ML121010475
| ML121010475 | |
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| Issue date: | 04/30/2012 |
| From: | Krotiuk W, Christopher Boyd NRC/RES/DSA |
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| S. Bajorek, RES/DSA | |
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ANALYSIS REPORT Comparisons of Jet Calculations to Test Data William J. Krotiuk Christopher Boyd April 2012 Office of Nuclear Regulatory Research Division of System Analysis
ii TABLE OF CONTENTS EXECUTIVE
SUMMARY
.......................................................................................................................... v
1.0 INTRODUCTION
.................................................................................................................................. 1 1.1 ANSI/ANS-58.2-1988 Jet Calculation....................................................................................... 1 1.2 Jet Calculation Using FLUENT ................................................................................................. 2 1.3 Marviken Full Scale Jet Impingement Tests .............................................................................. 3 2.0 ANSI/ANS-58.2-1988 JET MODEL AND TEST DATA COMPARISONS ........................................ 6 2.1 Comparisons with the Marviken Full Scale Jet Impingement Test 5.............................6 2.2 Comparisons with the Marviken Full Scale Jet Impingement Test 6...........................29
3.0 CONCLUSION
S................................................................................................................................... 67
4.0 REFERENCES
..................................................................................................................................... 69 iii
iv EXECUTIVE
SUMMARY
The objective of this study is to assess the jet calculation methodology contained in ANSI/ANS-58.2-1988 by comparing calculated results to test data for subcooled, saturated liquid, two-phase and steam jets obtained from the Marviken Full Scale Jet Impingement Tests. The ANSI/ANS-58.2-1988 predictions for a one-phase steam jet are also compared to computational fluid dynamics (CFD) results from the FLUENT code.
This report provides plots comparing the calculated jet impingement pressures to static and total pressures measured axially and radially within the jet for Marviken tests 5 and 6. The jet pressure distribution calculated using the ANSI/ANS-58.2-1988 standard is a local impingement pressure. Impingement pressure is a key parameter for assessing debris generation. (Impingement pressure is also referred to as jet pressure in some documents.) The impingement pressure includes entropy losses resulting from the impact of the fluid on a large object. Similarly, the measured stagnation pressure in a supersonic flow will include entropy losses as the flow passes through the shock wave that forms in front of the probe. (The Marviken reports use the terms total and stagnation pressure interchangeably.) The impingement pressure is generally higher than the stagnation pressure in the jet because it includes the thrust coefficient in the calculation of the jet impingement pressure. It is considered appropriate to compare the ANSI/ANS-58.2-1988 calculated impingement pressure to the measured total pressure because the impingement pressure which is defined as the load on an impinged surface divided by impinged area is the closest comparison to a measured total pressure.
The jet centerline is the most important location for comparing ANSI/ANS-58.2-1988 impingement pressure predictions with test data because the jet centerline pressures are considered in the determination of the Zone of Influence (ZOI) used in determining debris generation.
The jet calculation model in the ANSI/ANS-58.2-1988 will produce conservative to realistic impingement pressures for subcooled, saturated liquid and low-quality jets when using the recommended Henry-Fauske critical flow correlation for calculating jet nozzle flow rate. This conclusion has been reached by comparing calculations for impingement pressure to measured total pressures from the Marviken Full Scale Jet Impingement Test 6 for a break nozzle diameter of 509 mm (20.04 inches) and total pressures upstream of the jet nozzle ranging from 4049 to 2974 kPa (587.26 to 431.34 psia) with a maximum subcooling of 16°C (28.8°F).
Only one test time from the Marviken Full Scale Jet Impingement test 6 provides two-phase jet test data which can be compared to the ANSI/ANS-58.2-1988 jet calculation method using the HEM critical flow correlation. The impingement pressure calculations for this two-phase jet conditions did not always bound the measured total pressures on the radial probe supports; however, the calculated impingement pressures are close to or bound total pressure measurements along the centerline of the jet. Therefore, the conclusion that could be reached is that the ANSI/ANS-58.2-1988 calculation method provides only marginally acceptable impingement pressures near the external edges of a two-phase jet but conservative impingement pressures along the jet centerline. These conclusions were reached for a break nozzle diameter of 509 mm (20.04 inches) and a total pressure upstream of the jet nozzle of 1970 kPa (285.72 psia) with a quality of 4% ( ~70%).
In general, comparisons for the test 6 subcooled, saturated liquid and two-phase jets indicate that the ANSI/ANS-58.2-1988 model centerline impingement pressures at a specific centerline distance approximately equal or bound the total pressure test measurements at the same centerline location.
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A total of four steam jet test cases from the Marviken Full Scale Jet Impingement Tests were studied.
Three cases from Marviken test 5 used a 299 mm (11.77 inch) nozzle and one case from Marviken test 6 used a 509 mm (20.04 inches) nozzle. The total pressures upstream of the jet nozzle ranged from 4420 to 1345 kPa (641.07 to 195.08 psia). At the jet centerline the impingement pressures calculated using the ANSI/ANS-58.2-1988 jet calculation method provided conservative to realistic predictions of total pressure measured during testing.
It can generally be concluded from the Marviken test 5 and 6 steam jets cases test that the ANSI/ANS-58.2-1988 jet calculation model predicts conservative impingement pressures at the jet centerline. The model predicts conservative radial pressures at larger axial distances from the jet nozzle. The calculation under predicts the impingement pressure closer to the nozzle at some radial locations away from the centerline. The measured stagnation test data and CFD predicted stagnation pressures for the test 5 and test 6 steam jet cases indicate that peak pressures can exist at the jet edges due to the presence of regions of high Mach number. Comparisons between the ANSI/ANS-58.2-1988 model jet centerline impingement pressures and the CFD calculated total pressures near the jet edges show that the calculated jet centerline impingement pressures at a specific centerline distance always bound or approximately equal the CFD calculated radial total pressures at the same centerline distance and the total pressure test measurements at the same centerline location.
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1.0 INTRODUCTION
The objective of this study is to assess the acceptability of the jet calculation methodology contained in ANSI/ANS-58.2-1988 (reference 1) by comparing calculated results to test data for subcooled, saturated liquid, two-phase and steam jets obtained from the Marviken Full Scale Jet Impingement Tests (reference 3). The ANSI/ANS-58.2-1988 jet calculation results for a one-phase steam jet will also be compared to computational fluid dynamics (CFD) analysis results performed using the ANSYS/FLUENT (reference 2) code.
1.1 ANSI/ANS-58.2-1988 Jet Calculations The ANSI/ANS-58.2-1988 standard includes guidelines for evaluating jet impingement effects resulting from a high energy line break. The standard requires that systems and components should be protected or designed to withstand the results of a jet impingement. Additional concerns currently exist which relate to the debris generated as the result of a jet impingement on a surface and the effects that generated debris would have on the ability to cool a reactor core following a loss-of-coolant accident (LOCA). Appendices C and D of the standard describe a method for determining jet impingement forces and jet impingement pressures.
Although not specifically stated, the jet pressure distribution calculated using Appendix D of the ANSI/ANS-58.2-1988 standard is a local impingement pressure. The impingement pressure is the property that is important in assessing debris generation. (Impingement pressure is also referred to as jet pressure in some documents.) The impingement pressure includes entropy losses resulting from the impact of the fluid on a large object. In contrast, stagnation pressure is related to the entropy loss for flow along a streamline. The impingement pressure is generally higher than the stagnation pressure in the jet.
The ANSI/ANS-58.2-1988 standard states that the jet impingement load on a target may be calculated by establishing the pressure distribution on the target and integrating the pressure over the target surface.
The standard additionally states that the response of a target to a jet impingement loading is a function of the stiffness of the target and the jet impingement loading rate. The response of a target can be determined from a structural dynamic analysis or from a static analysis which uses a dynamic load factor (DLF). The ANSI/ANS-58.2-1988 standard refers to the DLF and a thrust coefficient (CT) interchangeably and includes the trust coefficient in the calculation of the jet impingement pressure.
The ANSI/ANS-58.2-1988 standard states that the most severe temperature produced by a jet at an impinged surface occurs when the jet is stagnated (stopped), resulting in a jet temperature on the target surface which is equal to or higher than the static temperature. However, the standard states that appropriate consideration can be given to the heat transfer from the fluid jet to the target and conduction within the target. Since stagnation can only occur at a single point, the standard states that the fluid conditions on a target are more realistically represented by the static fluid conditions. Consequently, the standard considers it conservative to assume that the target surface temperature is equal to the jet temperature at static conditions.
The jet calculation method described in the ANSI/ANS-58.2-1988 standard has been criticized and questioned by members of the Advisory Committee on Reactor Safeguards (ACRS) in references 6, 7 and
- 8. Reference 6 expressed concerns regarding several inconsistencies and errors in the zone-of-influence (ZOI) model based on the standard. The concerns regarding the jet model in the ANSI/ANS-58.2-1988 standard are expanded in the critical reviews from Graham Wallis and Victor Ransom provided in references 7 and 8.
1
Because of the criticisms regarding the jet model contained in the ANSI/ANS-58.2-1988 standard it was concluded that an assessment be made in which jet calculations performed using the standard model be compared to jet test data. Specifically, the jet calculations from the standard would be compared to the Marviken jet test data described in section 1.3.
A computer program was created which programmed the ANSI/ANS-58.2-1988 standard jet model in order to facilitate comparisons to test data. The computer program follows the jet model approaches contained in the standard. The only deviation relates to the calculation of choked flow conditions at the break nozzle. The standard indicated that the Moody critical flow model or the homogeneous equilibrium model (HEM) were acceptable for calculating break flow for flashing or steam-water mixtures. For subcooled flow the standard indicated that the Henry-Fauske model was acceptable. The computer program created for this study employs the HEM critical flow model for all conditions. Reference 9 compares various critical flow models with experimental measurements. This report concludes that the HEM provides the best prediction of critical flow rates except at low qualities where it under predicts the critical flow rates. Consequently, the comparisons between the ANSI/ANS-58.2-1988 standard jet model calculated results and the measured data reported in this study will account for the probable under prediction of break flow for the subcooled and low quality region.
