool. 3D product model data are both the foundation and starting point for all virtual prototyping and physical simulations today. So, often users do not want to convert geometry into other formats to use it subsequently in a traditional CFD workflow. Moreover, in particular cases, and generally for very complex geometrical assemblies, the adequacy of such conversions is not guaranteed.

2. Lack of a background in CFD as well as the theoretical basis of the numerical algorithms.

3. The need to run multiple optimization calculations with geometric variation rather than single conceptual calculation. In most cases the user needs a submachine gun that never jams, rather than a sniper rifle that is more exacting.

4. CFD calculations are not the users primary job function. These are auxiliary tasks, so an individual user may make calculations only occasionally, but then intensively for a period of time. Moreover, these calculations should be made as rapidly as possible, often with limited computational resource availability.

Naturally, the significance of each of the abovementioned characteristics depends on the specific industry in which the engineer is working. Nevertheless all characteristics should be taken into account to make the CFD tool less expensive to use and more suited to the general professional engineer as the target user persona. SOLIDWORKS Flow Simulation achieves this in part by being fully embedded in the mechanical design environment, SOLIDWORKS, for all general engineering applications.

The basic concept behind the design of SOLIDWORKS Flow Simulation is to automate preparing, performing and visualizing CFD predictions of real applied engineering problems.

To accomplish this, SOLIDWORKS Flow Simulation has some specific features, namely:

complete integration with SOLIDWORKS 3D CAD system; totally automatic grid generation; automatic prescription of solution control parameters; user-friendly pre- and post-processing; ability to perform parametric studies and compare results for design variants, etc. The code does not require the tuning of any numerical parameters associated with the underlying algorithms or the choice of one of ten (or more) physical models or numerical schemes. It is important to note that assignment of initial data (boundary and initial conditions), performing the calculation, and analysis of results (including visualization and report generation) takes place inside SOLIDWORKS with results displayed directly on and around the CAD model. The export of calculation results in MS Office formats and for import into structural analysis with SOLIDWORKS Simulation is also available.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 2

In comparison with traditional CFD codes oriented towards high-level specialists in CFD, SOLIDWORKS Flow Simulation is designed for practicing engineers with a different special interest: that of solving daily problems inherent in industrial product design and process optimization. As a rule, the software training period takes about two working days. In the event of a prolonged rest period, minimum effort is needed for the user to revive their proficiency.

Entire simulations from initial data handling to result analysis can be performed in the course of a single work day.

SOLIDWORKS Flow Simulations technology exhibits another significant difference from the traditional CFD approach in that it uses a number of engineering techniques and methods that assist the user in obtaining reliable predictions at lower computational and time costs. These combined possibilities allow engineers to accelerate the solution of their everyday problems, but place high demands on the softwares reliability, robustness and accuracy in order to automate these engineering methods. This challenge has been the driver behind SOLIDWORKS Flow Simulations Validation and Verification (V&V) procedures since its inception, which use a host of analytical and benchmark solutions as well as on experimental results available from publications and databases (e.g. Freitas, 1995; Fluid Dynamics Databases, 2002). Some of the results are discussed in the present work in framework of SOLIDWORKS Flow Simulations V&V methodology and classifications. Details of technology are not considered in the paper.

2. VALIDATION METHODOLOGY First and foremost, the essential distinction between code Verification and Validation should be discussed. Following Roache (1998), we adopt the succinct description of Verification as solving the equations right, and of Validation as solving the right equations. Another way to make the distinction between Verification and Validation is to follow the classical distinction between mathematics and science. Mathematics is a tool of science, often the predominant language of science. But mathematics exists by itself. Verification is seen to be essentially an activity in mathematics of numerical analysis. Validation is essentially an activity in science (and engineering science): physics, fluid dynamics, chemistry etc.

Most authors (e.g. Roache, 1998) strongly believe that complete Verification of a code (or a calculation) should precede any comparisons with experimental data, i.e., Verification first, then Validation. It is necessary to make some comment on this statement with regard to the immersed boundary CAD-embedded CFD code SOLIDWORKS Flow Simulation.

There are several methods utilized in code Verification. These are Richardson extrapolation (when applicable), calculation with a high- and low-order method on the same mesh, and straightforward repeat calculations with finer or coarser meshes. The last method, also known as a grid dependency test, is very popular in developing and testing of commercial CFD codes.

But one should keep in mind that Verification in strict sense is only realizable if all the following requirements are met during the test:

the same equations are solved and the same engineering techniques and models (including sub grid scale ones) are used in each computational cell;

the geometry of all components is retained for all meshes under investigation;

the mesh topology in the computational domain is the same; and

the order and type of all equations approximations in each computational cell are the same.

As mentioned above, SOLIDWORKS Flow Simulation uses a number of engineering techniques and methods. So, meeting the first requirement is not ensured for real engineering problems, because different engineering techniques or their combinations are used automatically as mesh gets finer or coarser. Therefore only relatively simple examples are acceptable for code Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 3

Verification as separate activity. For the rest of examples it is actually impossible to separate Verification and Validation. That is because a grid dependence study will show the integral accuracy of the code and not only correctness of the numerical algorithms.

We agree with Melnik et al. (1995) that for project-oriented engineers (and, of course, for code intended for them), the activity of code Verification and Validation almost form a continuum, and these terms are often used together to refer to the suite of activities, and even as an acronym for the process. That important factor has to be taken into account when planning and undertaking any SOLIDWORKS Flow Simulation validation activity.

Another point that arises from the use of engineering techniques and methods is that SOLIDWORKS Flow Simulation calculations reach acceptable accuracy on coarser meshes as compared with traditional CFD codes, confirmed by grid dependency tests for most examples and real engineering problems. Due to this, users can solve very complex 3D fluid flow and heat transfer problems using modest computational resources.

Let us now consider code Validation. Validation is the process of determining the degree to which a code, model, simulation, or combination of models and simulations, and their associated data are accurate representations of the real World from the perspective of the intended use (Missile Defense Agency, 2008). Put another way, does the solution of the equations implemented in the code bear any relation to a physical problem of interest?

Naturally, to engineers and scientists Validation is most important. Code Validation comes down to comparison (directly or indirectly) of code predictions with physical experiments, empirical correlations and analytical solutions. The comparison can be direct or indirect. Indirect comparison occurs when a previously validated code is taken as a benchmark.

It should be noted here that absolute certainty regarding the quality of experimental data is a rare occurrence. In many experiments the level of error cannot be determined with confidence.

It is now the dominant opinion (Roache, 1998) that there is a continuing need for high quality experiments that are designed specifically for CFD code Validation. Sourcing such experimental data, its analysis and estimation of its accuracy also forms part of the code Validation activity.

To move closer to our current subject of Concurrent CFD, one can formulate that Validation aims to provide users with comprehensive information about software functionality and its ability to correctly simulate the main physical phenomena underlying fluid flow and heat transfer processes, which occur in equipment when in operation.

There exist many classifications of validation examples and several approaches to Verification &

Validation have been analysed, e.g. Roache (1998); Stern et al. (1999); Oberkampf and Trucano (2002).

One approach is to classify according to the softwares ability to simulate certain class of physical phenomena (natural convection, compressible flows etc.). Another is to classify according to the possibility of employing software in certain technical areas and applications (power & energy, rotating machinery etc.). A third approach is a two-level (or two-class) classification, in which benchmarks and validation examples are decomposed into two classesfundamental tests and applied industrial problems. Each class has its own merits and demerits, but the two types complement one another nicely and formed the V&V procedure of SOLIDWORKS Flow Simulation code for many years (Balakin et al. 2004). A fourth approach extends the two-level classification to a multilevel one. It is this approach, using four classification levels, that is currently employed in our V&V procedure for SOLIDWORKS Flow Simulation, which we elaborate upon here.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 4

The first level, as in Balakin et al. (2004), involves the fundamental (academic) tests which are simple in terms of geometry (2D as the rule) and problem formulation.

As mentioned above, SOLIDWORKS Flow Simulations technology employs a large amount of engineering techniques and methods. These techniques and methods, first of all, touch on the simulation of wall effects (friction and heat transfer). Some of these techniques are unique, and at the same time largely unknown to users familiar with traditional CFD technology. That is why there is a rather comprehensive set of fundamental tests and examples in SOLIDWORKS Flow Simulations validation arsenal. These examples are associated with examination and demonstration of fundamental physical laws and phenomena (flows and convective heat transfer on a plate, in pipes, in channels and heat sinks etc.), as well as verifying algorithmic correctness.

The low cost of these tests makes it possible to conduct a parametric study of various regimes of heat and fluid flow over the maximum range investigated experimentally, numerically or analytically. Moreover, these fundamental tests are versatile, allowing the same configuration to be used to investigate various physical effects in either a coupled or segregated manner.

At the second level are groups of tests that demonstrate how well complicated functions of the software or particular physical models are working (e.g. conjugate heat transfer, cavitation, condensation, etc.).

The third level is comprised of industrial problems and benchmarks where, in addition to the complicated 3D geometry, a combination of different strongly-coupled physical phenomena takes place. Moreover, the exact values of material properties as well as operating conditions for device components are necessary in this case and so the level of experimental uncertainty is much higher. At this level software validations for specific equipment are considered (cyclones, heat exchangers, engines, blowers, pumps, etc).

The last level integrates validation tests and benchmarks from certain industry (aerospace

& defense, electronics, HVAC, process industries). Some authors (e.g., Melnik et al., 1995) associate this level with such activity as code Certification or even code Accreditation. A nuance is that code Certification and Accreditation are usually a part of engineering management.

These appear to be simply the process of some authority (perhaps legal or regulatory) officially declaring a code to be usable for a specific industry or project (Roache, 1998).

Of course, the borders between the levels are often fuzzy and the same validation example can be found at more than one level depending on the industrial application. In general the categorization of cases within these levels depends on example complexity, availability of reference data and its accuracy, and so on. As the levels progress in geometric and flow complexity, a tendency for decreased availability and reduced accuracy of experimental data is observed.

The V&V procedure currently employed for SOLIDWORKS Flow Simulation is shown in Fig. 1.

The diagram has a hierarchical structure and looks like an inverted pyramid, with each level being based on the previous one.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 5

Figure 1: The four-level hierarchy used in SOLIDWORKS Flow Simulations Verification & Validation.

SOLIDWORKS Flow Simulation is a general-purpose tool that has been successfully applied in many industries. Therefore, we actually have several pyramids as shown in Fig. 1. This is the reason why it would be more convenient to represent this pyramid aggregated in a 3D view analogous to the internal structure of Earth (Fig. 2).

Figure 2: A 3D view of SOLIDWORKS Flow Simulation code Validation as an Earth internal structure.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 6

Like Earth, SOLIDWORKS Flow Simulation also has a stable inner core composed of fundamental validations and tests. Specified industries placed on the surface are analogous to the continents on the surface of Earth. Unlike Earth, SOLIDWORKS Flow Simulation has a more dynamic structure. As SOLIDWORKS Flow Simulation is developed Earth grows in size. Functionality, applicability and validity of the SOLIDWORKS Flow Simulation code are also increased, meaning that new continents appear on Earths crust and the outer core and mantle increase in thickness.

Another distinction between SOLIDWORKS Flow Simulation and Earth is that SOLIDWORKS Flow Simulations internal structure can be asymmetric. This is because certain continents can be based on the layers with different thicknesses due to the different number of validation examples and physical models required for the different industries at the 4th level (code Certification).

It is also worth noting that as SOLIDWORKS Flow Simulation is developed Validation activity is shifted to higher levels (mantle and crust) and explains why the previous V&V procedure of SOLIDWORKS Flow Simulation code, based on two-class classification (Balakin et al., 2004), was replaced by the current V&V procedure based on four classification levels. It may well be that in the future SOLIDWORKS Flow Simulation code development will lead to another modification of V&V procedure based upon a more advanced classification of validation examples and tests.

The four-level classification of validation examples with its 3D its analogy to Earths internal structure seems to be very helpful in support and marketing activities. The four-level classification meets requests from users wanting to see simple validations to understand how well separate physical processes are simulated, and requests from users wanting to see how well the technology can predict complex real world equipment performance.

Validation and its methodology are associated with Quality Assurance (QA). Searching and collecting data for validations, data analysis, selection, performing calculations and documentation of cases examples takes a lot of time and resources of the QA team. These cases collectively form a battery of tests that has to be passed before the release of each software version or service pack. The number of validation examples is steadily increasing.

Example cases from the first and second levels are provided with the software as CAD geometry plus boundary conditions and other solution control settings needed to mesh and solve the problem, so the user can replicate validation cases on their own hardware, and use these to augment the tutorial examples provided with the software. The principle rule applied to the set up and solution of validation example test cases is that automatic settings of the code input parameters should be used in V&V procedure calculations. That means:

totally automatic mesh generation (for fundamental validations, for other validation levels it is highly advisable); and

settings for solution control convergence criteria are taken as their default values.

It is also possible to construct mesh in a non-automatic or manual way, e.g. a uniform mesh, or mesh stretching in accordance with user specified input parameters. In general at the first level of Validation fully automated meshing is used. Manual settings become more prevalent at the higher levels. Completeness and consistency of initial data as well as the mesh convergence are studied thoroughly for all examples and tests. Some typical V&V examples and tests are presented below.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 7

3. VALIDATION TEST AND EXAMPLES

1. Fundamental validations: flow over a plate with heat transfer A uniform 2D flows with a laminar boundary layer on a heated flat plate is considered. The statement of the problem is presented in Fig. 3. Reynolds number defined on the plate length of 0.31 m is equal to 3.1x104, therefore the boundary layer is laminar (Holman, 1997).

Figure 3: The statement of the problem.

The SOLIDWORKS Flow Simulation predictions of h and Cf calculated with a fully automatically generated mesh with the result resolution level (RRL) set to 7, and the theoretical curves (Holman, 1997) are shown in Figs. 4 and 5. One can see that the SOLIDWORKS Flow Simulation predictions are in good agreement.

Figure 4: Heat transfer coefficient along the heated plate.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 8

Figure 5: Skin-friction coefficient along the heated plate.

2. Fundamental validations: laminar and turbulent flows in pipes Prediction of 3D water flow through a long straight pipe with circular cross section is considered (see Fig. 6). A uniform inlet velocity Uinlet is set.

Figure 6: Statement of the problem.

Fig. 7 show the SOLIDWORKS Flow Simulation predictions performed at RRL=5 for smooth pipes in the entire Red range and compared with theoretical values (Schlichting, 1979; White, 1994).

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 9

Figure 7: The friction factor for smooth pipes.

It can be seen that the friction factor values predicted for smooth pipes are fairly close to the theoretical and empirical curve. The prediction errors do not exceed 5%.

3. Fundamental validations: flow in a 90-degree bend square duct In this case a steady-state flow of water in duct is considered (Humphrey et al., 1977). The geometry of the duct is shown in Fig. 8. ReD = 790 meaning that the flow is laminar.

Inlet temperature is equal to 293.2 K and inlet uniform velocity Uinlet = 0.0198 m/s.

Figure 8: The 90°-bend square ducts configuration indicating the velocity measuring stations and the dimensionless coordinates.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 10

The predicted dimensionless (divided by Uinlet ) velocity profiles are compared in Figs. 9, 10 with the measured ones at the following duct cross sections: XH = -5D, -2.5D, 0 (or =0°). The z and r directions are represented by coordinates (r-r0)/(ri-r0) and z/z1/2, where z1/2 = 20 mm.

Figure 9: The ducts velocity profiles predicted by SOLIDWORKS Flow Simulation (red lines) in comparison with the experimental data (circles).

Figure 10: The ducts velocity profiles predicted by SOLIDWORKS Flow Simulation (red lines) in comparison with the experimental data (circles) at z/z1/2=0.5 (left) and at z/z1/2=0 (right).

It is seen that the SOLIDWORKS Flow Simulation predictions are in good agreement with the experimental data (Humphrey et al., 1977).

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 11

4. Fundamental validations: flow in 2D channel with unilateral sudden expansion In this example laminar incompressible steady-state water flow through 2D (plane) channel with unilateral sudden expansion and parallel walls is examined. The sketch of the problem is shown in Fig. 11. Water temperature - 293.2 K, mean velocity - 8.25 mm/s.

Figure 11: Flow in a 2D (plane) channel with an unilateral sudden expansion.

At the inlet an experimentally measured mean velocity profile (Denham and Patrick, 1974) at the corresponding Reh=125 is specified. The 105 Pa static pressure is specified at the outlet.

The flow velocity field predicted by SOLIDWORKS Flow Simulation with automatically generated mesh (RRL=8) is compared in Figs. 12-14 with the measured values (Denham and Patrick, 1974).

Figure 12: The velocity profiles predicted by SOLIDWORKS Flow Simulation (red lines) in comparison with the experimental data (black lines with dark circles).

Figure 13: The recirculation zone length predicted by SOLIDWORKS Flow Simulation in comparison with the experimental data.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 12

Figure 14: The recirculation zones separation streamlines and vortex center, both predicted by SOLIDWORKS Flow Simulation in comparison with experimental data.

The flow X-velocity (u/U, where U = 8.25 mm/s) profiles at several X = const cross sections are shown in Fig. 12. It is seen that the predicted flow velocity profiles are very close to the experimental values both in the main stream and in the recirculation zone.

The recirculation zones characteristics, i.e. its length LR along the channels wall, the separation streamline, and the vortex center are shown in Figs. 13, 14. It is seen that they are in excellent agreement with the experimental data.

5. Fundamental validations: flow over a circular cylinder with and without heating First of all, an incompressible flow over a cylinder without heating has been studied numerically in a wide range of governing parameters as a transient problem. It is well-known that at low Reynolds number ReD < Reosc (Reosc is about 45) two vortices are formed in a closed near wake. Fig. 15 demonstrates a very good agreement between SOLIDWORKS Flow Simulation predictions and photo from Van Dyke (1982) for ReD = 41 predicted with automatically generated mesh (RRL = 7).

Figure 15: Predicted flow trajectories colored by the pressure magnitude (the upper) and photo from Van Dyke (1982) (the lower part) for ReD = 41.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 13

At higher Reynolds numbers the flow becomes unstable and a von Karman vortex street appears in the wake past the cylinder. The SOLIDWORKS Flow Simulation prediction of Strouhal number in comparison with experimental data (White, 1994) for Re103 is shown in Fig. 16.

Figure 16: The cylinder flows Strouhal number predicted with SOLIDWORKS Flow Simulation (triangles) in comparison with the experimental data (line with dashes).

The calculated at RRL=7 time-averaged cylinder drag coefficient is compared to the well-known experimental data on CD(Re) (Panton, 1996) in Fig. 17. It is easy to see that numerical results are close to experimental data in wide range of Re.

Figure 17: The drag curve for a cylinder.

The simplest modification of this problem is to consider convective heat transfer from a heated circular cylinder (with the total heat generation rate q) in an air flow.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 14

An excellent correlation in NuD between computations and measurements (Holman, 1997) has been obtained in the whole considered range of Re (see Fig. 18).

Figure 18: Nusselt number NuD for air flow over a heated cylinder.

6. Fundamental validations: buoyancy-driven cavity flow This 2D test is classical for convective heat transfer. In this test a free convection is considered in a square cavity with isothermal side walls of different temperature value and the thermally insulated top and bottom (see Fig. 19). The cavity is filled with air.

The benchmark solution (Davis, 1983) has been obtained from high-accurate predictions of about 40 computer codes and moreover, it agrees very well with the semi-empirical formula of experimental researches (Emery and Chu, 1965).

The square cavitys side dimension, L, is varied within the range of 0.0111...0.111 m in order to vary the cavitys Rayleigh number within the range of 103 - 106.

A mesh convergence study for considered range of the Rayleigh number is presented in Fig. 20.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 15

Figure 19: An enclosed 2D square cavity with natural convection.

Figure 20: Mesh convergence study for various Ra.

This figure demonstrates dependence of ratio Nu/Nubenchmark both on the value of mesh automatic generation level (RRL) and on cell number per reference L (square cavity size). This plot confirms grid convergence achieved at RRL = 8. Numerical results derived at this value of RRL are shown below.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 16

Fig. 21 shows the mesh derived after the dynamic adaptation to the solution peculiarities in the particular case of Ra = 106 predicted at the highest RRL = 8.

Figure 21: Adapted to the solution mesh at RRL = 8 for Ra = 106.

The next figures demonstrate a very good agreement between SOLIDWORKS Flow Simulation predictions and the benchmark solution (Davis, 1983) both in thermal (see Fig. 22) and hydrodynamic (see Fig. 23, 24) fields for all considered Rayleigh numbers.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 17

Figure 22: Average Nusselt number vs. Rayleigh number.

Figure 23: Maximum dimensionless velocity components vs. Rayleigh number.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 18

Figure 24: Dimensionless coordinates of the maximum velocities locations vs Rayleigh number.

7. Fundamental validations: flow over RAE 2822 airfoil In this example SOLIDWORKS Flow Simulation prediction of 2D air flow around RAE 2822 airfoils is considered. The airfoil geometry is presented in Fig. 25.

Figure 25: RAE 2822 airfoil.

The airfoil chord length is 1.0 m. Computational domain size is 30.24 m. Computational mesh has 350.200 cells with finer ones in the vicinity of the aerofoil. Total number of mesh cells is about 70000.

Five test cases are considered. Flow conditions specified for each case are shown in Table 1 (Cook et al., 1979).

Case M ,° Re T, K P, Pa 1 0.676 2.4 5.7e+6 300 38684.5408 2 0.676 -2.18 5.7e+6 300 300 38684.5408 3 0.725 2.55 6.5e+6 300 300 41132.45548 4 0.725 2.92 6.5e+6 300 300 41132.45548 5 0.728 3.22 6.5e+6 300 300 40962.95361 Table 1: Flow conditions for prediction flow over RAE 2822 airfoil.

Planar plot of computed Mach number is shown in Fig. 26.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 19

Figure 26: Mach number planar plot around the airfoil for test case 5.

In this test case a strong shock is visible on the upper surface at approximately the mid-chord position, which results in a thickening of the boundary layer downstream.

The comparison of SOLIDWORKS Flow Simulation predicted surface pressure coefficient distributions with experimental ones (Cook et al., 1979) for test case 5 is given in Fig. 27. In the presented case (Fig. 27) satisfactory agreement is seen between SOLIDWORKS Flow Simulation calculation results and experiment both for overall distributions and in the position of the shock.

Figure 27: Comparison of computed and measured surface pressure coefficients for case 5.

As regard to integral aerodynamic coefficients CL and CD, the calculated ones are also in good agreement with experimental data. The predicted values are CL =0.807 and CD =0.0192. They give relative prediction error 0.61% and 9.5%, respectively.

Unfortunately because of lack of space descriptions of tests devoted to Validation of radiation models, heat conduction in solids, flows of non-Newtonian liquids, condensation models, real gases and so on exceed the limits of this paper.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 20

8. Industrial problems and benchmarks: flow simulation over a generic car body shape (the Ahmed body)

A classical automotive external aerodynamics wind tunnel test case is the so-called Ahmed Body (Lienhart et al., 2000) is considered.

An approaching air flow of 40 m/s at corresponding Re = 7.68.105 is evaluated. All parameters of the car body were taken from Lienhart et al. (2000).

SOLIDWORKS Flow Simulation calculations were performed with a computational mesh of 209 cells in length, 58 cells in height, and 78 cells in width (Fig. 28).

Figure 28: The SOLIDWORKS Flow Simulation computational mesh over the model car body with the 250 rear slope.

SOLIDWORKS Flow Simulation calculated flow fields are shown in Fig. 29 for the two sloping rear angles. The SOLIDWORKS Flow Simulation calculated flow velocity profiles and body drag coefficients in comparison with the experimental ones (Lienhart et al., 2000) are shown in Fig.

30 and Table 2.

Figure 29: Calculated flow streamlines and velocity contours upstream, over and downstream of the model car body: 250 rear slope (left),

350 rear slope (right).

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 21

Figure 30: Velocity profiles in the bodys symmetry plane at different bodys slope angles (lines - calculation; red points - experiment): 250 rear slope (upper), 350 rear slope (lower).

Slope angle Cd,exp Cd,calc Error, %

25° 0.298 0.284 -4.8 35° 0.676 0.274 6.6 Table 2: The model car bodys drag coefficient calculated with SOLIDWORKS Flow Simulation and obtained in experiments.

It can be seen from Figs. 29 and 30 that calculated flow velocity profiles are close to the experimental ones. From Table 2 it is observed that the SOLIDWORKS Flow Simulation calculated body drag coefficients agree well with the experimental ones.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 22

9. Industrial problems and benchmarks: prediction of cooling tower external aerodynamics This validation example describes the results of SOLIDWORKS Flow Simulation technology application to analyze the flow around the cooling tower shell.

Hyperbolic shape of cooling tower shell is approximated by a short cylindrical throat joined onto two truncated cones, as can be seen in Fig. 31.

Figure 31: The cooling tower geometry.

The cooling tower base aperture was treated as sealed. The cooling tower was defined by the geometrical parameters given in Table 3. All presented parameters as well as experimental wind tunnel tests data were taken from Zdravkovich (2003), Cowdrey and ONeill (1956).

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 23

Geometrical parameters Units Value Overall height in 27.0 Base diameter in 2 2.0 Throat diameter in 10.5 Top diamter in 1 2.0 Cylindrical through height in 4.0 Upper truncated cone height in 3.5 Air flow properties Temperature K 293.2 Pressure atm 1.0 Reference velocity V.n mis 103.9 Friction velocity u, mis 7.86 Reynolds Number =6.0E6 Table 3: The coolir.g toWQr paramotcirs and flow conditions.

