ML20207K470

Final Review of Convection Heat Transfer Coefficients Utilized in Fort St Vrain Main Steam Line Break Analysis, Technical Evaluation Rept

ML20207K470
Person / Time
Site:	Fort Saint Vrain
Issue date:	12/31/1986
From:	White M Battelle Memorial Institute, PACIFIC NORTHWEST NATION
To:	NRC
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ML20207K406	List: ML20207K402 ML20207K470
References
FATE-86-117, FATE-86-117-01, FATE-86-117-1, TAC-42527, NUDOCS 8701090427
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FATE-86-117 TECHNICAL EVALUATION REPORT REVIEW OF CONVECTION HEAT TRANSFER COEFFICIENTS UTILIZED IN THE FORT SAINT VRAIN MAIN STEAM LINE BREAK ANALYSES

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E M. D. White December 1986 Prepared for the U. S. Nuclear Regulatory Comiss. ion represented by Norm Wagner APPROVED:

C. W. Stewart, Manager '

Fluid and Thermal Analysis Section Engineering Sciences Department BATTELLE PACIFIC NORTHWEST LABORATORY RICHLAND, WASHINGTON 99352 This report is a working paper intended for the sponsor and other contributors to the program. Do not reference in open literature at this time.

8701090427 870102 PDR i P ADOCK 05000267 PDR

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ABSTRACT Sensible convective heat transfer coefficient determination methodologies were reviewed for applications during confined or contained main steam line break analyses. A review perspective of conservatism with respect to predicting maximum environmental temperatures and pressures was taken. Concern specifically lies with the steam line break scenarios for the Fort Saint Vrain facilities technically addressed by the Public Service Company of Colorado.

Pacific Northwest Laboratory reviewed the sensible convective heat transfer coefficient determination methodology utilized by the Public Service Company

( of Colorado concurrently with other conventional approaches. Based on the

. present review and literature search, Pacific Northwest Laboratory concludes that the conventional approaches are preferred compared with the untested

scheme forwarded by the Public Service Company of Colorado.

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NOMENCLATURE Gr Grashof number -

Nu Nusselt number Pr Prandtl number Re Reynolds number g acceleration of gravity h average convective heat transfer coefficient k thermal conductivity i E characteristic length g mg mass of non-condensible pas my mass of steam vapor I

m mass flow rate q heat flux Q energy released (Btu) t p blowdown time (sec)

Tb bulk tempe.rature T

3 surface temperature T sat saturation temperature T temperature difference v velocity V building volume (ft3)

. p thermal coefficient of expansion v kinematic viscosity p density r pi .

Subscripts cond condensation E length max maximum sen sensible  !

tot total (overall) iv l

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CONTENTS i

ABSTRACT................................................................ iii NOMENCLATURE............................................................ iv INTRODUCTION..........................................................., 1 METHODOLOGY REVIEW...................................................... 2 CONVENTIONAL METHODOLOGIES.............................................. 5 .

RECOMMENDATIONS......................................................... 9 REFERENCES............................................................. 10 APPENDIX A............................................................. 11

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REVIEW OF CONVECTION AND CONDENSATION HEAT TRANSFER COE THE FORT SAINT VRAIN MAIN STEAM LINE BREAK ANALYSES INTRODUCTION In conjunction with the Fort Saint Vrain Environmental Qualification Program, the United States Nuclear Regulatory Commission (NRC) requested a technical investigation of several steam line break scenarios within the Fort 4 Saint Vrain facilities. The Public Service Company of Colorado (PSC) generated predictions of confinement buildings' environmental responses to such steam line rupture scenarios with a version of the CONTEMPT' computer program. The results of these siinulations included average environmental temperature and a pressure time histories.

The Pacific Northwest Laboratory (PNL), following a request by the Nuclear Regulatory Commission (NRC), independently made calculations of the pressure and temperature histories for the same Fort Saint vrain steam line rupture scenarios. The Pacific Northwest Laboratory's environmental responses were computed with the COBRA-NC code. Peak temperatures and temperature profiles predicted by PNL were markedly higher than those computed by PSC.