1.2 Jet Calculations Using FLUENT The FLUENT computational fluid dynamics (CFD) code is used to predict the flow conditions downstream of the nozzle for selected single phase conditions of the Marviken tests. Two-phase jet predictions with FLUENT were not attempted due to the limitations in the two-phase models within the code. FLUENT is a general purpose commercial CFD code with a variety of solver and modeling options.
The following options were used for the Marviken test predictions.
- Fluent v13
- steady state, axisymmetric solver
- pressure based solution
- k-omega turbulence model with compressibility, shear flow, and viscous heating options
- k-epsilon turbulence model compared as sensitivity study
- energy equation
- water vapor assumed to be ideal gas
- total pressure and temperature boundary conditions upstream of nozzle
- 2nd order differencing
- mesh refinement for shock capture The FLUENT code proved to be very unstable and required a carefully controlled solution procedure to ensure convergence with mass and energy balances. The basic process involved setting an initial CFL number less than 1 (0.1 was used) and increasing it slowly as unstable oscillations were reduced. A slight reduction in the under-relaxation factors was also applied in the code. The CFL number was increased to values greater than 100 as the solution proceeded.
The axisymmetric domain for the model was 10 m long in the axial direction and 4 m high in the radial direction. The nozzle centerline was on the axis and the nozzle exit was 2.18 m from the upstream edge of the model leaving 7.82 m of distance between the nozzle exit and the outlet boundary of the solution domain. The model included the central axial probe from the test setup but did not include the radial wings that held the pressure taps. Predictions were completed for the following conditions for tests 5 and 6.
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- Test 5, 10 seconds o P0 = 4,521 kPa (655.77 psia) total pressure upstream of nozzle o T0 = 255oC (491.0°F) total temperature upstream of nozzle o d = 0.299 m (11.77 inches) nozzle diameter
- Test 5, 40 seconds o P0 = 3,020 kPa (438.01 psia) total pressure upstream of nozzle o T0 = 232.7oC (450.9°F) total temperature upstream of nozzle o d = 0.299 m (11.77 inches) nozzle diameter
- Test 6, 75 seconds o P0 = 1,350 kPa (195.80 psia) total pressure upstream of nozzle o T0 = 189oC (372.2°F) total temperature upstream of nozzle o d = 0.509 m (20.04 inches) nozzle diameter FLUENT predicts the pressures, temperatures, velocities, and turbulence levels throughout the solution domain. The CFD model does not include the wings housing the pressure taps that spanned laterally from the central probe. These wings would stagnate the flow and a shock wave would form just upstream of the wing surface when in supersonic flows. Total pressure predictions from the CFD code are the full total pressure of the flow without the presence of the shock wave caused by the probe. Total pressure reported from the CFD code will be higher than the measured total pressures due to the presence of the shock wave. In order to compare the FLUENT predictions of total pressure to the measured total pressures a normal shock relation is used from the NACA report 1135 (reference 11).
/(1) 1/(1) 2 ( + 1)12 ( + 1)
=
1 ( 1)12 + 2 212 ( 1) 1 = Total pressure upstream of normal shock 2 = Total pressure downstream of normal shock 1 = Mach number upstream of normal shock
= specific heat ratio (1.3 used for steam)
This relation provides a means to determine the total pressure ratio across a normal shock. It is assumed that the flow is normal to the shock wave that forms in front of the probe support wings. The flow behind this shock will be subsonic and the total pressure measured by the probe is indicative of the total pressure behind the shock. This relation was used to apply a correction to the predicted total pressures from FLUENT in the areas where the flow was supersonic (M > 1). The FLUENT prediction of total pressure is assumed to be the upstream value (1 ) and the measured value is compared to the downstream value (2 ). It is noted that only the total pressure plots are corrected since these provide a direct comparison to the measured data. The contour plots of total pressure and all other reported values are not adjusted in this manner and come directly from the code.
1.3 Marviken Full Scale Jet Impingement Tests Test data obtained from the Marviken Full Scale Jet Impingement Tests are compared to results obtained using the ANSI/ANS-58.2-1988 jet calculation method and to the FLUENT predictions.
The Marviken tests investigated the behavior of jets and the loads experienced by targets in the jet stream.
Reference 3 provides a description of the test facility. Free expansion jets and jets directed towards 3
instrumented targets were included in the test program. The free expansion jets provided information about the axial and radial pressure distribution in the jet, and the jet impingement tests measured the total target force and the force distribution on the targets in the jet stream.
A total of twelve tests were performed with an initial vessel pressure upstream of the break nozzle of about 5 MPa (725 psia). Tests 1 through 6 were free jet expansion tests and tests 7 through 12 were jet impingement tests. The breaks were simulated using nozzles with diameters of 200, 299 and 509 mm (7.87, 11.77 and 20.04 inches). Test 5 and 6 provided the best free jet test data. Earlier free jet tests exhibited problems with the test measurement assembly which affected test measurements. Consequently, data from tests 5 and 6 will be used to compare to calculations. Test 5 was a single-phase steam test which used a 299 mm (11.77 inch) diameter nozzle. Test 6 consisted of various conditions upstream of the nozzle which included subcooled liquid, saturated liquid, two-phase and steam conditions. Test 6 used a 509 mm (20.04 inch) nozzle.
A central instrument probe having a diameter of 100 mm (3.94 inches) extended into the nozzle during the free jet tests. An instrumented test assembly was located below the test nozzle for the free jet tests.
This test section consisted of a central probe and six radial instrumented support beams located at five axial distances from the break nozzle. The beams were with the leading edge 0.15, 0.5, 1.0 1.5 and 2.0 meters (5.906, 19.685, 39.37, 59.055 and 78.74 inches) downstream of the nozzle. Beam 0 was positioned at the 0.15 meter location, beam 1 was at the 0.5 meter location, beams 2 and 3 were at the 1.0 meter location, beam 4 was at the 1.5 meter location and beam 5 was at the 2.0 meter location. This instrumentation permitted the measurement of static and total pressures at axial and radial locations downstream of the nozzle. The Marviken reports use the terms stagnation pressure and total pressure interchangeably. The stagnation or total pressure is the sum of the static pressure and the dynamic pressure.
The pressure source for the Marviken jet tests was a pressure vessel located upstream of the break nozzle.
During testing the vessel pressure was allowed to decrease as flow exited the nozzle. Consequently jet conditions were obtained at various upstream pressures during testing. Additionally, for test 6 the upstream fluid conditions varied during testing which enabled test results to be obtained for subcooled liquid, saturated liquid, two-phase and steam conditions.
Because the test durations extended over a period of time, specific test times were chosen for comparison to test calculations. Table 1.3-1 lists the test 5 conditions at the three times (10, 40 and 80 seconds) which were used for comparison with calculations. As previously stated, test 5 (reference 4) was a one-phase steam jet test. Similarly, Table 1.3-2 lists the conditions for test 6 (reference 5) at six times (5, 10, 20, 45, 60 and 75 seconds) which are used for comparison to calculations. The test 6 jet points include three upstream subcooled liquid conditions, one upstream saturated liquid condition, an upstream two-phase condition and a steam condition.
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Table 1.3-1: Marviken Steam Jet Test 5 Assessed Conditions (Nozzle diameter = 299 mm = 11.77 inches)
Analyzed Time 10 s 40 s 80 s Stagnation Pressure at 4420 kPa 2 3030 kPa 2 1970 kPa 2 Nozzle Entrance 641.07 psia 439.46 psia 285.72 psia (Diagram E:4) 1 Fluid State at Nozzle = 99.8% = 99.9% = 99.9%
(Diagram E:5) 1 x = 97% x = 99% x = 97%
Nozzle Temperature 255°C 233°C 210°C (Diagram E:3) 1 491.0°F 451.4°F 410.0°F Mass Flux 5900 kg/m2/s 2 3800 kg/m2/s 2 2400 kg/m2/s 2 (Diagram E:12) 1 1208.4 lbm/ft2/s 778.3 lbm/ft2/s 491.6 lbm/ft2/s Containment Pressure 107 kPa 105 kPa 103 kPa (Diagrams E:14, 15, 16, 17)1 15.52 psia 15.23 psia 14.94 psia 1
The Marviken Full Scale Jet Impingement Tests - Fourth Series, MXD-205 Interim Report - Results from Test 5, MX4-15, Studsvik - The Marviken Project, March 1981.
2 The Marviken Full Scale Jet Impingement Tests - Fourth Series, MXD-301 Interim Report -
Summary Report, MX4-20, Studsvik - The Marviken Project, August 1981.