The flow calculation problem was considered in following computational domain: length - 3.75 m, width - 1.25 m and height- 1.4 m. Only one half of cooling tCM1er was taken into account for calculations. SOLIDWORKS Flow Simulation calculations were performed with the initial mesh of 75 cells in length, 30 cells in height, and 25 eel Is in width which after refinement in the vicinity of the model gives computational mesh of about 580000 cells.

Fig. 32 shCM1s predicted CP distributions at ZIH=0.79 as compared with experiment.

t. Experiment Flow Simulation 0.25

0.

a. -0.25

I\ C.

-0.5 *

-0.75 *

-1 *

-1.25 *

-1.5 *

-1.75 -

0 15 30 45 60 75 90 105 120 135 150 16!; 18 Theta, degree Figure 32: locol CP distributions *n:,und cooling tower *t elwotion Z/H=0.79.

As can be seen almost for all angles the calculation results demonstrate good agreement with the experiment.

Distribution of CP with height in rear side of the model also shows good correlation with experimental data (see Fig. 33).

Validation Methodolog11 for Modern CAD-Embedded CFO Code: from Fundamental Tests to Industrial Benchmarks 24

Figure 33: Local CP distributions with height in rear side of the cooling tower (theta=180).

It should be pointed out very good SOLIDWORKS Flow Simulation prediction of the positions and the values of maximum suction for all elevations under consideration.

As example of complex multiphysics calculations Figs. 34-35 display the result of prediction of the visible saturated vapour plume formation.

First of all, attention should be paid to excellent resolution of counter-rotating vortex pair (see Figs. 34) which is typical for turbulent buoyant jets in crossflow.

Secondly, temperature and relative humidity distributions in downstream transverse cross-sections of the plume fully correspond to the vortex induced scalar parameters fields in turbulent jets (see Fig. 35).

It can be stated here that SOLIDWORKS Flow Simulation has been successfully validated on the problem of prediction of cooling tower external aerodynamics.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 25

Figure 34: Temperature distribution in vertical symmetry plane along with flow trajectories drawn in two lateral downstream sections and colored by relative humidity magnitude.

Figure 35: Velocity distribution on cooling tower shell along with flow trajectories colored by temperature magnitude and relative humidity contours in three downstream cross-sections.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 26

10. Industrial problems and benchmarks: prediction of cyclone performance at extreme temperature Gas cyclones are the most widely used separation devices which can be found in industry.

Overall view of the cyclone considered for Validation purposes is presented in Fig. 36. The cyclone was defined by the geometrical conditions given in Table 4. All presented parameters as well as experimental data were taken from Lorenz (1994).

Figure 36: Overall view of the cyclone model.

SOLIDWORKS Flow Simulation calculations were performed with a computational mesh of 350000 cells.

Transient approach was adopted for simulations. Time step tc can be given in general form:

where Dd - dust outlet diameter, Dvf - vortex finder diameter, Dbar - barrel diameter, Uinlet - velocity at cyclone inlet.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 27

Geometrical parameters Units Value Barrel diameter m 0.15 Vortex finder diameter m 0.05 Dust outlet diameter m 0.05 Overal cyclone height m 0.387 Inlet duct length m 0.245 Entrance height m 0.02 Entrance width m 0.08 Barrel height m 0.104 Vortex finder lower length m 0.11 Vortex finder upper length m 0.21 Straighener height m 0.05 Inlet square side length m 0.044 Gap between deflecting cone and dust outlet m 0.01 Cone slope angle deg. 10 Table 4: Main geometric dimensions of the cyclone model.

The results of calculations are shown in Figs. 37-39.

Figure 37: Pressure (left) and velocity (right) distributions within the cyclone for ambient air (200C) under volume flow rate of 80 m3/h after simulation of 3 s of physical time.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 28

Figure 38: Pressure drops of the cyclone under various temperatures.

Figure 39: Grade efficiency curves under volume flow rate of 60 m3/h and various air temperatures.

The flow field within the cyclone is presented in Fig. 37. Typical pressure and velocity distribution can be found there.

Fig. 38 shows the predicted pressure drop compared to the experimental data for different gas temperatures taken from Lorenz (1994). It demonstrates good agreement with the experiments for the most operating conditions. The differences between calculations and experiments are typically within 5-10%. Only for hot gas flow the difference gets a bit higher.

The SOLIDWORKS Flow Simulation predictions of cyclone grade efficiency operating from ambient to extreme temperature are shown in Fig. 39. Vertical bars at predicted values denote maximum and minimum removal probabilities obtained in 5 calculation series. The particle density was 2650 kg/m3.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 29

One can see the SOLIDWORKS Flow Simulation predictions of cyclone grade efficiency are in good agreement with reported data (Lorenz, 1994). Special attention should be paid for cut-off size (particle size under which 50% probability of particle removal is achieved) excellent prediction.

4. CONCLUSIONS Trend analysis on the worldwide CAE market clearly shows steady growth of market share of CFD calculations in the solution of todays engineering design problems. Formerly CFD calculations were mainly used in aerospace, automotive, power generation and electronic industries, but now such calculations are vitally important in almost for all industries.

SOLIDWORKS Flow Simulation is a typical example of the adaptation of CAE technology (namely fluid dynamics and heat transfer) for the everyday needs of design engineers.

For a code used by project-oriented engineers, it is actually impossible to separate the Verification and Validation procedures for most cases because of the high level of automation built into the code. This means that the activity of code Verification/Validation almost form a continuum, with the terms being used together when referring to a suite of activities and even abbreviated to V&V as an acronym for this.

Due to the use of a Cartesian-based mesh coupled with some engineering techniques and methods implemented in SOLIDWORKS Flow Simulation, numerical calculations reach acceptable accuracy on far coarser meshes when compared with traditional CFD codes. Due to this fact, users can make calculations of fluid flow and heat transfer for very complex 3D cases with relatively modest computational resources.

A four-level classification of validation examples and tests is employed in current practice for the V&V procedures used in the QA of SOLIDWORKS Flow Simulation. This can be portrayed graphically with the four levels displayed on an inverted pyramid, with each level being based upon, and supported by the previous level.

In general, the categorization of validation examples and test cases within these levels of classification depends on example complexity, availability of reference data and its accuracy, and so on. As the levels progress in geometric and flow complexity, a tendency for decreasing availability and accuracy of experimental data is observed. This four-level classification has dynamic structure. As the SOLIDWORKS Flow Simulation code is developed, the V&V activity, and particularly the development of new cases, is shifted more towards higher levels.

Presented typical validation examples and tests for each validation level confirm that SOLIDWORKS Flow Simulation code has been successfully validated on a variety of problems for many years. The experimental data and analytical solutions have been well reproduced numerically via SOLIDWORKS Flow Simulation simulation with acceptable degree of accuracy.

The combination of good performance for relatively coarse mesh, CAD-embedded capability and high level of automation and usability make SOLIDWORKS Flow Simulation code quite adequate and useful CFD tool for engineering design and analysis.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 30

REFERENCES Balakin, V., Churbanov, A., Gavriliouk, V., Makarov, M. and Pavlov A. (2004) Verification and Validation of EFD.Lab Code for Predicting Heat and Fluid Flow, Proceedings of ICHMT International Symposium on Advances in Computational Heat Transfer, Norway, April 19-24, 2004.

Cook, P., McDonald, M. and Firmin, M. (1979) Airfoil RAE 2822 Pressure Distributions, and Boundary Layer Wake Measurements, AGARD AR-138, p. A6.

Cowdrey, C.F. and ONeill, P.G.G. (1956) Report of Tests on a Model Cooling Tower for CEA:

Pressure Measurements at High Reynolds Numbers. Nat. Phys. Lab., Aero. Rep. 316a .

Davis, G. de Vahl (1993) Natural Convection of Air in a Square Cavity: a Bench Mark Numerical Solution, Int. J. Numer. Methods Fluids, Vol. 3, No. 3, pp 249-264.

Denham, M.K. and Patrick, M.A. (1974) Laminar Flow over a Downstream-Facing Step in a Two-Dimensional Flow Channel, Trans. Instn. Chem. Engrs., Vol. 52, pp. 361-367.

Emery, A. and Chu, T.Y. (1965) Heat Transfer across Vertical Layers, Trans. ASME, J. Heat Transfer, Vol. 87, p 110.

Fluid Dynamics Databases (2002), ERCOFTAC Bulletin, No. 52.

Freitas, C.J. (1995) Perspective: Selected Benchmarks From Commercial CFD Codes, Trans.

ASME, J. Fluids Eng., Vol. 117, No. 2, pp 208-218.

Holman, J.P. (1997) Heat Transfer, 8th ed., McGraw-Hill, New York.

Humphrey, J.A.C., Taylor, A.M.K. and Whitelaw, J.H. (1977) Laminar Flow in a Square Duct of Strong Curvature, J. Fluid Mech., Vol.83, part 3, pp.509-527.

Kamps, T. (2005) Model Jet Engines, UK.

Lienhart, H., Stoots, C. and Becker, S. (2000) Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed Model), DGLR Fach Symp. der AG STAB, Stuttgart University.

Lorenz, T. (1994) Heisgasentstaubung mit Zyklonen, VDI-Fortschritt-berichte, Reihe 3, Verfahrenstechnik No 366, VDI-Verlag, Dusseldorf .

Melnik, R.E., Siclari, M.J., Marconi, F., Barber, T., Verhoff, A. (1995) An Overview of a Recent Industry Effort at CFD Code Validation, AIAA Paper 95-2229, 26th AIAA Fluid Dynamics Conference, San Diego, California, June 19-23, 1995.

Missile Defense Agency (2008), Validation & Accreditation (VV&A) for Models and Simulations, Department of Defense Documentation of Verification, Missile Defense Agency.

Nandula, S.P., Pitz, R.W., Barlow, R.S. and Fiechtner, G.J. (1996) Rayleigh/Raman/LIF Measurements in a Turbulent Lean Premixed Combustor, AIAA Paper 96-0937, 34th Aerospace Sciences Meeting & Exhibit, Reno, NV, January 15-18, 1996.

Oberkampf, W.L. and Trucano, T.G. (2002) Verification and Validation in Computational Fluid Dynamics, Progress in Aerospace Sciences, Vol. 38, pp 209-272.

Validation Methodology for Modern CAD-Embedded CFD Code: from Fundamental Tests to Industrial Benchmarks 31

Panton, R.L. (1996) Incompressible Flow, 2nd ed., Wiley, New York.

Roache, P.J. (1998) Verification and Validation in Computational Science and Engineering He rmosa, Albuquerque, NM.

Schlichting, H. (1979) Boundary Layer Theory, 7th ed., McGraw-Hill, New York.

Stern, F., Wilson, R.V., Coleman, H.W. and Paterson, E.G. (1999) Verification and Validation of CFO Simulations', IIHR Report No. 407, Iowa Inst. Hydraulic Research, the University of Iowa.

Van Dyke, M. (1982) Rn Rlbum of Fluid Motion, The Parabolic Press, Stanford, CA.

White, F.M. (1994) Fluid Mechanics, 3rd ed., McGraw-Hill, New York.

Zdravkovich, M.M (2003) Flow Rround Circular Cylinders, Vol. 2: Applications, Oxford University Press, New York.

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SOFTWARE VALIDATION TEST PLAN AND REPORT FOR ANSYS-FLUENT VERSION 12.1 Prepared for U.S. Nuclear Regulatory Commission Contract NRC-02-07-006 Prepared by Kaushik Das Debashis Basu Center for Nuclear Waste Regulatory Analyses San Antonio, Texas November 2010 Approved by:

1 DatJ

CONTENTS Section Page FIGURES .......................................................................................................................iv TABLES .........................................................................................................................vi 1 INTRODUCTION ..................................................................................... 1-1 1.1 Scope of Validation.............................................................................. 1-3 1.2 Natural and Forced Convection ........................................................... 1-4 1.3 High Speed Flows ............................................................................... 1-5 1.4 Radiation Heat Transfer ...................................................................... 1-5 1.5 Multiphase Flows ................................................................................. 1-6 2 ENVIRONMENT ..................................................................................... 2-1 2.1 Software ..................................................................................... 2-1 2.2 Hardware ..................................................................................... 2-2 3 PREREQUISITES ..................................................................................... 3-1 4 ASSUMPTIONS AND CONSTRAINTS ........................................................... 4-1 5 NATURAL AND FORCED CONVECTION ...................................................... 5-1 5.1 Natural Convection in an Annulus Between Horizontal Concentric Cylinders ........................................................................... 5-1 5.1.1 Theoretical Basis ..................................................................... 5-2 5.1.2 Test Input ................................................................................. 5-3 5.1.3 Expected Test Results ............................................................. 5-3 5.1.4 Test Results ............................................................................. 5-3 5.2 Natural Convection Along a Vertical Flat Plate .................................... 5-6 5.2.1 Theoretical Basis ..................................................................... 5-6 5.2.2 Test Input ................................................................................. 5-7 5.2.3 Expected Test Results ............................................................. 5-8 5.2.4 Test Results ............................................................................. 5-8 5.3 Flow Over Back-Facing Step ............................................................. 5-10 5.3.1 Theoretical Basis ................................................................... 5-11 5.3.2 Test Input ............................................................................... 5-13 5.3.3 Expected Test Results ........................................................... 5-13 5.3.4 Test Results ........................................................................... 5-13 5.4 Flow and Heat Transfer Over Expansion Pipe .................................. 5-16 5.4.1 Theoretical Basis ................................................................... 5-17 5.4.2 Test Input ............................................................................... 5-17 5.4.3 Expected Test Results ........................................................... 5-18 5.4.4 Test Results ........................................................................... 5-18 ii

CONTENTS Section Page 6 HIGH SPEED FLOWS .................................................................................... 6-1 6.1 Flow Over Wedge ................................................................................ 6-1 6.1.1 Theoretical Basis ..................................................................... 6-2 6.1.2 Test Input ................................................................................. 6-3 6.1.3 Expected Test Results ............................................................. 6-4 6.1.4 Test Results ............................................................................. 6-4 6.2 Turbulent Mixing Layer of Compressible Flow .................................... 6-6 6.2.1 Theoretical Basis ..................................................................... 6-6 6.2.2 Test Input ................................................................................. 6-7 6.2.3 Expected Test Results ............................................................. 6-7 6.2.4 Test Results ............................................................................. 6-7 7 RADIATION HEAT TRANSFER ...................................................................... 7-1 7.1 Radiation Between Two Parallel Surfaces .......................................... 7-1 7.1.1 Theoretical Basis ..................................................................... 7-2 7.1.2 Test Input ................................................................................. 7-2 7.1.3 Expected Test Results ............................................................. 7-3 7.1.4 Test Results ............................................................................. 7-3 7.2 Radiation Between Two Concentric Cylinders .................................... 7-4 7.2.1 Theoretical Basis ..................................................................... 7-5 7.2.2 Test Input ................................................................................. 7-6 7.2.3 Expected Test Results ............................................................. 7-6 7.2.4 Test Results ............................................................................. 7-7 8 SPECIES TRANSPORT AND MULTIPHASE FLOWS ................................... 8-1 8.1 Diffusion Through Mixture Column at Constant Pressure and Temperature ................................................................................. 8-1 8.1.1 Theoretical Basis ..................................................................... 8-2 8.1.2 Test Input ................................................................................. 8-3 8.1.3 Expected Test Results ............................................................. 8-4 8.1.4 Test Results ............................................................................. 8-4 8.2 Condensation of Water Vapor Over Flat Plate .................................... 8-6 8.2.1 Theoretical Basis ..................................................................... 8-7 8.2.2 Test Input ................................................................................. 8-9 8.2.3 Expected Test Results ............................................................. 8-9 8.2.4 Test Results ........................................................................... 8-10 8.2.4.1 Test Results for Single-Phase Species Transport ... 8-10 8.2.4.2 Test Results for Multiphase Transport with Volumetric Condensation ........................................ 8-12 9 INDUSTRY EXPERIENCE .............................................................................. 9-1 10 NOTES .......................................................................................................... 10-1 11 REFERENCES ................................................................................... 11-1 iii

FIGURES Figure Page 5-1 Computational Domain for Kuehn and Goldstein Problem .............................. 5-1 5-2 Velocity Vectors and Temperature Contours for Different Rayleigh Numbers ........................................................................................... 5-5 5-3 Computational Domain and Grid for Natural Convection Over Vertical Heated Plate. ..................................................................................... 5-6 5-4 Velocity Vectors and Temperature Contours (a) of the Domain and (b) Near the Exit ........ ..................................................................................... 5-9 5-5 Comparison of Computed and Analytical Values of Nusselt Number Where the Upper and Lower Limit of Acceptance is Within 10 Percent of Computed Value. (a) Version 12.1 and (b) Version 6.3 ............................... 5-10 5-6 Velocity and Temperature Distribution at the Plane A-A.

(a) Version 12.1 and (b) Version 6.3 ............................................................. 5-10 5-7 Computational Domain, Grid, and Boundary Conditions for Back-Facing Step .......................................................................................... 5-11 5-8 Velocity Near the Vicinity of the Back-Facing Step.

(a) Version 12.1 and (b) Version 6.3 ............................................................. 5-14 5-9 Turbulent Kinetic Energy Near the Vicinity of the Back-Facing Step.

(a) Version 12.1 and (b) Version 6.3 ............................................................. 5-14 5-10 Comparison of Computed Skin Friction Coefficient With Experimental Data. (a) Version 12.1 and (b) Version 6.3............................. 5-15 5-11 Comparison of Computed Pressure Coefficient With Experimental Data (a) Version 12.1 and (b) Version 6.3 ............................................................. 5-15 5-12 Computational Domain Grid and Boundary Conditions for Flow and Heat Transfer Over Expanded Pipe .............................................................. 5-16 5-13 Velocity, Temperature, and Turbulent Kinetic Energy in the Flow Field Using Version 12.1 .... ................................................................................... 5-19 5-14 Comparison of Experimental and Computed Nu/NuDB Along the Heated Wall ............................................................................................. 5-19 6-1 Features of Supersonic Flows Over Wedge.................................................... 6-1 6-2 Domain, Grid, and Boundary Conditions for Flow Over Wedge ...................... 6-2 6-3 Simulated Density Field Using FLUENT Version 12.1 .................................... 6-4 6-4 Simulated Pressure Field Using FLUENT Version 12.1 .................................. 6-5 6-5 Comparison of Analytical and Computed Solutions Along the Floor (a) Mach Number and (b) Density Ratio ......................................................... 6-5 6-6 Computational Domain, Grid, and Boundary Conditions for Compressible Mixing Layer ............................................................................. 6-6 6-7 Velocity Distribution in the Mixing Layer.......................................................... 6-8 6-8 Turbulent Kinetic Energy Distribution in the Mixing Layer ............................... 6-8 6-9 Comparison of Computed and Experimental Turbulent Kinetic Energy at

= 100 mm ..................................................................................................... 6-9 6-10 Comparison of Computed and Experimental Axial Velocity at

= 100 mm ..................................................................................................... 6-9 iv

FIGURES Figure Page 7-1 Schematic of Radiation Heat Transfer Between Parallel Surfaces ................. 7-1 7-2 Temperature Contours Across the Gap Using DO Model in FLUENT Version 12.1 ..................................................................................... 7-3 7-3 Comparison of Analytical and Computed Solution of Temperature Across the Gap Along with the Acceptance Limit of +/-10 Percent Using DO Model for FLUENT Version 12.1 ............................................................... 7-4 7-4 Schematic of Radiation Heat Transfer Between Concentric Cylinders ........... 7-5 7-5 Temperature Contours Annulus Using S2S Model in FLUENT Version 12.1 .. ........... ..................................................................................... 7-7 7-6 Comparison of Analytical and Computed Solution of Temperature Across The Annulus Using FLUENT Version 12.1 ...................................................... 7-8 8-1 Schematic of Diffusion in Mixture Column ....................................................... 8-1 8-2 Water Vapor Mass Fraction Variation in the Flow Field Using (a) Version 12.1 and (b) Version 6.3 ............................................................... 8-4 8-3 Comparison of Analytical and Computed Solution of Mass Fraction Of Water Vapor. (a) Version 12.1 and (b) Version 6.3 ................................... 8-5 8-4 Comparison of Analytical and Computed Solution of Mass Fraction Of Air. (a) Version 12.1 and (b) Version 6.3 ................................................... 8-6 8-5 Schematic for Condensation of Humid Air Over Flat Plate ............................. 8-7 8-6 Air Mass Fraction Variation in the Flow Field ................................................ 8-11 8-7 Comparison of Analytical and Computed Results for Condensation Mass Flux for Inlet Velocity. (a) Equals 0.1 m/s and (b) Equals 1 m/s ......... 8-11 8-8 Relative Humidity Contours for Simulation with Single-Phase Species Transport and Inlet Velocity = 1 m/s .............................................................. 8-11 8-9 Air Mass Fraction Variation in the Flow Field with Multiphase Flow and Inlet Velocity = 1 m/s .............................................................................. 8-12 8-10 Comparison of Analytical and Computed Results for Condensation Mass Flux for Inlet Velocity Using Multiphase Flow Modeling.

(a) Equals 0.1 m/s and (b) Equals 1 m/s ....................................................... 8-12 8-11 Relative Humidity Contours for Simulation with Multiphase Species Transport and Inlet Velocity = 1 m/s .............................................................. 8-13 v

TABLES Table Page 5-1 Selected Experiments for FLUENT Simulations .............................................. 5-3 5-2 Properties of Nitrogen for FLUENT Simulation Conditions ............................. 5-3 5-3 Mesh Sizes for Grid Independence Study for FLUENT ................................... 5-3 5-4 Comparison of Measured and Predicted Equivalent Thermal Conductivity for Concentric Cylinders ............................................................. 5-4 5-5 Comparison of Measured and Predicted Equivalent Thermal for Three Grid Levels ...................................................................................................... 5-5 5-6 Flow Parameters for Flow Over a Back-Facing Step .................................... 5-11 vi

1 INTRODUCTION ANSYS-FLUENT Version 12.11 is a general purpose computational fluid dynamics software package developed by ANSYS Inc. It is widely used for design and analysis of applications ranging from aircraft components to sporting goods and garments. It is among the leading computer-aided engineering tools that engineers predominantly use for flow, chemistry, and heat transfer simulations in a continuum, though it has some added modules for magnetohydrodynamics and discrete particle problems. Industry reports, trade journals, and technical literature show that it is regularly used in the automobile industry, bio-fluids applications, electronic cooling in the semiconductor industry, high speed flows over aircraft wings and fuselage, multiphase flows in the nuclear industry, and turbomachinery flow simulations in rotating frames of reference.

The FLUENT software was initially developed by Fluent Inc., which was subsequently acquired by ANSYS Inc. ANSYS has combined a number of engineering analysis software, such as ANSYS-Mechanical, ANSYS-Meshing, and the computer-aided design (CAD) package Design Modeler (DM), to create an integrated workbench. In this integrated workbench, each software tool coexists as a separate entity, but users can select tools they need to address a particular problem on a seamlessly integrated platform, where data and information from one package is communicated automatically to others. For example, if an engineer is interested in combined thermal and mechanical analysis of a pipe flow system that carries high temperature fluid, he can use DM to do the solid modeling, ANSYS Meshing to discretize the domain and then ANSYS-Mechanical and FLUENT to perform the structural and fluid analysis in a coupled fashion with minimal user interaction. The process of creating an integrated benchmark is still underway. Before ANSYS Inc. acquired FLUENT, Geosciences and Engineering Division (GED) staff used FLUENT Version 6.3, which had undergone the validation and verification process (Das and Basu, 2007). After the merger, FLUENT Inc. stopped supporting Version 6.3 and GED staff switched to the ANSYS-FLUENT Version 12.1. The new version retained almost all the features of the older Version 6.3 and has some added capabilities. GED staff have also adopted the new integrated platform mentioned previously (ANSYS-Workbench) to perform simulation activities. However, GED currently retains a license only for the computational fluid dynamics (CFD) packages within the Workbench platform and presently does not perform any combined analysis that requires packages such as ANSYS-Mechanical.

FLUENT solves the generalized Navier-Stokes equations using the finite volume technique. It has a pressure- and a density-based solver to solve the incompressible and compressible flows, respectively. The standard version of FLUENT has a comprehensive suite of models to represent conduction, convection, and radiation heat transfer with options to simulate phase change and solidification-melting phenomena. A number of multiphase flow modeling techniques, including the volume of flow method, Eulerian-Eulerian model, mixture model, and the discrete particle tracking methods, are available in the solver. The standard solver can be customized to meet the requirements unique to a particular application by using the user-defined functions.

There are a number of added modeling tools that are available within the FLUENT 1

ANSYS-FLUENT Version 12.1will be referred to as FLUENT in this document.

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framework, along with the generalized flow solver, meant for analyzing specialized problems. For example, an automobile engineer can use the discrete particle model and the chemistry toolbox of FLUENT to study in-cylinder combustion of an engine, the heat exchanger module to design a radiator, and the pollutant module to assess the level of emissions from the exhaust gas. Similarly, FLUENT can be used to study external aerodynamics of an aircraft body and the specialized models to investigate gas turbine combustion and turbomachinery flows.

