ML20138C483

Topical Rept Evaluation of BAW-10156, LYNXT-Core Transient Thermal Hydraulic Program. Rept Acceptable for Ref in License Applications

ML20138C483
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Issue date:	12/03/1985
From:	Office of Nuclear Reactor Regulation
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_.

.h l ENCLOSURE L

i SER ON BAW - 10156 LYNXT I

L

1.0 INTRODUCTION

I

[ By letter dated January 20, 1984 (Ref. 1), Babcock & Wilcox Company submitted a topical report BAW-10156, "LYNXT - Core Transient Thermal-Hydraulic Program",

for staff review. LYNXT is a subchannel thermal-hydraulic code. The sub-K channel approach models a reactor core as a collection of quasi-one-dimensional flow channels that may represent a true subchannel, an entire fuel bundle, or other combinations of subchannels. The flow channels communicate

, with each other by diversion crossflow and turbulent mixing through the gap space between two fuel rods. The crossflow is assumed to exist only in the vicinity of the gap and to be generally small compared to the axial flow in the l adjacent channels. Thus the crossflow in any gap is independent of that in any other gap and depends only on the difference in conditions between adjacent channels. This allows the complicated geometry of a core to be modeled fairly

, simply.

LYNXT was developed from COBRA-IV (Ref. 2) with several features added to improve its computational stability and to add models compatible with other B&W codes. Some specific changes made in creating LYNXT are:

1 (i) Use of the direct elimination solution of the combined axial and

lateral momentum equations in place of COBRA-IV's iterative scheme

{ to improve numerical stability,

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f (ii) Installation ~of the 8&W DN8 subroutine package including the BWC,

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88W-2, CE-1, W-3, W-3R, and EPRI-1 correlations. ' -

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(iii) Use of internal functions to generate subcooled water properties at the given system pressure, rather than the saturation properties at lower pressures to approximate subcooled properties.

I (iv) Installation of an optional fuel / clad gap conductanca model from the TACO code (Ref. 3) in addition to an optional input constant for the gap conductance.

(v) Use of a modified central difference scheme with the scaling of the velocity and enthalpy rise between the neighboring channels for the transverse momentum and enthalpy convection terms.

i (vi) Addition of optional internal axial power profile generators and ability to vary the axial and radial power shapes in transients.

f (vii) Addition of an input factor applied to the computed critical heat

[ flux to initiate post-CHF heat transfer early based on the correlation design limit.

k (viii) Addition of various iterative ramps on crossflow solution parameters in an attempt to help enhance convergence.

I (ix) Ability to specify a different crossflow resistance, turbulent mixing coefficient, and gap-to-length ratio for each gap to allow modeling I channels of widely varying sizes.

(x) Installation of the standard B&W single- and two phase flow models

, from LYNX 1 (Ref. 4) and LYNX 2 (Ref. 5).

'l These changes are mainly peripheral to the. basic code. The problem fomulation -

} -

and s,olut.fon procedures in LYNXT are almost identical to those of C081IA-IV. ' -

f-COBRA-IV was developed under the sponsorship of the Energy Research and Development Administration and the Nuclear Regulatory Commission and has been 1

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i j used by the nuclear industry for subchannel thermal-hydraulic calculations and l by the NRC staff for audit calculations. Therefore the staff review of LYNXT f is particularly concentrated on the changes to COBRA-IV, and on the data ccm-

, parisons for verification and benchmark of the LYNXT code, i

t 2.0 STAFF REVIEW f

2.1 LYNXT Thermal-Hydraulic Model:

l i

!j . LYNXT uses the standard subchannel approach in formulating the flow-field

'f model. The basic conservation equations for mass, energy, axial momentum, I

and lateral momentum are the same as COBRA-IIIC (Ref. 6) and COBRA-IV. The subchannel formulation assumes that the crossflow between adjacent channels is relatively small and that one cr.ossflow has no direct effect on any other.

[ In practice this requires that the flow be friction dominated and that the resistance to lateral flow be large with respect to axial friction and form losses. This condition is satisfied very well by the rod bundle geometry of

} a reactor core where each small subchannel is in contact with a solid surface and the lateral flow area between channels is a relatively narrow gap.

The primary variables used in LYNXT are the enthalpy, axial mass flow rate, lateral mass flow rate per unit length (crossflow), pressure and density. The [

i lateral and axial flow rates, pressure, and enthalpy are obtained from the solution of the conservation equations. The density is related to the enthalpy through the equation of state and the selected subcooled boiling and bulk void models.

In single phase flow the density is obtained directly from the equations of  ;

state. COBRA uses saturation properties at the subcooled enthalpy to approxi-

~ mate true subcooled values assuming that pressure effects are negligible. LYNXT improves on COBRA in this area by using internal functions based on the 1979 'I i ASME correlations to compute subcooled properties at the reference pressure.

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While the difference is small, LYNXT is still more accurate.

i If the true quality is positive as computed by the selected subcooled quality model, two phase flow exists even though the average bulk fluid may still be

( subcooled. The subcooled void model is used to compute the void fraction I curresponding to the given quality including slip effects. The saturation a properties are assumed to be uniform over the entire computation mesh. That I

g is, they are computed at the input system reference pressure neglecting local

( pressure drop. This is termed the " thermally expandable flow" assumption. It is not completely incompressible because the density varies with enthalpy and void fraction. However, there is no effect of local pressure.

! This assumption is valid as long as the flow is entirely subcooled or the pressure drop is small compared to the system pressure as it is in a PWR. For example, if the system pressure is 2200 psia and the pressure drop is 50 psi, i ,

the inlet pressure is 2250 psia. Since there is very little difference in

!; saturation properties between 2250 psia and 2200 psia, the assumption of a uniform reference pressure introduces little error.