Table 1.3-2: Marviken Jet Test 6 Assessed Conditions (Nozzle Diameter = 509 mm = 20.04 inches)
Time Duration 0 s - 36 s 36 s - 48 s 51 s - 73 s 73 s - 77 s Analyzed Time 5s 10 s 20 s 45 s 60 s 75 s Stagnation 4049 kPa 2 3778 kPa 1 3330 kPa 1 2974 kPa 2 2640 kPa 1 1345 kPa 2 Pressure at 587.26 psia 547.95 psia 482.98 psia 431.34 psia 382.90 psia 195.08 psia Nozzle Entrance (Diagram E:3) 1 Fluid State at Subcooled Subcooled Subcooled Saturated Two-Phase Steam Nozzle Liquid Liquid Liquid Liquid (Diagram E:14, 15, 4) 1 16°C 2 11°C, 5°C = 20% 2 = 70% = 99.5% 2 28.8°F 19.8°F 9°F x = 0.45% x = 4% x = 70%
Nozzle 233°C 233.5°C 234°C 232°C 226°C 189°C Temperature 451.4°F 452.3°F 453.2°F 449.6°F 438.8°F 372.2°F (Diagram E:2) 1 Mass Flux 42,000 35,600 27,000 17,000 11,000 2,000 (Diagram E:12) 1 kg/m2/s 2 kg/m2/s kg/m2/s 1 kg/m2/s 2 kg/m2/s 1 kg/m2/s 2 8602.3 7291.1 5530.0 3481.9 2253.0 409.6 lbm/ft2/s lbm/ft2/ lbm/ft2/s lbm/ft2/s lbm/ft2/s lbm/ft2/s Containment 249 kPa 2 260 kPa 244 kPa 1 157 kPa 2 140 kPa 1 120 kPa 2 Pressure 36.11 psia 37.71 psia 35.39 psia 22.77 psia 20.31 psia 17.40 psia (Diagrams E:14, 15, 16, 17)1 1
The Marviken Full Scale Jet Impingement Tests - Fourth Series, MXD-206 Interim Report - Results from Test 6, MX4-18, Studsvik - The Marviken Project, April 1981.
2 The Marviken Full Scale Jet Impingement Tests - Fourth Series, MXD-301 Interim Report -
Summary Report, MX4-20, Studsvik -The Marviken Project, August 1981.
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2.0 ANSI/ANS-58.2-1988 JET MODEL AND TEST DATA COMPARISONS This section compares the ANSI/ANS-58.2-1988 jet model calculations to measured data from the Marviken jet tests 5 and 6. The computer program mentioned in section 1.1 was used to calculate jet conditions using the test conditions at the test times listed in Tables 1.3-1 and 1.3-2.
Sections 2.1 and 2.2 provide plots which compare the calculated jet impingement pressures to static and total pressures measured axially and radially within the jet. It is considered appropriate to compare the ANSI/ANS-58.2-1988 calculated impingement pressure to the measured total pressure because the impingement pressure which is defined as the load on an impinged surface divided by impinged area is the closest comparison to a total pressure. (The Marviken reports use the terms total and stagnation pressure interchangeably.)
The jet centerline is the most important location for comparing ANSI/ANS-58.2-1988 impingement pressure predictions with test data because the jet centerline pressures are considered in the determination of the Zone of Influence (ZOI) used in determining debris generation.
Table 2.1-1: Marviken Jet Test 5 Conditions for ANSI/ANS-58.2-1988 Jet Calculation (Nozzle diameter = 299 mm = 11.77 inches)
Analyzed Time 10 s 40 s 80 s Input and Measured 4420 kPa 3030 kPa 1970 kPa Stagnation Pressure 641.07 psia 439.46 psia 285.72 psia Fluid State Steam Steam Steam Calculated = 99.91% = 99.98% = 99.96%
Input and Measured x x = 97% x = 99% x = 97%
Calculated Temperature 256.3°C 234.4°C 211.6°C 493.38°F 453.91°F 412.90°F Measured Nozzle 255°C 233°C 210°C Temperature 491.0°F 451.4°F 410.0°F Input and Measured 107 kPa 105 kPa 103 kPa Containment Pressure 15.52 psia 15.23 psia 14.94 psia Calculated Critical 6,334 kg/m2/s 4,308 kg/m2/s 2,843 kg/m2/s Mass Flux1 1,297.4 lbm/ft2/s 882.4 lbm/ft2/s 582.3 lbm/ft2/s Measured Mass Flux 5,900 kg/m /s 2
3,800 kg/m /s 2
2,400 kg/m2/s 1,208.4 lbm/ft2/s 778.3 lbm/ft2/s 491.6 lbm/ft2/s (Calculated -Measured) 0.074 0.134 0.184 Measured Mass Flux 1
Mass flux is calculated using HEM choking model for liquid and two-phase nozzle conditions, and the maximum of HEM and sonic choking for vapor conditions. The ANSI standard recommends the Henry-Fauske model for subcooled conditions, and the Moody or HEM model for flashing or steam-water mixtures.
2.1 Comparisons with the Marviken Steam Jet Impingement Test 5 The computer program mentioned in section 1.1 was used to calculate the steam jet conditions for Marviken test 5 at the times and conditions listed in Table 1.3-1. Table 2.1-1 lists the measured input and calculated conditions from the programmed ANSI/ANS-58.2-1988 jet model calculations. As indicated on this table, the nozzle diameter used for Marviken test 5 was 299 mm (11.77 inches).
6
The calculated and measured fluid temperatures and void fractions for the three cases are close in value.
The differences between the measured and calculated mass fluxes for the three cases vary between 7.4%
and 18.4% which are close enough to permit comparison of the ANSI/ANS-58.2-1988 jet plume calculation results.
Figures 2.1-4 to 2.1-10 compare the calculated jet plume impingement pressures and static pressure at 10 seconds to measured static and total (stagnation) pressure conditions in the jet plume. Figures 2.1-14 to 2.1-20 compare the pressure predictions to measurements at 40 seconds and Figures 2.1-22 to 2.1-28 compare the pressure predictions to measurements at 80 seconds. Figures 2.1-1, 2.1-11 and 2.1-21 show the calculated impingement pressure contour plots for the steam jet at 10, 40 and 80 seconds.
2.1.1 Comparisons with the Marviken Steam Jet Impingement Test 5 at 10 Seconds The Marviken test 5 conditions used for this assessment are listed on Table 2.1-1. Figures 2.1-4 to 2.1-9 plots the calculated and measured static pressures, the measured total pressure and the calculated impingement pressure at the jet centerline and at radial locations for measurement beams 0, 1, 2, 3, 4 and
- 5. Figure 2.1-1 shows the calculated impingement pressure half-jet contour plot. The plots include CFD total pressure predictions along the jet centerline, for a radial location for beam 1 at a jet axial location about 20 inches (~1.7 L/d) from the nozzle and for a radial location for beams 2 and 3 at a jet axial location about 40 inches (~3.4 L/d) from the nozzle.
For the steam jet conditions at 10 seconds, the calculated centerline impingement pressures (Figure 2.1-4) are larger than the pressure measurements. The calculated centerline impingement pressures significantly exceed the static pressure measurement; however, calculated impingement pressures generally exceed the total pressures measured 70 mm (2.76 inches) radially from the centerline by a much smaller amount. The calculated impingement pressure and the measure total pressure 20 inches (1.7 L/d) from the nozzle are approximately equal in value. Near the jet source, the calculated impingement pressure exceeds the total pressure measurement by less than 40%. Further from the nozzle the calculated impingement pressure exceeds the measured total pressure by a larger percentage; but the magnitudes of the impingement pressure at those positions are less than 100 psia (6.9 x 105 Pa). The only static pressure calculated using the ANSI/ANS-58.2-1988 method is at the asymptotic plane located between regions 2 and 3 defined in the standard. The asymptotic plane is calculated to be at an axial location 24.19 inches (2.1 L/d) from the nozzle. The calculated static pressure agrees well with the test measurement.
The static pressure measurement location on beam 0 is axially located about 250 mm (9.84 inches) (~0.84 L/d) from the nozzle and the single total pressure measurement point is axially located 125 mm (4.92 inches) (0.42 L/d) from the nozzle. These measured pressures are compared to the calculated impingement pressure 10.46 inches (0.89 L/d) from the nozzle on Figure 2.1-5. This figure plots predicted and measured pressures as a function of jet plume radius. The calculated impingement pressure significantly exceeds the measured static pressure near the nozzle, but approaches the measurement about 20 inches radially from the plume centerline. The pressures at positions greater than 20 inch radius are at or below ambient pressure. It should be noted that the measured total pressure exceeds the calculated impingement pressure by a factor of approximately two at a position about 5 inches (~0.42 L/d) from the nozzle at a radius of about 2.7 inches. This indicates that the jet plume calculation is nonconservative at radial positions less than about 10 inches (~0.85 L/d) from the jet nozzle.
Figure 2.1-6 compares pressure predictions and measurements axially located about 20 inches (~1.7 L/d) from the jet nozzle as a function of jet plume radius. This figure shows that the calculated jet plume impingement pressure agrees closely with the measured total pressures, but exceeds the static pressure measurement. The calculated pressure approaches pressures at or below ambient at a radius of about 25 7
inches and the total pressure measurement approaches pressures at or below ambient at a 20 inch radius.
This figure indicates that the impingement pressure determined by the jet plume calculation predicts the measured total pressure at a 20 inches radius from the jet nozzle at about a 20 inch (~1.7 L/d) axial location from the nozzle. This figure includes the calculated static pressure at the region 2-3 asymptotic point 24.19 inches from the nozzle. The calculated static pressure agrees well with the static pressure measurement located about 6 radial inches from the jet centerline Figure 2.1-7 compares predicted and measure pressures axially located about 40 inches (~3.4 L/d) from the jet nozzle. The calculated impingement pressure exceeds the measured total pressure for the first 10 radial inches and then approaches the measurement. Pressure predictions approach ambient or fall below ambient pressure at a radius of about 30 inches. The pressure predictions exceed the measured static pressure up until the 30 inch radius position.
Figure 2.1-8 compares radial pressure predictions and measurements at a position about 60 inches (~5.1 L/d) from the jet nozzle. This figure displays the same behaviors as at the 40 inch (3.4 L/d) axial position (Figure 2.1-7).
Figure 2.1-9 shows pressure comparisons at about 80 inches (~6.8 L/d) from the jet nozzle. The pressure comparisons in this figure are similar to those observed at the 40 and 60 inch (3.4 and 5.1 L/d) axial positions (Figures 2.1-7 and 2.1-8).
