ML20029C824
| ML20029C824 | |
| Person / Time | |
|---|---|
| Site: | 05200003 |
| Issue date: | 12/31/1993 |
| From: | WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML19304C018 | List: |
| References | |
| NTD-NRC-94-4100, NUDOCS 9404290272 | |
| Download: ML20029C824 (32) | |
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Enclosure 3 to Westinghouse Letter NTD.NRC 94 4100 Non proprietary Copy Westinghouse AP600 Letter Reports Radiation Heat Transfer Through Fog in the PCCS Air Gap December,1993 Liquid Film Model Validation January,1994
.L 9404290272 940410 PDR ADOCK 05200003 A PDR
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Radiation Heat Transfer Through Fog in the PCCS Air Gap December,1993 Observadon of the air gap,,in the SST and LST during normal operation shows that fog somedmes forms in the air gap and obscures visibility of the hot pressure vessel, and in some cases condenses on the baffle.
Predictions for AP600 also indicate that fog may form in the PCCS riser under certalo operadng condidons of inlet temperature, humidity, and evaporation rate. Because fog affects the transmittal of
, visible light, it is reasonable to expect that fog will interfere with the transmittal of infrared radiation which, with dry PCCS air, is transferred from the hot pressure vessel surface to the cooler baffle. The presence of condensation in the PCCS riser may violate the assumptions of the model which calculates radiation heat transfer from the containment surface to the baffle inner surface.
Air at ambient temperature and humidity are drawn into the PCCS downcomer. The air is warmed slightly by heat transfer from the hotter baffle as it flows to the bottom of the baffle, then flows up the riser along the warm, wetted containment surface. As the liquid 61m evaporates, the humidity of the PCCS air increases until it reaches saturation, th'en further evaporation causes vapor to condense, forming fog. The condensation process releases the latent heat of the vapor, which increases the temperature of the saturated air, increasing the saturadon pressure of the air and the amount of vapor which the air can hold without condensadon, A one-dimensional conceptual model of condensadon (fog formation) in the air gap indicates that the humidity and temperature of the gap air increase from the inlet values due to the liquid film evaporadon and sensible heat transfer to the air. When the local bulk humidity exceeds 100%, fog fills the gap:
EGOTHICm calculations for AP600 with the airj etLtemperature at 115 F and 85 P wet bulb produced a peak outlet air temperature of approximately )%t these high air temperatures, the humidity of the bulk air at the outlet was well below the on condidon. With a lower inlet air temperature, fog .
formation becomes more likely, even though the containment heat rejection improves at lower air temperatures.
The actual development of fog in the gap is more complicated and is two dimensional. Figure 1 shows 1 a transverse temperature distribution measured in the STC Flat Plate TestsA which has temperature !
distributions at the hot surface and baffle surface similar to those expected in the LST and AP600 air gaps.
From the temperature distribution the saturation pressure was determined and is plotted in Figure 2. If the evaporation vapor flux is low, as for Gradient 1, the boundary layer air remains superheated and no fog appears. At a higher vapor flux, given by Gradient 2, the local vapor pressure may exceed the saturadon pressure and fog will form in portions of the boundary layer. Either of these surface gradients may combine with a low bulk vapor concentration, Bulk 1, which is too low to form fog throughout the bulk flow. Similarly, either may combine with a high vapor concentradon, Bulk 2, which does produce bulk co@ Won. Personal obsenation of several large scale tests has demo'nstrated the occurrence of three of the four combinadoes. The fourth, bulk condensation with a superheated boundary layer, may l have occurred but the bulk condensation obscured the boundary layer.
Analytical methods can be developed to calculate the deposition of radiant energy in a fog of nonuniform density between the pressure vessel wall and the baffle. However, the boundary layer models in EGOTHIC are valid only for nodes thicker than the boundary layer and thus cannot resolve detail within the boundary layer. Because the two-dimensional fog formadon as suggested by Gradient 2 in Figure 2 cannot be explicitly modeled with EGOTHIC, the consequences of neglecting radiation capture by fog in EGOTHIC must be determined.
