ML20072T529
| ML20072T529 | |
| Person / Time | |
|---|---|
| Site: | 05200003 |
| Issue date: | 08/31/1994 |
| From: | Gresham J, Ofstun R WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML20072T523 | List: |
| References | |
| PCS-GSR-004, PCS-GSR-004-R00, PCS-GSR-4, PCS-GSR-4-R, NUDOCS 9409150238 | |
| Download: ML20072T529 (45) | |
Text
___ _
PCS-GSR-004 Experimental Basis for the Convective Heat Transfer Correlations Selectedfor Modeling Heat Transfer from the AP600 Containment Vessel r 'gr q ;
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PRELIMINAC1Y EXPERDtENTAL BASIS FOR THE CONVECITVE HEAT TRANSFER CORRELATIONS SELEcrED FOR MODELING HEAT TuANsrtR ritOH THE AP600 COWAINMENT VF35EL EXPERIMENTAL BASIS FOR THE CONVECTIVE HEAT TRANSFER CORRELATIONS SELECTED FOR MODELING HEAT TRANSFER FROM THE AP600 CONTAINMENT VESSEL August 31,1994 l
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AP600 DOCUMENT COVER SHEET TDC: IDS: I S Form 58202G(5/94) AP600 CENTRAL FILE USE ONLY; 0058 FRM RFS#: RFS ITEM #: l AP600 DOCUMENT NO. REVISION NO. ASSIGNED TO PCS-GSR-004 0 Page 1 of 2 ALTERNATE DOCUMENT NUMBER: WORK BREAKDOWN #: ARPP-22662 DESIGN AGENT ORGANIZATION: WESTINGHOUSE TITLE: EXPERIMENTAL BASIS FOR THE CONVECTIVE HEAT TRANSFER CORRELATIONS SELECTED FOR MODELING HEAT TRANSFER FROM THE AP600 CONTAINMENT VESSEL i
ATTACHMENTS: DCP #/REV. INCORPORATED IN THIS DOCUMENT REVISION:
CALCULATION / ANALYSIS
REFERENCE:
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,D (_ v
/ APPRogAL ATE SIGNATUR)( T/
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l l
I
ParuutNAaY ExrtarMENTAL BASIS FOR THE CONVECTIVE HEAT TRANstra CORRELATIONS SEIE.CTED FOR MopEttNG HEAT TRANSITa ROM THE AP600 CONTAINMEyr VESSEL TABLE OF CONTENTS Section Title Page, EXECUTIVE
SUMMARY
l Introduction 1-1 1.0 2.0 Convective Heat Transfer Correlations 2-1 2.1 Annulus Region 2-1 2.2 Entrance Effects 2-3 2.3 Inside Containment 2-3 3.0 Experimental Basis for the Selected Heat Transfer Correlation , 3-1 3.1 'Ihe Hugot Tests 3-1 3.2 The Fckert and Diaguila Tests 3-9 3.3 The Siegel and Norris Tests 3-22 4.0 Conclusions 4-1 5.0 References 5-1 l
u:WXA1313w.wpf:Ib.090194 iii t
PREUMINARY EXPERIMENTAL Basts FOR THE CONVECrIVE HEAT TRANSFER CORRELATIONS sEtzerED FOR MODELLwo HEAT TRANSITR PROM THE AP600 CONTAINMENT VESSEL l EXECUTIVE
SUMMARY
1 Section 1.0 describes the heat transfer phenomena that will be required to be modeled for the AP600 containment analyses. A key aspect of modeling the heat removal from the containment is the (
l convective heat transfer correlation. The convective heat transfer correlation and the heat and mass transfer analogy provide the basis for calculating the magnitude of condensation and evaporation that are the dominant heat transfer mechanisms.
Section 2.0 describes the heat transfer correlations and solution method selected for modeling heat transfer from the AP600 containment Conventional free convection (McAdams) and forced convection (Colburn for channels and Schlichting for flat plates) heat transfer correlations were selected. Comparison to correlations for inclined and horizontal surfaces shows that free convection correlation remains valid for surfaces other than vertical.
An approximate method recommended by Churchill was implemented to combine the free and forced convection correlations for 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 gives free convection values at low Reynolds numbers, forced convection values at low Grashof numbers, and a combination of the two in mixed l l
convection. j i
A correlation for the entrance effect on heat transfer in channels is used to increase the forced l I
convection heat transfer coefficient near the entrance. The correlation uses coefficients for different entrance configurations published by Boelter, Iverson, and Young. No enhancement is applied to the free convection or the flat plate forced convection correlations. Comparisons show the entrance correlation generally fits the data except for values of x/D approaching zero. The AP600 channel H/D is approximately 50 and the length steps MI/D are on the order of 10, so all of the riser length is well approximated by the correlation. The entrance effect is only important for comparing predictions to test results for small values of x/D.
Section 3.0 presents a comparison of the predicted local Nusselt number, which is calculated using the selected heat transfer correlations, as a function of dimensionless height with test data from various sources. Comparisons of the analytical models to experimental data from the literature are provided 5
that cover a range of natural convection induced Reynolds numbers up to 3.8x10 and Grashof numbers (based on channel diameter) up to 7.2x10' . The AP600 riser Reynolds number ranges up to 1x105 and the Grashof numbers (based on channel diameter) range up to 4x10'.
As shown in Section 3.0, the method used to calculate heat transfer to the annulus of the AP600 produces good agreement with the available data.
u:\np600\1313w.wpf:lb-090194 ]
PCEtJMLNARY ExrERmtNTAL BASIS FOR THE CONVECTIVE HEAT TRANsITR CORRELATIONS sEIEcTED FOR MODELLNG HEAT TRANSFER 51 TOM TIIE AP600 CONTAINMENT VFa5EL
1.0 INTRODUCTION
A design basis accident (DBA), such as a loss-of-coolant accident, in AP600 has the potential to pressurize and, potentially, to challenge the design limit of the containment shell. The AP600 passive contaimnent cooling system (PCS) is designed to remove sufficient heat from containment during the limiting DBA to maintain peak containment pressures below the design limit. Heat is removed from the containment atmosphere by condensation and cNyective heat transfer to the shell, where it is conducted through the shell and rejected to the atmosphere on the outside of containment. Rejection to the atmosphere is by convection to the buoyant cooling air, radiation to the baffle, and evaporation of the external cooling film to the cooling air. The analytical models used to calculate the heat transfer include conventional radiation heat transfer, free and forced turbulent convection heat transfer, and condensation and evaporation mass transfer.
