ML20002C041

Methods for Analysis of Bwrs,Transient Thermal Margin Analysis Code (MAYUO4-YAEC).

ML20002C041
Person / Time
Site:	Vermont Yankee
Issue date:	12/30/1980
From:	Burns K, Slifer B, Turnage J YANKEE ATOMIC ELECTRIC CO.
To:
Shared Package
ML20002C040	List: ML20002C039 ML20002C041
References
YAEC-1235, NUDOCS 8101090009
Download: ML20002C041 (25)

Text

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E !O METHODS FOR Tile ANALYSIS OF BOILING WATER REACTORS TRANSIENT THERMAL MARGIN ANALYSIS CODE (MAYUO4-YAEC)

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I Prepared By K. J. Burns M8 /

(Date)

Reviewed By B. C. Slifer

/2/12to

( Da't e )

Approved By Cha it' TO M J.C.furnage ' (rate)'

l Yankee Atomic Electric Company

= Nuclear Services Division 1671 Worcester Road Framingham, Massachusetts 01701 I

l 81030-9006

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DISCLAIMER OF RESPONSIBILITY I This document was prepared by Yankee Atomic Electric Company on behalf of Vermont Yankee Nuclear Power Corporation. This document is believed to be completely true and accurate to the best of our knowledge I and information. It is authorized for use specifically by Yankee Atomic Electric Company, Vermont Yankee Nuclear Power Corporation and/or the appropriate subdivisions within the Nuclear Regulatory Commission only.

With regard to any unauthorized use whatsoever, yankee Atomic Electric Company, Vermont Yankee Nuclear Power Corporation and their officers, directors, agents and employees assume no liability nor make any warranty or representation with respect to the contents of this document I, or to its accuracy or completeness.

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l ABSTRACT A modified version of the MAYUO4 computer code has been developed for the evaluation of fuel transient thermal margins. The Critical Power I Ratio (CPR) approach is used to describe the conditions at which a boiling j transition from nucleate to film boiling occurs. Comparisons to transient boiling transition data are presented, and specific application to the Vermont Yankee Nuclear Power Plant is provided.

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I I TABLE OF CONTENTS Page D ISCLAIMER OF RESPO NSIB I LITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 ABSTRACT.................................................... iii TABLE OF C0NTENTS........................................... iv LIST OF FIGURES............................................. v I LIST OF TABLES.............................................. vi

1.0 INTRODUCTION

................................................ 1 1.1 Purpose................................................ I 1.2 Brief Description...................................... 1 1.3 Model Qualification.................................... 2 I- 1.4 Model Application to a Typical Transient............... 2 2.0 DESCRINI0N................................................. 3 2.1 Thermal-Hydraulics..................................... 3 2.2 Physical Correlations.................................. 4 2.2.1 Heat Transfer and Pressure Drop Correlations. . . . 4 2.2.2 Void Mode 1...................................... 4 2.2.3 Critical Quality Correlations................... 5 2.3 Thermal Margins........................................ 5 3.0 QUALIFICATION............................................... 9 3.1 I An alyt ic al Compa ri so ns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 Comparisons to Rod Bundle Transient Boiling Transition Data........................................

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3.3 Verification of the Fuel Rod Conduction Model.......... 10 l 4.0 A P P L IC AT I O N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 I 4.1 4.2 Abno rmal Ope ra tional Transients. . . . . . . . . . . . . . . . . . . . . . . .

Range of Applicability.................................

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5.0 REFERENCES

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LIST OF FIGURES Number Title Page 3.1 Normalized Power Versus Time for RETRAN and MAYUO4-YAEC Conduction Model Comparison 15 I 4.1 CPR Versus Time for a TTWOB Transient 18

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3.1 Comparisoa of Measured and Predicted Time and Locations of Boiling Transition 13 ,

I 3.2 Comparison of Predicted Heat Flux at the 6.5 Foot Elevation for RETRAN and MAYUO4-YAEC 14 I

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I 1.0 I INTRODUCTION 1.1 Purpose A modified version of the MAYUO4 computer code, hereafter referred to as MAYUO4-YAEC, will be used to calculate hot channel thermal margins under transient conditions. The modifications made to the original MAYUO4 code [1] include the addition of both the EPRI void model (2] and the GEXL critical quality versus boiling length correlation (3]. This report describes the modifications, the qualification of MAYUO4-YAEC, and the application of MAYUO4-YAEC to a typical reactor transient.

