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VEPCO Reactor Core Thermal-Hydraulic Analysis Using Cobra Iiic/Mit Computer Code.
	ML18136A022
Person / Time
Site:	Surry, North Anna
Issue date:	08/31/1979
From:	Bowling M, Cross R; VIRGINIA POWER (VIRGINIA ELECTRIC & POWER CO.)
To:	;
Shared Package
ML18136A021	List: ML18136A020; ML18136A022;
References
	VEP-FRD-33, VEP-FRO-33, NUDOCS 7910020422
	Download: ML18136A022 (93)
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VEP-FRD-33 AUGUST. 1979 I .

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I VEP-FRD-33 VEPCO REACTOR CORE THERMAL-HYDRAULIC ANALYSIS USING THE COBRA IIIC/MIT COMPUTER CODE I

BY I F. W. SLIZ II NUCLEAR FUEL ENGINEERING GROUP FUEL RESOURCES DEPARTMENT

'I VIRGINIA ELECTRIC AND POWER COMPANY RICHMOND, VIRGINIA I AUGUST, 1979 I

I I

RECOMMENDED FOR APPROVAL:

I I ;j R. W. Cross Nuclear Fuel Engineer I APPROVED:

I

!VI. L. Bowling \)

I Director, Nuclear Fuel Engineering I

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.I I CLASSIFICATION/DISCLAIMER I The data, information, analytical techniques, and conclusions in this I report have been prepared solely for use by the Virginia Electric and Power Company (the Company), and they may not be appropriate for use in situations I other than those for which they were specificalay prepared. The Company there-fore makes no claim or warranty whatsoever, express or implied, as to their I accuracy, usefulness, or applicability. In particular, THE COMJ>ANY ~.AKES NO I WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE, NOR SHALL ANY WARRANTY BE DEEMED TO ARISE FROM COURSE OF DEALING OR USAGE OF TRADE, with I respect to this report or any of the data, information, analytical techniques, or conclusions in it. By making this report available, the Company does not I authorize its use by others, and any such use is expressly forbidden except with the prior written approval of the Company. Any such written approval I shall itself be deemed to incorporate the disclaimers of liability and dis-I claimers of warranties provided herein. In no event shall the Company be liable, under any legal theory whatsoever (whether contract, tort, warranty, I or strict or absolute liability), for any property damage, mental or physical injury or death, loss of use of property, or other damage resulting from or I arising out of the use, authorized or unauthorized, of this report or the data, I information, analytical techniques, or conclusions in it.

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_I I ABSTRACT I The Virginia Electric and Power Company (VEPCO) has developed the I capability to perform core thermal-hydraulic analysis using the COBRA IIIC/MIT computer code. This capability is based upon a single stage method of analysis I which incorporates the geometries and methodologies used in traditional mul-tistage analyses. Using the single stage approach, an array of subchannels I representing the hot assembly is combined with an array of lumped channels which represent the remaining assemblies within an eighth core segment. Axial I and radial design power distributions along with an inlet flow distribution I are applied to this geometry, and engineering uncertainties are applied to the hot channel and the hot fuel rod. This thermal-hydraulic representation I of the core is then used in a single thermal analysis to determine hot channel fluid conditions and the resulting minimum departure from nucleate boiling I ratio (MDNBR).

I The accuracy of the VEPCO Thermal-Hydraulic Model is demonstrated through comparisons with analyses which were used in the design and licensing I of the Surry Nuclear Power Station. Steady state and transient MDNBRs calcu-lated using the VEPCO methods are in excellent agreement with those presented I in the licensing documents.

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I I ACKNOWLEDGEMENTS I I would like to acknowledge the work of the following persons:

I H.S. BERMAN for programming an operational version of the COBRA IIIC/MIT com-puter code; M.L. SMITH, N.P. WOLFHOPE, and S.M. MIRSKY for assisting in the I development of the Thermal-Hydraulic Model; Ms. CATHY BULLOCK, Ms. MARLENE SIMMS, Ms. MARY MOSS, and Ms. MIRANDA COOPER for typing the draft and final I manuscripts. I would also like to thank a number of people who reviewed and I provided comments on this report.

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I I TABLE OF CONTENTS I Page I

CLASSIFICATION/DISCLAIMER i I ABSTRACT ACKNOWLEDGMENTS ii iii I TABLE OF CONTENTS LIST OF FIGURES iv vi LIST OF TABLES viii I SECTION 1 INTRODUCTION 1-1 SECTION 2 COBRA IIIC/MIT COMPUTER CODE DESCRIPTION 2-1 I 2.1 2.2 Introduction . . .

Method of Solution 2-1 2-1 2.3 Models and Correlations 2-3 I 2.3.1 Void Fraction . .

2.3.2 Single and Two-Phase Friction Factors 2.3.3 Turbulent Mixing . . . . . .

2-3 2-3 2-4 2.3.4 Critical Heat Flux Correlation 2-5 I 2.4 2.3.5 Water Properties Computational Input Parameters 2-5 2-5 HYDRAULIC MODEL DESCRIPTION I SECTION 3 3.1 Introduction . . . . .

3-1 3-1 3.2 General Description of the Surry Core 3-1 I 3.3 3.4 Eighth Core Representation - 53 Channel Model Eighth Core Representation - 19 Channel Model THERMAL MODEL DESCRIPTION .

3-2 3-3 4-1 SECTION 4 I 4. 1 Introduction . . . . .

4.2 General Description of the Thermal-Hydraulic 4-1 Design of the Surry Core 4-2 4-3 I 4.3 4.4 4.5 Inlet Flow Distribution Power Distribution . . .

Reactor Operating Conditions 4-4 4-5 4.6 Forcing Functions for Transient Analysis 4-7 I SECTION 5 ENGINEERING UNCERTAINTIES 5-1 5.1 Introduction . . . . 5-1 I SECTION 6 5.2 Hot Channel Factors THER~..AL-HYDRAULIC MODEL VERIFICATION 5-1 6-1 6.1 Introduction . . . . 6-1 I 6.2 FSAR Analyses . . . . . . .

6.2.1 Introduction . . . .

6.2.2 Steady State Analysis at 100% Power 6-3 6-3 6-3 6.2.3 Excessive Load Increase Transient . 6-4 I

I iv

I I TABLE OF CONTENTS (Continued)

I Page I 6.2.4 Uncontrolled Control Rod Assembly Withdrawal at Power Transient . . 6-4 I 6.2.5 Complete Loss of Reactor Coolant Flow Transient . . . . . . . . . 6-5 6.3 Densification/Positive Moderator Temperature I Coefficient Reanalyses 6.3.1 Introduction ......... .

6.3.2 Steady State Analysis at 112% Power 6-16 6-16 6-16 I 6.3.3 Uncontrolled Control Rod Assembly Withdrawal at Power Transient . .

6.3.4 Complete Loss of Reactor Coolant 6-17 Flow Transient . . . . 6-17 I 6.4 Low Flow Assumption Reanalyses . . .

6.4.1 Introduction . . . . . . . .

6-29 6-29 6.4.2 Steady State Analysis at 102% Power 6-29 I 6.4.3 Complete Loss of Reactor Coolant Flow Transient

6-30 SECTION 7

SUMMARY

AND CONCLUSIONS 7-1 I SECTION 8 REFERENCES 8-1 APPENDIX A - VEPCO MODIFICATIONS ADDED TO THE COBRA IIIC/MIT I COMPUTER CODE . . . . . . . . . . . . . . . . . . . . . A-1 I

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I v

I I LIST OF FIGURES I Figure Title Page I

3-1 Fuel Assembly Arrangement of Surry Core 3-10 I 3-2 Cross Sectional View of Surry Fuel Assembly 3-11 3-3 Side View of Surry Fuel Assembly . 3-12 I 3-4 Assembly Geometry of 53 Channel Model 3-13 I 3-5 3-6 Subchannel Geometry of 53 Channel Model Assembly Geometry of 19 Channel Model 3-14 3-15 I 3-7 Subchannel Geometry of 19 Channel Model 3-16 4-1 Inlet Flow Distribution of 53 Channel Model 4-9 I 4-2 Inlet Flo~ bistribution of 19 Channel Model 4-10 4-3 Assembly Power Distribution, 53 Channel Model, I (Low Flow Assumption Reanalysis) . . . . . . . . . . . . . . . . 4-11 4-4 Assembly Power Distribution, 19 Channel Model, I 4-5 (Low Flow Assumption Reanalysis) . . . . . . .

Subchannel Power Distribution, 53 Channel Model,

. . . . . . . . l~- 12 (Low Flow Assumption Reanalysis) . . . . . , . . . . . . . . . . . 4-13 I 4-6 Subchannel Power Distribution, 19 Channel Model, (Low Flow Assumption Reanalysis) . . . . . . . . . . . . . . . 4-14 I 6-1 Assembly Power Distribution, 53 Channel Model, FSAR Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 6-9 I 6-2 Assembly Power Distribution, 19 Channel Model, FSAR Analysis . . . . . . . . . . . . . . . . . . . . . . 6-10 I 6-3 Subchannel Power Distribution, 53 Channel Model, FSAR Analysis . . . . . . . . . . . . . . . . . . . . . . . . 6-11 I 6-4 Subchannel Power Distribution, 19 Channel Model, FSAR Analysis . . . . . . . . . . . . . . . . . . . . 6-12 6-5 DNBR vs. Time, Excessive Load Increase Transient, I FSAR Analysis . . . . . . . . . . . . . . . . . . . . . . . . 6-13 6-6 DNBR vs. Time, Uncontrolled Control Rod Assembly I Withdrawal at Power Transient, FSAR Analysis . . . . . . . . . . 6-14 I vi

I I LIST OF FIGURES (Continued)

I Figure Title Page I

6-7 DNBR vs. Time, Complete Loss of Reactor Coolant I 6-8 Flow Transient, FSAR Analysis . . . . . . . . . . . . . . . . . 6-15 Assembly Power Distribution, 53 Channel Model, Densification/Positive Moderator Temperature I Coefficient Reanalysis . . . . . . . . . . . 6-22 6-9 Assembly Power Distribution, 19 Channel Model, I Densification/Positive Moderator Temperature Coefficient Reanalysis . . . . . . . . . . . 6-23 6-10 Subchannel Power Distribution, 53 Channel Model, I Densification/Positive Moderator Temperature Coefficient Reanalysis . . . . . . . . . . . 6-24 I 6-11 Subchannel Power Distribution, 19 Channel Model, Densification/Positive Moderator Temperature Coefficient Reanalysis . . . . . . . . 6-25 I 6-12 Reactor Core Thermal and Hydraulic Safety Limit Curve at 2200 PSIA, Three Loop Operation, 100% Flow . . . . . . 6-26 I 6-13 DNBR vs. Time, Uncontrolled Control Rod Assembly Withdrawal at Power Transient, Positive Moderator Temperature Coefficient Reanalysis . . . . . . . . . . . . . . 6-27 I 6-14 DNBR vs. Time, Complete Loss of Reactor Coolant Flow Transient, Positive Moderator Temperature Coefficient Reanalysis . . . . . . . . . . . . . . . . . . . . . 6-28 I 6-15 DNBR vs. Time, Complete Loss of Reactor Coolant Flow Transient, Low Flow Assumption Reanalysis . . . . . . . . . 6-33 I

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I vii

I I LIST OF TABLES I Table Title Page I

2-1 Computational Input Parameters 2-6 I 3-1 Assembly Hydraulic Parameters . 3-4 I 3-2 Axial Positions of Assembly Components 3-5 3-3 Assembly Hydraulic Data . 3-6 I 3-4 Unit Cell Hydraulic Data 3-6 3-5 Perimeter Cell Hydraulic Data 3-6 I 3-6 Corner Cell Hydraulic Data 3-7 I 3-7 3-8 Thimble Cell Hydraulic Data Hydraulic Data for Lumped Channels 3-7 3-8 I 4-1 Axial Power Distribution, (Low Flow Assumption Reanalysis) . . . . . 4-8 I 5-1 6-1 Hot Channel Hydraulic Data Listing of VEPCO Verification Analyses 5-3 6-2 I 6-2. Axial Power Distribution, FSAR Analysis 6-6 6-3 Reactor Conditions, FSAR Analysis 6-7 I 6-4 Parameters for FSAR Analysis 6-8 6-5 Axial Power Distribution, Densification/Positive I Moderator Temperature Coefficient Reanalysis . . . . . 6-19 6-6 Reactor Conditions, Densification/Positive Moderator I 6-7 Temperature Coefficient Reanalysis . . . . .

