ML20217M269
| ML20217M269 | |
| Person / Time | |
|---|---|
| Site: | 05200003 |
| Issue date: | 04/30/1998 |
| From: | WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML20217M240 | List: |
| References | |
| WCAP-14327, WCAP-14327-R02, WCAP-14327-R2, NUDOCS 9805040476 | |
| Download: ML20217M269 (122) | |
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4 TABLE OF CONTENTS (Continued)
Title P.gge Section 4.4 Measurement Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13 4.4.1 The Westinghouse Heated Flat Plate 'iest . . . . .....................4-13 4.4.2 The Westinghouse Large-Scale Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14 4.4.3 The University of Wisconsin Condensation Tests . . . . . . . . . . . . . . . . . . . . 4- 15 4.4.4 Open Literature Tests .......................... ... .... . . . 4-16 4.5 Mass Transfer Correlation Biases . . . . . . . . . .......................... 4-17 5-1 5 Conclusions .......................................................
6-1 6 Nomenclature . . . . . . . . . . . . . . . . . . . . ........... .....................
............... .................... 7-1 7 References . . . . . . . . . . . . . .....
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Rev sion 2 IV Apn! 1998
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LIST OF TABLES i
_Igbje Title PRRe l i 1-1 Operating Range for AP600 Heat and Mass Transfer Parameters . . . . . . . . . . . , . . 1-2 3.1-1 Entrance-Effect Multipliers for the Hugot Heat Transfer Tests . . . . . . . . . . . . . . . . . 3-2 I
' 3.1 Hugot Mixed Convection Heat Transfer Test Data . . . . . . .................. 3-8 i 3.2-1 Entrance-Effect Multipliers for the Eckert and Diaguila Heat Transfer Tests . . . . . . 310 i l 3.2-2 Eckert and Diaguila Mixed Convection Heat Transfer Test Data . . . . . . . . . . . . . . 3-11 3.3 1 . Entrance-Effect Multipliers for the Siegel and Norris Heat Transfer Tests . . . . . . . . 3 23 3.3-2 Siegel and Norris Mixed Convection Heat Transfer Test Data . . . . . . . . . . . . . . . . 3-24 i 3.4-1 Westinghouse Dry Flat Plate Test Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-34 3.5 1 Entrance-Effect Multipliers for the Westinghouse Large-Scale Dry I Heat Transfer Data ... ..........................................'338 l 3.5-2 Westinghouse Large-Scale Dry External Heat Transfer Test Data . . . . . . . . . . . . . 3-39 3.6 Gilliland and Sherwood Evaporation Test Data . . . . . . . . . . . . . . . . . . . . . . . . . . 3-42 l 3.6-2 ' Entrance-Effect Multipliers for the Gilliland and Sherwood Mass Transfer l Test s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .................. . . 3-45 l- 3.7-1 Westinghouse Flat Plate Evaporation Test Data . . . . . . . . . . . . . . .. . . . . . . . . . . . 3-49 l -3.8-1 Wisconsin Condensation Test Data .................. ............... 3-54 l 3.9-1 Westinghouse Large-Scale Internal Condensation Test Data ................. 3-64 I
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oA4040w.non:1b-o40798 Revision 2 y April 1998
. . LIST OF FIGURES .
ElEEt Il!!! E!Et 2.1-1 Metais and Ec' t Plot Showing the Downcomer, Riser, and Chimney Heat Transfer Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ 2-2 2.1-2 : Opposed Convection Nu-d as a Function of Gr-d for Various Re-d . . . . . . . . . . . . . 2-4 2.1 -3 Assisted Mixed Convection Nu-d as a Function of Gr-d for Various Re-d . . . . . . . . . 2-5 2.1-4 PCS Air Flow Path Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 2-9 2.6-1 Comparison of Eckert and Drake Correlation to Measured Air-Steam Diffusion Coefficients at 14.7 y.sia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-15 3.1-1 Nusselt Number Comparissn ;or Hugot Test 1 ............................ 3-3 3.1 Nusselt Number Comparison for Hugot Test 2 ........................... 3-4 3.1-3 Nusselt Number Comparison for Hugot Test 3 . . . . . . . . . . ................ 3-5 3.1-4 Nusselt Number Comparison for Hugot Test 4 ................ .......... 3-6 3.1-5 Nusselt Number Comparison for Hugot Test 5 ............................ 3-7 3.1 Comparison of Predicted-to-Measured Nusselt Numbers for Hugot Te st s 1 -5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .............. 3-9 3.2-1 Nusselt Number Comparison for Eckert and Diaguila Test 1. . . . . . . . . . . . . . . . . 312 3.2 2 Nusselt Number Comparison for Eckert and Diaguila Test 2 . . . . . . . . . . . . . . . . 3-13 3.2-3 Nusselt Number Comparison for Eckert and Diaguila Test 3 . . . . . . . . . . . . . . . . . 3-14 3.2-4 Nusselt Number Comparison for Eckert and Diaguila Test 4 '. . . . . . . . . . . . . . . . 3- 15 3.2-5 Nusselt Number Comparison for Eckert and Diaguila Test 5 . . . . . . . . . . . . . . . . . 3-16 3.2-6 Nusselt Number Comparison for Ecke:t and Diaguila Test 6 . . . . . . . . . . . . . . . . 3- 17
' 3.2 7 . Nusselt Number Comparison for Eckert and Diaguila Test 7... . . . . . . . . . . . . . . . . 3-18 3.2-8 Nusselt Number Comparison for Eckert and Diaguila Test 8 ...............3-19 3.2-9 Nusselt Number Comparison for Eckert and Diaguila Test 9. . . .............. 3-20 3.2-10 Nusselt Number Comparison for Eckert and Diaguila Test 10 . . . ............ 3-21 3.2-11 Comparison of Predicted-to-Measured Nusselt Numbers for the Eckert and Diaguila Tests . . . . . . . . . . . . . . . . .... .............. 3-22 3.3 1 Nusselt Number Comparison for Siegel and Norris Test 1. . ..... .......... 3-25 3.3-2 Nusselt Number Comparison for Siegel and Norris Test 2 . . . . . . . . . . . . . . . . . . . 3-26 3.3-3 Nusselt Number Comparison for Siegel and Norris Test 3 . . . . . . . . . ......... 3-27 3.3-4 Nusselt Number Comparison for Siegel and Norris Test 4 . . . . . . . . . . . . . . . . . . . 3-28 3.3-5 Nusselt Number Comparison for Siegel and Norris Test 5 . . . . . . . . . . . . . . . . . . 3 29 3.3-6 Nusselt Number Comparison for Siegel and Norris Test 6. . . . . . . . . . . . . . . . . 3-30 3.3-7 Nusselt Number Comparison for Siegel and Norris Test 7 . . ................ 3-31 3.3-8 Nusselt Number Comparison for Siegel and Norris Test 8 . . . . ....... . . . . . . 3-32 3.3-9 Comparison of Predicted-to-Measured Nusselt Numbers for the Siegel and Norris Tests . ....... ... .. . ................ 3-33 i
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LIST OF FIGURES (Continued) flEILrs .T.111s Eass
' 3.4-1 : Heat Transfer Data for the Dr; Mat Plate Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 3-35 3.4-2 Comparison of Pmdicted-to-Measured Nusselt Numbers for the Westinghouse Dry Flat Plate Tests .............................3-36 3.5-1 Comparison of Predicted-to-Measured Nusselt Numbers for the Westinghouse Large-Scale Test- ...............................3-40
'3.6-1 Calculated Steam Partial Pressure Distribution for a Typical
' Gilliland and Sherwood Evaporation Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-46 3.6 Comparison of Predicted-to-Measured Evaporation Rates for the Gilliland and Sherwood Evaporation Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-47 3.7-1 Bulk-to-Film Steam Partial Pressure Differences from Selected
' Westinghouse Flat Plate Evaporation Tests . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 3-50 3.7-2 Comparison of Predicted-to-Measured Sherwood Numbers for the Westinghouse Flat Plate Evaporation Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.7-3 Mass Transfer Data for the Westinghouse Wet Flat Pla'e Tests . . . . . . . . . . . . . . . 3-52 3.8-1 Bulk-to-Film Steam Partial Pressure Difference Variation Over Channe!-Length from Selected Wisconsin Condensation Tests '. . . . . . . . . . . . . . . . 3-57 3.8-2 The Effect of Surface Inclination on the Predicted-to-Measured Sherwood Number Ratio for the' Wisconsin Condensation Tests . . . . . . . . . . . . . . . 3 58 3.8-3 The Effect of Reynolds Number on the Predicted-to-Measured
- Sherwood Number Ratio for the Wisconsin Condensation Tests . . . . . . . . . . . . . . 3 -5 9 3.8-4 The Effect of Steam Concentration on the Predicted-to-Measured Sherwood Number Ratio for the Wisconsin Condensation Tests . . . . . . . . . . . . . . . 3-60 3.8-5 'Ihe Effect of Heat Flux on the Predicted-to-Measured Sherwood Number Ratio for theWisconsin Condensation Tests . . . . . . . . . . . . . . . . . . . . . . . 3-61 3.8-6 Mass Transfer Data for the Wisconsin Condensation Tests . . . . . . . . . . . . . . . . . . 3-62 3.9-1 Predicted to-Measured Condensation Sherwood Number Ratio for the Westinghouse Large-Scale Tests . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-66 3.9-2 The Effect of Heat Flux on the Predicted-to-Measured Condensation Sherwood Number Ratio for the Westinghouse Large-Scale Tests . . . . . . . . . . . . . 3-67 3.9-3 Comparison of Predicted-to-Measured Sherwood Numbers for the Westinghouse Large-Scale Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-68 3.9-4 Condensation Mass Transfer Data for the Westinghouse Large-Scale Tests ..............................................3-69 3.9-5 Predicted-to-Measured Sherwood Number Ratios for the MSLB Large-Scale Tests . . . . . . . . . . . . ..............................3-70 3.10 Data from the Wisconsin and Chun and Seban Tests Compared to the Chun and Seban Wavy Laminar and Turbulent Correlations . . . . . . . . . . . . . . . 3-72 OMO40w.non:Ib-080798 Revision 2 vii Apnl1998
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LIST OF FIGURES (Continued)
Title P.aage
/ Egy.re 4.1 -1 ne Effect of Reynolds Number on the Predicted-to-Measured Nusselt 4-3 Number Ratio for Convection Heat Transfer in a Channel . . . . . . . . . . . . . . . . . . .
4.1-2 The Effect of Grashof Number on the Predicted-to-Measured Nusselt 4-4 Number Ratio for Convection Heat Transfer in a Channel . . . . . . . . . . . . . . . . . . .
4.2-1 The Effect of Reynolds Number on the Predicted-to-Measured Sherwood.
Number Ratio for Evaporation .................................... . 4-6 4.2-2 The Effect of Grashof Number on the Predicted-to-Measured Sherwood Number Ratio for Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7 4.2-3 De Effect of Steam Concentration on the Predicted-to-Measured Sherwood Number Ratio for Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8 4.3-1 The Effect of Reynolds Number on the Predicted-to-Measured Sherwood Number Ratio for Condensation Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . 4- 10 4.3-2 The Effect of Dimensionless Density Difference on Predicted-to-Measured Sherwood Number Ratio for Condensation ...... ............................. 4-11 4.3-3 The Effect of Steam Concentration on the Predicted-to-Measured Sherwood Number 4- 12 Ratio for Condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Revrion 2 oM040w.non:lt9040798 . . .
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SUMMARY
The AP600 PIRT@ and scaling analysisW show' that condensation inside containment and evaporation outside containment are the dominant high importance transpon phenomena for calculating containment pressure during design basis accidents (DBA). Heat transfer inside and outside containment and conduction'through the liquid film were identified to be low-to-moderate importance,
. but require modeling correlations since they are included in the evaluation model.
Section 2 of this report describes the heat and mass transfer correlations selected for modeling heat transfer to and from the AP600 steel containment shell. De McAdamsW free convection and ColburnW forced convection heat transfer cormlations were selected for use. An approximate method recommended by Churchill @ was implemented to combine the free and forced convection correlations in the mixed convection regime. . A lower limit on the mixed convection correlation for assisting free and forced flows was selected based on work by Eckert and Diaguila*. The result is a single heat
- transfer correlation that reduces to free convection values at low Reynolds numbers, forced convection values at low Grashof numbers, and a combination of the two in mixed convection. De mass transfer correlation is derived from the Nusselt number by the heat and mass transfer analogy. The Chun and SebanW correlations for wavy laminar and turbulent conduction heat transfer were selected for both condensing and evaporating liquid films.
1 Heat and mass transfer data from individual data sets were compared to the analytical correlations in Section 3. The mean and standard deviation for each comparison was calculated and presented.
The individual data sets were combined and compared to the respective correlations for heat transfer in Section 4.1, for evaporation mass transfer in Section 4.2, and for condensation mass transfer in Section 4.3. Factors are determined in Section 4.5 that make the analytical mass transfer correlations from Section 2 into bounding correlations for evaporation and condensation. The range of dimensionless groups that characterize AP600 operation are shown to be within the range of the
- measured test parameters.
Test measurement errors were estimated and presented and the multipliers that make the heat and mass transfer correlations bound the test data are defined.
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! ~ 1 4- 1 INTRODUCTION l
The AP600 plant design utilizes a passive containment cooling system (PCS) to transfer heat from the containment shell to the environment following an accident. The AP600 PCS is designed to remove I
sufficient heat from containment during the limiting DBA to maintain containment pressure below the design limit. Reference i provides an overview of PCS design and operation (Section 1.3) and shows the containment systems and structures (Section 3.2).
Heat is removed from the containment atmosphere by condensation, radiation, and convective heat transfer to the free surface of the liquid film. The heat is conducted through the liquid film and shell
. and rejected to the atmosphere on the outside of containment. Air from the environment flows via natural draft cooling through the annulus region between the shield building and containment shell. A baffle divides the annulus into separate downcomer and riser regions. Water is applied to the exterior surface of the containmer t shell for evaporative cooling. Heat rejection from the shell to the atmosphere is by convection to the buoyant cooling air, radiation to the baffle, and evaporation of the extemal cooling film to the cooling air.
l The PIRW) and scaling analysis (2) show condensation and evaporation are the dominant heat transfer mechanisms for the AP600. Constitutive relationships are needed to calculate heat and mass transfer-to the condensing film inside containment, heat transfer through the condensed and evaporating films, evaporation and heat transfer from the external film, and heat transfer from the baffle to the riser and downcomer.
- An upper range of operating parameters was calculated for the AP600 heat and mass transfer
. correlations in the scaling analysis (2) The parameters, listed in Table 1-1, are those that should be covered by the range of the test parameters. The correlations that include these operating parameters are presented and discussed in Section 2 and the range of test parameters is summarized in Section 4.
L The parameters are defined in Section 6,' Nomenclature.
This report describes the correlations selected to model heat and mass transfer from the AP600 -
l containment and provides comparisons with test data to validate the use of these correlations.
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a oWMOw.non:lb4M0798 Revino a
I TABLE 11 OPERATING RANGE FOR AP600 HEAT AND MASS TRANSFER PARAMETERS Correlation Parameter AP600 Range Internal Free Convection: Ap/p < 0.401 Heat Transfer and Condensation Mass Transfer Sc ~ 0.52 i
External Mixed Convection: Red < 189,000 (Riser) !
< 151,000 (Downcomer)
Heat Transfer and Evaporation Mass < 282,000 (Chimney)
Transfer 9 Grd < l.2 x 10 (Riser)
< 6.2 x 10'(Downcomer)
< 2.1 x 1012 (Chimney)
Pr - 0.72 Sc - 0.52 Liquid Film Heat Transfer Re < 4000 Pr 1.5 to 3.0 l
u:WN0w.non:lb-040798 Revision 2 1-2 April 1998 .