FLUENT uses an unstructured grid and supports a number of grid elements, such as hexahedral, polyhedral, prismatic, and tetrahedral mesh. The solver employs the Message Passing Interface (MPI) routines for parallel processing in a number of platforms including Microsoft Windows NT, UNIX, and different variants of LINUX.

FLUENT has the dynamic and moving mesh capabilities required for specialized flows, such as in-cylinder flows in internal combustion engines, values, store separation, and release of objects from aircrafts. Users can choose from a number of turbulence models ranging from zero equation models to large eddy simulation techniques available with the standard solver to simulate turbulence as their problems require. A number of spatial discretization schemes, like the first-order upwind scheme, power law scheme, second-order upwind scheme, and central differencing scheme, are available with both implicit and explicit time integration techniques for temporal terms of the equations. The simulation boundary conditions could be defined using the options available with the solver, or users can define them through customized functions. Most of the standard boundary conditions, such as the velocity and pressure inlet boundaries, outflows, periodic conditions, and solid wall conditions, are available with the standard package.

A large database of fluid and solid properties is also provided with the solver to model the presence of fluids, solids, and mixtures. Special boundary conditions and numerical treatment needed for swirling and rotating flows and flows with nonstationary reference frames can be input as user options in the solver.

Previously, a separate grid generator and preprocessor called GAMBIT Version 2.42 was used for preprocessing activities. These activities include development of the geometry and grid generation. The GAMBIT preprocessor was also used to define boundary conditions and different fluid and solid materials and export the mesh for use in FLUENT simulations. Currently, the ANSYS Workbench has the CAD package DM and ANSYS-Meshing for building geometry and creating grids. Additionally, a postprocessor called CFD-POST is available for visualization of simulated results.

The validation study documented in this report for FLUENT covers the technical areas where the software has been applied to GED activities. Validation is done through the method of regression, where the case and data files from the previous versions are used to verify whether the new version is producing results within the acceptable limit. This validation report supersedes the previous versions.

The code was employed to perform a number of tasks involving thermal analysis of engineered and natural systems in potential high-level waste repository drifts at 2

GAMBIT Version 2.4 will be referred to as GAMBIT in this document..

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Yucca Mountain and to support other experimental and analytical work that the Center for Nuclear Waste Regulatory Analyses (CNWRA) performs. These tasks include Perform supporting calculation and independent verification of existing simulations of in-drift thermal environment, air flow, and moisture transport caused by the dissipation of decay heat from the radioactive waste and availability of liquid water in the drift wall Numerically simulate magma-waste package interaction in the event of a volcanic eruption in potential high-level waste repository drifts at Yucca Mountain Simulate the high speed viscous flow and heat transfer processes during magma ascent and propagation through dikes Develop and perform detailed erosion corrosion simulation of nuclear power plant components Perform high speed water flow simulations through dams and spillways and subsequently use the cavitation model of FLUENT to study spillway damage Perform flow analysis in the near-borehole area through fractured porous rocks for feedback to structural analysis Support calculation related to aerosol migration through the atmosphere in the near-coastal region Validate and verify the VSC-17 thermal model against experimental data Apply the thermal model to a proof-of-concept canister for storage, transportation, and transfer canisters Perform thermal hydraulic simulation of nuclear power reactor components In addition, FLUENT could be used as a tool to support and supplement other experimental and analytical work that involves fluid flow and heat transfer.

1.1 Scope of Validation As mentioned previously, the method of regression will be used to perform the validation exercise. validation simulations will focus on the following areas only.

Natural and forced convection

High speed flows

Radiation heat transfer

Multiphase flows and species transport These four categories cover the broad technical area where CNWRA intends to use the code. If needed, other physical models available in FLUENT will be validated based on the problem requirements. Users are advised to perform relevant tests pertinent to their specific needs when applying FLUENT to technical areas that are not validated here.

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The validation test cases are summarized in the following subsections. The input and output files for each validation test case are included in the attached electronic media.

1.2 Natural and Forced Convection The natural and forced convection simulation capabilities of FLUENT are validated through four test cases that are described in Chapter 6. The first two test cases relate to free or natural convection, and the subsequent two test cases are associated with forced convection and heat transfer. The four test cases are summarized next.

Natural convection between two concentric cylinders: Kuehn and Goldstein (1978, 1976) performed a series of experiments to investigate the thermal behavior of a gas in an annulus between concentric circular cylinders. The experimental results from this study will be used to validate FLUENT for both laminar and turbulent natural convection simulations as required by the potential use of the software.

Natural convection along a vertical flat plate: Analytical solution of transport equations for natural convection flow over a vertical, flat, heated plate is well documented (Incropera and Dewitt, 1996). A test case is set up to replicate the problem, and the computed results are compared with the analytical solution.

Flow over back-facing step: This test case is used to validate FLUENT for forced convection flows. The test case is modeled after the Driver and Seegmiller (1985) experimental investigation that studied incompressible turbulent flow over a rearward-facing step in a diverging channel flow. The measured and computed skin friction and pressure coefficients are matched as a part of the validation exercise.

Flow and heat transfer over an expansion pipe: The experiment Baughn, et al.

(1984) conducted to measure the local heat transfer coefficient downstream of an abrupt expansion in a circular channel is used as a benchmark to validate the capability of FLUENT in simulating forced convection flows. Computed Nusselt number distribution along the channel wall is compared with experimental data.

The forced convection test cases described in this section are relevant to the erosion corrosion studies that are being performed at GED. The natural convection studies are relevant to storage and disposal of spent nuclear fuel. The ventilation airflow around storage canisters usually creates a transitional or turbulent natural convection flow, whereas the backfill gas inside the canister may have natural convection. These test cases are also relevant to in-drift flow, moisture, and heat transfer processes. During the preclosure period, forced convection conditions are experienced due to active ventilation. In the postclosure period, in the absence of any active ventilation, the flow field is perturbed by the heated waste package and a natural convection flow starts in presence of gravitational force.

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1.3 High Speed Flows The test cases described in Chapter 7 validate the FLUENT code for application in high speed flows. Two test cases are considered in the validation exercise of high speed flows.

Flow over wedge: The analytical solution for supersonic flow over a wedge can be obtained from the theory of inviscid flows and oblique shocks as Anderson (1984) documented. The high speed supersonic flow contacts the leading edge of the ramp and generates an oblique shock, where the flow properties exhibit a sharp discontinuity.

A hypothetical test case is built to simulate the supersonic flow over a 15° wedge, and the results are compared with the analytical solution.

A detailed experimental study of the compressible turbulent mixing layer by Goebel and Dutton (1991) is used to validate the solver capability in computing compressible flows. Two fluid streams with different velocities are injected inside a rectangular chamber, where the turbulent mixing process takes place. The experimental investigation measured the turbulent kinetic energy and axial velocity profiles that are compared with simulated results.

The test cases described in this section will be relevant in modeling fragmented magma flow in the dike and drift in a potential volcanic eruption at the potential high-level waste repository drifts at Yucca Mountain. Fragmented magma flow inside the drift is generally considered as a compressible fluid and characterized by the presence of shocks, viscous interactions, and turbulence. Magmatic ascent of fluid through the dike could also be modeled as internal compressible flow. In addition, the water flow through the spillways and overflowing dams will use some of the FLUENT simulation techniques.

1.4 Radiation Heat Transfer Two simple test cases are considered to validate the radiation models of FLUENT in Chapter 8. FLUENT has a number of models to simulate radiation including complex scenarios like scattering, particleradiation interaction, optical media thickness, gray gas, and specular reflection. The test cases for the present validation exercise are restricted to modeling physical features that are relevant to the intended application

[e.g., surface-to-surface (S2S) radiation with nonparticipating media.] The test cases considered for radiation heat transfer follow.

Radiation between two parallel surfaces: One-dimensional analytical solution of radiation heat transfer between two parallel plates is well known (Incropera and Dewitt, 1996; Holman, 2002). This hypothetical test case test assumes no convective air flow in between the surfaces. The computed results are compared with analytical solution of temperature distribution and heat flux.

Radiation between two concentric cylinders: Analytical solution of radiation heat transfer between two concentric cylinders is well documented in open literature (Incropera and Dewitt, 1996; Ozisik, 1977). The fluid inside the annulus is maintained at very low pressure to simulate a vacuum. The computed temperature distribution and heat flux across the annulus will be compared with an analytical solution.

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Radiation will be the dominant mode of heat transfer in dry storage casks due to the high temperature of the spent fuel caused by decay heat. The test cases described here validate the models that will be required to simulate radiation in enclosed surfaces with inert, nonparticipating media as typically encountered in the casks. These test cases are also relevant to the simulation of the in-drift environment during the postclosure period because the radiation heat transfer will contribute significantly to the overall heat transfer rate.

1.5 Multiphase Flows Two test cases to simulate multispecies flows of air-vapor mixtures are considered and described in Chapter 9. The first test case is suitable for modeling evaporation columns where a fixed mass fraction of a species is maintained across boundaries. The second test case deals with forced convection flow of moist air over a cold flat plate resulting in phase change. The test cases are

Diffusion through a mixture column at constant temperature and pressure: A binary gas mixture of water vapor and air fills a rectangular box at a constant temperature and pressure, where water vapor diffuses across the domain in the presence of a concentration gradient. The analytical solution of this hypothetical problem under a steady-state condition is provided in the open literature (Bird, et al.,1960; Incropera and Dewitt, 1996), which is used as a basis for validating FLUENT. The analytical solution for species concentration across the rectangular domain is matched with predicted results.

Condensation of water vapor over a flat plate: Sparrow, et al. (1967) have analytically determined the condensed mass of liquid water formed over a flat plate due to flow of humid air. The validation test case models flow of an air-water vapor mixture at different velocities over a flat plate and simulates the condensation process through suitable source terms in the transport equations.

This test case will also be simulated using a modified user subroutine that models volumetric condensation to achieve equilibrium in the flow domain.

Simulated condensate mass distribution along the floor is compared with analytical solution.

Validation test cases for multiphase flows are highly relevant for simulation of the erosioncorrosion process inside pipelines. In addition, it will be applicable in modeling magma-waste package interaction that involves phase change. Multiphase flows could also be used to model the magma behavior inside the dike and drift during the posteruption period. Validated phase change and species transport simulation techniques are also relevant to the postclosure performance in a repository drift that is characterized by moisture transport, evaporation, and condensation. The in-drift moisture redistribution analysis performed by the U.S. Department of Energy uses the species transport model of FLUENT (Bechtel SAIC Company, LLC, 2004).

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2 ENVIRONMENT 2.1 Software The FLUENT software package was developed in the early 1980s and is the flagship software of Fluent Inc.a company that spun off from the New Hampshire-based research and development firm Creare, Inc. As mentioned in Chapter 1, Fluent Inc. was acquired by ANSYS Inc., which developed an integrated platform to perform a range of engineering analyses.

Since its inception as a general purpose fluid dynamics software, a host of models has been added to the original flow solver that could address a wide range of industrial applications. The flow solver can model combustion, reacting flows, turbomachinery flows, multiphase flows, aeroacoustics, heat transfer, and a number of other flow problems. The physical models available in FLUENT are detailed in the FLUENT Users Guide (ANSYS Inc., 2009a). The Fluent Inc. website (www.fluent.com) also illustrates various examples and test cases of flow modeling applications for industrial problems.

The present validation exercise will be carried out in the LINUX operating systemspecifically on Red Hat Enterprise Linux, Version 5.0. ANSYS Workbench preprocessors, Design Modeler and ANSYS-Meshing, will be used to generate the geometry and meshes used in the validation study. The preprocessor is evoked from LINUX by activating the graphical user interface (GUI) and proper selection of simulation options. The preprocessor and its methods of use are detailed in the ANSYS-Design modeler users guide (ANSYS Inc., 2009c) and ANSYS Meshing Users Guide (ANSYS Inc., 2009d) The main flow solver FLUENT can also be evoked either from the GUI or from a console by typing fluent at the command prompt. The in-build postprocessor for the Workbench is called CFD-Post and can also be evoked from either the Workbench GUI or from the console by typing cfdpost. Details on how to use CFD-Post are available from the CFD-Post Users Guide (ANSYS Inc., 2009e). FLUENT creates two filesnamely, the case and data filesthat store the grid information and flow parameters, respectively. The flow parameters that are being stored in the data file depend on the physical models that are being invoked in the solution and are determined by the software without any specific user input. Computational fluid dynamic simulations often take many hours or even days to complete; hence, users should retain files holding simulation results for future analyses and postprocessing.

The standard version of FLUENT has the option to include customized routines tailored to model-specific applications. The routines are known as user-defined functions that are compiled and dynamically linked to the standard solver. They are written in the C programming language using any standard text editor, and the source code file is saved with a .c extension. One source file can contain a single user-defined function or multiple user-defined functions, or a number of source files could be used to build one user-defined function depending on the complexity of the problem. Licensing constraints are detailed in the license agreement.

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2.2 Hardware FLUENT supports a number of platforms and operating systems that include Windows XP and Windows 2000 as well as different varieties of UNIX, including SOLARIS 9.0 and 10.0, HP-UX 11.23, AIX 5.2, and IRIX 6.5. FLUENT also supports a variety of LINUX operating systems including SuSE and RedHat. It can be used on both 32- and 64-bit architecture. The software is capable of performing parallel processing and uses different techniques to communicate between processors, including the standard MPI. It can use shared memory as well as distributed memory machines for parallel activities. The parallel processing capabilities are available in Windows NT, LINUX, and UNIX platforms.

The present validation study will be conducted in the CNWRA LINUX cluster (Katana).

The cluster has 64-bit processors and presently has 18 computer nodes.

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3 PREREQUISITES Users should be trained to use FLUENT and have experience in fluid mechanics and heat transfer.

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4 ASSUMPTIONS AND CONSTRAINTS FLUENT is currently installed in the cluster Katana and the stand alone machine Niagra.

Because of license requirements, it can only be used on these machines. Usage is restricted by the terms and conditions in the license agreement, which restricts redistribution of the software. The validation studies proposed here could also be used for installation testing of the software.

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5 NATURAL AND FORCED CONVECTION The test cases described in this section validate the FLUENT Version 12.1 code for application in natural and forced convection. The first two test cases relate to free or natural convection and are similar to the validation test cases for the flow solver FLOW-3D documented in Green and Manepally (2006). The final two test cases validate the flow solver for forced convection and heat transfer.

5.1 Natural Convection in an Annulus Between Horizontal Concentric Cylinders A well-reported experiment by Kuehn and Goldstein (1978) is used as a benchmark for validating FLUENT 6.3 for simulating natural convection flows. The experimental study measured temperature and heat flux of a gas in an annulus between concentric and eccentric circular cylinders. For the present validation study, only the concentric configuration is considered. The scientific community has used this experimental study to validate computational fluid dynamics calculations of natural convection flows. The validation simulations use nitrogen as the gas in the annulus to match the experimental conditions. Other physical parameters were chosen to replicate the test conditions that are described in Section 5.1.2.

The experiment facility consisted of two concentric cylinders sealed in a pressure vessel.

The outer diameter of the inner cylinder was 3.56 cm, and the inner diameter of the outer cylinder was 9.25 cm, resulting in an annular gap of 2.845 cm. The cylinders were Figure 5-1. Computational Domain for Kuehn and Goldstein Problem 5-1

20.8 cm in length. The inner cylinder was electrically heated, while the outer cylinder was cooled with a chilled water loop to maintain constant temperature conditions at the walls. The test chamber was filled with nitrogen as the test fluid. The nitrogen pressure was varied between 0.071 atm and 35.2 atm, and the temperature difference between the two cylinders was varied between 0.83 K and 60.1 K. This provided for a Rayleigh number range of 2.2 x 102 to 7.74 x 107. Temperatures in the annulus were measured via Mach-Zender interferometry, and surface temperatures were measured with thermocouples.

5.1.1 Theoretical Basis A hypothetical physical propertyequivalent thermal conductivitywas used to reduce the experimental data. It is the conductivity value that would result in equal heat flux across the annulus if conduction were the only mode of heat transfer. The equivalent thermal conductivity between the inner and outer cylinder was calculated for different test conditions. The equivalent thermal conductivity is defined as D

Q ln o (5-1)

Di K eff 2kT where Q Heat transfer rate at inner cylinder per unit length (W/m)

Do Diameter of the outer cylinder (m)

Di Diameter of the inner cylinder (m) k Thermal conductivity of the gas in the annulus (W/m-K)

T Temperature difference between the inner and outer cylinder (K)

The experimental study calculated the effective thermal conductivity for different test conditions that resulted in different flow patterns. These different test conditions could be expressed in terms of the nondimensional parameter Rayleigh number, which is given by gTL3Pr (5-2)

Ra 2

where Thermal expansion coefficient of gas (1/K)

Kinematic viscosity of the gas in the annulus (m2/s)

Pr Prandtl number of the gas g Acceleration due to gravity (m/s2)

L Characteristic length = 0.5(Do- Di) (m)

Simulation results for the present validation study are conducted under similar conditions and the effective thermal conductivity values are calculated from the simulated results that are compared against the experimental values.

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5.1.2 Test Input FLUENT mesh files are generated to mimic the experimental setup by Kuehn and Goldstein (1978) in a two-dimensional (2D) domain. Two sets of studies are conducted for this validation test case. In the first set of tests, the FLUENT solver is used to simulate three different flow conditions that correspond to three different Rayleigh numbers. The physical parameters used to simulate these three Rayleigh numbers are described in Table 5-1, and the corresponding properties of nitrogen are described in Table 5-2. The input parameters are the same as those in Das and Basu (2008).

A second set of studies was conducted to perform a grid independence test of the results. Three levels of mesh resolution are considered. The grid independence study is conducted for the Rayleigh number of 1.31 x 103, and the physical parameters corresponding to that Rayleigh number are used for all three tests. Table 5-3 provides the details of the mesh used in this study. Input for all the test cases is on the attached media in the directory named K-g-12.1/.

Table 5-1. Selected Experiments for FLUENT Simulations Rayleigh Number P (atm) T (°C) 1/2(Ti + To) (°C) Flow Regime 3

1.31 x 10 0.110 53.5 51.1 Laminar 6

2.51 x 10 34.6 0.91 27.7 Transitional 7

6.60 x 10 35.0 28.7 40.8 Turbulent Table 5-2. Properties of Nitrogen for FLUENT Simulation Conditions Rayleigh Cp k FLUENT Input Number kg/m3 1/K Pa-sec J/(kg-K) W/(m-K) File Name Ra 1.31 x 103 0.1158 3.08 103 1.903 x 105 1,033.37 0.0274 K-G-lam.cas 6 3 5 2.51 x 10 39.40 3.323 10 1.859 x 10 1,041.07 0.02793 K-G-tran.cas 7 3 5 6.60 x 10 38.07 3.185 10 1.916 x 10 1,040.67 0.02874 K-G-turb.cas Table 5-3. Mesh Sizes for Grid Independence Study for FLUENT Total Number Level of FLUENT Input File Rayleigh Number of Nodes Resolution Name 1.31 x 103 120,800 Fine k-g-fine.cas 1.31 x 103 3,700 Medium k-g-medium.cas 1.31 x 103 500 Coarse k-g-coarse.cas 5.1.3 Expected Test Results The acceptance criterion for the simulated equivalent thermal conductivity will be a deviation less than 25 percent of the experimental data.

5.1.4 Test Results For the first set of test cases, the medium grid level is used. Grids were clustered in the near-wall region to capture the boundary layer developed by the natural convection 5-3

currents. The problem was formulated in the 2D domain assuming the third dimension to be of unit length. Wall boundary conditions with constant temperatures are specified for both the inner and outer cylinder walls. For the transitional and turbulent flow test cases, a standard k- turbulence model is used. Standard wall functions were used in the near-wall region. The steady solution is obtained using the SIMPLE scheme for pressure velocity coupling with second-order discretization for the pressure, momentum, energy and turbulence equations. The experimental study reported turbulent eddies and fluctuating velocity for higher Rayleigh numbers, but in the present validation study, high fidelity techniques like Large Eddy Simulation are not used, because these fluctuating eddies will not have any significant impact on the heat transfer process.

The equivalent thermal conductivity is calculated for all three test cases with three different Rayleigh numbers. The results are shown in Table 5-4, which lists the computed Rayleigh numbers, corresponding experimental values, the computed value from FLUENT Version 6.3, and the percentage deviation of values of Version 12.3 with the experimental data as well as with the previous computation.

The equivalent thermal conductivity obtained from the grid independence study is highlighted in Table 5-5. With finer grid resolution, the percentage deviation from the experimental observation decreases, but the medium- and fine-grid solution produces an equivalent solution that is within the acceptable range of deviation from the experimental data. Hence, the medium-grid level was used for computational purposes to obtain computational economy without compromising accuracy.

Table 5-3 shows that all the values of equivalent thermal conductivity are within acceptable limits of deviation from the experimental data. For a Rayleigh number of 2.51 x 106, the flow is in the transitional regime and it was treated as regular turbulent flow without any transition modeling.

The general flow features of the validation case for all three Rayleigh numbers are highlighted in Figure 5-2, which shows that the flow pattern changes with increase in Rayleigh number. It can also be observed that the boundary layer at the inner and outer surface is well captured by FLUENT 6.3 especially for the laminar flow. For the transitional and turbulent flows, the boundary layer is not easily visible, because the plume of upward flow is stronger. This results in higher velocity near the wall. This result shows that the solver was able to reflect the change in physical parameters in the solution and effectively simulate turbulent natural convection.

Table 5-4. Comparison of Measured and Predicted Equivalent Thermal Conductivity for Concentric Cylinders Computed Percent Computed Percent Rayleigh Experimental Value Deviation Value Deviation Number Value (Version (from (Version (from) 12.1) experiment) 6.3) 1.31 x 103 1.14 1.08 5.22 1.1 3.5 6

2.51 x 10 7.88 7.80 0.95 8.02 1.77 7

6.60 x 10 18.65 18.75 0.57 18.88 1.23 5-4

Table 5-5. Comparison of Measured and Predicted Equivalent Thermal for Three Grid Levels Experimental Computed Value Grid Level Percent Deviation Value from Version 12.1 Coarse 1.14 1.20 5.2 Medium 1.14 1.10 3.5 Fine 1.14 1.12 1.7 Ra = 1.31 x 103 Ra = 2.51 x 106 Ra=6.60 x 107 Figure 5-2. Velocity Vectors and Temperature Contours for Different Rayleigh Numbers 5-5

5.2 Natural Convection Along a Vertical Flat Plate Natural convection along a flat, heated, vertical plate is one of the most basic flow configurations to test buoyancy driven convection and is considered as a test case for validation of FLUENT. The analytical solution for this test case is available in lncropera and Dewitt (1996) for laminar boundary layers where the Rayleigh number is less than 106* The analytical solution provides a local Nusselt number along the length of the vertical flat plate. The Nusselt number is a dimensionless temperature gradient at a surface and measures the efficiency of convection for heat transfer relative to conduction. The solution domain is shown in Figure 5 3.

5.2.1 Theoretical Basis The analytical and empirical correlation for the heat transfer coefficient and Nusselt number variation along the vertical flat plate is provided in lncropera and DeWitt (1996).

Ostrach (1953) numerically determined the Prandtl number dependence of the correlation and specific values of the Nusselt number for selected values of Prandtl 0.2 0.15 l*

. i.

Pressure Oullel MOOK

-so.1 0.05

- Pres1ure Inlet

- - T=300 K 0.05 o. t 0.15 0.2 x (m)

Figure 5-3. Computational Domain and Grid for Natural Convection Over Vertical Heated Plate 5-6

numbers. Later, LeFevre (1956) correlated these results by an interpolation formula to provide the Nusselt number in terms of Prandtl number and Grashof number Gr z 0.25 0.75 Pr 0.7 Nu z (5-3) 0.5 0.609 1.221Pr 1.238 Pr 4 where Nu(z) Local Nusselt number Pr Fluid Prandtl number Gr(z) Local Grashof number The Grashof number can be expressed as g z 3 Ts Tf Gr z (5-4) 2 where Thermal expansion coefficient of gas (1/K)

Kinematic viscosity of the gas in the annulus (m2/s)

Ts Wall surface temperature (K)

Tf Fluid temperature (K) g Acceleration due to gravity (m/s2) z Vertical distance 5.2.2 Test Input FLUENT mesh and case files (*.msh and *.cas) are developed to model the vertical flat plate natural convection. The model is developed with an isothermal vertical wall with a temperature of 340 K. The standard properties of air at 300 K available from the FLUENT database are used in the simulation. The case is modeled as a 2D laminar incompressible flow problem with gravity as the body force and the Boussinesq approximation to capture the thermal buoyancy effects. Input and results for the test cases are on the attached media in the directory named natconv-12.1/.

The input parameters for the test case follow.

0.0033 1/K Ts 340 K Tf 300 K Pr 0.7 L 0.2 m 5-7

5.2.3 Expected Test Results For the test result to be acceptable, computed Nusselt number distribution along the wall should be within 10 percent of the analytical solution. In general computation and measurement of Nusselt numbers, there is a higher degree of uncertainty (Incropera and DeWitt, 1996). Hence, matching of a computed Nusselt number within 10 percent could be considered sufficient condition acceptance. In addition, the computed flow field should qualitatively agree with the general understanding of the flow physics expected for natural convection flows along heated walls (Incropera and DeWitt, 1996; Ozisik, 1977).

5.2.4 Test Results The test performed is analogous to that used to validate FLUENT Version 6.3 (Das and Basu 2008). The grid generated in the previous study was adopted in Version 12.1.