! In practice, the errors of the uniform system pressure approach are conservative since it computes a higher void fraction. In the steady state, boiling will i  ; be predicted closer to the inlet. In transients with decreasing system pressure, more flashing will occur and more liquid will be expelled reducing

! I the coolant inventory. The thermally expandable flow assumption is generally l valid for PWR analysis.

ie fk For boundary conditions, the user specifies the inlet enthalpy and flow rate.

i l

Inlet crossflows are assumed zero and pressure drop is referenced to zero at

j' the exit. A nonuniform inlet flow and enthalpy distribution may optionally iF be specified by assigning specific values to each channel. The average core -

fh power and system reference pressure are.also'specified by input.- Ther's is il  ; also a capability to specify an exit enthalpy.for use when the exit flow f reverses. However, since LYNXT can compute only positive flow, this option is

! '. never used. -

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f Transient forcing functions for the inlet flow and enthalpy, system pressure, and average power may also be specified. These are defined in tems 'if tables

i of the fraction of the steady-state value versus time. LYNXT has the additional

!f feature of allowing the axial and radial power distribution to vary in a i transient. Linear interpolation is used in the code to compute forcing function values between table entries. The user is responsible for setting a small

enough time step to follow the detailed behavior of the forcing functions.

l{ .

I LYNXT also has a pseudo pressure drop boundary condition option for steady-f' state calculations. Ifused,thisfeatureadjuststhegiveninlebflowsduring solution iteration until the pressure drop is equal to the input value. The i

adjustment scheme assumes that the pressure drop less gravity head is pro-portional to the square of the inlet flow. LYNXT has a separate conver-gence criterion on pressure drop and a damping factor on inlet flow. This will  ;

i help in achieving the given pressure drop more precisely. This option cannot

'] be used in transients.

The development of the LYNXT finite-difference equations is similar to that of COBRA-IV with some modifications. The difference equations use the same vari-7

. able placement and cell structure as COBRA and are implicit in time. This' 3

L means that LYNXT has no numerical time step limitation in a transient. However, r

the time step must be small enough to follow the details of the changing flow l.

field to ensure accuracy. The details of each difference equation are discussed in Section 2.1.1.

! 2.1.1 Conservation Equations i

Continuity -

II ii

j. The continuity equation is exactly the same as COBRA.

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{ The energy difference equation in LYNXT is similar to COBRA. The volume-I averaged enthalp'y in the time derivative is related to the flowing enthalpy I ;by' Tong's function, $, (Ref. 7) with the resulting hfghseeninterm1 of Equation 2-15 in BAW-10156. This quantity is nonzero only in transients

'with two phase flow'where slip effects are included.

,The energy equation contains both axial and lateral conduction terms (Terms p i 7 and 9 of Equation 2-16) to account for the thermal conduction in the fluid.

These are important only in modeling liquid metal-cooled systems. In PWR L;.

. applications, thermal conduction in the fluid is insignificant and these terms can be neglected to save computation time and storage. Their use is optional

, }".

y in LYNXT.

f' Likewise, the conoucting wall model is of limited use in PWR analyses and could be eliminated. This would delete ters 6 in Equation 2-16 and the

development in Equations 2-23, 2-24, and 2-25 to simplify the energy solution I

considerably. The wall conduction term is related to the channel enthalpy

, via the specific heat in Equation 2-21. When the fluid temperature reaches saturation, Equation 2-21 is not used and the wall conduction term is made k explicit (i.e., placed all on the right-hand side of the equation). Sub-I'~

stituting enthalpy for temperature allows the wall conductjon to be computed

'N implicitly and the wall energy equation 2-23 and fluid energy equation can be solved simultaneously. .

t The lateral energy convection (ters 3 in equation 2-16) is modeled with a donor cell difference in COBRA. This means that a crossflow from channel i i! to j would transport the enthalpy in channel 1. This method is numerically

,l -

' stable and physically realistic. LYNXT, however, uses an interpolation j~ procedure defin~ed by' Equations 2-18 and 2-19 which computes the transported

.. enthalpy as a weighted average of the enthalpies in adjacent channels based on the relative distance of the gap from the centroid of.each channel. B&W

[, states that this is needed to model the large channels representing many t

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subchannels lumped together. The scaling of enthalpy transported by diversion

[ crossflow, however, is not appropriate and causes nonphysical effects. The -

enthalpy should not change value in the process of being transported between channels, regardless of geometry.

Ideally, LYNXT should be corrected to donor cell differencing. However, in actual plant simulations typical of intended LYNXT applications, the cross-flows will be small and the enthalples fairly uniform. Under these conditions the errors introduced by the scaling procedure will be small and conservative.

This is shown in the comparison of LYNXT, LYNX 2, and COBRA results in the '

j verification section of BAW-10156 and in the supplementary data comparisons

! supplied by B&W (Ref. 8). Therefore we conclude that the lateral enthalpy l scaling is' acceptable for this type of simulation (i.e., small crossflows and

[ fairly uniform enthalpy distribution).

4 The turbulent mixing of enthalpy (ters 8 in equation 2-16) is also scaled l based on the relative centroid distance between channels. Unlike the con- t r

vective scaling above, this scaling is necessary when modeling different I large-sized channels consisting of different numbers of subchannels. The

(

turbulence scale is on the order of the size of a single subchannel, and f'

turbulent mixing takes place between two adjacent subchannels. When many

. subchannels are lumped together into a larger computational channel, the  ;

turbulent mixing coefficient should be reduced in proportion to the number {

of subchannels between the centroids of the larger channels. The LYNXT li

! - scaling equation 2-20 performs this operation and is more accurate than COBRA l which uses a uniform constant mixing coefficient for lumped channel cases.  !