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2 ANALYTICAL BASES FOR THE IIEAT AND MASS TRANSFER CORRELATIONS 1 2.1 Heat Transfer in the Annulus Region The flow regime for turbulent convective heat transfer is typically qualified as either free, forced, or mixed. The combination of free and forced convection in the mixed regime is either assisting j' (i.e., they work in the same direction, as in upward flow in a hot pipe) or opposed (i.e., they work against each other, as in downward flow in a hot pipe). Operating points for the Grashof and Reynolds numbers are calculated in the scaling analysis (2) for the PCS air flow path (downcomer, riser, and chimney) and plotted on a Metais and Eckert(8) plot to determine the heat transfer regime.
The results are shown in Figure 2.1-1. The riser and downcomer operate in forced convection and the chimney operates in mixed convection. He convective heat transfer in the AP600 annulus, shown in Figure 2.1-1, is turbulent rather than laminar, since the Reynolds numbers are all greater than 3000(8) .
Based on a review of the literature, the turbulent free convection heat transfer correlation for gas mixtures has the form Nu = C (GrPr)N, with the value of C varying between 0.09 and 0.15, and the )
value of N varying between 0.3 and 0.4. The McAdams(3) correlation with C = 0.13 and N = 1/3, was selected for calculating turbulent free convection heat transfer in the annulus:
Nug,, = 0.13(Grd Pr)1/3 (g) l l
l Dis correlation is widely used to calculate turbulent free convection heat transfer from both vertical and inclined surfaces with either constant temperature or constant heat flux boundary conditions. The hydraulic diameter is the characteristic length in the Grashof and Nusselt numbers. The experimental work of Vliet(9) shows the full gravitational acceleration should be used to evaluate the Grashof 1 number, not just the vector component parallel to the plate.
l l
l OMG40w.rion Ib-(M0798 e 1st
1.0E + 06 -
Wsmiser
- Forced Convection . Scaling ~~~
~T Turbulent Flow / m-
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~
a s 1.0E +05 ,, , ,
Downcorner- . . ,
- Scaling E'-~
N -a
/ /
7 e 1.0E + 04 -
e Chirnney cc -
,e f 56siing.
/
/
[ Mixed Convection . _ _
Turbulent flow 1.0E + 03 / Free Convection
/
/ Turbulent Flow
/
/
1.0E + 02 ,,o".. " #. ." >>" ". . " "u" . > ".. ""'"i"'
1.0E + 03 .1 ".0 E + 0 5"...1.0E+07 1.0E + 09 " "" ' '.0 1 E + 1 1 1.0E +04 1.0E +06 1.0E +08 1.0E + 10 1.0E + 12 Ra D/L Figure 2.1 1 Metais and Eckert Plot Showing the Downcomer, Riser, and Chimney Heat Transfer Regimes owuow.non: b4wo79s Re g ,
The ColbumH) correlation was selected for calculating turbulent forced convection heat transfer in the annutur.:
l Nurore = 0.023Re[Pr '3 (2)
H The Colbum ) correlation is applicable to both constant temperature and constant heat flux boundary conditions for fully-developed flow in channels. The correlation is widely used to calculate turbulent forced convection heat transfer in long tubes rnd ducts. The hydraulic diameter is the characteristic length in the Reynolds and Nusselt numbers.
A length or distance dependent multiplier can be used to account for the increase in forced convection heat transfer as the boundary layer develops at the entrance of a heated channel. This is an important consideration when modeling heat transfer in short channels. The entrance-effect multiplier is described in more detail in Section 2.2.
A method for combining separate free and forced convection heat transfer correlations into a single correlation that covers free, mixed, and forced convection was recommended by Churchill 0 ) For opposed free and forced convection:
3 Nu = (Nu ff,, + Nufore)I'3 (3) and for assisting free and forced convection, Nuc is the larger of the following three expressions:
abs (Nuf,,,- Nufore)- ; Nu%, ; (4) 0.75Nufore The lower limit in the latter equation, which prevents the value of Nu c from going to zero when Nuf,,,
and Nufore are equal, comes from Eckert and DiaguilaW .
The opposed mixed convection correlation, Equation (3), is used for the downcomer and chimney.
Under opposed convection (downflow along a heated surface or upflow along a cooled surface), the mixed convection correlation increases the value of the predicted Nu number over the value predicted using either the free or forced convection correlations alone. The opposed mixed convection correlation is shown in Figure 2.1-2.
The outside surface of the containment shell is expected to operate in assisted convection (upflow along a heated surface or downflow along a cooled surface) during a DBA event. The assisted mixed convection correlation, Equation (4), shown in Figure 2.1-3 is asymptotic to both the individual free i oM040w.non:ltMM0798 Revision 2 l 2-3 Apnl 1998
4 1000 f
4 A a : : 4 : :
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s.
e : : : e : .e-e# *,s
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,, : : . : : .- J ..
i t '" ' ;
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i
)
i t
10 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+06 1.00E+09 1.00E+10 1.00E+11 1.00E+12 Gr4 i-+- RE=50000 -e- F.E=100000 -*- RE=1500001 i
A ,
l Figure 2.1-2 Opposed Convection Nu-d as a Function of Gr d for Various Re-d oMGlow.non:ib-040798 g,yg,,,, 2 2-4 Apni i998
.. a
1 4
t 9
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l l
1 l
1000 e
i j
- & =
- . s s = = .--s
. . = = = n-y f
a e : : : e /- l
/
- f100 l
i i
10 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07 1.00E+08 1.00E+00 100E+10 1.00E+11 1.00E+12 Gr<f I
j + RE=50000 - e - RE=100000 -e-- RE=150000 l l
l Figure 2.13 Assisted Mixed Convection Nu-d as a Function of Gr-d for Various Re-d oM040w.nowIb-040798 Revision 2 2-5 Apnl lW8 l
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and forced convection correlations, and penalizes heat transfer when free and forced convection are of 1 about the same magnitude.
~
- Equations 3 and 4 are asymptotic to both the individual free and forced convection correlations.
Consequently, it is unnecessary ,to a priori choose whether the heat transfer regime is free, forced, or -
mixed when Equation 3 or 4 is used. -
'As the angles of inclination approach horizontal, the assisting and opposed convection heat transfer coefficients should become equal. Although the correlations used for AP600 do not provide this, it is addressed for AP600 as follows:
- - Only free convection is assumed inside containment, so the definition of mixed convection is not relevant inside containment,
'= The downcomer and chimney have too little horizontal surface area and too little heat and mass transfer to be a concern.-
- Below the first water distribution weir on the containment dome, the slope is greater than 30*
so opposed / assisting are well defined. Above the first weir, the liquid film is subcooled. With little or no evaporation, and the surface area is less than 4 percent of the total shell area, so shallow slopes are not a significant concern for the external containment shell.
2.2: Entrance Effects The heat transfer coefficient at the entrance to a heated channel is significantly higher than the fully developed value predicted by the ColburnW forced convection heat transfer correlation. The increase in heat transfer at the entrance is attributed to the thinness of the boundary layer that develops with
- distance from the entrance. The entrance effect is important for modeling heat transfer in short s channels, so is used for all the test data comparisons in this report. Since the net entrancc effect on the long AP600 riser channel is only a small increase in heat transfer, it is recommended that entrance-effect multipliers may reasonably be neglected for AP600 licensing calculations.
The entrance-effect correlation and coefficients used m tr.is report are those recommended by Boelter.
. Young, and Iverson(30)-
b =1 +F A 3 (5) h, L oM040w.non:lb-040798 Revision 2 2-6 Apnl1998
o where:
- h. = the fully-developed heat transfer coefficient calculated from the ColburnW correlation hm = the mean or length-average heat transfer coefficient over length L Fj = a geometry-dependent constant from Reference 7 For step-wise calculations up a channel, an equation is needed that gives a length-average heat transfer coefficient between step boundaries xi and x2. Given an equation for h(x), the average value of h on the interval (x3 x2) IS:
l X2 fX I h(x)dx
=
hx,, x2 (6) x2 - X1 i
Analytically, E x,,,, cannot be derived from the above definition over the interval (0, L), since the equation produces a singularity when this is attempted. However, a modest change to the exponent results in: I 3
h x,,x2 d(xj -x '3) i
=1+F i (7)
- h. L 3(X2 - X1) a form that has the same average over length L, but with slightly lower values for small values of x, and with slightly higher values for higher values of x.
A Nusselt number multiplier, M, is defined with Equation 7 as M =xth , x2* . This multiplier increases the forced convection component of the mixed convection heat transfer coefficient when entrance effects are included. Entrance effects are not appropriate for, and are not applied to, free convection or to the free convection portion of the mixed convection heat transfer correlations.
The heat and mass transfer correlations calculated with entrance effects are compared to eight data sets in Sections 3.1 to 3.8. The comparisons show the heat or mass transfer coefficients (as represented by the Nusselt and Sherwood numbers) are underpredicted by 2 to 14 percent in six of the data sets, overpredicted by 3 percent in one (Eckert and Diaguila*, Section 3.2), and overpredicted by 18 percent in one (Hugot dataO U, Section 3.1). The Hugot overprediction reduces to 10 percent if heat j transfer at x/dh < l.0 is not included in the comparisons. The multipliers become large and increasingly uncertain for x/dh< 1.0. These comparisons show that overall, the entrance-effect multipliers improve the agreement between the test data and the analytical heat or mass transfer predictions.
The AP600 riser channel differs from the test geometries due to the 6-foot well, or tuming region at oM040w.non:Ib4 MOM 8 P.evision 2 2-7 Arni 1998 i
the bottom of the baffle. For modeling simplicity it is desirable to use a fully-developed heat transfer
, coefficient over the full channel height.' The following subsections show the use of a fully-developed heat transfer coefficient over the full riser height is conservative. The calculations show the heat ]
i transfer decrease (relative to fully-developed heat transfer) is more than offset by the heat' transfer increase due to neglecting the entrance effect in the channel above the well.' The geometric features of <
the well region and riser channel are shown in Figure 2.1-4.
- 2.2.1 Heat lSansfer in the Well Region Below the Bame he annular duct created by the baffle for the AP600 starts 6 feet above the bottom of an annular "well." This well is 4.5 feet wide and is heated on the inside surface. . In the AP600 evaluation model it is assumed, for simplicity, that the forced convection heat transfer correlations used in the annular region can be applied within this region as well. It is more realistic to assume a free convection heat transfer relationship on the heated containment shell side of the well.
Although the upper half of the 6-foot height may undergo transition to turbulent free convection, the laminar free convection correlation predicts lower heat transfer coefficients and is used. De effect of using forced convection in the 6-foot well is evaluated by comparing the total heat transfer calculated with laminar-free convection in the well to the total heat transfer calculated with forced convection everywhere.
The empirical formula of McAdams(3) was chosen for the laminar free convection mean Nusselt
. number:
Nii = 0.555(Rax )l'4 (8)
The Nusselt number for forced flow convection is given by the Colburn(4) relationship:
4 Nu = 0.023Re /5Pr I'3 (9)
Assuming the active length of the annulus above the baffle is 90 feet, then the active heat transfer length is 6 feet. . The fractional decrease in total heat transfer over the 96-foot height due to free convection in the 6-foot well region is equal to the factor $ determined by length-weighting.
Equations (8) and (9):
6 Ra,3'4 1 2(.555) (10)
$ = 96 6(.023) Re 4/5p,1/12 s
oMO40w. soft:1b-040798 i
l 1
l Chimney L
Weir # h I
( >-.- Containment Riser -
--S Shell -
Downcomer - --O l
jl Baffle 96' il Shield Building l
Annular Channel Entrance 3 l
Well h "
Region 6' u
-~ 4.5' ~
Figure 2.1-4 PCS Air Flow Path Features owuow.non::b-oxn9s 9 j ye ,s7,n,j
Equation (10) was evaluated for both wet and dry containment surfaces at temperatures between 125* and 205 F for annular flow velocities of 1,7, and 20 ft/sec. The density difference in the Grashof number was taken between dry air at ll5*F and saturated vapor / air mixtures at the assumed surface temperature for the wet surface, and between dry air and dry air at the surface temperature for the dry surface.
Calculations show there is very little change in the value of $ with surface temperature or with the assumption of wet or dry surface conditions. At an annulus velocity of I ft/sec, & is negative, indicating that the free convection heat transfer coefficient is greater than for forced convection. There is very little difference between $ values at 7 or 20 ft/sec with the greatest value of 0.056 occurring for the 20 ft/sec velocity at a dry surface temperature of 125 F. Most of the $ values are in the 0.03 to 0.04 range. The maximum effect is a 5.6 percent reduction in the net heat transfer from the shell due to the assumed laminar heat transfer below the baffle. As shown in the next section, this heat transfer reduction is less than the heat transfer increase due to the entrance effect.
2.2.2 Entrance Effects in the Riser Annulus The heat transfer enhancement due to developing thermal profiles is based on eigenvalue solutions from Hatton and Quarmby(12) for the developing thermal distribution within a hydrodynamically
. developed flow in an annulus. While the analytical solutions are quite complex, charts have been presented for enhanced heat transfer for Reynolds numbers of 7,100,73,600, and 495,000 at Prandtl numbers of 0.1,1.0, and 10.0. The AP600 Prandtl number is very nearly unity, and the riser Reynolds
. number ramps to 189,000. For reference, a velocity of 7 ft/sec yields a Reynolds number of about 70,000.
An empirical fit of Hatton and Quarmby's(12) curves for a constant heat flux Nusselt number, the condition giving the least heat transfer enhancement at a Prandtl number of 1.0, and a Reynolds number of 73,600, gives a ratio of the Nusselt number to that for fully-developed flow:
Nu(x/dh)
= 1.4667 (_x ) .1126 (j g)
Nu o dh The integration of Equation (11) between x = 0.0 and x/dh= 30, the position of intersection between Equation (11), and the fully developed Nusselt number yields:
l 1
Nii = 1.147Nu o (12) indicating that, on the average, the heat transfer over the first 60 feet of the annulus will exceed the fully-developed value by 14.7 percent. The average heat transfer coefficient increase over the 96-foot oMo40wmn:Ib-040798 Re isio
l length is 7.9 percent. The same calculation for the Reynolds number of 7,096 develops a heat transfer increase of 8.7 percent, and at Re = 495,000 yields a 10.8 percent increase. The reason for the l increase at the higher Reynolds number is that the thermal profile does not become fully developed in l
90 feet. l 2.2.3 Conclusions The heat transfer enhancement of 8 to 11 percent due to the entrance effect, more than offsets the heat transfer degradation of approximately 6 percent due to free convection in the well. Both deficit and enhancement calculations are conservative for the following reasons:
= The presence of a turbulent eddy within the well region will disrupt the free convection boundary layer and increase the heat transfer
- Any deviation of the velocity profile, from that for fully-developed turbulent conditions at the entrance to the annulus will also increase the heat transfer.
The calculations show it is conservative to neglect the free convection below the baffle and the entrance effects in the AP600 riser channel, and simply use a heat transfer correlation for fully-developed turbulent flow over the full height from the bottom of the well to the first weir.
2.3 Heat Transfer Inside Containment Heat is transferred from the containment atmosphere to the containment inner shell surface by condensation, radiation, and convection. The AP600 containment calculations assume condensation and convective heat transfer takes place at the outer surface of a thin liquid film that develops on the inside surface of the containment vessel. The liquid film provides a relatively small, additional resistance to heat transfer from the containment atmosphere to the wall. Heat transfer through the liquid film is characterized by the film Reynolds and Prandtl numbers, and is discussed in Section 2.4.