1.2 Brief Description MAYUO4-YAEC is a one-dimensional computer code which computes the transient thermal-hydraulic conditions of a single channel. The conservation equations, heat transfer and pressure drop correlations, and numerical solution scheme utilized by the code are described in detail in Reference

[1].

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Briefly, the vapor continuity, mixture continuity and mixture energy equations are solved by the method of characteristics to determine the channel transient the rmal-hyd raulics . The axial pressure gradient is neglected in the solution, hence the mixture momentum equation is solved for the channel pressure drop only as an edit calculation. The governing equations are expressed in terms of a drif t flux formulation in order to account for nonuniform phase velocities and radial distributions, although I

• GEXL is a General Electric Company proprietary critical quality vs. boiling I length correlation.

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I thermodynamic equilibrium is assumed between phases. The drift flux parameters C and V g are evaluated according to the EPRI void model [2],

9 and the void / equilibrium quality relationship implied by this model is utilized. Finally, thermal margins are measured in tems of the Critical Power Ratio (CPR), and evaluated via the GEXL critical quality versus boiling length correlation [3] using the local instantaneous thermal-hydraulic conditions.

1.3 Model Qualification MAYUO4-YAEC is used to predict 4x4 rod bundle transient boiling transition data. Although the GEXL correlation is not utilized in these predictions, a similar steady state critical quality versus boiling length correlation (based on steady state boiling transition data obtained from I the 4x4 rod bundle test section) is used in conjunction with MAYUO4-YAEC to predict the time and axial location of bo! ling trans! tion. The predictions of transient boiling transition were found to be generally satisfactory.

1.4 Model Application to a Typical Transient Typical inlet mass flux, inlet enthalpy, neutron power and channel pressure as functions of time for a Turbine Trip Without Bypass (TTWOB) transient are input to MAYUO4-YAEC (along with suitable channel geometry and power peaking factors), and the transient thermal-hydraulic conditions I are evaluated. These results are then used with the GEXL correlation to l

predict the occurrence of boiling transition, and a CPR is calculated at each time step. The CPR for the transient is defined simply as the initial steady state CPR minus the minimum value of CPR during the transient.

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2.0 DESCRIPTION

I 2.1 Thermal-Hydraulics I As stated in Reference [1], the following assumptions are made in the derivation of the conservation equations:

(1) The liquid and vapor phases are in thermodynamic equilibrium.

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(2) Subcooled boiling can be neglected.

(3) The kinetic and potential energy contributions to the mixture energy can be neglected.

I (4) The fluid flow is one-dimensional.

(5) The vapor phase flows only in the upward direction.

(6) Axial variations in pressure with respect to the system reference pressure are small.

I (7) The vapor and liquid phases can be coupled by a drif t flux model.

I (8) The flow area is constant in space and time.

I The resulting mixture continuity, vapor continuity and mixture energy equations are used to calculate the transient (cross sectional average) thermal-hydraulic conditions of the channel. Assumption (6) allows the momentum equation to be decoupled from the continuity and energy equations, hence the mixture momentum equation is solved only for editing purposes.

The time dependent boundary conditions required as input to the code consist of the bundle inlet mass flux, system pressure, bundle power and bundle I

I inlet enthalpy. Finally, a one-dimensional radial heat conduction model [1]

is used to calculate the time varying fuel rod surface heat flux.

2.2 Physical Correlations 2.2.1 Heat Transfer and Pressure Drop Correlations The heat transfer coef ficients required for solution of the radial heat conduction problem are calculated from the Dittus-Boelter relation for single phase licuid flow, from the Thom correlation for two phase nucleate boiling, and f rom the Dougall-Rohsenow correlation for co-current two phase film boiling. Single phase friction factors are given by a fit to the Moody curves. Two phase friction factors are obtained by multiplying the equivalent single phase friccion factor by a two phase friction multiplier, obtained f rom the Jones fit to the Martinelli-Nelson correlation

[1].

2.2.2 Void Model I The governing equations are expressed in terms of a drift flux fo rmula tion. The original MAYUO4 ramp void model (1) gives the drif t flux parameters oC and Vgj as functions of void fraction (a). This model is replaced by the EPRI void model [2], which also expresses the drif t flux parameters oC and Vgj as functions of a. The EPRI void model's drif t flux parameters are based on void / equilibrium quality data obtained from 6x6 rod arrays at typical BWR conditions.

