ML19310A231
| ML19310A231 | |
| Person / Time | |
|---|---|
| Site: | Saint Lucie  |
| Issue date: | 01/31/1980 |
| From: | ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY |
| To: | |
| Shared Package | |
| ML17208A685 | List: |
| References | |
| CEN-123(F)-NP, CEN-123(F)-NP-PT02, CEN-123(F)-NP-PT2, NUDOCS 8006060326 | |
| Download: ML19310A231 (100) | |
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STATISTICAL COMBINATION
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. ;.; UNCERTAINTIES f['.- . ..
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PART 2
'4 - JANUARY,1980
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~ POWER SYSTEMS
..;' 80060603 g COMBUSDON ENGINEERING. INC.
LEGAL NOTICE ,
THIS REPORT WAS PREPARED AS AN ACCOUNT OF WORK SPONSORED ~
BY COMBUSTION ENGINEERING, INC. NEITHER COMBUSTION ENGINEERING NOR ANY PERSON ACTING ON ITS BEHALF:
A. MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR IMPLIED INCLUDING THE WARRANTIES OF FITNESS FOR A PARTICUI, AR PURPOSE OR MERCHANTABILITY, WITH RESPECT TO THE ACCURACY, COMPLETENESS, OR USEFULNESS OF THE INFORMATION CONTAINED IN THIS REPORT, OR THAT THE USE OF ANY INFORMATION, APPARATUS, METHOD, OR PROCESS DISCLOSED IN THIS REPORT MAY NOT INFRINGE PRIVATELY OWNED RIGHTS;OR ;
B. ASSUMES ANY LIABILITIES WITH RESPECT TO THE USE OF, OR FOR DAMAGES RESULTING FROM THE USE OF, ANY INFORMATION, APPARATUS, l METHOD OR PROCESS DISCLOSED IN THIS REPORT. I e
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C Ell-123(F)-flP ST ATISTICAL C0f tBIf!ATIO!! 0F U!iCERTAlflTIES METHODOLOGY PART 2: COMBIf!ATI0li 0F SYSTEM PARAf1ETER UllCERTAltlTIES Ill THERMAL MARGIri Af1ALYSES FOR ST. LUCIE UilIT 1 i i
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AGSTRACT s'
This report describes the methods used to statistically combine system parameter uncertainties in the thermal margin analyses for the St. Lucie Unit 1 core. A detailed description of the uncertainty probability distributions and response surface techniques used is presented. This report demonstrates that there will be at least 95T probability with at least 95% confidence that the limiting fuel pin will avoid departure from nucleate tioiling (DliB) so long as the minimum DilB ratio found with the best estimate design TORC model remains above 1.23.
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- TABLE OF C0'lTEilTS Page Ti tle '
1.
i Abstract ,
11-
! Table of Contents IV-List of Figures V.
. List of Tables Vi. -
, Nomenclature and Abbreviations 1.0 Summary of Resu - l-1
't 2-1 2.0 Introduction Deterministic Method 2-2 i 2.1 2-2 2.2 Statistical Method ,
t 3.0 Sources of Uncertainty 3-1 - -
State Parameters Used in the Study 3-1 3.1 3.1.1 Method for Selecting State Parameters 3-2 i
3.1.2 Inlet Flow Perturbation Sensitivity 3-3 3.1.3 Enthalpy Rise Factor Sensitivity 3-3 3.1.4 Systematic Pitch Reduction Sensitivity 3-4 3-5 3.1.5 Most Adverse State Parameters 3-5 3.2 Radial Power Distribution 3.3 Inlet Flow Distribution 3-6 4
3-6 3.4 Exit Pressure Distribution 3-7 3.5 Enthalpy Rise factor 3 <
3.6 Heat Flux Factor 3-7 3.7 Clad O. D.
3-8 3.8 Systematic Pitch Reduction 3-8 3.9 fuel. Rod Bou ,
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LIST OF FIGURES 1
- Page
. _ Fig. No. Title 3-1 Inlet Flow Distribution Used to Establish State Paremeters for Response Surface 3-10 i*
- 3-2 Exit Pressure Distribution Used to Establish 3-11 State Parameters for Response Surface ,
3-3 Core Wide Radial Power Distribution Used to Establish State Parameters for Response Surface 3-12 3-4 Hot Assembly Radial Power Distribution Used to Establish State Parameters for Response Surface 3-13
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3-5 Channel Numbering Scheme for Stage 1 TCPC Analysis to Establish Response Surface State Parameters 3-14 3-6 Channel Numbering Scheme for Stage 2 TORC Analysis to Establish Response Surface State Parameters 3-15 3-7 Third Stage Channel and Fuel Pin Numbering Schemes Used in TORC Analysis to Establish Response Surface State Parameters 3-16 3-8 Inlet Flow Factors for Seized Rotor Analysis of 217 Bundle 14x14 Assembly Cores 3-17 3-9 Exit Pressure Distribution Used in Sensitivity Study 3-18 i Core Wide Power Distribuiton Used to Generate 4-1 Response Surface 4-5 4-2 Hot Assembly Radial Power Distribution Used to i
' Generate Response Surface 4-6 4-3 Intermediate (2nd Stage) TORC Model Used in Generating Response Surface 4-7 4 Subchannel (3rd Stage) TORC Model Used in Generating Response Surface 4-8 i Resultant MDNBR Probability Distribution Function - 5-5 5-1
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LIST'0F TABLES Page Table flo. Title -
3-1 Ranges of Operating Conditions for Which Response Surface Is valid 3-19 3-2 liominal and Perturbed Flow for Establishing
,,- Sensitivity of Flow Distribution Effects on MDilBR to Operating Conditions 3-20 3-3 Flow Perturbation Effects at Various Operating 3-21 Conditions
!. 3-4 Sensitivity of Enthalpy Rise Factor Effects to 3-22 Axial Shape Index (Isolated Hot Assembly ttodel) 3-5 Sensitivity of Enthalpy Rise Factor Effects
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to Operating Conditions (Isolated Hot Assembly 3-23 Model) 3-6 Sensitivity of Enthalpy Rise Factor Effects 3-24 to Axial Shape Index (Core Wide Analysis) i 3-7 Sensitivity of Systematic Pitch Reduction Effects 3-25 to Operating Conditions 3-8 State Parameters Which Maximize Sensitivity of MDllBR to 3-26 System Parameters 3-9 Sensiti'v ity of ND;;3R to Inlet Flow Distribution 3-27 Sensitivity of MD!!CR to Exit Pressure Distribution 3-28 3-10 3-29 3-11 As-Built Clad 0.D. (inches) Data for 14x14 Fuel As-Built Gap Width Data (inches) 3-30 -
l . 3-12 State Parameters Included as Variables in the 4-1 4-9 Response Surface Coefficients for MDilBR Response Surface 4-10 4-2
. ~ . .. .
5-1 Probability Distribution Functions Combined 5-4 by SIGMA A-1 Coded Set of Detailed TORC Cases Used to A-2 Generate Response Surface A-2 Comparison of TORC and Response Surface MD';BR for Cases Used to Generate Response Surface A-13 v.
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...,,....._.n.
F=.--
- -..--- . ~ -.
1
.s . ..
., . i f(0MENCLATURE AND ABBREVIATIONS b coefficient in response surface .
c constant in response surface f arbitrary functional relationship
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k number of independent variables in response surface n number of items in a sample p.d.f. probability distribution function
. psf pounds per square foot psia pounds per square inch (absolute)
. x system parameter y state parameter z MDNBR values predicted by response surface ASI axial shape index (defined in Table 3-3)
CE Combustion Engineering CilF Critical Heat Flux _
DNB Departure from Nucleate Boiling DNBR Departure from Nucleate Boiling Ratio F Fahrenheit , ,
Fa q engineering heat flux factor 11DNBR Minimum Departure from Nucleate Boiling T temperature T-H thermal-hydraulic a constant used to code system parameters (Table 4-1) e constant used to code system parameters (Table 4-1) n coded value of system parameters (Table 4-1) y mean a standard deviation A denotes difference between two parameters e
9 vi.
subscripts denotes vector quantity .
index 4
conditions at reactor core inlet in index j
O j;_upers u criots denotes estimate degrees average value e
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1.0 Summary of Resuit.s Methods tere developed to cc:abine statistically the uncertainties in reference thermal margin (Detailed TORC) analyses. These methods were applied to the St. Lucie Unit 1 core. This work demonstrated that there will be at least 95% probability with at least 95% con-fidence that the limiting fuel pin will avoid decarture from nucleate boiling (DiiB) so long as the flini: rum Dt:3 Ratio (f!Df;3R) found with the best estimate design TORC r.odel remains above 1.23.
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The 1.23 !!Df!CR limit includes allowances for reference analysis input uncertainties but does not take into account uncertainties in operating conditions (e.g. nonitoring uncertainties). An
. improved treatment of operating condition uncertainties has been developed in Part 1 of this report (1-1).
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2.0 Introduction
'C-E's thermal margin methodology for St. Lucie Unit 1 has been tr.odified by the application of statistical methods.
This part of the report focuses on the statistical combination of reference thermal-hydraulic (T-il) code input uncertainties.
This combination was accomplished by the generation of a Minimum D:lDR (NBNBR) response surface and the application of Monte Carlo methods.
A complete description of the methods used in the statistical combination is provided in this report. The remainder of this section outlines the previous deterministic and the new statistical
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thermal margin methods. Section 3.0 describes the sources of un-certainty that were considered in this effort. Section 4.0 describes the MD:lBR response surface. The application of flonte Carlo Methods is discussed in Section 5.0, and results are presented.
Finally Section 6.0 describes the changes in design analyses that result from this work.
Em 2-1.
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- 2.1 Deterministic Method Two types of problem dependent data are required before a detailed T-li code can be applied. The first type of data, system parameters, describe the pnysical system under consideration and are not monitored with the detail needed for detailed T-H analysis unile the reactor is operational. System parameters describe the reactor geometry, pin by pin radial pouer distributions, inlet and exit flow boundary condition,
-- etc. The second type of data, state parameters, describe the cperational state of the reactor. State parameters are monitored while the reactor is in operation and include the core average inlet temperature, primary -
loop flow rate, primary loop pressure, etc.
C-E thermal margin methods (2-1) utilize the TORC code (2-2) and the CE-l CHF correlation (2-3) with two types of models. The first model, detailed TORC, is tailored to yield best estimate MDMBR precictions in
- a particular fuel assembly for a specific power distribution. Both system and state parameter input are used in a detailed TORC model.
The second model, desien TORC, requi.res only state parameter data and may be applied to any fuel assembly for any power distribution that is expected to occur during a particular fuel cycle. System parameters are fixed in the design model so that the model will yield either accurate or conservative MDMBR predictions for all operating conditions within a specified range. ,
Design model MONBR results are verified by comparison with results from the detailed model of the limitino assembly in the deterministic method. After the design model is shown to yield acceptable (i.e.
accurate or conservative) results, additional adjustment factors are applied to account for uncertainties in system parameter input to the detailed model. For exenple, engineering factors are applied to the hot subchannel of the design model to account for fuel fabrication uncertainties. These adjustment f actors, thouch arrived at statisti-cally, are applied in a deterministic manner. That is, although each adjustment factor represents a 95/95 prebability/ confidence limit that the particular parameter deviation frcm ncninal is no worse than des-cribed by that factor, all factors are acplied simultaneously to the limiting subchannel. This is equivalent to assuming that all adverse deviations occur simultaneously in the limiting subchannel.
2.2 Statistical Method The probability of all adverse system parameter deviations from nominal occurring simultaneously in the limiting subchannel is extremely remote.
With a more reasonable, demonstrably censervative method, the prcbability of system parameter input being more adverse than specified can be taken into account statistically, as described herein.
The' improved methcdology involves a _ statistical combin 2 tion of system ,
parameter uncertainties with t .e un correlation uncertainties to determine 2-2.
4-- I 'M M 4Mem- e= M eMWm- e a-w a.,.A4-..e_.%- - J m.
a revised design MDNCR limit. Since uncertainties in system para-meters are taken into account in the derivation of the new f!DNCR limit, no other allowance need be made for them. A best estimate
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design TORC model is therefore used with the revised fiDNBR limit for thermal margin analysis. This best estimate design model yields conservative or accurate I!DNER results when ccapared with a best estimate detailed model. An increased MDUBR limit is then applied o' to tha design model to account for system parameter uncertainties.
The resultant best estimate design model and increased MONER limit ensure with at least 953 probability and at least a 95% confidence level that the limiting fuel pin will avoid a departure from nucleate boiling if the predicted MDNBR is not below the limit MDNBR.
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2-3.
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I '30' Sources of Uncertainty, l Four types of uncertainty are identified in !4DNBR~ predictions from
- , . the TORC code
- .
- 1) numerical solution parameter uncertainty
, 11) code uncertainty iii) state parameter uncertainty
. iv) system parameter uncertainty Numerical solution parameters are required input that would not be
- - necessary if analytic methods could be used (e.g. radial mesh size, axial mesh size, convergence criteria, etc.). The uncertainties associated with these parameters are dealt with in a conservative
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roanner(3-1) in C-E's present methodology.
i -The numerical algorithms in the TORC code represent approximations to the conservation ecuations of mass, eccentum, and energy. Because l of the approximations involved, an inherent code uncertainty exists.