The inside of the containment shell is expected to experience a high velocity flow of steam and air during the main steamline break (MSLB) event and the blowdown phase of a large loss-of-coolant accident (LOCA) event as the break jet vigorously circulates the gas (Ref. 2, Section 6.5). This indicates that heat and mass transfer during this period are turbulent forced or mixed convection. After the LOCA blowdown is complete, the atmosphere is circulated less vigorously and the velocity of the steam and air flowing along the inside surface of the containment shell is lower. This indicates turbulent free convection heat and mass transfer after blowdown. However, the inside of c,)ntainment is conservatively modeled using turbulent free convection throughout both transients. Section 3.9 presents data that show a significant increase in the mass transfer for a high kinetic energy source relative to free convection mass transfer.
The height-based Grashof number representing the lower limit for turbulent free convection heat o$4040w.non. Ib-040798 Revi
1 I
transfer is approximately'1010.4 After the first.few seconds of the transient, the height-based Grashof number is greater than 1010 over all but the lower 3 feet or less of the interior shell surface. Since the :
turbulent free convection heat transfer correlation underpredicts laminar free convection heat transfer, its use is conservative over the lower 3 feet.
The'McAdams(3) correlation, was selected for calculating turbulent free convection heat transfer inside containment. The correlation can be written as a function of local properties:
0 IU h hee = 0.13I(GrtPr)lO = 0.13 Pr (13)
L (v2 fg)tn p[. P_]IU De term (Ap/p) is the difference between the bulk density and the surface density, divided by the bulk -
2 density. De term (v fg)ta has the units of length and is used as discussed in Reference 2, subsection 4.3.1. Note that "g" is not reduced by the sine of the' slope from horizontal, consistent with Vliet(9) .
2.4 Liquid Film The AP600 containment calculations assume the liquid film is a distinct control volume with mass transfer, convection heat transfer, and radiation heat transfer into the free surface, and conduction to the solid surface. Heat is transferred through the thin films on both the inside and outside of the containment'shell. The Chun and Seban(7) correlation is shown in Section 3.10 to model both wavy laminar and turbulent heat transfer across the film. For wavy laminar films:.
Nu = 0.822 Re 4 22 (34)
For turbulent films (Re > 5800 Pr-1.06)
Nu = 0.0038 Re 0A0 Pr08 (15)
Note that the gravitational acceleration is multiplied by the sine of the slope above horizontal for liquid film calculations.
2.5 Mass Transfer Inside and Outside Containment l
J Convective mass transfer is a result of a concentration gradient between a flowing steam-air gas
- mixture and a surface. ' The steam concentration gradient is approximated as the difference in steam partial pressure between the bulk gas and liquid surface. Condensation occurs when the bulk gas steam concentration is greater than the concentration at the surface of the liquid. Evaporation occurs
. when the bulk gas steam concentration is less than the concentration at the surface of the liquid.
Kreith(13) defined th'e steam mass flux between the surface and the bulk gas to be:
oA4040w.non:lb-040798 Re sio
- _ _ _ . _ - . _ - - - - )
i 9
l rh,//1, = kg Mstm(Pstm.srf- Pitm. bulk) (16)
- The mass transfer coefficient, k g, can be predicted using _ empirical correlations similar to those for the convective heat transfer coefficient, he . He Sherwood number for mass transfer is analogous to the
- Nusselt number for heat transfer, and is derived from the Nusselt number using the heat and mass transfer analogy:
Sh = (17)
(Pr/Sc)30
%e mass transfer coefficient for gas-phase mass transfer is defined:
b k =
(18) 8 RTP g "k (W)l0 P g si a term that accounts for the change in heat transfer at high mass transfer rates. The Nusselt number is based on the heat transfer correlation evaluated at the boundary layer temperature. The properties in the Prandtl and Schmidt numbers are evaluated at the boundary layer temperature. I Equation 16 is used to calculate both condensation and evaporation mass transfer. Boundary layer
. properties are evaluated at the mean of the bulk and surface conditions.
2.6 Thermal Properties All of the thermal properties used in the heat and mass transfer correlations are represented by correlations to an estimated accuracy of 8 percent, with the exception of the air-steam diffusion coefficient. The condensation and evaporation mass transfer rates calculated for AP600 are linearly proportional to the air steam diffusion coefficient. The diffusion coefficient correlation that is used for all AP600 and test comparison mass transfer rates, overpredicts the measured diffusion data from the literature, and hence, overpredicts the mass transfer rates by approximately 10 percent over the AP600 containment temperature range of approximately 100 to 300 F. However, as noted in the following discussion, the mass transfer bias factors offset the diffusion correlation bias.
The diffusion coefficient correlation is from Eckert and Drake", Table B-9, p. 787. When the units are converted to English units, the Eckert and Drake equation is:
I' D' = 0.892 ft 2/hr (19)
, P , ,460.8, owwow.non:Iba0798 _
Re i,si,o
i 1
. where P is the total pressure in psia, and T is the gas temperature in degrees Rankine.
-: The Ecken and Drake (34) correlation, Equation 19 -is shown as the solid line in Figure 2.6-I.
compared to three data sets: ' Kestin(15) Rohsenow(16) and Eckert and Drake (34), The dotted line in Figure 2.6-1, is 0.9 times Equation 19, and appears to be a best-estimate fit to the data. Consequently, l Equation 19 overpredicts the air-steam diffusion coefficient by approximately 10 percent.
Equation 19 and the theoretical development presented in Bird, Stewart and Lightfoot(37) show the ' !
^
diffusion coefficient is proportional to 1/P. Although data were not included at higher pressures to support 1/P, the references agree on the expected 1/P pressure dependence. The correlations all give the temperature dependence to be T", where n is greater than 1.5. The theoretical development of Bird recommends temperature exponents of 2.334 for water vapor diffusing through a non-polar gas, and 1.823 for two non-polar gasses (water is a polar gas and air is non-polar). However, the Eckert :
- and Drake (34) value of n = 1.81 in Equation 19 appears to represent the measured temperature dependence very well. Consequently, Equation 19 properly represents the diffusion coefficient sensitivity to temperature change.
Equation 19 was used in all of the AP600 PCS analytical work, including evaluation of separate.
effects tests'(SETS) (Sections 3.6 to 3.9). Consequently, the mass transfer coefficient bias factors
' (defined in Section 4.5) reduce the (over) predicted mass transfer coefficients to values that lower-bound the measured coefficient data.
. oM(mow.non;tb-040798 Revision 2 2-14 ^P" '998
7 .
a.
a 4.5- - - - - - - - - - - - - - - - - - - - - - - --
- .e. - - - - - --
4- ~ ~ ~ - - ~ ~ ~ ~ ~ ~ ~ ~ ~ - - - - - - - - - ~ ~ -
- f*-~~~--
- ---- ---.Eckef! A Dm8e.Cgrew -----~~-
3.5- ,p' <~~* ~~-------
s 3- - - - - - - - - - - -
-- p ##. - - - - - - - - - - - -
........................................,W***s. I..m.......*............................<
p ...............................:..... .
1.5-'-~~~~~"...f**~~~~~--~~~----~~~~~~~~-~~~~----~~~
b 1-- t **:..- - - - - - - - - - ~ ~ ~ ~ ~ - - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ - - -
a 0.5- ---
mm %e' - - - - - - - - - - - - - - - - - -
C . . . . . . .
0 100 200 38 400 500 600 700 800 Temperature, Degrees F
= Kestin a Rhosenow a Eckert & Drake s
)
Figure 2.61 Comparison of Eckert and Drake Correlation to Measured Air. Steam Diffusion Coefficients at 14.7 psia oMNow.non:Ibol0798 Revinon 2
( 2-15 Apnl 1998
3 EXPERIMENTAL BASIS FOR THE HEAT AND MASS TRANSFER CORRELATIONS The experimental data used to validate the AP600 containment heat and mass transfer correlations are presented in this section. The analytical correlations for mixed convection heat transfer in channels, from Section 2.1, are compared to the data in Sections 3.1 through 3.5. The analytical correlations for condensation and evaporation mass transfer from Section 2.5 are compared to data in Sections 3.6 through 3.9. The correlations for liquid film heat transfer from Section 2.4 are compared to data in Section 3.10.
The validation of heat and mass tansfer correlations for the PCS air flow path uses test data fmm channel-type geometries. He Nusselt, Sherwood, Reynolds, and Grashof numbers for channel conelations are based on the channel hydmulic diameter. Data on heat and mass transfer inside the pressure vessel are correlated using (u2 j g)m as the length parameter in the Nusselt and Sherwood numbers.
The mean and standaid deviation is presented for each data set in Sections 3.1 to 3.9. Data sets are combined and further evaluated in Section 4.0. Error bars in the Westinghouse test are specified in Section 4.4 and shown on the figures in !. -:tions 3.4, 3.7, 3.8, and 3.9.
3.1 The Hugot Mixed Convection Hert Transfer Tests (ID Hugot(I U conducted heat transfer tests on a set of symmetrically heated, parallel, vertical, isothermal plates with closed sides. The channel width was 1.0 meter, the channel height was 3.3 m, and the plate separation distance was variable at 10 and 60 cm. The plate temperatures were varied between 40 and 160 C. Assisting mixed convection heat transfer for moderate Reynolds and Grashof numbers was validated by the test data.
He Hugot report (IU presented the local heat transfer coefficient, but did not report the air flow rate or velocity induced in the heated channel; therefore, it was necessary to use a computer model 'o calculate air flow rates as well as hear transfer. The tests were modeled using the EGOTHIC(10 code with nominal inputs. The test section was divided into 11 axial volumes. Because most of the rapid changes occur at the entrance, the first 10 volumes were each 1/15th of .he total volume; the last volume was 1/3 of the total volume. The code calculated the buoyancy-induced air velocity, air temperature, and heat transfer coefficient in each of the 11 volumes. The calculations assumed a combined entrance and exit form loss of 1.5. Since the air flow rate was calculated and the channel loss coefficient was estimated to be 1.5, the heat transfer calculation includes the effect of uncertainties on the air flow rate.
The Nusselt number, Nu, is defmed as Nu = hdh /k, where dh is the channel hydraulic diameter. The entrance-effect multipliers were calculated as described in Section 2.2 and are pre nted in Table 3.1-1.
The mixed convection Nusselt numbers were calculated as described in Section 2.1. The calculated Nusselt numbers for each of the five tests are compared with the test data as a function of dimensionless height in Figures 3.1-1 through 3.1-5. The rele. ant test parameters are presented in Table 3.1-2.
oM(M0w.l .non:Ib-040898 Re.ision 2 3-1 Apnl 1998
TABLE 3.1 1 ENTRANCE-EFFECT MULTIPLIERS FOR THE HUGOT HEAT TRANSFER TESTS Distance from bottom, ft 0.72 1.44 2.17 2.89 3.61 4.33 5.05 5.77 6.50 7.21 10.82 Multiplier for 5.539 2.049 1.723 1.569 1.476 1.414 1.368 1.333 1.305 1.292 1.224 dh= 2.46 ft.
Multiplier for 2.100 1.254 1.175 1.138 1.115 1.100 1.089 1.081 1.074 1.068 1.055 dh= 0.182 ft.
~
o:MO*0w-1.non:1t> 040798 Revision 2 3-2 Apnl 1998 l
'G 1, u,.
n' I'
l 800 500 I
400 l
J. '
l _
+
, e + + + + + + = - -
e +
100 0
0 1 2 3 4 5 h Height (X/d)
+ Test Data -W ProdL*on Figure 3.1-1 Nusselt Number Comparison for Hugot Test 1 (60 cm and 58'C) oAKM0w l.non:lb-(M0798 Revision 2 33 Apnl 1998
u i
r 600 500 400 I
l-1 e e + + + , . ; :
100
+
0 0 1 2 3 4 5 Dwnensionless Height (X/d)
- Test Data -W Predicton Figure 3.12 Nusselt Number Comparison for Hugot Test 2 (60 cm and 150.2*C) oMO60w l.non:Ib 040798 Reviuon 2 3-4 Apni 1998
____--_____-._-_____a
p- 1 I
l l
)
.. .00 -
)
400 T
t ha 1
1
, 200 e
100 *
- e , , e e e e +
0 0 5 -10 15 2C -
Dimensionless Height (X/d)
. Test Data -W Prodcton Figure 3.13 Nusselt Number Comparison for Hugot Test 3 (10 cm and 154.9'C)
I oM040w.t.non:Ib-040798 Revision 2 3-5 ^Pnl1998
l
.. e00 500 400 T
l l _
+
e 100 e.
- . e e 0
0 5 10 15 20 DWN*ionless Height (X/d) e Test Data -W Prediction Figure 3.1-4 Nusselt Number Comparison for Hugot Test 4 (10 cm and 89.1*C) ovo40w i.non:id-040798 ,
i
000 500 400 j -
1 -
- * * * * * * * , .. ~, .,
W 0
- O- 5 10 .15 20
% (X/d)
+ Test Data -W Prodcten i
t I
Figure 3.15 Nusselt Number Comparison for Hugot Test 5 (10 cm,60.9 C)
I oM040w.l.non:lb4)40798 3-7 fyi$$
TABLE 3.12 HUGOT MIXED CONVECTION HEAT TRANSFER TEST DATA Surface to Ambient Test Number Ild h AT ('C) Grd Range Red i 4.4 ~ 58.0 2.40 x 10' - 2.61 x 109 35400 9 9 2 4.4 150.2 3.31 x 10 - 3.65 x 10 42400 7
3 18.15 154.9 3.30 x 107 - 4.70 x 10 12900 7
4 18.15 89.1 3.25 x 107 - 4.45 x 10 12200 7
5 18.15 60.9 2.71 x 107 - 3.65 x 10 11000 A compilation of the predicted-to-measured Nusselt numbers for all five tests is shown in Figure 3.1-6.
The mean predicted-to-measured value is 1.179, and the standard deviation is 0.429. Both the mean .
and standard deviations are strongly affected by the relatively large predicted-to-measured Nusselt number ratios at the channel entrance. If only the first entrance value is removed from each data set, .
the mean falls to 1.095 and the standard deviation falls to 0.213.
. Except for the channel entrance, the predicted Nusselt numbers are close to the measured values for tests 1 and 2. These two tests had the highest Red numbers of the set and were performed with a gap width of 60 cm. The entrance-effect multiplier for the calculated forced convection heat transfer coefficient is height dependent, and has both a large value and a large uncertainty near the entrance.
The predicted Nusselt numbers are slightly higher than measured for tests 3 and 4. The overprediction is believed to be the result of laminar flow persisting to near mid-height at the lower Reynolds numbers. Since the AP600 external annulus operates in turbulent flow, tests 3 and 4 are not
. representative of AP600 conditions.
The predicted Nusselt numbers are lower than the measured values for test 5. Although the gap width is the same as tests 3 and 4, the trend in the Nusselt numbers was not the same. This test was performed at a relatively low temperature.
owxow.i.non:id.oso798 - negsi,og
-.A._
I 1
l 4
3.5 3
1 2 .5 1 ..
2 1.5 . .
+__...__.. : :
- y. ._ _ .
1 **...*tese . , , , ,
- * * + + . . . . .- . . . .
0.5 0
0 5 10 15 20 INmmwlonium Height dud)
. Data -Wn(1.179)
Figure 3.1-6 Comparison of Predicted to-Measured Nusselt Numbers for Hugot Tests 15 oMG40w.l.non:t b-040798 Revision 2 3-9 Apnl 1998
4 W
3.2 The Eckert and Diaguila Mixed Convection IIeat Transfer Tests Ecken and Diaguila(6) conducted heat transfer tests on a vertical tube that was 13.5-feet high with a 23.25-inch inside diameter. Inlet and outlet air pipes and dense screens (to assure a constant velocity) were located at each end. A 10-foot steam jacket supplied steam slightly superheated as the heat source. Sixteen condensation chambers collected and piped condensate to a station where the flow rate was measured and the local heat flux was determined. An air flow at approximately 80*F, at pressures from I atmosphere to 99 psia, was forced through the test section. Tests were conducted with forced flow in both the upward (assisting mixed convection) and downward (opposed mixed convection) direction. Thermocouples at the tube center and in the tube wall provided a temperature difference from which the local heat transfer coefficient could be determined. The test data were used to validate the mixed convection heat transfer correlation at prototypic Reynolds and Grashof numbers.