While both codes, COBRA-NC and CONTEMPT, are based on the conservation equations of mass, momentum and energy, the central issue of the present report involves the proportionality term which relates surface heat flux to the temperature difference between the bulk environment and condensing surfaces.

Both codes contain this proportionality term (the overall convective heat transfer coefficient) in divided form. The general form for expressing the overall heat transfer coefficient appears below (see Equation I), where a sensible term: convection heat transfer term adds with a condensation heat transf 9 total

• 9 sensible + 9 condensation h

b s -T );

total (T -T ) = hsensible(T b s -T ) + bcondensation(T sat 3 (1)

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where for superheat conditions Tb>Tsat' In PNL's investigation, it was noted that if the sensible convection portion of the overall heat transfer coefficient (presented in schedule form by PSC) was substituted for the natural convection based internally computed coefficient, then the COBRA-NC code would yield results in good agreement with the PCS's predictions.U) Follow-through work was requested by the NRC for PNL to review the methodology applied by PSC to determine this sensible portion of the overall convection heat transfer coefficient. This report specifically addresses the sensible convection heat transfer coefficient determination methodology proposed by PSC. The methodology is reviewed from i the perspective of conservatism in predicting peak environmental temperatures

, following main steam line ruptures. Additionally comparison is made between the PSC's methodology and other conservative approaches. -

METHODOLOGY REVIEW The methodology used by PSC to determine the sensible convection heat transfer coefficients for the Fort Saint Vrain steam pipe rupture analyses appears in attachments to the document EGP-306.(2) These two pages of methodology description are appended to this report for reference purposes (seeAppendixA). Basically the overall (total) heat transfer coefficient serves as an area-averaged portionality constant relating heat flux on the confinement building surfaces with the temperature difference between the confinement building environment and surfaces. It should be immediately noted that such an approach requires the assumptions that the confinement building environment and structure may be represented by appropriate single temperature values. The specifics of the above assumptiort are not considered in this study. Both PNL (COBRA-NC) and PSC (CONTEMPT) further divide the overall heat transfer coefficient into two components; one representing the sensible convection heat transfer, the second describing condensation heat transfer.

This review will specifically address the magnitude of the combined, i.e.,

overall coefficient and the relative magnitudes of the two components.

The methodology proposed by PSC implies that there exists the possibility of computing the sensible convection heat transfer coefficient by differencing the correlations developed by Tagami and Uchida. The crux of this methodology 2

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D assumes that the Uchida correlation independently predicts the component of condensation heat transfer dependent solely upon the mass ratios of non-condensible gases and vapor. Uchida's empirical correlation was obtained ~

from an experimental apparatus where the condensation environment was considered quiescent.I3) While velocity measurements were not recorded with Uchida's experimental results, Corradini(4) later predicted that the experimental condensing surfaces probably were exposed to steam velocities around 2 m/s.

Uchida's correlation, therefore, should strictly be limited to quiescent conditions or perhaps forced convection situations with maximum free stream velocities equal to 2 m/s. Slaughterbeck(5) is in accord with this because he recommends using the Uchida correlation as an overall heat transfer

.1 coefficient for the quiescent period (after the decompression of the primary I

coolant system) of a loss of coolant accident.

Analogous to sensible convection heat transfer coefficients, condensation heat transfer coefficients are de,'endent upon the imposed free stream velocity.

Therefore, it would not be expected that the Uchida correlation (velocity independent) should predict the condensation heat transfer during the turbulent blowdown period subsequent to a main stream line rupture. The effect of applying the Uchida correlation as the sole condensation heat transfer contribution during turbulent blowdown periods, would be a severe underprediction of the actual condensation rate. Moreover, with the PSC methodology, the sensible convection heat transfer coefficient would be overpredicted due to the additive nature of Equation 1 of the attachments (seeAppendixA). This point may be emphasized by considering that, given a specific overall heat transfer coefficient, a conservative condensation coefficient results in a liberal sensible convection coefficient. The sensible -

convection coefficient plays a significant role in predicting environmental temperatures.