Figure 2.1-4 shows CFD predictions of total pressure along the probe axis taken at locations 70 mm from the center line corresponding to the test measurement locations. The predictions are below or close to the test data points and are generally below the ANSI/ANS predictions. The radial predictions on beams 1 and beams 2 and 3 shown on Figures 2.1-6 and 2.1-7 are generally consistent with the data also. The CFD predictions show significant radial variations due to the shock patterns that are clearly seen in Figure 2.1-
- 2. The test data does not have the resolution to show these patterns. The ANSI/ANS model does not account for these high pressure regions either. The CFD predictions are higher than the ANSI/ANS predictions at radial locations corresponding to the high Mach number regions at the outer edges of the main jet region (see Figure 2.1-3).
The test data and CFD analysis for the steam jet at 10 seconds indicate that peak pressures can exist at the jet edges due to the presence of regions of high Mach number. Consequently, the jet centerline conditions may not represent the sole consideration in determining the ZOI if the total pressures at the jet edge are larger than jet centerline pressures at the same axial distance from the jet source. Comparisons between the ANSI/ANS-58.2-1988 model jet centerline impingement pressures in Figure 2.1-4 and the CFD calculated total pressures near the jet edges in Figures 2.1-6 to 2.1-7 show that the calculated jet centerline impingement pressures at a specific jet centerline distance always bound or equal the CFD calculated stagnation pressure at any radial distance at the same centerline distance.
It can generally be concluded from this test that the ANSI/ANS-58.2-1988 jet plume calculation model predicts conservative to realistic impingement pressures at the jet centerline. The model also predicts conservative radial impingement pressures at axial distances greater than about 10 inches (~0.85 L/d) from the jet nozzle. The calculation under predicts by about 50% the impingement pressure about 5 inches (~0.42 L/d) from the nozzle at a radius of about 2.7 inches. However, the centerline impingement pressures at a specific centerline distance always bound the radial total pressure test measurements at the same centerline location. This conclusion is illustrated in Figure 2.1-10 which compares the ANSI/ANS-58.2-1988 model jet centerline impingement pressures to the measured total pressures at several radial locations at several axial positions.
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Figure 2.1-1: Jet Impingement Pressure Contour for Marviken Test 5 at 10 Seconds 9
Figure 2.1-2: Mach Number Contour from CFD Model for Marviken Test 5 at 10 Seconds 10
Figure 2.1-3: Total Pressure (psig) Contour from CFD Model for Marviken Test 5 at 10 Seconds 11
Figure 2.1-4: Pressures at Jet Plume Centerline for Marviken Test 5 at 10 Seconds Figure 2.1-5: Pressures at Beam 0 in Jet Plume for Marviken Test 5 at 10 Seconds 12
Figure 2.1-6: Pressures at Beam 1 in Jet Plume for Marviken Test 5 at 10 Seconds Figure 2.1-7: Pressures at Beams 2 and 3 in Jet Plume for Marviken Test 5 at 10 Seconds 13
Figure 2.1-8: Pressures at Beam 4 in Jet Plume for Marviken Test 5 at 10 Seconds Figure 2.1-9: Pressures at Beam 5 in Jet Plume for Marviken Test 5 at 10 Seconds 14
Figure 2.1-10: Centerline and Radial Jet Pressure Comparisons for Marviken Test 5 at 10 Seconds 15
2.1.2 Comparisons with the Marviken Steam Jet Impingement Test 5 at 40 Seconds The Marviken test 5 conditions used for this assessment are listed on Table 2.1-1. Figure 2.1-11 provides a half-jet contour plot of the calculated impingement pressures from the ANSI/ANS-58.2-1988 model.
Figure 2.1-12 and 2.1-13 provide contour plots of the predicted Mach number and total pressure from the CFD model. The CFD model includes the central probe. Figures 2.1-14 to 2.1-19 plot the calculated static and impingement pressures and the measured static and total pressures at the jet centerline and at radial locations for measurement beams 0, 1, 2, 3, 4 and 5. The comparisons of the behavior of the calculated and measured pressures are similar to those for the 10 second measurement discussed in section 2.1.1.
However, the magnitudes of the pressures are lower at 40 seconds because the stagnation source pressure at 40 seconds (3030 kPa, 439.46 psia) is lower than that at 10 seconds (4420 kPa, 641.07 psia).
These plots include the CFD predictions that were completed for test 5 at 40 seconds. The CFD predictions of total pressure along the probe axis are taken at locations 70 mm from the center line corresponding to the test measurement locations. The predictions agree very well with the test data points and are generally below the ANSI/ANS predictions. The radial predictions on beam 0 through 5 are generally consistent with the data also. The CFD predictions show significant radial variations due to the shock patterns that are clearly seen in Figure 2.1-12. The test data does not have the resolution to show these patterns. The ANSI/ANS model does not account for these high pressure regions either. The CFD predictions are higher than the ANSI/ANS predictions over the first 8 inches of beam 0 and at radial locations corresponding to the high Mach number regions at the outer edges of the main jet region (see Figure 2.1-13).
As seen for the steam jet at 10 seconds, the test data and CFD analysis for the steam jet at 40 seconds indicate that peak pressures can exist at the jet edges due to the presence of regions of high Mach number.
Consequently, the jet centerline conditions may not represent the sole consideration in determining the ZOI if the total pressures at the jet edge are larger than jet centerline pressures at the same axial distance from the jet source. Comparisons between the ANSI/ANS-58.2-1988 model jet centerline impingement pressures in Figure 2.1-14 and the CFD calculated total pressures near the jet edges in Figures 2.1-16 and 2.1-17 show that the calculated jet centerline impingement pressures at a specific jet centerline distance always bound or equal the CFD calculated stagnation pressure at any radial distance at the same centerline distance.
The conclusions regarding the relationship between the calculated jet conditions and the measurement are identical to those observed for the assessments at 10 seconds. It can generally be concluded from this test that the ANSI/ANS-58.2-1988 jet plume calculation model predicts conservative impingement pressures at the jet centerline. The model also predicts conservative radial pressures at axial distances greater than about 10 inches (~0.85 L/d) from the jet nozzle with the exception of the high Mach number regions identified by the CFD predictions. The calculation under predicts by about 30% the impingement pressure about 5 inches (~0.42 L/D) from the nozzle out to a radius of about 8 inches. However, comparisons between centerline impingement pressures at a specific centerline distance always bound or equal the CFD calculated radial total pressures at the same centerline distance and the total pressure test measurements at the same centerline location. This conclusion is also illustrated in Figure 2.1-20 which compares the ANSI/ANS-58.2-1988 model jet centerline impingement pressures to the measured total pressures at several radial locations at several axial positions and also to the maximum calculated total pressure at several axial centerline positions.
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Figure 2.1-11: Jet Impingement Pressure Contour for Marviken Test 5 at 40 Seconds 17
Figure 2.1-12: Mach Number Contour from CFD Model for Marviken Test 5 at 40 Seconds 18
Figure 2.1-13: Total Pressure (psia) Contour from CFD Model for Marviken Test 5 at 40 Seconds 19
Figure 2.1-14: Pressures at Jet Plume Centerline for Marviken Test 5 at 40 Seconds Figure 2.1-15: Pressures at Beam 0 in Jet Plume for Marviken Test 5 at 40 Seconds 20
Figure 2.1-16: Pressures at Beam 1 in Jet Plume for Marviken Test 5 at 40 Seconds Figure 2.1-17: Pressures at Beams 2 and 3 in Jet Plume for Marviken Test 5 at 40 Seconds 21
Figure 2.1-18: Pressures at Beam 4 in Jet Plume for Marviken Test 5 at 40 Seconds Figure 2.1-19: Pressures at Beam 5 in Jet Plume for Marviken Test 5 at 40 Seconds 22
Figure 2.1-20: Centerline and Radial Jet Pressure Comparisons for Marviken Test 5 at 40 Seconds 2.1.3 Comparisons with the Marviken Steam Jet Impingement Test 5 at 80 Seconds The Marviken test 5 conditions used for this assessment are listed on Table 2.1-1. A half-jet contour plot of the calculated impingement pressures is shown on Figure 2.1-21. Figures 2.1-22 to 2.1-27 plot the calculated static and impingement pressures and the measured static and total pressures at the jet centerline and at radial locations for measurement beams 0, 1, 2, 3, 4 and 5. The comparisons of the behavior of the calculated and measured pressures are similar to those for the 10 and 40 second measurement times discussed in sections 2.1.1 and 2.1.2. However, the magnitudes of the pressures are lower at 80 seconds because the stagnation source pressure at 80 seconds (1970 kPa, 285.72 psia) is lower than at 40 seconds (3030 kPa, 439.46 psia) or at 10 seconds (4420 kPa, 641.07 psia).
The conclusions regarding the relationship between the calculated jet conditions and the measurement are identical to those observed for the assessments at 10 seconds. It can generally be concluded from this test that the ANSI/ANS-58.2-1988 jet plume calculation model predicts conservative impingement pressures at the jet centerline. The model also predicts conservative radial pressures at axial distances greater than about 10 inches (~0.85 L/D) from the jet nozzle. The calculation under predicts by about 40 % the impingement pressure about 5 inches (~0.42 L/d) from the nozzle at a radius of about 2.7 inches.
Additionally, as shown for the steam jets at 10 and 40 seconds, comparisons between centerline impingement pressures at a specific centerline distance always bound the total pressure test measurements at the same centerline location. This conclusion is also illustrated in Figure 2.1-28 which compares the ANSI/ANS-58.2-1988 model jet centerline impingement pressures to the measured total pressures at several radial locations at several axial positions.
