ML20080J271
| ML20080J271 | |
| Person / Time | |
|---|---|
| Site: | 05200003 |
| Issue date: | 01/31/1995 |
| From: | Spencer D WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML20080J268 | List: |
| References | |
| NUDOCS 9502270213 | |
| Download: ML20080J271 (13) | |
Text
- . -- . - --
Ci i .* f Prelimincry Basis for the Use of Forced Convection Heat Transfer Correlations
. In the AP600 PCS Natural Circulation Driven Air Cooling Path by: D. R. Spencer .
January,1995 Summary The Westinghouse SSAR calculations of heat and mass transfer from die AP600 containment shell to the PCS riser use a mixed convection correlation. De PCS scaling analysis' was performed using only forced convection in the riser, based on the fact that buoyancy effects are second order and hence, forced convection is adequate for a scaling analysis. This report provides additional information to support the selection of those correlations for the SSAR and scaling analysis.
- De approach taken in this analysis is to define the relationship between the Grashof and Reynolds numbers in the riser as the containment shell heats up during a design basis transient. The bulk flow rate in the PCS ah flow path was calculated using the control volume equation for mass, momentum, and energy developed in the AP600 PCS Scaling Analysis. 'lhose equations balanced the air flow path buoyancy with the drag forces based on measured form and friction loss coefficients, coupled with heat and mass transfer from the dry and wet containment surface into the riser air.
Following a postulated DECLG transient, the initial containment shell heatup is with a dry exterior containment surface, followed by cooldown with a wet external surface. De calculated Grashof Reynolds number relationship for the riser air during the transient heatup and cooldown defined the PCS air flow-path operating map. Examination of a criterion for the importance of buoyancy proposed by Jackson and llall 2shows that heat transfer in the AP600 riser, over the full range of wet and dry operation, is well characterized by forced convection heat transfer, with only minor buoyancy effects. Berefore, forced convection heat transfer correlations are good approximations for the PCS riser, and are fully justilled for use in an approximate scaling analysis.
A comparison shows the Westinghouse mixed convection heat transfer correlation (Appendix 1) produces Nusselt numbers approximately 1% less than the Dittus-Boeller correlation for forced convection with AP600 shell-to-environment temperature differences greater than 2 *F. An alternate' mixed convection correlation produces Nusselt numbers 3 to 5% less than Dittus Boelter over the same range of AP600 operation. Rese comparisons show that the Westinghouse mixed convection correlation is a good approximation to either Dittus-Boelter, or the alternate correlation.
Introduction he AP600 passive containment cooling system (PCS) maintains the peak containment pressure below the design limit during any design basis accident (DBA). De PCS uses an external air cooling system to remove heat from the containment shell during DB A. The external air cooling system consists of air inlet_
ports located around the upper circumference of the shield building, an annular downcomer that is bounded by the shield building and the baffic, and a riser bounded by the baffle and containment shell. A chimney extends the riser above the shield building. He design is shown in Figure 1. ,
A large tank of water at the chimney elevation supplies an external cooling water film to the outside of containment when initiated by a high containment pressure signal. The development of the water film
. requires a period of time to initiate flow, till piping, fill welts, and wet the surface. It is conservatively 9502270213 950216 PDR ADOCK 05200003 A PDR
Pnliminary assumed that this process takes approximately 11 minutes. Prior to 11 minutes the containment surface
, is asstimed to be dry.
As the containment shell heats up, heat transfer to the riser air induces a buoyant, natural circulation air flow through the downcomer and riser. The hotter the shell, the greater the buoyant forces and the higher is the resulting PCS air flow rate. De PCS air flow rate and temperatures were calculated by solving the coupled momentum and energy equations for the PCS air flow path and its boundaries (shell, baffle, and shield building) with shell temperature treated as a parameter. With the air flow rate and temperatures, the riser Reynolds and Grashof numbers were calculated, deOning an operating map for PCS operation.
De Reynolds and Grashof numbers corresponding to the AP600 operating map were used to characterite the mixed convection flow in the riser.