Parameters for Densification/Positive Moderator

. . . . . 6-20 Temperature Coefficient Reanalysis . . . . 6-21 I 6-8 Reactor Conditions, Low Flow Assumption Reanalysis 6-31 I 6-9 Parameters for Low Flow Assumption Reanalysis 6-32 7-1 Summary of Comparisons 7-2 I

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I I SECTION 1 - INTRODUCTION I The basic objective of core thermal-hydraulic analysis is the accu-I rate calculation of coolant conditions in order to verify that the fuel assem-blies constituting the reactor core can safely meet the limitations imposed I by departure from nucleate boiling (DNB). DNB, which could occur on the heat-ing surface of the fuel rod, is characterized by a sudden decrease in the heat I transfer coefficient with a corresponding increase in the surface temperature.

I DNB is of concern in reactor design because of the possibility of fuel rod failure resulting from the increased temperature.

I In order to preclude potential DNB related fuel damage, a design basis is established and is expressed in terms of a minimum departure from I nucleate boiling ratio (MDNBR). DNBR is the ratio of the predicted heat flux at which DNB occurs (i.e., the critical heat flux, CHF) and the local heat I flux of the fuel rod. By imposing a design DNBR limit, adequate heat transfer I between the fuel cladding and the reactor coolant is assured. DNBRs greater than the design limit indicate the existence of thermal margin within the I nuclear core. Thus, the purpose of core thermal-hydraulic analysis, or DNB analysis, is the accurate calculation of DNBRs in order to assess and quantify I core thermal margin.

In performing DNB analysis, a subchannel approach is commonly used I wherein a section of the core is modeled as an array of adjoining subchannels.

I Each subchannel is defined as the flow channel formed by four fuel rods, or by three fuel rods and a guide thimble tube. When the fuel rods are given I design radial and axial power distributions, the array represents the region of maximum design power generation. Within this array, the hottest subchannel I (hot channel) is identified with the fuel rod which has the highest integrated I

I 1-1

I I power (hot fuel rod). Engineering uncertainties are applied to the hot channel and the hot fuel rod in order to conservatively account for manufacturing I tolerances. A detailed thermal analysis of the core is then performed to I determine the flows and enthalpies at each axial position within the hot channel.

When performing the thermal. analysis, it is necessary to consider I the effect that the surrounding core region has on the subchannel flows. The problem is basically one of integrating the relatively small subchannel geo-I rnetry into a larger geometry which is representative of the entire core.

I Traditionally, the problem has been solved by using a multistage method in-valving at least two analyses (1 2 3 4)

' ' ' . In general, a core analysis is first I performed to provide crossflow boundary conditions which are used in the sub-sequent subchannel analysis. In the core analysis, each fuel assembly is I modeled as a single, lumped flow channel. In the subchannel analysis, the hot assembly is modeled separately as an array of subchannels. Hot assembly I crossflows determined in the first analysis are used as boundary conditions I in the second analysis in order to simulate the effects of the core on the subchannel flows.

I An alternate, more direct approach for performing the thermal analy-(5) sis is a single stage method. Using this method, a single analysis is per-I formed in which an array of subchannels representing the hot assembly is com-I bined with an array of lumped channels which represent the remaining assemblies within a core segment. Using this single geometry, boundary conditions are I not required since the effect of the core is inherently included when computing the subchannel flows. Although single stage analyses have been performed I previously (e.g., Reference 6), the thermal-hydraulic codes then in existence were capable of handling only a limited number of channels. This necessitated I coarse simulations of the core consisting of only a few subchannels together I 1-2

I I with very large lumped channels representing many assemblies.

( 7)

However, the recent development of the COBRA IIIC/MIT computer code has provided the I capability to analyze geometries consisting of up to 200 channels. Thus, it I is now possible to perform single stage thermal analyses using the same radial nodalization as used in the traditional multistage analyses.

I This concept has been applied by the Virginia Electric and Power Company (VEPCO) in the development of a core thermal-hydraulic analysis capa-I bility. This capability is based upon a single stage analysis which incor-porates the geometries and methodologies used in multistage analyses. The I accuracy of this approach has been verified through comparisons with analyses I which were used in the design and licensing of the Surry Nuclear Power Station.

Steady state and transient MDNBRs calculated using the VEPCO methods are in I excellent agreement with those presented in the Surry Final Safety Analysis (8) . . . (9 10 11 12)

Report (FSAR) and in subsequent licensing documents. ' ' '

The purpose of this report is to describe the VEPCO Thermal-Hydraulic Model and to present the comparisons which demonstrate the Model's accuracy.

I A discussion of the COBRA IIIC/MIT computer code is provided in Section 2.

I The hydraulic model of the Surry core and the corresponding thermal model are described respectively in Sections 3 and 4. Engineering uncertainties which I were applied in the analyses are described in Section 5. Section 6 then de-scribes the specific analyses which were performed and presents the comparisons I of VEPCO results with those given in the licensing documents. Conclusions are provided in Section 7.

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I I SECTION 2 - COBRA IIIC/MIT COMPUTER CODE DESCRIPTION I 2.1 Introduction I

. The COBRA IIIC/MIT computer code (7)

, developed at the Massachusetts Institute of Technology for the Electric Power Research Institute, is a modi-I fied version of the more generally known COBRA IIIC computer code (13)

. Both codes have the same basic organization, use the same conservation equations, I and use essentially the same method of solution. COBRA IIIC/MIT will therefore I yield essentially identical results to those of COBRA IIIC when applied to the same problem. However, the two distinguishing characteristics of COBRA I IIIC/MIT compared with COBRA IIIC are its reduced computational running time and its ability to handle larger geometries. Thus, the COBRA IIIC/MIT code I has the capability to more efficiently analyze detailed representations of I PWR cores.

For these reasons, the COBRA IIIC/MIT computer code became the start-I ing point in the development of the VEPCO Thermal-Hydraulic Model. In the course of this development, the original version was modified in order to I correct several shortcomings and to provide additional user oriented flexibil-ity. These modifications are sunrrnarized in Appendix A. A discussion of the I code's method of solution is provided in Section 2.2. The code's empirical I models and correlations that have been selected for use in the VEPCO Thermal-Hydraulic Model are described in Section 2.3. Computational input parameters I are described in Section 2.4.

I 2.2 Method of Solution:

I The COBRA IIIC/MIT computer code calculates the flow and enthalpy within interconnected flow channels by solving finite difference equations I

I 2-1

I I of continuity, energy, and momentum. The mathematical model is applicable to both steady state and transient conditions, and the model considers both I turbulent mixing and diversion crossflow. In formulating the mathematical I model, one-dimensional, two-phase, separated, slip-flow was assumed to exist during boiling. The two-phase flow structure was assumed to be fine enough I to allow specification of void fraction as a function of enthalpy, flow rate, heat flux, pressure, position, and time. Sonic velocity propagation effects I were not included. Within a channel, the diversion crossflow velocity was assumed to be small compared to the axial velocity. This assumption allowed I the use of a simplified equation for the conservation of transverse momentum.

I The equations are solved as a boundary value problem by using a semi-explicit finite difference scheme. The boundary conditions for the problem I are the inlet enthalpy, inlet mass velocity, and exit pressure. The boundary value solution is obtained by assuming a uniform exit pressure distribution.

I (The equations do not require actual pressures since only pressure differences I are used.) When performing a computation, the code iterates over the length of the core until convergence of the* flow solution is obtained. Convergence 1* is achieved when the change in any channel flow is less than a user specified fraction of the flow from the previous iteration.

I The same finite difference equations are used for both steady state and transient computations. For steady state calculations, the time step, I ~t, is set equal to an arbitrarily large value thereby negating the time depen-I dent terms. For transient calculations, the time step is set equal to a user specified value. When performing a transient calculation, a steady state I calculation is first performed to obtain initial conditions. Time dependent forcing functions consisting of inlet temperature, inlet flow, system pressure, I and core average heat flux are used to establish boundary conditions at succeed-I I 2-2

I I ing times. The calculation iterates over the first time step until the flow solution converges. The converged solution is then used as the initial con-I ditions for the new time, and the procedure continues for all of the subsequent I time steps.

Although the equations of continuity, energy, and momentum form the I basic structure of the mathematical model, their solution is still dependent upon the use of empirical correlations. Of major importance are the correla-I tions used in calculating the pressure gradient and those used in calculating I turbulent mixing. Once the flow solution is obtained, additional correlations are used in calculating the DNBR distribution. The COBRA IIIC/MIT computer I code allows user specification of the appropriate correlations. The models and correlations which have been selected for use in the VEPCO Thermal-Hydraulic I Model are described in the following subsection.

I 2.3 Models and Correlations I 2.3.l Void Fraction Void fractions are predicted using the Smith void fraction correla-I .

tion (14) .

in conjunction with the Levy subcooled void model.

(15)

The Levy model uses local heat flux and fluid conditions in predicting the true (non-equili-I brium) quality. This true quality is then used in the Smith correlation to predict the void fraction in both the subcooled and bulk boiling regions.

I 2.3.2 Single and Two-Phase Friction Factors

~ In computing single and two-phase pressure drops, an isothermal friction factor correlation is used in conjunction with a wall viscosity corre-I lation and a correlation for predicting two-phase friction multipliers. The isothermal friction factor, fISO' is calculated using the following correla-I t ion, (16)

I 2-3

I I o. 184(Re)-o

2 I where Re is the local Reynolds number. The isothermal friction factor is corrected for heating effects by the following relationship, ( l 7)

I I 1.0 +

Heated Per~meter Wetted Perimeter

[ (~)

µ 11 0. 6 _ l.O

µbulk J

I where fH is the heated friction factor, µbulk is the viscosity evaluated at the bulk fluid temperature, and µwall is the viscosity evaluated at the wall I temperature. The wall temperature, T wa 11

, is calculated using the following I relationship, q"

T h I wall Tbulk +

where q" is the surface heat flux and Tbulk is the bulk fluid temperature.

I The heat transfer coefficient, h, is calculated from the Dittus-Boelter corre-I .

1 ation (lS) using B aroczy corre 1 ation b u 1k fl ui. d properties.

. In t h e two-phase f low region, the

. use d to ca 1 cu 1 ate two-p h ase f riction (lg) is . . mu 1 tip

. l 'iers I which are applied to the heated friction factor.

2.3.3 Turbulent Mixing I The degree of turbulent mixing between adjacent channels is calculated I using the following relationship, w' SsG I where w' is the turbulent transverse fluctuating flow rate per axial length, I G is the average mass velocity of the adjacent channels, s is the common gap, and S is the mixing coefficient. The above relationship is used to predict I both single and two-phase mixing.