As an example, consider the calculation of the sensible convection heat transfer coefficient at the end of the blowdown for scenario HRH-2. An approximation of the steam vapor to non-condensible gas ratio after 13 sec equals 0.25(*) which by Uchida's correlation:

l (a) Assumes no loss of vapor nor dry air from confinement building. l l

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f hcond = 66 >(mg/mv)-0.707 Btu /h-ft 2 ,.F, (mg/mv) ( 20; (2) yields h cond 25.2 Btu /h-ft 2 ,,F. The Tagami correlation:

h tot g

= 72.5 (Q/Vtp)0.62; (3) yields h tot, max 98.7 Btu /h-ft 2 ,.F. As a conservative estimate the ratio (T sat -Ts )/(T b-T3) will be set equal to one. Substituting these values into

( Equation 1 of the attachments yields h cony = 73.5 Btu /h-ft 2 *F. Using conventional forced convection heat transfer coefficient correlations for the scenario HRH-2 with an imposed velocity of 80 ft/sec yields sensible convection heat transfer coefficients equal to 13.4 Btu /h-ft 2 *F. Maximum environmental velocities measured within the Carolinas Virginia Tube Reactor during the blowdoyn periods ranged from 10 ft/s to 30 ft/s.(6) This evidence suggests the sensible convection heat transfer coefficient calculated with the methodology proposed by PSC is large.

On the second page of the attachments the PSC presents an example of a calculation to obtain a value for h tot, max with the Tagami correlation.

Unfortunately the Tagami correlation is incorrectly represented (the quantity within the exponential should have been divided by the time period during blowdown, that is 13 sec.). The example calculation also deviates from the Tagami correlation listed in Slaughterbeck(5) in the choice of constants.

Slaughterbeck recommends a constant equal to 72.5 with English units while PSC chose a value equal to 2; with the justification of being a conservative approach. Perhaps the choice is conservative with the proper Tagami correlation, but as applied here the result seems quite meaningless. In fact it is not evident whether a sensible convection heat transfer coefficient approximately equal to 7.5 Btu /h-ft2,.F as calculated by PSC here is a conservative choice. The value of 7.5 Btu /h-ft 2 *F represents one half of the 2

15 Btu /h-ft *F reported for the maximum overall heat transfer coefficient of scenario HRH-2 (see Appendix A).

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CONVENTIONAL METHODOLOGIES Krotiuk and Rubin (7) demonstrated that the direct application of either the Uchida or the Tagami correlations in conjunction with the CONTEMPT-LT Mod 26 computer code to calculate overall heat transfer coefficients underestimated the heat reraoval rates measured during the Carolinas Virginia Tube Reactor natural decay test. Moreover, plots of containment pressure and temperature computed using the overall heat transfer coefficients defined by the correlations of Tagami and Uchida overpredicted the CVTR experiments.

Slaughterbeck(5) recommends a sequential application Tagami and Uchida for conservative approximations of environmental pressures and temperatures.

4-Slaughterbeck's specific. program is to apply the Tagami correlation in the extended form (where the transition to the maximum heat transfer coefficient occurs in a linear manner with respect to the t'me between pipe rupture and the end of coolant decompression) during the tri.nsient blowdown period.

Subsequent to decompression, Slaughterbeck recommends a smooth transition from the Tagami correlation to the Uchida correlation. Slaughterbeck's' recommendations do not include an initial sensible convection heat transfer coefficient of 5 Btu /h-ft 2 *F. Rather his rationale states that the overall average heat transfer coefficient "should start at values of about 5 Btu /h-ft 2 *F and increase as the blowdown progresses." The Slaughterbeck

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recommendations and the comparison work of Krotiuk and Rubin suggest that the overall heat transfer coefficient methodology with the Tagami and Uchida correlations conservatively predicts environmental temperatures and pressures for loss of coolant accidents within buildings.