\

1i Axial Momentum

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i j, The development of the axial momentum difference ecad! a O LYNXT follows o . <

I t the same steps as the rather complicated procedure et Ch... dIIC and COBRA-IV.

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y The LYNXT equation 2-28 matches the corresponding COBRA equations exactly

[ except for the scaling of the lateral momentum convection term.

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j The momentum scaling is performed in the same way as the energy convection

{ ( scaling in the previous section. As in the energy equation, this scaling

!. ' procedure will introduce unphysical errors and a donor cell difference as V

used in, COBRA would be preferable. However, the contribution of lateral momentum convection is quite small in PWR simulations and the radial 4

distribution of axial velocity is usually more uniform than the enthalpy profile. Therefore any errors resulting from lateral momentum scaling will be insignificant in normal LYNXT applications.

Transverse Momentum The forin of the LYNXT transverse momentum equation 2-30 has the same. form t

! as that in COBRA, but several changes have been made in some of the variables.

L The axial velocities in ters 2 of equation 2-30 that convect lateral momentum in the axial direction are scaled like the convected velocities in the axial momentum equation. The averaging process of scaling is perfectly appropriate here. In fact, using the donor cell value is more in error in this case.

Convected velocities (as-in Equation 2-28) should be donor cell and velocities I

that convect lateral momentum (as in Equation 2-30) should be averaged. ,

i j Ters 3 in Equation 2-30 is an attempt to provide lateral momentum coupling between gaps to reduce the restriction of the subchannel assumption that crossflows do not affect one another. However, the term is a fairly loose

! approximation and was found to cause some computational instability. This

[ is confir.ced by B&W in their responses to staff questions (Ref. 9). At any ,

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-rate, the term is optional and it is required that it not be used for l

'LYNXT. licensing analysis unless justification is provided.

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i l Tere 6 is a lateral gravity term that requires the gap orientation angle information supplied in Term 3. If the lateral momentum flux option is 4 not used, neither can the gravity term. It will be zero for all vertically-l oriented problems.

i The crossflow resistance, Term 5 in Equation 2-30, is the same as COBRA-IV l

, except for the definition of the density in the denominator of Definition 2-31 and the resistance coefficient, k g. The density is needed to convert i crossflow to lateral velocity. LYNXT uses the weighted-average density

!j ~ between adjacent channels computed by the scaling procedure used in the lateral convective terms of the energy and axial momentum equations. This is inconsistent with the definition of lateral velocity used elsewhere in the code where the donor channel density is applied. However, the error k arising from use of the inconsistent density is small if the density is i fairly uniform. Also, the crossflow resistance term does not have a. strong influence on the solution, especially for the small crossflows in normal g LYNXT analyses. Therefore the effect of the inconsistent density should I be insignificant and is acceptable.

6 Terms 4 and 5 contain the coefficient S/A which represents the gap width, S, divided by the distance between adjacent channel centroids, A. LYNXT multiplies 4

S/A by an input factor SLMULT that is intended to adjust the input centroid ,

distance so that the sum of all lateral momentum control volumes is equal to  !

i the total volume of the model, and therefore the lateral control volumes exactly '

overlap the axial control volumes. In response to staff questions, B&W stated j that the value of SLMULT for a typical bundle is 0.88. Since S/A has only a l weak influence on the results and SLMULT is close to unity, its use should f  !

cause no difficulties. However, if SLMULT deviates much farther from unity it l

l should not be used. LYNXT computes the S/A parameter for each gap based on i the actual gap width and controid distance. The crossflow resistance coefficient l

'I kGis also varied in proportion to the centroid distances. This is a necessary. j l

improvement over the uniform constant values of S/A and kgused in COBRA for  ;

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. i I simulations using different sizes of lumped channels. The crossflow resistance i

j. depends on the number of rows of gaps opposing flow between channels, so a

{ 1arger value of k must g be used between two subchannels. Likewise, S/A must be j allowed to vary to correctly represent the geometry.

i f

.{ The lateral pressure difference, P g_y - P j_y written as Term 4 of Equation 2-30 is treated with the identity (P j_y - P j_y) = (Pg - P g_y) + (P3 - P3_y) +

(Pg - P3).

4 The first two terms on the right side of the identity are the pressure

.[

difference between the top and bottom of the computation cells in channels i

{ and j, respectively. They are replaced by substituting the axial momentum Equation 2-28 for channels i and j. The lateral pressure difference g(P -P) 3 remains on the right side of Equation 2-34.

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The (Pg - P ) term is not computed directly from the current pressures but 3

is stored as a separate variable, AP j3 It is updated each iteration by means

.j of the expression APg ).y = [aP g3 - (P g - P 4_y) - (P3 - P3_y)Dp + (1-Dp ) af gj y

'l k where D p is a damping factor less than unity and AYij-1 is the previous iteration value.

1 This technique allows flow disturbances to be propagated upstream. It is

! also absolutely necessary since without it the solution is unstable.

i t

{ The treatment of the lateral pressure difference term is necessary to obtain any solution but is the cause of another kind of instability. There are cases j ~ , where the solutions diverge or fail to converge by entering'a stable oscillation.

I It-is not possible to determine beforehand if a particular simulation will exhibit this behavior. Also, the solutions for these cases may have " false f convergence" before departing to divergence or stable oscillation. Since l

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...._......,_.,-.,_r.;.,..,,.. ., ,

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[ LYNXT defaults to a tighter convergence criterion any stability problems L should show up in the printed iteration data and " false convergence" should

! not be a problem. Also, when it enters a stable oscillation, its predictions remain very close to those of the tightly converged Newton-Raphson solution so

- accuracy is not greatly compromised.

l i

LYNXT has a number of iterative adjustments to various parameters in order to enhance. convergence. These are:

(i) Ramp to apply channel area variations gradually over a specified number of iterations.