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This uncertainty is implicitly dealt with in the CE-1 CHF correlation l (3-3)(3-4). _
5, tate parameters, as explained in section 2.1, define the operational s; tate of the reactor. The treatment of uncertainties in these para- s l
neters is addressed in reference 3-2 . -
As explained in section 2.1, system parameters describe the physical environment that the working fluid encounters. This report establishes j the equivalent f1DN3R uncertainty that results from a statistical com-i bination of. uncertainties in system parameters.
3.1 5, tate Parameters Used in the Studv Generation of a response surface which simultaneously relates MDNBR to ll both system and state parameters would require an excessive number of 4 detailed TORC analyses. Consequently a conservative approximation is
- made and a response surface relating MDNBR to system parameters only is created. To achieve conservatism, it is necessary to generate the-surface for that set of state parameters wnich maximizes the sensitivity
! of MDNBR to syster parameter variations. That is, the response surface i
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can.be describ.ed as.:
MDNBR = g (x, y_o) 2 where yo, the vector of state parameters, is., selccted such that i 3(MDNBR) --- + maximum
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=
y a' m a g- - ,.~.-,,y.-y -
._g-.,,--,.,,,,--w, .,,.,-n - - - , ,y,+< , --,- -,m4-. . , - - , , , ,- w y- r w-
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l The set of state parameters, yo, that satisfies the above relation, is-referred to as the most adverse set of state parameters. The
- generation of the response surface is discussed in section 4.3, 3.1.1 liethod for Selecting State Parameters Allowable operating parameter ranges are presented in Table 3-1.
These ranges are based upon reactor setpoints including reasurement uncertainty. The response surface must be valid over these ranges.
As indicated above, a single set of operating conditions is chosen from these ranges to maximize the sensitivity of MDilBR to system parameters.
i This set of state conditions is determined from detailed TORC
!, analyses in the following manner. Two TORC analyses are performed for
!' a single set of operating conditions. In the first analysis, nominal system parameters are used and the core average heat flux is chosen to
- yield a MDilBR in the neighborhood of 1.19. The second TORC analysis uses the same heat flux and operating conditions but has one of the system pa ameters perturbed. The MD
- lBP, from the " perturbed" analysis is then i subtracted from the " nominal" f1Df!BR to yield a AMDNBR for the chosen set of j operating conditions. That is i
AMDilBR =
" Nominal" !!DMBR - " Perturbed" MDilBR (3.1 )
i The percent change in MDilBR is then determined according to the relation:
% Change = (AMDilBR/" Nominal" MD!lBR) x 100 (3.2)
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This process is repeated for several sets of operating conditions to j establish the sensitivity of the al1DNBR throughout the allowable operating range. Sets of operating conditions used in this sensitivity
- study are chosen to envelop the required ranges shown in Table 3-1.
l The operating conditions which yield the maximum percent change in 11DNBR are those which maximize the sensitivity of the MDNBR to the
- perturbed system parameter. These state. parameters are referred to as the "most adverse" state parameters.
- Since MDNBR is a smoothly varying function of these parameters (3-3),
j i
it is likely that the theoretical most adverse state parameters will be similar to the most adverse set found by the method described l -
above. Similarly, it is also highly unlikely that MDNBR sensitivities j observed with the theoretical most adverse set will dif fer appreciably j- from ilDNBR sensitivities which occur using the most adverse set found l'y the above method.
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..The detailed TORC model used in these cases is for one of the limiting asse' m bly candidates of the.Calvert Cliffs Unit 1, Cycle 3 core. In this model core geometry is identical, and boundary conditions are similar to the'St. Lucie Unit I core. Hence,-trends in the sensitivity 3-2. .
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g . - - -4a ywyom34+ .e. y p+p ,mi r.,c.w q v .-y- h , -
,,.e og ,g-, .,-.ege,..-n-m-,p-p 9 9,, ,yy, 4 y c,w e.-t -1 rr
of MOUBR to variations in system parameters at various operating conditions will be the same for these cores. The radial power distribution used in the sensitivity study differs from the dis-tribution used to generate the response surface. The sensitivity of MDNBk to state parameters will exhibit the same trends re-
' gardless of radial power distribution since the local coolant conditions in the hot assembly will be similar at 1.19 MDNBR.
llence, the most adverse set of state parameters found in this
.- study may be applied to generate the response surface.
Inlet flow and exit pressure bcundary conditions for the model are shown in Fig. 3-1 and 3-2. Core-wide and hot assembly power distributions are shown in Fig. 3-3 and 3-4 respectively. The detailed TORC analysis (3-1) consists of three stages. A core-wide analysis is done in the first stage, in which each fuel assembly near the limiting assembly is nodeled as an individual channel. Crossflow boundary conditions from the first stage are applied in the second stage to a more detailed model of the neighborhood around the limiting assembly. Each quadrant of the limiting assembly is represented by a channel in the second stage analysis.
Crossflow boundary conditions from the second stage are applied to the subchannel model of the limiting assembly hot cuadrant in the third stage, and the MDMDR is calculated. TORC models for the first, second, and third stages of the model used in the sensitivity study are shown in Fig. 3-5, 3-6, ar.d 3-7 respectively.
3.1.2 Inlet Flow Perturbation Sensitivity As indicated in Fig. 3-3, the hot assembly occurs in channel 9 of the first s tage TORC model . A perturbed model for use in determining the sensitivity of inlet flow distribution effects on !!DNBR to operating conditions is created by reducing the inlet flow fraction to the hot assembly and an adjacent assembly. Inlet flow is also increased accordingly in tuo assemblies far from the hot arsembly to preserve continuity. Inlet flow fractions for the perturbed and nominal models are presented in Table 3-2.
The sensitivity of flou distribution effects on MDNBR to operating con-ditions found with the above nodels is presented in Table 3-3. MDNBR is most axial sensitive shape to[ variations in the inlet flow distribution for an index of ]. Greatest sensitivity to flow perturbations is observed with a pressure / temperature / flow combination of [
]. Ilence the greatest sensitivity is expected to occur for the operating conditions:
3.1.3 Enthalpy Rise Factor Sensitivity, The method described in section 3.1.1 is altered slightly to determine the state parameters which maximize 11DNBR sensitivity to the enthalpy 3-3.
rise factor. The uncertainties accommodated by the enthalpy rise factor are discussed in Reference (3-4 . Since the enthalpy rise factor affects only the limiting subcha)nnel and adjacent subchannels,
.
- an isolated model of the limiting assembly hot quadrant is used to reduce corputational time. The isolated quadrant model is simply. '
the hot quadrant subchannel model shown in Fig. 3-7 with adiabatic, impervious- boundary conditions imposed on the sides of the quadrant.
- Observed trends in behavior found with TORC analyses of the isolated quadrant model are confirmed by multistage TORC analyses. Nominal cases are run with no enthalpy rise factor. An enthalpy rise factor of 1.03 is applied to the fuel pins which bound the limiting sub-channel in the perturbed cases.
Results found with the isolated TORC model are shown in Tables 3-4 and 3-5. The data in these tables indicate that MDMBR sensitivity to the enthalpy rise factor is maximized with [ ] axial shape indices, corresconding to [ ] power distributions, and the pressure / temperature /ficw combination [
]
Data from multistage TORC analyses are presented in Table 3-6. These data show a similar trend wnen compared with the isolated quadrant model data of Table 3-4, however maximum sensitivity is seen at a [ ]
axial shape index. The greatest sensitivity of MDMER to the enthalpy rise factor is expected to occur for the operating conditions:
3.1.4 Systematic Pitch Reduction Sensitivity ,
i Systematic pitch reduction uniformly decreases fuel rod pitch throughout an entire fuel assembly. Nominal pitch for 14 x 14 C-E fuel is 0.58".
Hot assembly fuel pitch is reduced to[ ]in the limiting assembly of the perturbed model used to establish the sensitivity of systematic pitch reduction effects on MDUBR to operating conditions.
- Results from nominal and perturbed pitch TORC analyses are shown in Table 3-7. Based upon these data, maximum MDNBR sensitivity to systematic
. pitch reduction is expected to occur at:
Data in Table 3-7 also indicate that the sensitivity of MDNGR to systematic pitch [ ].
3-4.
3.'l.5' Most Adverse State Parcraters As explained in section 3.1.0, the set of state parameters chosen 0 - for use in generating the response surface should maxinize MD:!BR sensitivity to variations in system parameters; this is the most ,
adverse set of state parameters. The most adverse set of parameters is chosen for use in generating the response surface so that the resultant ID:!BR uncertainty will be maximized. This introduces conservatism into the overall treatment.
The state parameters which maximize t'D1CR sensitivity to various system parameters are listed in Table 3-8. This comparison indicates that( ] psia and[ 3 design flow are respectively the most adverse system pressure and flow rates. The most adverse axial shape index (A.S.I.) and inlet temcerature (Tin) are not evicent frem this compari-son. The magnitude and irpact of each system paraneter uncertainty must also be considered in choosing the most adverse values of A.S.I.
and Ti n-Magnitudes of each of the system parameter uncertainties are assigned and discussed in Sections 3.2 - 3.8. The mac'nitude and impact of
-the [ ] those of the other system parareters. Therefore the A.S.I. and Tin which tend to maximize MD: BR sensitivity to the [ ] are used to generate the response surface. Although maximum MDI!SR sensitivity to
[ ] is cbserved with [ ] A.S.I . , this sensitivity is only slightly less than the sensitivity observed with a!- ]A.S.I.,
as shown by the data in Table 3-3. Since sensitivity to enthalpy rise factor increases witnl ]A.S.I.,[ 3is selected as most adverse. The most adverse set of state parameters is thus:
where 100% design flow is 376,000gpm.
3.2 Radial Power Distribution.
The PDQ corrputer code (3-5) is used to predict planar radial power distributions throughout the life of a core for enveloping operating condi ti ons . Limiting pcwer cistributions are selected frca the above
- set and are used as input to TORC D:!B analyses. Cenparisons between PDQ predictions and measured data (3-6) show that PDQ overpredicts radial peaking factors in the peripheral regions of the reactor (i.e. the outermost three rows of fuel assemblies).
Inlet flow distributions for four-loop operation and seized rotor accident analysis of CE's 14 x 14 cores are shown in Fic 3-1 and 3-8 respectively. These distributions manifest the fulic. ting trend: the central portion of the core receives higher than average 3-5. t
i inlet flow while the peripheral assemblies receive lower than average inlet flow. For this reason, the limiting assembly for DNB analysis is found on the core periphery. ,
Since the PDQ power distributions overpredict power in the peripheral assemblies, and the limiting assembly for DNS analysis is among these
- assemblics, the use of PDQ data in DNS analyses is conservative. This inherent conservatism in the thermal margin methodology makes it unnecessary to account for uncertainties in the radial power distri-
!" butions that are used in TORC DNS analyses.
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3.3 Inlet Flow Distribution ,
m I. An inlet ficw Loundary condition is used in detailed TORC analysis.
! P.atios of the tocal to core average mass velocity are input for every flow channel in the core-wide analysis. Mean values of the inlet flow
- splits for three pump operation are presented in Fig. 3-8. A large part of the uncertainty in the ficw splits results from measurement a uncertainty. This measurement uncertainty is censidered random and may be characterized by a normal probability distribution function (p.d.f.).
j A sensitivity study, conducted to determine the effects of inlet flow variations in assemblies which neighbor the limiting assembly, l
yields the results presented in Table 3-9. Channel numbers in this table refer to Fig. 3-5. Flow in the assemblies diagonally adjacent to the limiting assembly is decreased by 3, 6, and 9 percent for bottom
- peaked axial power profiles and by 9 percent for a top peaked profile.
These perturbations are in excess of inlet flow uncertainties, yet
- only' minor changes in MDNER are observed. Therefore, it is concluded that only inlet flow in the limiting assembly and those assemblies immediately adjacent to it are needed in the response surface.
i "3. 4 Exit Pressure Distribution
& Sensitivity studies conducted to establish the impact on MDNER of variations in the exit pressure distribution are summarized j in Table 3-10. Detailed TORC analyses are performed with nominal and extreme exit. pressure distributions, as
- shown in Fig. 3-9. The exit pressure in the limiting assembly is increased to the 955 crobability level while the exit pressures i in the assemblies adjacent to the limitino assembly are also increased
! to yield an approximate 95? probability level for the three adjacent i assembly exit pressures in the extreme exit pressure distribution.
!, Channel 4 of Fig. 3-5 is the limiting channel in this; study. Detailed TORC-analyses performed with both bottcm peaked and-top peaked
- axial power profiles ' demonstrate that MDNBR is extremely insensitive 2
to variations in the exit pressure distribution. - Consequently, the exit p,ressure distribution need not be included in the.MDNBR response surface.
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j 3-6.
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, ye - - . . . , , . . --w , 95" confidence than these values. that the population nean and standard deviation are no l 3.7 Clad 0.D.
Variations local heatinflux. clad diameter change subchannel flow area and also change the The ircpact of both random and systematic variations in fuel clad 0.D. on the local heat flux is cccounted for by the engineering factor on heat flux, discussed in section 3.6. The effect of random variations in clad 0.D. on subchannel flow area is included in the rod bow penalty, discussed in section 3.9. The effect of systematic variations in clad 0.D.
on the subchannel hydraulic parameters is addressed here.