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Figure 2.1-21: Jet Impingement Pressure Contour for Marviken Test 5 at 80 Seconds 24
Figure 2.1-22: Pressures at Jet Plume Centerline for Marviken Test 5 at 80 Seconds Figure 2.1-23: Pressures at Beam 0 in Jet Plume for Marviken Test 5 at 80 Seconds 25
Figure 2.1-24: Pressures at Beam 1 in Jet Plume for Marviken Test 5 at 80 Seconds Figure 2.1-25: Pressures at Beams 2 and 3 in Jet Plume for Marviken Test 5 at 80 Seconds 26
Figure 2.1-26: Pressures at Beam 4 in Jet Plume for Marviken Test 5 at 80 Seconds Figure 2.1-27: Pressures at Beam 5 in Jet Plume for Marviken Test 5 at 80 Seconds 27
Figure 2.1-28: Centerline and Radial Jet Pressure Comparisons for Marviken Test 5 at 80 Seconds 28
2.2 Comparisons with the Marviken Full Scale Jet Impingement Test 6 The computer program mentioned in section 1.1 was used to calculate the jet conditions for Marviken test 6 at the times and fluid conditions listed in Table 1.3-2. Table 2.2-1 lists the measured input and calculated conditions from the programmed ANSI/ANS-58.2-1988 jet model calculations. As indicated on this table, jet plume conditions are assessed for four fluid conditions, subcooled liquid, saturated liquid, two-phase fluid and steam.
Table 2.2-1: Marviken Jet Test 6 Conditions for ANSI/ANS-58.2-1988 Jet Calculations (Nozzle Diameter = 509 mm = 20.04 inches)
Analyzed Time 5s 10 s 20 s 45 s 60 s 75 s Input and Measured 4049 kPa 3778 kPa 3330 kPa 2974 kPa 2640 kPa 1345 kPa Stagnation Pressure 587.26 psia 547.95 psia 482.98 psia 431.34 psia 382.90 psia 195.08 psia Fluid State Subcooled Subcooled Subcooled Saturated Two-Phase Steam Liquid Liquid Liquid Liquid Input Subcooled 16°C, 11°C, 5°C ,
Temperature 28.8°F 19.8°F 9°F Calculated = 20% = 72.4% = 99.67%
Input and Measured x x = 0.45% x = 4% x = 70%
Calculated 235.1°C 236.0°C 234.7°C 233.4°C 226.9°C 193.2°C Temperature 455.10°F 456.75°F 454.45°F 452.05°F 440.34°F 379.72°F Measured Nozzle 233°C 233.5°C 234°C 232°C 226°C 189°C Temperature 451.4°F 452.3°F 453.2°F 449.6°F 438.8°F 372.2°F Input and Measured 249 kPa 260 kPa 244 kPa 157 kPa 140 kPa 120 kPa Containment Pressure 36.11 psia 37.71 psia 35.39 psia 22.77 psia 20.31 psia 17.40 psia Calculated Critical 38,900 31,328 18,764 13,744 10,556 2,267 Mass Flux1 kg/m2/s kg/m2/s kg/m2/s kg/m2/s kg/m2/s kg/m2/s 7967.41 6397.71 3843.07 2815.05 2162.13 464.35 lbm/ft /s 2
lbm/ft2/s lbm/ft2/s lbm/ft2/s lbm/ft2/s lbm/ft2/s Measured Mass Flux 42,000 35,600 27,000 17,000 11,000 2,000 kg/m2/s kg/m2/s kg/m2/s kg/m2/s kg/m2/s kg/m2/s 8602.3 7291.1 5530.0 3481.9 2253.0 409.6 lbm/ft2/s lbm/ft2/s lbm/ft2/s lbm/ft2/s lbm/ft2/s lbm/ft2/s Calculated-Measured -0.074 -0.120 -0.305 -0.192 -0.040 0.134 Measured Mass Flux 1
Mass flux is calculated using HEM choking model for liquid and two-phase nozzle conditions, and the maximum of HEM and sonic choking for vapor conditions. The ANSI standard recommends the Henry-Fauske model for subcooled conditions, and the Moody or HEM model for flashing or steam-water mixtures.
The calculated and measured fluid temperatures and void fractions for the six cases are close in value.
The differences between the measured and calculated mass fluxes for the six cases vary between -30.5%
and 13.4%. The differences between the measured and calculated mass fluxes for the two-phase and steam jet cases are -4% and 13.4% which are close enough to permit comparison of the ANSI/ANS-58.2-1988 jet plume calculation results. The differences between the measured and calculated mass fluxes for the subcooled and saturated liquid jet cases are -7.4%, -12.0%, -30.5% and -19.2%. This wide range illustrates the conclusion stated in section 1.1 that the HEM critical flow model under predicts critical flows for subcooled and low quality conditions. These under predictions must be considered when assessing the ANSI/ANS-58.2-1988 jet plume calculations.
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Figures 2.2.1-2 to 2.2.1-24 compare the calculated jet plume impingement and static pressures for subcooled liquid jets at 5, 10 and 20 seconds to measured static and total pressure measurements in the jet plume. Figures 2.2.1-1, 2.2.1-8 and 2.2.1-15 provide half-jet contour plots of calculated jet impingement pressures at 5, 10 and 20 seconds. Figures 2.2.2-2 to 2.2.2-8 compare the saturated liquid jet pressure predictions to measurements at 45 seconds and Figures 2.2.3-2 to 2.2.3-8 compare two-phase jet pressure predictions to measurements at 60 seconds. Figures 2.2.4-4 to 2.2.4-10 compare calculated vapor jet pressures to test measurements at 75 seconds.
2.2.1 Comparisons with the Marviken Subcooled Jet Impingement Test 6 at 5, 10 and 20 Seconds The Marviken test 6 conditions used for the assessment of three subcooled liquid jet conditions are listed on Table 2.2-1. Figures 2.2.1-2 to 2.2.1-7 plot the calculated impingement and static pressures and the measured static and total pressures at the jet centerline and at radial locations for measurement beams 0, 1, 2, 3, 4 and 5 at a 5 second test time for a liquid jet with 16°C (28.8°F) subcooling. Figures 2.2-9 to 2.2-14 plot similar information at a 10 second test time for a 11°C (19.8°F) subcooled liquid jet and Figures 2.2.1-16 to 2.2.1- 21 plot the information at a 20 second test time for a 5°C (9°F) subcooled liquid jet.
Figures 2.2.1-1, 2.2.1-8 and 2.2.1-15 show half-jet contour plots of calculated impingement pressures at 5, 10 and 20 seconds.
Figures 2.2.1-2, 2.2.1-9 and 2.2.1-16 compare the calculated and measured pressures along the jet plume centerline axis for the subcooled jet conditions. These plots show that the jet calculation significantly exceeds both the static pressure measurements along the jet centerline, and the total pressure measurement which is at a radial position 70 mm (2.76 inches) off the jet centerline for a significant distance along the jet centerline. The calculated centerline impingement pressure exceeds the measured total pressure by about 50% close to the jet source. The impingement pressure drops and approaches the measured total pressure at an axial location of about 40 inches (~2.0 L/d) for the 5 second case, at about 37 inches (~1.8 L/d) for the 10 second case and at about 34 inches (~1.7 L/d) for the 20 second case.
However, the calculated impingement pressure exceeds the measured total pressure even after these indicated distances. For these three cases, the calculated static pressures at the region 2-3 asymptotic point agrees with the static pressure measurements.
It should be noted that the ANSI/ANS-58.2-1988 calculation of impingement pressure includes a thrust coefficient multiplier of 1. 32 for the 5 second case, 1.28 for the 10 second case and 1.23 for the 20 second case. Figure 2.2.1-9 shows that the calculated impingement pressure is still greater than the measured total pressure even if the calculated impingement pressure is divided by the thrust coefficient multiplier.
Figures 2.2.1-3, 2.2.1-10 and 2.2.1-17 show the calculated and measured pressures for beam 0 radial distances at axial positions between approximately 5 and 19 inches (~0.25 and ~0.95 L/d) from the nozzle. The calculated impingement pressure exceeds the measured total pressure by about 50% below 10 inches radius. Of course the calculated and measured pressures at 5 seconds exceed the values at 10 and 20 seconds because the source stagnation pressure at 5 seconds (4049 kPa, 587.26 psia) exceeds the source stagnation pressure at the 10 second (3778 kPa, 547.95 psia) and 20 second (3330 kPa, 482.98 psia) cases. The calculated impingement pressure approaches ambient pressure at a radius of about 33 inches for the 5s case, about 29 inches for the 10 s case and about 24 inches for the 20 s case indicating that the higher pressure jet approaches ambient pressure at a larger radial position.
30
Figures 2.2.1-4, 2.2.1-11 and 2.2.1-18 show the calculated and measured pressures for beam 1 radial distances at an axial position about 20 inches (~1.0 L/d) from the nozzle. These figures show that the calculated impingement pressure exceeds the measured total pressure below about 30 inches radius for all times. At about 30 inches radius the calculated impingement pressure approaches the ambient pressure.
Figures 2.2.1-5, 2.2.1-12 and 2.2.1-19 plot the calculated and measured pressures for beams 2 and 3 for radial distances about 40 axial inches (~2.0 L/d) from the nozzle. The plots show that the calculated impingement pressures exceed the measured total pressure until a radius of about 40 inches where the calculated pressure approaches the ambient pressure. The calculated impingement pressure exceeds the measured total pressure by over 40% at small radial positions.
The calculated and measured pressure in Figures 2.2-6 and 2.2-7 for the 5 second time, Figures 2.2.1-13 and 2.2.1-14 for the 10 second time, and Figures 2.2-20 and 2.2-21 for the 20 second times show similar behavior. These figures plot radial pressures for beams 4 and 5 at distances of about 60 to 80 axial inches
(~3.0 to ~4.0 L/d) from the nozzle. The calculated impingement pressure exceeds the measured total pressure until a radius of about 40 inches where the calculated pressure approaches the ambient pressure.