Quantification Summary Following a postulated LOCA, heat removal from the dry shell is by radiation to the baffle and convection to the riser air. The dry shell heat fluxes are low, on the order of 500 B/hr-ft2 -T. In contrast, the condensation heat transfer from the containment gas to the shell inner surface is on the order of 10,000 B/hr ft2 -T. The large difference between the condensation heat flux into the shell and the dry heat flux out of the shell is accommodated by the heat capacity of the shell. De shell heat capacity gives it a time constant of approximately 4 minutes, so the shell outer surface heats up rather slowly, i.e., from its initial temperature of 120 T to Y vak temperature of approximately 266 T with a time constant of 4 minutes.
In contrast, the time consta mr heating up the air in the PCS air flow path is approximately 40 seconds for a shell temperature of 130 T, and decreases with increasing shell temperature. With a time constant signiGcantly less than that of the shell, the external PCS can be modeled as quasi-steady. A quasi-steady model of the AP600 external PCS was developed and used in the PCS scaling analysis'.
AP600 Operating Man The model of the external PCS developed for the scaling analysis was used to calculate the dry shell heat removal and PCS air flow rates with the external containment temperature treated as a parameter. The resulting riser Grashof and Reynolds numbers (based on the riser hydraulic diameter) are presented in Figure 2 for a parametric shell-to-environment temperature difference range of 0.5 to 200 "F. For a given difference between the shell and environment temperatures, the energy and momentum equation solutions provide a bulk flow rate and temperature from which the corresponding riser Reynolds and Grashof numbers can be obtained. He relationship between the Grashof and Reynolds numbers corresponding to each shell temperature is shown in Figure 3. His relationship defines an operating map for the dry operation of the AP600 PCS up to a maximum external shell surface temperature of approximately 266 "F (or shell-to-environment temperature difference of 146 T). Ahhough the PCS may start up from a shell to-environment temperature difference less than 0.5 T such low temperamres are of little practical interest, since they imply that internal containment pressures are very low. In practice, the total heat removed from the shell prior to wetting is quite small', so the behavior of the PCS prior to wetting has no significant effect on containment pressure.
After the external liquid film develops, the buoyancy induced by the sensible heating of the riser and the additional buoyancy of the light water vapor maintain the high velocity riser air flow. Heat removal from the containment shell is primarily by evaporation of liquid water into the riser air. Smaller quantities of heat are also removed from the containment shell by convection to the cooler riser air and by radiati6n to the cooler baffle. Operating points at 2000,4000 and 8000 sec, were taken from the scaling analysis, resulting in the wet operating points shown in Figure ' Note that wet operation has nearly the same Grashof-Reynolds number relationship as dry operation.
i
. . .c p ..
Preliminary 2
, The wet, and dry AP600 PCS operating maps define the relationship between the riser Reynolds and Grashof numbers. The Reynolds, Grashof, and Prandtl numbers define the Nusselt numbers from wtuch the convective heat transfer to the riser is determined. Because the mole fraction of steam in the riser is always less than approximately 10%, the Prandtl number can be simply approximated as that of dry air, with a value of 0.72 over the entire PCS operating range. Thus the dimensionless groups that characterize convective heat transfer to the riser are known over the entire PCS operating range.
Jackson and Hall Criterion Jackson and Hall recommend a criterion for determining when the influence of buoyancy on the heat transfer coefficient is less than 5% of the forced convection value:
Ui* < 10-5 (t)
Re,"
Gr, is approximately equal to Gr/2. Using this relationship, the ' Jackson and Hall criterion is ,
approximately:
b Gr* < 2x10-5 (2)
Re "
The values of Gr/Re" are plotted in Figure 4 over the full range of AP600 PCS operation. With a peak value of Gr/Re" equal to 2x10 4at a Grashof number corresponding to 0.5 "F and values of Gr/Re" significantly less than 2.0x10 for wet operation and higher temperature dry operation, the Jackson and Hall criterion shows the influence of buoyancy on boundary layer heat transfer correlations is less than 5% over the full range of AP600 operation.
Westinchouse Correlation Comparison to Dittus-Boelter ,
Re Jackson and Hall criterion indicates that heat transfer in the riser is dominated by forced convection.
Consequently, the Westinghouse mixed convection correlation (Appendix 1) was compared to the well-known Dittus-Boelter forced convection correlation:
a u (3)
Nu, = 0.023 Re 'Pr over the range of AP600 PCS operation. The results are presented in Table 1, and show that the !