Manufacturing tolerances on the fuel clad allow for the possibility that the clad diameter will be systematically above nominal throughout an entire fuel assembly.
That is to say, the mean as-built value of the clad 0.D. may differ from the nominal value.
The distribution of the mean clad 0.D. for fuel assemb-lies may be characterized by a normal p.d.f. with a mean equal to the mean clad 0.D.and a standard deviation given by the relation ( 3-D :
- o. = d (U-n) '
jn(N-fT (3.3) where sampleH is the number of specimens in the parent population and n is the size.
3-7.
w-A-m h ib pm, 4,,,,,,.., q ,_p,1,
Ar. built data for C-L's 14 x 14 fuel are presented in Table 3-11.
The minimum systematic clad 0.D. is [ j uhile the maximum systematic clad 0.0. is [ ]. Since the idverse of fect of clad 0.D. variations is already taken into acccunt by the engineerinq heat flux factor, and use of a less than nominal clad O. D. uculd increase subchannel flow area, benefitting the MDMBR, the maximum value [ ] is used in this study. The standard deviation of the mean at the 96% confidence limit is ['
in. The double j
accounting for both the adverse effect of a decrease
.. in clad 0.D. in the engineering factor on heat flux and the adverse ef fect of a systematic increase in clad 0.D. on subchannel flow area
. adds conservatism to the analysis.
3.8 Systematic pitch Reduction The rod bow penalty, discussed in section 3.9, takes into account the
' adverse effect on MDNBR that results from random variatiers in fuel rod pitch. The rod bow penalty does not take into account the adverse ef fect of systematic variations in fuel rod pitch. This systematic pitch reduction ef fect must be discussed separately.
Manuf acturing tolerances on fuel assemblies allow for the possibility that the as-built fuel pitch will be less than nominal throughout an entire fuel assembly. Thus the systematic pitch refers to the mean value of the pitch in an assembly. The systematic pitch distribution is assumed to be a normal distribution characterized by the maan value of the pitch and the standard deviation of that mean value.
As-built gap width data for C-E's 14 x 14 fuel are presented in Table 3-12. The minimum systematic can width is seen to occur n the Calvert i Cliffs 1[ ]'
and is[' . inches. This , combinea with the maximum ciad O.D. f rom section 3.7 indicates that the mini, mum D1tch is [*. ~ J At the 954 confidence level, the standard deviationofthemeanis[ iinches.
3.9 fuel Rod Bow The fuel rod bow penalty accounts for the adverse impact on MDNBR of random variations in spacing between fuel rods. The methodology for determining the rod bow penalty is the subject of a C-E topical report (3-8). Appendix G of that report (3-9) applies a formula derived by the NRC (3-10) to ;ompute the rod bow penalty for C-E fuel. The penalty at 45,000 mwd /liTU for CE's 14 x 14 fuel is 0.6% in DNBR. This penalty is applied directly to the new MDNBR limit derived in Section 5.
3.10 Cilf Correlation The C-E 1 Critical lleat Flux (CilF) correlation (311) (3-12) is used in the TORC code (3-1) to determine whether a departure from nucleate boiling (DNB) will occur. This correlation is based on a set of 731 3-8.
data points. The mean of the ratio of observed to predicted CHF using the CE-1 correlation is 0.99983, while the standard deviation of that ratio is 0.06757. CHF correlation uncertainty may be characterized by a normal distribution with a mean of 0.99983 and standard deviation of 0.06757. This yields a 1.13 I:D"BR limit to satisfy the criterion or "953 probability at the 953 confidence level that the limiting fuel pin does not experience DMS". Mcwever, because the flRC staff has not yet con-cluded its review of the CE-1 correlation, a SS penalty has been applici;
,. this raises the 95/95 DNBR limit to 1.19. This penalty may be conserva-tively treated by assuming a displaced Gaussian distribution with a mean of 1.06 and the same standard deviation as above.
3.11 TORC code Uncertainty The TORC computer code (3-1) represents an approximate solution to the conservation equations of mass, momentum, and energy. Simpli fying assumptions .':ere made, and experimental correlations were used to arrive at the algorithms contained in the TORC code. Hence, the code has associated with it an inherent calculational uncertainty. Comparisons between TORC predictions and experimental data (3-10)(3-13) have shown that TORC is capable of adequate predictions of coolant conditions.
As explained in Section 5.0 of Reference (3-13), the TORC code was used to determine local coolant conditions from data obtained during the CE-1 CHF experiments. These local coolant conditions were taen used to develop the CE-1 CHF correlation. Thus, any calculational uncertainty in the TORC code is implicitly included in the MDMBR limit that is used with the TORC /CE-1 package in thermal margin analyses.
e 9
g 3-9.
q , -
P
/
/
t l
1 1
i e .
I I
i i
E i
FIGURE 3-1 INLET FLOW DISTRIDUTION USED TO ESTABLISFI STA FE PARAMETERS FOR RESPONSE SURFACE 3-10
I 8
i I
i 1
i i
i i'
l.
i l
l I<l j
FIGUilE 3-2 EXIT PRESSURE DISTRIBUTION USED TO ESTABLISH STATE PARAMETERS FOR RESPONSE SURFACE 3-11.
1 2 HOT ASSEMBLY
- 0.8349 1.041 STAGE 1 TORC ANALYSIS - ~
3 ,4 5 6 7 i
CHANNEL NUMBER 0.8384 1.007 1.212 1.112 0.9970 ASSEMBLY AVERAGE 8 9 10 11 12 13 l /
RADI AL PEA!(ING FACTOR .-0.9123 1.249 1.038 0.949G 0.9302 1.280 14 15 10 17 18 19 20 0.0087 1.100 0.9971 0.9223 1.213 0.0155 0.9174 22 23 24 25 26 27 28 I
21 1.030 i
0.8305 1.245 0.9941 1.240 0.8632 0.8736 0.9778_
l l l I l
1.037 1.065 g 1.035 0.0270 l 0.8083 g 0.8519 l 1.02G l0.9020 l
- _. ._ p _ _ .- __ _ 4 ._. _ p ._ __ __ _ __ 9 ._ __ 9 _
i 1.209 I .0443 0 1.213 I
0 ! 1 .038 0.8304 I 0.9512 I .8320 0
I l.8745 l l 1
,,,,,,r._._+____ __ __ , _ _ q_ _ _ _--T--+-
0.9195 0.9358 l 1 .02G 0.9523 0.9538 l 1.110 ! 0.9352 l 0.9G13 -
i l 1 l 1.038 l-- - - - - - - - -t- - T- - - -- - - -t- - ~
1.280 0.9259 1.084 0.9356 0.8308 0.9408 0.8234 ._
k- ~~ 0.9932 , .
1 f i
'i flote: Circled channel numbers denote flow channels in which several -
fuel assemblies have been " lumped" into a single channel for T-il analysis.
~
(
l 1
FIGURE 3-3
, CORE WIDE RADI AL POWER DISTRIBUTION USED TO ESTABLISH STATE PARAT.1ETERS FOR RESPOTJSE SURFACE 3-12.
.~ -
. _ r- l d
7 enotes asser.bly quadrant average radial peaking fac.:
l
, J/
FR= Fn=
1.185 1.333 LOCATION 9
J 1.174 1.139 1.214 1.243 1.2EG 1.374 1.210 1.231 1.2G1 1.282 1.297 1.335 1.338 1.25G 1.298 1.359 1.370 1.333 1.310 1.313 1.299 1.371 p , 1.384 1.309 1.284 FR" 1.314 1.332 1.319 1.333 1.387 1.304 1.272 1.321 1.358 1.409 1.40G 1.347 1.293 1.269 1.341 1.357 1.373 1.365 1.335 1.305 1.287 i*
FICUP.E 3 !.
HOT ASSEMBLY RADIAL POWER DlSFRIBUTION USED TO ESTABLIS11 STATE PARAMETERS FOR RESPONSE SURFACE 3-13.
v w m,- -,w, ,- w - - r , -- +
C L .
I l
1 2 Cil ANNEL NUMBER ,3 4 5 6 7 IN FIRST STAGE MODEL i
8 9 10 11 12 13 i
14 15 1G 17 18 19 20 21 22 23 24 25 2G 27 28 l
I I I i I
l l I I
- _. _ .__ I __ _ _ _ _. __ ll ._. __ _l __ _ ____.l_
._ __ __I _ ._ _
l 1 l l l l l 20 ! ! 30 l l 31 I i_ __ _ I __ __ ___ __ _l _ ._ ._ i _ _ __ ____ _i_ __ _I_ __ _
l ! l !
l l
--M 1 I i I
L.
I
__ __ l __ _ _ __ __i .___ 1
_. ._l ___ ______ __ I_.i _ _ __I __ ._ ._.
I l 1 I Q.--
i l i I I -k I I i I I .
I i 1 i
- ~ - .. .._. .
FIGURE 3-5 i
ClfAll:iEL :.'G:222I: G CCI.~i"'E FOR STAGE 1 TORC A!IALYSIS TO ESTABLISi! RECI'O::SE SURFACE STATE PAPE.ETERS l 3-14.
w_: -
. ~ . -
CilANNEL NUMBER IN -- 25 6
/
t l'"
SECOND STAGE ?.10DE L /
/
i 7 0 2 1
/
/
3 4 /
. CROSSFLOW BOUNDARY '
CONDITIONS APPLIED ALONG THIS BOUNDARY- 14 '; 9 10- 11 $
/
15
/ /
/ /
/ /
/
/ / // /// ////// / / //// //
16 17 18 l
l l
c _ ._.
- -C L l
1
= 1 1
1' -
I FIGURE 3-6 CII/Ji:iEL :,J:HiERI:!G SCI!E"E FOR STAGE 2 TORC /J7ALYSIS TO ESTADLIS!! RESP 0:ISE SURFACE STATE PAR /o'ET-33
)
l
- i l
l0 3-15.
I TillRD STAGE TORC ANALYSIS TillRD STATE TORC ANALYSIS j CllANNEL NUMBER FUEL PIN NUMBER 35 k ,
l 3 4 I 5 G 2 l 1 1
I 9,
1 l y 21 21 11 10 11 l 12 13 7 8 9 l 17 18 - 19 20 14 15 1G 22 l 2 27 12 23 24 25 36 37 21 22 l 13 7 3 32 28 23 23 29 30 2G l 27 14 8 5 4 33 29 24 l 18 33 34 35 36 37
-1 31 32 25 19 15 0 6 34 30 40 41 42 43 l 44 l 38 39 31 2G 20 16 10 38 i
FIGURE 3-7
) THIRD STAGE CHANNEL AND FUEL PIN NUMBERING SCilEME USED IN TORC
! ANALYSES TO ESTABLISH RESPONSE SURFACE STATE PARAT.1ETERS 3-16.
f I -
i i
I i
t i
l i
- k l<
FIGllRE 3-8 i
!!!LET FLOU FACTORS FOR SEIZED ROTOR A: t. LYSIS OF 217 ClJ:lDLE 14x14 ASSE!13LY CORES 3-17..
1 :
. VALUES DENOTE DEVIATION OF ASSEMBLY AVERAGE EXIT PRESSURE FROM CORE AVERAGE EXIT PRESSURE (PSF) '
l l
l t- I I
l FIGUPI 3-9 l EXIT PRESSURE DISTRIBUTIONS USED IN SENSITIVITY STUDY i
3-18.
~ s ,- - ,, , n
s Range .
Operating Conditions Units Axial Shape Index * -0.55 < A.S.I.< 0.55 Inlet Temperature F 465< Tin <580 psia 1750< P *2400 System Pressure _ s3's -
% design
- 77< w <120 System Flow Ilotes
- See note (1) on Table 3-3 for definition of axial shape index
- Thermal Margin design flow = 370,000 gpm e
e TABLE 3-1: RA:'GES OF OPEPATI!!G C0:tDITIO. S FOR llHICli RESPO*!SE SURFACE IS VALID l
I l
I=
l l
3-19.
Inlet Flew Fractir,r*
Stage 1 Channel Number Nominal Perturneo Assembly Inlet Mass Velocity
- Inlet Flow Fraction =
Core Average Mass Velocity TABLE 3-2: MOMINAL AtiD PERTURGED FLO'd FOR ESTABLISHING '
SENSITIVITY OF FLO'd DISTRI3UTIO:1 EFFECTS 0.l MDNBR TO OPERATIiG C0:iDITIO::S 1 i l
4 3-20.