The analytical values of the Nusselt number along the vertical plate were computed using the custom field functions option available in FLUENT so that a comparative study could be done. The postprocessing of the solution was done using the visualization software Tecplot-360. The analytical solution and computed solution for the Nusselt number was exported from FLUENT and postprocessed in Tecplot-360.

The validation test case described previously was solved using FLUENT as a 2D steady laminar flow problem. The heat transfer module of the FLUENT solver was enabled.

The operating pressure of the domain was the specified 10132.5 Pa used elsewhere. At the heated wall, an isothermal boundary condition was used. At the bottom and top of the domain, a pressure inlet and outlet condition were specified. A symmetry boundary condition was imposed on the right end of the domain. Both the flow and energy equations were solved using the SIMPLE algorithm for pressure-velocity coupling. The PRESTO! Scheme was used to discretize the pressure equations, and the momentum as well as the energy equations used a second order upwind scheme for spatial discretization. Boussinesq approximation was used for density evaluation. The Boussinesq approximation neglects the effect of fluid-density dependence on pressure of the air phase, but includes the density dependence on temperature. It enables the flow to be treated as incompressible flow but still accounts for density variation locally in the momentum and energy equations. As the Rayleigh number of the flow will be less than the critical value, no turbulence models were used in the solution.

Figure 5-4 (a) shows the flow field simulated by the solver. The boundary layer profile and the velocity vectors are similar to those obtained from the previous validation study.

The section AA shown in the figure is the cross section, where the exit velocity and temperature profile will be shown in Figure 5-6. Figure 5-4 shows that the boundary layer generated by the convective flow is well captured. The velocity vectors are shown for every other node for increased clarity. A zoomed section near the exit of the plate is highlighted in Figure 5-4 (b) for a better understanding of the boundary layer development. Both hydrodynamic and thermal boundary layers have developed due to the heated plate. The thermal boundary layer is shown by the colored contours, whereas the hydrodynamic boundary layer is illustrated by velocity vectors. As expected, both hydrodynamic and thermal boundary layer thicknesses increase as the flow moves vertically upward. This is consistent with the analytical solution (Incropera and DeWitt, 1996).

5-8

Figure 5-5 (a,b) compares the analytical Nusselt number along the vertical plate with computed results for Versions 12.1 and 6.3, respectively. The Nusselt number calculations were carried out using the custom field functions in FLUENT. The local Nusselt number increases monotonically for both the computed and analytical solution.

The general trends are in good agreement with each other. The figure also shows two lines depicting the acceptable limits that are imposing the acceptance criteria on the analytical solution. It appears that the results predicted from Version 6.3 are slightly better than the newer version but both the results are within an acceptable limit.

Therefore, the results of this test case are acceptable for software validation.

Figure 5-6 (a,b) shows the variation of the thermal and hydrodynamic boundary layers along the horizontal line A-A shown in Figure 5-5 for Versions 12.1 and 6.3, respectively.

The patterns of these boundary layers are in agreement with those available in open literature (Incropera and DeWitt, 1996). The hydrodynamic boundary layer increases from a value of zero at the wall to a maximum value and then decreases to the free stream value of zero again. The thermal boundary layer has its maxima at the wall and then asymptotically decreases to the free stream value. These results indicate that the computed results satisfy the criteria of overall goodness and established understanding of the physical phenomena. There is a slight difference in results predicted for Version 12.1 as compared to 6.3.

Though the magnitude and velocity pattern matches, there is a slight difference in the velocity pattern. For Version 6.3, the velocity tapers off at the end of the domain, but for Version 12.1, it remains constant. These features, however, will not affect the near-wall region, where the buoyancy-driven flow plays a major role.

(a) (b)

Figure 5-4 (a,b). Velocity Vectors and Temperature Contours (a) of the Domain and (b) Near the Exit 5-9

(a)

(b)

Figure 5-5 (a,b). Comparison of Computed and Analytical Values of Nusselt Number Where the Upper and Lower Limit of Acceptance is Within 10 Percent of Computed Value. (a) Version 12.1 and (b) Version 6.3 (a) (b)

Figure 5-6 (a,b). Velocity and Temperature Distribution at the Plane A-A. (a) Version 12.1 and (b) Version 6.3 5.3 Flow Over Back-Facing Step Driver and Seegmiller (1985) conducted experiments for incompressible turbulent flow over a rearward-facing step in a diverging channel flow. They measured mean velocities, Reynolds stresses, and triple products using a laser Doppler velocimeter.

Skin friction coefficient distribution, pressure coefficient distribution along the floor, eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) terms are extracted from the data. The present validation study is similar to that conducted for Version 6.3, and the skin friction and pressure coefficient 5-10

measurement from the experimental study will be used for FLUENT validation. The computed reattachment point of the flow downstream of the step will also be compared with experimental data.

Figure 5-7 shows the computational domain of the problem that mimics the experimental setup of Driver and Seegmiller (1985). The step height (H) is 0.0127 m and the expansion ratio is 1.125. The inlet computational domain is placed 4H upstream of the step, and the outlet is placed 40H downstream of the step. The upper end of the computational domain is placed at a distance of 9H from the bottom wall. The computational mesh and boundary conditions used in the simulation are also highlighted in Figure 5-7. Grid points are clustered at locations where a steep gradient of flow quantities is expected and in the near-wall region to capture the boundary layer. The dimensionless turbulent wall coordinate y+ of 5 was used to obtain good resolution of flow features near the wall. The distance of the inlet plane from the step was not long enough to establish a turbulent boundary layer profile. As a result, approximate profiles of velocity, turbulent kinetic energy, and dissipation rates obtained from analytical solution were specified at the inlet to simulate a developed turbulent boundary layer. A pressure outlet boundary condition was used at the exit, and no-slip adiabatic conditions were specified at the wall boundary.

Figure 5-7. Computational Domain, Grid, and Boundary Conditions for Back-Facing Step 5.3.1 Theoretical Basis Table 5-6 lists the flow parameters that Driver and Seegmiller (1985) used and that were adopted for the present validation study.

Table 5-6. Flow Parameters for Flow Over a Back-Facing Step Parameter Value Centerline velocity 44.2 m/s Kinematic viscosity of air 1.5 x 10-5 m2/s Density of air 1 kg/m3 5-11

Based on these parameters, the Reynolds number based on the step height is 37,400.

As mentioned in the previous section, approximate velocity, turbulent kinetic energy, and dissipation rate profiles were used at the flow inlet. These profiles were derived based on the one-seventh-power law (Schlicting, 1960), which is given by 1/ 7 y (5-5) u U where y Normal distance from the wall (m) u Velocity at y (m/s)

U Free stream velocity (m/s)

Boundary layer thickness (m)

The boundary layer thickness at the lip of the step was assumed to be half of the step height. The distributions of turbulent kinetic energy and dissipation at the inlet were approximated by profiles similar to the results of fully developed channel flow simulations.

Numerical results computed from the simulation were compared with the experimental data of Driver and Seegmiller (1985) for the bottom wall skin friction and static pressure coefficients. The skin friction coefficient is given by w

Cf (5-6) 1 2 U

2 where w Shear stress at wall (Pa)

U Free stream velocity (m/s)

Density of air (kg/m3)

The pressure coefficient is given as Pw Pfs Cp (5-7) 1 U 2 2

where Pw Wall pressure (Pa)

Pfs Free stream pressure (Pa) 5-12

5.3.2 Test Input The input file used for the Version 6.3 validation study is used here. The model development intends to mimic the physical experiment Driver and Seegmiller (1985) conducted, and simulation parameters for the computation are selected to closely match the experimental conditions. The centerline velocity is set at 44.2 m/s, and air at 300 K is used as the working fluid to have a flow Reynolds number of 37,400. This test case is modeled in a 2D domain as turbulent incompressible flow and solved using the pressure-based incompressible Navier-Stokes equations without energy equation.

Turbulence is simulated using a standard k- model with shear flow corrections.

Domain size, grid, and boundary conditions are detailed in Section 5.3. The SIMPLEC algorithm is used for pressure-velocity coupling. Second-order upwind schemes are used for spatial discretization of momentum and turbulent transport equations. Input and results for this test case are on the attached media in the directory named /bfs-12.1/.

5.3.3 Expected Test Results The acceptance criterion for the simulated equivalent thermal conductivity will be a deviation less than 25 percent of the experimental data.

Computed pressure and skin friction coefficient distribution will be compared with experimental observation for overall goodness of fit and visual matching. There should be a visual similarity between the computed and experimental results in terms of general trend, inflection, and curvature. The maximum deviation of the computed result from the experimental data at any point should not exceed 20 percent of the overall range of the parameter.

The location of the computed reattachment point downstream of the step height will also be compared against experimental results. As the flow separates from the step, it creates a circulating eddy and then gets attached to the bottom wall. The predicted reattachment location should be within 20 percent of the experimental observation.

5.3.4 Test Results Figure 5-8 (a,b) shows the x-velocity contours near the vicinity of the back-facing step for Versions 12.1 and 6.3, respectively. For both the test runs, a vortex forms as the flow separates just downstream of the step. The flow subsequently reattaches to the wall after a certain distance away from the step. The figure shows that FLUENT was able to qualitatively capture the basic flow features described in the experimental work of Driver and Seegmiller (1985). The quantitative comparisons will be made later in this chapter.

The figure also highlights the formation of boundary layers characterized by lower velocities in the lower and upper wall of the domain.

Likewise, Figure 5-9 (a,b) shows the distribution of turbulent kinetic energy around the step for Versions 12.1 and 6.3, respectively. As can be seen, the kinetic energy patterns are very similar and both follow the pattern observed in the experiment. There are some minor differences in pattern at the end of flow domain between the simulated cases that can be attributed to localized truncation error effect.

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(a)

(b)

Figure 5-8 (a,b). Velocity Near the Vicinity of the Back-Facing Step. (a) Version 12.1 and (b) Version 6.3 (a)

(b)

Figure 5-9 (a,b). Turbulent Kinetic Energy Near the Vicinity of the Back-Facing Step. (a) Version 12.1 and (b) Version 6.3 Figure 5-10 (a,b) compares the computed skin friction coefficient values with the experimental data along the floor downstream of the step for Versions 12.1 and 6.3, respectively. Both the computed and experimental data exhibit similar patterns and show almost identical trends. For both experimental values and computed data, the skin friction coefficient rapidly decreases just downstream of the cavity and subsequently increases before it asymptotically converges to a constant value. The maximum deviation of the computed results is within 6 percent of the experimental data and lies within the acceptable limit of the test condition of 20 percent deviation.

Figure 5-11 (a and b) shows the comparison of pressure coefficient values between the experimental and computed data for Versions 12.1 and 6.3, respectively. Like Figure 5-10 (a and b), a general qualitative agreement between the experimental and computed data can be seen because the data follow the same pattern and curvature for both cases. The two versions of FLUENT also provide nearly identical results. The maximum deviation of the computed results from the experimental observation is within 12 percentwithin the acceptable limit of deviation.

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As indicated in Figures 5-10 and 5-11, the computed and experimental reattachment points are approximately determined from the results. The reattachment points are defined at locations where the pressure coefficient or skin friction coefficients recover from abrupt change and follow a nearly constant value. The simulated reattachment occurred at a 4.07H distance downstream of the step, and the experimental data show the reattachment point at 3.7H. This means that computed results overpredict the location by 10 percent of the experimental value, but this deviation is within acceptable limits of the validation tests. In addition, predicting the reattachment point is difficult using a numerical tool and FLUENT has provided a reasonably good result for the reattachment location.

(b)

(a)

Figure 5-10 (a,b). Comparison of Computed Skin Friction Coefficient With Experimental Data. (a) Version 12.1 and (b) Version 6.3 (a) (b)

Figure 5-11 (a,b). Comparison of Computed Pressure Coefficient With Experimental Data.

(a) Version 12.1 and (b) Version 6.3 5-15

5.4 Flow and Heat Transfer Over Expansion Pipe The test case of flow and heat transfer over an expansion pipe is selected to validate the capability of FLUENT. The test case numerically replicates the experiment Baughn, et al. (1984) conducted that provides a good benchmark to validate forced convection and heat transfer. The experimental study measured the local heat transfer coefficient downstream of an abrupt expansion in a symmetric, circular channel with a constant heat flux applied to the wall.

A constant heat flux of 0.3 W/m3 was imposed on the pipe wall for the expanded larger pipe, whereas an adiabatic boundary condition with zero heat flux was used as the pipe boundary for the smaller pipe.

The computational domain of the validation test case is shown in Figure 5-12. The domain geometry, flow, and boundary conditions are selected to accurately replicate the experimental setup and test conditions. The 2D solution domain covers only half of the pipe, taking advantage of the symmetry. The inlet is placed 1 m upstream of the expansion step, which is shown as H in the figure. The expansion ratio d/D of 0.4 with an entry diameter of d = 1.33 m is used. The downstream boundary is placed at a distance of 40H from the step. Grids are clustered near the wall and the step to capture the steep gradient of flow quantities in these regions. Suitable profiles of velocity and turbulent quantities were specified at a velocity inlet. At the exit, a pressure outlet was specified.

Figure 5-12. Computational Domain Grid and Boundary Conditions for Flow and Heat Transfer Over Expanded Pipe 5-16

5.4.1 Theoretical Basis The heat transfer coefficient obtained from the Baughn, et al. (1984) experiment is presented in terms of Nusselt number ratios along the heated wall of the larger pipe.

The Nusselt number for internal flows is calculated based on bulk temperatures. The relevant quantities required to calculate bulk temperature and Nusselt numbers are described here.

The bulk temperature is given by q x 4 x TB x 273 (5-8)

Re c p where q x Local heat flux (W/m2)

Re Flow Reynolds number cp Fluid-specific heat (J/kg-K) x Distance (m)

The local Nusselt number is given as q x D Nu x (5-9)

Twall x TB x k where Twall(x) Local wall temperature (K)

K Fluid thermal conductivity (J/m-K)

The experimental results are provided in terms of the ratio of the local Nusselt number and the Dittus-Boelter correlated Nusselt number (Todreas and Kazimi, 1990). The Dittus-Boelter correlation is given by Nu DB 0.023 Re 0.8 Pr 0.4 (5-10) where Pr Flow Prandtl number = 0.7 for the present simulations 5.4.2 Test Input The proposed test is one of the standard documented validation studies of FLUENT (Fluent Inc., 2007a,c). The grid and case file available from the validation repository are used for the study (Fluent Inc., 2007b). Test input parameters are selected to match the simulation conditions with experimental setup and conditions. The grid, domain, and 5-17

boundary conditions related to the test case were already discussed in Section 5.4. The problem was modeled in an axisymmetric domain, and the incompressible Navier-Stokes equations are solved in conjunction with the energy equations. A standard k- turbulence model with standard wall functions is used to simulate turbulence. Air properties used in the simulation are obtained from the FLUENT database. The SIMPLE algorithm is used to couple pressure and velocity. For spatial discretization, a second-order upwind scheme is used for the momentum and turbulence equations. At the inlet, profiles of fully developed axial and radial velocities as well as profiles for turbulent kinetic energy and dissipation are used. Input and results for the test cases are on the attached media in the directory named /exp-pipe-12.1/.

5.4.3 Expected Test Results The computed Nusselt number ratio (Nu/NuDB) will be compared with the experimental data Baughn, et al. (1984) provided. The predicted distribution will be compared with experimental observations for overall goodness of fit and visual matching. There should be a visual similarity between the computed and experimental results in terms of general trend, inflection, and curvature. The maximum deviation of the computed result from the experimental data at any point should not exceed 20 percent of the overall range of the parameter. The general features of the flow field should also be in qualitative agreement with the current understanding of internal flows and expansion pipes.

5.4.4 Test Results For this specific study, simulated results using FLUENT Version 12.1 are presented.

Figure 5-13 shows the velocity, temperature, and turbulent kinetic energy distribution of the flow field. There is a separation region in the velocity field immediately after the constriction. The temperature distribution shows elevated temperature in the near-wall region. The turbulent kinetic energy shows the mixing pattern that follows the sudden expansion. These behaviors are in qualitative agreement with the experimental observation (Baughn, et al., 1984) and are almost identical to the calculated turbulent kinetic energy contours obtained using FLUENT Version 6.3.

Figure 5-14 shows the comparison of experimental Nu/NuDB to the computed solutions along the heated wall. The computed and experimental data exhibit similar patterns and trends. The distribution increases steadily to reach a peak value 10 m from the step and then decreases asymptotically. In general, the computed results overpredict the Nusselt number. However, the maximum deviation from the experimental data does not exceed 6.9 percent, which is within acceptable range as stated in Section 5.4.4.

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Figure 5-13. Velocity, Temperature, and Turbulent Kinetic Energy in the Flow Field Using Version 12.1 Figure 5-14. Comparison of Experimental and Computed Nu/NuDB Along the Heated Wall 5-19

6 HIGH SPEED FLOWS The test cases described in this section validate the FLUENT code for application in high speed flows. Unlike the tests related to heat transfer and multiphase flows, all the test cases for high speed flows use the density-based solver of FLUENT, which is meant for simulating compressible flows.

6.1 Flow Over Wedge An analytical solution of supersonic flow over a wedge provides a method to validate the accuracy of FLUENT for high speed compressible flows. The test assumes an isentropic flow of ideal compressible gas.

The flow physics of the test case are shown in Figure 6-1. The high speed supersonic flow contacts the leading edge of the ramp and generates an oblique shock at an angle as shown in the schematic.

The flow properties and parameters across the shock exhibit a sharp discontinuity. The flow features and analytical treatment are detailed in Anderson (1984). The present validation study will focus on validating the capability of FLUENT in predicting the general compressible flow features and capturing the flow properties across the shock.

Figure 6-2 shows the domain, grid, and boundary conditions of the test case for Version 12.1 that are identical to those used in validating FLUENT Version 6.3. The wedge angle for the test geometry is 15°, with an inlet Mach number of 2.45. These conditions will produce an oblique shock at an angle of 38° and an exit Mach number of 1.8. At the inlet, the total and static pressure are specified and produce a Mach 2.45 stream. At the outlet, pressure outlet conditions are specified. The present test case considered inviscid flow because the objective was to assess the capability of FLUENT in capturing characteristic features of high speed flow like shock and discontinuity across the shock. Intricate details of compressible boundary layer development and shock boundary-layer interaction were not considered in the study. Hence, at the bottom wall, Figure 6-1. Features of Supersonic Flows Over Wedge 6-1

Figure 6-2. Domain, Grid, and Boundary Conditions for Flow Over Wedge slip boundary conditions are specified. A symmetry boundary condition is imposed at the upper plane of the domain. Uniform grid spacing is used throughout the computational domain, and unlike the previous test cases, grids were not clustered in the vicinity of the wall, because there will be no velocity gradient without viscous forces.

The grid and flow conditions used in the present validation test are obtained from a similar study using the NPARC-WIND flow solver (Bush, et al., 1998; Georgiadis, et al., 2006).

6.1.1 Theoretical Basis The analytical solution for the present validation case is documented in open literature (Anderson, 1984). The principal flow quantities of interest are the ratio of the Mach number and other flow parameters such as density and temperature across the shock.

The Mach number ratio across the shock is given by M2 sin (6-1)

M 1 sin 6-2

where M1 Inlet Mach number M2 Mach number after the shock Shock angle Wedge angle The shock angle is computed from the following relationship M 2 sin 2 1 tan 2 cot 2 1 (6-2)

M 1 cos 2 2 where Ratio of specific heat = 1.4 The dependent quantity has a transcendental relationship with the independent variable , and cannot be determined using a direct algebraic relationship. As a result, Eq. (6-2) must be solved using a numerical technique to obtain the value of shock angle .

The density ratio across the shock is given by 2

1M12 sin 2 (6-3) 1 1M 12 sin 2 2 where 1 Inlet density 2 Density after shock The ratio of other quantities like static temperature and pressure can be derived from Eqs. (6-1) through (6-3) and the ideal gas law for air.

6.1.2 Test Input A hypothetical test case is constructed to replicate the flow problem shown in Figure 6-1.

The grid, domain, and boundary conditions related to the test case were already discussed in Section 6.1. The problem is modeled in a 2D domain, and the density-averaged implicit compressible Navier-Stokes equations are solved in conjunction with the energy equations. The Green-Gauss cell-based gradient option is used in the solution. The convective flux terms are solved using a Roe scheme. A second order upwind scheme is used for spatial discretization. As mentioned previously, air was 6-3

treated as inviscid flow in the solution. Air properties used in the simulation are obtained from the FLUENT database. Input and results for the test case are on the attached media in the directory called /wedge-12-1/.

6.1.3 Expected Test Results To acceptably simulate high speed flows, the flow solver should predict a flow field that is in qualitative agreement with the theoretical understanding of supersonic flow in ramps (Anderson, 1984). The computed flow field data should be able to capture the shock, and the computed shock angle should be within 10 percent of the value of analytical value. Mach number ratio across the shock will be compared against the analytical solution, and the computed values should lie within 20 percent of the analytical solution.

Similarly, the predicted density ratio across the shock is expected to lie within 20 percent of the analytical value. The acceptance criteria are identical to those used in validating Version 6.3.

6.1.4 Test Results As observed in any transonic flows, a sharp oblique shock is generated at any sharp corner on the ramp. Figure 6-3 illustrates this feature in the simulated density field of the domain. The flow field is in agreement with the general understanding of supersonic flow over wedges. The fluid density undergoes a sharp change across the shock and does not vary anywhere else, which is in agreement with the existing studies (Anderson, 1984). The shock angle for the computed solution was calculated from the flow field data. The analytical value of the shock angle is 37.56, and the computed value obtained from FLUENT Version 12.1 is approximately 37.50. Hence the deviation between computed and experimental data is approximately 0.156 percent and is well within the acceptable range as outlined in the previous section.

Figure 6-4 shows the pressure contour in the simulated flow field. It is analogous to the density field and creates the same shock angle at the ramp. The numerical value of this angle is 37.50, whereas the analytical value is 37.56. The percentage difference is below 0.2 percent and lies within the acceptable limit.

Figure 6-3. Simulated Density Field Using FLUENT Version 12.1 6-4

Figure 6-4. Simulated Pressure Field Using FLUENT Version 12.1 Figure 6-5 (a,b) shows the comparison of Mach number and density ratio (2/ 1) with analytical solution along the floor of the computational domain. These results are almost identical to those obtained using Version 6.3. Both these flow quantities encounter a sudden change across the shock. The simulated results match reasonably well with the analytical data. For the Mach number distribution, the maximum deviation of the computed result is well within 2.7 percent of the analytical solution. For the density distribution, the deviation between the analytical and computed solution is within 1.6 percent. Therefore, the computed results are in agreement with the analytical solution within the acceptable limits.

(a) (b)

Figure 6-5 (a,b). Comparison of Analytical and Computed Solutions Along the Floor. (a) Mach Number and (b) Density Ratio 6-5

6.2. Turbulent Mixing Layer of Compressible Flow Goebel and Dutton (1991) performed a detailed experimental study of the turbulent mixing layer, which is used as a validation benchmark for FLUENT for modeling viscous compressible turbulent flows. It is one of the tests documented in the validation archive of FLUENT (Fluent Inc., 2007a) and was also used to validate Version 6.3. The experimental investigation measured the turbulent kinetic energy and axial velocity profiles that are used to compare the simulated results in the present test case. In this test case, two fluid streams with different velocities are injected inside a rectangular channel. Due to the velocity gradient, a turbulent mixing process will start and continue as the flows travel downstream.

The computational domain and grid, along with boundary conditions, are shown in Figure 6-6. The length of the computational domain is chosen such that the local Reynolds number at the exit of the test section, based on the velocity difference between the streams and the mixing layer thickness, is greater than 10,000, which is needed for the complete development of the mixing layer. This is because the experimental study found that the development of the mixing layers required a Reynolds number (based on the free stream velocity difference and local mixing-layer thickness) on the order of 1 H 105. Pressure inlet boundary conditions were separately specified for each incoming fluid. The inlet Mach numbers for the two fluid streams are 2.35 and 0.38. At the outlet, the gauge pressures are specified. Symmetry boundary conditions are used in the upper and lower wall, as resolving the near-wall flow field is not as important as resolving the mixing layer for this test.

6.2.1 Theoretical Basis Goebel and Dutton (1991) investigated the compressible turbulent mixing layer by pressure measurements, Schlieren photographs, and velocity measurements with a two-component laser Doppler velocimeter system. They examined seven cross-sectional areas along the domain and found that in the fully developed regions of the mixing layers, transverse turbulence intensities and normalized kinematic Reynolds Figure 6-6. Computational Domain, Grid, and Boundary Conditions for Compressible Mixing Layer 6-6

stresses decrease with increasing relative Mach number. On the other hand, the streamwise turbulence intensities and kinematic Reynolds stress correlation coefficients remained relatively constant. The relative Mach numbers were computed based on the relative velocity between the two mixing streams.

6.2.2 Test Input Mesh files available from the FLUENT validation repository are used for this study (Fluent Inc., 2007b). Inputs files that were used for validating FLUENT Version 6.3 are also used for the present study. Test input parameters in the case file (*.cas) were generated to match the simulation conditions with the experimental setup and conditions as Goebel and Dutton (1991) described. The grid, domain, and boundary conditions related to the test case were already discussed in Section 6.2. The problem is modeled in a 2D domain, and the density-averaged compressible Navier-Stokes equations are solved in conjunction with the energy equations. Turbulence is simulated using a standard k- turbulence model with standard wall functions. The convective flux terms are solved using a Roe scheme. A second-order upwind scheme is used for spatial discretization for the momentum and turbulence transport equations. Air properties used in the simulation are obtained from the FLUENT database. Input and results for the test case are on the attached media in the directory called /mixing-12.1/.