When compared to total pressure measurements it can generally be concluded that impingement pressure predictions for the three subcooled jets using the ANSI/ANS-58.2-1988 jet plume calculation model are conservative at all axial and radial positions when using the HEM critical flow model. If the recommended Henry-Fauske critical flow model is used, the calculated flow rate is expected to be larger and closer to measurement. A larger impingement pressure would be expected to be calculated with a larger flow rate. Consequently, the ANSI/ANS-58.2-1988 subcooled jet calculation using the Henry-Fauske model would be expected to predict more conservative loadings than those calculated using the HEM model.
Additionally, as shown for the Marviken test 5 steam jets, comparisons for the test 6 subcooled jets indicate that the centerline impingement pressures at a specific centerline distance always bound the total pressure test measurements at any radii for the same centerline location. This conclusion is illustrated for the test 6 subcooled jets at 5, 10 and 20 seconds in Figures 2.2.1-22, 2.2.1-23 and 2.2.1-24 which compare the ANSI/ANS-58.2-1988 model jet centerline impingement pressures to the measured total pressures for several radial locations at several axial positions.
31
Figure 2.2.1-1: Jet Impingement Pressure Contour for Marviken Test 6 at 5 Seconds 32
Figure 2.2.1-2: Pressures at Subcooled Jet Plume Centerline for Marviken Test 6 at 5 Seconds Figure 2.2.1-3: Pressures at Beam 0 in Subcooled Jet Plume for Marviken Test 6 at 5 Seconds 33
Figure 2.2.1-4: Pressures at Beam 1 in Subcooled Jet Plume for Marviken Test 6 at 5 Seconds Figure 2.2.1-5: Pressures at Beams 2 and 3 in Subcooled Jet Plume for Marviken Test 6 at 5 Seconds 34
Figure 2.2.1-6: Pressures at Beam 4 in Subcooled Jet Plume for Marviken Test 6 at 5 Seconds Figure 2.2.1-7: Pressures at Beam 5 in Subcooled Jet Plume for Marviken Test 6 at 5 Seconds 35
Figure 2.2.1-8: Jet Impingement Pressure Contour for Marviken Test 6 at 10 Seconds 36
Figure 2.2.1-9: Pressures at Subcooled Jet Plume Centerline for Marviken Test 6 at 10 Seconds Figure 2.2.1-10: Pressures at Beam 0 in Subcooled Jet Plume for Marviken Test 6 at 10 Seconds 37
Figure 2.2.1-11: Pressures at Beam 1 in Subcooled Jet Plume for Marviken Test 6 at 10 Seconds Figure 2.2.1-12: Pressures at Beams 2 and 3 in Subcooled Jet Plume for Marviken Test 6 at 10 Seconds 38
Figure 2.2.1-13: Pressures at Beam 4 in Subcooled Jet Plume for Marviken Test 6 at 10 Seconds Figure 2.2.1-14: Pressures at Beam 5 in Subcooled Jet Plume for Marviken Test 6 at 10 Seconds 39
Figure 2.2.1-15: Jet Impingement Pressure Contour for Marviken Test 6 at 20 Seconds 40
Figure 2.2.1-16: Pressures at Subcooled Jet Plume Centerline for Marviken Test 6 at 10 Seconds Figure 2.2.1-17: Pressures at Beam 0 in Subcooled Jet Plume for Marviken Test 6 at 20 Seconds 41
Figure 2.2.1-18: Pressures at Beam 1 in Subcooled Jet Plume for Marviken Test 6 at 20 Seconds Figure 2.2.1-19: Pressures at Beams 2 and 3 in Subcooled Jet Plume for Marviken Test 6 at 20 Seconds 42
Figure 2.2.1-20: Pressures at Beam 4 in Subcooled Jet Plume for Marviken Test 6 at 20 Seconds Figure 2.2.1-21: Pressures at Beam 5 in Subcooled Jet Plume for Marviken Test 6 at 20 Seconds 43
Figure 2.2.1-22: Centerline and Radial Jet Pressure Comparisons for Marviken Test 6 at 5 Seconds Figure 2.2.1-23: Centerline and Radial Jet Pressure Comparisons for Marviken Test 6 at 10 Seconds 44
Figure 2.2.1-24: Centerline and Radial Jet Pressure Comparisons for Marviken Test 6 at 20 Seconds 45
2.2.2 Comparisons with the Marviken Saturated Liquid Jet Impingement Test 6 at 45 Seconds The Marviken test 6 conditions used for the assessment of the saturated liquid jet conditions are listed on Table 2.2-1. Figures 2.2.2-2 to 2.2.2-7 plot the calculated impingement and static pressures and the measured static and total pressures at the jet centerline and at radial locations for measurement beams 0, 1, 2, 3, 4 and 5 at a 45 second test time. Figure 2.2.2-1 presents the calculated impingement pressure half-jet contour plot.
Figure 2.2.2-2 compares saturated liquid jet pressure calculations along the jet centerline to pressure measurements. The impingement pressure predictions along the jet centerline are close to the total pressure measurements until about 37 inches (~1.8 L/d) axial length. After that length the calculated impingement pressure is above 50 psia, but the total pressure measurements are close to the ambient pressure of 22.77 psia. The calculated static pressure at the region 2-3 asymptotic plane at an axial length of 37.96 inches (1.9 L/d) agrees with the measured static pressure.
Figure 2.2.2-3 plots radial pressures from beam 0 at an axial position 5 to 10 inches (0.25 to 0.50 L/d) from the nozzle. The calculated impingement pressure and measured total pressure at about a 3 inch radius from the jet centerline are close in value. The calculated impingement pressure drops to ambient pressure at a radius of about 6 inches and is close to the static pressure measurement.
Figure 2.2.2-4 plots calculated and measured pressure for beam 1 at radial positions located about 20 axial inches (~1.0 L/d) from the nozzle. The measured total pressure exceeds the calculated impingement pressures for radial positions less than about 18 inches. The calculated impingement pressure and the measured total pressure converge in value at a radius of about 18 inches, and the calculated impingement pressure approaches the ambient pressure at a radius of about 30 inches.
Figures 2.2.2-5, 2.2.2-6 and 2.2.2-7 present similar trends in the comparison of calculated and measured pressures. These figures plot the radial pressures for beams 2 and 3 at about a 40 inch (~2.0 L/d) axial length, for beam 4 at about a 60 inch (~3.0 L/d) axial length, and for beam 5 at about an 80 inch (~3.0 L/d) axial length. In all cases the calculated impingement pressure exceeds the measured total pressure until a radius less than about 20 inches. The calculated impingement pressure approaches ambient pressure at a radius of about 30 inches.
In general the ANSI/ANS-58.2-1988 calculation model for a saturated liquid jet produces conservative impingement pressures when compared to measured total pressure for most axial and radial positions. The only exception is the radial pressure comparisons at an axial position about 20 inches (~1.0 L/d) from the nozzle. However, it should be recognized that the calculated mass flux for this cases under predicts the measured flow rate by 19.2%. The reported calculations used the HEM critical flow model to calculate the jet flow. If the Henry-Fauske critical flow model is used the calculated flow rate is expected to be larger and closer to measurement. A larger impingement pressure would be expected to be calculated with a larger flow rate. Consequently, the ANSI/ANS-58.2-1988 saturated liquid jet calculation using the recommended Henry-Fauske critical flow model would be expected to predict impingement pressures closer to the total pressure measurements than those calculated using the HEM critical flow model.
Additionally, as shown for the Marviken test 5 steam jets and the test 6 subcooled jets, comparisons for the test 6 saturated liquid jet indicates that the centerline impingement pressures at a specific centerline distance approximately equal or bound the total pressure test measurements at the same centerline location. This conclusion is illustrated for the test 6 saturated liquid jet at 45 seconds in Figures 2.2.2-8 46
which compares the ANSI/ANS-58.2-1988 model jet centerline impingement pressures to the measured total pressures for several radial locations at several axial positions.
Figure 2.2.2-1: Jet Impingement Pressure Contour for Marviken Test 6 at 45 Seconds 47
Figure 2.2.2-2: Pressures at Saturated Liquid Jet Plume Centerline for Marviken Test 6 at 45 Seconds Figure 2.2.2-3: Pressures at Beam 0 in Saturated Liquid Jet Plume for Marviken Test 6 at 45 Seconds 48
Figure 2.2.2-4: Pressures at Beam 1 in Saturated Liquid Jet Plume for Marviken Test 6 at 45 Seconds Figure 2.2.2-5: Pressures at Beams 2 & 3 in Saturated Liquid Jet Plume for Marviken Test 6 at 45 Seconds 49
Figure 2.2.2-6: Pressures at Beam 4 in Saturated Liquid Jet Plume for Marviken Test 6 at 45 Seconds Figure 2.2.2-7: Pressures at Beam 5 in Saturated Liquid Jet Plume for Marviken Test 6 at 45 Seconds 50
Figure 2.2.2-8: Centerline and Radial Jet Pressure Comparisons for Marviken Test 6 at 45 Seconds 51
2.2.3 Comparisons with the Marviken Full Scale Two-Phase Jet Impingement Test 6 at 60 Seconds The Marviken test 6 conditions used for the assessment of the two-phase jet conditions are listed on Table 2.2-1. Figures 2.2.3-2 to 2.2.3-7 plot the calculated impingement pressure and the measured static and total pressures at the jet centerline and at radial locations for measurement beams 0, 1, 2, 3, 4 and 5 at a 60 second test time. A half-jet contour plot of the calculated impingement pressures is shown on Figure 2.2.3-1.