Sta te l'arameters MfX:UR
/$xial Shape inlet System flominal l' ort or$c4 Index l'ressure lemperature flow flow I low
- A 7, Change (1) psia F " design
-(2) (3)
-0.07 2200 550 100 4
-0.02 2200 550 100
. 0.00 2200 550 100 0.317 2200 550 100 0.337 2200 550 100 0.441 2200 5'J O 100 0.527 2200 550 100
-0.070 2400 580 120
-0.070 1750 580 120
-0.070 2400 465 120
-0.070 1750 465 120
-0.070 2400 580 77
-0.070 1750 580 77
-0.070 2400 465 77
-0.070 1750 465 77 0.337 1750 580 77 0.337 1750 465 77 0.337 1750 580 120 _ , , ,
! o L/2 Fz d2 - f 2dz core a w age FZ = axial peaking factor s .
l (1) Axial Shape Index = 3 2 o = core midplane LI L = active core length i
[ F Zdz l -L/2 l (2) AMDrillR = "flominal" MDMBR "Ferturbed" MDilBR (3) ; Change in MDilBR = ( AMONBR /flaminal 11DllilR ) x 100
- see Table 3-2 l'
~
TABLE 3-3: FLOW PERTUPBAT10:1 EFFECTS AT VARIOUS OPERATitlG C0:lDIT10!!S
\
! 3-21.
l
~. -. .-= . _. . . . - - - -__ . -- _
t ,
14 D fl B R EllTHALPY RISE AXIAL SHAPE f;0!!It'AL FACTOR APPLIED 4 '
% chat:GE IllDEX (3) l
- (2)
(1) -
i.- -0.527
-0.359
-0.070 i
-0.020
. 0.00(C)*
0.00(S)*
0.337 l
0.444 0.527
-0.317
-0.162
' O.317 -
- Doth a cosine (denoted by "C") and saddle (denoted by "S")
Axial Shape were used for 0.00 A.S.I.
~0PERATIf;G CONDITIOlS:
Pressure = 2200 psia Inlet Temperature = 5500F System Flow = 100% design l .
!- (1) .' - See flotes on Table 3-3 '
(2)
(3) .
l TABLE 3-4: SDISITIVITY OF E?tT!!ALPY PISE FACTOR EFFECTS TO AXI AL SHAP lilDEX (ISOLATED 1:0T ASSEIELY 10 DEL) 3-22.
e e,n, -w +- y .- -r--- -'r.,-, ',,y-vm--- ,7 7 - - " * - + - " " ' ' = -- -
e PARAMETERS iIDNSR
~
5 TATE Inlet System Enthalpy Rise Axial Shape Factor Applied a % Change Pressure Temperature Flow I'ominal Index psia F % design - -
(2) (3)
(1) .
. i
~
\ ._
(1)
(2)
- See Notes on Table 3-3 (3) .
. TABLE 3-5: SENSITIVITY OF EilTHALPY RISE FACTOR EFFECTS TO OPERATIliG' C0liDITIO:is (Isolated Hot Assembly Model)
'3-23. i j
w--e- +
s . .
- !! D fl B R l- -
Axial Shape Enthalpy Rise Factor Applied a % Change Index Nominal
~(2) (3)
(1)
OPERATIts CONDITIOllS Pressure = 2200 psia Inlet Teinperature = 5500F System Flou = 100% design (1) '
(2) -
See tlotes on Table 3-2 (3) .
TABLE 3-6: SEi;SITIVITY OF EilTHALPY RISE FACTOR EFFECTS TO AXIAL SHAPE It!DEX (Core Wide Analysis) j i
l l
I 3-24.
l i
. .. ..., , w ..
d PARAMETERS MDNBR STATE Inlet System " educed i
Axial Shape Pitch a. 5 Change Pressure Temperature Flow Nominal l fndex psia F % design - -
(2) (3)
(1)
L 1
l*
~
I l
1 l
F t'
(1) 3 (2)
See Notes on Table 3-3 (3) J I
I
'~
TABLE 3-7: SENSITIVITY OF SYSTEMATIC PITCH REDUCTI0il EFFECTS TO OPERATII:G CO:;DITICIS l 3-25.
9 L -
i % .
- STATE P A R A l1 E T E R S axial Shape Inlet Index Pressure Temperature System Flow
. System Parameter psia F % Design (1)
Inlet Flcw Distribution Enthalpy Rise Factor Systematic Pitch Reduction _ ,
(1) See note on Table 3-3 TABLE 3-8: STATE PARAMETERS k'HICH MAXIMIZE lid:iBR SEilSITIVITY TO SYSTEM PARN1ETERS l
l e
i I
3-26.
1
__= __ - . _ . , _ , - - . - -
3
MD:CT Change in MDNBR Axial Shape Index Flow Split Reducticn*
TABLE 3-9: !!D:lBR SEilSITIVITY TO I!!LET FLO'd DISTRIBUTIO:1 4
3-27.
s .
Change In Axial Shape Exit Pressure MD:lBR Distribution MDNBR Index
.\
A TABLE 3-10: SE!!SITIVITY OF MD:lBR TO EXIT PRESSURE DISTRIBUTIO1 e
l l
I 3-28.
'W _e..
1, t
2 3 4 5 0YCLE 1 A,B,C D E F G BATCH i .
'! 0MAllA MILLST0ilE CC #2-CC #1
- ST. LUCIE 1 1
l MAINE YANKEE l
l l - Mean
- Standard Deviation I - Standard Deviation cf the Mean l
- I' tiote: !1ominal Clad 0.D. = 0.44 inches TABLE 3-11 AS BUILT CLAD 0.D. (inches) DATA r0P,14 X 14 FUEL 1
d l
l l
. 3-29.
1
,;, i '
5 0
1 C
1' 3
I l I C '
s C f l I f ,
i
. l C
t 2 r 1 s n
. e 0 t a v - n e l C e m a m C e f r o
. u s n )
a o S e i E m t H
. 0 a C f i N 1
0 o ve I
- (
C r d e A b d T l m u a r A D
n d n H a
)
+ t s
T D
I x W x
e ee (
x P nk x x A i n x x G t
aa xi >
f- Y x x T L
> I U
B n -
a S c A I !
t ':
rs 2 ef 1 vf -
li 3 al CC E L
B
, A T
e n
o t
s l
l i
t I-n u
o th .
rl oa FC .
r e
nb am pu 8 7 6 5 4 3 2 )
SM l: i l
> YE-
- 4. 0 f1DritiR Response Surf ace A response surface is a functional relatic v;bip which involves several independent variables and one dependent vcria' ale.
The surfacn is created by Fitting the constants to data obtained from experinents.
of an asstned functional rglationship The response surface provides a convenient reans by which accurate estimates of a complex or unknown function response may be obtained.
Since the response surface is a relatively ;imple 'exp res s i on .
it may be applied in analytic techniques wFere rnore complex functions O
would make an analytic solution intractable.
in the present application, a single detailed TORC analysis is treated as an " experiment". A carefully selected set of detai'ed TORC "expcri-ments" is conducted, and a functional relationship is fitted to the 11DimR results. This response surface is then used in conjunction with
~ Mon;e Carlo techniques to combine probability distribution functions (p.d. f. 's) for each of the independent variables into a resultant MDf!BR p.d.f..
4.1 TORC 11odel Used The inlet flow distribution (shot , in Fig. 3-8) is compared with radial power distributions for the Ccivert Clif fs Unit 1 and Unit 2 reactors to determine the limiting location for Df!B analysis.
For the purpose of generating the response surface, the limiting location is defined as the assembly in which the irnpact of system para-meter uncertainties on MD!lBR is the greatest. The core wide and limiting assembly radial powar distributions used to generate the response sur-f ace are shown in Fig. 4-1 and 4-2, respectively.
The first stage TORC model used in this ar -
is is shown in Fig. 3-5.
The limiting assembly occurs in channel' this model. Second and third stage models used in this analysis ave snown in Fig. 4-3 and 4-4 respectively.
4.2 yariable;Used A careful examination of the sources of uncertainty discussed in Section 3 shows that several of these sources of uncertainty can be omitted from the response surface.
l The state variables mentioned in section 3.1 are treated in part 1 of this report (4-1).
As explained in Section 3.2, inherent conservatism in the calculation of radial peaking factors makes the need to account for uncertainty in
- the radial power distribution radial power distribution was omitted used in DilB analyses unnecessary, tience, the from the response surface.
4-1. '
~
-- ~
i . .
The sensitivity study discussed in Section 3.4 indicates that large perturb-
~
ations in the exit pressure distribution have negligible effect on the pre-dicted lid:lBR. Thus, the exit pressure distribution is not included in the
. response surface.
The heat flux factor (F n) q is applied to the !!DilBR calculated by TORC in the following manner:
. . - MDfiBR TORC liDiiBR = (4.1)
Fu q
Since the functional relationship between lid;!SR and F,," is known, the heat flux factor is not used in generating the response sdeface. Instead, this factor is combined witn tne resultant surface, as explained in section 4.5.
A method has already been developed (4-s) to account for red bow uncertainty.
tio rod bow effects are included in the response surface. Instead, the rod bow penalty found with existing rethods (4-2) is applied to the design limit MDil6R f ound in the present alaiysis.
The calculational uncertainty associated with MDlBR predictions found with the TORC /CE-1 package is inplicitly included in the CHF distribution uncert-ainty, as explained in Secticns 3.10 and 3.11. Hence no explicit allowance for code uncertainty is included in the response surface.
The system parameters included as variables in the response surfacc are listed in Table 4-1.
4.3 Experiment Design An orthogonal central composite experimental design (4-3) is used to gen-l erate the response surface applied in this study. The total number of exper-l iments needed to generate a response surface using this experiment design is t
2k + 2k + 1 where k is the number of variables to be considered. The desired response surface consists of seven variables, hence 143 " experiments" or detailed TORC analyses
- were needed for a full orthogonal central composite design. The results of these experiments may then be manipulated by means of the least squares estimator b= {n'n}-I[n'}z, , (4. 2 )
l 4-2.
s4 S M'88 dDOMp5 t
Cas*M_C#%1"
w;1ere z is the vector of experimental results,
- to yield the coefficients which define the response surface 7
2 = MD:iBR g3
= bg + bj nj + b$$(n -c) + 7 b
nj t1j (4.3) i <j In the above equations, the n. are coded values of the system parameters ( )
l to be treated in the respense surface, as indicated in Table 4-1. The b r p-resent the constants found frca the TCRC results by c.eans of Eq. 4.2, and c is a constant determined by the number of experiments conducted. .
The number of TORC analyses needed to generate the response surface could be reduced significantly if some of the interaction effects (i.e. b jj nn j j) were neglectea.
4.4 Des _ign !!a_trix The set of experinents used to generate the response surface is referred to as the design matrix. This matrix, in coded form, corprises the second through eighth columr.s of the a matrix cidted in Eq. (4.2). Both coded and uncoded versions of the design natrix used in this study are presented in Appendix A along with resultant NC:!3R values. The design matrix was con-structed such that each independent variable included in the response surface extends just beyond the 2a range of its associated p.d.f.
4.5 Response Surface Equation (4.2) was solved numer:cally using the data in Appendix A.
Constants for the response surface as given by Eq. 4.3) are presented in Table 4-2. Comparisons made between TORC predicted i:EIBR and response surface predictions shcw excellent agrcecent. The 95% confidence estimate of the response surface standard deviation is 0.00378.
The heat flux factor is included analytically in the response surface by combining Eq. (4.0) with Eq. 4.3). The final relationship is given by I 7 7 2 7 7 MD!!BR
= T q.. ' b6+t bj nj+ ri=1 bjj(nj -c)+i=1
, I a=1 b jj njnj (4-4) i=1 i<j 4-3.
The coefficient of determinaticn, r, provides an indication of hcw well the response surface explains the total variation in the response variable
- (4-4). When r=1, a true model has been found. The r value associated with the response surface generated in this work is 0.9995, which indicates that this response surface is a good model.
Another indication of model performance is provided by the standard0.003408.
error of estimate (4-5). The standard error for the respcnse surface is The relative error is 0.295, indicating that this model performs well.
I l
r r
l.
l-4-4.
9.
I
- ~
I .
l' ~
l' 2
, 1.1813 1.5170
! * =
1 i , 3 4 5 6 7 1.1444 1.5640 1.0551 1.3508 1.G570 BOX NUh GER 8 0 10 11 12 13 3
ASSEf1BLY AVERAGE 1.0481 1.5205 1.4035 1.0014 1.2227 0.70G2 1' ilADIAL PEAKING FACTOR
~
14 15 10 17 18 10 20 1.0472 1.0862 1.0014 1.4707 1.0502 0.50GG 0.G33G
- 21 22 23 24 25 26 27 28 1.1410 1.5271 1.0031 1.4170 1.1005 0.4147 0.5007 0.5148 i
~
! 20 30 31 32 33 34 35 3G l . 1.403G 1.3099 1.4713 1.032 0.84G1 0.7310 0.5170 0.4752 37 38 30 40 41 42 43 44 1.G445 1.0368 1.0560 0.4151 0.7312 0.5020 0.5554 0.3023 45 4G 47 48 40 50 51 52 53 s, 1.34G0 i.2iGs 0.3046 0.5800 0.5232 0.5534 0.3574 0.3053 1.5030
. 55 56 57 58 50 60 01 62 Q, - - 1.G443 0.7744 0.0307 0.502G 0.4520 0.3008 0.30G2 0.18G1---q 4.
Figure 4-1
~
CORE WIDE POWER DISTRIBUTION USED TO GENERATE RESPONSE SUHFACE I .
4-5.
l l .
t . _ _ ,. . _ _ _ _ , -_. _
4 x Figure 4-2 liOT ASSEMBLY RADIAL POWER DISTRIBUTIOtJ USED TO GENERATE RESPOT1SE SURFACE i
4-6.
i l
i i
l 1
i 1
Figure 4-3 INTERMEDIATE (2ND STAGE) TO!1C MODEL USED IN GENERATING RESPONSE SURFACE 4-7.