6.2.3 Expected Test Results The computed turbulent kinetic energy and axial distribution 100 mm from the inlet will be compared with experimental data of Goebel and Dutton (1991). The predicted distribution will be compared with experimental observation for overall goodness of fit and a qualitative match. There should be a visual similarity between the computed and experimental results in terms of general trend, inflection, and curvature. The maximum deviation of the computed result from the experimental data at any point should not exceed 25 percent of the overall range of the parameter. The general features of the flow field should also be in qualitative agreement with the current understanding of mixing layer. The contours of turbulent kinetic energy and axial velocity should be able to qualitatively predict the mixing zone.

6.2.4 Test Results Some marked differences were noticed when trying to use the FLUENT Version 6.3 files to validate the FLUENT Version 12.1 software. The original input file used multigrid technique to achieve faster convergence, with a Courant number of 3. The new version, however, diverged with that setup. As an alternative, a multigrid initialization with a low initial Courant number was specified that was gradually increased as the solution converged. From this exercise, it can be concluded that the convergence criteria for high speed flows are different for Versions 12.1 and 6.3.

Figure 6-7 shows the axial velocity in the computational domain; the mixing layer thickness gradually increases as the flow moves downstream. This is in agreement with the established understanding of mixing layer physics through various experimental and computational studies of mixing layers in splitter plates, exhaust nozzles, and cavities.

6-7

Figure 6-7. Velocity Distribution in the Mixing Layer The figure also shows that the mixing layer achieves a developed stage near the end of the domain where the Reynolds number based on relative velocity is about 105.

Previous studies have indicated that the flow inside the mixing layer is usually unsteady in nature, but the present validation study employs the steady version of the Navier-Stokes solver as it is only necessary to obtain average flow field variables for comparison.

The turbulent kinetic energy distribution for the domain is shown in Figure 6-9. It highlights the same trend observed in Figure 6-7. The results are very similar to those obtained using Version 6.3. The mixing layer grows along the downstream direction, and the maximum value of turbulent kinetic energy is along the centerline of the flow where the velocity gradient is also maximum. Figures 6-7 and 6-8 highlight the fact that the flow solver captured the basic physical phenomena of fluid mixing.

Figure 6-9 shows the comparison of experimental turbulent kinetic energy to the computed solutions 100 mm from the inlet across the solution domain. The computed and experimental data exhibit similar patterns and trends. The distribution increases steadily to reach a peak value along the centerline of the domain and then decreases to its initial value. In general, the computed results underpredict the turbulent kinetic energy. The deviation is maximum near the centerline of the domain.

The predicted results show a vertical shift in comparison to the experimental data. As a result, the peak turbulent kinetic energy is predicted at a different height. This causes a higher deviation of computed values from experimental observation on the bottom half of the domain where the slope of kinetic energy is high. The deviation can be better Figure 6-8. Turbulent Kinetic Energy Distribution in the Mixing Layer 6-8

estimated if the experimental data are compared with computed data at an equivalent location on the predicted turbulent kinetic energy curve.

Figure 6-10 compares experimental and computed axial velocity profiles at the same location. The profile shows that the simulation well captured the velocity gradient across the two fluids.

Figure 6-9. Comparison of Computed and Experimental Turbulent Kinetic Energy at = 100 mm Figure 6-10. Comparison of Computed and Experimental Axial Velocity at x = 100 mm 6-9

The experimental and computed results show a good agreement in terms of trend, curvature, inflection, and overall goodness of fit. The maximum deviation occurs near the bottom of the domain because in the simulations, the effect of the bottom and top wall was neglectedas the main focus was to capture the mixing zone. The effect is greater on the bottom wall because, due to the lower velocity of the flow, the boundary layer is thicker compared to the upper wall. However, the deviation of the computed result is not more than 6 percent of the experimental data, which is within the range of deviation as per the validation requirement described in Section 7.2.3.

6-10

7 RADIATION HEAT TRANSFER In this section, two test cases are presented for validation using the FLUENT code to model radiation heat transfer. These validation tests will only focus on surface radiation through nonparticipating, transparent, homogenous media. The convective flow between the surfaces was neglected. Radiation configuration factors or the view factors were calculated using the FLUENT solver and were not supplied externally.

7.1 Radiation Between Two Parallel Surfaces A one-dimensional analytical solution of radiation heat transfer between two parallel plates provides a method to validate the accuracy of FLUENT for modeling the radiation process. To establish radiation heat transfer as the dominant mode of energy exchange between the two surfaces, this test assumes no convective flow in the gap. However, conduction heat transfer through the air gap will take place but will have a minor contribution to overall heat transfer rate.

Figure 7-1 shows the schematic of the problem. It is modeled as a rectangle with a length-to-gap aspect ratio of 5 to minimize the edge effect near the midspan. The gap thickness between the upper and lower surfaces is 0.5 m. Sidewalls are excluded from the radiation process. The hot upper surface is maintained at a temperature of 400 K, and the cold lower surface has a constant wall temperature of 300 K. All the walls are treated as isothermal surfaces, and internal conduction heat transfer through these surfaces was not considered in the test.

Figure 7-1. Schematic of Radiation Heat Transfer Between Parallel Surfaces 7-1

7.1.1 Theoretical Basis The analytical solution for the present validation case is detailed in Incropera and DeWitt (1984).

Thermal flux between two parallel plates due to radiation is given by q

Th4 Tc4 (7-1) 1 1 1

h c where Th Temperature of hot lower surface = 400 K Tc Temperature of cold upper surface = 300 K h Surface emissivity of hot lower surface = 0.9 c Surface emissivity of cold upper surface = 0.9 Stefan Boltzmann constant = 5.67 x 10-8 W-m-2-k-4 In the absence of any convective flow, the fluid in the gap will act as a solid medium.

The temperature distribution in the gap is given by T Tc T ( x ) Tc x h (7-2) t where t Gap thickness = 0.5 m x Distance along the gap (m)

In terms of dimensionless temperature and distance, Eq. (7-2) reduces to the form T

x* (7-3) where T ( x ) Tc T* Dimensionless temperature =

Th Tc x

x* Dimensionless distance =

t 7.1.2 Test Input The test input for the present study uses the case file generated for Version 6.3. The solution domain shown in Figure 7-1 is meshed with a uniform grid without any clustering 7-2

because no steep gradient is expected due to the absence of any convective flow. The hot upper surface and the cold lower surface are included in the radiation heat transfer, and the sidewalls are excluded from the process. The gap between the plates is filled with air, but the flow equations are not solved and the media is treated as a stationary object. Most of the test is identical to that done for FLUENT Version 6.3, but here the discrete ordinate (DO) model is used instead of the S2S radiation model. In the DO model the radiative transport equation is solved for the absopting, emitting and scattering medium for a number of solid angles. Input and results for the test case and research are on the attached media in the directory called /radflat-12.1/.

7.1.3 Expected Test Results For acceptance, the computed flow field data should be able to predict the temperature distribution across the gap so that it lies within 10 percent of the overall range of the analytical solution. The net radiation heat exchanged between the surfaces should also be within 10 percent of the analytical value.

7.1.4 Test Results Figure 7-2 shows the temperature variation across the gap near the center of the computational domain. The temperature decreases steadily and uniformly from the hot upper wall to cold lower wall. This pattern of temperature distribution indicates that there is no convective flow in the gap and the material inside the gap effectively behaved as a solid body. This is in agreement with the intended modeling approach for the present problem where the convective flow is disregarded, as the objective is to establish radiation as the only mode of heat transfer. The temperature pattern is also almost identical to that obtained using FLUENT.

The analytical and computed data for temperature distribution along the central line are shown in Figure 7-3 for a line across the center of gap. The figure also shows two dotted lines indicating the acceptable range of variation for the computed data. The computed and analytical solution almost overlap each other, and the computed results are well within the acceptable range.

Figure 7-2. Temperature Contours Across the Gap Using DO Model in FLUENT Version 12.1 7-3

Figure 7-3. Comparison of Analytical and Computed Solution of Temperature Across the Gap Along with the Acceptance Limit of +/-10 Percent Using DO Model for FLUENT Version 12.1 The overall heat flux values the simulation predicts are compared to the analytical solution obtained from Eq. (7-2). The computed heat flux is 859.7 watts compared to the 811.84 watts obtained from the analytical solution. Therefore the deviation is around 6 percent, which is within the acceptable range of variation as per the validation requirement indicated in Section 7.1.3.

7.2 Radiation Between Two Concentric Cylinders A one-dimensional analytical solution of radiation heat transfer between two concentric cylinders is used to validate the capability of FLUENT to model radiation heat transfer.

The annulus between the concentric cylinders contains fluid at very low pressure, and the effect of gravity is neglected. This is done to maintain the radiation heat transfer process as the dominant mode of energy exchange between the outer and the inner walls and maintain a static medium in the annulus.

Figure 7-4 shows the schematic of the problem, which is similar to the validation test case described in Section 5-1. The geometric configuration of the domain shown in Figure 7-4 is identical to that of the validation case in Section 5-1, but the present test case does not have any fluid in the annulus between the concentric cylinders and the effect of gravity is neglected. This is done to maintain the radiation heat transfer process as the dominant mode of energy exchange between the outer and the inner walls and maintain a static medium in the annulus. The inner cylinder is at an elevated temperature of 700 K, and the outer cylinder is maintained at a constant temperature of 200 K. No internal heat generation was considered. Both the inner and outer cylinders participated in the radiation heat transfer process unlike the previous validation case, where the two sidewalls were not included in radiation heat transfer. Specifying a vacuum in the annulus ensured a transparent and nonparticipating medium in the annulus.

7-4

Figure 7-4. Schematic of Radiation Heat Transfer Between Concentric Cylinders 7.2.1 Theoretical Basis The analytical solution for the present validation case is detailed in Incropera and DeWitt (1996).

Thermal flux between two concentric cylinders due to radiation is given by q

Ti 4 To4 (7-4) 1 1 o ri i o ro where To Temperature of outer cylinder surface = 300 K Ti Temperature of cold upper surface = 700 K o Surface emissivity of outer surface = 0.7 i Surface emissivity of cold upper surface = 0.9 Stefan Boltzmann constant = 5.67 x 10-8 M/m2-K4 ro Radius of outer surface (m) ri Radius of inner surface (m) 7-5

T i To r T (r ) ln To (7-5) r i ro ln ro In the absence of any convective flow, the fluid in the gap will act as a solid medium.

The temperature distribution in the gap is given by r ri ri ln r

o (7-6)

ro ro T

r ln i ro where r Radial location in the annulus In terms of dimensionless temperature and distance, Eq. (7-5) reduces to the form where T ( r ) To T* Dimensionless temperature =

T i T0 r ri r* Dimensionless distance =

ro r i 7.2.2 Test Input The case file generated to validate FLUENT Version 6.3 is used here. Note that the solution domain shown in Figure 7-5 is geometrically identical to the one described in Section 5-1, and as a consequence, the same mesh was used for the radiation study in this section. For the present validation study, the hot inner and cold outer surfaces are specified as isothermal walls at 700 K and 300 K, respectively. To simulate the effect of a vacuum in the annulus, it is simulated as air at extreme low pressure. To bypass the effect of convection and establish radiation as the dominant mode of heat transfer, flow equations are not solved. The surface-to-surface (S2S) radiation model of FLUENT is used. View factors for the geometry are calculated through the solver and are not supplied externally. Input and results for the test case are on the attached media in the directory called /k-g-rad-12.1/.

7.2.3 Expected Test Results For acceptable performance, both the predicted temperature distribution across the gap and the net radiation heat exchanged between the surfaces should be within 10 percent of the overall range of the analytical solution.

7-6

7.2.4 Test Results Figure 7-5 shows the temperature distribution in the gasp. The temperature values decrease constantly in the radial direction. This is expected as there is no other form of heat transfer except radiation and the fluid in the annular space does not participate in either conduction or radiation. This is similar to the observation made in the previous study and is consistent with the analytical finding described in Section 7.2.1.

Figure 7-6 shows the variation of computed temperature across the annulus and compares it with an analytical solution. The figure also shows two dotted lines indicating the acceptable range of variation of the computed data, which are obtained by adding the deviation to the analytical solution. The results are similar to those obtained in the previous study for validating FLUENT Version 6.3. The computed and analytical solutions are in excellent agreement with each other, and the computed results lie within the acceptable range of deviation from the analytical data, indicating that FLUENT Version 12.1 effectively simulated radiation using the S2S method.

The analytical solution of overall heat flux values is obtained from Eq. (7-4) and is compared with the computed value. The computed and analytical heat fluxes are 1065.26 and 1029.83 watts, respectively. This shows that the simulated value deviates only by 3.33 percent from analytical data, which is within the acceptable range of variation as per the validation test plan as discussed in Section 7.2.3.

Figure 7-5. Temperature Contours Annulus Using S2S Model in FLUENT Version 12.1 7-7

Figure 7-6. Comparison of Analytical and Computed Solution of Temperature Across the Annulus Using FLUENT Version 12.1. (Acceptance Limit is Within +/-10 Percent of Analytical Value) 7-8

8 SPECIES TRANSPORT AND MULTIPHASE FLOWS Two test cases to validate the capability of the FLUENT solver in simulating multiphase flows are presented in this chapter. Standard FLUENT has a number of techniques to model multiphase flows using the discrete particle method, Eulerian model, mixture model, and the volume of flow approach. Based on the potential application of the solver, the validation test cases discussed in this chapter focus on non-reacting species transport technique and solve two phase flows.

8.1 Diffusion Through Mixture Column at Constant Pressure and Temperature Analytical solution of diffusion in the binary gas mixture provides a method to validate the accuracy of FLUENT for multispecies flows. The test case assumes constant pressure and temperature throughout the solution domain.

The computational domain and boundary conditions are shown Figure 8-1. A mixture of water vapor and air fills the domain. The mass fractions of water vapor at the left and right wall are fixed at 0.9 and 0.1, respectively. This difference in water vapor mass fraction produces a concentration gradient, and water vapor travels from the left wall toward the right wall due to diffusion. For a steady one-dimensional condition with no chemical reactions, the mass flux or molar flux of water vapor must be constant. As the pressure and temperature at every point of the flow are constant, the molar concentration is also constant and the sum of the mass fraction of air and water vapor at any point should be equal to unity. To maintain this condition, air should also diffuse from the right to the left of the domain. However, a steady-state condition can only be maintained if the leftward diffusion of air is counterbalanced by a rightward bulk motion.

This is to ensure that the absolute flux of air is zero at any location. Hence there will be diffusive mass transfer for both air and water vapor, but a bulk flow from right to left to ensure a zero flux of air at any cross section of the domain.

Figure 8-1. Schematic of Diffusion in Mixture Column 8-1

8.1.1 Theoretical Basis The analytical solution for the present validation case is detailed in Incropera and Dewitt (1996) and in Bird, et al. (1960). The transport equation for water vapor in a one-dimensional domain with bulk mixture flow can be written as dx H 2O NH2O D xH 2O NH2O (8-1) dx where NH2O Mass flux of H2O vapor from left to right of the domain (kg/m2-s)

Total density (kg/m3) x H 2O Mass fraction of H2O vapor D Diffusion coefficient (m2/s) x Distance from left wall (m)

Eq. (8-1) can be rearranged in the form D dx H 2O NH2O (8-2) 1 x H 2O dx Under steady-state conditions dNH2O 0 (8-3) dx So, for steady-state conditions, Eq. (8-2) could be written as d 1 dx H 2O 0 (8-4) dx 1 xH 2O dx The boundary conditions for the validation test case could be given as x = 0; xH 2O = 0.9; x = 0.5; xH 2O = 0.1.

The solution of Eq. (8-4) is given by xH 2O 1 0.19 x / 0 .5 (8-5) 8-2

As the sum of the mass fractions of air and water vapor is unity, the mass fraction variation of air could be given as x air 0.19 (8-6) x / 0 .5 8.1.2 Test Input The mesh and case file used for the validation exercise of Version 6.3 is used here. The mesh file was loaded inside the workbench to impose boundary conditions using ANSYS Meshing. The domain and boundary conditions related to the test case were already discussed in Section 8.1. Uniform grid spacing without any clustering of grids is used to mesh the domain. The problem is modeled in a 2D domain, and the incompressible Navier-Stokes equations are solved without any turbulence models, because the flow is expected to be laminar. Species transport equations with inlet diffusion and a diffusion energy source are solved for the vapor phase. The working fluid is specified as a mixture of water vapor and air, and the fluid density was determined using the volume-weighted mixing law. The input and results file for this test case are on the attached media in the drive /BSL/single-phase. A number of simulations are also done using the multiphase flow subroutine, but this is not discussed in this report. Relevant files are in the directory /BSL/multiphase.

The test case setup used to validate Version 12.1 is slightly different from that used to validate Version 6.3. Previously, a user-defined diffusion coefficient was used to model the one-dimensional mass transfer inside the domain. In the present scenario, the wall boundary condition was modified to account for mass addition or removal from the system due to specification of constant flux boundary condition at the wall.

The existing case uses air and water vapor mixture in a constant pressure and volume chamber to study the diffusion process. It is possible to repeat this exercise with any combination of fluids. The species mass flux at the interface is given as air x air m x air v - D (8-7) n x h2o h o x h o v - D m (8-8) 2 2 n

where x H2O Mass fraction of H2O vapor x air Mass fraction of air n Vector in normal direction m air Mass flux of air m h o Mass flux of water vapor 2

Equations (8-7) and (8-8) are modified to account for source terms in the near-wall region due to the addition of water vapor species at a constant rate. These source terms 8-3

are coded in a user defined subroutine, compiled using the GNU c-compiler, and then hooked into the FLUENT Version 12.1 solver.

8.1.3 Expected Test Results The predicted water vapor mass fraction across the domain will be compared with the analytical solution. The computed variation of mass fraction values of different phases should be within 10 percent of the analytical value.

8.1.4 Test Results Figure 8-2 (a,b) shows the variation of the water vapor mass fraction in the domain using FLUENT Versions 12.1 and 6.3 of FLUENT, respectively. In general, it can be observed that there is a one-dimensional variation of mass fraction with a higher value near the left wall and a lower value at the right wall. Additionally, this variation is not linear in nature, confirming that the computed solution is able to qualitatively capture the species distribution. There is, however, some clear distinction in the species distribution pattern between the solutions. Figure 8-2(a) clearly shows a distorted bulge of the contour lines near the center of the domain, whereas for the Version 6.3 solution, the contour patterns almost follow a regular vertical pattern. This is because the Version 6.3 solution was obtained using the modified diffusion coefficient and any edge or wall effect was eliminated. The theoretical distribution described in Section 9.1.1 does not consider wall effect. The modified diffusion coefficient provided a solution that was closer to the theoretical distribution, but in reality, the diffusion coefficient does not vary across the flow domain. Instead the mass transfer and adjustment process near the wall causes species movement and the wall effect on flow pattern cannot be neglected for a realistic flow situation. The species distribution near the centerline for Version 12.1 was least Figure 8-2. Water Vapor Mass Fraction Variation in the Flow Field Using (a) Version 12.1 and (b) Version 6.3 8-4

influenced by the wall and provides the closest approximation to the theoretical distribution as will be shown in next two figures.

Figure 8-3 (a,b) compares the computed and analytical solutions of the water vapor distribution across the domain from the left wall to the right wall along the centerline for Versions 12.1 and 6.3, respectively. The distance from the left wall is nondimensionalized with respect to the gap length between the right and left walls. The computed values of the mass fraction are in reasonable agreement with the analytical solution. Both the analytical and computed data show similar trends, but the agreement is closer near the walls. At the middle of the computational domain, the simulated results deviate from the computational results, but the maximum deviation is still within acceptable limits. Both Versions 12.1 and 6.3 provide almost identical results, and the edge effects are minimal along the centerline.

Figure 8-4 (a,b) compares the computed and analytical solutions of the air mass fraction distribution across the domain from the left wall to the right wall along the centerline for Versions 12.1 and 6.3, respectively. The results obtained using these two solvers are almost identical and are within the acceptable limits specified in Section 8.1.3.

Based on the comparison between the theoretical distribution and computational values, it can be concluded that the solution lies within acceptable limits and the solver is suitable for simulating species transport problems.

(a) (b)

Figure 8-3 (a,b). Comparison of Analytical and Computed Solution of Mass Fraction of Water Vapor. (a) Version 12.1 and (b) Version 6.3 8-5

(a) (b)

Figure 8-4 (a,b). Comparison of Analytical and Computed Solution of Mass Fraction of Air. (a) Version 12.1 and (b) Version 6.3 8.2 Condensation of Water Vapor Over Flat Plate Sparrow, et al. (1967) provided an analytical solution for condensation of water vapor from humid air over a flat plate. This analytical solution was used as a validation benchmark to assess FLUENTs capability to model moisture transport and condensation including multiphase flow and interphase mass transfer. The proposed validation test is also archived and documented as an application brief by Fluent, Inc.3 The application brief only includes single-phase species transport with film condensation at the wall. It does not consider the effect of volumetric condensation when the local water vapor mass fraction exceeds the saturation limit in certain locations. The condensation module ANSYS-FLUENT provides has been modified to include the effect of volumetric condensation to establish local equilibrium and has been validated using this test case. Hence, a modified user-defined function was used to validate FLUENT Version 12.1.

When a mixture of air and water vapor contacts a surface at a temperature below the saturation value, condensation takes place on the cold surface, forming a liquid film that moves due to shear and gravity forces. Air accumulates at the condensed liquid and airvapor mixture interface during the condensation process, slowing down the rate of condensation. A number of factors, including the complex heat transfer process through the air and liquid film, determine the rate of condensation. For the present test case, the mass fraction of air in the free stream is high and the thermal resistance of the liquid film formed due to condensation is small. Under this circumstance, the diffusion of water vapor through the accumulated air in the interface between liquid and vapor primarily governs the condensation rate. This test will model the condensation process and compare the computed distribution liquid water mass with an analytical solution at the cold wall. It will also model the volumetric condensation process to establish localized equilibrium in the domain that ensures that water vapor mass fraction does not exceed saturation value.

3 Private communication with ANSYS Inc. technical representative.

8-6

The computational domain, grid, and boundary conditions for the condensation problem are shown Figure 8-5. A mixture of water vapor and air is specified as the working fluid in the domain. The free stream velocity is specified at the velocity inlet of the domain along with temperature and mass fraction of water vapor. A pressure outlet boundary condition with specified backflow temperature and water vapor mass fraction is specified at the downstream outlet as well as at the top of the domain. A number of customized source terms for the continuity, momentum, energy, and species equations are introduced through user-defined functions to model the effect of mass removal due to condensation at the cold bottom wall. To capture the boundary layer and the condensation process, grids are clustered near the bottom wall.

8.2.1 Theoretical Basis Sparrow, et al. (1967) presents the analytical solution for condensation of humid air in a flat plate. The present validation test case simulates the same problem and models the condensation process along the cold wall. ANSYS Inc.4 developed user-defined functions to model the condensation process and incorporate the effect on the flow and transport equations. Assumptions for the condensation modeling include the following:

1. Thermodynamic equilibrium occurs at the liquid-mixture interface.

2. The condensed water at the wall does not contain any dissolved air.

3. Film condensation takes place on the cold surface; dropwise condensation is neglected.

4. The liquid film formed on the surface offers viscous resistance to the mixture but offers no thermal resistance.

Figure 8-5. Schematic for Condensation of Humid Air Over Flat Plate 4

Private communication with ANSYS Inc. technical representative.

8-7

A number of assumptions are also made to model the volumetric phase change process that include the following:

1. The condensed water in a particular cell or in the domain does not form large bubbles that will rain out. Instead it will be floating with the existing mixture and diffusing through it as mist.

2. Slip velocity between the water droplets formed, and the mixture phase is neglected.

3. Volumetric evaporation is not considered in the simulations, because for the cases considered, it will be negligible. Moreover, the relative humidity is likely to be very high in most of the domain resulting in minimal volumetric evaporation.

4. The modules are developed for the mixture multiphase model of FLUENT and will not work with volume of fluid or Eulerian models.

The species mass flux equation for water vapor (Bird, et al.,1960) at the cold wall could be written as dx H 2O mH2O D x H 2O v (8-7) dy where mH2O Volumetric mass source removed from the domain that condenses on the wall (kg/m2)

Mixture density (kg/m3) x H 2O Mass fraction of H2O vapor D Diffusion coefficient (m2/s) y Vertical distance from bottom wall (m) v Normal fluid velocity at the condensed water mixture interface (m/s)

Eq. (8-7) can be modified in the form x H2O dx H2O Acellwall mH2O D (8-8) x H2O 1 dy Vcell where Acellwall Cell face area at the wall (m2)

Vcell Volume of the cell (m3)

Eq. (8-8) is used to formulate the source terms used in the mass, momentum, energy, and species transport equations.

8-8

The interphase mass transfer process, where the water vapor forms liquid water droplet mist, is modeled using Eq. (8-9), which describes the mass transfer rate required to achieve local thermodynamic equilibrium.