A key aspect of modeling the heat removal from the containment is the convective heat transfer correlation. The convective heat transfer correlation and the heat and mass transfer analogy provide the basis for calculating the magnitude of condensation and evaporation that are the dominant heat transfer mechanisms.
De air flow through the annulus region between the baffle and the outside of the containment shcIl is buoyancy-induced. The flow along the inside of the containment shell is buoyancy-induced after blowdown. The heat and mass transfer on both the inside and outside of the containment shell are strongly influenced by the significant natural circulation driven air flows. Consequently, the heat and mass transfer are generally qualified as mixed free and forced convection.
Because the scale of the AP600 containment heat transfer surface is on the order of 100 ft. high, over 95 percent of the surface operates in turbulent convection. For the small portion of the inner surface that operates with laminar flow, turbulent free and forced convection correlations for flat plates underpredict heat transfer that is actually laminar. For the small portion of the outer surface that operates with laminar flow, turbulent free and forced convection correlations for channels overpredict heat transfer that is actually laminar. De overprediction is by less than a factor of two. The small fraction of the surface that is laminar and the limited errors introduced by the use of turbulent correlations make the consequences of using turbulent free and forced convection correlations for heat transfer insignificant for the prediction of total containment pressure during a limiting DBA.
His report describes the correlations selected to model the convective heat transfer for the AP600 containment. A comparison with experimental data is also provided to justify the use of these correlations in the annulus region. Both the scaling requirements and the mass transfer correlations for condensation and evaporation (which depend on the convective heat transfer correlations) are described in a separate report.
1 u:hp60rA1313w.wpf:IMN0194 1-1
PREuwmARY l EXPERLMENTAL basts IVR THE CONVECTIVE HEAT TRANSFER CORRELATIONS SELECTED FOR MODELING HEAT TRANSFER IROM THE AP600 COP (TAINMEf(T VESSEL 2.0 CONVECTIVE HEAT TRANSFER CORRELATIONS his section presents the correlations for modeling convective heat transfer within the annulus region
- and the inside walls of the AP600 containment. As described in Section 1.0, the convective heat ;
- transfer in the AP600 wi'r primarily be turbulent rather than laminar. Derefore, the laminar heat i transfer regime has not been modeled.
1 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, i.e., they work in the same direction, as in upward flow in a hot pipe; or opposed, i.e., they work i
against each other, as in downward flow in a hot pipe. The convective heat transfer is further qualified with regard to orientation (vertical or inclined) and geometry (open or chann:1ed). The boundary condition for heat transfer is also qualified as either constant temperature or constant heat flux.
2.1 Annulus Region !
c ne modeling of convective heat transfer within the vertical annulus region of the AP600 requires a i correlatha that is based on experimental data taken from asymmetrically heated, vertical parallel plates. Since the liquid film flowing down the vertical wall is expected to reach saturation quickly, a i 2 convntive heat transfer correlation based on a constant temperature boundary condition should be j conn.Hed. l The McAdams") correlation, shows below, has been selected for calculating turbulent free convection l
heat transfer in the annulus.
Nu, = 0.13(GrPr)" (1)
! This correlation assuses that in turbulent free convection the local heat transfer coefficient is independent of distance from the leading edge. This correlation is widely used to calculate turbulent free convection heat transfer from both vertical and inclined heated flat plates with both constant temperature and constant heat flux boundary conditions.
The work of Vlietm howss that Equation 1 underpredicts the heat transfer from a horizontal flat plate.
j Even though it may slightly underpredict heat transfer from the horizontal surfaces, Equation 1 will be used to calculate turbulent free convection heat transfer for both horizontal and vertical flat plates.
1 i
u:W1313w.wpf:1b490194 2-1
PRELIMINARY EXPERIMENTAL B4sts puR THE CONVECTIVE HrAT TRANsrER CORRE!ATIONS SELE.CTED FOR MODELING HrAT TRANSFIR f1 TOM THE AP600 CONTAINMENT VFSSEL Re Colburn* correlation, shown below, has been selected for calculating turbulent forced unvection heat transfer in the annulus.
Nu,, = 0.023RefPr m (2)
His correlation is applicable to both constant temperature and constant heat flux boundary conditions for fully developed flow in long ducts. This correlation is widely used to calculate turbulent forced convection heat transfer in long tubes and ducts.
Because both of the correlations listed above are dimensionless and developed from similarity theory, they are scalable.
It should be noted that a length or distance dependent multiplier is required to account for the increase in heat transfer at the entrance of a heated channel. This entrance effect multiplier is described in more detail in Section 2.2.
For calcuhtional purposes, a single correlation (or combination of free and forced convection correlations; is needed to cover the entire range of mixed convection. A method for calculating mixed free and fecced convection heat transfer was recommended by Churchill
- and is given below. For opposed fiee and forced convection: 1 h
Nu, = (Nul,+Nu',)w (3)
< r e
i and for assisting free and forced convetion, Nu, is the larger of the following three expressions:
i 1 (4I abs (Nul,- Nul,,) ; Nu,, ; 0.75Nu,,
l 4
- The lower limit in the latter equation, which pret ats the value of Nu, from going to zero when Nu u ,
and Nu,r are equal, comes from Eckert and Diaguila.W The method for calculating mixed convection heat transfer is asymptotic to both the individual free
- and forced convection correlations. Consequently, it is unnecessary to consider whether the heat transfer regime is free, forced, or mixed.