Westinghouse mixed convection correlation Nusselt numbers are within 1% of the Dittus-Boetter Nusselt numbers for shell temperatures greater than 2 "F above the environment. De Westinghouse correlation, ,
although a mixed convection correlation, predicts almost pure forced convection for the AP600 nser. ;
i Alternate Correlation Comparison to Dittus Boelter An alternate correlation that has been suggested for consideration' is the Cotton and Jackson equation for ;
ascending flow in a uniformly heated vertical tube: 1 1
i r w- a
- -~ .. . . . - ,- .
Fg) ..
4 a
Preliminary g et d h. " "
0.46
~
- r 3 -2
'Nu , ; _ 8x10dGr
- Nu (4)
Nu, ,
Re 2' Pr " Nu, ,
J
- he absolute value of the quantity in brackets is taken before raising to the 0.46 power.
t he Grashof number based on wall heat flux, Gr*, can be shown to be ' equal to the product GrNu, so Equation 4 becomes:
0.46 5
.f T2 Nu , 3 _ 8x10*GrNu Nu, (5)
Nu r ,
Re 23 Pr " s Nu , ,
The Cotton and Jackson correlation is compared to the Dittus-Boelter correlation in Table 1. The
' comparison shows the Cotton and Jackson correlation predicts Nusselt numbers within 5% of the Dittus-Boelter correlation for the AP600 riser with a shell temperature greater than 2 F greater than the environment. The Table I comparisons show that in all cases of interest, heat transfer in the AP600 riser is well into the forced convection dominated region, regardless of whether the Cotton and Jackson correlation is used, or the Westinghouse mixed convection correlation is selected.
Conclusions he Jackson and Hall criterion indicates that the riser operates predominantly in forced convection and
. consequently, buoyancy induced mixed convection effects are expected to be minor, he use of forced i convection in the riser scaling analysis is justified by the dominance of forced convection. -
De Cotton and Jackson correlation for upward buoyant mixed convection flow produces a Nusselt number j for the' AP600 riser that differs only a few percent from the Nusselt number for pure forced convection .,
with the difference smaller at higher Reynolds numbers (higher shell-environment temperature differences)..
De Westinghouse mixed convection correlation produces results nearly identical to the Dittus-Boelter correlation for pure forced convection. The Westinghouse mixed convection correlation is appropriate for the operating range of the PCS riser.
References
- 1. Letter, N. J. Liparuto (Westinghouse) to R. W. Borchardt (U.S. NRC), NTD-NRC-94-4318, October 27,1994,"AP600 Passive Containment Cooling System Scaling Report",(WCAP 14190, Scaling Analysis for AP600 Passive Containment Cooling System (PCS), October,1994).'
- 2. J. D. Jackson and W. B. Hall, Influences of Buoyancy on Heat Transfer to Fluids Flowing in Vertical Tubes under Erbulent Conditions, Turbulent Forced Convection in Channels and Bundles Theory and Application to Heat Exchangers and Nuclear Reactors, 2, Advanced Study Institute Book (eds. S. Kakac, and D. B. Spalding), 1979, 613-640.
- 3. M. A. Cotton and J. D. Jackson, " Comparison Between Theory and Experiment for Turbulent Flow of Air in a Vertical Tube with interaction," Mixed Convection Heat Transfer -- 1987, edited by V. Prasad, ;
l l
l l
q
.j; ii , ,N k.,. . Prelimirry
,:. 4..: Letter, T. J. Kenyon (US NRC) to N. J. Liparuto (Westinghouse), " Request for Additional Information -
W[ ' _ ., on the'AP600" Docket No.52-003, April 29,1994. Enclosure 2, " References Heat Transfer Correlations", .
from R 'Viskanta.
/'%.