Figure 2.2.3-2 compares the calculated impingement pressure along the jet centerline to pressure measurements. The total pressure measurement is taken a radial position about 70 mm (2.76 inches) from the jet centerline. The impingement pressure predictions exceed the total pressure measurements for the first 10 inches (0.50 L/d) of axial length by about 13% and also over predict measurements at axial lengths greater than about 40 inches (~2.0 L/d) by about 70%. However, the calculated pressures at axial distances greater than about 30 inches (~1.5 L/d) range between the relatively low values of approximately 80 and 60 psia. The calculated static pressure at the region 2-3 asymptotic plane at an axial length of 32 inches (1.6 L/d) agrees with the measured static pressure.
Figure 2.2.3-3 plots the calculated and measured pressures for beam 0 at radial positions between 5 and 10 inches (0.25 and 0.5 L/d) along the jet centerline. The calculated impingement pressure at about a 3 inch radius is close to the measured total pressure. The calculated impingement pressure drops below the measured static pressure at a radius of about 5 inches and approaches the ambient pressure shortly after that radial position. The measured static pressure approaches the ambient pressure between a radius of 10 and 20 inches.
Figures 2.2.3-4 and 2.2.3-5 exhibit similar trends in comparing the calculated impingement pressure and the measured total pressure. Figure 2.2.3-4 presents beam 1 radial pressures about 20 axial inches (~1.0 L/d) from the nozzle and Figure 2.2.3-5 plots radial pressured for beams 2 and 3 about 40 inches (~2.0 L/d) from the jet nozzle. The measured total pressure exceeds the calculated impingement pressure until a radial position about 18 inches from the jet centerline. The calculated impingement pressure approaches the measured static pressure and ambient pressure about 30 inches (~1.5 L/d) from the nozzle.
Figures 2.2.3-6 and 2.2.3-7 plot the calculated and measured radial pressures for beams 4 and 5 at positions about 60 and 80 inches (~3.0 and 4.0 L/d) from the nozzle. The calculated impingement pressure exceeds the measured total and static pressures until a radius of about 30 inches. The pressures are close to ambient pressure for radii greater than 30 inches.
This is the only test that compares the two-phase jet calculations to test data. The critical flow rate calculated using the HEM model is close to the test measurement; consequently, this critical flow model is considered acceptable for the test quality value of 4%. The impingement pressure calculation calculated along the jet centerline is fairly close to and bounds measurements close to the nozzle and over predicts pressures at larger axial locations. However, the radial pressure calculations do not bound the measurements at axial points less than 40 inches from the nozzle. Consequently, the ANSI/ANS-58.2-1988 jet calculation for the Marviken test 6 two-phase jet provides only marginal agreement with test data for radial locations along the jet centerline, but provides conservative impingement pressures along the jet centerline.
Additionally, as shown for the Marviken test 5 steam jets and the test 6 subcooled and saturated liquid jets, comparisons for the test 6 two-phase jet indicates that the centerline impingement pressures at a specific centerline distance approximately equal or bound the radial total pressure test measurements at the same centerline location. This conclusion is illustrated for the test 6 two-phase jet at 60 seconds in 52
Figure 2.2.3-8 which compares the ANSI/ANS-58.2-1988 model jet centerline impingement pressures to the measured total pressures for several radial locations at several axial positions.
Figure 2.2.3-1: Jet Impingement Pressure Contour for Marviken Test 6 at 60 Seconds 53
Figure 2.2.3-2: Pressures at Two-Phase Jet Plume Centerline for Marviken Test 6 at 60 Seconds Figure 2.2.3-3: Pressures at Beam 0 in Two-Phase Jet Plume for Marviken Test 6 at 60 Seconds 54
Figure 2.2.3-4: Pressures at Beam 1 in Two-Phase Jet Plume for Marviken Test 6 at 60 Seconds Figure 2.2.3-5: Pressures at Beams 2 and 3 in Two-Phase Jet Plume for Marviken Test 6 at 60 Seconds 55
Figure 2.2.3-6: Pressures at Beam 4 in Two-Phase Jet Plume for Marviken Test 6 at 60 Seconds Figure 2.2.3-7: Pressures at Beam 5 in Two-Phase Jet Plume for Marviken Test 6 at 60 Seconds 56
Figure 2.2.3-8: Centerline and Radial Jet Pressure Comparisons for Marviken Test 6 at 60 Seconds 57
2.2.4 Comparisons with the Marviken Full Scale Steam Jet Impingement Test 6 at 75 Seconds The comparisons between the ANSI/ANS-58.2-1988 jet plume calculation for the Marviken test 6 one-phase steam jet conditions and test measurements provide additional information which should expand the observations for the Marviken test 5 steam jet results discussed in section 1.0. The test conditions for the Marviken test 6 steam jet experiment are shown in Table 2.2-1; similar information for the test 5 conditions are shown in Table 2.1-1. As indicated in these tables the nozzle diameter for test 6 was 509 mm (20.04 inches) and the nozzle diameter for test 5 was 299 mm (11.77 inches). Figures 2.2.4-4 to 2.2.4-9 plot the calculated impingement and static pressures and the measured static and total pressures at the jet centerline and at radial locations for measurement beams 0, 1, 2, 3, 4 and 5 at a 75 second test time for Marviken test 6. Figure 2.2.4-1 provides a half-jet contour plot of calculated impingement pressures.
Figure 2.2.4-2 and 2.2.4-3 provide contour plots of the predicted Mach number and total pressure from the CFD model. The CFD model includes the central probe.
Figure 2.2.4-4 shows that the calculated impingement pressure exceeds the measured total pressure along the jet centerline. It should be noted that the total pressure is measured at a radial position 70 mm (2.76 inches) from the jet centerline. At the first measurement locations, approximately 5 inches (~0.25 L/d) from the nozzle, the calculated impingement pressure exceeds the measured total pressure by about 30%.
The ANSI/ANS-58.2-1988 jet model does not predict the drop to pressure near ambient as observed from test data at an approximate axial location of 40 inches (2.0 L/d). Consequently, the calculated impingement pressure exceeds the measured total pressure for all positions along the centerline. At axial distances greater than 20 inches the calculated impingement pressure exceeds the measured total pressure by approximately 80%. The CFD predictions are close to the test data along the centerline axis. The comparisons between the calculated impingement pressure and the measured total pressure along the jet centerline observed for test 6 are similar to the observations seen in test 5. The ANSI/ANS-58.2-1988 calculated static pressure at the region 2-3 asymptotic plane at an axial length of 13.48 inches (0.67 L/d) is close to the measured static pressure.
Figure 2.2.4-5 compares the predicted impingement pressure and the measured static and total pressures for radial distances along beam 0 which is located at an axial location 5 to 10 inches (0.25 to 0.50 L/d) from the nozzle. The ANSI/ANS-58.2-1988 calculated impingement pressure is close to the measured total pressure at a radial location of about 3 inches. However, the calculations predict that the impingement pressure drops to a value near the ambient pressure at about a 5 inch radius, and the static pressure measurement approaches the ambient pressure at about a 10 inch radius. In test 5 the measured total pressure exceeded the calculated impingement pressure close to the nozzle. The calculated impingement pressure for test 6 dropped to ambient conditions closer to the jet nozzle than the predicted impingement pressure for test 5. Additionally, the calculated static pressure at the region 2-3 asymptote is below the measured static pressure. The CFD predictions are close to the measurement point near 3 inches. The CFD model predicts a radial spread for the jet out to approximately 14 inches. Some of the difference between the CFD predictions and the ANSI/ANS model could be due to the inclusion of the central probe in the test and the CFD predictions. The ANSI/ANS model does not account for the central probe.
Figure 2.2.4-6 compares the calculated impingement pressure to the measured static and total pressures for radial locations on beam 1 which was located about 20 inches (~1.0 L/d) from the nozzle. The behaviors observed for beam 1 were similar to those observed for beam 1 in test 5. The calculated impingement pressure is close in value to the measured total pressure. The CFD predictions are also shown on this figure and show reasonable agreement with the data. The variations in the CFD predictions between 15 and 21 inches cannot be confirmed by the data with 3 measurement locations. The 58
ANSI/ANS model does not predict pressure peaks due to high Mach number regions at the edge of the jet.
The calculated impingement pressure is predicted to approach ambient pressure at a radius between 20 and 25 inches on beam 1 for the test 6 and test 5 cases.
The relationship between the calculated impingement pressure and the measured total pressure for test 6 on beams 2, 3 and 4 shown on Figures 2.2.4-7 and 2.2.4-8 are similar to those observed on beams 2, 3 and 4 for test 5. Beams 2 and 3 were located at an axial location about 40 inches (~2.0 L/d) from the nozzle and beam 4 was located about 60 inches (~3.0 L/d) from the nozzle. The calculated impingement pressure exceeds the total pressure measurement at radial positions below about 20 inches; however, the measured total pressure is slightly larger than the calculated impingement pressure close to 20 inches in radius. The CFD predictions add more insight to this trend since they provide a continuous trace along the radial direction. The jet pressure is elevated at regions impacted by the shock wave pattern. Figures 2.2.4-2 and 2.2.4-3 add insight into the complex nature of the shock wave and total pressure patterns.
Figure 2.2.4-9 compares the calculated radial impingement pressures and the measures radial static and total pressures for beam 5 which was located about 80 axial inches (~4.0 L/d) from the nozzle. The behavior observed for beam 5 is similar to that observed for beam 5 in test 5. The calculated impingement pressure exceeds the measured total pressure at small radii and the calculated impingement pressure approaches the ambient pressure between 20 and 30 inches in radius. The CFD predictions are consistent with the single pressure measurement at approximately 3 inches and show a peak in the pressure between 10 and 20 inches which corresponds to the high pressure region from Figure 2.2.4-3 at the edge of the supersonic jet region. These peaks predicted by the CFD code cannot be compared to the test data due to the limited number of probes.