The Nusselt number, Nu, is defined as Nu = hdh /k, where dh is the hydraulic diameter. Entrance-effect multipliers were calculated as described in Section 2.2 and are presented in Table 3.2-1. The mixed convection Nusselt numbers were calculated as described in Section 2.1. The calculated Nusselt number for each of the ten assisting convection tests are compared with the measured data, and are shown as a function of the dimensionless height in Figures 3.2-1 through 3.2-10. The relevant test parameters are presented in Table 3.2-2.
TABLE 3.2-1 ENTRANCE-EFFECT MULTIPLIERS FOR THE ECKERT AND DIAGUILA HEAT TRANSFER TESTS Distance from bottom, ft 0.63 1.25 ! .88 1 2.50 3.13 3.75 4.38 5.00 5.63 6.25 6.88 7.50 8.13 8.75 9.38 10.0 Multiplier 2.89 1.44 1.30 1.24 1.20 1.17 1.15 1.14 1.13 1.12 1.11 1.10 1.10 1.09 1.09 1.08 for dh "
1.94 ft.
l t
l l
l l
l ammm ,_ , 9 y;gg l
l L
i l
L. ,
I TABLE 3.2 2 , 1 ECKERT AND DIAGUILA MIXED CONVECTION HEAT TRANSFER TEST DATA .
l Tect Number Grdh Range Red l
l I 6.9 x 10' - 1.1 x 1010 377000 2 6.9 x 109 - 1.1 x 10 10 180000 3 6.9 x 10' - 1.4 x 1010 100000 4 7.5 x 10' - 1.6 x 1010 36000 5 1.4 x 1030- 1.8 x 10 30 231000 6 1.3 x 1010- 2.5 x 10 10 134000 7 1.4 x 1010 3.7 x 1010 55000 8 3.5 x 1030- 5.1 x 10 10 314000 9 3.5 x 1030 - 5.5 x 10 10 ' 246000 10 3.4 x 1030- 7.2 x 10 30 77000 The predicted-to-measured Nusselt numbers for all ten tests are shown in Figure 3.2-11. The mean value is 1.028 with a standard deviation of 0.272. The Eckert and Diaguila(6) data showed'large, unexplained variations in the original report; thus, the standard deviation reported here is not >
)
excessive. However, the good agreement with the mean indicates that the significant trends are represented by the correlation. '
The calculated Nusselt numbers are about equal to or slightly higher than the measured values for
' cases with lower Reynolds numbers (tests 4,7, and 10). 'Ihe calculated Nusselt numbers decrease in comparison with the measured values as the Reynolds number is increased. The apparent trend of the Eckert and Diaguila(6) data with the Reynolds number may be due to the fact that the measur.:d ,
l centerline temperature is not the same as the bulk temperature, i.e., the difference between the bulk and centerline temperatures change as the flow develops away from the entrance. The data were scaled from figures in the referenced paper and this process may also have introduced some of the scatter.
oW50*.I.non:Ib4M0798 Revision 2 3 11 Apnl 1998
+
4
\
I U
1600 e
1400 1200 y1000 , ,
k e
- e ,
^'s :,
e e 800
- e
, 0 ;
800
- 0 g
200
+
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-Dunermonlees @ (XO) e Test Data -W Predete i
Figure 3.2-1 Nusselt Number Comparison for Eckert and Diaguila Test 1 owwow-i.non:ibao79s 3-12 38 8
.Y
I'
),
o j
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l I
l l
t 1000 soo soo 70o T eco .
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- 200 100 o
o- o.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Dwneneenlose Height QUD) ,
e Test Data -W Predeten l
Figure 3.2-2 Nusselt Number Comparison for Eckert and Diaguila Test 2 o:WM0w.l.non:It>O40798 Revision 2 3-13 Apnl 1998
i e
1 L
l 1
550 500 450 400 1
J. 250 e e
^
e e e ~-
e e
. 200 e e e e
150 100 50 0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Height (X/D) e Test Data -W Predetion
, Figure 3.2-3 Nusseh Number Comparison for Eckert and Diaguila Test 3 s-oM040w 1.norrib-040798 Raisi n 2 3~14 Apnl 1998
e 0
400 360 300
'N -
I,,, .
200 *
- 150 e
100 50 0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 h Heght (X/D) e Test Date -W Predation Figure 3.2 4 Nusselt Number Comparison for Eckert and Diaguila Test 4 oM040w 1.non:Itm798 Re ist
e e
1000 m
800
- e e
- e e 1- e e
-500 e 400
'300 200 100 0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Die Height 000) e Test Date -W Prodction Figure 3.2-5 Nusselt Number Comparison for Eckert and Diaguila Test 5
^
o:M040w 1.non:lb-040798 Revision 2 3-16 Apnl 1998
i r
l l
l j-
'i
(
soo 700 ]
eco i
i Soo 400
~ .- *
. i soo- * * !
aoo .
'100
! 0 0~ 0.5 .I 1.5 2 2.5 . 3 3.5 4 4.5 5 h Height (X/D) j .. . Tem om. -W Predcton i
i Figure 3.2-6 Nusselt Number Comparison for Eckert and Diaguila Test 6 o:WM0w 2.non:Ib4M0798 Revision 2 3-17 Apn11998
l i.-
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l l
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1 Figure 3.2-9 Nusselt Number Comparison for Eckert and Diaguila Test 9 0:M040w-2.non:Ib-040798 Revision 2 3-20 apni 1998
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3.3 The Siegel and Norris Mixed Convection Heat Transfer Tests (10 Siegel and Norris(IM conducted heat transfer tests on a set of symmetrically heated, parallel, vertical flat plate channels. The channel width was 4.417 feet, the channel height was 5.833 feet, and the plate separation distance ranged from 0.125 to 1.25 feet. A constant uniform heat flux of approximately 1100 Btu /hr-ft.2 was applied.
The effects of reduced air flow were also investigated by adding extensions to the bottom of the test !
section channel and successively decreasing the lateral area for flow into the test section. Only those tests that had the test section open at the bottom were examined for comparison. The tests generated l data that validated the assisting mixed convection heat transfer model for low Reynolds numbers and -
moderate Grashof numbers.
)
Since the air flow rate was not given, the tests were modeled using the WGOTHIC(30 code. The test section was divided into 11 axial volumes. Because the most rapid changes occurred at the entrance, the first ten volumes were each 1/15th of the total volume; the last volume was one-third of the total j volume. The code calculated the velocity, air temperature, and heat transfer coefficient in each of the 11 volumes. The effects of reduced air flow were analyzed by relating the flow area reduction in the test to an increase in the inlet loss coefficient. !
The Nusselt number, Nu, is defined as Nu = hdh /k, where dhis the channel hydraulic diameter. ]
Entrance-effect multipliers were calculated as described in Section 2.2 and are presented in Table 3.31. l The Nusselt number was calculated using the assisting mixed convection correlation described in Section 2.1. 'Ihe calculated Nusselt numbers for each of the eight tests are shown in Figure 3.3-1 through 3.3-8 as a function of the dimensionless length. The test parameters are shown in Table 3.3-2.
TABLE 3.31 ENTRANCE-EFFECT MULTIPLIERS FOR THE SIEGEL AND NORRIS IIEAT TRANSFER TESTS ,
1 Distance from bottom, ft !
0.39 0.78 1.17 1.56 1.94 2.33 2.72 3.11 3.50 3.89 5.83 Multiplier for 7.67 2.54 2.06 1.84 1.70 1.61 1.54 1.49 1.45 1.41 1.31 dh = l 949 ft-Multiplier for ! 80 2.11 1.76 1.60 1.50 1.44 1.39 1.35 1.32 1.30 1.22 dh= 1.401 ft.
Multiplier for 3.61 1 1,42 1.33 1.27 1.24 1.21 1.19 1.18 1.16 1.12 da= 0.761 ft Multiplier for 2.62 1.37 1.26 1.20 1.17 1.15 1.13 1.12 1.11 1.10 1.09 i
dh= 0.473 ft Multiplier for 1.83 1.19 1.13 1.10 1.09 1.08 1.07 1.06 1.06 1.05 1.04 dh= 0.243 ft 3.,, g; I
TABLE 3.3 2 SIEGEL AND NORRIS MIXED CONVECTION HEAT TRANSFER TEST DATA Test Number Ud h Air Temp. (*F) GrdPr Range Red Range 1 3.00 80.6 - 86.4 4.23 x 108 - 6.10 x 10 8 1.07 x 104 - 1.13 x 104 2 4.16 80.9 - 88.5 1.58 x 108 - 2.42 x 108 8.73 x 103 - 9.18 x 10 3 3 7.66 81.2 - 93.5 2.40 x 107 - 4.19 x 107 5.77 x 103 - 6.03 x 10' 4 12.33 81.5 - 99.4 4.40 x 106 - 1.05 x 107 4.01 x 103 - 4.18 x 10 3 5 24.00 82.6 - 114.6 6.43 x 105 - 1.48 x 106 2.20 x 103 - 2.28 x 103 7
6 12.33 81.5 - 100.3 5.42 x 106 1.17 x 10 3.82 x 103 - 3.98 x 103 7 12.33 82.1 - 107.6 6.43 x 106 - 1.17 x 107 2.76 x 103 2.89 x .0 3 8 12.33 83.4 - 123.4 6.70 x 106 - 1.29 x 107 1.65 x 103 1.73 x 103 The predicted-to-measured Nusselt numbers for all eight tests are shown in Figure 3.3-9. The mean predicted-to-measured value is 0.857 and the standard deviation is 0.0903.
As demonstrated in tests 1 through 5, the calculated Nusselt numbers match the measured data fairly well at lower values of Udh, but increasingly underpredict as the Ud h value increases. Tests 4,6,7, and 8 demonstrate the effect of reduced air flow (at constant Ud h) by increasing the channel loss coefficient from 1.5 to 35.6. The calculated Nusselt numbers increasingly underpredict the measured values as the air flow is reduced.
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3.4 The Westinghouse Dry Flat Plate Tests
De test section was a vertical,6-foot long, heated flat steel plate that had been coated with a highly wettable, inorganic-zine coating. A clear acrylic cover provided a channel 23 inches wide and 4 inches deep for the forced air flow. The plate temperature and air flow rates were varied for each test. The measured parameters for each test are shown in Table 3.4-1.
De Nusselt number, defined in terms of the channel hydraulic diameter, is used for the data comparison. A length-averaged, entrance-effect multiplier of 1.13 was calculated as described in Section 2.2. The mixed convection Nusselt number was calculated as described in Section 2.1. The data are compared with the mixed convection correlation and shown as a function of the Reynolds number in Figure 3.4-1. . Since these tests were forced convection-dominated, the results correlate well with the Reynolds number. The measured data are compared to the mixed convection Nusselt number correlation in Figure 3.4-2. The mean value is 0.983 with a standard deviation of 0.072.
TABLE 3.4-1 WESTINGHOUSE DRY FLAT PLATE TEST DATA a,b oM040w-2.non:t b-042298 Revision 2 3-34 April 1998
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Figure 3.4 2 Comparison of Predicted to-Measured Nusselt Number for the Westinghouse Dry Flat Plate Tests o:WO40w.2.non:lb-040798 Revision 2 3-36 Apal 1998
1 J3.5 The Westingbouse Large-Scale Dry External Heat Transfer Tests (21)
- A series of heat transfer tests was performed at the LST facility at the Westinghouse Science and Technology Center (21). The purpose was to compile data for developing and validating the analytical
. heat transfer models. Circumferentially-averaged, external heat transfer data were determined from the
- dry LST data.'.
Ve ,
De dry heat transfer tests were performed over a range of intema! test vessel pressures that bounded a: ; the AP600 containment design pressure to obtain heat transfer data at prototypic conditions, and to
. characterize heat transfer over a range of air cooling velocKes.
The LST facility is approximately a 1/8-scale of the AP600. The AP600 containment shell is modeled -
y by a 20-foot tail,15 foot diameter pressure vessel. The vessel contains air at I atmosphere when cold, and is supphed with 'steam at piessures up to 100 psig. Steam is injected in various source configurations to dernonstrate the effect of momentum, buoyancy, and direction on heat and mass transfer performance.
A plexiglass cylinder surrounds the vessel, simulating the baffle that forms the air cooling annulus.
Air flows upward through the annulus to cool the vessel, resulting in condensation of the steam inside
~t he vessel. . A fan is located at the top of the annular shell to achieve higher air velocities than can be achieved by natural convection.
Dermocouples are located on both the inner and outer surfaces of the vessel at various circumferential angles, at each of ten different elevations to measure the shell temperature and heat flux distribution.
Thermocouples are also located inside the vessel on a rake to measure the bulk gas temperature at various radial and vertical locations. The external cooling air temperature and velocity are measured at several locations in the annulus. The steam inlet perssure, temperature, and flow rate, and the
. crndensate temperature and flow rate are measured to characterize the total heat in and out of the vessel.
' Data that varied with time, angular position, and elevauon were collected for each test. Nusselt numbers were calculated from the data using measuied surface-to-bulk gas temperature and heat fluxes that were averaged over time and circumferentially-averaged at each measuring elevation. Bulk gas temperatures in the annulus were not measured at each elevation, where surface temperature and heat flux were measured, so the gas temperature was interpolated from values at the next higher and lower elevations.
. The steady-state, circumferentially-averaged heat transfer data from 14 of the 16 dry LSTs were used to define hydraulic diameter-based Nusselt number values. He Nusselt number values were compared-with predictions of the turbulent, mixed convection correlation as described in Sections 2.1. (Tests RC015 and RC016 were omitted from this comparison because the forced asymmetric annular air flow rate imposed for these tests affected the circumferential-averaging.) Entrance-effect multipliers cA4odow-3.non:Ib-040798 Reymon 2 3 37 Apni 1998
calculated as described in Section 2.2 are presented in Table 3.5-1. The ratio of the predicted-to-measu ed Nusselt numbers is shown as a function of dimensionless length from the bottom of the riser. Test parameters are presented in Table 3.5-2.
A compilation of the predicted-to-measured Nusselt numbers for all 14 tests is shown in Figure 3.51.
The average, predicted-to-measured values at each location and mean values over all locations are also shown. The mean value is 0.895 with a standard deviation of 0.122.
TABLE 3.5-1 ENTRANCE-EFFECT MULTIPLIERS FOR THE WESTINGHOUSE LARGE-SCALE DRY HEAT TRANSFER TESTS Distance from bottom, ft 2.76 5.!1 8.26 10.26 11.62 13.87 15.74 17.52 Multiplier for dh = 0.50 ft. 1.70 1.16 1.11 1.09 1.00 1.00 1.00 1.00 o:WO40w-3.non:Ib-(M0798 Revision 2 3-38 Apnl 1998
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Figure 3.51 Comparison of Predicted to-Measured Nusselt Numbers for the Westinghouse Large-Scale Tests oM040w 3.non:lb4M0798 Revision 2 3-40 Apni 1998
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r 3.6 The Gilliland and Sherwood Evaporation Tests (22)
Isothermal evaporation mass transfer rates were measured in a veitical pipe by Gilliland and Sherwood(22)- A water film was applied to the inside wall of the pipe and the evaporation rate was measured for both countercurrent and concurrent flow.
The test section was a ll7-cm long, vertical pipe with a 2.67-cm inside diameter. Calming sections were added at both ends of the test section. A falling liquid film covered the inside surface of the test section. The film flow rate was held constant in all tests at approximately 790 cc/ min while the air flow rate was varied.' De inlet air and liquid film temperatures were maintained within 3*C. He reported parameters for each test are shown in Table 3.6-1. Since the liquid and air temperatuits are nearly the same ' isothermal) in these tests, the evaporative mass transfer was almost entirely driven by the difference in partial pressure between the liquid film surface and bulk mixture.