, , (8-9) where Relaxation factor Mixture density

, Cell water vapor mass fraction

, Cell saturated mass fraction at cell temperature acts simultaneously as a rate constant as well as a numerical underrelaxation parameter. The numerical experiments also showed that the relaxation factor is highly dependent on the flow and turbulence. For natural convection flow problems, it can be as high as 0.80.95, whereas for forced convection problems, it is almost restricted to 0.10.4 depending on other flow parameters.

8.2.2 Test Input The computational domain, grids, and boundary conditions relevant to the test case were discussed in Section 8.2. The test case is modeled as a 2D steady laminar two-phase flow problem, and the incompressible Navier-Stokes equations are solved without any turbulence models. Species transport equations with inlet diffusion and a diffusion energy source are solved for the vapor phase. Two different velocities with fixed water vapor concentration at the inlet are studied, and results are compared with experimental data. The working fluid is specified as a mixture of water vapor and air, and fluid density is determined using the volume-weighted mixing law. The customized, user-defined function to incorporate the source terms is compiled and hooked to the mass, momentum, energy, and species transport equations using the standard FLUENT interface. The user-defined functions, mesh, and the basic case file were obtained from ANSYS Inc.5 and later modified to include the modifications needed for multiphase flows.

Input and results for this test case are on the attached media in the directories /conden-12.1/single-phase and /conden-12.1/multiphase for single and multiphase flows, respectively.

8.2.3 Expected Test Results The overall flow field species fraction distribution should be in agreement with the general understanding of channel flow and should qualitatively predict the mass fraction distribution pattern in the flow field and near the wall. The computed condensation mass fraction at the wall should not deviate more than 25 percent from the overall range calculated from the analytical solution for both single- and multiphase-flow solutions. In addition, the multiphase model should demonstrate that it was able to achieve localized equilibrium that can be demonstrated through a relative humidity or saturation condition.

For acceptance, the maximum level of supersaturation should not exceed 10 percent of the saturation value.

5 Private communication with ANSYS Inc. technical representative.

8-9

8.2.4 Test Results Figures 8-6 through 8-9 show results obtained using the single-phase species transport model with film condensation at the wall, whereas Figures 8-10 through 8-13 highlight results obtained from multiphase flow simulations that account for interphase mass transfer due to volumetric condensation. Both these test cases were run for two different mixture inlet velocities of 1 m/s and 0.1 m/s, but the mass fraction of vapor in the mixture was fixed at 0.47967.

8.2.4.1 Test Results for Single-Phase Species Transport The air mass fraction contours for an inlet velocity of 1 m/s are shown in Figure 8-6. The thickness of air mass fraction increases along the cold wall because the mixture loses water vapor due to condensation and the mass fraction of water vapor in the mixture decreases. Consequently, the mass fraction of air in the mixture increases near the bottom wall of the domain. This is consistent with the understanding of the physics of film condensation on cold flat plates.

Figure 8-7 (a,b) compares condensed mass flux at the cold bottom wall for an inlet velocity of 0.1 m/s. In the downstream region, the pattern of the computed results is in good agreement with the analytical solution, though the computed result slightly underpredicts the data. The analytical and computed solutions have some deviation near the leading edge of the plate, though near the trailing edge, the deviations do not exceed 10 percent of the overall range. The computed solutions do not take into account the boundary layer development and assume a fully developed layer from the leading edge. The leading edge results should be excluded from comparison, and the study is considered validated for the downstream flow. The deviation in the trailing edge occurs because the analytical solution makes certain assumptions regarding the boundary layer thickness near the plate leading edge that are different from the simulated case. This deviation is within an acceptable range as described in the software validation test plan.

Figure 8-8 compares the computed and analytical solution for an inlet velocity of 1 m/s.

It shows the same trend as the previous test case with a different inlet velocity. Results show some deviation between simulated and analytical solution that is within 10 percent based on the total range and is within the acceptable range, as described in Section 8.2.3.

Figure 8-8 shows the contours of relative humidity for the entire flow domain for an inlet velocity of 1 m/s. Although the majority of the domain is either at a saturated or unsaturated condition, a thin area near the condensation zone shows supersaturation.

As mentioned in Section 8.2.1, the single-phase simulations do not consider volumetric condensation, where the excess water vapor that causes supersaturation is allowed to condense and form liquid droplet water. In reality, some of the water that exceeds the local saturation limit will condense and form mist droplets that will diffuse through the flow. This highlights the deficiency of using a single phase with a species transport model in capturing the actual physical process.

8-10

Figure 8-6. Air Mass Fraction Variation in the Flow Field (a) (b)

Figure 8-7 (a,b). Comparison of Analytical and Computed Results for Condensation Mass Flux for Inlet Velocity. (a) Equals 0.1 m/s and (b) Equals 1 m/s Figure 8-8. Relative Humidity Contours for Simulation with Single-Phase Species Transport and Inlet Velocity = 1 m/s 8-11

8.2.4.2 Test Results for Multiphase Transport with Volumetric Condensation Figure 8-9 shows the air mass fraction distribution in the domain. It is similar to that shown in Figure 8-6 for single-phase flow. This can be attributed to the fact that the volumetric water condensation rate is significantly smaller compared to the wall condensation rate to affect the species distribution pattern. Due to the high wall condensation rate, the air mass fraction near the bottom cold wall gets affected. Inside the domain, away from the wall, volumetric condensation is the only mechanism that can affect species distribution. As the volumetric condensation rate is orders of magnitude less compared to wall condensation, the species distribution appears to be unaffected.

Figure 8-10 (a,b) shows the wall condensation mass flux for two different test runs for multiphase flow modeling. For both runs, computed results reasonably predict the experimental data. However, unlike the test cases described in Section 8.4.2.1 in connection with single-phase flows, where the computed results slightly underpredicted the condensation rate, here the computed solution slightly overpredicts it. The disparity between computed and analytical solution in upstream region is more compared to the single phase solution. This can be attributed to a number of factors.

Figure 8-9. Air Mass Fraction Variation in the Flow Field with Multiphase Flow and Inlet Velocity = 1 m/s (a) (b)

Figure 8-10 (a,b). Comparison of Analytical and Computed Results for Condensation Mass Flux for Inlet Velocity Using Multiphase Flow Modeling. (a) Equals 0.1 m/s and (b) Equals 1 m/s 8-12

1. The analytical solution was derived for wall condensation only and did not consider volumetric condensation. Therefore, some disagreement between the multiphase flow solutions that consider volumetric condensation with experimental data was expected.

2. Removal of water vapor from the mixture phase may have caused a steeper gradient of species concentration, causing higher diffusion flux of water vapor toward the wall.

3. The volumetric condensation process affects the species distribution of water vapor near the cold wall and can affect the diffusion flux of water vapor through the boundary layer that ultimately affects the condensation rate.

4. As explained in Section 8.4.2.1, a number of assumptions were made in the analytical solution near the flat plate leading edge regarding boundary layer development that was not present in the computational solution. The boundary layer development in the computational solution did not follow the prescribed profile specified for the analytical solution.

Figure 8-11 shows the relative humidity contours for the flow domain, where most of the domain is in saturation condition and only a thin band of area near the cold wall exhibits some degree of supersaturation. The supersaturation values are, however, less than 10 percent of the saturation condition and are within the acceptable limit as prescribed in Section 8.2.3.

Based on the results obtained from the previously mentioned tests, it can be concluded that the single-phase simulations using FLUENT Version 12.1, along with the user-defined routine, can be used to simulate the wall condensation rate. The multiphase modification of the user-defined routines can be used to calculate both wall condensation and volumetric condensation rate throughout the domain. It can also be used to calculate the species fraction distribution and relative humidity in the flow domain.

Figure 8-11. Relative Humidity Contours for Simulation with Multiphase Species Transport and Inlet Velocity = 1 m/s 8-13

9 INDUSTRY EXPERIENCE None.

9-1

10 NOTES None.

10-1

11 REFERENCES ANSYS Inc. FLUENT Users Guide. Version 12.1. Canonsburg, Pennsylvania:

Fluent, Inc. 2009a.

. ANSYS-Workbench Users Guide. Version 12.1. Canonsburg, Pennsylvania:

Fluent, Inc. 2009b.

. ANSYS-Design Modelers Users Guide. Version 12.1. Canonsburg, Pennsylvania: Fluent, Inc. 2009c.

. ANSYS-Meshing Users Guide. Version 12.1. Canonsburg, Pennsylvania:

Fluent, Inc. 2009d.

. ANSYS-CFD-Post Users Guide. Version 12.1. Canonsburg, Pennsylvania:

Fluent, Inc. 2009e.

Anderson, J.D. Modern Compressible Flow. New York City, New York: McGraw Hill Inc. 1984.

Baughn, J.W., M.A. Hoffman, R.K. Takahashi, and B.E. Launder. Local Heat Transfer Downstream of an Abrupt Expansion in a Circular Channel with Constant Wall Heat Flux. Journal of Heat Transfer. Vol. 106. pp. 789-795. 1984.

Bechtel SAIC Company, LLC. In-Drift Natural Convection and Condensation.

MDL-EBS-MD-000001. Rev. 00. Las Vegas, Nevada: Bechtel SAIC Company, LLC. 2004.

Bird, R.B., W.E. Stewart, and E.N. Lightfoot. Transport Phenomena. New York City, New York: John Wiley & Sons. 1960.

Bush, R.H., G.D. Power, and C.N. Towne. WIND: The Production Flow Solver of the NPARC Alliance. 36th Aerospace Sciences Meeting and Exhibit. Reno, Nevada, January 12-15, 1998. AIAA-98-0935. Published on CD-ROM. Reston, Virginia:

AIAA. 1998.

Das, K. and D. Basu. Software Validation Test Plan for FLUENT Version 6.3.

San Antonio, Texas: CNWRA. 2007.

Das, K. and D. Basu. Software Validation Report for FLUENT Version 6.3.

San Antonio, Texas: CNWRA. 2008.

Driver, D.M. and H.I. Seegmiller. Features of Reattaching Turbulent Shear Layer in Divergent Channel Flow. AIAA Journal. Vol. 23. pp. 162-171. 1985.

Fluent Inc. FLUENT Validation Manual. Version 6.3. Lebanon, New Hampshire:

Fluent Inc. 2007a.

11-1

. FLUENT 6.3 Validation Solution Files. Lebanon, New Hampshire: Fluent Inc. 2007b.

Georgiadis, N., D. Yoder, and W. Engblom. Evaluation of Modified Two Equation Turbulence Models for Jet Flow Predictions. 44th AIAA Aerospace Sciences Meeting and Exhibit. Reno, Nevada, January 9-12, 2006. AIAA-2006-490. Published on CD ROM. Reston, Virginia: AIAA. 2006.

Goebel, S.G. and J.C. Dutton. Experimental Study of Compressible Turbulent Mixing Layers. AIAA Journal. Vol. 29, No. 4. pp. 538-546. 1991.

Green, S. and C. Manepally. Software Validation Test Plan for FLOW-3D Version 9.

Rev. 1. San Antonio, Texas: CNWRA. 2006.

Holman, J.P. Heat Transfer. 9th Edition. New York City, New York:

McGraw-Hill. 2002.

Incropera, F.P. and D.P. Dewitt. Fundamentals of Heat and Mass Transfer. 4th Edition.

New York City, New York: John Wiley & Sons, Inc. 1996.

Kuehn, T.H. and R.J. Goldstein. An Experimental Study of Natural Convection Heat Transfer in Concentric and Eccentric Horizontal Cylindrical Annuli. ASME Journal of Heat Transfer. Vol. 100. pp. 635-640. 1978.

Kuehn, T.H. and R.J. Goldstein. An Experimental Study and Theoretical Study of Natural Convection in the Annulus Between Horizontal Concentric Cylinders. Journal of Fluid Mechanics. Vol. 74, Part 4. pp. 695-719. 1976.

LeFevre, E.J. Laminar Free Convection from a Vertical Plane Surface. Proceedings of 9th International Congress of Applied Mechanics, Brussels. Vol. 4. p. 168. 1956.

Ostrach, S. An Analysis of Laminar-Free Convection Flow and Heat Transfer About a Flat Plate Parallel to the Direction of the Generating Body Force. NASA TR-1111.

Cleveland, Ohio: NASA. 1953.

Ozisik, M.N. Basic Heat Transfer. New York City, New York: McGraw-Hill. 1977.

Schlicting, H. Boundary Layer Theory. New York City, New York: McGraw Hill Inc. 1960.

Sparrow, E.M., W.J. Minkowycz, and M. Saddy. Forced Convection Condensation in the Presence of Noncondensables and Interfacial Resistance. International Journal of Heat and Mass Transfer. Vol. 10. pp. 1,829-1,845. 1967.

Todreas, N. and M.S. Kazimi. Thermal Hydraulic Fundamental and Elements of Thermal Hydraulic Design. Vols. I-II. New York City, New York: Hemisphere Publishing Corporation. 1990.

11-2

ISORAD-TC1 Compared to Formula/Constant ISORAD-TC1 qin = qin = q decay qin = 65 58.1 qout = qc + qr qout = 65 58.1 qr = Radiative Heat Transfer qr = 43.938 37.859 qc= Convective Heat Transfer qc= 21.062 20.241 qc = qside + qtop qc = 21.062 20.241 qside = qside = 18.872 18.079 qtop = qtop = 2.19 2.16 qcside = hc-side Aside(Tw-Ta) qcside = 18.872 18.079 hc-side = Avg Conv Heat Tran Coef for Vertical (Side) Surfaces hc-side = 4.020918 4.197 Aside = Area of the Vertical (Side) Surface Aside = 0.745709794 0.602330768 Aside = 2rz Aside = 0.745709794 0.6023307675200

= = 3.14159 3.14159 r= Radius of the Outer Container r= 0.2015 0.184 z= Height of the Outer Container z= 0.589 0.521 hcside = 5k Nuz/4z hcside = 4.020918 4.197 k= Fluid Thermal Conductivity of Air at 38°C k= 0.027224182 0.027256692 Nuz Nusselt Number Nuz 69.5655 64.18520221 Nuz = 0.60(Grz x Pr) 0.20 Nuz = 69.5655 64.185 W W= 65 58.1 Tw = Surface Temperature Tw = 44.294 45.151 T = Ambient Air Temperture 38°C or 311.15°K T = 38 38 Tw = - Temperature of the surface (Simulation) Tw = 44.63188755 45.20009475 Grz = Modified Grashof Number Grz = 29661375840.325500 19835043909.360700 Pr = Prandtl Number Pr = 0.70635466 0.706293404 ISORAD-TC1 vs 1 27 JAN 2020

ISORAD-TC1 Compared to Grz = gqwz^4 / kv^2 Grz= 29,661,375,840.3255 19835043909.3607000000 g= Gravitational Acceleration (9.81 m s-2 ) g= 9.8 9.8

= Volume Coefficient of Expansion = 1/T (°K-1) = 0.003181703929720 0.003178887766768 qw = Constant Heat Flux through the wall (W/m2) qw = q/A qw= 64.946677627000000 71.283970308570000 2

v= Kinematic Viscosity (m /s) Temp Kelvin v= 0.000017369530960 0.00001739672843 C= Specific Heat of Air at 38°C C= 1005 1005 k= Fluid Thermal Conductivity of Air at 38°C k= 0.0272355704200 0.02725669245025

= Fluid Density of Air at at 38C = 1.114054891597180 1.114054891597180 Pr = v*C/k Pr = 0.70635466 0.706293404 qtop = hc-top Atop (Tw - Ta ) qtop = 2.18885 2.1620248 hc-top = Avg Conv Heat Trans Coef for Top Surface hc-top = 2.7263972 2.84260395 Atop = Area of the Top Surface Atop = 0.1275556225775000 0.1063616710400000 hc-top = k Nul /L hc-top = 2.7263972 2.8426039620161 k= Therml Conductiity k= 0.027354961300 0.02739230867537 Nul = Nuslet Number Nul = 10.041487941225 9.547189600000 L= L= 0.10075 0.1063616710400000 Pr Nul= 0.706008490000 0.705900106663 Nul = 0.13(Grl

Pr)^0.333 Nul = 10.0415 9.5472 Grl = g(tw-ta)L^3 /v^2 Grl = 653612.946073670 561840.6629800000

= Volume Coefficient of Expansion = 1/T (°K-1) = 0.003181703832140 0.003178887766768 v= Grl velocity v= 0.00001752323044 0.000017571352642 qr = A(Tw^4-Ta^4) Radiative Heat Transfer' qr = 43.938 37.859

= Stefan-Boltzman Coef (5.669)10^-8 = 0.00000005669 0.00000005669

= Emissivity = 0.992 0.92 Atotal = Total Surface area of Container Atotal = 1.0008 0.81505 Ta = Ambient 38°C or 311.15°K Ta = 311.15 311.15 Tw Drum Surface Tw = 317.44 318.29 ISORAD-TC1 vs 2 27 JAN 2020

CONFIDENTIAL BUSINESS INFORMATION ISO-RAD Canada Inc By: Kevin J. Schehr, DBA Ottawa, ON, Canada T: +1-504-305-4320 Date: October 25, 2021 T: +1-504-717-7811 (m)

E: kjs@isorad-canada.com

Subject:

Manual Calculation to Verify Hawk Ridge Technical Report The following report details the method used to verify and validate that the Normal Conditions of Transport (NCT) thermal condition 1 result in the Hawk Ridge Systems Thermal Analysis is accurate.

qin = qout. qout = 65 Watts qin = qdecay qin = 65 Watts and qout, = qc + qr where: qc = Convective Heat Transfer = 21.062 qr = Radiative Heat Transfer = 43.938 qout = qc + qr qout = 21.062 + 43.938 qout = 65.000 The convective term, qc, can be expressed as convection from the cylindrical side surface, qc-side, and from the cylinder top surface, qc-top:

qc = qc-side + qc-top Where: qc-side = 18.872 qc-top = 2.190 qc = qc-side + qc-top qc = 18.872 + 2.190 qc = 21.062 Convection from the Side From Holman [3-10] the convection term from vertical (side) surfaces, qc-side, can be expressed as:

qc-side = hc-side Aside (Tw - Ta )

where: hc-side = Average Convective Heat Transfer Coefficient for Vertical (Side) Surfaces 4.020918 Aside = Area of the Vertical (Side) Surface (0.745709794) qc-side = hc-side Aside (Tw - Ta )

qc-side = ((4.020918)*(0.7457104234046))*((44.294 - 38))

qc-side = (2.9984404642551774228)*(6.294)

qc-side = 18.8721842820220866991032 or 18.872 and Aside = 2rz Where: r = Radius of the Outer Container (0.2015 m) z = Height of the Outer Container (0.589 m)

Aside = 2rz Aside = (2(3.14159)) * (0.2015)(0.589)

Aside = (6.28318)(0.1186835)

Aside = 0.745709794 Also, from Holman [3-10], the Average Convective Heat Transfer Coefficient for Vertical (Side)

Surfaces, hc-side, can be expressed as:

hc-side = 5k Nuz/4z where: k = Thermal Conductivity (0.02723557042)

Nuz = Nusselt Number (69.5655) z = Height of the Outer Container (0.589 m) hc-side = 5k Nuz/4z hc-side = (5(0.02723557042)*(69.5655))/4(0.589) hc-side = (0.1361778521)*(69.566))/2.356 hc-side = 9.47328037026255 / 2.356 hc-side = 4.0209179653066850594227504244482 or 4.020918 Over the range of temperatures for this problem, from data provided by Holman [3-10, Table A-5], the Thermal Conductivity as a function of temperature (°Kelvin) can be expressed as:

Table 1: Thermal Conductivity of Air Vertical Grashof Number k -Grz Ambient T °C Wall T °C 0.026996839 38 38 0.003393 0.00007586 0.027034769 38 39 0.003393 0.00007586 0.027072699 38 40 0.003393 0.00007586 0.027110629 38 41 0.003393 0.00007586 0.027148559 38 42 0.003393 0.00007586 0.027186489 38 43 0.003393 0.00007586 0.027224419 38 44 0.003393 0.00007586 0.02723557042 38 44.294 0.003393 0.00007586 0.027262349 38 45 0.003393 0.00007586 0.027300279 38 46 0.003393 0.00007586 0.027338209 38 47 0.003393 0.00007586 0.027376139 38 48 0.003393 0.00007586 0.027414069 38 49 0.003393 0.00007586 0.027451999 38 50 0.003393 0.00007586 October 25, 2021 pg. 2 Draft Revision 0

Table 2: Thermal Conductivity of Air Top Grashof Number k - Grl Ambient T °C Wall T °C Wall T -0.25 0.026996839 38 38 0.003393 0.00007586 37.75 0.027034769 38 39 0.003393 0.00007586 38.75 0.027072699 38 40 0.003393 0.00007586 39.75 0.027110629 38 41 0.003393 0.00007586 40.75 0.027148559 38 42 0.003393 0.00007586 41.75 0.027186489 38 43 0.003393 0.00007586 42.75 0.027224419 38 44 0.003393 0.00007586 43.75 0.02735493613 38 44.294 0.003393 0.00007586 44.044 0.027262349 38 45 0.003393 0.00007586 44.75 0.027300279 38 46 0.003393 0.00007586 45.75 0.027338209 38 47 0.003393 0.00007586 46.75 0.027376139 38 48 0.003393 0.00007586 47.75 0.027414069 38 49 0.003393 0.00007586 48.75 0.027679579 38 50 0.003393 0.00007586 49.75 Also, from Holman, [3-10, Eq 7-28], the Nusselt Number for vertical constant heat flux surfaces can be expressed as:

Nuz = 0.60(Grz x Pr)0 20 Where: Grz = Modified Grashof Number 29,661,375,840.3255 Pr = Prandtl Number (0.706354660)

Nuz = 0.60(Grz x Pr)0 20 Nuz = 0.60(29,661,375,840.3255) x 0.706354660)0.20 Nuz = 0.60(20,951,451,046.82533284183)0.20 Nuz = 0.60(115.942542911)

Nuz = 69.5655257466 or 69.5655 The Modified Grashof Number is expressed as Holman [3-10, Eq 7-30]:

Grz = gqwz4 / kv2 Where: g = Gravitational Acceleration (9.8 m s-2 ) 9.8

= Volume Coefficient of Expansion = 1/T (°K-1) 0.00318170392972 qw = Constant Heat Flux through the wall (W/m2) 65/1.000821039 = 64.94667627 k = Thermal Conductivity of Air = 0.02723557042 v = Viscosity (m2/s) of Air at 44.5°C 1.735 x 10-5 (0.00001736953096) z = Drum Height 0.589 m Grz = gqwz4 / kv2 Grz = ((9.8) 0.00318170392972)(64.94667627)(0.589^4)) / (0.02723557042)*(0.00001736953096)2 Grz = ((0.031180698511256)*(64.94667627)*(0.12035418024)) /(0.02723557042)*( 3.017006058E-10)

Grz = ((2.02508273208301438309512)*(0.12035418024)) / (8.216988094216347286500691072e-12)

Grz = (0.24372717213803074370554248154443) / (0.00000000000819969267953680516256)

Grz = 29,661,375,840.325464335352231789701 or 29,661,375,840.3255 Over the range of temperatures for this problem, from data provided by Holman [3-10, Table A-5], the Kinematic Viscosity as a function of temperature (°Kelvin) can be expressed as:

October 25, 2021 pg. 3 Draft Revision 0

v = (1.3333 x10-5) + (9.768 x10-8) T Table 3: Kinematic Velocity for Vertical Grashof Number v - Grz Ambient T °C Wall T °C 0.000017062132 38 38 0.000013331 0.000000097568 0.000017110972 38 39 0.000013331 0.000000097568 0.000017159812 38 40 0.000013331 0.000000097568 0.000017208652 38 41 0.000013331 0.000000097568 0.000017257492 38 42 0.000013331 0.000000097568 0.000017306332 38 43 0.000013331 0.000000097568 0.0000173455172 38 44 0.000013331 0.000000097568 0.00001736953096 38 44.294 0.000013331 0.000000097568 0.000017404012 38 45 0.000013331 0.000000097568 0.000017452852 38 46 0.000013331 0.000000097568 0.000017501692 38 47 0.000013331 0.000000097568 0.000017550532 38 48 0.000013331 0.000000097568 0.000017593372 38 49 0.000013331 0.000000097568 0.000017648212 38 50 0.000013331 0.000000097568 Table 4: Kinematic Velocity for Top Grashof Number v - Grl Ambient T °C Wall T °C Wall T -

0.25 0.000017062132 38 38 0.000013331 0.000000097568 37.75 0.000017135392 38 39 0.000013331 0.000000097568 38.75 0.000017208652 38 40 0.000013331 0.000000097568 39.75 0.000017281912 38 41 0.000013331 0.000000097568 40.75 0.000017355172 38 42 0.000013331 0.000000097568 41.75 0.000017428432 38 43 0.000013331 0.000000097568 42.75 0.000017501692 38 44 0.000013331 0.000000097568 43.75 0.00001752323044 38 44.294 0.000013331 0.000000097568 44.044 0.000017574952 38 45 0.000013331 0.000000097568 44.75 0.000017648212 38 46 0.000013331 0.000000097568 45.75 0.000017721472 38 47 0.000013331 0.000000097568 46.75 0.000017794732 38 48 0.000013331 0.000000097568 47.75 0.000017867992 38 49 0.000013331 0.000000097568 48.75 0.000017941252 38 50 0.000013331 0.000000097568 49.75 Over the range of temperatures for this problem, from data provided by Holman [3-10, Table A-5], the Prandtl Number, as a function of temperature (°K), can be expressed as:

Pr = (0.7755 - 0.00022) T Table 5: Prandtl Number for Vertical Nusselt Number PR - Nuz Ambient T °C Wall T °C 0.70704700 38 38 0.7755 0.00022 0.70693700 38 39 0.7755 0.00022 0.70682700 38 2240 0.7755 0.00022 0.70671700 38 41 0.7755 0.00022 October 25, 2021 pg. 4 Draft Revision 0

0.70660700 38 42 0.7755 0.00022 0.70649700 38 43 0.7755 0.00022 0.70638700 38 44 0.7755 0.00022 0.706354660 38 44.294 0.7755 0.00022 0.70627700 38 45 0.7755 0.00022 0.70616700 38 46 0.7755 0.00022 0.70605700 38 47 0.7755 0.00022 0.70594700 38 48 0.7755 0.00022 0.70583700 38 49 0.7755 0.00022 0.70572700 38 50 0.7755 0.00022 Table 6: Prandtl Number for Top Nusselt Number Pr - Grl Ambient T °C Wall T °C Wall T -0.25 0.70704700 38 38 0.7755 0.00022 37.75 0.70688200 38 39 0.7755 0.00022 38.75 0.70671700 38 40 0.7755 0.00022 39.75 0.70655200 38 41 0.7755 0.00022 40.75 0.70638700 38 42 0.7755 0.00022 41.75 0.70622200 38 43 0.7755 0.00022 42.75 0.70605700 38 44 0.7755 0.00022 43.75 0.706008490 38 44.294 0.7755 0.00022 44.044 0.70589200 38 45 0.7755 0.00022 44.75 0.70572700 38 46 0.7755 0.00022 45.75 0.70556200 38 47 0.7755 0.00022 46.75 0.70539700 38 48 0.7755 0.00022 47.75 0.70523200 38 49 0.7755 0.00022 48.75 0.70506700 38 50 0.7755 0.00022 49.75 The values of k, and v are evaluated at the film temperature, which is taken as the average between the wall temperature and the ambient temperature.