1 1
\
a ;
j
- l-35 j 2 j 4 }
2 3 1
t.
i
- 1G 17 18 8
4 5 7 l
23 24 25 37 3G 21 l 22 i
LOCATION 12 13 14 9 10 11
- b3- ,
28 29 30 -
2G 27 20 21 22 15 1G 17 18 l
33 34 35 3G 37 H-32 25 2G 27 28 29 23 24 l
39 40 41 ,
42 43 4 H ,
30 31 32 33 34 l
38
- f.
- rigure 4-4 SUBCf!ANNEL (3RD STAGE) TORC MODEL USED IN GENERATING RESPONSE SURFACE 4-8.
\
)
System Parameter Variable Index(i) Coded Variable ** '
a p 1
x1 hot assenhly) inlet flow factor
. (channe1[.]
x2 2 channel [ '] inlet flow factor 3
channel [. ] inlet ficw factor x3 xq 4 channel [ '] inlet ficw factor 5 1.0001 0.0119 enthalpy rise factor xs 6
systematic pitch x3 I
7 systcmatic clad 0.D. x7 _
- channel numbers refer to Figure 3-5 9- where the a. )
- variables coded according to relation 7.=*i~g; i
i 0 at nominal ccnditions, ar.d the q are chosen are chosen such that such that the range of t nj =he response surface will include 27 ranges of each of the system parameters TABLE 4-1: STATE PARAMETERS INCLUDED AS VARIABLES Ili THE RESP 0MSE SU s
4-9.
% e
- s 1
i
- e
.i 1
4 4
) -
i, ,
4 i
I Y v ' 7 i
MDilBR g3 - =
b,4 { % + [ b;,( f; - d + hil>g p3
- ,1 ...
iq;-
'J TABLE 4-2: COEFFICIEilTS FOR MD:lBR RESP 0 rise SURFACE 3
t-i 4-10. .
y yie- 6 -y ---g r y----t J' h-' te %wN? 9 p M t-upew er e r ==- -r--T -t*T e
- t
5.0 Combination of Probability Distribution Functions The MDin1R response surfac[ discussed in Section 5 is applied in ftonte Carlo methods to combine numerically the system parameter probability distribution functions (p.d.f.'s) discussed in Section 3 with the CliF correlation uncer-tainty. A new 95/95 f1D:lBR limit is then selected from the resultant p.d.f.
This new limit includes the effect of system parameter uncertainties and thus may be used in conjunction aith a best estinate design TORC model.
. 5.1 Method The SIGMA code applies !bnte Carlo and stratified sampling techniques to
. combine arbitrary p.d.f.'s numerically (5-1). This code is used with the response surface to comi.ine system parameter p.d.f.'s with the CE-1 CHF correlation p.d.f. into a resultant tiDt:BR p.d.f. The r:ethods used to achieve this combination are discussed belcw.
The effect of system parameter uncertainties on MDf!BR is ccmbined with the effect of uncertainty in the CHF correlation by computing a t.MDi'BR caused by deviation of the system parameters from neminal:
, MDriBRRS MDMBR 3 -
tWM (5.1) where MD!!BRg 3 is the MDi;BR found by substituting the set of system parcmeters into the response surface and MDilBR:C:1T is the MDilBR value predicted by the response surface with nominal system parameters. A point is then randomly chosen from the CHF correlation p.d.f. and combined with the al>DiiBR f"om Eq. (5.1) to yield a MDiiBR value:
MDNBR = MDMBRggy + t'!!DllBR (5.2)
This process is repeated by the SIGl'A code for 2000 randomly selected sets of system parameters and randenly selected points from the CHF correlation p.d.f.,'and a resultant MDNBR p.d.f. is generated.
The system parameter p.d.f.'s input to SIG!!A are listed in Table 5-1. Both "best estimate" and 95'l confidence estimates of the standard deviation are included. Standard deviations at the 95" confidence level are input to 31G 1A to ensure that the standard deviation of the resultant MDMBR p.d.f. is at least i
at the 953 confidence limit. .
I .
5-1.
5.2 Results The resultant l'DliER p.d.f. is shown in Fig. 5-1. The mean and standard deviation of this p.d.f. are 0.J23 and 0.099451, respectively. As Fig.
~
5-1 indicates, the resultant : GDR p.d.f. approximates a normal distri- .
bution. .
5.3 Analytic Comparison An approximate value of the standard deviation of the resultant MD:iBR p.d.f.
- may be found by analytic methods. These methods are based upon the assumption that the uncertainties are small deviations from the r.:can (5-2). Given a functional relationship y = f(x),x2 ' -
- n) the effects of small perturbations in x on y may be found from (5.4)
Ay= dye Axj + Ax2+* ^*n .
llence, if several norni distributions are combined by the relationship exprelsed in Eq.(5.3), the variance of the resultant p.d.f. is y =( E )2 a 2 ,[M ax
)2 c2 , , , , , (g ) 2 g2* '
~
ax) x) 2 x D*n n 2
kherethepartialderivativesareevaluatedatthemeanvaluesofthexj's.
The response surface relates PDiiBR to system parameters by the relationship found on Table 4-2:
7 7 7 7 MD!1BRg3 =b g +{,)bnj+j,)bjj(nj j -c)+{_) g) bjj nj nj (5.6) i<j i
Xi -Ei (5.7)
=
where n'.
Bj Applying Eq. 5.5 to the response surface yields the following expression for the variance:
7 2
7 o (5.8)
- o 2 =ri=1 (a(MDilBR) 3'i_x.)i RS an j ax j 5-2.
L _ -
. Differentiating Eq. (5.6) and (5.7) with respect to nj and xj :
~
afiD:lBR f- (5.9)
=b$ +2bj5 nj +3_j,) b$3 nj
. 39i anj j (5.10) ax; (3; Substituting Eq.(5.9) and (5.10) into Eq.(5.8) results in a relation be-tween the resultant flDilBR variance and the system paior.ater variances:
X
= =1 (bj +2bjj nj+ ,44) b5 ) nj ) ( i )2 (5.11)
S ,
/34 This equation is simplified when evaluated at the raean values of the ng: (i.e.ni=0) 7 o
2
,I b.
x (5.12)
I RS i=1 g,2 1
The CHF correlation p.d.f. and system parameter p.d.f. 's are related to the resultant l4D lBR in Eq.(5.1) and Eq.(5.2), the heat flux factor is related .
by Eq. ( 4.1) . The resultant liDilBR variance is given by 2 2 2 2 0 liDilBR , "R S CllF , Fq" (5.13) 2 "2 Fq" E U l1DilBR CHF
'Substitutinq values from Tables 4-1, 4-2, 5-1, and Section 4.5 into Eq. (5.11) and Eq (5.13) yields
=
fiDilBR 0.09923 which is in excellent agreement with the value predicted by the SIGl% code simulation using the response surface.
5-3. s t =
STAi!DARD DEVIATIO:1 DISTRIbuTIO!i f1EAfl CL5T ESTI". ATE 95." C0:lFIDE!:CE hot assembly inlet flow factor .
(channel [ ])
channel [ ] inlet ficw factor channel [ ] inlet flow factor
, channel [ ] inlet ficw factor ,;
enthalpy rise factor 1.0 -
.0100+
systematic pitch (inches) systematic clad 0.D. (inches) ,
heat flux factor 1.0 - .0150**
CE-1 CHF Correlation .998 .0676 .07384
- channel numbers refer to Figure 3-5
+ entire fuel pin population was sampled, hence >95% confidence
- standard deviation based upon tolerance limits, hence >95!; confidence TABLE 5-1: PROBABILITY DISTRIBUTIO1 FUlCTI0ilS COMBIllED BY SIGMA e
9 9
5-4.
i I i i 6 1 i A
n FREQUENCY =
2000 . ~
TRUE GAUSS!AN
~
n = NUMBER OF POINTS IN INTERVAL O ACTUAL DISTRIBUTION 0.10 -
(DN3R - 1/2 3DNSR, DNBR + 1/2 3DNBR)
Obtained From ifonte Caric O Code and Response Surface O .-s O
/ UN
/ g 0.03 - j
\
O6/
g g
3 '
/
V' E /
g 0.0G /
w -
E f \
/ ^
\
/
0.04 - h 9 O\ .
/ \
/ g
- / Os -
' s 0.02 - O,0. ON 7
. O/ ON 4 '
Q 0 Q%,
' ,/
I '4 I ' ' I I 1.2 1.3 1.4 0 0.9 1.0 1.1 0.6 0.7 0.8 0.5 DNBR
.j. -
l Figure 5-1 RESULTANT MDNBR PROB ABILITY DISTRIBUTION FUNCTION
6.0 @ p_li, cation to Design Analvses This section discusses the application of the statistically derived MDNBR p.d.f.
to design analyses. Determinisi.ic cethodology (6-1) involves use of a design model for TORC analysis which includes deterninistic allowances for system para-meter uncertainties. These deterninistic penalties This are replaced with a higher higher ilDNDR limit is used with 11DNBR limit in the statistical methodology.
a "best estimate" design model in thermal margin analyses.
6.1 Statistica,l_ly_ Derived MDNBR Limi,t, The MDNBR p.d.f. descriid in Section S.O is a norcal distribution having'a mean of 0.983 ard a stancarj deviation of 0.10354. This standard deviation A comparison of TORC results and
~
is at least at the 955 confidence level.
response surface predictions indicates that the lo error associated with the response surface is o = 0.00.
s
% 03; at the 95% confidence level, this value is
= 0.00378 o393 The root sum square of the MDNBP standard deviation and the response surface The standard deviation at the 95% confidence level is otot = 0.102113.
corresponding 95% confidence estimate of the mean is 0.991 Since thn 5-1, theresultant one-sidedMD::BR95", prob..d.f.
ability linit is is a nornal 1.645o. Hence distribution, there is a 95% as shown in probability with at least 955 confidence that the limiting fuel pin will not experience DNB if the best estimate design medel TORC calculation yields a MDNBR value greater than or equal to (0.991 + 1.c45 x ').102113) = 1.16.
6.2 [Mustments. to Statistically Derived MONGR Limit The statistical MDNBR limit derived in Section 6.0 CF contains has applied noanallowance NRC method for the adverse impact on DNBR of fuel rod, bowing. This application for taking rod bow into account in DMUR calculations (6-2) . For 14x14 fuel, this shows that the maximum penalty occurs at fuel end-of-life.
penalty is 0.6% in MD"BR. Thus, the new limit, including an allowance for rod bow is (1.006 x1.160) or 1.167.
The NRC has not yet completed review of the application of the CE-1 Consequently, CHF corr- l elation ( 6-3 ) to non-uniform axial heat flux shape data ( 6-4) . The interim a 5% penalty was applied tc the 1.13 MCNBR limit by the NRC.
MDNBR limit for use with the CE-1 CHF correlation, pending GRC approval of CE's non-uniform axial heat flux snape data, is 1.19. For the purposes of this study, a conservative application of this penalty is to shift the mean of the l 11DilBR p.d.f. by 0.06. This shif t results in a MDNBR limit of 1.227. l l
Thus the new !!Dt:Cp. limit which contains allowance for uncertainty in the CHF j correlation and system parameters as well es a rod bow penalty and the interin 55 penalty on the CE-1 correlation irposed by the NRC is 1.23.
6-1
6.3 [gglication to TORC Design Model Statistical combination of system parameter uncertainties into the !!Df1BR limit precludes the need for deterninistic application of penalty factors to the design TORC model . The design TORC model used with the new f D :SR limit of 1.23 consists of best estimate system parameters with no engineering factors or other adjustments te acccmodate system parameter uncertainties. The inlet flow split
- will, however, continue to be chosen such that the best estimate design TORC model will yield accurate or conservative IG!;BR predictions when compared with MD!!BR values from detailed TORC analyses ( 6-1 ).
9 9
9 l
l O
e 6-2 e
G
- w e +g w __ ,a b+..e. q w ,p. gg,mq pw p w e
- * * ' sN4M _
7.0 Conclusions Use of a 1.23 IEMPR limit with a best estimate design TORC model for the St. Lucie Unit 1 core will ensure with at least 953 probability and 95% confidence, that the hot pin will not experience a de;>arture fren nucleate boiling. The 1.23 P.9:L3R limit includes explicit allowances for system parameter uncertainties, CIIF
"' cprrelation uncertainty, rod bow, and the 5% interim penalty imposed by tM !!RC on the CE-1 CilF correlation.
7.1 C_onservatisms <n the Methodolocy_
Several conservatisms are included in the present application. The significant conservatisms include:
i) combination of system parameter p.d.f.'s at the 9C%
confidence level to yield a resultant MDMBR at a 95% +
confidence level ii) use of pessimistic (generic) system parameter p.d.f.'s iii) derivation of the new MD!iBR limit such that it applies to s both 4-pump operation and seized rotor analyses iv) use of the single most adverse set of state parameters to generate the response surface 3 v) application of the 5% interim penalty imposed by the 11RC on the CE-1 CliF correlation i
i i
s e
O 7-1
8.0 References 8.1 Section 1.0 References (1-1) " Report on Statistical Combination of Uncertainties Methodolcay, Part 1, C-E Calculated Local Power Density and Themal l'argin/ Low Pressure LSSS for St. Lucie Unit 1", CEii-123(F)-P, December 13, 1979.