Relatively low air flow rates, compared to the mass transfer rates, were used in these mass transfer tests. The lower air flow rates caused a large difference in the bulk steam partial pressure from inlet-to-outlet, as shown for a typical test in Figure 3.6-1, Because of the large change in the bulk air / steam ,
- mixture properties over the length of the test section, average properties could not be used to evaluate j the test data. A simple,' 10-cell FORTRAN model was developed to evaluate the test data.
The Nusselt and Sherwood numbers were defined in terms of the channel hydraulic iameter.
' Entrance-effect multipliers presented in Table 3.6-2 were calculated and used es described i:1 Section 2.2. De mixed convection Nusselt and Sherwood numbers were calculated as described in Sections 2.1 and 2.5. The predicted local evaporative mass flux was integrated and compared with the measured total evaporation rate. The predicted-to-measured total evaporation rate is shown as a function of the Reynolds number for all 71 tests in Figure 3.6-2. The mean value for all tests is 0.925 4 and the standard deviation is 0.072.
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TABLE 3.6-1 GILLILAND AND SHERWOOD EVAPORATION TEST DATA l Air Evap T,i, Top T,i, Bottom T ,,,,, Top T,,,,,-Entiom Pressure Flow Rate Test *C *C *C "C mm-Ilg g/ min ec/ min 1 30.8 27 31.1 26.1 770 250 3.8 3 29.6 27.9 29.8 27.8 772 243 3.6 5 32.1 25.8 32.5 24.9 777 125 1.6 l l
9 32.6 28.3 33.1 27.4 777 143 1.8 11 32.1 28.1 33 27.4 770 51 0.73 13 32.2 26.8 32.9 26.2 770 214 2.5 15 28.7 27.3 29.4 26.7 772 324 4.7 17 30 27.8 30.6 27.I 770 218 3.2 19 32.6 28.9 33.1 28.3 770 158 2.7 21 32.3 28.6 32.9 28.2 770 103 1.8 23 32.4 29.2 32.9 28.5 770 74 1.4 25 41.1 38.4 41.7 37.8 785 220 6.2 27 40.4 41.3 41.4 40.8 800 80 2.4 29 38.9 35.8 39.5 35.2 782 48 1.5 31 40.5 28 30.1 26.5 775 502 7.4 33
- t.4 37.2 42.6 36.6 777 111 3.7 35 42.4 38.8 43.5 38.1 775 141 4.4 37 42 36.9 43.1 36.7 777 174 5.4 39 41.7 37.4 42.2 36.9 760 215 7.4 41 41.1 38.5 41.9 38 760 197 5.7 43 40.7 38.9 41.3 38.3 770 143 4.1 45 40.7 39.9 41.3 39.5 770 96 3.2 47 45.2 39.7 44.3 39.5 765 51 2 49 44.1 39.7 44.7 38.6 765 457 12.9 51 43.8 40 44 38.4 765 625 17 o:WM0w-3.non:lb.(M(T,98 Re isio 4
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i GILLILAND AND SHERWOOD EVAPORATION TEST DATA l Air Evap T,i, Top T,i,-Bottom T,,,,,-Top T,,,,, Bottom Pressure Flow Rate Test 'C 'C 'C 'C mm Hg g/ min ec/ min 53 56.1 50.9 55.2 50 760 46 3.3 l 55 52.8 46.1 53.5 45.4 802 96 5.9 57 51.6 49.2 50.1 48.4 767 88 5.3 59 52.6 43.2 53.2 42.7 767 119 6.5 61 53.9 48.2 53.5 47.8 785 248 13.2 63 54.5 49.1 54.3 48.5 785 168 9.6 l 65 53.1 48.3 53.3 47 787 475 22.8 l
67 52.1 49.6 54.7 49.1 782 126 8.1 2 34.9 33.4 35.6 33.2 772 63 1.6 l
4 33.8 32.1 34.5 32 114 60 12 6 36.2 34.9 36.4 34.6 2006 66 0.65 8 31.8 26.7 32.5 26.3 407 125 4.4 10 32.6 27.6 32.8 27.1 1480 127 1.1 12 31.9 28.1 32 27.9 269 122 6 14 33.1 28.6 31 28 941 123 1.6 I
i 16 31.4 28.8 32 28.5 1966 121 0.75 18 32.8 28.3 32.5 28 556 217 4.8 20 31 28.1 32 27.5 1419 216 1.75 22 30.8 26 31.9 25.2 424 214 6.7 24 25.8 25.1 36 34.6 2325 65 0.44 i 27 31.9 27.6 33.6 27.I 1248 213 2.3 i.
l 29 32.1 26.7 32.7 26.2 1958 218 1.5 31 32.9 29.1 34.I 28.7 9I9 374 4.8 33 43.8 38.9 44.3 39.5 765 51 1.9 t 35 40.8 37 41.9 36.5 112 47 15 l eM040w 3.non:lb-040798 Revision 2 l 3-43 Apnl 1998 l
TABLE 3.6-1 (Cont.)
GILLILAND AND SHERWOOD EVAPORATION TEST DATA Air Evap T,i,-Top T,3, Bottom T,,,,, Top T,,,,, Bottom Pressure Flow Rate Test 'C 'C "C 'C nm Hg g/ min cc/ min 37 42.8 40.4 43.6 40.2 1695 51 1 0.8 39 40.6 37.1 41 35.9 249 48 6.3 41 42.1 37.7 42.8 37.2 992 49 1.5 43 42.7 39.4 43.3 38.9 1922 50 0.9 45 42.6 38.4 43.2 37.9 505 138 7.0 47 42.8 39.7 43.2 39.2 1385 137 2.4 49 41.8 35.8 42.3 35.3 396 134 9.1 51 41.8 37.8 42.5 37.2 1183 147 3.0 53 41.8 38.1 42.6 37.7 607 187 7.2 55 41.2 37.1 41.7 36.6 411 187 11.3 57 40.3 36.3 40.9 36 1235 195 3.6 59 42.7 38.6 43.1 37.9 1045 339 7.1 61 51.8 49.6 52.3 49 762 88 5.2 63 51.9 47.9 53.1 45.8 1321 88 3.2 65 53.4 49.4 56 49 320 121 20.8 67 55.1 49.9 55.6 49.6 1418 123 4.0 69 53.9 47.6 55.2 48.5 518 120 13.1 71 53.6 46.8 54.2 46 757 201 11.8 73 54.6 47.7 55.2 47.1 951 201 8.7 75 55.9 47.1 56.2 46.9 574 354 24.8 o:wM0w.3 non:Ib-480798 Re sion
TABLE 3.6 2 ENTRANCE-EFFECT MULTIPLIERS FOR THE GILLILAND AND SHERWOOD MASS TRANSFER TESTS I
Distance from bottom, ft 0.38 0.77 1.15 1.54 1.92 2.30 2.69 3.07 3.45 3.84 Multiplier for 1.16 1.037 1.026 1.020 1.017 1.015 1.013 1.012 1.011 1.010 dh= 0.088 ft.
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REYNOLDS NUMBER Figure 3.6 2 Comparison of Predicted-to Measured Evaporation Rates for the Gilliland and Sherwood Evaporation Tests oMG40w 3.non:1MM0798 3-47 Revision 2 Apnl 1998
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c 3.7 The Westinghouse Flat Plate Evaporation Tests (2m A series of liquid film evaporation tests was performed at the Westinghouse Science and Technology
- Center (2m. The purpose was to observe the behavior of the liquid film and to provide data on evaporative mass transfer. The test conditions were selected to simulate the outside of the AP600 steel containment vessel with the PCS in operation.
The test section was a vertical,6-foot long, heated flat steel plate that was coated with the AP600 inorganic-zine coating. A clear acrylic cover provided a 23-inch wide, by 4-inch deep channel for the forced air flow and allowed observation of the applied liquid film. The plate temperature, applied liquid film temperature, and both the liquid and air flow rates were varied for each test. Measured parameters for each test are presented in Table 3.7-1. Tests 27-32 were conducted with the plate sloped 15' from horizontal, while all other tests were conducted on a vertical surface. j 1
Relatively high air flow rates, in comparison to the evaporation mass transfer rate, were'used in these
)
tests. Thus, as shown in Figure 3.7-1, the change in the bulk-to-film steam partial pressure difference .l
- from inlet-to-outlet was small, and decreased as the air flow rate increased. Herefore, inlet and outlet .l 1
- average properties were used to calculate the Sherwood number for comparison with the test data. i The Sherwood numbers wem defined using the channel hydraulic diameter, ne data from the 23 Westinghouse flat plate evaporation tests (2m were compared with predictions using the turbulent mixed convection correlation, with an entrance-effect multiplier of 1.13, as described in Sections 2.1,2.2, and 2.5. The predicted-to-measured Sherwood numbers for each of the 23 tests are shown as a function of the Reynolds number in Figure 3.7-2. The mean value is 0.936 with a standard deviation of 0.139.
Since the results of this test were forced convection-dominated, the results correlate well with the Reynolds number, as shown in Figure 3.7-3.
oM040w.3.non:lb-040798 Revision 2 3-48 Apnl 1998
- j. i TABLE 3.71 WESTINGHOUSE FLAT PLATE EVAPORATION TEST DATA j
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1.0 e , .
. a e e .
- 0.5 l
0.0 0 20000 40000 00000 00000 100000 120000 140000 l ReynoWe Hunter
. Test Data -- M.an (0.938)
Figure 3.7 2 Comparison of Predicted-to-Measured Sherwood Numbers for the Westinghouse Flat Plate Evaporation Tests
- o:WM0w-3 non:Ib-(M0798 Revision 2 3-51 APnl IW8
a,b 4
l
.q i
Figure 3.7-3 Mass Transfer Data for the Westinghouse Wet Flat Plate Tests o:WO40w 3.non:Ib-G40798 Revision 2 3-52 Apnl 1998
I
.. j l
_4- 4
- 3.8. The University of Wisconsin Condensation Tots (23)
[. A series of condensation tests was conducted at the University of Wisconsin (23). The purpose' was to f provide data on condensation mass transfer in the presence of a noncondensible gas at various 1 inclination angles, velecities, and steam / air concentrations, t
h he test section was 6.25 feet long, with a 2.75-foot entrance length, and a 3.5-foot condensing surface
]
(. length.'- De channel cross-section was square with an area of 0.25 ft2 De top of the test section !
- was a thick aluminum plate costed with the AP600 inorganic-zinc coating. Seven 0.5-foot long -
cooling plates were attached to the back of the aluminum test plate to remove heat.- Each cooling i plate had both flux meters and cooling coils with thermocouples to provide redundant, diverse energy measurements. The test section could be inclined from 0 to 90 degrees from horizontal. Plate number
]
4
' I was located at the end nearest the air / steam source and was always at the highest level when the test section was inclined. Test parameters are shown in Table 3.8-1.-
Relatively high air flow rates, in comparison to the mass transfer rates, were used in these tests. As a result, the change in the bulk-to-film steam partial pressure difference from inlet to outlet was small. . i as shown in Figure 3.81. Therefore, inlet-to-outlet average properties were used to calculate the predicted Sherwood number for comparison with the test data.
' The data from the 59 University of Wisconsin condensation tests (23) were converted to hydraulic diameter based Sherwood numbers and compared to Sherwood numbers calculated from the assisting mixed convection mass transfer correlation described in Section 2.1 and 2.5. An average entrance--
- effect multiplier of i.10 was calculated as described in Section 2.2. De predicted-to-measured-Sherwood numbers for each of the 59 tests are shown as a fu Ntion of the inclination angle in Figure 3.8 2, as a function of the steam / air Reynolds number in Figure 3.8-3, as a function of the bulk -
air / steam concentration in Figure 3.8-4, and as a function of heat flux in Figure 3.8-5. The measured data are compared with the mixed convection mass trensfer correlation in Figure 3.8-6. The mean
- value is 0.932 with a standard deviation of 0.179.
Five of the Wisconsin tests were conducted without noncondensables. These tests,95-99, were used for the liquid film heat transfer correlation comparisons presented in Section 3.10.
I
'. o:\4040w-3.non:1b-040798 - Re s o
TABLE 3.81 WISCONSIN CONDENSATION TENT DATA Avg. Heat Flux Temp In Temp Out T wall Velocity Test W/m 2 .C 'C 'C m/s Angle 83 27342 95.6 95.7 45.9 1 90 82 27493 95.4 - 95.7 - 49.5 1 45 80 26395 95.2 - 94.9 45.2 1 12 81 27117 95.1 94.8 45.6 1 12 78 27257 94.9 95.1' 44.5 1 0 79 27189 94.6 94.6 47 1 6 86 27260 94.5 94.2 44.3 1 45 74 16913 90.1 89.9 29.2 1 12 73 16675 90.1 89.8 29.3 1 45 75 17681 90.3 89.7 30.7 1 6 76 16615 90.2 89.7 28.9 1 0 72 17178 89.7 89.7 31.3 1 45 7I- 14651 90 89 29.9 1 90 77 16645 89.3 89.7 29.5 '1 0 l
94 25223 90.5 89.3 39.5 2 0 55 11692 80.6 80.4 29.9 2 0 70 1417I 80.5 79.7 29.9 3 90
.57 8592 80.1 80 29.8 1 12 48 8166 80.4 79.6 29.9 1 90 43 10140 80.4 79.6 29.5 1 6 50 10168 80.1 79.6 29.6 2 90 69 '14069 80.6 79.9 29.7 3 0 68 14537 79.9 79.9 29.7 3 6 0 h .1.non:Ib.040798 1l$8
i O
TABLE 3.8-1 (Cont.)
WISCONSIN CONDENSATION TEST DATA Avg. Heat Flux Temp In Temp Out T-wall Velocity Test . W/m2 *C 'C 'C m/s Angle 64 . 14553 79.8 79.8 30.2 3 90 44 10589 80 79.6 30.1 1 12 51 10515 79.9 79.5 29.7 2 45 52 10807 80.1 79.3 29.6 2 12
)
56 7983 80 79 29.3 1 12 47 7973 80.2 78.8 30.1 1 45 54 10939 79.7 79.4 30 2 6
)
34 9931 80.6 78.8 30.1 1 0 j t
53 10023 79.9 79 29.6 2 6 i i
67 13100 79.5 79.3 29.8 3 12 66 14523 79.4 79.2 30.2 3 45 85 15974 79.4 79.3 30.4 3 0 31 9881 78.7 78.7 30 1 0 32 9924 77.4 77.4 30.1 1 0 36 8194 72.2 72.1 30.1 2 0 62 8733 71.7 71.8 29.9 3 45 42 8170 72.5 70.9 29.6 2 6 61 9286 71.5 71.3 30.3 3 12 59 8888 71 71.6 29.3 3 6 3
39 7960 71.8 71.4 30.2 2 0 46 6743 71 71.4 30.6 2 45 49 6561 70.8 70.8 29.3 2 90 41 8677 71.7 70.6 29.6 2 0 87 5572 71 70.2 30.2 1 0 91 4736 70.6 69.9 29.7 1 45 l
l oM(Mow-3.non:IMM0798 Resg 1
TABLE 3.8-1 (Cont.)