(ii) Ramp to apply grid spacer loss coefficients gradually over a specified number of iterations.

L (iii) Ramp to gradually increase crossflow by increasing the S/2 parameter over a specified number of iterations.

J (iv) Ramp to gradually increase crossflow by decreasing the lateral loss coefficient from a large number over a specified number of iterations.

The first two features are similar to those for COBRA and are of limited I -

value. The use of ramps on area variations only delays the onset of in-stability until after the ramps are completed. If a case will not run with-

. out ramps, it probably will not run with ramps. B&W confirms in their response to staff questions (Ref. 9) that the additional ramps on S/A and i

crossflow resistance are also of small benefit. While these features will not affect the results of a converged solution, it is recommended that they i not be used.

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j 2.1.2 Numerical Solution:

i

! In response to a staff question, B&W confirms that the LYNXT solution procedure j is identical to COBRA. For each axial level, the solution steps are in the

! following order:

i (i) Solve the fuel conduction equations for new rod surface temperature and

compute the surface heat flux.

l' t (ii) Solve the energy Equation 2-25 for new enthalpies and compute new densities.

(iii)SolvethecombinedmomentumEquations2-34fornewcrossfiow.

(iv) Compute new pressures with the axial momentum Equation 2-28. .

c (v) Compute new axial flow with the continuity Equation 2-15.

(vi) Update the lateral pressure difference at the level below.

There is a major difference from COBRA in that direct inversion is used to solve the combined momentum equations in LYNXT whereas COBRA-IV uses the Gauss-

! Seidel iteration method. Use of direct inversion eliminates the requirement of the iteration method that the coefficient matrix be diagonally dominant and, I therefore, eliminates the need to add an extra axial momentum convection term on both sides of the momentum Equation 2-34.  !

i 2.1.3 Constitutive Models: -

\

i Constitutive models are necessary to define parameters that are not computed j as part of the main solutions. The heat transfer correlations used in LYNXT are the same as those in COBRA-IV. LYNXT also incorporates standard B&W t constitutive models which have been approved in conjunction with the review

'i of the LYNX 1 and LYNX 2 codes. These constitutive models include a subcooled i

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void model, bulk void model, friction factor, two phase multiplier and grid loss coefficient. In addition, a variable lateral resistance model is in-corporated where the crossflow resistance coefficient K I

IJ varies with the  ;

t pitch to diameter ratio and Reynolds number. These constitutive models are '

I acceptable for LYNXT applications so long as the input values satisfy the conditions to be simulated.

2.1.4 Fuel Model:

j I A two-dimensional heat conduction equation is used to calculate the temperature distribution of the fuel rods in the axial and radial directions. The interface between the fuel pellet and the cladding interior surface is simulated by a

. fuel-cladding gap conductance. Separate equations are also used to calculate the heat transfer between fluid channels separated by a heat conducting wall.

l The orthogonal collocation technique is used to solve the fuel rod heat

{ conduction equations. Collocation is a numerical technique that approximates I the solution of a differential equation by a series expansion. The residual, l the difference between the exact and approximate solutions, is then minimized at the collocation points to yield the expansion coefficients which are the solution sought after. This method has been widely used and is acceptable.

2.1.4.1 Gap Conductance Model:  ;

In addition to the options of using a constant gap conductance or an axially lr varying gap conductance, LYNXT also incorporates a variable gap conductance

,( model. If this model is used, the user provides input parameters obtained

!I from the results of analysis of a fuel performance code such as TACO (Ref. 3) i i or TAC 02 (Ref. 10). The input parameters include the radial power profile,

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k-2 f . .

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I fuel and cladding diameters, gap width ratio, internal pin pressure, gas

} composition and gap surface roughness. The gap conductance model in LYNXT is

[ based on the TACO, TACO 2 and TAFY (Ref. 11) models, which have been approved

! for licensing calculations. However, in LYNXT, it is assumed that the

radial power profile, and gas composition are invariant through the transient.

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This assumption is acceptable in the sense that the parameters considered have

h much longer time constants than the time constant associated with thermal-hydraulic transients.

v f

.I j 2.1.5 Heat Transfer Correlations:

The LYNXT heat transfer correlations and heat transfer logic are based on the i } RELAP4/ COBRA-IV-I heat transfer package. The detailed logic of selecting

different cerrelations for different heat transfer modes is provided in i

response to a staff question (Ref. 9). .

I

! The modifications over the RELAP4/C08RA-IV-I package in LYNXT are

i 4

(i) The check on exceeding CHF is based on the uniform CHF and the M 4 i l

parameter, rather than basing this check on the uniform CHF alone

! l as in COBRA-IV-1. .

(ii) When post-CHF conditions are present the minimum of,the pre- and post-CHF heat transfer correlations is used.

In the first change, the parameter M q is an input correction factor to account' i

<g for the non-uniform axial power shape factor (F-factor) and the statistical

'j' DN8R limit. Thus the use of the constant Mq is acceptable provided that the

' input value of Mq results in conservative prediction of DNB. The second change

I ' is also acceptable because it will make the fuel rod temperature calculation

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The ranges of the transients to be analyzed in LYNXT are given by B&W in

[ response to a staff question (Ref. 9) as i

I 6 Mass flux - 0.2 to 3.0 M1ba/hr-ft ,2  ;

i 1

_g Pressure range - 1000 to 3000 psia,  ;

i Local heat flux - 0.05 to 0.8 Mbtu/hr-fts, i I These ranges are evaluated to be acceptable for the heat transfer correlations l

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used.

f- Since the correlations and associated logic put together in RELAP4 (Ref.12)

'I were specifically for a system blowdown situation, the similarly constructed k LYNXT code should not be used in reflooding transients unless separate i  ! justifications are provided on a case-by-case basis by the user.