I I 2-4

I I 2.3.4 Critical Heat Flux Correlation In predicting the non-uniform critical heat flux, the W-3 correla-I ti.on(20) i"s used in

conJunc

t"ion wi"th th e ""f

~- ac t or corre 1 a t" 2

ion. ( 0) In deter-I mining the lower bound of the F-factor integral, the Jens and Lottes correla-tion(2l) is used to predict the axial position where nucleate boiling begins.

I 2 When appropriate, the coldwall factor( 0) and the 1-grid or R-grid spacer (22) factor are used with the W-3 correlation to predict the critical heat flux.

I (If required, other CHF correlations can be easily added to the code as options.)

I 2.3.5 Water Properties Water properties (enthalpy, specific volume, viscosity, conductivity, I and specific heat) are calculated using the HOH routines which were obtained from Reference 23.

I 2.4 Computational Input Parameters I The computational input parameters that were used in the Surry analy-I ses described within this report are listed in Table 2-1. For steady state analyses, 156 axial intervals were s-pecified (l" intervals), and for transient I analyses, 78 axial intervals were specified (2" intervals). Values chosen for the crossflow resistance coefficient, the mixing coefficient, and the I momentum factors are representative of those which would be used in subchannel (13)

I analyses.

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I I 2-5

1, I TABLE 2-1 I CO.HPUTATIONAL INPUT PARAfIETERS I Number of Axial Intervals, Steady State Analysis 156 Number of Axial Intervals, Transient Analysis 78 I Fraction of Heat Generated in the Fuel 0.974 I Convergence Criteria Crossflow Resistance Coefficient, k 0.005 0.5 I Mixing Coefficient, S 0.019 Turbulent Momentum Factor, ft 0.0 I Transverse Momentum Factor, s/i 0.5 I

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I I SECTION 3 - HYDRAULIC MODEL DESCRIPTION I 3.1 Introduction I The techniques used in formulating the hydraulic representation of the Surry core are applicable, in general, to all pressurized water reactors.

I (These same techniques will be used in formulating the hydraulic models for the North Anna cores.) Basically, eighth core symmetry is assumed, and thus I only a 1/8 core segment is modeled. It is also assumed that the hot assembly is located at the center of the core, and therefore, due to symmetry the 1/8 I core segment contains 1/8 of the hot assembly. The hot assembly is modeled I as an array of subchannels, while the remaining assemblies are modeled as an array of lumped channels. For steady state analysis, a fine mesh geometry I is used in which each lumped assembly and each.hot assembly subchannel are modeled as individual flow channels. For transient analysis, a coarse mesh I geometry is used in which assemblies and subchannels are combined to form I larger channels. Because the coarser geometry contains fewer channels, less computational time per iteration is required, allowing the transient analysis I to be performed without excessive expeditures of computer time.

Using the above mentioned general techniques, hydraulic models have I been developed at VEPCO which are applicable specifically to the Surry units.

A 53 channel model has been developed for steady state analysis, and using I this model as a basis, a 19 channel model has been developed for transient I analysis. Detailed descriptions of these models along with a general description of the Surry core are provided in the following subsections.

I' 3.2 General Description of the Surry Core I The Surry Units No. 1 and 2 are Westinghouse designed pressurized water reactors with cores consisting of 157 fuel assemblies. The arrangement I

I 3-1

I I of the fuel assemblies is shown in Figure 3-1. Each fuel assembly is hydrau-lically identical and consists of 204 fuel rods, 20 guide thimble tubes, and I a centrally located instrumentation tube. As shown in Figure 3-2, the fuel I assembly elements are arranged in a 15 x 15 square array.

parameters are listed in Table 3-1.

Assembly hydraulic I Seven grids are used in each fuel assembly to support the fuel rods.

Each grid consists of individual slotted straps interlocked and brazed in an I "egg-crate" arrangement. The grids maintain the lateral spacings between fuel rods, and they are located at intervals _along the assembly length. The I five middle grids are called mixing vane grids since they contain tabs which I project into the coolant stream. These grids are used in the high heat flux region to promote better mixing of the coolant. The internal straps of the I two end grids do not contain mixing vanes, and they are therefore called non-mixing vane grids. All seven grids are mechanically attached to the guide I thimble tubes. The guide thimble tubes are in turn attached to the upper and I lower nozzles and thus provide assembly structural support.

the Westinghouse 15 x 15 assembly is *shown in Figure 3-3.

A side view of I

3.3 Eighth Core Representation - 53 Channel Model I In modeling the Surry core for steady state analysis, a 53 channel model was developed representing a 1/8 core segment. This 53 channel model I consisted of 25 lumped assembly channels and 28 subchannels. The assembly I radial geometry is shown in Figure 3-4, and the subchannel radial geometry is shown in Figure 3-5. In the axial direction, the seven grids were modeled I by using grid loss coefficients at the axial positions listed in Table 3-2.

The upper and lower nozzles had been initially modeled, however, they were I subsequently deleted after it was found that they had only a minor effect on I the flow solution.

I 3-2

I I Within the assembly geometry, each lumped assembly was modeled by using a lumped flow area, lumped heated and wetted perimeters, and an effective I gap. These hydraulic data, listed in Table 3-3, were calculated by considering I the individual elements comprising the fuel assembly. The effective gap for crossflow was calculated by subtracting from the assembly pitch the blockage I caused by a row of fuel rods (i.e., 15 x fuel rod diameter). Half assemblies, fanned by the lines of symmetry, were modeled by multiplying the assembly I hydraulic data by 0.5.

I Within the subchannel geometry, four different types of subchannels were modeled. As shown in Figure 3-5, these subchannel types consist of a I unit cell, a perimeter cell, a corner cell, and a thimble cell. The unit, perimeter, and corner cells are all flow channels which are basically formed I by four fuel rods. However, the perimeter and corner cells are modeled to include the flow region between the fuel rods of adjacent assemblies. The I fourth type of subchannel is the thimble cell which is formed by three fuel I rods and a guide/instrumentation thimble tube. All the subchannels were modeled using the hydraulic data shown in Tables 3-4 through 3-7.

I 3.4 Eighth Core Representation - 19 Channel Model I In modeling the Surry core for transient analysis, a 19 channel model was developed to represent the 1/8 core segment. This model was derived from I the 53 channel model by combining assemblies and subchannels to form larger, I lumped channels. As shown in Figures 3-6 and 3-7, the 19 channel model con-sists of 4 lumped channels and 15 subchannels. The lumped channels were modeled I using the hydraulic data shown in Table 3-8. The subchannels were modeled using the data provided in Tables 3-4 and 3-7.

I I

I 3-3

I I TABLE 3-1 I ASSEMBLY HYDRAULIC PARAMETERS No. of Fuel Rods ,204 I No. of Guide Thimble Tubes 20 I No. of Instrumentation T~imble Tubes Fuel Rod Outside Diameter (inches) 0.422 1

I Guide Thimble Tube Outside Diameter (inches) 0.546 Instrumentation Thimble Tube Outside Diameter (inches) 0.546 I Fuel Rod Pitch (inches) 0.563 Fuel Assembly Pitch (inches)

I 8.466 I

I I

I I 3-4

I I TABLE 3-2 I AXIAL POSITIONS OF ASSEMBLY COMPONENTS Description Position-I (inches)

Start of Assembly 0.00 I Start of Rodded Region 2.30 Start of Active Fuel 3.00 I Non-mixing Vane* Grid 4.42 I Mixing Vane Grid Mixing Vane Grid 28.62 54.81 I Mixing Vane Grid 81. 00 Mixing Vane Grid 107.19 I Mixing Vane Grid 133.38 J.

End of Active Fuel~ 146.60 I Non-mixing Vane Grid 152.06 I End of Rodded Region End of Assembly 154. 10 156.00 I

Based upon an active fuel length of 143.60 inches I

I I

I I 3-5

I I TABLE 3-3 ASSEMBLY HYDRAULIC DATA I Fuel Assembly Flow Area (square inches) 38.22 Fuel Assembly Wetted Perimeter (inches) 306.5 I Fuel Assembly Heated Perimeter (inches) 270.5 I Fuel Assembly Effective Gap (inches)

Fuel Assembly Non-mixing Vane Grid Loss Coefficient 2 .136 0.7378 I Fuel .Assembly Mixing Vane Grid Loss Coefficient 0.9182 I

I TABLE 3-4 UNIT CELL HYDRAULIC DATA Unit Cell Flow Area (square inches) 0. l 771 I Unit Cell Wetted Perimeter (inches) 1. 326 I Unit Cell Heated Perineter (inches)

Fuel Rod to Fuel Roe Gap (inches)

1. 326 O. lLd I Unit Cell Non-mixing Vane Grid Loss Coefficient 0.6732 Unit Cell Mixing Vane Grid Loss Coefficient 0.8377 I

I TABLE 3-5 PERIMETER CELL EYDPAVLIC DATA I Perimeter Cell Flow Area (square inches) 0.2716 I Perimeter Cell Wetted Perimeter (inches)

Perimeter Cell Heated Perimeter (inches)

1. 989 1.989 I Fuel Rod to Fuel Rod Gap (inches)

Perimeter Cell Non-mixing Vane Grid Loss Coefficient 0 .141 0.6732 I Perimeter Cell Hixing Vane Grid Loss Coefficient 0.8377 I

I 3-6

I I TABLE 3-6 COP.NER CELL P.:YDRAULIC DATA I Corner Cell Flow Area (square inches) 0.4163 Corner Cell Wetted Perimeter (inches) 2.983 I Corner Cell Heated Perimeter (inches) 2.983 I Fuel Rod to Fuel Rod Gap (inches)

Corner Cell Non-mixing Vane Grid Loss Coefficient 0.141, 0.222 0.6732 I Corner Cell ~fixing Vane Grid Loss Coefficient 0 .8377 I

TABLE 3-7 THIMBLE CELL HYDP.AULIC DATA I

Thimble Cell Flow Area (square inches) 0 .1535 I Thimble Cell Wetted Perimeter (inches) 1. 423 Thimble Cell Heated Perimeter (inches)

I Fuel Rod to Fuel Rod Gap (inches) 0.99LL 0 .141 I Fuel RoC. to Guide Thimble Tube Gap (inches)

Thimble Cell Non-rdxing Vane Grid Loss Coefficient 0.079

0. 8953 I Thimble Cell I-fixing Vane Grid Loss Coefficient 1.114 I

I I

I I 3-7

I I TABLE 3-8 HYDRAULIC DATA FOR Ll.J1'JPED CHANNELS I

I Channel No. 1 Flow Area (square inches) 57.33 I Wetted Perimeter (inches) 459.75 I Heated Perimeter (inches)

Effective Gap (inches) 405.75 3.204 I Non-mixing Vane Grid Loss Coefficient 0.7378 Mixing Vane Grid Loss Coefficient 0.9182 I

Channel No. 2 I Flow Area (square inches) 649.74 Wetted Perimeter (inches) 5210.5 I Heated Perimeter (inches) 4598.5 I Effective Gap (inches)

Non-mixing Vane Grid Loss Coefficient 3.204 0.7378 I Mixing Vane Grid Loss Coefficient 0.9182 I Channel No. 3 I Flow Area (square inches)

Wetted Perimeter (inches) 38.22 306.5 I Heated Perimeter (inches) 270.5 Effective Gap (inches) 3.204, 1.068 I Non-mixing Vane Grid Loss Coefficient 0.7378 Eixing Vane Grid Loss Coefficient 0.9182 I