WISCONSIN CONDENSATION TEST DATA
- Avg. Heat Flux Temp In T:mp Out T. wall Velocity Test W/m 2 *C 'C 'C m/s Angle 63 8100 70.7 . 69.7 29.7 3 90 69.7 70.5 29.7 1 12 90 5173 92 4457 69.9 70.1 29.4- 1 88 88 5364 70 70.2 29.8 1 6 40 9353 70 70 .30.1 2 0 45 7868 69.4 69.4 29.5 2 12 60 9624 69.6 69.6 30 3 0
~ 89 5411 69.2 69 29.9 1 12 58' 4869 61.1 61.9. 29.9 2 6 93 2769 60.4 60.4 29.7 1 0 65 6449 59.2 60.4 29.9 3 45 4
i
.o m -3.non:m a n9s l 3-56 55IIE8 L_._.-....... . .
e 42 e ,, -
S 10 - =
e 8
t . -
2 g' e -
o 7 -
h E
6 -
=
C 3 -
C e-- =
E 0 3 -
(:
2 -O 5
2 '
- Channel Length Cf t)
-e Test 83 -+ Test 74 -* Test 55 - _ Test 36 -e Test SE Figure 3.81 Bulk to. Film Steam Partial Pressure Differences Variation Over Channel Length from Selected Wisconsin Condensation Tests OM)w-3.non:lt>4M0798 Revmon 2 3-57 April 1998
2.0 1.5 j . . 8 t .
. g ;
1.0 ;.,. . . s t
o e.
y e I e j O.5 ll 0.0 10 20 x 4a 3, ,, w Phn. Inchn. Won ftorn %muJ (%)
. Tar o r. - u..n <0.os2) l l
! Figure 3.8 2 The Effect of Surface Inclination on the Predicted to-Measured Sherwood Number Ratio for the Wisconsin Condensation Tests 0:WM0w-3.non:lb.(M0798 Revision 2 3-58 Apnl 1998 1
I 1
l I
i 2.0 1.5 j h
%E h e IM g- .. . .
t :g .
e e .
0.5 0.0 5000 10000 15000 20000 25000 30000 Reynolds Number e Test Date -Mean(0.932)
Figure 3.8-3 The Effect of Reynolds Number on the Predicted to-Measured Sherwood Number Ratio for the Wisconsin Condensation Tests oM040w 3.non:ll>O40798 Revision 2 3-59 Apnl 1998
4 l
2.0 l
1.5 g ,
z
-l
.; 2..
. 3, . _ .
]t0 s
- 0.5 1
0.0 0% 10 % 20 % 30 % 40 % 50 % 60 % 70 % 80 %
l St m Mol. Fraction (%)
. T t Data -M.an (0.932) l f.
Figure 3.8-4 The Effect of Steam Concentration on the Predicted to-Measured Sherwood Number Ratio for the Wisconsin Condensation Tests o.WO40w-3.non: t b-040798 Revision 2 1 3-60 Apnl 1998 l
O l
i 1
i 2.0 1
1.5 i l
i
. . . .* .e 1.0 * #. ' ..*
. l p
- e 40.5 i l I
0.0 0 1000 2000 3000 4000 6000 0000 7000 0000 9000 10000 H t Flux (BTUMr-ft2)
. T t o.m - u n <0.ea23 Figure 3.8 5 The Effect of Heat Flux on the Predicted-to-Measured Sherwood Number Ratio for the Wisconsin Condensation Tests Reymon 2 oM040w-3.non:lb4M0798 3-61 Apnl 1998
1000 )
C j _ e+ .i
' Sh.0.023 Re^0.8 Sc^1/3 e
to 1.00E+03 1.00E+04 1.00E+05 Reyneide Number o Test Data -Correletum j 1
Figure 3.8-6 Mass Transfer Data for the Wisconsin Condensation Tests 0:WM0w-3.non:lb-040798 Revision 2 3-62 Apnl 1998
a i-t 4 3.9 The Westinghouse Large Scale Internal Condensation Tests *)
The Phase 2 (confirmatory) heat and mass transfer tests were performed at the large-scale test (LST) facility at the Westinghouse Science and Technology Center *). The Phase 2 tests provided data on l the transient heat transfer and distribution of noncondensible gas in a geometry similar to the AP600 L containment vessel. The purpose.was to provide data to develop and validate heat and mass transfer .)
I models.
The LST test facility is approximately a 1/8-scale of the AP600. De AP600 containment shell is -
modeled by a 20-foot tall,15-foot diameter pressura vessel. He vessel contains air at I atmosphere -
when cold, and is supplied with steam at pressures up to.100 psig. Steam is injected in various source configurations to demonstrate the effect of momentom, buoyancy, and direction on heat and mass :
transfer performance.
A plexiglass cylinder surrounds the vessel, simulating the baffle that forms the air cooling annulus.
Air flows upward through the annulus to cool the vessel, resulting in condensation of the steam inside the vessel. A fan is located at the top of the annular shell to achievs higher air velocities than can be achieved by natural convection. A liquid film is applied to the outside of the test vessel to provide additional, evaporative cooling. i hermocouples are located on both the inner and outer surfaces of the vessel, at various circumferential angles, at each of ten different elevations to measure the shell temperature and heat flux distribution. Thermocouples are also located inside the vessel on a rake to measure the bulk gas temperature at various radial and vertical locations. The external cooling air temperature and. velocity are measured at several locations in the annulus. The steam inlet pressure, temperature, and flow rate, and the condensate temperature and flow rate are measured to charac:erize the total energy in and out Lof the vessel.
2 The Sherwood numbers inside the LST are defined in terms of (v 3/ ) , for the length parameter, as described in Section 2.3. The measured Sherwood numbers were based on surface to bulk gas density differences and shell heat fluxes that were averaged over time and averaged circumferentially at each measuring elevation. Steam partial pressures were not measured at each elevation, so the steam partial pressures were interpolated from the next higher and lower measurement elevations.
De steady-state, circumferentially-averaged mass transfer data from 7 of the 25 Phase 2 tests were converted to Sherwood numbers and compared with predictions of the free convection mass transfer correlations described in Section 2.3. The Phase 2 tests all had a diffuser located below the simulated steam generator. - Only tests with film coverage greater than 90 percent were included in the comparison because lower film coverage biases the circumferentially-averaged test measurement. This eliminated 17 of the tests. Test RC062 (blind test for y(GOTHIC validation) was also on.itted from the comparison because the data was not available when the evaluation was done. Relevant test parameters are presented in Table 3.9-1.
. owuow-4. nom n><wo79s jegsjog
TABLE 3.91 WESTINGHOUSE LARGE-SCALE INTERNAL CONDENSATION TEST DATA a.b 4
A compilation of the predicted to-measured Sherwood numbers for all seven tests is shown in Figure 3.9-1. The mean value is 1.045 with a standard deviation of 0.167. Figures 3.9-2, 3.9-3, and 3.9-4 provide a comparison of the measured data with the mass transfer correlation as a function of heat flux, steam concentration, and Ap/p. The correlation matches the trend in the data.
The argument has been used that free convection heat and mass transfer on the inside of the shell is conservative during blowdown, when a significant increase in the transfer coefficient is expected due to the blowdown induced forced convection. LST RC064 (222.3) and RC066 (222.4) predicted-to-measured mass transfer coefficients, from steady-state portions A and B of both tests, presented in Figure 3.9-5 show the effect of high internal break source kinetic energy. These two tests were conducted in a configuration that simulated an MSLB at the top of the steam generator. The steam source was a 3-inch inside diameter pipe elevated to a level that simulated the top of the steam generator, rather than the LOCA configuration with a steam diffuser under the simulated steam generator model. Both tests consisted of two steady-state segments with approximately a factor of two on steam flow rate. Test RC064 had the steam source pointed horizontally at the far wall, and test RC066 had the steam source pointed vertically. The tests are described in Reference 24, Sections 4.15 and 4.16.
oMO40w-4.non:Ib-042398 Revision 2 3-64 Apnl 1998
4
.i 1
~I The data in Figure 3.9-5 show the predicted to-measured mass transfer coefficients are 5 to 10 times
]
greater than the free convection mean value presented in Figure 3.9-1 for LSTs with the diffuser below the steam generator. The location of the maximum corresponds to the elevation where the jet impinges: at x/L = 0.4 for the horizontal jet, and x/L = 1.0 for the verticaljet. At gli elevations the measured mass transfer coefficients are as high or higher than the mean of the measurements for free
) convection, with an average value approximately twice that of the free convection mass transfer l
!. ' coefficient. )
l
[
5 I
l l
i I
l 1
c:WO40w-4.non:1b440798 Revision 2 3-65 Apni i998
4 3.0 2.5 -
2.0 -
1 1.5 -
3 .
e * .
e i e ? e e a a 1.0 - W e 3 g . ;
e . s g ,
- e 0.5 -
LEVEL 0 C B A W X Y Z l ! I I I I VERTICAL WALL DOME 02 0.4 0.6 0.8 1.0 1.2 0.0 Dimensionlese Length.sA.
. Test Data -Wenn (1.045)
Figure 3.91 Predicted to-Measured Condensation Sherwood Number Ratio for the Westinghouse Large-Scale Tests o:WM0w-4.non:lb 040798 Revision 2 3-66 Apni 1998
e a
t l
i j
l 1
i l 3.0 2.5 -
l 2.0 - l
} u. . l i
e *
- a
- t.0 t,.*,% .
0.5 0.0 0 1000 2000 3000 4000 5000 8000 7000 8000 9000 Heat Mux (BTuthr-ft^2) e Test Dete Figure 3.9 2 The Effect of Heat Flux on the Predicted to-Measured Condensation Sherwood Number Ratio for the Westinghouse Large-Scale Tests OMG40*-4 non:lb-M0798 Revision 2 3-6~ Apnl 1998
i 3.0 2.5 -
2.0
- i. .
.. *
- e.
, .0 .~~ .. . -.-,.
l .# .
. t l
"" 0.5 -
0.0 0% 10% 20 % 30 % 40 % 50 %
Steam Mole Prec6on (%)
' ' . Tut osta i Figure 3.9-3 Comparison of Predicted to-Measured Sherwood Numbers for the Westinghouse Large-Scale Tests
~
oMM0w4 non:tb-M0798 Revision 2 3-68 April 1998
e om ,
0.15-S 0.10 -
e %
' , 0 05 ~
f f
.* *b *
- Sh = 0.13 (ap/prt4 So^14 I'
02 0.00 0.20 0.40 09/P ,
. Test Data -Corrointion i
Figure 3.9-4 Condensation Mass Transfer Data for the Westinghouse Large Scale Tests owwo.4non:it>oun9s 3-69 11 8
e 2.0 LEVEL 0 C B A w. X Y Z l !
l l l l '
l Mi VERTICAL WALL l DOME ,
Ii 1
- ?
1.0 -
. , s 0.s
+ +
0.0 0.0 02 0.4 0.6 0.3 1.0 92 m w.a
. aco= w to ww . . acon w m - w m st.m = co,a m t o m n %
Figure 3.9-5 Predicted-to Measured Sherwood Number Ratios for the MSLB Large-Scale Tests o:WM0w-4.non:Ib4MU798 Re on 2 3-70 Apnl 1998
3.10 Chun and Seban Liquid Film Conductance Model(7)
. De Chun and Seban correlation is used to predict heat transfer through the condensing and evaporating liquid films. De correlation applies to both turbulent and wavy laminar films and was
)
{
compared to data in the original paper. Data from tests at the University of Wisconsin (23) extend the validity of the Chun and Seban correlation to condensing wavy laminar flow and to surfaces that are inclined, as in the dome region of the AP600.
%c Wisconsin test facility is described in Section 3.8. Five of the Wisconsin (23) tests (95 through 99) were conducted without a noncondensible gas present. Without a noncondensible gas, the ge-to-liquid heat transfer coefficient is so high that the gas-to-liquid temperature drop is negligible compared to the temperature drop across the liquid film. Consequently, the temperature of the liquid film -
surface may be assumed equal to the gas temperature and the' liquid film heat transfer coefficient can _ I J be calculated from the heat flux divided by the liquid film temperature drop. Since the heat flux, solid surface temperature, and liquid film surface temperature are known, the heat transfer coefficient may be derived directly from the measurements. De Wisconsin tests thus provided a direct indication of the liquid film heat transfer coefficient for a range of surface inclinations from vertical to horizontal, .l covering a range of film Reynolds number in the wavy laminar regim t The Wisconsin (23) and Chun and Seban(7) data are compared to the Chun and Seban laminar and turbulent correlations in Figure 3.10-1. The correlation predicts nearly best-estimate values over the full Reynolds number range of data. The range of film Reynolds numbers on the outside of AP600 is also shown in the figure and falls well within the range of the test data. Reynolds numbers on the inside of containment are less than outside due to film removal at the crane rail and stiffener ring, and the fact that the inside film flow rate starts at zero at the top of the dome and increases as the filn:-
l' flows down. The AP600 liquid film Prandtl number range is approximately 1.5 < Pr < 3.0, whereas the range of the Chun and Seban data Prandtl numbers is 1,77 < Pr < 5.9, which adequately covers the AP600 range. Comparison of the correlation to the test data show that the Chun an'd Seban correlation is a good, best-estimate representation of the data.
The large scatter in the Wisconsin (23) liquid film heat transfer data is believed to result from operating the tests at (or beyond) the range of operation for which the test facility was designed. The presence of even small amounts of noncondensible gases would bias the results.
ovo4ow-4.non:ib4ao79s ne isiogn
1 1 Chun and Seban Turbulent Correlation Chun and Seban Wavy ~
Nu = 0.0038 (Re ^ 0.4) (Pr^ 0.65)
Laminar Correlation -
Nu = 0.822 (Ro^-0 22) Pr = S.1
- l -
Pr = 6.7 Pr =2.91 M
j 4
M M
M g M A dPr =1.77 s * =
- u. v N
- ~
Bold X'c are Wicconcin Data. All othero are Chun g
- and Seban data.
AP600 Range (from oecond wei;)
0.1 . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . . ... 0.1 10 1 00 1000 1 0000 1 00000 Uquid Filrn Reynolds Nurnber, Re l
t Figure 3.101 Data from the Wisconsin and Chun and Seban Tests Compared to the Chun and i
Seban Wavy Laminar and Turbulent Coraclations 0:WM0w-4 non:1b-040798 Revision 2 3-72 Apni 190s
O 4 ASSESSMENT OF RESULTS AND STATISTICS ne ratio of the predicted-to-measured Nusselt number (for convection) or Sherwood number (for condensation and evaporation) was calculated, and comparisons for each of the individual tests were presented in Section 3. The predicted-to-measured ratios are combined by mode of heat transfer opposed mixed (convection heat transfer, opposed mixed convection evaporation mass transfer, and free convection condensation mass transfer) for an assessment of the combined statistics. The results show that the heat and mass transfer correlations represent the phenomena inside the AP600 containment vessel and in the PCS air flow path over the expected ranges of the dimensionless groups during a DBA event.
4.1 Convection Heat Transfer De combined convection data consists of the Hugot03) Eckert and Diaguila(6) Siegel and Norris(39)
Westinghouse flat plateGO) and dry Westinghouse large-scale tests (21) The predicted-to-measured Nusselt number ratio was calculated from these Ota and Equation 4 for opposed mixed convection.
De ratios are shown as a function of the Reynolds number in Figure 4.1-1 and as a function of the Grashof number in Figure 4.1-2. The mean predicted-to-measured Nusselt number ratio is 0.976 with a standard deviation of 0.278. The mean predicted-to-measured Nusselt number value near 1.0 indicates that the heat transfer correlation fits the measured data very well. The large standard deviation is believed to result from poor fidelity in the data for the following reasons:
The convective heat transfer correlation serves as the basis for the prediction of condensation and evaporation mass transfer. As shown in Sections 4.2 and 4.3, the standard deviation for the predicted-to-measured evaporation and condensation mass transfer is much lower than the 0.278 value for heat transfer. Since the mass transfer data do not show large scatter, the variation in the heat transfer data may be attributed to more uncertain data measurements.
The deviation between predicted and measured Nusselt numbers was large in four of the Hugot testsU 3) discussed in Subsection 2.2.1. The entrance-effect multiplier overpredicted the Nusselt number at small distances from the channel entrance (Ud h < l.0) due to the asymptotic singularity at x = 0 in the entrance-effect relation.