In the transition and stable film boiling heat transfer regimes, two.

4 multipliers, XTRANS and XSTABLE, are used as multipliers to the empirical

l transition and stable film boiling heat transfer coefficients. B&W stated t in response to a staff question that for standard analysis, the default h values of 1.0 are used for these two multipliers. To assure conservatism, the values of these multipliers should not be set to be greater than 1.0 unless otherwise justified.

2.1.6 DNBR Analysis With LYNXT:  ;

LYNXT is intended for one pass DNBR analysis of PWR cores as opposed to the two pass approach to the LYNX 1 and LYNX 2 combination. In one pass analysis

[ the hot subchannel and several neighboring subchannels are modeled in detail.

The rest of the hot bundle is modeled as a large single channel consisting of the sum of the remaining subchannels in the bundle. Several surrounding i bundles are each modeled as separate lumped channels and the remainder of the core beyond.is modeled as one or more very large channels consisting of the i, sum of,several bundles. Thus the entire core or a section of symmetry is l[ , . modeled economically in one simulation with a high degree of detail near the

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hot subchannel and a progressively oarser representation in less critical

, regions.

I i f l In the two pass approach, two separate cases must be run. The first case

[ (using LYNX 1) models each bundle in the core or section of symmetry as a

'I single lumped channel. The second case (using LYNX 2) models each subchannel I

l in the hot bundle separately and uses average crossflow, enthalpy, and axial

(. flow taken from LYNX 1 at each axial level to represent communication from the

} neighboring bundles.

i The chief advantage of one pass analysis is that direct communications are provided between the hot subchannel and the rest of the core and is, therefore, a more realistic simulation.

LYNXT possesses all the features necessary to handle the varying channel sizes used in one pass analysis. These features are:

(i) Crossflow resistance proportional to distance between channel

centroids, 1.

J . (ii) Turbulent mixing coefficient inversely proportional to It.

f (iii) The S/2 parameters representing the actual gap width, S, and r centroid distance, 1, for each gap.

l (iv) Solution arrays and logic allowing for more than four lateral connections to each channel.

! In the one pass analysis, the location of the hot subchannel must be known so

( .

the detailed geometry can be placed properlyt- The LYNXT user must develop a ,

method to ensure that the hot subchannel is chosen before the main analysis [

is performed. The hot subchannel is the one with the lowest MDNBR. It is i

usually, but not necessarily always the one surrounded by the highest power

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[

I 1

[ rods. If a slightly lower power subchannel sees a lower flow rate or is

[ surrounded by hotter subchannels than the highest power subchannel, it may 1

b have a lower MDNBR. Usually a simplified model with several subchannels

,j can be used to investigate candidates for the hot subchannel.

I I

4 Once the hot subchannel is located, the user must perform sensitivity studies

r. to ensure that the channel layout selected provides sufficient detail. At least one ring of neighboring subchannels and the remainder of the hot bundle i

is needed to provide realistic boundary conditions on the hot channel.

'I

+, Additional layers of subchannels and bundles will tend to provide hotter

.6 2

surroundings to the hot subchannel and lower the PONBR assuming that power f , decreases uniformly away from the hot bundle.

t There are eleven CHF correlations available as options for the DNB analysis, i.e., B&W-2, MF71, BWC, W-3, W3R, W35, W3RG, W3CRS, W3LG, CE-1, and EPRI-1.

5 Among these correlations, the BWC (Ref. 13) and B&W-2 (Ref. 14) correlations

are reviewed with appropriate CHF data to qualify them to be used in. con-3 junction with LYNXT (this will be discussed in Section 2.2 of this SER).

Therefore, the use of BWC and B&W-2 correlations in LYNXT is acceptable for ,

DNBR analysis. For other CHF correlations, a similar statistical analysis is required for each correlation to qualify them for DNBR analysis.

Since both B&W-2 and BWC critical heat flux correlations and their respective

]

DNBR limits were developed with steady state CHF test data and steady state thermal-hydraulic codes, it is questionable as to whether these DNBR limits

' in connection with the LYNXT transient solution provide the required protec-

[ tion against DN8 at a 95/95 probability / confidence level. In response to a lr staff question (Ref. 15), B&W cited the transient CHF test data and analysis in Il connection with the development of the B&W-2 correlation, and other open ll- literature which conclude that the use of steady state CHF correlations and

h their associated DNBR limits for transient application is appropriate. Though

'I '

it appears to have been a common perception that transient CHF can be predicted I

,r

i 17'

,.- ----= - . -. _ . _ . _ . _ _ _ ... _._ _ .._. -

",, _g.._,,,,,..... - ~ _ . , . . , _ _ _ . , . - _ _ , . . . . _ . . . , _ . , . _ _ . . _ . . - _ , , _ . , - . . . . , _ . . . , _ . - . _ . . . - . . , . . - . . . ,

^

t l' i

'L l

i

!! by using the steady state CHF data for a rod bundle having the same geometry {

^ !. and tested under the same local fluid conditions, B&W performed additional f f studies (Ref. 16) at the request of NRC to demonstrate the adequacy of LYNXT E i transient DNBR calculations. A comparison was made between the DNBRs cal-( culated using LYNXT transient analysis and quasi-steady state analysis for the licensing transient events such as steamline break, RCS flow coastdown and  !

control rod withdrawal. The results show that the minimum DNBR's calculated r

by the transient and quasi-steady state approaches are essentially the same ,

c with a maximum difference of less than 3 percent. A study was also made of the j

't i

9 existing experimental CHF tests simulating power and flow transients. A total ~

of 43 data points on the time-to-DNB were analyzed by LYNXT/B&W-2 calculations.