As seen for the test 5 steam jets at 10 and 40 seconds, the test data and CFD analysis for the test 6 steam jet at 75 seconds indicate that peak pressures can exist at the jet edges due to the presence of regions of high Mach number. Comparisons between the ANSI/ANS-58.2-1988 model jet centerline impingement pressures in Figure 2.2.4-5 and the CFD calculated total pressures near the jet edges in Figures 2.2.4-6 to 2.2.4-9 show that the calculated jet centerline impingement pressures at a specific jet centerline distance always bound or equal the CFD calculated stagnation pressure at any radial distance at the same centerline distance.
In summary, the jet observations for the test 6 steam jet with a 509 mm (20.04 inch) nozzle diameter were similar to those observed for the test 5 steam jet which used a 299 mm (11.77 inch) diameter nozzle. It can generally be concluded from this test that the ANSI/ANS-58.2-1988 jet plume calculation model predicts conservative impingement pressures at the jet centerline. The model predicts conservative radial pressures at axial distances greater than about 10 inches from the jet nozzle. The calculation under predicts the impingement pressure about 5 inches (~0.25 L/d) from the nozzle at a radius of about 2.7 inches. However, comparisons between centerline impingement pressures at a specific centerline distance always bound or equal the CFD calculated radial total pressures at the same centerline distance and the radial total pressure test measurements at the same centerline location. This conclusion is also illustrated in Figure 2.2.4-10 which compares the ANSI/ANS-58.2-1988 model jet centerline impingement pressures to the measured total pressures for several radial locations at several axial positions and also to the maximum calculated radial total pressure at several axial centerline positions.
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Figure 2.2.4-1: Jet Impingement Pressure Contour for Marviken Test 6 at 75 Seconds 60
Figure 2.2.4-2: Mach Number Contour from CFD Model for Marviken Test 6 at 75 Seconds 61
Figure 2.2.4-3: Total Pressure (psia) Contour from CFD Model for Marviken Test 6 at 75 Seconds 62
Figure 2.2.4-4: Pressures at Steam Jet Plume Centerline for Marviken Test 6 at 75 Seconds Figure 2.2.4-5: Pressures at Beam 0 in Steam Jet Plume for Marviken Test 6 at 75 Seconds 63
Figure 2.2.4-6: Pressures at Beam 1 in Steam Jet Plume for Marviken Test 6 at 75 Seconds Figure 2.2.4-7: Pressures at Beams 2 and 3 in Steam Jet Plume for Marviken Test 6 at 75 Seconds 64
Figure 2.2.4-8: Pressures at Beam 4 in Steam Jet Plume for Marviken Test 6 at 75 Seconds Figure 2.2.4-9: Pressures at Beam 5 in Steam Jet Plume for Marviken Test 6 at 75 Seconds 65
Figure 2.2.4-10: Centerline and Radial Jet Pressure Comparisons for Marviken Test 6 at 75 Seconds 66
4.0 CONCLUSION
S The objective of this study is to assess the acceptability of the jet calculation methodology contained in ANSI/ANS-58.2-1988 by comparing calculated results to test data for subcooled, saturated liquid, two-phase and steam jets obtained from the Marviken Full Scale Jet Impingement Tests. The ANSI/ANS-58.2-1988 jet calculation results for a one-phase steam jet are also be compared to computational fluid dynamics (CFD) analysis results performed using the FLUENT code.
This report provides plots which compare the calculated jet impingement pressures to static and total pressures measured axially and radially within the jet for Marviken tests 5 and 6. The jet pressure distribution calculated using the ANSI/ANS-58.2-1988 standard is a local impingement pressure. The impingement pressure is the property that is important in assessing debris generation. (Impingement pressure is also referred to as jet pressure in some documents.) The impingement pressure includes entropy losses resulting from the impact of the fluid on a large object. In contrast, stagnation pressure is related to the isentropic deceleration of flow along a streamline. (The Marviken reports use the terms total and stagnation pressure interchangeably.) The impingement pressure is generally higher than the stagnation pressure in the jet because it includes the thrust coefficient in the calculation of the jet impingement pressure. It is considered appropriate to compare the ANSI/ANS-58.2-1988 calculated impingement pressure to the measured total pressure because the impingement pressure which is defined as the load on an impinged surface divided by impinged area is the closest comparison to a total pressure.
Additionally, the jet centerline is the most important location for comparing ANSI/ANS-58.2-1988 impingement pressure predictions with test data because the jet centerline pressures are considered in the definition of the Zone of Influence (ZOI) used in determining debris generation.
The jet calculation model in the ANSI/ANS-58.2-1988 will produce conservative to realistic impingement pressures for subcooled, saturated liquid and low-quality jets when using the recommended Henry-Fauske critical flow correlation for calculating jet nozzle flow rate. This conclusion has been reached by comparing calculations for impingement pressure to test total pressure measurements from the Marviken Full Scale Jet Impingement Test 6 for a break nozzle diameter of 509 mm (20.04 inches) and stagnation pressures upstream of the jet nozzle ranging from 4049 to 2974 kPa (587.26 to 431.34 psia) with a maximum subcooling of 16°C (28.8°F).
Only one test time from the Marviken Full Scale Jet Impingement Test 6 provides two-phase jet test data which can be compared to the ANSI/ANS-58.2-1988 jet calculation method using the HEM critical flow correlation. The impingement pressure calculations for this two-phase jet conditions did not always bound the measured radial pressures; however, the calculated impingement pressures are close to or bound total pressure measurements along the centerline of the jet. Therefore, the conclusion that could be reached is that the ANSI/ANS-58.2-1988 calculation method provides only marginally acceptable radial impingement pressures for a two-phase jet but conservative impingement pressures along the jet centerline. These conclusions were reached for a break nozzle diameter of 509 mm (20.04 inches) and a stagnation pressure upstream of the jet nozzle of 1970 kPa (285.72 psia) with a quality of 4% ( ~70%).
In general, comparisons for the test 6 subcooled, saturated liquid and two-phase jets indicate that the ANSI/ANS-58.2-1988 model centerline impingement pressures at a specific centerline distance approximately equal or bound the total pressure test measurements at the same centerline location.
A total of four steam jet test cases from the Marviken Full Scale Jet Impingement Tests were studied.
Three cases from Marviken test 5 used a 299 mm (11.77 inch) nozzle and one case from Marviken test 6 used a 509 mm (20.04 inches) nozzle. The stagnation pressures upstream of the jet nozzle ranged from 67
4420 to 1345 kPa (641.07 to 195.08 psia). At the jet centerline the impingement pressures calculated using the ANSI/ANS-58.2-1988 jet calculation method provided conservative to realistic predictions of total pressure measured during testing.
It can generally be concluded from the Marviken test 5 and 6 steam jet cases test that the ANSI/ANS-58.2-1988 jet calculation model predicts conservative impingement pressures at the jet centerline. The model predicts conservative radial pressures at larger axial distances from the jet nozzle. The calculation under predicts the impingement pressure closer to the nozzle at some radial locations. The measured stagnation test data and CFD predicted stagnation pressures for the test 5 and test 6 steam jet cases indicate that peak pressures can exist at the jet edges due to the presence of regions of high Mach number.
Comparisons between the ANSI/ANS-58.2-1988 model jet centerline impingement pressures and the CFD calculated total pressures near the jet edges show that the calculated jet centerline impingement pressures at a specific centerline distance always bound or approximately equal the CFD calculated radial total pressures at the same centerline distance and the total pressure test measurements at the same centerline location.
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5.0 REFERENCES
(1) Design Basis for Protection of Light Water Nuclear Power Plants Against Effects of Postulated Pipe Rupture, ANSI/ANS-58.2-1988, American Nuclear Society/American National Standard, 1988.
(2) ANSYS/FLUENT, Theory Guide, version 13, http://www.ansys.com.
(3) The Marviken Full Scale Jet Impingement Tests - Fourth Series, MXD-301 Interim Report -
Summary Report, MX4-20, Studsvik - The Marviken Project, ADAMS ML063410287, August 1981.
(4) The Marviken Full Scale Jet Impingement Tests - Fourth Series, MXD-205 Interim Report -
Results from Test 5, MX4-15, Studsvik - The Marviken Project, ADAMS ML063460278, March 1981.
(5) The Marviken Full Scale Jet Impingement Tests - Fourth Series, MXD-206 Interim Report -
Results from Test 6, MX4-18, Studsvik - The Marviken Project, ADAMS ML063460280, April 1981.
(6) Safety Evaluation of the Industry Guidelines Related to Pressurized Water Reactor Sump Performance, Letter from Mario V. Bonaca to Nils J. Diaz, US Nuclear Regulatory Commission Advisory Committee on Reactor Safeguards, ADAMS ML042920334, October 18 2004.
(7) Graham B. Wallis, The ANSI/ANS Standard 58.2-1988: Two-Phase Jet Model, ADAMS ML050830344, September 15 2004.
(8) Victor Ransom, Comments on GSI-191 Models for Debris Generation, ADAMS ML050830341, September 14 2004.
(9) M. N. Hutcherson, Contribution to the Theory of Two-Phase Blowdown Phenomenon, ANL-75-82, Argonne National Laboratory, December 1975.
(10) Safety Evaluation by the Office of Nuclear Reactor Regulation Related to NRC Generic Letter 2004-02, Nuclear Energy Institute Guidance Report, Pressurized Water Reactor Sump Performance Evaluation Methodology, Appendix I - ANSI/ANS Jet Model, ADAMS ML042640274, September 2004.
(11) Equations, Tables, and Charts for Compressible Flow, Report 1135, National Advisory Committee for Aeronautics, Ames Aeronautical Laboratory, Moffett Field, CA, 1953.
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