Table 7: Volume Coefficient of Expansion (Vertical and Top)

Ambient T °C Wall T °C 0.00321388397879 38 38 0.00320872773945 38 39 0.00320358801858 38 40 0.00319846473693 38 41 0.00319335781574 38 42 0.00318826717679 38 43 0.00318319274232 38 44 0.00318170392972 38 44.294 0.00317813443509 38 45 0.00317309217833 38 46 0.00316806589577 38 47 0.00316305551162 38 48 0.00315806095058 38 49 0.00315308213779 38 50 October 25, 2021 pg. 5 Draft Revision 0

Convection from the Top From Holman [3-10], the convection term from top surface, q-top, can be expressed as:

q-top = hc-top Atop (Tw - Ta )

Where: hc-top = Average Convective Heat Transfer Coefficient for Top Surface (2.7264)

Atop = Area of the Top Surface (0.12755573031922) q-top = hc-top Atop (Tw - Ta )

q-top = (2.7263979270411414392059553349876)*(0.12755573031922)*((44.294-38))

q-top = (0.34776767872454028258123942332506)*(6.294) q-top = 2.1888497698922565385663209304079 or 2.189 The value for hc-top is based on a "characteristic dimension", defined in Holman [3-10 Eq 7-39] as L=r/2 Where: r = Radius of the Outer Drum Top (0.2015 m)

L = r/2 L = 0.2015/2 L= 0.10075 Also, from Holman [3.10] the Convective Heat Transfer Coefficient for Top Surface, hc-top, can be expressed as:

hc-top = kNuL / L Where: k = Thermal Conductivity of Air at 44.294°C = (0.02735493613)

NuL = Nusselt Number = 10.0415 L= 0.10075 hc-top = kNuL / L hc-top = (0.02735493613)( 10.0415) / 0.10075 hc-top = (0.274684591149395) / 0.10075 hc-top = 2.7263979270411414392059553349876 or 2.7264 Again, from Holman, [3-10, Eq 7-40], the Nusselt Number can be expressed as:

NuL = 0.13 * (GrL

Pr)0.3333 Where: GrL = Grashof Number 653,612.9461 Pr = Prandtl Number 0.706008490 NuL = 0.13 * (GrL

Pr)0.3333 NuL = 0.13 * (653,612.9461* (0.706008490)0.3333 NuL = 0.13 * (461,456.289120512389)0.3333 NuL = 0.13

77.2422149325 NuL = 10.041487941225 or 10.0415 October 25, 2021 pg. 6 Draft Revision 0

The Grashof Number is expressed as Holman [3-10, Eq 7-21]:

GrL = g (Tw - Ta) L3 / v2 Where: g = Gravitational Acceleration (9.8 m s-2 )

= Volume Coefficient of Expansion 3400 x 10-6 (0.0034) or 0.00315308214 L = Characteristic Length 0.10075 v = Viscosity (m2/s) of Air at 40°C 1.1752 x 10-5 (0.00001752323044)

GrL = g (Tw - Ta) L3 / v2 GrL = 9.8*(0.00318170383214)* (44.294-38) (0.2015/2)3 / (0.00001752323044)2 GrL = (0.031180697554972)*(6.29401928)*((0.10075)^3) / (0.0000000003070636050533425936)

GrL = (0.19625191157484262786016)*(0.00102266917) / (0.0000000003070636050533425936)

GrL = (0.0002007007795211577031143687032672) / (0.0000000003070636050533425936)

GrL = 653,612.94607367 or 653,612.9461 Radiation from All Surfaces The radiative term, qr, can be expressed as:

qr = A(T4w - T4a )

Where: qr = radiative heat transfer

= Stefan-Boltzman Coefficient (5.669 x 10-8 W/m2 °K)

= Emissivity 0.992 Atotal = Surface Area of the Container (1.00082188404308 m2)

Ta = Ambient Environmental Temperature (311.15 °K)

Tw = Surface Temperature of the Outer Drum (317.44438°K) 317.44 qr = A(T4w - T4a )

qr = ((0.00000005669)(0.992)(1.00082188404308)) * (317.444-311.154) qr = (0.00000005623648)(1.000821884043) * (10154202902.03-9373013041.13) qr = 0.000000056244962528861795

781,189,860.93 qr = 43.93799445593460674724016935 or 43.938 For validation of this methodology, we compared the following results determined through a SolidWorks Flow Simulation performed by Hawk Ridge Systems as noted in the opening paragraph.

Using a decay heat load of 65 Watts and an emissivity of 0.992, Hawk Ridge calculated an average surface temperature to be 44.63°C. This manual calculation provided a result of 44.294 and variation is 0.759%.

Therefore, ISO-RAD concludes that this calculational methodology is suitable to examine the effects of certain variations in these parameters. The formulas above were placed into a spreadsheet and then can calculate variations based on certain parameters in the following sections.

As a first step, ISO-RAD examined the effect of changing the convection heat transfer coefficient (hc) by a very large value: 20% using the spreadsheet. Lowering the hc by 20% caused a change to the average temperature from 44.294 °C to 44.717 °C, an increase of 0.423°C. Raising the hc by 20%

caused a change to the average temperature from 44.294 °C to 43.932 °C, a decrease of 0.362 °C. It is concluded, the outside surface temperature is not sensitive to large changes in the convection heat transfer coefficient.

October 25, 2021 pg. 7 Draft Revision 0

Secondly, we examined the effect of changes in the emissivity. These results are shown in the table below:

Table 8: Emissivity Variance Effect on Surface Temperature Emissivity Average Temperature Delta T 0.992 44.294 0 0.95 44.474 0.18 0.92 44.609 0.315 0.90 44.702 0.408 0.80 45.210 0.916 0.7936 45.245 0.951 The results in Table 8 demonstrate that a substantial change in emissivity of 20% results in a 0.951°C change in the Outer Drum external surface temperature. Consequently, although the external surface temperature is more sensitive to changes in emissivity than to changes in the convection heat transfer coefficient, even quite large changes in emissivity cause only small changes in the Outer Drum external surface temperature.

Finally, ISO-RAD examined the combined effect where the convective heat transfer coefficient was changed by 20% and the emissivity was changed by a range of 15% - 20% (0.8432 - 0.7936 emissivity).

The results were calculated to be:

Table 9: Heat Coefficient and Emissivity Variance Effect on Surface Temperature Emissivity hc Average T Delta T 0.992 Normal 44.294 0 0.8432 (-15%) -20% 45.406 1.112 0.8184 (-17.5%) -20% 45.656 1.362 0.7936 (-20%) -20% 45.812 1.518 Conclusion Even in this case, with emissivity changed by 15% and the convective heat transfer coefficient changed by 20%, the maximum surface temperature changes by 1.112 °C. Therefore, based on the SolidWorks Flow Simulation Thermal Analysis conducted by Hawk Ridge (using a decay heat load of 65 Watts and an emissivity of 0.992, the maximum temperature was found to be 48.82°C, ISO-RAD concludes that the ISORAD-TC1 package would still satisfy the IAEA criteria of 50°C (48.82°C + 1.112°C = 49.932° C) or less even if the uncertainty of the value for the emissivity were as large as 15%.

In Addition, the actual wattage limit for the ISORAD-TC1 is 60.88 watts. The reduced wattage would lower the average surface temperature from 44.294 °C to 43.929 °C a difference of 0.365 °C. The reduced wattage would correspondingly lower the maximum surface temperature by 0.365 °C to 48.455°C.

October 25, 2021 pg. 8 Draft Revision 0

Burnley Burnley Technology, Inc.

380 Lafayette Road, Unit 11-162; Seabrook, NH 03874; USA; Tel: +1.978.340.0156; e-mail: munroiii@gmail.com Report By: John J. Munro III Date: 06 October 2021

Subject:

ISORAD-TC1 Bremsstrahlung Dose Rates A study was undertaken to determine the maximum dose rate at the surface of the ISO-RAD Canada (ISO-RAD) model ISORAD-TC1 transport container and the maximum dose rate at 1 meter from the surface due to Bremsstrahlung radiation generated from beta emitters transported within the container.

The energy of the Bremsstrahlung radiation is proportional to the energy of the beta radiation and the Atomic Number of the material with which the betas interact. An examination of the radionuclides authorized for transport in the TC1 container, as listed in Canadian Nuclear Safety Commission Type B Certificate CDN/2101/B(U) (Rev. 0), reveals that there are 17 beta emitters authorized. These are listed in Table 1 in order of descending energy. 1 The highest energy beta is emitted from 90Yttrium. This radionuclide is listed independently (with a maximum activity of 1.73 TBq; 46.7 Ci) but also occurs in secular equilibrium with 90Strontium (with a maximum activity of 1.85 TBq; 50 Ci). The maximum energy of the 90Yttrium beta is 2.279 MeV; the average energy is 0.932 MeV.2 In the TC1 container, the radioactive material is enclosed in its own source encapsulation and/or within a source holder. As a minimum, the radioactive source is enclosed by 1.12 mm of stainless steel in the Special Form Capsule Body (Drawing 191023-401). The Special Form Capsule resides within the containers Cavity Insert which further encloses the source with an additional 1.52 mm of stainless steel (Drawing 180831-217). Therefore, the source is surrounded by a minimum of 2.64 mm of stainless steel.

The range of a 2.5 MeV electron in stainless steel is 1.699 g/cm2. 3 As stainless steel has a specific gravity of 7.8 g/cm3, the range of a 2.5 MeV electron in stainless steel is 0.218 cm or 2.18 mm. Since the maximum energy of all betas transported inside the TC1 container is less than 2.5 MeV, and since the thickness of the stainless steel enclosure (2.64 mm) is greater than the range in stainless steel of a 2.5 MeV beta (2.18 mm),

then all electron interactions, for all radionuclides, will occur within the stainless steel and all Bremsstrahlung production will occur within this thickness of stainless steel.

On this basis, we have assumed a simplified model of the source/enclosure system for analysis. We have postulated a 1 mm diameter spherical source enclosed by a spherical shell of stainless steel 2.5 mm thick.

We calculated the Bremsstrahlung dose rate in air at a distance of 1 centimeter from the center of the source using Monte Carlo techniques.

Dose Calculation Monte Carlo methods using MCNP v.6 4 were used to calculate the dose rate in air. Using the atomic and mass densities and source geometry described above, appropriate electron cross-section libraries were chosen from the libraries supplied with the MCNP software. Beta input energies were taken from Eckerman et al. 5 1

Burnley The dose rate and energy of bremsstrahlung radiation resulting from the slowing down of the betas from these sources within the stainless-steel enclosure were calculated using this Monte Carlo technique. These values of dose rate and energy were calculated on the surface of a sphere of 1 cm radius concentric with the source.

A total of 1x108 source beta histories were processed. Statistical uncertainties were typically less than 1%.

The average Bremsstrahlung energy, the median Bremsstrahlung energy, and the mode Bremsstrahlung energy were calculated and are listed in Table 1.

The Bremsstrahlung photon dose rate in air at a distance of 1 cm from the center of the source was calculated for each radionuclide and are listed in Table 1.

Shielding Calculations The TC1 container has a minimum of 62 mm of Uranium shielding. The transmission of these Bremsstrahlung photons through this shielding was calculated using the relationship:

()

= = ()

0 0 where: D: Dose Rate with shielding D0: Dose Rate without Shielding

Transmission B(E, x): Buildup Factor for the specific energy and thickness of the shield

µ/(E): Mass Attenuation Coefficient for the specific energy

Density of the Material x: Thickness of the Shield Mass Attenuation Coefficients were taken from NIST 6 and buildup data were taken from ANSI/ANS-6.4.3-1991 7. The calculated values of the derived transmission for a thickness of 62 mm of Uranium is presented in Table 1.

Dose Rate on Container The dose rate on the surface of the ISORAD-TC1 container was calculated using the relationship:

=

2 where: D: Dose Rate (Rad/hr)

Dose Rate in air at 1 cm for Bremsstrahlung (Gy-cm2/h-TBq; Rad-cm2/h-Ci)

A: Maximum Activity of the source (TBq; Ci) d: Distance from the source to the surface of the container (20 cm)

Transmission Factor for 62 mm of Uranium for the spectrum From this relationship, the dose rates at the surface of the container and at one meter from the surface of the container were calculated and presented in Table 1.

2

Burnley The maximum dose rate on the surface of the container as a result of Bremsstrahlung radiation from all radionuclides (194Iridium) is 49.4 µGy/h (4.9 mRad/hr) and the maximum dose rate at one meter from the surface of the container as a result of Bremsstrahlung radiation is 1.4 µGy/h (0.1 mRad/hr).

Conclusion The regulatory requirement for dose rate at the surface of the container and at 1 meter from the surface of the container is satisfied for all Bremsstrahlung radiation resulting from the beta emitters permitted to be used in the container.

Table 1: Results of Monte Carlo calculations:

Radionuclide Ebmax Max Act Bremsstrahlung Photon Dose Rate Trans- Dose Rate Spectrum at 1 cm Const mission Surf 1 meter

[keV] [TBq] Mean Median Mode Gy-cm2/h-TBq µGy/h µGy/h

[(Ci)] [keV] [keV] [keV] (Rad-cm2/h-Ci) (mRad/h) (mRad/h) 90 Y 2,280 1.73 234 167 93 15.25 1.25E-04 8.22 0.22 (47) (56.41) (0.82) (0.02) 90 Sr/90Y 2,280 1.85 229 163 99 16.75 6.67E-05 5.17 0.14 (50) (61.97) (0.52) (0.01) 194 Ir 2,228 2.05 308 245 66 31.54 3.06E-04 49.43 1.37 (55) (116.72) (4.91) (0.14) 188 W/188Re 2,120 0.64 292 232 60 27.06 1.66E-04 7.21 0.20 (17) (100.06) (0.72) (0.02) 228 Ac 2,067 0.63 218 170 92 11.28 2.40E-05 0.42 0.01 (17) (41.54) (0.04) (<0.01) 152 Eu 1,864 3.00 234 106 179 12.40 4.05E-05 3.81 0.11 (81) (45.90) (0.38) (0.01) 32 P 1,710 5.57 199 152 96 6.79 4.87E-06 0.46 0.01 (150) (25.13) (0.05) (<0.01) 89 Sr 1,501 12.19 191 148 98 5.27 1.75E-06 0.28 <0.01 (329) (19.51) (0.03) (<0.01) 134 Cs 1,454 7.04 140 122 89 1.07 2.62E-12 <0.01 <0.01 (190) (3.95) (<0.01) (<0.01) 187 W 1,311 22.38 211 181 60 3.83 5.82E-07 0.12 <0.01 (604) (14.19) (0.01) (<0.01) 137 Cs 1,175 143.86 140 120 94 1.05 1.46E-08 <0.01 <0.01 (3,888) (3.87) (<0.01) (<0.01) 192 Ir 670 374.63 172 158 66 1.49 2.09E-12 <0.01 <0.01 (10,125) (5.52) (<0.01) (<0.01) 67 Cu 562 690.31 121 57 41 0.23 1.50E-17 <0.01 <0.01 (18,657) (0.85) (<0.01) (<0.01) 177 Lu 497 370.63 73 62 66 <0.01 4.02E-77 <0.01 <0.01 (10,017) (<0.01) (<0.01) (<0.01) 175 Yb 470 995.30 132 60 122 0.45 7.35E-20 <0.01 <0.01 (26,900) (1.68) (<0.01) (<0.01) 33 P 248 370.63 113 84 102 0.10 3.77E-23 <0.01 <0.01 (10,017) (0.38) (<0.01) (<0.01) 227 Ac 45 2.51 NC NC NC NC NC <0.01 <0.01 (68) (<0.01) (<0.01)

NC: Not calculated due to the extremely low beta energy 3

Burnley 1

Brookhaven National Laboratory Decay Radiation database version of 9/16/2021; https://www.nndc.bnl.gov/nudat2/indx dec.jsp (accessed 28 Sep 21) 3 https://physics.nist.gov/cgi-bin/Star/e table.pl (accessed 28 Sep 21) 4 Goorley T, et al., "Initial MCNP6 Release Overview", Nuclear Technology, 180, pp 298-315 (Dec 2012).

5 Eckerman KF, Westfall RJ, Ryman JC, Cristy M, Availability of Nuclear Decay Data in Electronic Form, Including Beta Spectra Not Previously Published, Health Phys. 67, No. 4, pp. 338-345 6

https://physics.nist.gov/PhysRefData/XrayMassCoef/ElemTab/z79.html (accessed 28 Sep 21) 7 ANSI/ANS-6.4.3-1991 Gamma-Ray Attenuation Coefficients & Buildup Factors for Engineering Materials 4

Burnley Burnley Technology, Inc.

380 Lafayette Road, Unit 11-162; Seabrook, NH 03874; USA; Tel: +1.978.340.0156; e-mail: munroiii@gmail.com Report By: John J. Munro III Date: 17 October 2021

Subject:

ISORAD-TC1 Gamma Dose Rates The USNRC, in a Request for Additional Information relating to the ISO-RAD Canada model ISORAD-TC1 transport container, asked:

RAI 5-1. Demonstrate that the dose rate for a package containing Iridium-192 is bounding for all the other isotopes listed in the Canadian Competent Authority certificate.

The following isotopes listed in the Canadian Competent Authority Certificate emit, or have the potential to emit, either gamma particles with energies greater than the 612 keV gamma emitted by Iridium-192: Cesium-134, Cesium-137, Europium-152, Phosporus-32, Strontium-89, Yttrium-90, and Zinc-65. Although the quantities of material authorized for shipment in the Canadian Competent Authority Certificate for each of these isotopes is less than the amount authorized for Iridium-192, no information has been provided which demonstrates that a smaller quantity of material emitting higher energy particles results in package dose rates which meet the regulatory limits. Because some of the isotopes listed emit beta particles with energies greater than 1 MeV, the response should also address Bremsstrahlung radiation. In addition, the response should also provide additional information on the gamma radiations resulting from bremsstrahlung reaction of high energy beta particles with Tungsten-187.

This information is necessary to satisfy the requirements in 10 CFR 71.33(a), 71.47, and 71.51(a).

The radionuclide is a pure beta emitter and the photons generated are in the form of Bremsstrahlung radiation. A separate report (dated 06 October 2021) demonstrated that the regulatory requirement for dose rate at the surface of the container and at 1 meter from the surface of the container is satisfied for all Bremsstrahlung radiation resulting from the beta emitters permitted to be used in the container, including 32 Phosphorus, 90Yttrium and 187Tungsten.

A study was undertaken to determine the maximum dose rate at the surface of the ISORAD-TC1 transport container and the maximum dose rate at 1 meter from the surface due to gamma radiation generated from NRC-listed isotopes transported within the container.

In the ISORAD-TC1 container, the radioactive material is enclosed in its own source encapsulation and/or within a source holder and is surrounded by a Cavity Insert. The source is surrounded by a minimum of 2.64 mm of stainless steel. The cavity insert is surrounded by a minimum of 62 mm of Uranium. The Uranium is encased in a further thickness of stainless steel.

We have assumed a simplified model of the source/shielding system for analysis. We have postulated a 1 mm diameter spherical source located in the center of the container. The source is shielded by a minimum of 62 mm of Uranium metal. No additional attenuation provided by self-absorption within the source 1

Burnley material, by attenuation by the source encapsulation, the stainless steel cavity insert, the inner container housing, or the outer container is taken into account. Only shielding by the 62 mm thick Uranium is taken into account.

Dose Calculation The dose rate in air for each radionuclide is calculated using the methodology described below.

The flux density at a distance r from a source of photons of a single energy, Ei, can be expressed by:

=

4 2 where: E : i Flux Density fi: Abundance of the ith photon (photons/decay)

A: Activity (decay rate) of the Source r: Distance from the source to the point of interest The energy flux density, therefore, is expressed as:

4 2 where: i: Energy Flux Density Ei: Energy of the ith photon (MeV)

From Chilton et al. 1, the energy flux density is related to the dose rate by:

=

4 2 where: : Dose Rate due to the ith photon

µen/: Mass Energy Absorption Coefficient (expressed in cm2/g)

The Dose Rate Constant, , is defined as the Dose Rate at a unit distance from all photons emitted from a unit activity source. This can be expressed as:

4 2 For a unit distance of 1 cm, the exposure rate constant can be expressed as:

= (4.589104 ) Gy/h-TBq

= (1.699105 ) Rad/h-Ci 2

Burnley The values for photon energies, Ei, and abundances, fi, are obtained from the Brookhaven National Laboratory web site. 2 The values for the mass-energy absorption coefficients are obtained from the National Institute of Science and Technology web site. 3 Many of the radionuclides include a number of low energy x-rays (less than 12 keV), which are effectively removed by their source encapsulation and due to self-absorption within the source itself. Therefore, to properly calculate the exposure rate of an encapsulated source, photons with energies below 12 keV ar excluded.

The gamma photon dose rate in air at a distance of 1 cm from the center of the source (Dose Rate Constant) was calculated for each radionuclide and are listed in Table 1.

Shielding Calculations The TC1 container has a minimum of 62 mm of Uranium shielding. The transmission of these Bremsstrahlung photons through this shielding was calculated using the relationship:

()

= = ()

0 0 where: D: Dose Rate with shielding D0: Dose Rate without Shielding

Transmission B(E): Buildup Factor for the specific energy and thickness of the shield

µ/(E): Mass Attenuation Coefficient for the specific energy

Density of the Material x: Thickness of the Shield Mass Attenuation Coefficients were taken from NIST 4 and buildup data were taken from ANSI/ANS-6.4.3-1991 5. The calculated values of the derived transmission for a thickness of 62 mm of Uranium is presented in Table 1.

Dose Rate on Container The dose rate on the surface of the ISORAD-TC1 container was calculated using the relationship:

=

2 where: D: Dose Rate (Gy/hr; Rad/hr)

Dose Rate in air at 1 cm (Gy-cm2/h-TBq; Rad-cm2/h-Ci)

A: Maximum Activity of the source (TBq; Ci) d: Distance from the source to the surface of the container (20 cm)

Transmission Factor for 62 mm of Uranium for the spectrum From this relationship, the dose rates at the surface of the container and at one meter from the surface of the container were calculated and presented in Table 1.

3

Burnley Conclusion The regulatory requirement for dose rate at the surface of the container and at 1 meter from the surface of the container is satisfied for five of the identified gamma emitters permitted to be used in the container.

Table 1: Results of Dose Rate and Shielding calculations:

Radionuclide Photon Ran e Max Act Dose Rate Const Trans-mission

Dose Rate Surf 1 meter

[keV] Gy-cm 2/h-TBq tGy/h (Rad-cm 2 /h-Ci)

Chilton AB, Shultis JK and Faw RE, Principles of Radiation Shielding, Eq. 5-26, p. 132, Prentice Halt, 1984 2 Brookhaven National Laboratory Decay Radiation Database (http://www.nndc.bnl.gov/nudat2£indx dec.ts,ol accessed 06 September 2010.

3 NIST Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients (http://physics.nist.gov/PhysRefData/XrayMassCoef/ComTab/air.html ) accessed 06 September 2010.

4 https://physics.nist.gov/PhysRefData/XrayMassCoef/ElemTab/z92.html (accessed 28 Sep 21) s ANSI/ANS-6.4.3-1991 Gamma-Ray Attenuation Coefficients & Buildup Factors for Engineering Materials 4

Burnley Burnley Technology, Inc.