I I 3-8

I TABLE 3-8 HYDRAULIC DATA FOR Lu~1PED CHJ....NNELS (Continued)

I I Channel No. 4 Flow Area (square inches) 2. 729 I Wetted Perimeter (inches) 21.06 I Heated Perimeter (inches)

Effective Gap (inches) 19.55 1.068 I Non-mixing Vane Grid Loss Coefficient

0.7099 Hixing Vane Grid Loss Coefficient 0.8833 I

I I

I 3-9

I I FIGURE 3-1 I FUEL ASSEMBLY ARRANGEMENT OF SURRY CORE I

I I

I I I

" I

/

" /

I I' l

I

/

". I /

I ' '

I I /

/

' I /

I "'

I I /

/

- - - - ..:. - -- - - ,___ - ,_ - "-x- I /

I /

./ I I "

/*

I '* '

I /

/

I I

.I '

I

/

/ I

/

I '

/

i "'

I /

/

I I I I

I I I

I I 3-10

FIGURE 3-2 CROSS SECTIONAL VIEW OF SURRY FUEL ASSEMBLY

' I /

" - r 000000000000000 oc~\o o o ooQo ooo o/c-:/o 000000000000000 000000000000000 o o o oQo o*Q o 00*0 o o o 0000000000'00000 000000000*000000

- k30 000 8-G~G-G 00G 0 -

Q /

/ I I

Instrumentation Tube O

0 0 /G~ide I ' ' 0 0 Q Cf-Thimble

'j{,dJ- Tube 1

Q

~

O 0 // 0 ', 0

*o 0 /

/

o o : o l;Fuel Rod.

o,. o0'-

0/0 0 0 0 0 0 c0 0 0 0 0 0 0 \~)

/

3-11

I I FIGURE 3-J SIDE VIEW OF SURRY FUEL ASSEMBLY I

I I

I I 3-12

I I FIGURE 3-5 I SUBCHANNEL GEOMETRY OF 53 CHANNEL MODEL I

I I PERIMETER CELL CORNER CELL\

I I

I

I I

I I

THJJ."1BLE CELL I

I I CENTER OF THE CORE I

I I 3-14

I I FIGURE 3-6 I ASSEMBLY GEOMETRY OF 19 CHANNEL MODEL I

1 I

I 2 I I I

I

---l-------1 I

I I

-t - - -- - ----------.

I

- --l I

I -- - --f I

I -l --

1 I

I 3 I

I CENTER OF THE CORE I

I 3-15

I I FIGURE 3-7 I SUBCHANNEL GEOMETRY OF 19 CHANNEL MODEL I

I I

4 I

I - - - - I- - _I - j I

I 5 6 8 I

I I

I CENTER OF THE CORE I

I I 3-16

I I SECTION 4 - THERMAL MODEL DESCRIPTION I 4.1 Introduction I The techniques used in formulating the thermal representation of the Surry core are applicable, in general, to all pressurized water reactors.

I (The same techniques will be used in formulating the thermal models for the North Anna cores.) The thermal model basically consists of an inlet flow I distribution, radial and axial power distributions, and appropriate reactor I operating conditions. For transient analysis, time dependent forcing functions of system pressure, inlet flow, inlet temperature, and core average heat flux I are also specified.

Thermal-hydraulic design parameters form the basis of the model.

I N Thus, the radial power d~stribution is based upon the design value of F~H' and the axial power distribution is based upon the reference axial flux shape. The I thermal design flow rate is used in determining the core average mass velocity, I and thermal-hydraulic design values for inlet temperature, system pressure, and power level are used as operating conditions.

I In formulating the inlet flow distribution, the inlet flow to the hot assembly (i.e., the subchannel array) is conservatively reduced by 5% in order I to account for the possibility of inlet flow maldistribution. In order to I conserve the total core flow rate, the peripheral assemblies are given inlet flow fractions slightly greater than 1.0. The average of all the flow frac-I tions is forced to equal 1.0.

In formulating the subchannel portion of the radial power distribu-I tion, the fuel rods which form the hot channel are given relative powers equal N

to the design value of F~H Lower relative powers for the remaining fuel rods I are then assigned to create a gradual power gradient which peaks around the I hot channel. The average of all the fuel rod relative powers is forced to I 4-1

I I equal the hot assembly relative power. (In general, power peaking within the hot assembly is assumed to be 5%, i.e., the ratio of FN and the hot assembly I relative power is 1.05.)

6H I In formulating the assembly portion of the radial power distribu-tion, the hot assembly relative power is also assigned to the two assemblies I which are adjacent to the subchannel array. Lower relative powers for the remaining assemblies are then assigned to create a second power gradient which I peaks around the hot assembly. The average of all the assembly relative powers is forced to equal 1.0.

I The above mentioned general techniques are used to formulate the I overall thermal model. The thermal model is then imposed upon the hydraulic model in order to obtain the complete thermal-hydraulic representation of the I core. Since this representation is dependent upon thermal-hydraulic design parameters, revised representations must be considered in the event of any I subsequent design changes. In general, the hydraulic model remains relatively I fixed since it is affected only by changes in the mechanical design of the fuel. However, the thermal model can be significantly affected by changing I any one of the previously mentioned design parameters. Two such changes have occurred since the original design of the Surry units. These design changes I are discussed in Section 4.2. Sections 4.3 through 4.6 then describe the thermal model which has been formulated based upon current Surry design para-I meters. (The thermal models which are based upon earlier designs are de-I scribed in detail in Section 6.)

I 4.2 General Description of the Thermal-Hydraulic Design of the Surry Core The Surry Units No. 1 and 2 are Westinghouse designed, three loop I pressurized water reactors with thermal ratings of 2441 MWt( ).

8 The thermal I design flow rate is 265,500 gprn which is based upon three reactor coolant I 4-2

I I pumps each rated at a design capacity of 88,500 gpm at 543 °F. The assumed fraction of flow effective for heat removal from the core is 0.955 (i.e., 4.5%

I core bypass). The nominal inlet temperature is 543 °F, and the nominal I operating pressure is 2250 psia. The fuel rods have a nominal active length of 144.0", and the fraction of heat generated in the fuel is 0.974. In the I N original design of the Surry units, F~H was 1.58, and a chopped cosine with a 1. 72 peak was used as the reference axial power distribution.

I Several revisions to the above parameters have been required since the publication of the original FSAR. In December, 1972, the design peaking I factors were revised in the densification reanalysis. ( )

9 N F~H was reduced from I 1.58 to 1.55, and the reference axial power distribution for DNB analysis was changed to a chopped cosine with a 1.55 peak. Due to the phenomenon of fuel I densification, the active length was reduced from 144.0 inches to 142.3 inches.

In August, 1977, the thermal design flow rate was reduced to 238,950 I gpm at 543 0 .

F which is 90% of the original thermal design flow rate.

(12)

This I reduction in flow was a result of conservative assumptions concerning increased flow resistance associated with a liwiting steam generator tube plugging level.

I Based upon revised fuel parameters, the active length of the fuel was assumed to be 143.6 inches.

I 4.3 Inlet Flow Distribution I The inlet flow distribution used with the 53 channel model is shown I in Figure 4-1, and the inlet flow distribution used with is shown in Figure 4-2.

the 19 channel model These distributions were used in all the DNB analyses I described within this report. As shown in the figures, the hot assembly (i.e., the subchannel array) is given an inlet flow fraction of 0.95, while the I peripheral assemblies are given flow fractions slightly greater than 1.0. The I average of all the flow fractions is approximately equal to 1.0.

I 4-3

I I 4.4 Power Distribution I The design radial power distribution which has been formulated by VEPCO for the current thermal model is shown in Figures 4-3 through 4-6.

I (Since this thermal model is based upon the reduced thermal design flow

( 12) rate, it is referred to as the Low Flow Assumption Reanalysis.) Figure I 4-3 shows the assembly power distribution which is applicable to the 53 channel model. As shown, a power gradient exists which peaks around the hot assembly located at the center of the core. The hot assembly as well as the I adjacent assemblies are given relative powers of 1.475, while lower relative powers are assigned to the remaining assemblies. The average of all the I assembly relative powers is 1.0. The assembly power distribution for the 19 channel model is derived from that of the 53 channel model by averaging all I but the three central assembly relative powers. Figure 4-4 shows the result-I ing assembly power distribution used with the 19 channel model.

Figure 4-5 shows the subchannel portion of the radial power distri-I bution applicable to the 53 channel model. Within the subchannel array, a second power gradient exists, and it. peaks around the hot channel which is a I thimble cell. As shown in Figure 4-5, the three fuel rods surrounding the hot thimble cell are each given relative powers of 1.55, while lower relative I powers are assigned to the remaining fuel rods. The average of all the fuel I rod relative powers is equal to the hot assembly relative power, or 1.475.

The subchannel power distribution for the 19 channel model is derived from I that of the 53 channel model by averaging the relative powers of the fuel rods located within the lumped subchannel. Figure 4-6 shows the resulting I subchannel power distribution used with the 19 channel model.

I The same axial power distribution is used in both the 19 and 53 channel models. For the current thermal model, the reference axial flux I

I 4-4

I I shape is a 1.55 chopped cosine which is based upon an active length of 143.6 I inches. Values of relative flux as a function of axial position are obtained by using the following equation, I rrz' F(z') 1.55 cos H I e where F(z') =relative axial flux I z' distance from the core center, feet I H e

extrapolated length, feet I In determining the extrapolated length, H , the integral of the e

above equation is averaged over the active length and set equal to 1.0. An I iterative process is then used in order to determine the value of H which e

I satisfies the resulting equation. Table 4-1 lists axial flux values which define the axial power distribution used in the current thermal model.

I 4.5 Reactor Operating Conditions I Reactor conditions consist of a power level, a core flow rate, a core inlet temperature, and a system pressure. As previously discussed in I Section 4.2, the Surry units are rated at 2441 MWt, the reactor thermal I design flow rate is currently 238,950 gpm, the nominal inlet temperature is 543 °F, and the nominal system pressure is 2250 psia. When performing tran-I sient analysis, maximum steady state instrumentation errors are applied to these rated values so that the initial reactor conditions obtained are the I most adverse with respect to thermal margin to DNB. This is accomplished by I increasing the power by 2% to 2490 MWt, by increasing the temperature by 4 °F to 547 0

F, and by decreasing the pressure by 30 psi to 2220 psia.

I I 4-5

I I The power level is input as a core average heat flux which is calcu-lated using the following equation, I

3 (FRAC) (POWER) (3413 x 10 Btu/hr)

I Q" (HP)(ACTIVE LENGTH) x MW I where Q" core average heat flux, Btu/hr-ft 2

FRAC fraction of rated power I POWER nominal thermal power, MW HP total core heated perimeter, feet I ACTIVE LENGTH = core active length, feet I

The core average heat flux is based upon the total heat generation I rate because it is used within the COBRA IIIC/MIT code to determine the total I heat added to the coolant. Modifications have been added to the code by VEPCO in order to account for the fraction of the heat which is actually generated I within the fuel (See Appendix A).

The core flow rate is input to the COBRA IIIC/MIT code as a core I average mass velocity. The core average mass velocity is calculated using the following equation, 3

I G (FRAC)(Q)(p)

(FLOW AREA) x (60 min) hr x

( 1 ft 7.4805 gal

)

I where G core average mass velocity, lbm/hr-ft 2

FRAC fraction of reactor flow effective for heat removal from the core (i.e., 0.955)

Q reactor volumetric flow rate, gpm I p fluid density at inlet, lbm/ft 3

FLOW I AREA total core flow area, ft 2

I 4-6

I I 4.6 Forcing Functions for Transient Analysis I When performing a transient analysis, forcing functions are applied to the initial reactor conditions in order to obtain subsequent reactor con-I ditions. For each reactor parameter that is changing with time, a forcing function is input as a table set with each entry consisting of the ratio of

! I the transient condition to the initial condition and a corresponding time.