- The LST dry heat transfer test data have an uncertainty on the measured wall heat flux (AT) that is as large or larger than the value of AT.
- The Eckert and Diaguila(6) data have a large variation that changes with distance due to the use of the tube centerline temperature to represent the bulk temperature.
- Re Hugot03) and Siegel and Norris09) tests may exhibit higher deviations due to the use of a predicted, rather than measured, test air flow rate.
oMG4ow-4 non:Ib-040798 Revision 2 41 Apnl 1998
5 During a DBA event, the riser Reynolds number can be as high as 1.9 x 10 and the riser Grashof number can 'be as high as 1.2x109 . The convection test data covered a Reynolds number range up to 5
-x 10 5, and a Grashof number range up to 10Il. Therefore, the test data cover the expected range of both dimensionless groups within the annulus.
It is concluded that Equation 4 provides an adequate mean prediction of the dry, assisting, mixed convection heat transfer for the AP600 vertical wall and dome. The test data encompass the expected range of AP600 Reynolds and Grashof numbers. Since the phenomenon is not ranked high in the PIRfI) it is unnecessary to bound the test results in the evaluation model. However, the same multiplier developed for mass transfer in Section 4.5 is applied to convective heat transfer in the evaluation model.
oM040w-4.non:1b-040798 Revision 2 4-2 Apni 1998
2 u- . . : -
- n:- ,. : ..:. *:
1 1
.e, -
. a q ,. 5 i :
i *
,; i .ii. , : , ::
l1 : . .
- :.il'; . ,.s. s -
- i .s * -
- ! , 1;-
- ! F5, -
l.
l s' I !
- r. .
I 0.s < *I
- e, AP600 Range p 0
1.00E+03 1.00E +04 1.00E+05 1.00E+06 Reynolds Number Figure 4.1 1 The Effect of Reynolds Number on the Predicted to-Measured Nusselt Number Ratio for Convection Heat Transfer in a Channel ouo4ow-4.non::bwons 4-3 I8
e 2
e
- e e
1.5 -
. ;g g
. 8 . . . . ,g.
. . e. 4
, *4 . ,.
...'.s ). .
1 1,. r. .
,3,. p. , . -
r t
.: y; t. :-
~i 0.
p:
- t.> 1 g.
. S i
- 1 i: .
0.5 - !*
- e *.
AP600 Range r
0 1.0E+06 1.0E+07 1.0E+08 1.0E+09 1.0E+10 1.0E+11 1.0E+12 Grashof Nurnber Figure 4.12 The Effect of Grashof Number on the Predicted to-Measured Nusselt Number Ratio for Convection Heat Transfer in a Channel 0:N4non:IMM0798 Revision 2 4,4 Apnl 1998
4.2 Evaporation The combined evaporation test data consists of the Westinghouse flat plate evaporation tests (20) and the Gilliland and Sherwood evaporation tests (22). The predicted-to-measured Sherwood number ratio for the Westinghouse flat plate evaporation tests is shown as a function of the Reynolds number, Grashof number, and dimensionless steam concentration in Figures 4.2-1 through 4.2-3. The mean predicted-to-measured Sherwood number ratio is 0.936 with a standard deviation of 0.139.
The evaporation test data covered a Reynolds number range up to 1.2 x 105 and a Grashof number 30 range up to 7.0 x 10 , based on hydraulic diameter. The evaporation test data adequately covers the expected AP600 range of both the Reynolds number (1.8x105 ) and Grashof number (1.2x109 ) in the riser annulus during a DBA event.
The Gilliland and Sherwood evaporation tests (22) provided a comparison of the measured and predicted total evaporation rates at relatively low Reynolds and Grashof numbers. As shown in Section 3.6, the heat and mass transfer correlations predicted the measured total evaporation rates with a predicted-to-measured mean value of 0.925 and a standard deviation of 0.072. However, local evaporation measurements were not made and internal variations in partial pressure vary too much to represent the data by an average Sherwood number. Consequently, comparisons between the measured and predicted Sherwood numbers are not meaningful for the Gilliland and Sherwood tests. However, the range of Gilliland and Sherwood data are shown in Figure 4.2-1.
In conclusion, Equations 4 and 16 are considered to adequately model evaporation mass transfer on the AP600 sidewall and dome. When multiplied by the factor developed in Section 4.5, the evaporation correlation becomes a bounding correlation appropriate for use in the evaluation model. The predicted-to-measured Sherwood number using the bounding correlation is shown in Figure 4.2-3. The range of Reynolds and Grashof numbers in the texts is sufficient to support the use of the correlation over the expected operating range in AP600.
oMG40*.4.non:ltMU98 Revision 2 45 Apnl 1998
e a
2.0
+
1.5 -
1 .
, _. _ g e e 8 e e l .54 0
AP600 Range 7
- Gilliland & Sherwood Data 0.0 1.00E+03 - 1.00E+04 1.00E+05 1.00E+06 WW e Test Data --Mean(0.938)
. Figure .21 The Effect of Reynolds Number on the Predicted-to-Measured Sherwood Number Ratio for Evaporation ovo4ow4non:id-o4ans yevi[i,og 4,
e a
2.0 1.5 e
e e
- e 1.0 e ,, , , ,
- e' ,
e e 4
0.5 -
0.0 2.00E+10 4.00E+10 6.00E+10 8.00E+10 Grashof Number e Tout Data . Mean (0.936)
Figure 4.2 2 The Effect of Grashof Number on the Predicted to-Measured Sherwood Number Ratio for Evaporation I
o:WM0w-4.non:Ib-040798 Revision 2 47 Apnl 1998
3.0 1.5 e
e e
1.0 e , ,, e ,
- e e
- e e ,
t 0.5 0.0 0% 10% 20 % 30 % 40 %
Steam Mole Frachon (%)
e Test Data -Mean (0.936)
Figure 4.2 3 The Effcet of Steam Concentration on the Predicted-to Measured Sherwood Number Ratio for Evaporation 4 oM040w-4.non:IMM0798 Revision 2
~
48 Apnl 1998
e 4.3 Condensation The combined condensation data consists of the Wisconsin (23) condensation tests and intemal condensation' data from the Westinghouse LSTs(20. The predicted-to-measured Sherwood ratio is l' s'hown as a function of the Reynolds number, Ap/p, and dimensionless steam concentration in Figures 4.3-1 through 4.3-3. The mean pn:dicted-to-measured Sherwood number ratio is 0.988 with a standard l deviation of 0.182. Since Reynolds numbers could not be determined inside the LSTs, only the Wisconsin condensation test data are shown in Figure 4.3-1.
4 The combined test data covered a Reynolds number range up to 2.6 x 10 and a density ratio, Ap/p of 0.08 to 0.55. The Reynolds number will vary with time and position inside the AP600 containment -
vessel during a DBA event. During the relatively short blowdown phase, the velocity and corresponding Reynolds number will be largest on the wall nearest'the break location and decrease as the flow moves away from the break. A natural circulation flow pattern is expected to develop during the depressurization phase when the PCS is in operation. The Reynolds number along the wall will be small during natural circulation. The value of Ap/p in AP600 ranges up to 0.40, so it is bounded by the test data.
In conclusion, Equations 13 and 16 are considered to adequately model condensation mass transfer inside AP600. When multiplied by the factor developed in Section 4.5, the condensation correlation becomes a bounding correlation. The predicted-to-measured Sherwood number ratio using the bounding correlation is shown in Figure 4.3 3. The range of Ap/p measured in the tests encompass the range expected in AP600, oumow-4.non:ib-040798 Regsi,oyn 3
2.0 I
1.5 d
! go I .
nn
?
e 1" .
- g. . .
1 0.5 0.0 10000 18 0 20000 2m 30000 Reynolds Number Figure 4.31 The Effects of Reynolds Number on the Predicted-to Measured Sherwood Number Ratio for Condensation Mass Transfer
- ma:1b4e98 Rewuon 2
.4-10 Apn] 1998
l
)
{
l l
1.5 -
+.. * .
l
- , s..' .. f g *, .
1-
. +.
- t.
g*
. . .. **$ s ,** ' .
0.5 <
AP600 Range p 0
02 0.40 0.60 APIP Figure 4.3-2 The Effect of Dimensionless Density Difference on the Predicted to-Measured Sherwcod Number Ratio for Condensation I
) ownow-4 non: b-oso798 41]
Revision 2 Apnl 1998
2 j 1.5
=
E
- es
- f
- . # +
- *+** * **
]n 1- + 'I+
,.g.
,+, ,
{
+ :
]
2 . *
- 0.5 -
0 0% 20% 40 % 60 % 80% 100 %
Steam Mole Fraction (%)
l l
Figure 4.3-3 The Effect of Steam Concentration on the Predicted to-Measured Sherwood Number Ratio for Condensation oM040w-4.non:lb-o40798 Revision 2 4-12 Apnl 1998
+
.4.4 Measurement Uncertainty _
ne test measurements used to determine the " measured" results presented in this report (Nusselt numbers, Sherwood numbers, Reynolds numbers, and steam concentration) all have some uncertainty associated with them. Error estimates presented with the test results were determined by applying test instrument uncertainties to the individual measured parameters used to calculate the measured results.
For example, the Nusselt number is determined from' measurements of the bulk fluid temperature, the wall surface temperature, and the wall heat flux. The uncertainties associated with the individual measured parameters were applied to determine an estimate of the maximum error associated with the -
reported results. Therefore, the error estimates are coasidered to be conservative, in that it is not likely that the individual instrument errors would be simultanecusly acting to maximize uncertainty.
Error estimates were determined for the Westinghouse Heated Flat Plate Test (20) (mixed convection g, and evaporation data), the Westinghouse Large-Scale Test (20 (mixed convection and internal condensation data) and the University of Wisconsin Condensation Tesa23) (cc,ndensation data).-
Individual instrument uncertainties associated with these tests are discussed in the following section.
Error bars for these tests are shown on the corresponding figures in Sections 3.4, 3.7, 3.8, and 3.9.
The error bars tr.e limited to the outer envelope of data points to avoid er.cessive clutter on the figures.
Errors were not estimated for the open literature tests.
' 4.4.1 ' The. Westinghouse Heated Flat Plate Test (20r Test measurement uncertainties for the Westinghouse Heated Flat Plate Tests are discussed in Reference 20. As reported, heat flux to the plate was determined by deducting experimentally determined heat losses from the total integrated electrical power supplied to the plate heaters. The power to the plate heaters was measured using a watt transducer. He accuracy of this type of-transducer is typically within 0.5 percent of full-scale which corresponds to approximately 683 Btu /hr.
for a 40 KW range transducer. Based on reported heat flux measurements, total heat flux to the plate
- measured electrically was within 4.5 percent (218 Btu /hr.) of that determined based on heat transfer to the air, and viidn 9.9 percent (480 Btu /hr.) of measured heat transfer to the plate heating fluid. Since the experimentally determined results are within typical accuracy limits of a watt transducer, the typical watt transducer accuracy of 683 Btu /hr. (59M Blu/hr.-ft2 ) is assumed for the heat flux measurement uncertainty.
Copper-constantan (Type T) thermocouples were used to measure plate wall temperatures, annulus air
- temperatures, ambient temperature, and the temperature of the water film flow onto the plate.
Assuming a typical thermocouple accuracy of 0.9T and a data logger error 2 0.8"F results in a total D
uncertainty of 1.2*F. The temperature of the excess film flow was measured using chromel-alumel (Type K) thermocouples. Assuming a typical Type K thermocouple accuracy of 2 2*F and a data logger error of 2 0.8*F results in a total uncertainty of 2.15*F.
Loes.non:m.ouma jeg E% ~ _________m
Duct air velocity measurements were obtained using a standard wedge probe and pressure transducer.
- Assume a flow coefficient of 0.825 for a typical commercial pitot tube and a typical differential pressure transducer accuracy of 0.5 percent of full-scale. Based on the observed range of air velocities recorded in the tests, a differential pressure transducer having a full-scale range of 400 inches of water would be required resulting in a differential pressure measurement errer of 2 inches of water. Considering the range of measured test air velocities and applying the relationship:
V =K 4 *g *h (20) where:
K = flow coefficient. 0.825 for commercial pitot tube
~
V = the velocity in ft/sec.
g = acceleration of gravity,32.17 ft/sec.2 h = differential pressure in feet of flowing fluid j the air velocity measurement uncertainty is 0.32 ft/sec.
l A variable area flow meter was used to measure film flow onto the plate. Assuming a typical l
commercial accuracy of
- 2 percent of reading with a repeatability within I percent results in a tota! ,
uncertainty of 2.236 percent of reading. Applying a temperature measurement uncertainty of 21.2*F and calculating the flow measurement error over the range of test flowrates (approximately 0.2 to l 4.2 GPM) and film flow temperatures (70 to 150 F) results in an overall uncertainty of z 2.3 percent for mass flow onto the plate. Excess film flow or mass flow out was measured with a weigh tank using a scale accurate to " fractions" of a gram and a stop watch. Assuming that the mass of water was determined to within 2 2 grams and elapsed time was measured 0.5 seconds over a period of l
1 minute results in an uncertainty of approximately 21.2 percent for mass flow out.
l l The measurement uncertainties discussed above resulted in measured Nusselt number uncertainty within 20 percent for the reported Westinghouse Dry Flat Plate tests (20) with higher uncertainty corresponding to lower heat flux tests. The uncertainty reduced to 9 percent for tests in which the j measured wall heat flux was greater than 1000 Btu /hr.-ft.2. The measured Sherwood number uncenainty was within 5 percent for the Westinghouse Flat Plate evaporation tests that were typically conducted with a higher wall heat flux than the dry flat plate tests.
4.4.2 The Westinghouse Large *cale Test (20 Test measurement uncenainties for the Westinghouse Large-Scale Test (20 are presented in Reference 21.
~
o:WMow-5.non:lb4M0798 Revision 2 4-14 Apnl 1998
a.
t
(
Chromel-alumel (Type K) thermocouples were used for all test temperature measurements. Assuming a typical Type K thermocouple accuracy of 2*F and a data logger error of 0.8*F results in a total uncertainty of 2.15*F for the Westinghouse Large-Scale Test (20 temperature measurements.
The reported total pressure measurement uncertainty for the LST is 20.26 psi. The measurement uncertainty is 0.9 psi for the air panial pressure measurement and 15 percent of reading for the helium partial pressure. The resulting steam pressure measurement uncertainty, based on the comidned total pressure and air partial pressure measurement uncenainties is 10.94 psi.
Annulus outlet air velocity was measured using a fixed anemometer having a reported measurement uncertainty of 0.5 ft/sec.
LST wall heat flux measurements were made using calibrated thermocouple pairs. The wall AT measurement uncertainty for a typical thermocouple pair is estimated to be within 0.25"F. LST wall heat flux measurement uncertainty is estimated as a function of the wall AT measurement uncertainty with respect to the overall measured wall temperature difference (i.e., Heat Flux Uncertainty =
2 0.25/AT x Measured Heat Flux). The resulting wall heat flux uncertainty for the reported large-scale internal condensation tests was I to 15 percent with the greater uncertainty being associated with the lower AT or heat flux measurements, as expected.
The above measuirment uncertainties resulted in measured Sherwood number uncertainty within 26 percent for large-scale internal condensation tests with measured heat flux greater than 2500 Btu /hr.-ft.2. The uncenainty for tests with measured wall heat flux between 1000 and 2500 Bru/hr.-ft.2 is approximately 40 percent. Tests conducted at low wall heat flux (500 to 800 Btu /hr.-ft.2) reflected measured Sherwood number uncertainty from 50 to 75 percent as the measured wall AT associated with these low heat flux measurements approached the estimated wall AT measurement uncenainty.
Because wall heat flux associated with the dry LSTs was typically very low, the resulting measured wall AT's were of the same magnitude as the estimated wall AT measurement uncertainty ( 0.25*F).