~
8.2 Section 2.0 References
. (2-1) " TORC Code: Verifi:ation and Simplified Modeling liodels",
CEllPD-206-P, January 1977.
(2-2) " TORC Code: A Computer Code for Determining the Themal Margin of a Rt er Core", CEllPD-161-P, July 1975.
Critical Heat Flux: Critical Heat Flux Correlation for (2-3)
C-E fue: 'ssemblies with Standard Grids, Part 1: Uniform Axial Power Distribution", CEllPD-162-P, Septcaber 1976.
8.3 Section 3.0 References (3-1) " TORC Code: A Ccmputer Code for Determining the Thermal Margin of a P,eactor Core, CEllPD-161-P, July 1975, pp. 5-1 to 5-8.
(3-2) " Report on Statistical Combination of Uncertainties Methodology, Part 1, e-F Chlculated Local Power Density end Thermal Margin / Low Pressure LSSS for St. Lucie Unit 1", CEN-123 (F)'-P, December 13, 1979.
(3-3) Combustion Engineering Standard Safety Analysis Report, (System 80).
Docket #STri-50-470F, October 26,1979, Fig . 4.4-7.
(3-4) ibid, Subsection 4.4.2.2.2.2.C.
(3-5) W. R. Cadwell, "PDQ-7 Reference Manual", WAPD-TM-678, January, 1968, Westinghouse Electric Corporation.
(3-6) A. Jonsson, et al., " Core Physics Validation for the Combustion Engineering PUR", Combustion Engineering Technical Paper TIS 6368 Presented at the American iluclear Society Winter Meeting, llovember 12-16, 1979, San Francisco.
(3-7) Green & Bourne, " Reliability Technology", Wiley-Interscience, a division of John Wiley & Sons Ltd., p. 326.
(3-8) " Fuel and Poison Rod Bowing", CEtiPD-225-P, October 1976.
t (3-9) " Fuel and Poison Rod Bowing-Supplement 3", CEflPD-225-P, Suppicment 3, June 1979.
8-1.
m ~
(3-10) Letter froa D. .B. Vassallo (f!RC) to A. E. Scherer (C-E),
June 12, 1978.
(3-11) "C-E Critical !! eat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblics with Standard Spacer Grids, Part 1: Uniform Axial Power Distribution", CEliFD-162-P, September 1976.
, (3-12) "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Grids, Part 2: tionuniform Axial Power Distribution", CEfiPD-207-P, June 1976 (3-13) " TORC Code: Verification and Simplified Modeling Methods",
. CEllPD-206-P, January 1977.
8.4 References for Section 4 (4-1) " Report on Statistical Combination of Uncertainties Methodoloav Part 1, C-E Calculated Local Power Density and Thermal Margin / Low Pressure LSSS for St. Lucie Unit 1", Celi-123(F)-P, December 13, 1979.
(4-2) " Fuel and Poison Rod Bowing, Supplement 3", CEt!PD-225-P, Supplement 3-P, June,1979.
(4-3) R. H. Myers, Response Surface Met _hodolocy, Allyn and Bacon, Inc.,
Boston,1971.
(4-4) fi. R. Draper, H. Smith, Apolied Regression Analysis, John Wiley &
Sons, litw York,1966, p. 62.
(4 -) ibid., p. 118.
8.5 R_eferences for Section 5 (5-1) F. J. Berte, "The Application of Monte Carlo and Bayesian Probability Techniques to Flow Prediction and Determination", Combustion Engineering Technical Paper TIS-5122, presented at the Flow Measurement Symposium, sponsored by the flational Bureau of Standards, Gaithersburg, liaryland, February 23-25, 1977.
(5-2) E. L. Crow, F. A. Davis, M. W. Maxfield, Statistics Manual, Dover Publications, Inc., llew York,1960.
8.6 References for Section 6 (6-1) " TORC Code: Verification and Simplified Modeling Methads",
CEliPD-206-P, January 1977.
~
(6-2) " Fuel and Poison Rod Bouing, Supplement 3", CEi!PD-225-P, Supplement 3-P, June 1979.
(6-3) "C-E Critical Heat Flux: Critical Heat Flux Correlation for C-E Fuel Assemblics with Standard Spacer Grids, Part 1: Uniform Axial Power Distribution", CEliPD-162-P, September,1976.
(6-4) "C-E Critical Heat Flux: Cr.tical Heat Flux Correlation for C-E Fuel Assemblies with Standard Spacer Grids Part 2: flonuniform Axial Power Distribu tion", CEllPD-207-P, June,1976.
8-2
Appendix A: Detailed TORC Analyses Used To Generate Response Surface An orthogonal central comoosite experiment design (A-1) was used to generate the response surface (R S) used in this study. All first order interaction effects (i.e. xjxj terms) were retained in the R S. The R S used in this study included seven variab.les. The coded set of detailed TORC analyses performed to generate the R S is presented in Table A-1; variables were coded as shown in Table 5-1. The actual values of the input parameters are presented in Table A-2 along with the resultant MDNBR values.
References (A-1) R.11. Myers, Response Surface Methodology, Allyn & Bacon, Inc., Boston, 1971, p.133.
O e
A-1
F Case .I.__._.- _. _..._._ _ _ Inlet Flegi oc tort.
tnthalpy l Sys t.euatic lsy.temitic j,. ::o; . r Ch. nc i [ (( Cl;', .n 1 [ ]_ rhat : cl[ ]li.;;.yn..i.[. _ _l n e : c c cc - .
1itrh
! CloJ u.:t l 1 -1 s1 -1 -1 -1 l -1 l, -l i ,
' ' i
. 2 : -1 -l ! -l
-1 -1 -1 1 :
I . j ! l l 3
-1 1 -1 -1 -1 -1 1 -l ,
I 2 ; .
.I i !
l '
! 4
-l ! -1 -l 1 -1 i -1 1 1
i i 1 I -1 5 -1 { -1 -1 -1 ,
1 -1 l.
-1
!6
-1 -1 l
-l -1 1 .
i 1 i I
' i -1 7 -1 -1 l -1 -1 1 1 l I
. 8 -1 ; -l ;
-1 .
1 1 1
! > , ; i
~
9 +
-1 -1 -1 1 -1 -1 -l
\
10 ! -l
-1 -1 1 -1 -1 1 I i
- i
! -1 -1 11 . -1 : -1 -1 1 1 .
I t
- 3 12 -1 -1 -1 1 -1 1 1 i
i 13 -1 5
-1 -1 i -1 -1 l-1 1 ,
g .E--------
(. ..... - .
_.. ...-, .. $.. - .. ' . . . - . ~ . . - . . . . -- -~ ~ ~ - ~ . -- O - -
- c. hun:01 ter.xes r- . r t o t i p . 3- L :.ce lente 4-1 for codc 6 i cia tionships l'cte: Coded values determined by methods described in Rei'erence (A-1).
1[ 1 e .A- 1 : Cod.u Sec of th tailed lu.4C Canes t! sed to Gencrc.te 1:est onse Surfat c A-2 9
Cr.e :
[ nth.11py Systeadtic ! $ystelaai.ic i:uctor : C! on. ; [. ]I.._ Cb'_1: neln[ !.:tT. , CFlo.eh.n i n fe ac l [. .[tort
. t n . . . :i [ ]__
ilise f acwr Pi t : h Clad F.D.
7 l I l -1 14 ; -1 l
-1 -1 1 1 j 1 I
. i i 13 -1 -1
-l 1 1 ,
1 .
-1 -
, I i.
15 -1 -1 -1 -
1 1 1 1 l
' -1 -1 -l -1 17 ! -1 -l 1 ,
l -1 18 l -1 -1 1 -1 i -1 .
8 1 l 3
, i t.
t
. 19
-1 -1 1 -1 -1 .
1 : -1 i
20 -1 -1 1 -1 -1 1 l 1 l
21 ! -1 -1 1 -l l -l -I
- . t ,
I I ' -I I 22 .
-1 -1 1 -l 1 23 t
-1 -1 1 -1 1 1 -1 t
- : 1 I i s
-1 'l 1 i
24 ; -1 i 1 -l I ,
l
' ' -1 -l
-1 I 25 t
-l -1 1 1
,i l i ! -1 -1 1 -
26 -1 . -1 1 I
-.I 1
. l ._. ._ ._ . i .. ... __. . . _-__._-..> . - _ . - - . . --.
5 : ..nnel nu:.Lers refer to Fig. 3- 5 see ' lob:0 4 -1 for coded relaticaships Note: Coded values determined by methods described in Reference (A-1).
5
! Tiib!c A-1: Coded Sec of Detailed T0i!L Lases Ustd to 'iencrate hesponse Surface (con't.) ;
o
~
3 A-3 1 -
1
- . ..j Fu !.ha l py { Sys t et:*a ti c
[- - L.. .--
- ; c- .[ . -. . . . . - . .
i n ! n t, r_1
- g. _ r nc to rg u, }u , . d 1 F. a i a.:tr l Sy sPiRh te :a ti c' C h.i: 0. ! .
, p .ar i Ch,.: peg] Q:.'aipJl. J rSg:e13 . .
i 27 -1 -1 1 1 -1 1 -l 1 '.
' - ! 1 - 1
-1 -1 1 1 1 -l 28 ;
-1 1 1 -l j -1 23 l
-1 1 1 e
! 1 i
' -1 -1 1 1 1 -1 - 1 30 !.
i
'! -1 1 1 1 -1 31 -1 1 l
. 1 1
-1 1 1
-1 32 ' 1 :c 1 l I
! -1 -1 -1 -1 33
-1 1 -l 1
-1 1 -1 -1 -1 -l , 1 34 l l j a s '
I s
1 -1 -1 : -1 1 -1 1 35 -l ,
I i
1
-1 -l : -1 1 1 ,
36 ; -l !
1 , n l . l g ' '
-1
! 37 -1 : 1 -1 -1 1 -l
'l 1 -1 -1 1 -1 1 i 38 -l t
-1 -1 1 1 -1 !
', -1 1 39 t....-....s-....
{
i i
[ = } l .J
'O an :el nu::Sers refer to fig. 3 -5 see Table 4-i for coded retetionships Note: Coded values determined by methods described in Reference (A-1).
,Tp;. . , A; 1 :
Cin!cd Set of Detailed T0;;C Cases 1.ked t.o Generate Response Surface (con't) e r
A-4 .
' Ent.halpy S.'.':. t edi t i c Sy'~ t.ema ti c Case L._______ .l',0AL. .
.ie ; [ ];"isefact,.i- C iad u.D. .
i:u.,:her i ria.:n. j f 3 j. C ..innel [Op]u Fact ors ] ., l4.h..
Cf:anneQ Pi r._ b H
[
i 40 1 -1 1 -1 -1 1
i 1 1 1 i ! i
-1 l' -1 -1 -
-1 41 i -l' 1 i i
1 1
i 3 -1 1 -1 -1 1 l 42 . -1 .
1
' I
-1 -1 i~
43 -1 1 -1 l
1 '. 1 I
-1 -1 1 -1 1 1 i
44 ! 1
- I I
!. ' -1 -l I
- 45 ! -l j. 1 -1 1 1 i '.
. i i I
' -1 1 1 -1 t 1 l
46 ! -l 1 -
l 1 -l j 47 -1 1 -1 1 1
, l t I l .- '
1 1 1 1
48 .,
-1 ! 1 -l i. l
-1 -1 -1 -1 l l 49 -1
- 1 1 ;
i i I .
-1 -1 -1 1 50 i -1 ; 1 1 8
8 -1 -1 1 -1
. 51 -1 1 1 I i
-1 1 1 I, -1 -1 1 1 3 i 52 ; i I i ,
_._.._-. . .- - I _. . .. . . 1. -. ..-....- L . --..--_...----_i
- c!:innci nu:nner; r ef er to Fig. 3-5 see Tab':e 4-1 .or codc<J reiocionships Note: Coded values determfr.ed by methods described in Reference (A-1).
Tct;ic A-i; Coded Set ct Detailed TORC Lases Uscet t.; Gencrate P.: spo';: u Surface (con't.)
A-5 n
Syst e.atic iSyLi.e:::atic 1 Case j -__-___...,
.Inl.qt F. . - . - . . _ F.nthalpy
. Cicd 0.9.
' ihr 'ur ! Cl..a. ie1 [ ] ' Cha:. .ci 'll [ _ lou Factorst ho n:w l,[ [,u i,;. ;,e[7 ,
Fa c t n- I'i t c f.
I , !
-1 -1 1 -1 -1 53 1 1
- l. 'l : .
- I !
-1 -1 : 1 -1 . 1 :
5'4 li 1 ! 1
'l i.
' -1 1 -1 1 1 -1 i
- 55 1 ,
i t
I t l i i
55 ; -1 -
1 1 -1 -
1 1 1 t, '
' l -1 -1 -1 i 57 -1 1 1 1
! l l
-1 -1 -1 i 1 58 1 i-
- 1 j 1 l 1 i
1 1 . I 59 -1 1 1 1
-1 1 -1 l,
l i -1 1 1 i 60 i -1 l 1 1 1
, t*
61 -1 1 1 1 1 -1 -1
< ! ; }
i '
62 ; -1 j 1 1 1 1 -1 ,
1 ,
- j ;
i 1 1 1 -1 l 63 -
-1 1 1
1 1 . .
i
! 5 1 1 1 1 64 l -1 1 1 1 l
65 1 -1 -1 -1 -1 . -1 -1 I b.- -. I I
- - -. . .. ~ .... -- l -. . - - - . . - - - - - - ...----...I--.. -
' th...nnel nun N r:. refer to l ig. 3-5 see Table 4-1 f or coded relationships
{,
4 Note: Coded values deterrained by methods described in Reference (A-1).
, 1c.bie A-1: Co 'ed Set. of Deutiled TORL Cases lised to Generale Respense Surface (con't.)
i A-6 1
.4
~
P e-- . ..