]
j unap600\1313w.wpf:ltm194 2-2
PREllMINARY EXPERIMENTA!. BASIS FOR THE CONVECTIVE HEAT TRANSFYR CORRELATIONS sEuCTED FOR MoDELING HEAT TRANSFER FROM THE AP600 CoterAINMEPff VESSEL 2.2 Entrance Effects The Colburn forced convection correlation does not produce the significantly higher heat transfer coefficients that exist at the entrance to a heated channel or plate. The correlation and coefficients recommended by Boelter, Young, and Iverson* are used to account for the entrance effect; (5) b = 1 + F*.d_ L h.
where:
- h. is calculated from the Colburn correlation based on diameter d h, is the mean or length aver 2;e heat transfer coefficient over length L F i is a multiplier from Reference 11 An equation is needed that w31 give a local value of h(x) or average between x3 and x2 Given an equation for h(x), the average value of h on the interval (x3 ,x2 ) is:
1 h,,' = x -X }>r,h(x)dx (6) 2 i Analytically, h(x) could be derived from the above definition over the interval (0, L), but the equation produces a singularity when this is attempted. A modest change to the exponent, however, results in:
h,,,,, ,
d(x[-x[) g
- h. p' L (x,-x )
J 3
E a form that has the same average over length L, but with slightly lower values for small value; of x, and with slightly higher values for higher values of x.
?
2.3 Inside Containment i
i The modeling of convective heat transfer to the containment shell requires a correlation for vertical j and inclined plates in an open geometry. The containment shell will be heated as air and steam flow
- along it. The flow may be either upward or downward and consequently, the mixed convection heat j transfer regime can be either assisting or opposing.
)
i
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PDEUMINARY EXPERIMENTAL basts FOR THE CONVECTIVE IIEAT TRANSFER CORRELATIONS r
SELECTED FOR MODELING lifAT TRANsstR #1 TOM TuE AP600 ConAINMENT VESSEL The McAdams correlatwn, described in Section 2.1, is used for calculating turbulent free convection heat tnmsfer inside containment with the length parameter based on height.
The flat plate correlation"), shown below, has been selected for calculating turbulent forced convection heat transfer inside containment.
Nu, = 0.0296Re,*Pr n (8)
It should be noted that this correlation is applicable to an open geometry, therefore, the Re, and Nu, i
numbers are dependent on the distance from the leading edge of the plate and not the channel l
l hydraulic diameter.
The Churchill method for calculating mixed convection heat transfer in the annulus, which is described in Section 2.1, is also used to calculate mixed convection heat transfer inside containment.
l l l l
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PRELIMINARY EmRIMINTAL BASIS FOR TIIE CONVECTIVE HEAT TRANSFER CORRELATIONS SELECTED FOR MODELING HEAT TRANSFER MtOM TIIE AP600 CONTAINMENT VESSEL 3.0 EXPERIMENTAL BASIS FOR THE SELECTED HEAT TRANSFER CORRELATION j The method of combining the free and forced convection correlations to model turbulent mixed convective heat transfer in the annulus has been verified by comparison to test results from various
! sources. Because the calculated local Nusselt number has a nonlinear dependence on the Reynolds and Grashof numbers, it is necessary to present a comparison of the predicted and measured local Nusselt numbers as a function of the dimensionless height for each of the tests.
3.1 The Hugot Tests m
, Hugot conducted heat transfer tests on a set of heated, parallel, vertical, isothermal plates with closed sides. The channel height was 3.3 m and the plate separation distance was variable between 5 and 60 cm. The plate temperatures were varied between 40 and 160*C. The tests provide data for validating assisting mixed convection heat transfer for moderate Reynolds and Grashof numbers.
Hugot did not report the air flow rate or velocity induccd in the heated channel hence, it was necessary to use a computer model that could calculate air flow rates as well as heat transfer. The tests were modeled using the WGOTHIC"* code. The test section was divided into 11 axial volumes.
The first 10 volumes were each 1/15th of the total volume; the last volume was 1/3 of the total j volume. The code calculated the velocity, air temperature, and heat transfer coefficient in each of the 11 volumes. The WGOTHIC calculations assumed a combined entrance and exit form loss of 1.5.
- Consequently, the WGOTHIC heat transfer calculation includes uncertainties on the air flow rate. The local heat transfer coefficient was calculated using the method for combining the free and forced convection correlations described in Section 2.1.
Hugot reported heat transfer coefficients based on the (T, - Tu , ) temperature difference. l I
Consequently, the WGOTHIC predictions, which are based on the (T - Tw o ) temperature difference, were transformed to a basis comparable to the Hugot data for presentation.
]
I The calculated local Nusselt number results for each of the 5 tests are compared with the test data and 4
are shown as a function of dimensionless height in Figures 3.1-1 through 3.1-5. Some relevant test parameters are shown in the following table.
t u:W1313w.wpf:lb-090194 3-1
l l
PREUMINARY ExtentMENTAL Bast $ FDR THE CONYECriVE HEAT TRANSFER CORRELATIONS SELECTED FOR MODELLNG llEAT TRANSFER FROM THE AP600 COYTAINMENT VE85EL Test Number 11D a Plate Temp. (C) Gro Range Re a 4
1 4.4 68.0 2.40E09 - 2.61E09 35400 4
2 4.4 160.8 3.31E09 - 3.65E09 42400 3 18.15 172.5 3.64E09 - 5.18E09 13700 4 18.15 101.5 3.25E09 - 4.45E09 12300 5 18.15 72.9 2.79E09 - 3.76E09 11000 A compilation of the predicted-to-measured local Nusselt numbers for all 5 tests is shown in Figure 3.1-6. He mean predicted-to-measured value of 1.169 is also shown. He standard deviation of the predicted-to-measured values for all 5 tests is 0.406. Both the mean and standard deviation are -
strongly affected by the relatively large predicted-to-measured local Nusselt number ratios at the channel entrance. If these entrance values are removed, the mean falls to 1.085 and the standard deviation falls to 0.160.