Krotiuk and Rubin I ) further demonstrated that with several simplifying assumptions the overall heat transfer coefficient could be divided into two separate components; one describing sensible 5 eat transfer, and the other describing mass transfer (i.e. condensation). This approach is identical to the methodologies followed in both the CONTEMPT computer code utilized by PSC and the COBRA-NC computer code maintained by PNL, and requires the calculation of both sensible convection heat transfer and convection mass transfer coefficients. Correlations are available which allow the calculation of either heat and mass convection transfer coefficients. Natural convection correlations generally depend upon the driving potentials across the boundary layer while 5

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forced convection correlations require some knowledge of the surface velocities.

The crucial aspect of predicting conservative transfer coefficients during the transient decompression period, typically marked by turbulent flows, is establishing appropriate average surface velocities.

With the split heat transfer coefficier.t approach using " standard" correlations, Krotiuk and Rubin compared the predicted environmental conditions with measured values from the CVTR blowdown experiments. The results revealed that average surface velocities between 10 ft/s and 15 ft/s conservatively predicted heat transfer coefficients which in turn resulted in elevated environmental pressures and temperatures compared with the measured values g from the CVTR tests. Maximum surface velocities of 15 ft/s to 30 ft/s following the simulated pipe rupture were measured by ultrasonic anemometers during the CVTR experiments. Heat transfer coefficients based on the, largest measured velocities, however, differed greatly from the measured values, in a o non-conservative direction. Thus the problem of choosing appropriate surface velocities during the transient decompression stage remains. After the decompression period, natural convection coefficients become appropriate, because the invironment returns to approximately quiescent conditions. The COBRA-NC computer code considers, for the purposes of calculating sensible convection heat transfer coefficients, the transient decompression period to be quiescent. That is, natural convection correlations are utilized even during the transient period. Obviously, this approach is rather conservative due to the larger transfer coefficients expected during the turbulent blowdown period.

Several velocity prediction methods and resulting sensible heat transfer coefficients are shown below for the steam pipe rupture scenario HRH-2. These calculations are shown in an effort to resolve the question about conservative sensible convection heat transfer coefficients. First, consider the quiescent case with the driving force being a reasonable maximum environmental temperature and the initial wall temperature. For this case, natural convection i

correlations are used to compute the sensible convection heat transfer coefficient.

Approximate gas properties @ 8 sec. into blowdown 0 film temperature:

y= 1.066 x 10-3 ft2 /s 6

k = 1.786 x 10-2 Btu /h-ft *F Pr = 0.89 p = 1.370 x 10-3 1/R.

A volumetric hydraulic diameter was calculated as:

f. = 6(volume)/(heat transfer area) = 11.4 ft.

With the parameters shown above, a sensiole natural convection heat transfer coefficient may be obtained through the following series of equations:

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Gr = g# I 10

= 1.96 x 10 ;

t p

Nu = 0.10(Gr Pr)II3 = 259.1; h =

Nu k cg3y = 0.406 Btu /hr-ft *F. (4)

This value sets a conservor comparison with the other forced convection derived sensible heat transfer coefficients.

The NRC model for environmental qualification for main steam line breaks includes acceptable methodologies for safety-related component thermal analysis.

These methodologies provide conservative estimates of the heat transfer coefficients for predicting heat transfer rates to various components subjected to the confinement building environments during main steam line ruptures.

During periods for which condensing heat transfer dominates the recommendation is to apply coefficients four times those of the Tagami or Uchida correlations.

Otherwise, a forced convection coefficient should be used until blowdown has ceased, where the characteristic velocity is defined as follows:

' V(ft/s) = 25 m (lb hr) (5)

V(ft )

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. l If we assume the velocities calculated with equation 5 result in forced convection coefficients four times greater than those applied to environmental heat extraction, then an estimate of the sensible forced convection heat transfer coefficient may be perfonned. Consider the HRH-2 rupture scenario after 8 sec.', where the steam injection rate equals 2.433 x 10 6 lb/hr.