Case g-
,_ i n j e_t,I] n.. - _ - . .Fac tors j E r. tie l;>y Sys teuaticl,syrA ct ia t'ic cica o.n.
l ti:.am 1: aiw r.lTiorl. e: ten l'.u. .a. e.r.q- C.i.u.+n.e_i.[ . -] Cl.:n.n.
1.L l.;.,. ECn.a_nt..
-1 1 -1 1 66 t 1 -1 -1 -1 l
' -1 -1 . -1 -1 i 1 j -1 67 ; 1 l l, 68 : 1 -1 -1 -1 -1 1 1
, i 69 1 -1 -1 -1 1 -1 -1 70 1 1 -1 -1 1 -1 1
[.
-i -1 -1 1 1 -1 71 1 3
5 72 1 -1 -1 -1 1 1 1 ;
-1 -1 1 -1 -1 -1 l
} 73 i 1 4
74 ; 1 -1 -1 1 '
-1 -1 l 1 1 ,
i I
-1 -1 1 -1 1 -1 75 : 1 l
' -1 7G 1 -1 -1 1 1 1 77 1 -
-1 -1 1 1 1 -1
) : l 73
-1 I -1 1 1 -1 1 .
! . 1 ,
b._..--l.-.---.-..___....._..-._....---......
l - . . ._.!- --
"ci.annel r.x ers refer to fig. 3- 5 see Table 4-1 for coded relatienships Note: Coded values determined by methods described in Reference (A-1).
) Ja_bjp. A-1.: Coutd 5et of Detailed 10i:C Cases Used to Generate Response Surf ace (con't.)
i A-7 i
1 1-I N )
C, - l Inl<!t Flou Fac.tcr; Enthalpy Sysis Clir ' h.stema tic l
[ . _Jl:.'i st-rau ur Pia.h Ciad ,.D. l
. . . .a . L.:._.: n:v.1.[. J ' u i. . n n.] I1[ch.anm i[. J.! Ch : .n.
- I
...c....-. .
-1 1 1 -l 79 1 -1 1 1
1 EO .
1 l -1 -1 -
1 1 1 i I i -1 -1 -1 -l 81 !, 1 -1 1
-1 -l -1 1 I.
82 1 -1 1 ,
83 1 -1 1 -1 -1 1 -l
-1 -l ; 1 1 8: ! 1 -1 1 8 1 i
e '
j i
-1 1 -1 1 -1 : -1 85 + 1 1
-1 -l 1 85 '. 1 -1 1 1 ,
1 '
87 ,
1 ! -l
' l
-1 1 l ; -1 88 l 1
-1 1 -1 1 i 1
. I l 89 1
1 -1 1 1 -
l -1 i -1
- i. '
90 l 1 -1 1 1
-1 -l 1
-1 1 -1 1 -1 .
91 ! 1 1
._. _ _ . _ L _ _._ --.i____.____.i___. _. . __. . . __ . .. . _ _.- - _ . _ _ . _ . .4
% .'nnci nwSers refer to i'ig . 3 - b see T.: ole 4-1 for coded reictionshipe, fiote: Coded values determined by method described in Reference (A-1).
lable A 1: (.oded Let of Detailed TDRC Cases Used te Generate Response Surface (cont.)
A-8 k
H
'. ~ ~ ~ '
~~~~}~Enth.ilpv
~
C$se I ]_TCham:elT
_~1 5c].~Tj F SysteiOtit lSys te:::a ti c s.I 2 or.l_t ]TJ : " . iJEni..c o.itor _...i'itcn ; Cic I i
- . i i
' -1 -l ! -l -1
!113 1 i 1 1 ,
i
- 1 l 114 1
- 1 1 -1 -! -l
!. l :
, i . I 115 1 1 1 1 -l ; -1 1 ; -l ,
i I
-1 I -1 1 1 l l llo :
1 l 1 1 i [
-1 -
I
- 117 1 .
1 i 1 -1 .
1 l -1 L- -_ i .l - . . - -. I.-- - .. --- -. . -. - --_L- - - ------ L - L -- -----. .d h .
' h:mnci nscers refer to fig. 3 5 see Table 4-1 for coded relationship;
, fiote: Coded values determined by method described in Reference (A-1).
T<.!> i . A- 1 : Cv::cd Se:. of v,:Leiled TUXC Ca!.es U;cd to Cri:: i rate la:Opunte Surface (con't.)
i I
i A-10 1
1 1
1
' l- .;'l* - . . ,::: il::il l!
- d. i s w0
- p t . .
O
. h a0 1 l 1 1 1 l 1 1 l 1 1 0 .
. s
. - - - - - . n n.M o
- i. l 3
i v I' t s g: :I ';
_ o n
,:' ' .r!i!!.i , -!.
. ,l;
_ e c r )
i .
- d t e
. :c _
. d o 'n h..t 1 1 1 1 i I 1 1 l 1 1 0 0 c o
- - - - - - c c (
_ yi
_ r
.s o e f c
' 1lt t . 'l i a
.. - ~l f r
-m .
u
. y ' ..
4 S
_ 1 .
_ e .
1 1 l 1 1 1 l 1 1 1 l 0 0 .- l, ) e
!..l - - - - ! s t . . o 1
- n
. n i l A o
. if : ( u
_ e s
_ lt ' 1j .l;i j! - e e u s c R
. !!l,~
,i
] _
_ n e
_ ,_ e
. r ie
[ .
e r 1
,i
._ f 1
_ 1 1 l 1 1 1 l 1 1 1 1 0 O e -n -
. - - - R :. A
._ n i.
4 i
L t o
,j
- I d i' ,' ,
- ll e
] b d e i e
- r s
(( c U
_s 1 s
_. r . _
e -
.o r 1 1 l l 1 1 1 1 1 1 1 0 0 d <
.t_
_. r t u_
d a.
. p e. o C h
.f_r
. ]
- ; ' 'Il ile!, .ii I' ;l' l 5
t e i d.
m 0 1 n ]_. 3 T
._'[-
f g
y b de l
_t i d l
.M e.-
i 1 1 1 1 l 1 1 1 1 1 1 0 0 F e i I
n a
t.
o i n at
_ h_ t m c r.. r r e
. [l _. *c
. e! l iil f i . . 1 lili- I' t
. e d e o
- _ t t
[
._ s e i 1
. s e S e 9 _ i. u J n i 1 1 1 1 1 1 1 1 1 1 0 . :. l n
r.
1 . :.
a v a.
e h u .
C r
' .'I' - - !: ' .-iil .i' *.t
! ! :ii bid .
. n n
r d C e
o C :
n 3 9 0 2 3 4 5 6 7 3 9 0 A
- e' n 1 1 2 1
2 2 2 2 2 2 2 2 2 3 . !
e.
_L 1 1 1 1 1 1 1 1 1 1 1 1 1 _ < e
- .. - t ' . _
o :.
- ' i i Ij - Il 1! -t 1 '
N 1.. ,
.. . _ . . . . . _. . . . - . - . . ~ - - = m u '
l *' *.
l 'e.2,f m m
.,~.
l ..
1-Cn On e'~
i 3 O O O O O O O O O O O
- a
- r-- & .
..; .,l o
I
.1 l ~g n , " ' . , . . _ , _ - - . . . . -.. q
.=.
- . > n
- f. ] *
' L 43 1.5 ~~)
- ; _C f e-- r- .i:'. C I
.3- Ch oi l -.
G o
'O O O O O O O O O *
- O O O
,. r- r-- U v
- v. t ,
l -
-
- a u o I t.
r U
=
- 9 I -t I : L
- 0. : e V
- *..s,g e
.1 2 .8, i "
- P F-* . ,.
.r,..l Cn Ch * -
O O O O O O O O O O
{
"a - e ii .i O r--
r--
r-- -
t r .sg 8 H I 9 i._. l *** -
G8 v c .
a
- ' .,. . . . . . . . . . _ . - - -- - - - - - - - - - - - - U g3 )'
( 0 c .>
l GB N l L r '.*!
6 ta "
C7 -
' r~- 4- C' gy t
Ch m
On O 7- A'
, 81 O O O O O * - O O O O O O 4 Cz" -
r- r-- .
i*.. I g C ,,
=r-y ..>
e s...~. .. _ -.-....__ -- .o
'- t c *C C,
- ; .O r* . - - /
' it . *
- 5. ::
O -
t",
,e. r-- r-. e v1 u.
- s2 6- C) Os c) *
-l O O O . . O O O O O O O O O t1
')
g **
9-= r-=
.-! : . , I j V .-)
o
_C ?
'.l . . . . _ . .. .. -- -- . - - - - - . . -- . ..;
e** a
. ;~.
t M D . .-
- mi., ,e i
- >. 7, t
s' 4 L l .C- -
,c.
. Os C) L o r-
.:;,' e ', O O O O O O O O O O O j ci c 3 ~; c; e-r-
, O C ,.
." *r= u.
l .. 8 5
- ::s j
- L
, . . _ - - . . . . - . - . . - - . - - .- ~
O c.s ..
l .r--1 1 " 43 C
?
O CD I . ,
, L O w u
e I y >, .
, v l 6 v,
GD r.
l .' r== -'
. L' C) i r, :3 i i; - O O O O O O O O O O O O t -i -
W g .. U *>
1 -s, I
- , > 0 t)
C <- o G1
. , - - . _ . . . . . . . . . - . - - - - - - -~ ~-
--- -- - ~. .
r-
) *U **
s ;, I C O .~
C U e
.; '.. r-= N M e* In to tw Cf3 01 O e -- N g
q l 'J.n ~p* ' or M.y e M -M M (q rq M rq M M ,: .cf a
Q -y r- e-~ e- r- e-- e- r-- r-= r-= m r.r.
r- - _) .. *; *
.. c, ._
^ .
M .
I , ___ .
. _ _ . . ~ . . . . - . . .
,9
. w
Systematic l'e to i l ed l'.;u l kespen.o TudG iEviuialpy sys tera tic o s i ,, ., . !
inter i:nu ractor Pitch ** Clait 0.0.** r:.v; : g
)_ ;gy:;t:
e i..d e i _
- . . s. . r i r , . . n .. . .( j 3,r,.g y,ig,g 4 igng ji Pisn ra: tor
.5753
~
.000
] .9332 1 .C04
.9892 . 5;'53 i
2
..C03 9832 .5703
! 3 . 002 i
.9382 .5703 i 4
, , .C03 1.012 .5753 5 l l
.C04 1.012 .5753 6 .C02 1.012 .5783
- 7 . . C"J2 1 1.012 .57C3 6 .C
- ?
l .57G3
! .9932 7 9 .
- .c2' l
.9032 5763 I
10 .C03
' .9382 .57E3 11 5 .002
.sce2 .5:ac
' 12 .C~ J
- 1.012 .5753 13 .004
- 1.012 . sis 3 14
.002 1 1.012 .5733 ,
15 ,
~
l ,
..... - - .. - ... - - .~. i .. - . .
- w. . . . . . . . . .. -
amt .y;tu. i ;. i ,- w s d.r..,n iudess c.n cat syste.ctic ; it !.
- th . . r.t. r c.rs rt:ri:r to t ig. 3-.5 end cl..<; U.11. (in.fi.s)
TAOLE A-2: Cnnpu rison of Tt;i:C arut Respun;e Surf ace :M: P. for C.is. '. U .. if to %wrat.e ke<ponse sta t.tcc A-13
l l
Sy s te.:o ti c Uc u t led
. tc>e ; inlet e tcw tactor. i tntna lpy I syste.matic
' ' ' " " lUac l Respotisc
"""#304. ' ' ' ' ' ' ' " , ~ l' i'u? i ."? t"" L"i '2"
. ... . , e i , ... - . . . i _ ] ! (G.....nii [I u'aenc:L 'l ' ( ""'T 0$ d " U ' " . .
i t i ~
i - .001 1.0120 .5783 15 I .C03
.9302 .5763 17 ,
.C03
.9322 .5763 13
.CO2
.9502 .5703 19
.CO2
.9232 .5723 20
.CO2 1.0120 .5753 21
.C31 1.0120 .5753 .
22
.5783 .C23 1.0120 - ,
23
.C31 1.0120 .5783
! 24
.001 1
- 25 .SSS2 .5753
.C02 25 l .9322 .5753 l
- i .C33
.9002' .5788 27
.C31
.9032- .5783 ,
28 ,
.C02 1.0120' .5753 23
.CO2 1.0120 .57G3 ,
33 ~ --
f
- l j ]
.: P,a ra:.. nu.bers refer a fig. 3'S 'll >yt.t n. par ou tt.r s diiaen icoless ci.tept syt tei:u tic. pitch ar.d clad 0.0. ( i n c l.e'. )
TA?tE A-2: Cu..iparison of 10RC arid Res;oe:te Surface IC:2tR for Ca es tbed to Generate itest ense Surf.:ce (cen't.)