l The results show that the transient DNBR calculations conservatively predict L

earlier time-to-DNB (DNB is assumed to occur when the calculated DNBR is less l 2

i

! than 1.0) for 41 of the 43 data points, and that the LYNXT prediction is with-

in 0.2 seconds of the test results for the other two data points. We therefore

, conclude that the use of a steady-state CHF correlation and its DNBR limit in j

.; LYNXT DNBR analysis is acceptable.

l i

f 2.2 Verification of LYNXT: l 4

BAW-10156 presents comparisons of LYNXT results to isothermal two-bundle flow j distribution test data and to results of LYNX 1, LYNX 2 and COBRA-IIIC. Sen-l

. . sitivity studies are also provided with respect to. axial node length, conver- l' gence criteria, inlet flow distribution, and core power. In response to staff 4 questions-(Refs. 8 & 9), B&W provided more details.on LYNX 1/ LYNX 2/ COBRA-IIIC comparisons, a detailed CHF data comparison using 53 data points out of the I l set taken by B&W to verify the BWC correlation, and a comparison with the TEMP i

code (Ref. 17) using 31 data points from the set used to verify the B&W-2 ,

} correlation. Individual results are discussed below.

lk  !

• . 2.2.1 Isothermal Bundle Crossflow Data -

. l ll l

i. I

! The results of four tests are presented with bundle inlet velocity ratios  !

h i

(flow in bundle 2/ flow in bundle 1) ranging from 0.75 to 0.95. One additional  !

'F test at 0.9 velocity ratio applies an unspecified exit pressure profile. Plots j i! l lj 18  ;

lI  !

ij  !

m . .. . . _ . _ . . - _ _ . . _ _ _ _ . _ _ . . - _ _ . . . . _ _ _ . . . _ .

l

i a

u of velocity ratio versus distance are given for each test. The results show I that the maximum difference between LYNXT and the data on velocity ratios is less than 4% and the average difference is less than 0.5%. Though LYNXT does not show the effect of flow redistribution at the three grid spacers seen in the test data, the small overall difference shows that the LYNXT flow solution f

l performs properly.

2.2.2 Comparison of LYNXT and LYNX 1 Closed Channel Models A single lumped channel (no crossflow) representing a typical bundle under normal operating conditions was run to compare the effects of the constitutive l models in LYNXT with those of LYNX 1. A one-dimensional problem removes the

differences caused by lateral momentum and energy transport so that only the effects of void, quality, and axial friction models are shown. Since LYNXT has essentially identical constitutive models as LYNX 1, the plots of axial pressure drop, void fraction, density, and enthalpy profiles are virtually indistinguishable between LYNX 1 and LYNXT. This indicates that the models have been coded correctly.

2.2.3 LYNXT/ LYNX 1/ COBRA-IIIC Comparison - North Anna Model A 1/4 section of symmetry of the North Anna plant core is modeled with one bundle per channel using LYNXT, LYNX 1, and COBRA-IIIC. Runs are made for 90%, 100%, and 112% power and plots of hot bundle void fraction, mass flow, and enthalpy profiles are made for each of the three codes. The COBRA-IIIC l results cannot be compared directly because it uses different models for f subcooled void and bulk void.

The maximum difference between LYNXT and LYNX 1 exit flow and enthalpy are less than 0.5%. The plots show that LYNXT always yields a slightly higher enthalpy and void fraction than LYNX 1'as a' result of the lateral enthalpy i.

r convection scaling in LYNXT. The differences are extremely small, with

! the LYNXT results on the conservative side.

I i

19 i

w .

=

}. .

I '

i I

( 2.2.4 LYNXT Sensitivity Studies

'I i sensitivities to axial node size, core power, and inlet flow distribution j and convergence criteria are investigated using the North Anna core model.

f Results are presented as plots of the hot bundle mass flow rate profile.

f P

j Axial node lengths of 3, 4.5, and 6 inches produce less than 1% change in mass flow and MDNBR (B&W-2). LYNXT is not sensitive to axial noding and the

( 3 inches node length used in most analyses will give accurate results.

, Core power levels increasing from 0% to 112% show the expected effects of L two phase acceleration in lowering the hot bundle flow rate.

Variation of hot bundle inlet flow from 95% to 105% of the average has the expected small effect beyond the inlet region. The flow is redistributed to essentially the same radial profile after about 1/4 of the total length. A small difference persists throughout because boiling begins slightly before i

the flow redistribution is complete. Minimum DNBR changes less than 1.2%

over this range of hot bundle inlet flows.

( Variation of the axial flow convergence criterion from 0.001 to 0.0001 l quadrupled the number of iterations (21 to 85) but changed the hot bundle flow less than 0.8%. As a general rule, full convergence can usually be achieved with the number of iterations equal to the number of axial nodes. '

l Further iterating makes insignificant changes in results. This is demon-strated by the test case where 48 axial nodes are used to simulate the 144 inch core, and the plot of hot bundle mass flow shows a visible

difference between 21 and 41 iterations (ERR =0.001 and 0.0005) but no

,l effective change at 85 iterations (ERR =0.0001).

}

~

'I f.

20 i

i I

. '/ ._ . . . . . . _ . . . . . . . . . _ . .. ~ _ ~ .

Y. .

l l

l I

i 2.2.5 Comparison of LYNXT One-Pass Model to LYNX 1/ LYNX 2 Two-Pass Model  ;

i '

BAW-10156 presents a typical DNBR simulation of a generic B&W 3800 Mwt, i 205 assembly plant operating at 112% and 102% power. Two LYNXT one pass l .models were used: a 17 channel model with one layer of subchannels around the hot subchannel and a 38 channel model with two layers of subchannels.

?