Per Equation 5 the estimated characteristic velocity equals:

6 y , 25(2.433x10 lb/hr) = 113.7 ft/sec. 534.730 ft This velocity translates as follows into a sensible convection heat

\ transfer coefficient:

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Re = = 1.216 x 10 Re > 5 x 10 5 turbulent; I liug = 0.036 Pr0 .43 (p,0.8 - 9200) = 2212.2; h

cony

=

b = 0.866 Btu /h-ft 2 *F. (6)

Consider now the maximum measured velocities within the Carolinas Virginia Tube Reactors of 30 ft/s as defining the appropriate average surface velocity.

Using the previously calculated homogeneous gas properties at 8 sec into the rupture period of the tRH-2 scenario, the following sensible convection coefficient is obtained:

5 5 Re=f=3.21x10 Re}10 turbulent; 0

iTug = 0.036 Pr .43 (p,0.8 - 9200) = 555.1; h

cony

=

E = 0.870 Btu /h-ft 2 ,.p, (7)

It should be noted that the choice of a characteristic length is of minor importance in the calculation of a heat transfer coefficient, since the resulting effect is proportional to CO.2 .

Even the sensible convective heat 8

6 transfer coefficient resulting from a 30 ft/sec flow field is less than the value of 7.5 Btu /h-ft 2 *F reported by PSC. While the results of the Carolinas Virginia Tube Reactor do not necessarily reflect the environmental conditions which would exist during one of the Fort Saint Vrain steam pipe rupture scenarios, it must be questioned whether a sensible convection heat transfer 2

coefficient equal to 7.5 Btu /h-ft ,.F as suggested by PSC is conservative.

The above methodology which considers the confinement building as a pipe, has not been experimentally verified. It was used as an academic approach to obtaining surface velocities and should not be used for loss of coolant accident

-problems until examined in detail.

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RECOMMENDATIONS E

The recommendations from this review are dependent on the heat transfer

• coefficient approach used. If overall heat transfer coefficients are required by a loss of coolant accident computer code, then the Slaughterbeck recommendations of sequentially applying the Tagami and Uchida correlations appears to be a conservative approach. If the overall heat transfer coefficient is divided into two components, one sensible the other condensation, then an appropriate prediction of an average surface velocity is required to generate transfer coefficients through " accepted" techniques. In the absence of appropriate velocity prediction methodologies, the conservative choice of

~ natural convection based sensible heat tranfer coefficients appears reasonable

, although probably notably conservative. There is no justification for subtracting the Uchida correlation from the Tagami correlation to obtain sensible convection heat tranfer coefficients.

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l REFERENCES l

1. Wheeler, C. L., R. E. Dodge, and J. R. Skarda, " Independent Calculation-of Pressure and Temperature Profiles for a High Energy Line Break Outside Containment Fort Saint vrain Nuclear Generating Station Unit 1" FATE-86-114 Battelle, Pacific Northwest Laboratory. August (1986).

2. Dahms, F. C., September 16,(1986). Letter to Mr. Fred Tilson transmitting attachments to document EGP-306.

3. Uchida, H., A. Oyama, and Y. Togo, " Evaluation of Post-incident Cooling Systems of Light-Water Power Reactors," Proc. Int. Conf. Peaceful Uses i

of Atomic Energy, 13, 93, A' CONF:28/P436, International Atomic Energy Agency (1965).

4. Corradii11, M. L., " Turbulent Condensation on a Cold Wall in the Presence of Nonsondensing Gas," Nuclear Technology, Vol. 64, pp. 186-195, Feb.

(1984).

5. Slaughterbeck, D. C., " Review of Heat Transfer coefficients for Condensing Steam in a Containment Building Following a Loss of Coolant Accident,"

IN-1388, Idaho Nuclear Corp. (1970).