Except for the channel entrance, the predicted local Nusselt numbers are very close to the measured values for both tests 1 and 2. Rese two tests had the highest Re4 numbers of the set and were performed with the gap width set to 60 cm. It should be noted that the entrance effect multiplier for the calculated-forced convection heat transfer coefficient is height-dependent, and can have a large value when volumes with small elevation differences are modeled at the entrance. The difference between the calculated and measured local Nusselt numbers near the entrance is due to the relatively large entrance effect multiplier on the calculated forced-convection heat transfer coefficient.
He predicted local Nusselt numbers are slightly higher than measured for both tests 3 and 4. He trend in the rate of change for the measured local Nusselt numbers was not predicted by the code.
The rate of change in the measured local Nusselt number data for both tests 3 and 4 begins to level off around an x/d value of 7, then increases rapidly between the x/d values of 8 and 12, returning to the original rate of change after that. These phenomena were not observed in any of the other tests. Both test 3 and test 4 were performed at relatively high temperature with the gap width set to 10 crn.
The predicted local 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 rate of change of the local Nusselt numbers was not the same. This test was performed at a relatively low temperature.
u:W1313w.wpf:ll 090194 3-2
J PREIJMINARY EXPERIMENTAL Basis FOR THE CONVECTIVE HEAT TRANSFER CORRELATIONS SE!ECTED FOR MODELING HEAT TRANSFER FROM THE AP600 CONTALWENr VESSEL l
I l
1 10e ..
600 -
500 - W t m S 400 w
a -
z o n 2
300 -
C o
" m 200 -
n w
100 -
m M
' ' ' ' l 0
0 1 e 3 4 5 Olmensionless Height (X/d) r.' Test Data + W Co' relation i l
l l
l Figure 3.1-1 Local Nu Number Comparison for Hugot Test 1 a:W,1313w.wpf:lM)90194 3-3
1 l
PREUMINARY ExFERIMENTat Basts FOR TIIE CONVECTTVE HEAT TRANSFER CORREIATIONS SELECTED FOR MoneuNo HEAT TRANSFER FROM THE AP600 CONTAINMENT VFJSEL i
soo 800 -
700 -
t eco -
0
'** ~
2 5
w -
c 8
> soo -
2% -
y n
100 -
n a
o 1 2 3 4 5 Dimensionless Height (X/d) m Test Datn + W Correlation i
Figure 3.12 Local Nu Number Comparison for Hugot Test 2 n:W1313w.wpf:1b090194 3-4
PREuMINARY ExrERIMerTAL BASIS FOR THE CONVECTIVE HEAT TRANSFER CORRELATIONS SEtETED FOR MODEuNo HEAT TiuNsFER FROM THE AP600 CONTAINMENT VESSEL 600 500 -
W W
M g 400 -
0 W
W 3
2 3 m - y z
W O
J 200 - , w y K W
- I 400 - m Y
W l 0
O 5 10 15 20 Dirnensionless Height (X/d) m Test Data + w correlation t
i Figure 3.1-3 Local Nu Number Comparison for Hugot Test 3 l uAap60(A1313w.wpf:1M)90194 3-5 l
i
~_ . . . .. . . . . - - .
i
= PRELIMINARY i EXPERIMENTAL BASIS FOR THE CONVECTIVE HEAT TRANSFER CORRE!ATIONS i SE1.ECTED FOR MoDEUNG HEAT TRANSITR FROM THE AP600 CONTAINMENT VESSEL I<
l i
a j 1
4 i j i
1 l 4 l 1-1 i
t 4
i 1
i SW i
4 s
500 -
g
]
$ W g 400 -
y O
Y
- a
- z i
) 2 x0 -
j 2 1
C O N O
- .J 200 - N M
, mW M '
3 100 -
' l i; * ,
0
- O 5 10 15 20 i l
Dimensionless Height (X/d) (
, Test Data + W CorreIation i
4 i
b l l
1 i l
1 I Figure 3.1-4 Local Nu Number Comparison for Hugot Test 4 i
i me a:W1313w.wpf:1b-090194 3-6 J
, - - - . ,r -
sA
ParuMINARY EXPERIMENTAL BASIS FOR THE CONVECTIVE IIEAT TRANSFER CORRELATIONS SELECTED FOR MODELING llEAT TRANSFER FROM THE AP600 COWAtmtENT VLt5EL 500 m
u M
400 -
M w
E f 300 -
z a n z
c 200 -
o u s
100 -
M 0 20 5 10 15 O
Dimensionless Height (X/d)
, Test Data + w correlation l
l Figure 3.15 Local Nu Number Comparison for Ilugot Test 5 u:W1313w.wpf lt>&>0194 3-7
PREUMLN ARY EXPERIMENTAL BASIS FOR THE CONVECIt 4 Es." TRANSPTR CORREIATIONS SELECTED FOR MoDELING HEAT TIuMSFER FRbH THE 11P600 CONTAINMENT VESSEL
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I l
l t
4 3.5 -
N m l 3 -
2.5 -
2 -
y w
w 1.5 -
M y, g
,w *
=
[w
- w y n
=
1 - , ,;,, ***f,*hEI w wa m - - -
m , , , j [ [ ) I f I O,5 0 5 10 15 20 Di-ensionless Length (X/d)
, Data Points Mean value C1.169) i I
Figure 3.1-6 Comparison of Predicted to-Measured Local Nu Numbers for All Tests u:W1313w.wpf:1b-090194 3-8
PRELJhtINARY ExFERI)tENTAI. Basts pVR THE CONVECMT IIEAT TRANSFTR CORRELATIONS sEtzCTED Fon MODELING HEAT TRANstEn Fuoht Tut AP600 COVTAINhtENT VESSEL 3.2 The Eckert and Diaguila Tests")
Eckert and Diaguila conducted heat transfer tests on a vertical tube that was 13.5-ft. high with a 23.25-in. inside diameter. Inlet and outlet air pipes and dense screens were located at each end. A 10-ft. steam jacket supplied steam with a few degrees of superheat 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 determined. An air flow at approximately 80*F at pressures from 1 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.