380 Lafayette Road, Unit 11-162; Seabrook, NH 03874; USA; Tel: +1.978.340.0156; e-mail: munroiii@gmail.com Report By: John J. Munro III Date: 17 October 2021

Subject:

ISORAD-TC1 75Selenium and 169Ytterbium Dose Rates The USNRC, in a Request for Additional Information relating to the ISORAD Canada model ISORAD-TC1 transport container, asked:

RAI 5-2. Provide the method used to extrapolate the package dose rates when loaded with Selenium-75 and Ytterbium-169 from the package dose rates obtained from Iridium-192 and demonstrate the method is valid.

Information presented in SAR Section 5.5.2 asserted that the package will meet the dose rate regulatory limits when transporting Selenium-75 and Ytterbium-169 based on the extrapolated package dose rates for Iridium-192. However, a description of the extrapolation method and a demonstration that the method is appropriate to obtain dose rates was not provided. In addition, the applicant needs to provide the valid range of this extrapolation because in most of the cases, an extrapolation method is valid only within given ranges of the parameters.

This information is necessary to satisfy the requirements in 10 CFR 71.33(b), 71.47, and 71.51(a).

As described in the Report ISORAD-TC1 Gamma Dose Rates dated 17 October 2021, the dose rate on the surface of a transport container is calculated using the relationship:

=

2 where: D: Dose Rate (Gy/hr; Rad/hr)

Dose Rate in air at 1 cm (Gy-cm2/h-TBq; Rad-cm2/h-Ci)

A: Maximum Activity of the source (TBq; Ci) d: Distance from the source to the surface of the container (20 cm)

Transmission Factor for 62 mm of Uranium for the spectrum The Specific Dose Rate Constants (Dose Rate in air at 1 cm) for 75Selenium and 169Ytterbium are lower than that of 192Iridium:

Radionuclide Specific Dose Specific Dose Rate Constant Rate Constant (Gy cm2/h TBq) (Rad cm2/h Ci) 192 Iridium 1,095 4,050 75 Selenium 481 1,780 169 Ytterbium 428 1,583 1

Burnley Therefore, for equivalent activity, 75Selenium and 169Ytterbium sources will exhibit lower unshielded exposure rates than an equivalent activity source of 192Iridium.

Additionally, the photon energies of 75Selenium and 169Ytterbium are generally lower than those of 192 Iridium. Therefore, the photons from 75Selenium and 169Ytterbium are more greatly attenuated by a given thickness of shielding than the photons of 192Iridium. The attached figure shows the relative transmission of photons from each of these radionuclides through Uranium:

Therefore, for equivalent activity, the shielded dose rate from a 75Selenium source and for a 169Ytterbium source will be lower than that from an 192Iridium source for all thicknesses of shielding. The shielding thickness that is sufficient for 192Iridium will be more efficient for the attenuation of photons from an equivalent activity of 75Selenium and 169Ytterbium.

Consequently, because of the lower specific gamma ray constant and the greater shielding efficiency, the exposure rates on the outside of a package containing 75Selenium or 169Ytterbium will be substantially lower than the exposure rates from 192Iridium for an equivalent activity.

2

ISORAD-TC1 Transport Package Shielding Efficiency Test Report ISO-RAD Canada Inc Kevin J. Schehr, DBA Managing Director October 19, 2021 Revision 1

ISO-RAD Canada Inc Shielding Efficiency and Pre NCT Radiation Profile Test Report By: Kevin J. Schehr Date: 19 OCT 2021

Subject:

Revised Shielding Efficiency Test of MPIC ISORAD-TC1 Transport Package The report is being revised based on new conversion factors based on the Burnley Technology, Inc.

ISORAD-TC1 75Selenium and 169Ytterbium Dose Rates Test Report.

Original Method Used The extrapolation for Se-75 and Yb-169 was performed by Rafael A. Bustillo using standard calculations based on the Ir-192 direct survey readings using NDS ND-2000 Survey Meter S/N 96219, which was calibrated on 03 JAN 2020 with Certificate of Calibration number NDTT-20000301.

For Se-75, the ratio based on the Gamma Constant of Ir-192 (0.48 R m2/hr Ci) to Se-75 (0.203 R m2/hr Ci) 0.203/0.48 =0.423.

For Yb-169, the ratio based on the Gamma Constant of Ir-192 (0.48 R m2/hr Ci) to Yb-169 (0.125 R m2/hr Ci) 0.203/0.48 =0.261.

Prototype MPIC-1, which is the Round version, was loaded with 1262.3 curies of Ir-192 on 14 DEC 2020 and a radiation profile survey was performed. The MPIC was loaded with 10 model ISO150 sources that totaled 1262.3 curies. The entire outer surface of the ISORAD-TC1 was surveyed using the survey meter and the highest exposure rate observed on each surface was recorded on the Shielding Efficiency Test Survey Form labeled with Prototype # MPIC-1.

New Method Used The new method uses the following formula provided from the Burnley Technologies Inc. Test Report. The Specific Dose Rate Constants (Dose Rate in air at 1 cm) for 75Selenium and 169Ytterbium are lower than that of 192Iridium:

=

2 where: : Dose Rate (Gy/hr; Rad/hr)

Dose Rate in air at 1 cm (Gy-cm2/h-TBq; Rad-cm2/h-Ci)

A: Maximum Activity of the source (TBq; Ci) d: Distance from the source to the surface of the container (20 cm) t: Transmission Factor for 47.4 mm of Uranium for the spectrum 19 OCT 2021 Page 2 of 6 Revision 1

ISO-RAD Canada Inc The data tables are provided by Burnley Technology Inc. with the following information:

Table 1: = Dose Rate Constant Radionuclide Specific Dose Specific Dose Rate Constant Rate Constant (Gy cm /h TBq) 2 (Rad cm2/h Ci) 192 Iridium 1,095 4,050 75 Selenium 481 1,780 169 Ytterbium 428 1,583 Table 2: t = Transmission Radionuclide 47.4 mm DU 63 mm Du 192 Iridium 0.00000486 4,050 75 Selenium 0.0000000013 1,780 169 Ytterbium 0.000000000000000000127 1,583 where: : Dose Rate (Gy/hr; Rad/hr)

Dose Rate in air at 1 cm (Gy-cm2/h-TBq; Rad-cm2/h-Ci) (See Table 1)

A: Maximum Activity of the source (TBq; Ci) 1500 curies d: Distance from the source to the surface of the container: 18.38 cm t: Transmission Factor for 47.4 mm of Uranium for the spectrum (See Table 2)

= (*A / d^2) t

= (4050(1500) /18.38^2)

0.00000486

= (6075000/337.8244)* 0.00000486

= 17982.71528

0.00000486

= 0.087395996 RAD = 87.395996 mRem (Ir-192)

= (*A / d^2) t

= ((1780*1500) /(18.38^2))

0.0000000013

= (2670000/337.8244)* 0.0000000013

= 7903.51437

0.0000000013

= 0.000010274568681 RAD = 0.01027 mRem (Se-75) 19 OCT 2021 Page 3 of 6 Revision 1

ISO-RAD Canada Inc

= (*A / d^2) t

= ((1,583 *1500) /(18.38^2))

0.000000000000000000127

= (2374500/337.8244)* 0.000000000000000000127

= 7028.799578

0.000000000000000000127

= 0.000000000000000892657546406 RAD = 0.000000000000000892657546406 mRem (Yb-169)

Using the above formula does not take into account the other materials that provide shielding such as the stainless steel and brass. Please not the actual MPIC dose rate using Ir-192 sources was 50.82 mRem per hour on the surface of the drum. The above calculated result was 87.4 mRem per hour on the surface of the container.

Conclusion The information provided in the original report is more conservative than the result of using the method based on the transmission factor method. The conclusion is the dose rate on the surface of the container is multiple times lower than of Ir-192 and the safety factor necessary for the use of Se-75 or Yb-169 in the MPIC has been met.

Report by: Approval by:

Rafael A. Bustillo Kevin J. Schehr, DBA General and Quality Manager Managing Director 19 OCT 2021 Page 4 of 6 Revision 1

ISO-RAD Canada Inc Shielding Efficiency Test (Pre NCT)

Survey Form Prototype S/N Prototype # MPIC-1 Sealed Source S/N Multiple (See List)

Isotope Ir-192 Curie Strength 1262.3 __________

Container ISORAD-TC1 MPIC - Round Survey Meter S/N 96219__________

Date of Survey 14 DEC 2020 Surveyor Rafael A. Bustillo_________

Side of Highest Surface Highest Surface 1 m from Highest 1 m from Highest Container Reading mSv/hr Reading mR/hr Surface Reading Sv/hr Surface Reading mR/hr Side 1 0.39 38.9 0.015 1.5 Side 2 0.39 38.9 0.015 1.5 Side 3 0.39 38.9 0.015 1.5 Side 4 0.39 38.9 0.015 1.5 Top 0.17 16.6 0.010 1.0 Bottom 0.25 24.9 0.009 0.9 Method to determine extrapolation factor: Max curie strength for container = M; Actual curies strength of test source = A; and Extrapolation factor = E. M = 1500 /A= 1262.3 =E 1.188307059.

E was rounded to 1.188. Extrapolated to 1500 Curies of Ir-192.

Side of Highest Surface Highest Surface 1 m from Highest 1 m from Highest Container Reading mSv/hr Reading mR/hr Surface Reading Surface Reading Side 1 0.39 X 1.188 = 0.462 38.89 X 1.188 = 46.20 0.015 X 1.188 = 0.0179 1.5 X 1.188 = 1.791 Side 2 0.39 X 1.188 = 0.462 38.86 X 1.188 = 46.16 0.015 X 1.188 = 0.0179 1.5 X 1.188 = 1.791 Side 3 0.39 X 1.188 = 0.462 38.88 X 1.188 = 46.19 0.015 X 1.188 = 0.0178 1.5 X 1.188 = 1.782 Side 4 0.39 X 1.188 = 0.461 38.84 X 1.188 = 46.14 0.015 X 1.188 = 0.0178 1.5 X 1.188 = 1.777 Top 0.17 X 1.188 = 0.198 16.63 X 1.188 = 19.76 0.010 X 1.188 = 0.0118 1.0 X 1.188 = 1.182 Bottom 0.25 X 1.188 = 0.296 24.94 X 1.188 = 29.63 0.009 X 1.188 = 0.0107 0.9 X 1.188 = 1.073 Distance Correction Factor (From ANSI N43.9 Table 1[B.1]: Distance from center of probe to package surface 1.56 cm x Half Linear Dimension of Package 69.957 = Correction Factor 1.0, but used 1.1 for conservatism.

Side of Highest Surface Highest Surface 1 m from Highest 1 m from Highest Container Reading mSv/hr Reading mR/hr Surface Reading Surface Reading Side 1 0.462 X 1.1 = 0.508 46.20 X 1.1 = 50.82 0.0179 X 1.1 = 0.0197 1.791 X 1.1 = 1.970 Side 2 0.462 X 1.1 = 0.508 46.16 X 1.1 = 50.77 0.0179 X 1.1 = 0.0197 1.791 X 1.1 = 1.970 Side 3 0.462 X 1.1 = 0.508 46.19 X 1.1 = 50.81 0.0178 X 1.1 = 0.0196 1.782 X 1.1 = 1.960 Side 4 0.461 X 1.1 = 0.508 46.14 X 1.1 = 50.75 0.0178 X 1.1 = 0.0196 1.777 X 1.1 = 1.955 Top 0.198 X 1.1 = 0.217 19.76 X 1.1 = 21.73 0.0182 X 1.1 = 0.0096 1.182 X 1.1 = 1.300 Bottom 0.296 X 1.1 = 0.326 29.63 X 1.1 = 32.59 0.0107 X 1.1 = 0.0118 1.073 X 1.1 = 1.180 19 OCT 2021 Page 5 of 6 Revision 1

ISO-RAD Canada Inc Shielding Efficiency Test (Pre NCT)

SuNey Form Prototype S/N Prototype# MPIC-1 Sealed Source S/N Multiple (See List)

Isotope lr-192/Se-7/ 5 Yb-169 Curie Strength 1 _ 2""'62 _ _.______

3 _

Container ISORAD-TCl MPIC- Round Survey Meter S/N 9 ,;;;. .;:;.621_ ______

=.:9 _

Date of Survey14 DEC2020 Surveyor Rafael A. Bustillo lr-192 Extrapolated Readings from previous lr-192 direct survey test report Side of Highest Surface Highest Surface 1 m from Highest 1 m from Highest Container Reading mSv/hr Reading mR/hr Surface Reading ,4.urtace Reading Side1 12.1uz ,A\

V !:2Z.Q Side2 aQ:.ZZ 0.0197 !:2ZQ.

Side3 0.0196"' !:.2§Q.

Side4 0.508 50.75 0.0196 T 1.955

_A< .

Top 0.217 21.73 ,(0.0130 1.300 Bottom 0.0118 !:.!§Q.

Se-75 E xtrapo ate d R ead.ings (Ir-192 reading muI. tip I 1edb11,the ratio O.423)

Side of Highest Surface Highest Surface !"1 l m from Highest 1 m from Highest Container Reading mSv/hr Reading mR/hr Surface Reading Surface Reading Side1 Side2 0.215 21.492 --.j 21,476.J Q.OOS3 Q,0083 Q&.ll Side3 21.493 0.0083 -2:m Side4 21!1§2 Q,QQS3 Q.all Top

- 0.0055 Bottom r"'*

LY ll12 0.0050 Yb -169 Extrapolated Readings (lr-192 reading multipliedby the ratio0.261)

Side of Highet Surface Highest Surface 1 m from Highest 1 m from Highest Container Reading mSv/hr Reading mR/hr Surface Reading Surface Reading Side1 v Ull 0.0051

.\0.133 13.25 0.0051 0.514

'v J Side2 Side3 /8 'Y 0.133 13.26 0.0051 0.512 Side4:l 0.133 13.25 0.0051 0.510 Top 0.057 5.67 0.0034 0.339 Bottom Q.Jll!.a 0.0031 19 OCT2021 Page 6of6 Revision 1

ISO-RAD Canada Inc Ottawa, ON, Canada By: Kevin J. Schehr, DBA and Wayne Pettipas, Eng. T: +1-504-305-4320 T: +1-504-717-7811 (m)

Date: October 29, 2021 E: kjs@isorad-canada.com

Subject:

Thermal Conductivity and Heat Transfer Analysis Introduction The purpose of this report is to answer the United States Nuclear Regulatory Commission (USNRC)s Request for Additional Information (RAI) 3-1.

The RAI is as follows:

Provide temperature-dependent thermal properties or provide adequate justification for using single values for the thermal properties used to perform the thermal evaluation of the ISORAD-TC1 transportation package. Except for cork material, SAR Chapter 3 Thermal Evaluation provided only single values for thermal properties without adequate justification or explanation that single property values would be bounding. The staff needs this information to determine that adequate temperature dependent thermal properties are used in the analysis or to determine that single values bound the equivalent temperature-dependent property.

This information is needed to determine compliance with SSR-6 Paragraphs 654, 656, 657, and 728.

ISO-RAD Canada Inc. (ISO-RAD) detailed some of the thermal aspects of the ISORAD-TC1 in the Thermal Validation report as part of the answer for RAI 3-3. ISO-RAD continues with a brief overview of heat transfer then explores the effect of thermal conductivity on heat transfer. Next, presents the thermal conductivity and specific heat values for the metals contained in the ISORAD-TC1 package.

Then concludes with the effect of thermal conductivity and heat transfer on the surface temperature of the ISORAD-TC1.

Heat transfer occurs when there is a temperature differential between two materials or two objects.

Holman describes Conductive Heat Transfer as, When a temperature gradient exists in a body, experience has shown that there is an energy transfer from the high-temperature region to the low-temperature region. (pg. 1). The heat will flow from the higher temperature object to the lower temperature object as long as at least one degree Kelvin temperature differential exists. At some point in time, the temperatures will equal out and reach a steady state. The steady state is when both objects reach the same temperature and will stay there unless conditions change to create a new temperature differential.

Thermal conductivity is a component of heat transfer. Thermal conductivity refers to the value a metal, liquid, or gas and is expressed as W/m-°K. Thermal conductivity expresses the energy flowing/dissipating over a given area and, if it is a solid, the thickness of the solid is also a factor.

In the case of metals, as the temperature increases the thermal conductivity increases. The effects of temperature on the thermal conductivity, specific heat, and density of the materials included in the ISORAD-TC1 are shown in Table 1. Authoritative agreement of which thermal conductivity value to Revision 0

Thermal Conductivity Report October 29, 2021 Page 2 assign a metal at a certain temperature is in great debate. After researching several published articles and authoritative sources such as ASME Boiler and Pressure Vessel Code,Section II, Part D, Argonne National Lab, and Heat Transfer by Holman, one must conclude agreement on the thermal conductivity values or the specific heat values does not exist. The effect of higher thermal conductivity values is that the heat transfer from the hotter object to the colder object increases in speed.

Table 1: Thermal Properties of ISORAD-TC1 Package Materials Material Temp ° C Thermal Conductivity Specific Heat Density W/m*K J/kg/K Kg/m3 AISI 304 01 16.3 Room Temp 205 16.26 502.42 8030 205-213 16.3 -14.9 460 - 83 7817 - N/A 26.852 12.97 510.371 7894 383 15 486 -

933 16.1 506 -

1005 16 500 8000 1001 17 - -

126.852 14.59 523.768 7860 1493 16.9 520 -

2053 18 535 -

226.852 16.2 537.166 7823 2603 18.9 544 -

3001 19 - -

3163 19.5 551 -

326.852 17.82 550.564 7783 3713 20.4 559 -

426.852 19.44 564.38 7742 4273 21.1 562 -

526.852 21.06 577.778 7698 5383 22.8 577 -

5923 23.5 583 -

6001 22 - -

626.852 22.67 591.176 7652 6493 24.2 585 -

7053 25.1 591 -

726.852 24.29 604.574 7603 7603 25.8 596 -

8001 27 - -

8163 26.5 601 -

826.852 25.91 617.971 7552 Brass -165 -182.225 105.5 0 -1005 370-380 3.895 - - 8553 201 111 385 8522 1001 128 - -

2001 144 - -

238

Thermal Conductivity Report October 29, 2021 Page 3 Material Temp ° C Thermal Conductivity Specific Heat Density W/m*K J/kg/K Kg/m3 Titanium 205 17.15 581.97 4539.5 21.11 - 298.895 15.57 255 26.855 525 4510 126.855 20.4 555 4490 226.855 578 4480 326.855 19.4 597 4470 426.85 526.855 19.7 627 4440 726.855 20.7 670 4410 Uranium 04&6 23.1 117.5 18650 205 26.81 117.23 19016.1 21.11 - 298.895 24.41 1005 26.36 117.23 19016.1 127 29.6 3006 - 142 -

327 34 4006 32.5 - -

527 38.8 727 43.9 Cork -55 0.028

-0.156 0.055 - 290 321 0.045 1888 150 32.856 .06 - 290 87.856 .071 - 290 124.85 .0777 - 290 146.856 .081 - 290 Iridium 205 58.52 129.79 22503.76 22160

1. Holman, J. P., Heat Transfer, 10th Edition, McGraw-Hill, New York 2010.

2. Chong S. Kim, Thermophysical Properties of Stainless Steels, Argonne National Laboratory September, 1975.

3. American Society of Mechanical Engineers (ASME), Boiler and Pressure Vessel Code,Section II, Part D, 2001 Edition.

4. Lowenstein, Paul. Industrial Uses of Depleted Uranium. American Society for Metals. Metals Handbook, Volume 3, Ninth Edition

5. Eugene A. Avallone and Theodore Baumeister III, Mark's Standard Handbook for Mechanical Engineers, Tenth Edition, New York: McGraw-Hill, 1996. Pages 6-7, 6-11, 6-50, 6-51

6. Croft & Associates, Model 3977 Safety Analysis Report. 2012.

Thermal Conductivity Report October 29, 2021 Page 4 ISO-RAD Canada chose conservative values for the test parameters and settled on the stated values as reported in the ISORAD-TC1 SAR (See Table 2 and Table 3). The first two test conditions are under Normal Conditions for Transport (NCT) and the temperature ranges are on the lower end of the Thermal Conductivity scale. Under the Hypothetical Accident Conditions Test (HACT), the temperatures of the exterior of the AISI 304 stainless steel drum rose to just above 800°C and the thermal conductivity value ranges from 25.91 W/m-°K to 27 W/m-°K. At the same time, the ISORAD-TC1 inner container temperature remained at approximately 245°C. At 245°C, the inner container thermal conductivity values range from 16.2 W/m-°K to 18.9 W/m-°K.

Lower thermal conductivity values for the metals represents a more stringent test by potentially increasing the surface temperature. As demonstrated in the Thermal Analysis Validation report ISORAD-TC1 Hand Calculations, surface temperature is affected by changing the heat transfer coefficient (hc). Increasing the hc by 20% decreases the average surface temperature by less than 1°C.

Lowering the hc by 20% increases the average surface temperature by less than 1°C. By using higher Thermal Conductivity values, the average surface temperature will be lower.

Table 2: Mechanical Properties of Principal Transport Package Materials (SAR Table 2.2.1.A) 300 Series Brass Titanium Uranium Tungsten Cork Stainless Steel C360/C260/ Grade 2 (Depleted) #4 (Weathered)/ C230 #2 (Painted White)#1 Modulus of 190 GPa 100 GPa 116 GPa 205 GPa 400 GPa 0.02 GPa Elasticity (27 Mpsi) (15 Mpsi) (16.8 Mpsi) (30 Mpsi) (58 Mpsi) (0.0029 Mpsi)

Poissons 0.29 0.33 0.361 0.21 0.28 0.0 Ratio Density 8000 kg/m3 8500 kg/m3 4621 kg/m3 19,000 kg/m3 19,270 kg/m3 154.23 kg/m3 (0.29 lb/in3 (0.32 lb/in3) (0.163 lb/in3) (0.69 lb/in3) (0.70 lb/in3) (0.00544 lb/in3)

(Ultimate) 517 MPa 478 MPa 344 MPa 365 MPa 980 MPa 0.85 MPa Tensile (75 kpsi) (69 kpsi) (49.9 kpsi) (53 kpsi) (142 kpsi) (0.12 kpsi)

Strength Yield 207 MPa 240 MPa 275 MPa 172 MPa 750 MPa N/A Strength (30 kpsi) (35 kpsi) (39.9 kpsi) (25 kpsi) (109 kpsi)

Coefficient 17.3 µm/m°C 20.2 µm/m°C 8.90 µm/m°C 13.3 µm/m°C 4.5 µm/m°C 40 µm/m°C of Thermal (9.9 µin/in°F) (11.2 µin/in°F) (4.94 µin/in°F) (7.4 µin/in°F) (2.5 µin/in°F) (22.2 µin/in°F)

Expansion Thermal 16 W/m-°K 100 W/m-°K 11.4 W/m-°K 27.5 W/m-°K 163.3 W/m-°K 0.04 W/m-°K Conductivity (9.2 Btu/h-ft-°F) (63 Btu/h-ft-°F) (6.6 Btu/h-ft-°F) (16 Btu/h-ft-°F) (1130 Btu/h-ft-°F) (0.023 Btu/h-ft-°F)

Emissivity 0.85/0.992 0.22 0.31 0.15 0.23 (1500°C) 0.95 Specific 500 j/kg °K 390 j/kg °K 522.3 J/kg °K 120 j/kg °K 0.13 j/kg °K 2000 j/kg °K Heat (0.12 Btu/lb-F°) (0.09 Btu/lb-F°) (0.125 Btu/lb-F°) (0.03 Btu/lb-F°) (0.03 Btu/lb-F°) (0.48 Btu/lb-F°)

Melting 1,427 887/954/1000 1,668 1,130 3,410 400 Point °C

Thermal Conductivity Report October 29, 2021 Page 5 Table 3: Thermal Properties of Principal Transport Package Materials (SAR Table 3.2.A)

Material Density Melting/ Thermal Thermal Emissivity Modulus Source kg/m3 Combustion Expansion1 Conductivity Of (lb/in3) Temperature µm/m°C W/m-°K Elasticity

(µin/in°F) (Btu/h-ft-°F) GPa (Mpsi)

Depleted 19,000 1,130 13.3 27.5 0.15 205 #2, #1, Uranium (0.69) (2,066) (7.4) (16) (30) 6-11 Tungsten 19,270 3,370 4.5 163.3 0.23 400 #1, (0.70) (6,098) (2.5) (1130) (1500°C) (58) 6-51 Brass C360 8500 887°C(1628.6°F) 20.2 100 0.22 100 Brass C260 (0.32) 954°C (1749.2°F) (11.2) (63) (15)

Brass C230 1000°C(1832°F)

Titanium 4621 1,690°C 8.90 11.4 0.31 116 GPa #4, Grade 2 (0.163) (3,074°F) (4.94) (6.6) (16.8) 6-50 Stainless 8000 1,427 17.3 16 0.852 190 #1, Steel - 304 (0.29) (2,600) (9.9) (9.2) 0.9923 (27) 6-11 Cork 154.23 400 40 0.044 0.95 0.02 (0.00544) (752) (22.2) (0.023) (0.0029)

Conclusion The use of more conservative thermal conductivity values (lower) for the thermal simulation produced more conservative surface temperatures (higher). Therefore, the thermal simulation results are more stringent. Also, to be more conservative, the ISORAD-TC1 package thermal simulation analysis was conducted at 65 watts versus the actual package limit of 60.88 watts.

Kevin J. Schehr, DBA Managing Director ISO-RAD Canada Inc.

ML21330A020

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