6. Whitley, R. H., " Condensation Heat Transfer in a Pressurized Water Reactor Dry Containment Following a Loss of Coolant Accident," MS Thesis, University of California at Los Angeles (1976).

7. Krotiuk, W. J. and M. B. Rubin, " Condensing Heat Transfer Following a Loss of Coolant Accident," Nuclear Technology, Vol. 37, pp.118-128, Feb.

(1978). "

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l APPENDIX A l

l BASIS FOP. HEAT TRANSFER COEFFICIENTS FOR. FORT ST. VRAIN STEAM PlPE RUPTURE ANALYSES The Slaughterbeck report is used as the basis for the overall heat transfer coefficients, ht ot, defined on pages 1 and 2 of that report as the area-averaged proportionality constant between the total heat l flow to the surface and the temperature difference between bulk gas 4

and heat sink surface. The Uchida correlation is used for condensation heat transfer alone (based on the difference between the saturation temperature and the surf ace temperature). Convective heat transfer coefficients (given in a previous transmittal) are the difference between the overall coefficients and the Uchida coefficients. In equation form:

heet = hcony + bcond

[Tsat-Tsh (1) b -T)s

, where hcond is the Uchida heat transfer coefficient Scony is the convective heat transfer coefficient T sat is the saturation temperature Tb is the bulk gas temperature Ts is the heat sink surface temperature in the CONTEMPT-G program, hcond is internally computed and hconv is input (values previously transmitted).

The recommended approach by Slaughterbeck is to start with a total heat transfer coefficient of 5 stu/ft2.hr-of at time zero. This value

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is attributed to natural convection, per Eq. 1. As the blowdown 11 .

APPENDIX A BASIS FOR HEAT TRANSFER COEFFICIENTS FOR. FORT ST. VRAIN STEAM PIPE RUPTURE ANALYSES  ;

The Slaughterbeck report is used as the basis for the overall heat transfer coefficients, ht og, defined on pages 1 and 2 of that report ,

as the area-averaged proportionality constant between the total heat flow to the surface and the temperature difference between bulk gas g

and heat sink surface. The Uchida correlation is used for condensation heat transfer alone (based on the difference between the saturation temperature and the surface temperature). Convective heat l transfer coefficients (given in a previous transmittal) are the difference between the overall coefficients and the Uchida coefficients. In equation form:

htot = heony + bcond

[Tsat*Is\ (1)

(b -T/ s

[ where hcond is the Uchida heat transfer coefficient i Scony is the convective heat transfer coefficient T 3at is the saturation temperature i Tb is the bulk gas temperature i Ts is the heat sink surf ace temperature t

in the CONTEMPT-G program, hcond is internally computed and h conv is input (values previously transmitted).

The recommended approach by Slaughterbeck is to start with a total heat transfer coefficient of 5 stu/ft2.hr-or at time zero. This value

. r is attributed to natural convection, per Eq. 1. As the blowdown  !

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Attachment to EGP-306 page 2 of.2 progresses, the total heat transfer coefficient increases to a peak value given by the so-called Tagami correlation, which was discussed-In the previous FSV equipment qualification document, Gulf-GA-A12045, Appendix 0 with respect to the variation with volume. in the present submittal, we are not dealing with different volumes, but the Tagami correlation is also a function of energy released, which is a function of time:

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ht ot, max = c (Q/V)0.62 (2) where Q is the cumulative energy release, Btu 5 V is the' building volume, ft3 e is a constant, conservatively chosen For the scenario HRH-2, the maximum total HTC is 15 stu/f t 2-hr OF at about 13 sec, about equally proportioned between convective and condensation terms. This value is about ten times lower than the lowest Carolinas Virginia Tube Reactor test data indicate or as

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recommended by Slaughterbeck for typical values of c used in PWR analysis. For HRH-2, c is equal to 2.

l Except for added conservative factors to ensure low heat transfer coefficient values, this approach (including use of the Tagami correlation) is the same as required in Standard Review Plan 4.2.1.5 for calculations of the minimum containment pressure for PWR ECCS periormance.

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