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I 2.2.3 Critical Quality Correlations The solution of the governing equations yields the time varying thermal-hydraulic conditions of the channel at each axial node. At every time step, the critical quality is evaluated from a critical quality versus boiling length correlation, using the local instantaneous thermal hydraulic conditions. For a given bundle, such a correlation gives the critical quality as a function of boiling length, pressure and mass flux. It has been observed (3) that this form of correlation satisfactorily correlates BWR boiling transition data for all axial power profiles of interest. That is, the critical quality versus boiling length type of correlation implicitly accounts for the ef fects of nonuniform axial heat flux on boiling transition.

Boiling transition is predicted whenever the local quality calculated by MAYU04-YAEC equals or exceeds the critical quality given by the correlation.

The correlation used in the qualification of MAYUO4-YAEC (Section

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3.2) is based on steady state boiling transition data for the specific test section of interest. In the application of the code to an actual reactor transient (Section 4.1), however, the GEXL correlation [3] is utilized.

This correlation is based on steady-state boiling transition data obtained f rom a multitude of electrically heated test sections, including simulated full size BWR bundles.

2.3 Thermal Margins As stated earlier, the figure of :nerit used to quantify thermal margin is Critical Power Ratio (CPR). CPR is defined as the ratio of the power necessary to obtain the critical quality at some elevation (for given hydraulic conditions of mass flux and pressure), to the actual operating I

I power. The original version of MAYUO4 calculates an approximate CPR according to the following formula:

I CPR = (CPR(Z)] min. =

c (LB,P,G) + Ahsub h

fg X(Z) + dh sub (t) h gg min.

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LB = boiling length (ft) l P = pressure (psia)

G = mass flux (ibm /hr-ft2)

Ahsub = inlet subcooling (Btu /lbm) h gg = latent heat of vaporization (Btu /lbm)

X = local quality X

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= critical quality, evaluated from the correlation as a function of LB, P and G.

Equation (1) is an exact expression for CPR under steady-state conditions, provided that the boiling length (LB) corresponds to the critical power.

I However, CPR > 1.0 (i.e., LB < LB c) f r cases of interest here, and since Xc increases with increasing LB, it follows that the approximation given by Equation (1) yields a value for CPR which is less than the exact value. Thus, the exact CPR can be calculated in an iterative fashion as I

follows:

(1) Calculate an initial estimate for CPR using Equation (1).

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-I (2) For the instantaneous hydraulic conditions, calculate a new enthalpy

< W distribution corresponding to a power level which is a factor of CPR higher than the original power level, h'(Z) = CPR (h(Z) - hin) + hin

.I where:

.I h'(Z) = revised enthalpy at elevation Z (Btu /lbm)

!I h in = inlet enthalpy (Btu /lbm)

I h(Z) = original enthalpy at elevation Z (Btu /lbm)

W (3) Compute a revised boiling boundary bar . on the revised enthalpy l distribution, and calculate a revised critical quality at each elevation based on the revised boiling lengths (using the same local instantaneous values for the hydraulic parameters P and C).

(4) Use the values of X ccalculated in Step (3) to calculate CPR' (the approximate CPR at the increased power level) from Equation (1).

I (5) If the value of CPR' is 1.0 (within the required convergence criterion),

then the value of CPR which was used in Step (2) was correct.

Otherwise, increase CPR by the additive factor (CPR'-1.0) and proceed to Step (2).

t 3 (6) Repeat Steps (2) - (5) until the iteration converges in Step (5).

A subroutine which utilizes the above iterative procedure for calculating transient CPR was incorporated into MAYUO4-YAEC. Although the CPR concept is not well defined under transient conditio1s, CPR values I

'I calculated according to the above procedure are exact under steady conditions

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l (and for CPR=1.0), and provide a convenient measure of thermal margin during transients.

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I 3.0 QUALIFICATION I 3.1 Analytical Comparisons Reference [1] provides a comparison of MAYUO4 to an exact solution for an exponential flow decay transient assuming constant drif t flux parameters, Co and V gj. As seen from the results presented [1], MAYUO4 closely approximates the exact solution, especially for large boiling lengths representative of those at which the thermal margin usually reaches its minimum value.