Hermocouples at the tube center and in the tube wall provided a temperature difference from which the local heat transfer coefficient could be determined. He tests provided heat transfer measurements to validate the mixed convection heat transfer correlation at prototypic Reynolds and Grashof numbers.
The Eckert and Diaguila tests covered both assisting and opposed convection. The calculated local Nusselt number results for each of the 10 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. Some relevant test parameters are shown in the table below.
Test Number Gr oPr Range Re a 1 6.9E09 - 1.1E10 377000 2 6.9E09 - 1.1E10 180000 3 6.9E09 - 1.4E10 100000 4 7.5E09 - 1.6E10 36000 5 1.4E10 - 1.8E10 231000 6 1.3E10 - 2.5E10 134000 7 1.4E10 - 3.7E10 55000 8 3.5E10 - 5.1E10 314000 9 3.5E10 - 5.5E10 246000 10 3.4E10 - 7.2E10 77000 A compilation of the predicted-to-measured local Nusselt numbers for all 10 tests is shown in Figure 3.2-11. The average predicted-to-measured value at each location and mean value over all locations are also shown. The mean value is 1.028 with a standard deviation of 0.272. It should be u;W1313w.wpf;1b-090194 3-9
PRELIMINARY ExFERIMEMAL BA315 FUR THE CONVECTIVE HEAT TRANsfTR CoRRztaTioNs sEncrED FOR MoDELING HEAT TRAN5fTR FROM THE AP600 CONTAINMENT VESSEL noted that the Eckert and Diaguela data showed large, unexplained variations in the original report, thus the standard deviation reported here is not excessive.
De calculated local Nusselt numbers are about equal to or slightly higher than the measured values for cases with lower Reynolds numbers (tests 4,7, and 10). The calculated local Nusselt numbers' decrease in comparison with the measured values as the Reynolds number is increased. The apparent trend of the Eckert and Diaguila data with the Reynolds number may be due to the fact that the measured centerline temperature is not the same as the bulk temperature. It is likely that the data scatter is also due to the changing difference between the bulk and centerline temperatures as the flow develops away from the entrance.
i u:\ap600u313w.wpf:lt>090194 3 10
PazuMINARY ExrEaSIEV. TAL Basts tua THE CONVECTDT HEAT TRANSITR CORRELATIONS SEUCCTED FOR MODEUNG HEAT TRAN5fTR FROM THE AP600 CONTAINMENT VESSEL 3500.o m
3000.0 -
g b
2300 o -
t Q
z N
_# m j 2000.o -
- m
$ n z
$ 1500.0 - m 3
m 1000.0 -
m
, . . i i c.o 1.0 2.0 3.o 4.o 5.o s.o Dimensionless Height (X/D) m Test Data ,_W Correlation l
l Figure 3.2-1 Local Nu Number Comparison for Eckert and Diaguila Test 1 c:\ap601A1313w.wpf;1b-090194 3-11
PRELIMINARY EXPERIMENTAL BASIS FOR THE CONVECT!YE IIEAT TRAN$rER CORRELATIONS SEticTED ron MODELING IlEAT TRANSFER PROM THE AP600 COWAINMENT VESSEL
=
m 6
m 20C0.0 M N =
<saO.o -
- t Z W W
- C N
f g 2000.0 - m 8 m
- z 0
3 E 500.0 - M 0.0 O.0 1.0 2.n 3.0 4.0 5.0 5.0 Dimensionless Height (X/ D) m Test Data , W Correlation l
l Figure 3.2-2 Local Nu Number Comparison for Eckert and Diaguila Test 2 l
r u:WSXA1313w.wpf:ltM90194 3-12
PRELIMINARY EXPERotENTAL BASIS FDR Tile CONVECTIVE HEAT TRANserR CORRELATIONS SELECTED FOR MODELINc HEAT TRAN5f7R FROM TIIE AP600 COPffAINMEW VESSEL 4
4400.0 1200.0 -
1000.0 -
N ,
z e00.0 -
- w w E
Q s00.0 -
, y i
8
- a 400.0 -
u 200.0 -
0.0 0,0 1.0 2.0 3.0 4.0 5.0 6.0 Dimensionless Height (X/D) y Test [hta W CorreiatIon Figure 3.2-3 Local Nu Number Comparison for Eckert and Diaguila Test 3 l ,--
l
- a:w.1313=.wpt:164>o194 3-13 L________________________________. _ _ .
PaEuMLNARY EXPERIMENTAL Basts roR THE CONVEcmt HEAT TRANSFER CORRELATIONS SELECTED FOR MoDELING llEAT TRANSITR FaoM THE AP600 CONTAINMENT VESSEL 4
1400.0 1200.0 -
m 1000.0 -
f x =
c
}
600.0 -
m 5
j s00.0 -
m E
- o W 3 400.0 - M m . .