The COBRA IIIC/MIT computer code has the capability of handling four different I forcing functions, e.g., core average heat flux versus time, inlet flow versus I time, inlet temperature versus time, and system pressure versus time.

For the Surry transient analyses described within this report, the II forcing functions were obtained from the FSAR and other licensing documents.

It has also been demonstrated that the forcing functions can be obtained from I transient analyses performed using a system thermal-hydraulic code such as RETRAN. (Z 4 )

I I

I I 4-7

I I TABLE 4-1 I AXIAL POWER DISTRIBUTION (LOW FLOW ASSUMPTION REANALYSIS)

I F(z')

7fZ I .

1

55 cos (12.12993429)

I Axial Flux Shape: 1.55 Cosine (143.6" Active Length)

I z z' I Axial Position (inches)

Fuel Position (feet) z/156.0 Relative Position F(z')

Relative Flux I 0.0 2.96 3.0 -5.98333333 0.0000 0.0190 0.0192 0.0000 0.0000 0.0328 10.0 -5.4 0.0641 0.2656 I 17.2 24.4

-4.8

-4.2 0.1103 0.1564 0.4988

0. 7199

31. 6 -3.6 0.2026 0.9237 I 38.8 46.0 53.2

-3.0

-2.4

-1. 8 0.2487 0.2949

0. 3410

1. 1052 1.2601 1.3846 60.4 -1. 2 0. 3872 1.4757 I 67.6 74.8

-0.6 0.0 0.4333 0.4795

1. 5313 1.5500 82.0 0.6 0.5256 1. 5313 I 89.2 96.4 103. 6 1.2

1. 8 2.4 0.5718 0.6179 0.6641 1.4757 1.3846 1.2601 I 110. 8 118.0 125.2 3.0 3.6 4.2

0. 7103

o. 7564 0.8026 1.1052

0. 9237

0. 7199 132.4 4.8 0.8487 0.4988 I 139.6 146.6 5.4 5.98333333 0.8949 0.9397 0.2656 0.0328 146.64 0.9400 0.0000 I 156.0 1. 0000 0.0000 I

I I

I 4-8

I I FIGURE 4-1 INLEI' FLOW DISTRIBUTION OF 5J CHANNEL MODEL I

I I 1.001 1.001 I

1.000 1.001 1.001 1.001 I

I 1.000 1.000 1.000 1.000 1.001 I

I 1.000 1.000 1.000 I

I 1.000 1.000 1.000 1.000 I

I 1.000 1.000 ---Inlet Flow Fraction I

I I

I 4-9

I I FIGURE 4-2 I INLET FLOW DISTRIBUTION OF 19 CHANNEL MODEL I

I 1.004 I

I I I I I I - -l -!- - - - -

I

-- ----~

I

-l -- - - - -I - -- -* -- -i -. - - ----

I 1.000 I - - -j --+ - --- - -- -1 I

I I -j -- -

I

- - -l I

I I

I I 4-10

I I FIGURE 4-J I ASSEMBLY POWER DISTRIBUTION, 5J CHANNEL MODEL (LOW FLOW ASSUMPTION REANALYSIS)

I I 0.50 0.60 I

I 0.70 0.70 0.70 0.70 I

0.831 0.90 0.80 0.80 0.80 I

I 1.20 1.10 1.20 1.00 I

I 1.JO 1.JO 1.JO 1.20 I

I 1.40 1.40 *Assembly Relative Power I

I I 1.475 I

I 4-11

I I FIGURE 4-4 I ASSEMBLY POWER DISTRIBUTION, 19 CHANNEL MODEL (LOW FLOW ASSUMPTION REANALYSIS)

I I 0. 9713 I

I I I - - -l - -f -

I

- - -- -1.-* - -- - ------~

I

-- -I --- -- -I -- - -* - -i -* -* - -** -j - - -- --- *-*

I 0,9711 I

I -- - -t --- I - -** - *- -*!

1 I

I - -J -- -- I I

I

~--Assembly Relative Power I

I 1,

I I 4-12

I I FIGURE 4-5 I SUBCHANNEL POWER DISTRIBUTION, 5J CHANNEL MODEL (LOW*FLOW ASSUMPTION REANALYSIS)

I I

--Fuel Rod Relative I Power I

I I

I I 4-13

I I FIGURE 4-6 I SUBCHANNEL FOWER DISTRIBUTION, 19 CHANNEL MODEL (LOW FLOW ASSUYlPTION REANALYSIS)

I I

I - - - I I 1.L~J4

- _I - J_

I I I

.1 I

I I

Fuel Rod Relative I Power I

I I

I I 4-14

I I SECTION 5 - ENGINEERING UNCERTAINTIES I 5.1 Introduction I After formulating the overall thermal-hydraulic representation of the core (see Sections 3 and 4), engineering uncertainties are then applied I to account for manufacturing tolerances used in the fabrication of the fuel.

These fabrication tolerances are assumed to occur in the hot channel, and they I are therefore called hot channel factors. These factors and their application are discussed in detail in Section 5.2.

I I 5.2 Hot Channel Factors Three hot channel factors were used in all the DNB analyses described I within this report. These factors consist of a pitch reduction, an engineering factor on the enthalpy rise (F~H)' and an engineering factor on the heat flux I E (FQ). The pitch reduction takes into account fuel rod spacing variations which may occur within the as-built fuel assembly. This reduced pitch is I accounted for by modeling the hot channel with reduced gap spacings and a I reduced flow area. Since a reduced flow area causes a greater pressure loss 25 across t h e spacer gri. d s, ( ) t h.is e ff ect is

. ta k en into

. account b y using

. in-I creased grid loss coefficients. Table 5-1 lists the hydraulic data which was used in modeling the hot channel.

I The engineering factor on the enthalpy rise (F:H) takes into account I the effect of enrichment and-density variations which may occur in as-built fuel rods. This factor is accounted for by increasing the relative power of I the hot fuel rod. For all the DNB analyses described within this report, the relative power of the hot fuel rod was multiplied by a factor of 1.02.

I I

I 5-1

I I The engineering factor on the heat flux (F~) takes into account the I effect of enrichment, density, diameter, and eccentricity variations which may occur in as-built fuel pellets. This factor is accounted for by applying I a heat flux spike on the hot fuel rod at the position of MDNBR. Before the heat flux spike can be applied, however, a thermal analysis must first be I performed in order to determine the axial position of MDNBR. Based upon these I results, the axial heat flux shape for the hot fuel rod is then adjusted to include a heat flux spike at the determined position. The spiked flux shape I is included in a second thermal analysis from which the final results are obtained.

I An engineering factor on the heat flux was applied to all the DNB analyses described within this report. However, it should be noted that recent I spike DNB tests have shown that the actual spike effect on DNB is very small.

(26)

E I Based upon these tests, it was concluded that FQ no longer had to be considered in DNB evaluations since its effect could be adequately accounted for in the I DNBR design limit.

I I

I I 5-2

I I TABLE 5-1 HOT CHANNEL HYDRAULIC DATA I

I Hot Thimble Cell Pitch Reduction (inches) 0.0065 I Reduced Flow Area (square inches) 0 .1463 Reduced Fuel Rod to Fuel Rod Gap (inches) 0.1345 I Reduced Fuel Rod to Thimble Tube Gap (inches) 0. 0725 Increased Non-mixing Vane Grid Loss Coefficient 0.9866 I Increased Mixing Vane Grid Loss Coefficient 1.2280 I Hot Unit Cell I Pitch Reduction (inches) 0.0065 Reduced Flow Area (square inches) 0.1698 I Reduced Fuel Rod to Fuel Rod Gap (inches) 0 .1345 I Increased Non-mixing Vane Grid Loss Coefficient Increased Mixing Vane Grid Loss Coefficient 0.7321 0.9110 I

I I

I 5-3

I I SECTION 6 - THERMAL-HYDRAULIC MODEL VERIFICATION I 6.1 Introduction I Three steady state and six transient DNB analyses were performed by VEPCO using the models and methods described in the preceeding sections.

I These analyses are listed in Table 6-1, and they are representative of those (8)

I contained in the original Surry FSAR ments. C9 ,lO,ll,l 2 )

and in subsequent licensing docu-The later reanalyses update the FSAR and reflect the I thermal-hydraulic design changes which were discussed in Section 4.2.

The analyses were performed in order to verify the calculational I accuracy of the VEPCO Thermal-Hydraulic Model. For this reason, they were formulated to duplicate as closely as possible the original analyses contained I in the above mentioned documents. Verification was obtained by comparing I minimum DNBRs calculated using the VEPCO methods with those given in the licensing documents. These comparisons along with detailed descriptions of the analyses I themselves are given in the following subsections.

I I

I I 6-1

-i I

I TABLE 6-1 LISTING OF VEPCO VERIFICATION A.l.'l"ALYSES I (8)

FSAR Analyses I Steady State at 100% Power Excessive Load Increase Transient I Uncontrolled Control Rod Assembly Withdrawal at Power Transient I Complete Loss of Reactor Coolant Flow Transient I . ( 9 )/P ositive Densi'f'ication . . Md ro erator Temperature Coe ff'icien

. t(lO,ll) Reana 1yses I Steady State at 112% Power Uncontrolled Control Rod Assembly Withdrawal At Power Transient I Complete Loss of Reactor Coolant Flow Transient I

. (12)

Low Flow Assumption Reanalyses I Steady State at 102% Power I Complete Loss of Reactor Coolant Flow Transient I

I I

I I 6-2

I I' 6.2 FSAR Analyses I 6.2.l Introduction The original FSAR analyses, which were performed using the VEPCO I methods, consist of a steady state analysis at 100% power and three transient analyses. The radial power distributions for both the 53 and 19 channel models I are shown in Figures 6-1 through 6-4. Relative flux values composing the axial power distribution are listed in Table 6-2. Reactor conditions and parameters I which are applicable to the FSAR analyses are listed in Tables 6-3 and 6-4, I respectively.

As identified in Table 6-4, the original Surry design included a I high pressure DNB penalty. At the time, this penalty was applied for con-servatism because of the relatively small amount of DNB data then available I at higher operating pressures. DNBRs calculated using the VEPCO methods were thus adjusted so that they could be compared to those given in the FSAR. A I DNBR divisor based upon the system pressure was calculated using the following I relationship, I DNBR Divisor where p system pressure, psia (P>2000)

I It should also be noted that the models developed by VEPCO for the I FSAR group of analyses incorporate a unit cell as the hot channel (see Figures 6-3 and 6-4). These models reflect the fact that the unit cell had been assumed I to be the limiting channel when the Surry units were first designed. All MDNBRs pertaining to this group of analyses are therefore based upon a hot unit cell.

I 6. 2. 2 Steady State Analysis at 100% Power I The Surry FSAR gives a MDNBR at nominal operating conditions of 1.97.

Using the VEPCO methods along with the 53 channel model, a HDNBR of 1.94 was I

I 6-1

I I calculated. A MDNBR of 1.94 was also calculated using the VEPCO methods along with the 19 channel model.