I 3.2 Comparisons to Red Bundle Transient Boiling Transition Data I Reference [4] provides both steady-state and transient boiling trar,cition data for single-rod, 9-rod and 16-rod electrically heated test sections. The 16-rod assembly data was chosen for use in the qualification of MAYU04-YAEC, since this geometry most closely approximates full size BWR assembly geometries. The axial heat flux profile for this 16-rod i I assembly was that of a chopped cosine, and the nominal radial peaking factor wa s uni fo rm. Steady-state boiling transition data were used in Reference

[4] to develop a critical quality versus boiling length correlation for the test section.

A total of nine flow decay transients were analyzed using MAYUO4-YAEC. Boiling transition was predicted whenever the local instantaneous

.I quality equaled or exceeded the critical quality, as calculated from the correlation using the local instantaneous thermal-hydraulic co.tditions predicted by MAYUO4-YAEC. These flow decay transients conservatively simulate a pump seizure accident, since the flow is quickly reduced to about I

I half of its initial value, while the power level re=ains essentially constant. The inlet enthalpy, inlet mass flux, channel pressure and channel power data for each case were taken from Reference (4] and used to prepare input decks for MAYU04-YAEC.

I Table 3.1 compares the MAYU04-YAEC predicted results and the experimental results for boiling transition (BT), where experimental BT was indicated by rod thermocouple temperature excursions. Both the time to initial BT and the spacer locations of initial and subsequent BT are shown. A boiling transition was experimentally observed for all nine cases, and was also predicted by MAYUO4-YAEC for those nine cases. Furthermore, the time to initial BT was predicted within _+0.35 sec. for seven out of nine cases, and was predicted conservatively in time for the remaining two cases. Finally, the locations of both the initial BT and its subsequent penetration were predicted within one spacer location of the experimentally observed location in all nine cases.

I The above results support the quasi-steady state use of a critical quality versus boiling length correlation (along with local instantaneous thermal-hydraulic parameters) for the prediction of transient BT. In addition, these results reflect the adequacy of the MAYUO4-YAEC solution technique, as well as the applicability of its various constitutive models, including the EPRI void model.

I 3.3 Verification of the Fuel Rod Conduction Model I The one-dimensional radial heat conduction model contained in MAYUO4-YAEC was not utilized in Section 3.2, since the power input to the electrical heaters appeared directly in the clad, and since the power was held constant I

I for these ficw decay transients. In order to apply MAYUO4-YAEC to actual reactor transients, however, it is necessary to utilize the fuel rod conduction model in order to calculate the correct time varying surface heat flux. Thus, it is desirable to check this model against some standard.

The RETRAN code was chosen as the standard for two reasons. First, RETRAN has undergone extensive verification and qualification studies [5].

Secondly, it is necessary to show that the RETRAN and MAYUO4-YAEC conduction solutions are consistent, since RETRAN will provide the transient thermal hydraulic input conditions for MAYUO4-YAEC in licensing calculations.

I A RETRAN run was made for the power versus time history shown in Figure 3.1. The fuel rod was modeled with 6 radial conduction nodes in the fuel region and 4 nodes in the clad region. A constant gap conductance of 1000 Btu /hr-ft 2oF was assumed. A uniform axial power profile was utilized, and all of the heat transferred out of the fuel was assumed to appear as a heat flux at the clad surface. The fuel and clad material properties as functions of temperature were obtained from Reference (6] .

The heat flux at a particular axial node as a function of time for the RETRAN run was then compared to the time varying heat flux predicted by MAYUO4-YAEC. MAYUO4-YAEC was run utilizing the same geometry, radial conduction nodalization, gap conductance, axial power peaking factors, I material properties and channel power as a function of time as used in the RETRAN run. Furthermore, the channel pressure, inlet mass flux and inlet enthalpy as functions of time required as inpu: to MAYUO4-YAEC were obtained from the RETRAN results. Table 3.2 compares the RETRAN and MAYUO4-YAEC predicted results fo r surf ace heat flux for selected time steps at an elevation of 6.5 feet from the bundle inlet (the transient pressure versus I

time at this elevation was used as the channel average pressure in the MAYUO4-YAEC run). As seen from this table, the percentage difference between the RETRAN and MAYUO4-YAEC predicted heat flux is on the order of 1-2%, with the highest percentage difference occurring near the time at which the heat flux reaches its peak value. Although these results do not rigorously qualify the MAYUO4-YAEC conduction model, they do serve to support both the validity of the model and the consistency between the RETRAN and MAYUO4-I YAEC conduction models.