200.0 -
M N m
0.0 O.0 1.0 2.0 3.0 4.0 5.0 5.0 Dimensionless Height (X/D) m Test Data ,_W CorreIat1on s
Figure 3.2-4 Local Nu Number Comparison for Eckert and Diaguila Test 4 n:\ap600\l313w.wpf:1b-090194 3-14
PREUMNARY ExrtantEmAL Basis inn Tut CONVECTIVE IIEAT TRANSFER CORRE!ATIONS SELECTED FOR MODELING IIEAT TRANSFER PROM Ti!E AP600 COWAIMIENT VESSEL 2500.O m x N
2000.0 - M w
u * ,
a z 1sco.O -
m u a ic1 %
2 1000.0 -
E 8 N J
$n0.0 -
c.0 O.0 1.0 2.0 1.0 4.0 5.0 6.0 Dirrensionless Helgt.t (X/ D) w Test Data + W Correlation Figure 3.2-5 Local Nu Nunber Comparison for Eckert and Diaguila Test 5 a:wt313w.=pt:ib-o>o194 3-15 l
l w-__-__-______- _ - _ _ _ - _ _ _ _ _ _ _ _ _
PRELIMINARY EXPERIMENTAL BA$ts FOR THE CONVECTIVE HEAT TuANstEn CORRELATIONS SE12CTED Foa MODELING Hrat TaANsna FROM THE AP600 COWAINMENT YESSEL 2000.O I
1s00.0 -
D 9 " \1 S
- e g 1000.0 -
x m 8
z m 3
)
500.0 -
E n
N 0.0 O.0 1.0 2.0 3.0 4.0 5.0 6.0 Dimensionless Height (X/D) y Test Data W Cor re lat ion F
Figure 3.2-6 Local Nu Number Comparison for Eckert and Diaguila Test 6 u:\ap60tA1313w.wpf:14090194 3-16
I i PSEllMINARY EXPERIMENTAL Basts fDR THE CONVECMVE IIEAT TRANSitR CORRELATIONS SEtzCTED FOR MoDEttNo llEAT TRANsitR rRoht THE AP600 CONTAINMENT VESSEL l
2000.0 1500.0 -
b 9
- a =
u s-
.a.
O 1000.0 - M 2
z , ,
._ W e
o 8 s00.o - *
- R n
0.0 O.0 1.0 2.0 3.0 4.0 5.0 6.0 Dimensionless Height (X/ D) m Test Data ,_W Correlation l
1 l
Figure 3.2-7 Local Nu Number Comparison for Eckert and Diaguila Test 7 l
u:\ap600\l313w.wpf:lb-090194 3-17
PREUMLNARY EXPERIMENTAL BASIS FOR Tite CONVECTIVE HEAT TRANSITR CORRELATIONS SELECTED roR MODELING HEAT TRANsprR f1 tom Ti1E AP600 CONTAINMENT VESSEL 3000.0 2500.0 - W W
Z 2000.0 -
W W
+J Y
h 1500.0 -
b O M J
10n0.0 -
N W
S00.0 O.0 1.0 2.0 3.0 4.0 5.0 6.0 Dirnensionless Height CX/D)
W Test Data + W Correlation Figure 3.2-8 Local Nu Number Comparison for Eckert and Diaguila Test 8 a:\ap60(M313w.wpf:1b-090194 3-18
PRELIMINARY EXPERIMENTAL BAST > FOR THE CONVECTIVE IIEAT TRANSFER CORRELATIONS SE12CTED Foa MooELING IIEAT TRANSFER FROM THE AP600 COSTAINMEvr VESSEL l
l l
2s00.0 W
2000.0 - M N
i b Z 1500.0 -
W a
3 *
$ W E So00.0 - w E
8
_a M
500.0 -
m 0.0 O.0 1.0 2.0 3.0 4.0 5.0 6.0 Olmensionless Height (X/D)
W Test Data , W Correlation Figure 3.2-9 Local Nu Number Comparison for Eckert and Diaguila Test 9 unap601A1313w.wpf:lt490194 3 19
PREUMINARY ExrERatENTAL BASIS FUR TIIE CONVECTIVE HEAT TRANsrER CORRELATIONS SEMCTED FOR MODELING IIEAT TRANSFER FROM THE AP600 CONTAINMENT VESSEL 2500.0 2000.0 -
S 1500.0 -
u m 8
I M N 1000.0 -
c 5 a
o
_J M
$00.0 - M N
M 0.0 O.0 1.0 2.0 3.0 4.0 5.0 Dimensionless Height (X/D) y Test Data + w Correlation Figure 3.2-10 Local Nu Number Comparison for Eckert and Diaguila Test 10
! ar.p6m1313w.wpcib-090194 3-20
PREUMINARY EzrERaimTAL Basts FOR THE CONVECT!YE HEAT TRANssTR CORRELATIONS SELECTED FOR MODELING HEAT TRANSITR 71 TOM THE AP600 CONTAINMENT VESSEL 2.0 m
b
$ w m z m 1.5 -
m y l y 3 3
2 m w *
- j c
m y
W j *
- w
- E g M
b a v g*
w I A 0 i '- -
g *;* M ,*
g*E*wm wgM NW mgg 3 w M w E , , w
$ E
- m M ,
h y w 0.5 -
[
2
?
k 0.0 O.0 1.0 2.0 3.0 4.0 5.0 8.0 Dimensionless Height (X/d) y Data Points Average Value Mean Value (1.028)
Figure 3.2-11 Comparison of Predicted-to-Measured Local Nu Numbers for All Tests u:w1313w.wpf:ib-mo194 3-21
PREUMINARY ExrERLurxrAL BASIS FDR THE CONVECT!YE HEAT TRANSFER CORRELATIONS sE12crED FOR MODELING !! EAT TRANSFER FROM THE AP600 COvrAINMENT VESSEL 3.3 The Siegel and Norris Tests
- Siegel and Norris conducted heat transfer tests on a set of heated parallel vertical flat plates on which a constant wall heat flux was maintained. De channel height was 5.833 ft. and the plate separation distance was variable between 0.125 to 1.25 ft. A constant, uniform heat flux of approximately 1100 Btu /hr-ft2 was applied. Only the tests in which the test section was open at the bottom were examined for comparison. The tests provide data for validating assisting mixed convection heat transfer for low Reynolds numbers and moderate Grashof numbers.
The tests were modeled using the.WGOTHIC code. He test section was divided into 11 axial volumes. The first 10 volumes were each 1/15th of the total volume; the last volume was 1/3 of the total volume. The code calculated the velocity, air temperature, and heat transfer coefficient in each of the 11 volumes. The local heat transfer coefficient was calculated using the method for combining the free and forced convection correlations described in Section 2.1.
Siegel and Norris reported heat transfer coefficients based on the (Tw - Tw ,,) temperature difference.
Consequently, the WGOTHIC predictions, which are based on the (T - Tm) temperature difference, were transformed to a basis comparable to the Siegel and Norris data for presentation.