I 6.2.3 Excessive Load Increase Transient I An Excessive Load Increase trqnsient is defined as a rapid increase in the steam generator steam flow that causes a power mismatch between the I reactor core power and the steam generator load demand. The transient could result from either an administrative violation such as excessive loading by I the operator or an equipment malfunction in the steam bypass control or turbine speed control. Since the Reactor Control System is designed to accommodate I a 10 percent step load increase without a reactor trip, analyses are performed I to demonstrate that in such cases the MDNBR does not fall below the design limit.

I The case analyzed is a 10 percent step increase at EOL with the reactor at full power under manual control. Forcing functions of nuclear I power, system pressure, and inlet temperature were obtained from the Surry FSA..~.

I The inlet flow was assumed to be constant throughout the transient.

(It should be noted that by using nuclear power instead of heat flux, the thermal lag of the fuel was neglected. This approximation is reasonable, however, since the nuclear power is changing slowly.) DNBR results, which I were obtained using the 19 channel model, are shown in Figure 6-5. The FSA..~

shows a MDNBR of 1.55 while Vepco results show a MDNBR of 1.53.

I 6.2.4 Uncontrolled Control Rod Assembly Withdrawal at Power Transient I An Uncontrolled Control Rod Assembly Withdrawal at Power transient results in an increase in core heat flux. Since the heat extraction from the I steam generator remains constant, there is a net increase in the reactor coolant temperature. Unless terminated by manual or automatic action, the power mis-I match and resulting coolant temperature rise would eventually result in DNB.

I I 6-4

I The case analyzed is a slow control rod assembly withdrawal (2.0 I x 10

-5 6K/sec) from full power. Forcing functions of nuclear power, system pressure, and inlet temperature were obtained from the Surry FSAR. The inlet I flow was assumed to be constant throughout the transient. Reactor trip on overtemperature 6T occurs after approximately 48 seconds. DNBR results, which I were obtained using the 19 channel model, are shown in Figure 6-6. The FSAR I shows a MDNBR of 1.36 while VEPCO results show a MDNBR of 1.34.

6.2.5 Complete Loss of Reactor Coolant Flow Transient I A complete loss of forced reactor coolant flow may result from a simultaneous loss of electrical supplies to all reactor coolant pumps. If I the reactor is at power at the time of the accident, the immediate effect of loss of coolant flow is a rapid increase in the coolant temperature. Unless terminated by reactor trip, the coolant temperature rise would result in DNB.

I The case analyzed is a complete Loss of Reactor Coolant Flow tran-sient with three pumps operating and the reactor at full power. Forcing func-tions of core average heat flux and core flow were obtained from the Surry FSAR.

System pressure and inlet temperature were assumed constant thr-oughout the I transient. DNBR results, which were obtained using the 19 channel model, are I shown in Figure 6-7.

a MDNBR of 1. 48.

The FSAR shows a MDNBR of 1.46 while VEPCO results show I

I I

I.

I I 6-5

I.

TABLE 6-2 I AXIAL POWER DISTRIBUTION FSAR ANALYSIS I cos nz'(l.56523) 12 - cos n(l.56523) 2 F( z 1 ) 1. 72 -------TI-(-1-.5_6_5_2_3_)_ _ __

.I 1 - cos 2

.I* Axial Flux Shape: 1. 72 Cosine 044. O" Active Length)

I z Axial Position z'

Fuel Position z/156.0 F(z')

(inches) (feet) Relative Position Relative Flux 0.0 0.0000 0.0000 3.0 -6.0 0.0192 0.0000 I 10. 2 17 .4

-5.4

-4.8 0.0654

0. 1115 0 .1714

0. 3776 24.6 -4.2 0. 15 77 0.6064 I 31. 8 39.0 46.2

-3.6

-3.0

-2.4 0.2038 0.2500

0. 2962 0.8438 1.0757

1. 2881 1* 53.4 60.6 67.8

-1. 8

-1. 2

-0.6 0.3423 0.3885 0.4346 1.4682

1. 6052

1. 6909 75.0 0.0 0.4808 1. 7200 I 82.2 89.4

96. 6 0.6

1. 2

1. 8 0.5269 0.5731 0.6192

1. 6909

1. 6052

1. 4682 103.8 2.4 0.6654 1. 2881 I 111. 0 118.2 3.0 3.6

0. 7115

0. 75 77 1.0757 0.8438 125.4 4.2 0.8038 0.6064 I 132.6 139.8 147.0 4.8 5.4 6.0 0.8500

0. 8962 0.9423

0. 3776 0.1714 0.0000 1.0000 0.0000 I 156.0 I

I I

I 6-6

I.

I TABLE 6-3 I REACTOR CONDITIONS, FSAR ANALYSIS I

Steady State Analysis

.I Power (% of nominal 2441 MWt) 100 6 2

.I* Core Average Heat Flux (10 I n 1et Ternperature ( OF)

Btu/hr-ft ) 0.196206 543 I System Pressure (psia)

Core Average Mass Velocity (10 6

lbm/hr-ft )

2 2250 2.308 Transient Analysis (Initial Conditions)

I Power (% of nominal 2441 MWt) 102 6 2 Core Average Heat Flux (10 Btu/hr-ft ) 0.200130 I n 1et Temperature ( OF) 547 I System Pressure (psia) 6 . 2 2220 Core Average Mass Velocity (10 lbm/hr-ft ) 2.295 I

I I

.I 6-7

I

.I TABLE 6-4

'I PAR.Al.'1ETERS FOR FSAR ANALYSIS I

F~H (Hot Unit Cell) 1. 58

.I*

1. 72 I

Hot Assembly Relative Power 1.432 I

Active Fuel Length (inches) 144.0 Reactor Flow (gpm at 543°F) 265,500 I 1. 03

.I 1.02 I

Pitch Reduction (inches) 0.0065 I

CHF Correlation W-3 with F-Factor I High Pressure DNB Penalty 1.05 per 200 psi I above 2000 psia I

I I 6-8

I

.I FIGURE 6-i

!I. ASSEMBLY POWER DISTRIBUTION, jJ CHANNEL MODEL FSAR ANALYSIS 1*

I* 0.50 0.60

.I I 0.70 0.70 0.70 0.764 I

a.so o. 90 a.so a.so a.so I

I 1.20 1.10 1.20 1.00 I

I 1.JO 1.JO 1.JO

'I 1.40 1.40 Assembly Relative Power

'I I

I 1*

I 6-9

I

.I FIGURE 6-2 I ASSEMBLY POWER DISTRIBUTION, 19 CHANNEL MODEL FSAR ANALYSIS I

1*

,, 0.9741 I

,. I I

t I

I

t I

1 I

-l -- - - - -I - - - - -i - - - -*

I 0. 9737 I - -I -+ - - --1 I

I I

I -l I

I

1 I

---Assembly Relative Power

.1 I

I I

I 6-10

I

.I FIGURE 6-J I SUBCHANNEL POWER DISTRIBUTION, 53 CHANNEL MODEL FSAR ANALYSIS I

I I

1*

I

.I I

I I - - F u e l Roe_ Relative Power I

.I I

I

,, 6-11

.1

.I. FIGURE 6-4 I SUBCHANNEL ?OwER DISTRIBUTION, 19 CHANNEL I<IODEL FSAR ANALYSIS I

I

.I I

~1* 1.350

- - - I I

-'-I -' - j_

I I

.I I Hot Fuel Rod I Hot Unit Cell I

--Fuel Rod Relative I Power I

1

.I I

I\ 6-12

I FIGURE 6-5 I. DNBR vs TIME EXCESSIVE LOAD INCREASE TRANSIENT FSAR ANALYSIS I

.I I

1

.I 1.6 I

I.

I --***-1* -

: i 1

2 ~1:':!l5ll~~~1~~~~1~mm~~1~~~~1;ms:~~~1~~~ll'.§:;1~~~~r I 0 20 40 60 TINE I 80 SECONDS 100 120 140 I

I I 6-13

I I FIGURE 6-6 DNBR vs TIME UNCONTROLLED CONTROL ROD ASSEMBLY WITHDRAWAL AT POWER TRANSIENT FSAR ANALYSIS

.f I

I I

I TIME SECONDS I

I

.1 I

I 6-14

I I FIGURE 6-7 I DNBR vs TIME COMPLETE LOSS OF REACTOR COOLANT FLOW TRANSIENT FSAR ANALYSIS I

I

.I I

.I

.(

I I

I

.TH'iE, SECONDS I

I I

I 6-15

I 6.3 Densification/Positive Moderator Temperature Coefficient Reanalyses I 6.3.1 Introduction The densification and positive moderator temperature coefficient I reanalyses, which were performed using the VEPCO methods, consist of a steady state analysis at 112% power and two transient analyses. The radial power I distributions for both the 53 and 19 channel models are shown in Figures 6-8 I. through 6-11. Relative flux values composing the axial power distribution are listed in Table 6-5. Reactor conditions and parameters which are applica-I ble to this group of reanalyses are listed in Tables "6-6 and 6-7, respectively.

As shown in Table 6-7, the parameters used in this group of reanaly-ses changed considerably when compared to the parameters used in the *original FSAR analyses. Significant changes include the identification of the thimble cell as the limiting channel, the reduction of the radial and axial peaking factors, and the application *of the coldwall and L-grid spacer factors to the W-3 CHF correlation. The fuel densification phenomenon was taken into account I E by reducing the active fuel length, increasing the magnitude of FQ, and by E

applying a densification heat flux spike. For this group of reanalyses, FQ I and the densification heat flux spike were combined to form a single spike I with a magnitude of approximately 1.244.

6.3.2 Steady State Analysis at 112% Power I . .

The steady state analysis performed by VEPCO was based upon the safety

. . . . f. . ( 9) limit curves which were revised to include the effects of fuel densi ication.

I The safety limit curve for 2200 psia is shown in Figure 6-12. The horizontal segment of the curve, showing a constant average temperature, is an arbitrary (but conservative) upper limit such that the hot-leg temperature is less than l the saturation temperature. The sloping segment of the curve represents the loci of points of thermal power, system pressure, and average temperature for I

I 6-16

l I

I. which the MDNBR is approximately 1.30. The reactor operating conditions for I the steady state analysis were thus derived by choosing a point on the sloping segment of the curve. As depicted on the figure, at 112% power and 2200 psia, I the average temperature is 588°F. This average temperature corresponds to an inlet temperature of approximately 554°F.

I Using the VEPCO methods along with the 53 channel model, a MDNBR

.I of 1.30 was calculated. Using the VEPCO methods along with the 19 channel model, a MDNBR of 1.27 was calculated. It should be noted that these two I steady state analyses demonstrate the conservatism of the 19 channel model when reactor conditions are such that the resulting MDNBR approaches the design I limit of 1.30. Under these conditions, a 19 channel steady state analysis will predict a MDNBR which is 2-3% lower than that predicted by a 53 channel I analysis.

I 6.3.3 Uncontrolled Control Rod Assembly Withdrawal at Power Transient As described in References 10 and 11, this transient was reanalyzed I with an assumed positive moderator temperature coefficient. Margin to DNB was of concern since a positive moderator temperature coefficient would augment the mismatch in steam flow and core power. The particular case analyzed using

-5 I the VEPCO methods is a slow rod withdrawal (2.3 x 10 D.K/sec) from full power.

Forcing functions of heat flux, inlet temperature, and system pressure were I obtained from Reference 11. The inlet flow was assumed to be constant through-out the transient. DNBR results, which were obtained using the 19 channel model, are shown in Figure 6-13. Reference 11 gives a MDNBR of 1.32 while VEPCO results show a MDNBR of 1.36.