COBRA-IIIC was also run on the 17 channel model but, since COBRA-IIIC does not have the necessary features of one pass analysis, its results are for information only.

Plots of hot subchannel mass flux and enthalpy profiles from COBRA were presented in BAW-10156. Later, B&W also supplied additional plots of these variables plus void fraction profiles and the LYNX 2 results (Ref. 9). These comparisons show that:

(i) LYNXT always shows a higher enthalpy and void fraction than LYNX 1/ LYNX 2

, due to the use of lateral enthalpy scaling, h

(ii) The LYNXT 38 channel model always shows a higher hot channel enthalpy r and void fraction than the 17 channel model because the hot channel sees hotter surroundings with two layers of subchannels than with one; and a

t (iii) Both LYNXT one pass models show a smoother, more realistic, hot channel mass flux profile than LYNX 2. The numerics in LYNX 2 force sudden flow

' readjustments to grid spacers and boiling while LYNXT propagates these disturbances upstream for a more gradual readjustment.

f i The overall results show that the LYNXT 38 channel model gave the lowest MDBNR

[- at both power' levels (based on BWC) and that the difference between the results

'i - of the LYNXT 17 channel case and LYNX 1/ LYNX 2 case are within 0.8K. This

't demonstrates that LYNXT one pass analysis .is as accurate as the . LYNX 1/ LYNX 2 jt two pass method for DN8R analysis.

t*

l\ ~

[

21 i

h , . ., . - _ . . . . _ _ . - - - _ __ _ . . , _ . _ . . . . . _ . . . _ _ . . .

I* . _ _ . _ . _ _ _ _ _ _ _ _ . _ _ _ _ _ _ . . . _ . _ _ _ _ . , . _ _ _ _ _ _ _ _ . _ _ _ . . , _ . _ _ _ _ _ _ _ _ _ _ . _ _ . _

} . .

F l

n A second convergence sensitivity study was performed with both the 17 and 38 channel models by varying the axial flow convergence factor from ~0.001 to j 0.005. Ninor differences in the hot channel mass flux profile similar to the I preceding convergence study are shown.

I l 2.2.6 LYNXT DN8 Data Comparisons Usina BWC BAW-10156 provides comparisons between the LYNXT and LYNX 1/ LYNX 2 results, 4

including M)N8R's for a variety of plant simulations. These runs show that i LYNXT matches LYNX 1/ LYNX 2 results closely. However no comparisons with experimental DNB are given. In response (Ref. 8) to a request for such data, B&W provides comparisons to 53 DNB data points selected with a statistical procedure from the set used to qualify nonsymmetric axial power profiles, with and without an unheated guide tube.

The 53 data points were run with LYNXT and LYNX 2 both using the BWC correlation.

Results are presented as plots of LYNXT versus LYNX 2 DNBR, LYNXT DNBR versus quality, mass flux and pressure at DNS and LYNX 2 DNBR versus the same three i

variables at DNB. Plots of LYNXT versus LYNX 2 quality and mass flux at

, CHF are also given as well as LYNXT and LYNX 2 hot channel mass flux and enthalpy profiles for five of the data points. The comparisons show that:

(1) ' The maximum difference between LYNXT and LYNX 2 DNBR;is SE and only 7 of the 53 points show LYNXT less conservative (by ~1%); .

(ii) The plots of LYNXT DNBR versus quality, mass flux and pressure, show LYNXT to be 3 to 5% conservative with respect to the data. Scatter is roughly *1%; .

I

( (iii) Neither LYNXT nor LYNX 2 shows any systematic bias.in DNBR versus quality,

'l mass. flux or pressure; i2 l

i I 22 i

,_ -. _ . . . . . . . . . _ _ . = - _ . _ _ - - . . . , . _ _ _ _ . . . _ .. , . _ . _ ._ _.

l

{' (iv) LYNXT shows a slightly higher quality at DN8 and higher hot channel enthalpy profile than LYNX 2 as a results of using lateral enthalpy 1

convection scaling in LYNXT; and I (v) LYNXT mass flux profiles follow those of LYNX 2 except for disturbances j at inception of slightly subcooled boiling caused by the LYNX 2 numerics.

! l j These results show that LYNXT using the BWC correlation is conservative with l respect to LYNX 2 and the data, and that LYNXT with BWC is acceptable for DNB l analysis. I 2.2.7 LYNXT DN8 Data Comparisons Usina B&W-2 l None of the LYNXT calculations presented in BAW-10156 used the B&W-2 correlation in a way that would verify the' LYNXT/B&W-2 combination for DN8R analysis. Since B&W desires to use 8&W-2 correlation with LYNXT, they submitted a series of B&W-2 DN8 comparisons between LYNXT and the TEMP code to provide the required verification (Ref. 18). These comparisons were made using 31 of the 207 rod bundle data points which were used originally with TEMP to develop the B&W-2 correlation. The data points were selected to cover the anticipated operating  !

ranges of enthalpy, pressure, and mass flux. ,

Both LYNXT and TEMP simulate the experimental rod bundle on a subchannel basis.

. However, TEMP models only turbulent mixing between subchannels and does not '

allow diversion crossflow resulting from subchannel pressure differences. When boiling occurs, TEMP maintains an artificially high mass flux and low quality

in the hot channel by not allowing diversion crossflow to its cooler neighbors.