The calculated local Nusselt number results for each of the 8 tests are compared with the test data and are shown as a function of dimensionless height in Figures 3.3-1 through 3.3-8. Some relevant test parameters are shown in the table below.
Test Number llD. Air Temp. (*F) GroPr Range Re, Range 1 3.00 80.6 - 86.4 4.23E08 - 6.10E08 1.07 - 1.13E04 2 4.16 80.9 - 88.5 1.58E08 - 2.42E08 8.73 - 9.18E03 3 7.66 81.2 - 93.5 2.40E07 - 4.19E07 5.77 - 6.03E03 4 12.33 81.5 - 99.4 4.40E06 - 1.05E07 4.01 - 4.18E03 5 24.00 82.6 - 114.6 6.43E05 - 1.48E06 2.20 - 2.28E03 6 12.33 81.5 - 100.3 5.42E06 - 1.17E07 3.82 - 3.98E03 7 12.33 82.1 - 107.6 6.43E06 - 1.17E07 2.76 - 2.89E03 8 12.33 83.4 - 123.4 6.70E06 - 1.29E07 1.65 - 1.73E03
PRELIMLNAkV EXPERIMLWTAL BASIS FOR TIIE CONVECTIVE IIEAT TRANSFTR CORRELATIONS SELECTED FOR MODELLNG HEAT TRANSITR 51 TOM Tite AP600 CONTAINMEVT VESSEL A compilation of the predicted-to-measured local Nusselt numbers for all 8 tests is shown in Figure 3.3-9. The mean predicted-to-measured value of 0.857 is also shown. The standard deviation of the predicted-to-measured values for all 8 tests is 0.0903.
As demonstrated in tests 1 through 5, the calculated local Nusselt numbers match the measured data fairly well at lower values of UD,, but increasingly under-predict as the UD, value increases. Tests 4, 6,7, and 8 demonstrate the effect of reduced air flow (at constant UD )n by increasing the channel loss coefficient from 1.5 to 35.6. The calculated local Nusselt numbers increasingly under-predict the measured values as the air flow is reduced.
u:\ap60A1313w.wpf:lli.090194 3-23
PREUMINARY ErrERIMENTAL BASIS FOR THE CONVECTIVE IIEAT TRANSIT.R CORRELATIONS SELECTED FOR MODELING IIEAT TMNSFER FROM Tite AP600 CoNTAINutur VESSEL 300 250 - W t 200 -
o z
15c g -
E o
J 100 - m M
$0 -
w 0
O 0.5 1 1.5 2 2.5 3 3.5 Dirnensionless Height (X/ d) m Test Data + w Correlation Figure 3.31 Local Nu Number Comparison for Siegel and Norris Test I u:W1313w.wpf:1b-090194 3-24
4 i
4 i PREuMINARY IEXPERDIENTAL BASIS FOR TIIE CONVECTIVE HEAT TRANSFER CORRE1.ATIONS i set,1CTED FOR MODEUNC HEAT TRANSFER FROM THE AP600 CO.VTAINMENT VESSEL 5-
' i l
1 1
l
\
i 1
l i
300 250 -
200 -
)
t o
Z ,
a sso -
l Z
c ,
O j o i J 100 - w !
l m .l so -
W o ,
O 1 2 3 4 5 Dimensionless Heir,. CX/d)
, Test Data +. w orrelatlen Figure 33-2 Local Nu Number Comparison for Siegel and Norris Test 2 a:W1313w.wpf:1b-090194 3-25
J e
i i PREUMINARY ExFERIMENTAL BASIS FOR Tile CONVEcTtvE HEAT TRANSFER CORRELATIONS SELECTED FOR MODEUNG HEAT TRANSFER FROM THE AP600 CowrA!NMENT YESSEL f
e 250 W
200 -
L 150 N f3 -
Z -
3 Z
100 - g O
J K
I 50 -
I 1
l m
' i , ,
' ' i D g 0 1 2 3 4~ 5 6 7 e Dimensionless Height (X/d)
. Test Data + w correlation J
l i
i Figure 3.3-3 Local Nu Number Comparison for Siegel and Norris Test 3 m:W1313w.wpf:lb-090194 3-26
. _ . . . _ _ . _ _ _ ._.i
1 1
PCEUMINARY EXPERIMENTAL BASIS FOR THE CONVECTIVE HEAT TRANSFER CORRELATIONS SP1ECTED FOR MODELING HEAT TRANSFER FROM THE AP600 CONTA!hMENT VESSEL I
4
.4 250 m
200 -
b S 150 -
m 5
z g 100 -
o 50 -
a w
0 O 5 10 15 Dimensionless Height (X/d)
. Test Data _ _w correlation i
l l
l l
l 4
l I
l Figure 3.3-4 Local Nu Number Comparison for Siegel and Norris Test 4 1
n:W1313w.wpf:Ib-090194 3-27 I
PaEUMINA Y ExrERIMENTAL BAS 15 FOR THE CONVECnVE HEAT TRANSFER CORRELATIONS SEtzerED FOR MootLtNo HEAT TRANSFER FROM THE AP600 CowrAINMENr VESSEL 250 N
200 -
g-150 -
S3 2 m S
c 100 -
S N
50 -
N
,w O 30 5 10 15 20 25 0
Dirnensionless Height (X/d) y Test Data +W Correlat ion i
I l
Figure 3.3 5 Local Nu Number Comparison for Siegel and Norris Test 5 ,
1 u:W1313w.wpf:lb-090194 3 28
- e e . - - -r ,
j PREUMINARY EIFERIMENTAL BASIS FOR THE CONVECTIVE HEAT TRANSFER CORRELATIONS I
SELECTED FOR MODEuNo HEAT IRANSFER FROM THE AP600 CONTAINMENT YESSEL I
1 J
250 i l l
1 1
l m ,
l l
I l
i t
l t o
150 -
z s
e 100 -
o; W
50 -
- 1 e ,
o q$
0 5 10 Dirnensionless Height (X/d) m Test Data + w correlation Figure 3.3-6 Local Nu Number Comparison for Siegel and Norris Test 6 n:W1313w.wpf:!M190194 .3 29
. _ - - .- . . _ . . - - . . . . _ . . . . . _ . _ . - . ._ . . _ . - ..._ , _.~ _
4 a PREUMINACY 4
ExrEamErtrAL BASIS FOR THE CONVECTIVE HEAT TRANSFER CORRELATIONS SELECTED FOR MODELING HEAT TRANSFER FROM THE AP600 CONTAINMENT VESSEL l
250 4
200 -
n L
e 150 -
2 m z
g 100 -
0 N
-.s n
so -
w i
o 4 a -.