I 6.3.4 Complete Loss of Reactor Coolant Flow Transient I As described in Reference 10, this transient was reanalyzed to deter-mine the effect of an assumed positive moderator temperature coefficient on I

I 6-17

I I the nuclear power and the resultant effect on DNBR. The case analyzed using I the VEPCO methods is a complete Loss of Reactor Coolant Flow transient with three pumps operating and the reactor at full power. Forcing functions of I core average heat flux and flow were obtained from Reference 10. System pres-sure and inlet temperature were assumed constant throughout the transient.

~1 Reference 10 states that the densification power spike penalty was removed

.I when the reanalysis of this transient was performed (as justified in Reference 26). Accordingly, the densification heat flux spike was not included in the I VEPCO anaiysis. DNBR results, which were obtained using the 19 channel model, are shown in Figure 6-14. Reference 10 gives a MDNBR of 1.54 while VEPCO I results also show a MDNBR of 1.54.

I

.1-I

'I I

I I

I I 6-18

I I TABLE 6-5 1 AXIAL POWER DISTRIBUTION DENSIFICATION/POSITIVE MODERATOR TEMPERATURE COEFFICIENT REANALYSIS I F(z') =

rrz' 1

55 cos (12.0201229)

I Axial Flux Shape: 1.55 Cosine (142.3" Active Length)

.I z z' Axial Position Fuel Position z/156.0 F(z')

(inches) (feet) Relative Position Relative Flux I 0.00 2.98 3.00 -5.92916667 0.0000 0.0191 0.0192 0.0000 0.0000 0.0328 9.35 -5.4 0.0599 0.2461 1- 16. 55

23. 75

30. 95

-4.8

-4.2

-3.6

0. 1061 0.1522 0.1984 0.4821

0. 7062 0.9130

.1* 38.15 45.35

-3.0

-2.4 0.2446 0.2907

1. 0975

1. 2549 52.55 -1. 8 0.3369 1. 3816

59. 75 -1. 2 0.3830 1. 4744 I 66.95 74 .15

-0.6 0.0

0. 4292 0.4753

1. 5310 1.5500

81. 35 0.6 0.5215 1. 5310

1 88.55

95. 75

1. 2

1. 8 0.5676 0.6138

1. 4744

1. 3816 102.95 2.4 0.6599 1.2549 110. 15 3.0 0. 7061 1.0975 I 117. 35 124.55 3.6 4.2

0. 7522

0. 7984 0.9130

0. 7062 131. 75 4.8 0.8446 0.4821 I 138.95 145. 30 5.4 5.92916667 0.8907 0.9314 0.2461 0.0328 145.31 0.9315 0.0000 I 156.00 1. 0000 0.0000 I

I I

I 6-19

I TABLE 6-6 REACTOR CONDITIONS DENSIFICATION/POSITIVE MODERATOR TEMPERATURE COEFFICIENT REANALYSIS Steady State Analysis Power (% of nominal 2441 MWt) 112 6 2 Core Average Heat Flux (10 Btu/hr-ft ) 0.222376 I n 1et Temperature ( OF) 554 I System Pressure (psia) 2200 6 2 Core Average Mass Velocity (10 lbm/hr-ft ) 2.273 I

I Transient Analysis (Initial Conditions)

Power (% of nominal 2441 MWt) 102 I Core Average Heat Flux (10 6 2 Btu/hr-ft ) 0.202521 I n 1et T emperature ( OF) 547 I System Pressure (psia) 2220

,_ Core Average Mass Velocity (10 6 2 lbm/hr-£t ) 2.295 I

I I

I 6-20

I

,( TABLE 6-7 I PARAMETERS FOR DENSIFICATION/POSITIVE MODERATOR TEMPERATURE COEFFICIENT REANALYSIS I

I F H (Hot Thimble Cell) 6

1. 55

1. 55 I Hot Assembly Relative Power 1. 476 I Active Fuel Length (inches) 142.3 0

Reactor Flow (gprn at 543 F) 265,500 1.05

1 I 1. 02 I Pitch Reduction (inches) 0.0065 W-3 with F-Factor, I CHF Correlation Coldwall Factor, and L-Grid Spacer Factor (k = 0.046)

I s (TDC = 0.019)

Densification Heat Flux Spike 1.185 Applied at the Axial Location of MDNBR I

I I

I 6-21

I I FIGURE 6-8 I ASSEMBLY POWER DISTRIBUTION, 53 CHANNEL MODEL DENSIFICATION/POSITIVE MODERATOR TEMPERATURE COEFFICIENT REANALYSIS I

I

,, 0.50 0.60 I 0.70 0.70 0.70 0.70 I

0.829 0.90 0.80 0.80 0.80 I

.I 1.20 1.10 1.20 I

I 1.JO l.JO 1.JO 1.20 I

I 1.40 1.40 ...,_-~Assembly Relative Power I

I I

I I 6-22

I

.I FIGURE 6-9 1 ASSEMBLY POWER DISTRIBUTION, 19 CHANNEL MODEL DENSIFICATION/POSITIVE MODERATOR TEMPERATURE COEFFICIENT REANALYSIS I

0,9706 I I I I I --l----**f I

- - - --t I I

- - l - - - - - - - - - - - i -* - - -** -1 I 0,9711 I

I - -l -- --- -- *-* -T -*- -* - -l I

I I

I - -j --

1

-l----

1

1 I

---Assembly Relative Power I

I I

I 6-23

I

,I FIGURE 6-10 I SUBCHANNEL POWER DISTRIBUTION, 53 CHANNEL MODEL DENSIFICATION/POSITIVE MODERATOR TEMPERATURE COEFFICIENT REANALYSIS I

I I

I

~+----+-+--+--+---¥ 1.52-Fuel Rod Relative I Power I

I I

I I 6-24

I

,, FIGURE 6-11 I SUBCHANNEL POWER DISTRIBUTION, 19 CHANNEL NODEL DENSIFICATION/POSITIVE MODERATOR TEMPERATURE COEFFICIENT REANALYSIS I

I I

I I -- - I 1.4J6

_,_ - - -' - j_

I I I I

I I

I

--Fuel Rod Relative I Power I

I I

I 6-25

I I FIGURE 6-12 I REACTOR CORE THERMAL AND HYDRAULIC SAFETY LIMIT CURVE AT 2200 PSIA, THREE LOOP OPERATION, 100% FLOW I

I I

I 0 Ii<

I E-<

0 u

~

...:1

+

I E-<

E-<

0

c:

I ~

r-l r:il p:;

I :::i E-<

~

P-<

~

I E-<

r:il CJ

~

&1 I :>

I I

I %RATED POWER I

I I 6-26

I I FIGURE 6-13 I DNER vs TIME UNCONTROLLED CONTROL ROD ASSEMBLY WITHDRAWAL AT POWER TRANSIENT POSITIVE MODERATOR TEMPERATURE COEFFICIENT REANALYSIS I