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I TABLE 3.1 Comparison of Measured and Predicted Time and Locations of Boiling Transition I Time of First Spacer Location BT (sec.) of BT (Time BT Measured-Run No. Measured Predicted Time BT Predicted) Measured Predicted 102 2.8 3.05 -0.25 3 2 105 3.5 3.19 0.31 3,4 2,3 106 3.0 2.75 0.25 3,2 2,3 108 4.0 3.78 0.22 3,4,2 2,3 110 5.2 4.32 0.88 3,2 2,3,4 111 3.5 3.80 -0.30 3,4 2 2,3,4 112 6.2 4.07 2.13 3 2,3 113 5.2 5.53 -0.33 3,2 2 114 4.5 4.61 -0.11 3,4,2 2,3 I '

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I TABLE 3.2 Comparison of Predicted Heat Flux I at the 6.5 Foot Elevation for RETRAN and MAYUO4-YAEC Heat Flux (Btu /hr-ft2_op )

I Time Percentage (sec) MAYUO4-YAEC RETRAN Difference

,I 0.0 80457 80454.8 0.0027 0.10 I 0.20 0.30 81182 81176 81207 80417.7 80396.0 80414.3 0.9504 0.9702 0.9858 0.40 81158 80404.6 0.9370 I 0.50 0.60 0.70 80577 81104 85769 79808.0 80099.0 84711.6 0.9636 1.2547 1.2482 I 0.80 0.90 1.00 95977 109646 117456 94508.5 107722 115154 1.5538 1.7861 1.9991 1.10 117070 114449 2.2901 I 1.20 1.30 113766 110954 111702 109063 1.8478 1.7339 1.40 108412 106756 1.5512 1.50 105937 104545 1.3315 I

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m M M M M M M M M M M M M m l

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l 80/12/29 NORi1 CORE POWER VS. TIME

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l'ICllRE 3.1 Norm Iized Power Versus Time for !!ETRAN and !!AYt104-YAEC Conductica flodel Comparison

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4.0 APPLICATION 4.1 Abnormal Operational Transients In order to demonstrate the application of MAYUO4-YAEC to a typical reactor transient, the code was run for the case of a Turbine Trip Without Bypass (TTWOB) transient. An outlet peaked axial heat flux distribution and geometric characteristics for an 8x8 fuel assembly were used, along with representative local rod peaking factors. The axial power shape remained constant during the transient, as required by the code. Transient values of channel power, channel pressure, inlet mass flux and inlet enthalpy were obtained from the re sul t s o f a RETRAN [ 5 ' code run fo r a TTWOB .

2 For I the fuel rod conduction model, temperature dependent material specific heat and material conductivity for both the fuel and the clad were obtained from Reference (6), and a fuel-to-clad gap conductance of 1000 Btu /hr-f t2.op was assumed.

A plot of the transient CPR as a function of time calculated by

?!AYUO4-YAEC is presented in Figure 4.1. CPR was calculated in the manner described in Section 2.3. The CPR, defined as the initial CPR minus the minimun CPR during the transient, was calculated to be 0.14.

4.2 Range of Applicability As stated in Reference [1], with the proper set of correlations i

MAYUO4-YAEC is capable of analyzing the following types of transients:

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l (1) Pressure, power and flow transients, including LOCA up to core spray initiation time.

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5.0 REFERENCES

[1] Punches, W.C., ".AYUO4 - A Method to Evaluate Transient Thermal Hydraulic Conditions in Rod Bundles, CEAP-23517, NRC-EPRI-CE Cooperative Report, March, 1976.

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[2] Letter from B.A. Zolotar to A.F. Ansari, "An Approximate Form of the I EPRI-Void Formation Model", February 7,1980.

lI l [3] Ceneral Electric BWR Thermal Analysis Basis (CETAB): Data, Correlation and Design Application, Licensing Topical Report, NEDO-10958, November, l 1973.

[4] Transient Critical Heat Flux - Experimental Result s, AEC Research and Development Report, CEAP-13295, September,1972. -

[5] REMN - A Program for One-Dimensional Transient Thermal-Hydraulic Analysis of Cceplex Fluid Flow Systems, EPRI CCM-5, December, 1978.

[6] WREM: Water Reactor Evaluation Model, Revision 1, NUREC-75/056, Division of Technical Review, NRC, May, 1975.

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