O : 10 15 L nansionless Height (X/d) r
, Test Data _ _w correlation l
Figure 3.3-7 Local Nu Number Comparison for Siegel and Norris Test 7 a:WWMA1313w.wpf:Ib4J90194 3-30 ,
_ _ _ . - . . _ . . . _ __ . . - _ . _ . . . . - _ - - . = .. ..
l l
PRELIMINARY j
ExFERIMorrAL BASIS FOR THE CONVECTIVE HEAT TRANSFER CORAEIATIONS i
SELECTED FOR MODELING HEATTRANSFER FROM THE AP600 CONTAINMENT VFmEL I
l
.i 1
200 150 -
l L i o w
l 2 l 3 100 - /
Z l to v w 0
J 50 -
w u
O O 5 10 15 Dimensionless Height (X/d) y Test Data +W Cort e lat ion I
J 1
1 l
l J
Figure 33-8 Local Nu Number Comparison for Siegel and Norris Test 8 .
l n:W1313w.wpf.1bo90194 3 31
i
$_ PREuMLNACY ExPERLMEP(TAL BA$1S FOR THE CONVECTIVE HEAT TRANSFER CORREIATIONS j SELECTED FOR MODELLNG HEAT TRANSFER FROM THE AP600 CONTAINMEPfT VESSEL j
6 I
i i
1 i
t 1
]-
1.6 i
b 1.4 g -
J 3 z
a 2
1.2 g
- e U
O J w 1 V 1 -
S ya b ww W un e w
- W" w j *- w w a o.s Jik* w w
- w De) I *m ,
y y
4 v
_O 3 a.s
! k
' ' i i D.4 25 C 5 10 15 20 Dimensionless Length CX/d) y Data Points Mean Value (0.857)
Figure 3.3-9 Comparison of Predicted-to-Measured Local Nu Numbers for All Tests u:W1313w.wpfilb-090194 3-32
PRELIMINARY EXPERIMENTAL BASIS FOR THE CONVECrIVE HEAT TRANSFER CORRELATIONS SELECTED Poa MoDELING HEAT TRANSFYR 71 TOM THE AP600 CONTAINMENT VL9sEL i
5
4.0 CONCLUSION
S The heat transfer correlations that are used in the WGOTHIC code to model the convectiu.. heat transfer from the AP600 containment have been presented in this report. These correlations have been
, widely used and accepted for the calculation of heat transfer for similar geometries.
A number of separate effects tests utilizing geometries representative of the AP600 annulus have been examined. These tests cover the range of expected conditions for convective heat transfer within the AP600 annulus.
The method of calculating the annulus convective heat transfer coefficient in the WGOTHIC code has been compared with these test data and yields acceptable results. The comparisons to the available test data show that the calculated local hea: transfer coefficients demonstrate the proper trends.
The capability to model the AP600 DBA pressure and temperature response and associated uncertainties in an integral setting will be assessed using results from the large-scale tests.
l l
l l
l uAap600\l313w.wpf:1b-(N0194 41
PREUMINARY l J
EXPERIMENTAL BASIS FOR THE CONVECTIVE HEAT TRANSFER CORREtATIONS SE12CTED FOR MODELING HEAT TRANSFER 51 TOM Tile AP600 CONTAINMENT VESSEL I
5.0 REFERENCES
l
- 1. W. H. McAdams, Heat Transmission, Bird Edition, McGraw-Hill,1954. j I
- 2. A. P. Colburn, "A Method of Correlating Forced Convection Heat Transfer Data and a Comparison With Fluid Friction," Transactions of the AIChE, Vol. 29 (1933), p.174.
- 3. 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. Schlunder, Ed. in-Chief, Heat Exchanger Design Handbook, Hemisphere Publishing Corp.1983.
- 4. E. R. G. Eckert and A. J. Diaguila, " Convective Heat Transfer for Mixed, Free, and Forced Flow % rough Tubes," Transactions of the ASAfE, May,1954, pp 497-504.
- 5. L. M. K. Boelter, G. Young, and H. W. Iverson, NACA TN 1451,1948.
- 6. R. Siegel and R. H. Norris, " Test of Free Convection in a Partially Enclosed Space Between Two Heated Vertical Plates," Transaction of the ASME, Journal of Heat Tre.nsfer, April 1957. l
- 7. G. Hugot, " Study of the Natural Convection Between Two Plane, Vertical, Parallel, and Isothermal Plates," derived from doctoral dissertation University of Paris,1972, translated by D. R. de Boisblanc, Ebasco Services Incorporated, June 1991.
- 8. H. Schlichting, Boundary Ioyer Theory, Sixth Edition, McGraw-Hill.
- 9. G. C. Vliet, " Natural Convection Local Heat Transfer on Constant-Heat Flux Inclined Surfaces," Journal of Heat Transfer, November 1969, pp 511-516.
- 10. J. Woodcock, et. al. WCAP-13246, " Westinghouse-GOTHIC: A Computer Code for Analysis of Thermal Hydraulic Transients for Nuclear Plant Containments and Auxiliary Buildings,"
July 1992.
- 11. L. C. Burmeister, Convective Heat Transfer, John Wiley & Sons,1983.
u:\ap600\l313w.wrf:Ib-090194 5-1