/ In subcooled conditions the reverse would tend to occur due to the lower viscosity and gravity head in absence of strong boiling acceleration.

j- -

l l .

l

! l 4

6 t

i 23 I

s I i y... .....,_..m.... . , . , . .. ,. _ _ .

y_ .. - ._ . -. .-. - .-. -. . - - - - - ._. .. . _ _

l Since the B&W-2 corre19 ion was developed to give the true CHF at the high l I mass flux and low qual ty supplied by TEMP it will be conservative during l f boiling using the more correct lower mass flux and higher quality given by

, LYNXT. In subcooled cases LYNXT should be slightly nonconservative since it will give a slightly higher hot channel flux and quality

,, The data presented by B&W have very little crossflow and conseqLently a very close correspondence between LYNXT and TEMP. B&W computed the mean of the ratio of TEMP to LYNXT DNBR's as 1.0014 showing that LYNXT is slightly p conservative. The plots of TEMP versus LYNXT DNBR, mass flux and quality at the CHF locations show the predictions of the two codes to be nearly identical.

The quality comparison, in particular, shows almost an exact correspondence and is the strongest evidence that there is little crossflow.

The potential nonconservatism of LYNXT/8&W-2 relative to TEMP /8&W-2 in subcooled conditions is not significant in practical applications. In fact, the B&W-2 experimental data base extends only slightly into the subcooled regime and this limits the applicability of the correlation to regions where it will be conservative. The B&W-2 correlation is acceptable for use with LYNXT so long as it is used under operating conditions within the data base of the correlation. Babcock and Wilcox points out that the limiting DNBR conditions for reactor operatioa satisfy this condition.

2.2.8 Verification of Fuel Rod Heat Transfer Models The LYNXT fuel rod heat transfer model was benchmarked by comparisons to an analytical solution and to solutions from the B&W TACO and RADAR codes I (Ref. 19).

! ~In the comparison to the analytical solution, a simplified transient problem .

l was modeled. It was assumed that there was no axial heat transfer in the l rod; the fuel-cladding gap thermal resistance was zero; and the properties of the fuel, cladding, and fluid were constant. The results indicated a i

k i 24

. _ _ . _ . . . _......_,..,r_... .._ ,,. . .. .. . . . . . .

a

4.

difference of less than 0.5% on the fuel centerline temperatures. This comparison shows that the basic equations and the numerical schemes used k in the LYNXT fuel rod heat transfer calculations are correct.

l Comparisons with the TACO and RADAR codes provide verifications on the models l of variable gap conductance, the fuel and cladding dimensional changes due to

) thermal expansion, and the transient MDNBR analysis.

[,

The LYNXT/ TACO comparisons are performed at both steady state and quasi-steady state conditions. The steady state comparison showed that the fuel-cladding gap conductance, fuel centerline temperature and fuel surface temperature i profiles compare favorably. The maximum difference of these parameters at the hot spot is about 1.5%.

The power ramped LYNXT/ TACO comparison is performed to verify the fuel-cladding 1

dimensional changes due to power level changes during a transient. In the g comparison, LYNXT was initialized to 102% power, then put through a series I of transient power ramps. The results at each " quasi" steady state point during the transient were then compared to a series of sep rate TACO runs.

r The comparison showed a maximum deviation of 1.9% on centerline temperature, I

3.7% on pin pressure, 4% on fuel surface temperature and 5.5% on gap conductance at the hot spot. Judging from the magnitudes of the errors,

( the results are acceptable.

I Further investigation on the LYNXT transient capability was provided by the LYNXT/ RADAR comparison. Since RADAR does not have crossflew capabilities, l the RADAR comparison provides a check on the coupled fuel rod and fluid heat f transfer calculations for an isolated channel. A four pump coastdown transient was run on both LYNXT and RADAR. Within a transient time of 3 seconds where j the minimum DNBR is experienced, the maximum difference is ~3% for the maximum

( -

l .

1 25-i I

r. - ,. . .

, . , . = . , .. . . , . . _ . .

I

b. .

e I t

fuel centerline temperature and ~4.5% for the hot spot radial average fuel f temperature. The times of the minimum DNBR for RADAR and LYNXT were the same, l and the difference on the MONBRs is ~2.5%. These comparisons indicate that the j coupling between the fluid and fuel heat transfer is modeled correctly. It j should be noted that the LYNXT modeling in both fluid hydrodynamics and fuel-

! cladding heat transfer is more realistic then that of RADAR. The merit of comparing LYNXT to RADAR is that RADAR is an NRC-approved code and its results

,I are reasonable.

l In summary, the fuel rod heat transfer and the fuel-cladding gap conductance

! modeling in LYNXT are found to be accurate. The heat transfer coefficient from rod to coolant was also calculated correctly.

3.0 SUMARY AND CONCLUSION

< i r The staff has reviewed the topical report BAW-10156 and concludes that the LYNXT computer code is acceptable for licensing calculations of PWR core

, thermal-hydraulics. This acceptability is subject to the following conditions.

1. Among the eleven CHF correlations available in LYNXT, only the BWC and B&W-2 correlations have been validated with LYNXT. Therefore F

only BWC and B&W-2 can be used for DNB analysis with LYNXT. The j applications are restricted to the ranges of applicability of these i

correlations.

2. LYNXT contains the necessary features for performing the one pass hot

. channel DNB analysis for PWR cores. Therefore, the one pass hot channel

. analysis is acceptable. The LYNXT users should develop a method to

} ensure that the correct hot subchannel is chosen for the one pass modeling.

Sensitivity studies should also be performed to ensure that the channel i

layout selected provides sufficient detail to provide corre,ct boundary t

~1 -

)

conditions to the hot channel.

t

\  !

I l i l i 26

._ r .

. . . - _ . . _ . . . . . _ ~ . . . _ .. . ,. ,. _ _.. = - - -

C.l .

^

i 3. To assure conservatism, the heat transfer coefficient multipliers for the f

,. transition and stable film boiling regimes, XTRANS and XSTABLE, should not ,

[ be set greater than 1.0 unless otherwise justified.

i i

I i

p e

i r

F L-L -

[

[ .

t t

ie 27

. _~~

7. - - - ~ . . . _

ti