A-14 ,
~ A
4
.4 a O
~ % 'Q u9> /// ,Q
$2+J) - . - -
%d<,7 TEST TARGET (MT-3) 1.0 2'4 m 732 9l 22
,_ ; 3 lhi-m I.i [ ^ lllIlE I.8 1.25 IA 1.6 4 b >
MICROCOPY RESOLUTION TEST CHART
+4%
g/ 4),Y' 37 '4;gh 4>j;;
4,,,,,7 y
ay
+ Ab '
'l th'yt ,l'Qp, f//,, -:[= 'q>
e
,ffV 4g g// /gs gte, y,,+ , eEEm e 1,em
- TEST TARGET (MT-3) 1.0 'PH E a a2 l1lla=2
= 2 733 l.l ::
I ielll"ll2.0 I
l.25 IA 1.6 4 6" >
MICROCOPY RESOLUTION TEST CHART wn>%>/7$ i, /!b w+
v- sp a o ip+y
Uetaile: It ha, Xespuose lu:G J LothalPy 5/ 5 tema t1 C S/ste"4 tic " *, 3R it. Toil Frv6ot
- J t tc.e Iniet f~iTa rector _ _ _
i !? t <.e F.tc t er i'i tc h*
- riad 0.0.**
in..,ncij .gi 4 ,
- ..ei -
1.v. ... : ( i
.l g_e n "_"_c # [ Jtg-- nn n e i [
i _
.C03 1.0120 .57E8 21 1 .001 I 1.0?20 .57S3
- .C;
.0002 .5763
! .004 I 33 I
f .9882 5763 24 .003 l .5703
.5C32 35 .001
.5082 .57S8 ,
I 25 .C;3 j 5763 i
1.0120 37 .004 1.0120 5763
. .002 l
- l l 1.0120 1 .5728 2' I .C02 1.0120 .5733
}
- 30 . .001 I .9332 .5763 I
' 41 .CO' l . .0032 .5753
! .002
' 42 t .0022 .5753 f- 43 4
.C:2
.93$2 .5783 1
84 l .Os l
} .5763
't 1.0120 I 45 !
I '
. . - -... J ....I.
all .ysta. paraix o.i.
ilh :nsionles: exc e: t syster.atic pitti,
'cnc o ; , n.e t.ce s re fer to I i J. 3-5 aid clad 0.15 (intl :s)
}
j -
8 I for Cest s U .t t1 to Geni r,ite itt -etnse surbec (cen't.)
TAELE A-2: Ccerarison of 10::C and Respo ce stirface r:Nr.T: .
l A-15
- _ _ _ _ . - _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ -- _ . - _ _ - _ _ _ _ __ ~
e e
e e=
or" e.s r2 M N c'% N 9'* *~ N N w+ c)
M ts 94 01 ( F1 ("I CD C1 CD 1 (D CD () () CD (1 FD CD C.> (1 O. tJ. CJ. U. U. O. O. O. 3
.. O. U. U. O. O.
8 8 9 I 0 8 4 6 0 0 C'b' a
3 x N
v ' . -*
- 2
- O D C k g 9.
c s ,-
d o:g
.. M.
w-4 ed wi
) ,h
.Y.
I *
"f- ^
c: LJ "
~3 .T , v M
, . u.
-f7 . .
O *E O
- *.. @ U 4
- sa
- ey CE
."1 e
-- U
- . C O
- 3 *J
- .e %
qq*
e.
@ "o-
- J M Jq O. *2 i' C.) =
- g .U s
- ,3
. ., i e C
- v. e. , 4% .* C
- , - u :.
n"%uf t s s .u s u
)
L'*--C ::
u I !) W *J e
09 M C1 C' 8')
- 4
-
- r"t 07 fS f*1 f*) C7 c) f'1 M C") (11 W
f')
CJ fC O ".- 'a "L 4 AS CJ CO sf1 Q CJ c) W W (d rw Lf3 N
LD F% N N
- C
- r. N C' CJ LJ N N N N N N N N U') ts) Q gli.
2O 6' # A t/1 ed st) 4A 60 O. LD. C. s
@*** e e e hD. . m. . . . w
+J -C O h C. @ r: Q A h- .O., e-*
3 o
.- ._ i 3
I -t *J+ et L
cp N N o o O O N N N N g - n C D O N N r1 c: fD t') e Q .'
te N N
+' N N t4 c. ) c) La fu N.- m C') CO O) (O l *M D
%V' e- e- D) c) W CJ e= e- e O O "C3 CD CS CID O C4 CTn in, A O
- 16, ~) e e - . CT. . O. O. O. - OT. . l *D e= e= r e= e=
- h e* e==
C 0
.Ls v U t .*-
D C.: %-
O g-.. .
i +
. .e t ij 1
.J. .
~'
a C- e
- U e' O J
d M
l F
J 1
C
- O
.: :1
.C c s
%4
- /t (J 7 D C C~ C:
LD t.
'*, s' ? -
u.-~]* ci *G 4 e (3 t
D ::
es -
C C 4
,o - y t.
r -
=
' 8 - g, g O O
- i .P e
- * - w a
,- C e 1 6 L !
1,3
.i .. -
~' J C
~~
m.
- N 1
- - - . .. s .
C et l
- a .1 bI I S / O Of af tfD L(3 f% C3 (*t O L .I j gn N ft) O e"* f'l W1 W1 O J ts)
O aj - y m.F M V a.) hn C en ' ta s til ts t in
- C j
e i,y
- H
. . . . . . J [
1 i
=
w mr ]
5 . .
~
}
l\
d 2
't .
4 5
.4
} .
4 Syster a tic l dyst: aut LMaiice tus F.e.pon.c !Cru I i tnt!:a s py ",-:- ,;: e.n . w c sicg.!
inirt Flw ractor I ri,,,; c.n,.. .
j e t.
I
, i - , .. n i , . . . , ,. i j- .
c n s n ... ) .- i u s.i .i r e.r i.t.- Rir. r ctne-- Pitek**
- _ . - _ _ - ; ,i ; .
.003 e
1.0120 .5763 l I 61 -.C 2 1.0123 .5703 62 .033 t
1.0120 .5783 E3 .001 l
1.0120 .5703 j G: .C02
' .950.2 .5763 C5 .C:5
.9S32 .5763 65 .C]!
.S282 .5723 I, 67 .005 a c3S2 .5703
} En ' .0:2
) .
1.0120 .5763 r
I 59 t ..C:5 l 1.0123 .5703 70 t - .001 3
1.0123 .5733 5 t 71 .C02
- f. 1.0210 .57ES t 72 .C03 f
.0832 .5753 73 .005
.9832 .5763 j .
7' .C;3
.9822 .57C8 i "
1 , ;
75 - L.
- ~ - - - . -
. . .. s c- - -.- -
- _ . ~. ..-
.i t ! vstc 1 m m tc.. . iii.co, ion cess s:,.. op . p. ten.atic pitch
'. P::i s ref er to f ig.3 5
'ua,t. r ants cl.rd D.D. (inch. .)
( .
5 -
I TAttE A-2: Lts. pari:.on of TORC at:d P.esponse Surf ace MK:r't for Cases U .ed to Generatt L. si oose Surf ace (cen't.) '
j A-17
'I
s e . . . .
dys t e.ca t i c Letailed ;UsL kespor.se IUEC j L n tr.a l py ' Systu :atic l Lt s i r';a i intet rlew Factor Pitc5" Clad 0.0.** F"" M f T * " '<
, [ Cese j -i e i.n wnc. 4r Riso F,i c to r i ...+.-ri i.c..nc g ; i c ..
c,.
y N c n...w. ii= ri r,d . .
.C05
.9332 .5733 75 .003 1.0120 .5763 77 .C;5 l
1.0120 .5763 7 .C;;
1.0120 5783 79 .034 i
1.0120 .5768 EC .COI
.0032 .5763 el .C03 l .9332 .5763 E2 .C02
.96G2 .5783 32 .C02
.9052 .5703
( C' .00) 1.0120 .5763 85 - .C03 1.0120 .5763 i e5 .C01
' *l l ,
1.0120 5703 R7 .COI
. 1.0120 .57SS ES .C0]
.98S2 .5753 3? .C03
.9832 .5763 .
i I I
- 90 - .. _,_ .
l I I .f
- *all ,ysteio t.ei .u:cters dii..unsicr.icss escept systee.atic pi tcle f
- t' arm.- nm.Lers re fer to Fig. 3- S ' clad 0.D. (ir.hes)
- a n-i i
f t T,*,9LE A 2: Co.:.parisen of TORC and Respunte Surface KD;rJR for Cases U;cd to Cencrate Respanse So
.(con't.) '
i
.D t
A-18
. 'I
- l L::uleo iCnc 1csrocse ;ui.L Syste auc PD*C R fSTR :>s M A ce>e ; t e lo t t io.: r a.c t o r jL'itdaipyE'do'- l bystceatic d IM 'd' Pitch" CWC.'"
[
e i .
.- r i 3,, - c . . i i w , .. : -[ ]ani s.ro m. i- rali8L"n" ' ' f_ .002
.3'32 4 .5783 -
l .002 j 31 l .9032 .57CS
.COI 8
92 , '
1.0120 .5763 93 .C 4 1.0120 .5753 94 .C22 1.0123 .5703 95 .C02 1.0120 .5703 95 .C03
.9232 .5763 1 97 C]5
.0002 .5763 i .C;0 i 93
.9322 .57E8
< 93 .005
.9082 .5783 ,
101 - .C03 1.0120 .5763 101 .C04 i
- 1.0120 . 5753
.C01 102 1 1.0120 .5783 103 .004 1.0120 .5703 1
.C04 104
.9002 .5703 ,
I 105 J " * -
. . L. , _.
i _ __ ~_ -_J___._ **.11 yste. , sra:. secs Ji. . ..;f ..icss except syste,catic piten
- t an.c. i.uotvrs refer to i19. 3- 5 cnd . lad i .t). (inci:e ,)
Co .i t'. i rt to Cenrest Respon:o Surface (cc.*t.)
1'S :
"- g: Ct, parison of T0% and Response Surface T-int UR IN .
A-19
Syster;;1c Octatlec 1020 itntna'ry i systematic
?"'d Fes'Janse
'70R idh0 l 82t'-/31 r . . v.; .- :nle: fita ractoe Cl-d 0. 0. '
- 1, . . . , ,, i
- 1. ~ . . . ,, , t [, t . . . , . o r. . L { j fm ..Ft i., t e simi.. J 't i t a rietar 1 Pitch" ,
1 .
.- i
, .004
.0052 .5753 ICS .C02
.9302 .5723 107 .004 t
.90S2 .5730 100 .005
.5763 t 1.0120 ici '
.0 4 1.0120 .5753 g 110 .001 1 1.01:0 .5783 f'
- 111 .C03
! [
1.0120 .57E3 '
112 l .000
- .5753
.S392 113 .004
.5032 .5763 11: .003 l . 93?,2 .5703
- ils l.
- .002.
I, .9302 .5703~
I 115 .001 1.0120 .5703 117 1
.C 5 1.0110 .5753
, 118 .003 1.0120 .5783 119 : .002 1.0120 .5703 -
120 , 1 .__
_ . . .- . - ~ . . .
_f ._ __ _ J .L. __
. ell yste:a pare:i.etet s dii..cm.icn. css c:. cept systematic pitch
' . r . .. m .. riu:.6er 5 refer to l'ig. 3-5 otid clad 0.0. (ir.ches)
Surface (cen't.)
T AE'.! A-2: Cc ;urisca of TORC nd Pesponse Surface MOM 3P. for Cases used to Cei. erat Respom., .
A-20
r = 6 e ,
itnthalpy $ysteratic l systems;ic jUttailco 3 ": lu-L
- n l Hes;cnse i :csC f :M r? .i D'1 iniatj^ics hic:nr ,_
n:<iw ractor Pitch" ,i_C1cd 0.D.** ,
- [ ta e t .001 i r:..1,- t i . ,,2. . : i t g.,a , s. .1L fi t.r.'r <' L c*I,en., m.il .
.9822 .5753 i.
.C05
.121
.3332 .5753
.C:2 l 122 5783
.9332 .C:2 123
.9332 5753
.C01 12:
1.0120 .5763
.C;5 125 1.0129 .5753
.022 125 1.0120 .5783
.C32 1:7 .5723 3.01:3 .C:2 i' 13 1.C003 .5776
.:iG l 12) 1.0000 .5776 1
.G10
! 123 .
1.CCou 5776
- 1 .001 I
121 i .5776 1.0003 ,
.C21 122 l .5776 l; 1.0300
.007
' 113 1.0000 .5776 ,
.CCC 13; ,
1.0000 .5776 f
~
- t I i 125
, f I .. _ ~. ,
?
t
-m
- 111
. , ystet paran.eiers dio.ensionless c>. cept syster.:atic pitch
't, * '
- :.r.'. i ru:$. rs refer to Tig. 3-5 ced clod 0.D. (incites) l
.i & (cen't.)
9 TA?tE A-2: Cc?pariscq sf TC.kC and Response Surface IL:; fir for Cases Used to Centrate Prsponse Surface -
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