%[ _ _
i 3
Prelimintry Nomenclature . ,
l
' c, Constant pressure specific heat ,
.d. Channel hydraulle diameter g Gravitational acceleration j
- h. Ileat transfer coefficient !
k' Thermal conductivity - l' q, Wall, or shell, heat flux V Bulk channel velocity p Coefficient of volume expansion = 1/T for a perfect gas p Density p The average density across the boundary layer defined:
ji = (T.I -T,) fr, p dT (6) v Kinematic viscosity p Dynamic viscosity <
Subscripts 1
abs 'Ihe absolute temperature b The bulk flow value F Forced convection '!
w The surface value Dimensionless Groups Grashof Number Gr = gd'(p.-p )/pov2 ,
Gr* = g dq/kv2 l Gr = gd'(p-p )/p v2 Nusselt Number Nu = hd/k )
l Prandtl Number pe,/k j i
Reynolds Number Re = Vd/v l I
Richardson Number R1 = Gr/Rc2 = gd(p,-p )/v 2p i
v
f]NQ
.i Preliminary PCS Water : ! ..
' ' ..!~
Storage Tank - ,
.A
?}
'. h (... .
Air $$h%$ Air inlet Inlet g#gjg;,.{.;+%
.. :. .. a w-a=ax=- an Steet . Concrete Containment ,.
Agg; ge p Shield Building Vessel Jener [.y.g k.. C
%! . . % W @@Ka '
Air Flow mR*f . 'M V
- jga ' ' , , i' '
Baffle : ,
,u
~ ~
' @bg 4
a AP600 Ultimate Heat Sink Figure 1 AP600 Passive Containment Cooling System Design Schematic I
I l
l
L 9 .,
Prelimicry 1E+10... . . . . . . . . . 1 E+06 v6 -
'8 O 1E+09.=a. . : ' . = .- . : ...m..:. .. .: . . . + : ..: : :
.=- a C
...... .. ... .. . ... ... . .. ...........n...- . . . . . . . . . . = . . . = .. . . . . . .
. . s 3
E f ..... . ........... ......... ........ . . ......... . . . . . . . . . . . . . . . . . . . . . . 2 z ,2 z
- 1E+08=. . ..n. m. .m.
. . u. . . . . ' m. . . .n. . . . : . . : ...=.==..a..n-
.. .. . .a.. . .. .:::. ..n.. . . . -:n. . . . . .. u. . . ......-1 m E+05 *
................................n...a..
,u.
O .. . . . . . . . . . . . . . . . . . . . . . . . . ...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
- u. m. : : .. . . . . .. . 4 '
1 E+07.:.
. .. .. .... . ..-........'..m...u.'=.m...
. . . . .. .....................'.=:'.':..'.=.'......=..m....n...
1E+06 . . . ...... . . . . . . . . . . . . . ..... . ...... 1E+04 s 0.1 1.0 10.0 100.0 1000.0 Shell-Environment Temp Difference, F
-+- Reynolds Number 4- Grashof Number Figure 2 Dry PCS Operation with Shell-to-Environment Temperature Difference as a Parameter L
4
'.a t
1.
!t* . '
Prelimirry w
A t y .
1N.............................................................................
g .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
tc .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
m Z
1N.. . . . . . . . ... .. .. ... .. . .. ... . .. ... .. .. ... .. . .. ... . .. ... .. .. ... .. . .. ... . .. ... .. .. ... .. . .. ... . .. ... .. . ... .. . .. ... . . . . . . . . . . . . . . . . . . . . . .
y .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
}
.J 10000 - ...... . . . . . . ~ ... - .. -
1E+06 1E+07 1E+08 1E+09 1E+10 LocalGrashof Number,Grd
-e- Dry Operation
- Wet Operation Figure 3 Parametric Relationship between PCS Air Flow Path Reynolds and Grashof Numbers
37~
?_,-4e L
.e-. J y
- Preliminry ,
m <
4 h
n k
0.0001....................................................................................................
ts T
O. _ - _
% 1EM.- .... ..-....... N r . ............................................................
g .