This resulted in wall heat flux measurement uncertainties between 6 and 70 percent which resulted in high (greater than 100 percent) estimates of the maximum Nusselt number error for tests associated with the lowest wall heat flux measurements (approximately 100 Btu /hr.-ft.2),
4.4.3 The University of Wisconsin Condensation Testst23)
Test measurement uncertainties for the University of Wisconsin Condensation Test are discussed in Reference 23.
ovo40w-5.nonsonn9s 4 15 NN 1
As discussed in the reference repon, heat flux to the plate was determined experimentally using heat flux meters and by performing coolant energy balances, resulting in an uncertainty within 3 percent associated with the reponed heat flux measurements.
Chromel-constantan (Type E) thermocouples were used for all test temperature measurements.
Assuming a typical Type E thermocouple accuracy of 2 0.5*C and an instmmentation error of 2 0.02*C results in a total uncertainty of 0.5*C or 0.9*F.
Duct air velocity measurements in the Wisconsin Condensation Tests (23) were obtained using a pitot tube and pressure transducer as in the Westinghouse Flat Plate Tests (20). Assuming instrumentation similar to that considered in Subsection 4.5.1 was used in the Wisconsin Condensation Tests and that the resulting air velocity measurement uncenainty of 0.32 ft/sec is typical for the range of recorded t'"* velocities results in an air velocity measurement uncertainty of 0.32 ft/sec or 0.098 m/sec.
These test measurement uncertainties result in measured Sherwood number uncertainty within 12 percent for the reported University of Wisconsin condensation tests (23) ,
4.4.4 Open Literature Tests Information on uncertainties in the Hugot(11) Eckert and Diaguila(6), Siegel and Norris(19) Gilliland and Sherwood(22) and Chun and Seban(7) tests is limited to what is provided in these open literature references.
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.. 1 4
4.5 Mass Transfer Correlation Biases The mass transfer correlations selected for use on AP600 were compared to data from both SETS and integral effects tests (IETs). The data comparisens were presented in the form of predicted-to-measured Shenvood numbers. The comparisons show the correlations underpredict the data with mean predicted-to acasured values of 0.936 for evaporation and 0.988 for condensation. Thus, the selected correlations exhibit an underprediction of the mean data.
As a conservative approach the correlations can be biased. This can be expressed as:
CP s1 (21)
M where:
C is the bias factor P is the predicted mass transfer coefficient value M is the measured mass transfer value Thas, the value for C can be determined from the most overpredicted data point as:
CsM (22)
P l
The evaporation test data are plotted in Figure 4.2-3 and have a peak value of P/M = 1.191. Thus, the value of the bias factor for the evaporating data is C = 0.840.
De condensation test data are plotted in Figure 4.3-3 and have a peak value of P/M = 1.541. This particular value lies wmewhat above the bulk of the data and conesponds to a single elevation on the LST, while five other simultaneous measurements at different elevations in the same test produced lower P/M values. This peak value is considered a local anomaly that does not represent integral condensation rates.
Consequently, the next highest value, P/M = 1.369 was selected for evaluating the bias factor. Thus, the value of the bias factor for the condensing data is C = 0.730.
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o 4
5 CONCLUSIONS Objectives )
l l
This document presents and validates correlations that can be used to calculate energy transfer, by heat and mass transfer, between the containment gas and the extemal PCS air flow path, and between the PCS air flow path and the baffle, shield, and chimney. The correlations represent the common phenomena of convective heat transfer, condensation mass transfer, and evaporation mas; transfer.
Specific objectives of this repon are:
i
- 1. Identify appropriate correlations for the various heat and mass transfer regimes for the PCS surfaces.
I
- 2. Compare the correlations to SETS that cover the range of dimensionless parameters for AP600 operation.
l
- 3. Evaluate correlation uncertainties.
- 4. Develop biases that can be applied to the correlations to bound the test data.
Energy Transfer Model The correlations developed in this document are used in the AP600 evaluation model, so are defined I consistently with the way energy transfer is modeled across the containment shell and in the PCS air flow path. The evaluation model energy transfer is calculated as follows:
1 I
. With condensation or evaporation a liquid film is present. Energy is transported between the bulk gas and a solid through the liquid film by the following processes:
I l
Between the bulk gas and the liquid film free surface by radiation heat transfer, convection heat transfer, and mass transfer By conduction through the liquid film to the solid surface
. Dry surfaces do not have liquid films or mass transfer. Energy is transported between the bulk gas and the solid surface by radiation heat transfer and convection heat transfer.
. The correlations assume the local bulk gas thermodynamic states are known both inside and outside containment. Phenomena that influence the distribution of bulk gas propenies are separately evaluated to develop an overall bounding approach (PIRTW, Subsection 4.4.2.4).
owuow.5.non:ltm798 Reiso
4 Heat and Mass Transfer Correlation Validation
- Analytical correlations selected from the literature are presented in Section 2 to represent heat and mass transfer to and from the AP600 containment shell and PCS air flow path surfaces. The
. correlations embody the correct physics to model energy transport consistent with the energy transfer model described above. 'Ihe correlations are compared to SET data and uncertainties are evaluated in Sections 3 and 4.' Biases are evaluated in Section 4.5. The correlations selected for calculating heat and mass transfer and how the four goals are achieved for each follows.
. . Opposed mixed convection heat and mass transfer occur in the PCS air flow path on the downcomer side of the shield and baffle, and on the chimney. Equation 3, from ChurchillW, is used to'model opposed mixed convection heat transfer in the PCS air flow path. Since heat and mass transfer on the baffle and chimney are both low ranked phenomena in the PIR'IG, it is sufficient to model these without additional uncertainty, consistent with the conclusion from the PIRT that only high ranked phenomena require uncenainties (or bounding). However, the bias factor 0.73, determined for evaporation mass transfer (Section 4.5) is applied in the evaluation model.
- Assisting mixed convection heat transfer occurs in the riser and chimney ponions of the PCS air flow path on the shell and baffle. Equation 4, from Churchill
- and Eckert and DiaguilaW, is used for assisting mixed convection heat transfer in the PCS air flow path. Since heat transfer on the shell and dome are rr.nked medium or low in the PIRT, it is sufficient to model those without additional uncertainty, consistent with the conclusions from the PIRTmt hat only high ranked phenomena require uncertainties (or bounding). However, the bias factor 0.73, determined for evaporation mass transfer (Section 4.5) is applied in the evaluation model.
Comparisons of the assisting mixed convection heat transfer correlation to test data are presented in Section 4.1. The comparisons show the correlation underpredicts the mean Nusselt number by 2.4 percent, and the test Grashof and Reynolds numbers cover the range expected for AP600 operaton.
- Assisting mixed convection evaporation mass transfer occurs in the riser and chimney portions
! of the PCS air flow path on the shell and baffle. Equations I and 2. McAdamsW and-ColburnW, define the free and forced convection components of the mixed convection heat transfer correlation in the PCS air flow path. Comparison of the assisting mixed conyction evaporation predictions and the data are presented in Section 4.2. The comparisons show the nominal corn lation underpredicts the mean data by 7.5 percent. Since this transport phenomena is ranked high in the PIRTW, the data are used to develop a conservative multiplier. The
!' correlation is biased with a multiplier of 0.84, in Section 4.5, to produce a conservative evaporation mass transfer correlation. The comparisons show the test data encompass the expected range of AP600 operating conditions.
Reymon 2 oA4040w-5.non:Ib-040798 5-2 Apnl 1998
o
- Free convection heat transfer is assumed on the inside of the shell throughout all transients.
Equation 13, the modified McAdams(3) correlation presented in Section 2.3 is used to calculate heat transfer to the shell inside containment. Only free convection is assumed inside containment. Since free convection heat transfer inside the shell is ranked medium or low in the PIRW), it is sufficient to model this without additional uncenainty, consistent with the conclusions from the PIRT. The McAdams modification consists of replacing the characteristic geometric dimension, "L", with the local fluid property (v 2fg)1n in the Nusselt and Grashof numbers.
- Free convection condensation mass transfer is assumed on the inside of the shell throughout all transients. Equations 16 and 18, from Kreith(33) and the mass transfer analogy, Equation 17 are used to calculate mass transfer in the PCS air flow path and inside containment to the shell.
Free convection mass transfer, similar to free convection heat transfer inside containment, 2
replaces the. characteristic geometric dimension, "L", with the local fluid property (v fg)in in the Sherwood and Grashof numbers. Comparison of the free convection condensation predictions and the data are presente.1 in Section 4.3. The nominal conelation underpredicts the mean data by 1.2 percent. Since thi- unsport phenomena is ranked high in the PIRT(3) the data are used
- to develop a conservative multiplier. 'Ihe correlation is biased with a multiplier of 0.73, in Section 4.5, to produce a conservative condensation mass transfer conelation. The comparisons also show the range of the test data encompasses the expected range of AP600 operating -
conditions.
- Conduction heat transfer through the liquid film occurs on the inside and outside of the containment shell and may occur on the inside of the baffle and chimney if condensation takes place. Equations 14 and 15, from Chun and Seban(7) are used to calculate the heat transfer through the internal and extemal liquid films. Comparisons of predicted and measured film Nusselt numbers are presented in Section 3.10. The comparisons show the correlation is a good nominal prediction of the film Nusselt number for both condensing and evaporating films. The comparisons also show the test data encompass the expected range of AP600 operating conditions. Since film conduction is ranked medium or low in'the PIRT(3) it is sufficient to model this without additional uncenainty, consistent with the conclusions from the PIRT.
- Radiation heat transfer occurs on all surfaces, but is ranked low in the PIRT(3) on all surfaces.
Consequently, it is acceptable to use a traditional f model with an emissivity and beam length (for opaque gases). The radiation heat transfer model is not validated in this document.
O." *
- W'.
9
< 6 NOMENCLATURE df- = hydraulic diameter -
D.y .= air-steam diffusion coefficient g ' =' gravitational acceleration-h = heat transfer coefficient k = ' thermal conductivity i,- = ' gas phase mass transfer coefficient -
L = .- length rh,//
, - =. condensing or evaporating mass flux M, -
. = molecular weight of steam P = total pressure Psun.srf
= Partial pressure of steam at the interface Psun,buit- = Partial pressure of steam in the b'u lk gas mixture pw
= ' log mean partial pressure of air (Pair. bulk - Pair.stf)/In (Pair
. bulk /Pa r.sg)
R = universal gas constant T = absolute boundary layer temperature (T,,g + Tbulk W v = channel average velocity-x = distance F- = film flow rate v = kinematic viscosity 0 = angle ofinclination from horizontal
.p- = dynamic viscosity Dimensionless Groups:
3 Grd , = -
6E-- 8 h channel Grashof number -
P pv2 Pbulk - Psurf Ap/p = density ratio Ebulk Nu = h (y 2/g sin 0)l/3 liquid film Nusselt number k,
bd Nu = h channel Nusselt number k
E Pr' = P Prandtl number l k )
. o:wMow.5.non:lb-040798 Revision 2 6-1 Arni1998
e Ra -= ~ GrPr Rayleigh number Re .= I liquid. film Reynolds number P
Vd h Red .
= channel Reynolds number u
Sc = v/D ySchmidt number kRTP 8 hhd Sh d = channel Sherwood number DP y
i i
I
'l 0:WG80w 5.non:1b-040798 Rt: vision .2 6-2 Apnl 1998
7 REFERENCES
- 1. Loftus, M., Spencer, D. R., Woodcock, J., " Accident Specification and Phenomena Evaluation for AP600 Passive Containment Cooling System," WCAP-14811, December 1996, Westinghouse Electric Corporation.
- 2. Spencer, D. R., " Scaling Analysis for AP600 Containment Pressure During Design Basis Accidents," WCAP-14845, Revision 3, March 1998, Westinghouse Electric Company,
- 3. McAdams, W. H., Heat Transmission, Third Edition, McGraw-Hill,1954.
- 4. - Colburn, A. P., "A Method of Correlating Forced Convection Heat Transfer Data and a Comparison With Fluid Friction," Transactions of the AIChE, Vol. 291933, p.174.
- 5. Churchill, S. W., " Combined Free and Forced Convection Around Immersed Bodies" (Section 2.5.9) and " Combined Free and Forced Convection in Channels" (Section 2.5.10), Heu Exchanger Design Handbook, Hemisphere Publishing Corp.,1983.
- 6. Eckert, E. R. G., Diaguila, A. J., " Convective Heat Transfer for Mixed, Free, and Forced Flow Through Tubes," Transactions of the ASME, May,1954, pp. 497-504.
- 7. Chun, K. R., Seban R. A., " Heat Transfer to Evaporating Liquid Films," Journal of Heat Transfer, November 1971.
- 8. Metais, B., Eckert, E. R. G., Journal of Heat Transfer, Vol. 86, pp 295-296,1964.
- 9. Vliet, G. C., " Natural Convection Local Heat Transfer on Constant-Heat Flux Inclined Surfaces," Journal of Heat Transfer, November 1969, pp. 511-516.
- 10. Boelter, L. M. K., Young, G., Iverson, H. W., NACA TN 1451, 1948.
- 11. Hugot, G., " Study of the Natural Convection Between Two Plane, Venical, Parallel, and Isothermal Plates," derived from doctoral dissenation University of Paris,1972, translated by D. R. de Boisblanc Ebasco Services Incorporated, June 1991,
- 12. Hatton, A. P., Quarmby, Alan, "The Effect of Axially Varying and Unsymmetrical Boundary Conditions on Heat Transfer wit!' Turbulent Flow Between Parallel Plates," Inter. Journal of Heat Transfer Vol. 6, pp 903.'14,1963.
- 13. Kreith, F., Principles of Heat Transfer, Second Edition, pp 549-561, International Text Book Company,1965.
5 oM040w 5.non:lb-o40798 Revision 2 7-) Apnl 1998
n l
- 14. Eckert, E. R. G., Drake Jr., R. R., Analysis of Heat and Mass Transfer,1972, McGraw-Hill.
- 15. Kestin, J., et al.,1. Phys. Chem. Ref Data, 13,229,1984.
- 16. Rohsenow W. M., Hartnett, J. P., Handbook of Heat Transfer,1973, McGraw-Hill. )
i
- 17. Bird, R. B., Stewart, W. E., Lightfoot, E. N., Transport Phenomena,1960, John Wiley & Sons. !
- 18. "EGOTHIC Application to AP600," WCAP-14407, Section 3, September 1996, Westinghouse 1 Electric Cornoration. f
- 19. Siegel, R., Norris, R. H., " Test of Free Convection in a Partially Enclosed Space Between Two Heated Vertical Plates," Journal of Heat Transfer, April 1957.
' 20. Stewater, W. A., Pieczynski, A. T., Conway, L. E., " Tests of Heat Transfer and Water Film Evaporation on a Heated Plate Simulating Cooling of the AP600 Reactor Containment,"
WCAP-12665, April 1992, Westinghouse Electric Corporation.
l
- 21. " Heavy Water Reactor Facility (HWRF) Large-Scale Passive Containment Cooling System Confirmatory Test Data Report," HWRF-RPT-93-001, July 1993.
l
- 22. Gilliland, E. R., Sherwood, T. K., " Diffusion of Vapors into Air Streams," Industrial and l~ Engineering Chemistry, Vol. 26, No. 5, pp. 516-523, l
- 23. Huhtiniemi, I., Pernsteiner, A., Corradini, M. L., (University of Wisconsin), " Condensation in j the Presence of a Noncondensable Gas: Experimental Investigation," WCAP-13307, April 1991, Westinghouse Electric Corporation.
i
- 24. Peters, F. E., " Final Data Report for PCS Large-Scale Tests, Phase 2 and Phase 3,"
WCAP-14135 Rev.1. April 1997, Westinghouse Electric Corporation.
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