I I

I 1.8

~~;---=: ~~~-~j_ ::~=f---~--=:__t=_~~~ *--~~*;:~.~-~ -

~ - ~ :t-:-~-~t==7 ~t=f ~ ~ ~f~~~*~~~~~

~~~h~k~~~~l-~:-~~~~~l=-~E_=E~- ~g;:-.~~~~~

I c~-=r~~~~=E=:::+/-:o--:::'~-f~J~=-~-' :~::+:~=-:-:~

~-;=~:. :~.:==:_~t ~=i-=--= ==-~~ =----=-=--== ~~~ ~~=~::~1_-:~= f:~-: ~~~f ~-=--~~ :_

~:::-~ ,~~~ ::i.§~~~;::::_: :.:.:-:::=~~-:=~~=-1:--::::lr. =~~:::f 0HT 1.6 I

I )Btliii~i;;0~T

-c~~~~:~~~~~t:~~~~:r;-_mTT-~

I :~~-; ~~~ -~~~~~~ ~~f ~-~ ~§ ~~~~~- ~-§ ~~f~~~r:~it~~~i ~.i~~. ~ ~: ~

-t::: ~: :*: - r:::: -: : =r---: t:.:::-P~=~ ::::~: :-:n~:~: !::: : 1=::~r: :: t:::: ~:: ::-r::: . - -

,_ l.2-a,~~8li!l!:~~m:mii1!1l!!ll~~i5M~~ilS!lEl;5!!E/1~~mm~~~

0 I

10 I

20 JO I

40 I

50 TIME, SECONDS I

I I

I I 6-27

I I FIGURE 6-14 I DNBR vs TINE COMPLETE LOSS OF REACTOR COOLANT FLOW TRANSIENT POSITIVE MODERATOR TEMPERATURE COEFFICIENT REANALYSIS I

I I

I THIE, SECONDS I

I I

I I 6-28

I I 6.4 Low Flow Assumption Reanalyses I 6.4.1 Introduction The low flow assumption reanalyses, which were performed using the I VEPCO methods, consist of a steady state analysis at 102% power and a complete Loss of Reactor Coolant Flow transient. The radial power distributions for I both the 53 and 19 channel models have been previously described in Section 4 I and are shown in Figures 4-3 through 4-6. The relative flux values composing the axial power distribution are listed in Table 4-1. Reactor conditions and I parameters which are applicable to these reanalyses are listed in Tables 6-8 and 6-9, respectively.

I As shown in Table 6-9, several parameters used in the low flow assumption reanalyses have again changed when compared to the parameters used I in the densification reanalyses. Significant changes include the reduction I in reactor flow to 90% of thermal design and the use of a revised densification model. The revised densification model is reflected in the active fuel length, I . . E in the engineering factor on the heat flux, FQ' and in the elimination of the densification heat flux spike. It should be noted, however, that the effect I of the densification heat flux spike for the Surry units was identified as I a 7% DNB margin which was subsequently taken to partially offset the effects of fuel rod bowing on DNB. (

27

) Thus, DNBRs need to be reduced by 7% if they I are obtained from analyses in which the densification heat flux spike has been eliminated.

I 6.4.2 Steady State Analysis at 102% Power The steady state analysis performed by VEPCO was a state point analy-I sis based upon the initial conditions of the complete Loss of Reactor Coolant I Flow transient described in Reference 12. At the start of this transient, Reference 12 shows a MDNBR of approximately 1.50. Using the VEPCO methods I

I 6-29

I I along with the 53 channel model a MDNBR of 1.49 was calculated. A MDNBR of I 1.49 was also calculated using the VEPCO methods along with the 19 channel model. (Since the densification heat flux spike was not included in these I analyses, all DNBRs were reduced by a factor of 1.07.)

6.4.3 Complete Loss of Reactor Coolant Flow Transient I The case analyzed using the VEPCO methods is a complete Loss of Reactor Coolant Flow transient with three pumps operating and the reactor at I full power. Forcing functions of core average heat flux and core flow were I obtained from Reference 12. System pressure and inlet temperature were assumed constant throughout the transient. Since the densification heat flux spike I was not included in this analysis, all DNBRs were reduced by a factor of 1.07.

DNBR results, which were obtained using the 19 channel model, are shown in I Figure 6-15. Reference 12 gives a MDNBR of 1. 33 while VEPCO results show a I MDNBR of 1. 35.

I I

I 6-30

I I TABLE 6-8 I REACTOR CONDITIONS LOW FLOW ASSUMPTION REANALYSIS I

I Power (% of nominal 2441 MWt)

Steady State Analysis 102

.I Core Average Heat Flux (10 6 2 Btu/hr-ft ) 0.200687 I n 1 et Temperature ( OF) 547 I System Pressure (psia) 2220 6 2 I Core Average Mass Velocity (10 lbm/hr-ft ) 2.065 I Transient Analysis (Initial Conditions)

Power (% of nominal 2441 MWt) 102 I Core Average Heat Flux (10 6 2 Btu/hr-ft ) 0.200687 I n 1et Temperature ( OF) 547 I System Pressure (psia) 2220 I Core Average Mass Velocity (10 6 2 lbm/hr-ft ) 2.065 I

I I

I I 6-31

I I TABLE 6-9 I PAR.Ai.'1ETERS FOR LOW FLOW ASSUMPTION REANALYSIS I

F~H (Hot Thimble Cell) 1. 55 I

1. 55 I

Hot Assembly Relative Power 1.475 I Active Fuel Length (inches) 143.6 I Reactor Flow (gpm at 543 F) 0 238,950 I 1. 03 I

1. 02 I

Pitch Reduction (inches) 0.0065 I CHF Correlation W-3 with F-Factor Coldwall Factor, and I L-Grid Spacer Factor (k = 0. 046) s (TDC = 0.019)

I Penalty to Partially Offset Rod 1. 07 I Bow Effects on DNB I

I I

I 6-32

I I FIGURE 6-15 I DNJ3R VS TIME COMPLETE LOSS OF REACTOR COOLANT FLOW TRANSIENT LOW FLOW ASSUI'1E'TION REANALYSIS I

I I

TIME, SECONDS I

I I

I I 6-33

I I SECTION 7 - Sill-'IMARY .AND CONCLUSIONS I The Virginia Electric and Power Company (VEPCO) has developed the I capability to perform core thermal-hydraulic analysis using the COBFA IIIC/}ITT computer code. The basic models and methods have been documented in this I report, and the accuracy of the capability has been established through compari-I sons with analyses which were used in the design and licensing of the Surry nuclear Power Station. These comparisons, suTilIIlarized in Table 7-1, show that I the steady state and transient l'IDNBRs calculated using the 1/EPCO methods are in excellent agreement with those presented in the licensing documents. This I agreement indicates that the capability can be used to provide design and licensing support for VEPCO reactor operations.

I I

I 7-1

I I TABLE 7-1

SUMMARY

OF COMPARISONS I

MINIMUM DNBR I FSAR Analyses FSAR VEPCO I Steady State at 100% Power 1. 97 1. 94 Excessive Load Increase 1. 55 1.53 I Uncontrolled Control Rod Assembly Withdrawal at Power 1.36 1. 34 Complete Loss of Reactor Coolant Flow 1.46 1.48 I

I Densification/Positive Moderator Temperature Coefficient Reanalyses Steady State at 112% Power 1.30 1. 30 I Uncontrolled Control Rod Assembly Withdrawal at Power 1.32 1. 36 I Complete Loss of Reactor Coolant Flow 1.54 1.54 I Low Flow Assumption Reanalyses Steady State at 102% Power 1. 50 1.49 I Complete Loss of Reactor Coolant Flow 1. 33 1. 35 I

I I

I I 7-2

I I SECTION 8 - REFERENCES I

1. J. SHEFCHECK, "Application of the THnl'C Program to PWR Design," WCAP-7359-L, I 2.

Westinghouse Electric Corporation (August, 1969), Proprietary.

L. E. HOCHREITER and IL CHELEMER, "Application of the THING-IV Program to PWR Design," WCAP-8054, Westinghouse Electric Corporation (September, I 1973), Proprietary.

3. B. R. HAO and J. M. ALCORN, "LYNXl - Reactor Fuel Assembly Thermal-Hydraulic I 4.

Analysis Code," BAW-10129, Rev. 1, Babcock and Wilcox (November, 1976).

"LYNX2 - Subchannel Thermal-Hydraulic Analysis Program," BAW-10130, Rev.

1, Babcock and Wilcox (April, 1977).

I 5. P. MORENO, J. LIU, E. KHAN, and N. TODREAS, "Steady-State Thermal Analysis of PWRs by a Simplified Method," Transactions of the American Nuclear I 6.

Society, Vol. 26, p. 465 (June, 1977).

R. N. GUPTA, "Maine Yankee Core Thermal-Hydraulic Model Using COBRA-IIIC, 11 I 7.

YAEC-1102, Yankee Atomic Electric Company (June, 1976).

R. BOWRING and P. MORENO, "COBRA IIIC/MIT Computer Code Manual," prepared by MIT for EPRI (March, 1976).

I 8. Final Safety Analysis Report - Surry Power Station Units 1 and 2, Virginia Electric and Power Company (December, 1969).

I 9. "Fuel Densification - Surry Power Station Unit 1, 11 WCAP-8012, Westinghouse Electric Corporation (December., 1972), Proprietary.

I 10. VEPCO (C. M. Stallings) to NRG (K. R. GOLLER) letter dated June 5, 1975, Serial No. 553, Docket Nos. 50-280 and 50-281.

I 11. VEPCO (C. M. STALLINGS) to NRG (B.C. RUSCHE) letter dated January 29, 1976, Serial No. 876, Docket Nos. 50-280 and 50-281.

12. VEPCO (C. M. STALLINGS) to NRG (E. G. CASE) letter dated August 9, 1977, I Serial No. 344, Docket Nos. 50-280 and 50-281.

13. D. S. ROWE, "COBRA IIIC: A Digital Computer Program for Steady State and I Transient Thermal-Hydraulic Analysis of Ro.cl Bundle Nuclear Fuel Elements,"

BNWL-1695, Pacific Northwest Laboratory (March, 1973).

14. S.L. SMITH, "Void Fractions in Two-Phase Flow: A Correlation Based Upon I an Equal Velocity Head Model," Proceedings of the Institution of Mechanical Engineers, Vol. 184, Part 1, No. 36, P. 647 (1969-70).

I 15. S. LEVY. "Forced Convection Subcooled Boiling - Prediction of Vapor Volume-tric Fraction," GEAP-5157, General Electric Company (April, 1966).

I I 8-1

I I 16. J. P. WAGGENER, "Friction Factors for Pressure Drop Calculations,"

Nucleonics, Vol. 19, p. 145 (1961).

I 17. L. S. TONG, "Pressure Drop Performance of a Rod Bundle," Heat Transfer in Rod Bundles, ASME, pp. 57-69 (1968).

I 18. F. W. DITTUS and L. M. K. BOELTER, "Heat Transfer in Automobile Radiators of the Tubular Type," University of California Publications in Engineering Vol. 2, p. 443 (1930).

I 19. C. J. BAROCZY, "A systematic Correlation for Two-Phase Pressure Drop,"

NAA-SR-MEM0-11858, North American Aviation (March, 1966).

I 20. L. S. TONG, "Boiling Crisis and Critical Heat Flux," TID-25887, U. S.

Atomic Energy Commission (1972).

I 21. W. H. JENS and P. A. LOTTES, "Analyses of Heat Transfer, Burnout, Pressure Drop, and Density Data for High Pressure Water," USAEC Report ANL-4627, Argonne National Laboratory (1951).

I 22. F. F. CADEK and F. E. MOTLEY, "Application of Modified Spacer Factor to L Grid Typical and Coldwall Cell DNB," WCAP-8030-A, Westinghouse Electric I 23.

Corporation (January, 1975).

"PDQ7V2 for System 370," IBM-LB21-1467-0, International Business Machines Corporation (May, 1975).

I 24. Electric Power Research Institute Report EPRI CCM-5, "RETRAJ.'J - A Program for One-Dimensional Transient Thermal-Hydraulic Analysis of Complex Fluid I 25.

Flow Sys terns," Energy Incorporated (December, 1978).

K. REHME, "Pressure Drop Correlations for Fuel Element Spacers," Nuclear Technology, Vol. 17, p. 15 (January, 1973).

I 26. J. M. HELLMAN, "Fuel Densification Experimental Results and Model for Reactor Application," WCAP-8219-A, Westinghouse Electric Corporation I 27.

(March, 1975).

Westinghouse (C. EICHELDINGER) to NRC (V. STELLO) letter dated August 13, 1976, Serial No. NS-CE-1163.

I I

I I 8-2

I I

I I APPENDIX A I

I I

I VEPCO MODIFICATIONS ADDED TO THE COBRA IIIC/MIT COMPUTER CODE I

I I

I I The following list is a summary of the VEPCO modifications which were added I to the original version of the COBRA IIIC/MIT computer code, I 1. The code was modified so that the axial heat fluxes listed in the output were indicative of the corresponding axial positions. In the unmodified I version of the code, the heat fl1.L~ calculated for a particular axial position was actually the heat flux at the midpoint of the preceding I axial interval. The code was further modified so that the heat added to I the coolant over an axial interval was based upon the average of the heat fluxes at the beginning and the end of the interval.

I

2. The code was modified so that the calculation of the two-phase density I in the subcooled void region was based upon the saturated vapor density and the subcooled liquid density. Analyses performed using the unmodi-I fied version of the code showed that the coolant density decreased I abruptly at the axial position where subcooled voids were first formed.

This discontinuity occurred because the two-phase density was calculated I using the saturated liquid density when in reality the liquid was still subcooled, When the subcooled liquid density was used in the calcula-I tion, the discontinuity was eliminated. The code was further modified I so that the subcooled void fractions could be retained for printout.

I J, The code was double precisioned, I 4. In order to better understand how the flow solution was progressing, the code was modified so that the largest convergence error was printed I after each iteration.

I I A-1

I I 5, The code was modified so that DNBRs were printed out by channel number I instead of by rod number, Thus, minimum DNBRs and corresponding rod numbers were printed for each channel.

I 6. In order to perform more current DNB analyses, the W-J L-grid and R-grid I spacer factor correlations(ZZ) were added to the code as options, I 7, The code was modified to take into account the fraction of heat generated I in the fuel and cladding. Because the heat fluxes calculated within the code are used for determining the heat added to the coolant, they are I based upon the total heat generation rate (i.e., they include direct gamma heating of the coolant). These psuedo heat fluxes were therefore I multiplied by the fraction of heat generated in the fuel and cladding in order to obtain actual heat fluxes. This adjustment was applied in the I calculation of DNBRs, in the Jens and Lattes correlation(Zl) for deter-I mining the start of nucleate boiling, and in the Levy subcooled void model. (l5)

I 8, The format of the DNBR data section was expanded so that at eaci1 axial I position the actual heat flux, the fuel rod number, the F-factor, the cold-I wall factor, the spacer grid factor, the critical heat flux, and.the DNBR would be printed out for each channel.

I 9, The code was modified so that the calculation had to iterate at least I twice before a converged solution would be accepted for printout.

I 10. The code was modified so that a variable damping factor could be input.

I The damping factor is used to obtain more rapid convergence.

I I A-2

I I 11. The option was added so that different crossflow resistance coefficients I and different mixing coefficients could be input and applied to the rod gaps.

I 12. The calculation using the Jens and Lattes correlation(Zl) for determining I the start of nucleate boiling was corrected.

I lJ, The code was modified so that from one to six different axial heat flux I shapes could be input and applied to different fuel rods.

I 14. The code was modified to correct the calculation of the true (non-equilib-rium) quality within the Levy subcooled void model. (l5) Levy's paper I states that the empirical constants used in developing the model were calculated using saturated liquid properties. Thus, to be consistent with I the model, the code was modified so that the saturated liquid properties I were used in calculating the true quality.

I 15. The code was modified so that all water properties (enthalpy, specific volume, viscosity, conductivity, and specific heat) were calculated using I 2 the HOH routines which were obtained from the PIQ?V2 computer code, ( J)

I I

I I A-3

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