1E-06 1E+ 06 1E+07 1E+08 1E+09 1 E+10 -
LocalGrashof Number,Grd -
l 1
]
Figure 4 AP600 Riser Richardson Number and Comparison to Jackson and Hall Criterion for
- Significant Buoyant Effects h
l 1
i 1
1
\
l
'1 i
4 Preliminary -
Table I Parametric Characterization of Heat Transfer in AP600 PCS Riser ,
Jackson & Nusselt Numbers Nusselt Ratios AT Hall (T) Gr, Re, Gr/Re" Dittus- Cotton & Westing- West /D-B C&J/D-B Boelter Jackson house 0.5 3.29e+06 11232 1.91e-05 35.08 32.09 34.44 0.982 0.915 1.0 6.69e+06 15683 1.57e-05 45.81 42.59 45.15 0.985 0.930 2.0 1.32e+07 22187 1.22e-05 60.47 57.18 59.91 0.991 0.940 3.0 2.09e+07 26579 1.18e-05 69.87 66.13 69.16 0.990 0.947 5.0 3.60e+07 33156 1.12e-05 83.39 79.11 82.51 0.989 0.949 10.0 7.48e+07 44839 1.03e4)5 106.I7 101.06 105.02 0.989 0.952 20.0 1.53e+08 60372 9.45e-06 134.69 128.66 133.22 0.989 0.955 40.0 2.98e+08 80817 8.37e-06 170.08 163.24 168.41 0.990 0.960 80.0 5.49e+08 106629 7.30e-06 212.31 2Gt.76 210.58 0.992 0.9 M 120.0 7.46e+08 124497 6.53e-06 240.32 232.63 238.83 0.994 0.968 146.0 8.50e+08 133758 6.13e4M 254.53 246.87 253.25 0.995 0.970
- 200.0 1.0le+09 149287 5.41e-06 277.80 270.49 277.15 0.997 0.973 56.5 1.12e+09 137655 7.47e-06 260.43 250.75 257.47 0.989 0.963 66.8 1.12e+09 146119 6.36e46 273.17 2M.56 271.29 0.993 0.968 69.8 1.lle+09 148597 6.02e46 276.87 268.61 275.35 0.995 0.970
y ,- ,
mb :s.
4, , -
Preliminry i
Appendix 1:
'. Westinghouse Convective Heat Transfer Correlations
- (
1.1 Outside Containment ne McAdams' turbulent free convection heat transfer correlation:
Nut ,,, = 0.13(Gr,Pr)" (1) and the Colburn: turbulent forced convection heat transfer correlation:
Nu,,,, = 0.023Re['Pr m (2) are used for the external convective heat transfer to or from the surfaces. ,
1.2 Inside Containment The McAdams turbulent free convection heat transfer correlation:
Nu,,,, = 0.13(Gr,Pr)in (3) and the smooth flat plate' turbulent forced convection heat transfer correlation:
Nu,,,,, = 0.0296Rc['Pr " (4) are used for the internal convective heat transfer to or from the surfaces.
1,3 Combined Free and Forced Convection The correlations for combined free and forced convection heat transfer from Churchill' are, for turbulent opposed free and forced convection:
Nu = (Nu/,,+Nu,',,,)w (5). ,
and for assisting free and forced convection, Nu is the larger of the following three expressions- !
l
' (O abs (Nu/,,-N,,)* ; N u ,,,, ; 0.75 Nu,, l l'
ne lower limit in the latter equation, that prevents the value of Nu from going to zero when Nu,,, r and 5
Nu,r are equal, comes from Eckert and Diaguila .
l 1
References
- 1. W. H. McAdams, Heat Transmission, Bird Edition, .McGraw-Hill,1954.
- 2. A. P. Colburn, "A Method of Correlating Forced Convection Heat Transfer Data arxl a Comparison With Fluid Friction", Transactions of the AIChE, Vol. 29 (1933), p.174.
H. Schlichting, Bom dary layer Theory, Sixth Edition, McGraw-Hill. I 3.
ev.; ,
c ,7.p -, n. - (.
T '
Preliminary
- 4. , ~ S. W. Churchill, " Combined free and Forced Convection Around Immersed Bodies", Section 2.5.9,
- .and " Combined Free and Forced Convection in Channels", Section 2.5.10 in E. U c Schlunder,=
Ed.-in-Chief, Heat Exchanger Design Handbook, Hemisphere Publishing Corp.1983.
- 5. E. R, G. Eckert and A. J. Diaguila, " Convective Heat Transfer for Mixed, Free, and Forced Flow Through Tubes" Transactions of the ASME, May,1954, pp 497 5G4.
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