It can be shown with the help of se.veral cases of high and low heat flux, wet and dry large scale tests, that radiation only produces a significant fraction of the total pressure vessel heat rejection for cases
l l
without an evaporadog water Sim. With an evaporadog film, radiadon is negligibly sm'all. Table I presents the measured temperatures from which the total and radiation heat flux were calculated at the B instrumentation level (26 ipches below the upper spring line) for six large scale test cases and for AP600 )
just below the spring line. Radiation heat transfer is approximately 1/2 of the total heat transfer for the dry tests, while for the wet tests, radiation is less than 5% of the total heat transfer. AP600, at comparable internal pressures, has heat fluxes and temperatures which are comparable in magnitude to those in the IET. The LST wall, baffle, and wall temperature difference in Table 1 are measured values"4 The total heat flux was calculated from the measured wall temperature difference and the conduction equation 4" = dx8 (1) where k has a value of 27 BTU /hr ft Fm, and dT/dx is the wall temperature gradient defined at steady state as the wall temperature difference divided by the 27/32 inch distancem between the wall thermccouples.
The mdiant heat flux was calculated from the baffle and wall absolute temperatures using the net radiation heat transfer equadon (2) 4" = aF(TL-T&
with a grey body shape factor, F, of 0.91, calculated with emissivities for the vessel and baffle of 0.95W.
The AP600 values were taken from SSARNcalculations for the double ended cold leg guillotine break at 700 seconds. -
It may be concluded from the results presented in.Table I that neglecting the radiation absorption of fog, if fog is present, introduces an error ofless than.5% on containment heat rejection. By considering where the radiation is deposited, it can be shown that the actual enor is even less.
When fog appears in the riser, a fraction of the radiation from the pressure vessel is deposited in the fog and the remainder is deposited in the baffle. Figure 3 shows that the air and baffle temperatures differ by only a few degrees, whereas both are significantly less than the pressure vessel surface temperature.
Thus, whether the radiation is deposited in the fog or in the baffle has little affect on the containment radiation heat transfer, and containment radiation heat transfer was shown in Table I to be less than 5%
of the total. It may be conclu&d that fog in the air gap does not significantly affect the calculation of either local or global containment heat rejection.
Radiation heat transfer is a more significant fraction of the total heat input to the baffle and to the air than from the pressure vessel. If it is assumed that fog does not affect the radiadon heat transfer, the radiation to the baffle will be overestimated and deposition in the fog will be underestimated. In AP600 the overestimadon of heat transfer to the baffle will increase the baffle temperature and overestimate the heat loss to the downcomer air. This results in a small decrease in the buoyant head, a small reduction in the natural convection air flow rate, and a small reduction in the dominant convective heat and mass transfer from the pressure vessel. Unless a very accurate predicdon of the baffle is required, the overpredicted baffle temperature will only result in a small underprediction of the containment heat removal and a small overprediction of the containment pressure and temperature.
Neglecting the radiant deposition in the fog results in an underestimate of the humid air tempeinture. The amount by which the air temperature is underestimated can be quantified and shown to be on the order of I to 2 F by the following simple e:tample.
Assume there is sufficient fog in the gap to capture all of the radiation from the pressure vessel. At the
Table 1 LARGE SCALE TEST RESULTS AND AP600 CALCULATIONS SHOWING TiiE RATIO OF RADIATION HEAT TRANSFER TO THE TOTAL HEAT TRANSFER TEST CASE 104.2 115.1 119.1 206.1 201.1 203.2 AP600 Dry Dry Dry Wet Wet Wet Wet
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PRESSURE (psig)
VELOCIT( (ft/sec)
TEMPERATURES (F) ;
Wall Outer Baffle Inner Wall AT L m -,
2 CALCULATED HEAT FLUX (BTU /hr-ft ) ,
q
~
0.) O Radiation l
1 Ratio: Rad / Total _
peak heat load the heat off the vessel is approxituately 10' BTU /hr. Since radiation accounts for less than i 5% of the total heat rejected, the captured energy will be 5x10' BTU /hr, or 1389 BTU /sec. This heat will go primarily into reevaporating some of the fog and to a minor extent into increasing the enthalpy of the humid air. Considering only the evaporadon, and with hgapproximately 1000 BTU /lbm,1.389 lbm/sec of fog will be reevaporated, if there is not enough fog available to suppon this evaporation rate, then the radiation will not be captured. A sensible temperature increase is required to increase the local saturation j pressure enough to suppon the increased vapor load. With an air flow rate of 290 lbm/sec, corresponding to 10 ft/sec in the vertical annulus, the increase in the humidity ratio is com % , = 1.389
= 0.00479 (3) 290 The humidity ratio at saturadon is related to the steam saturation pressure by the equation 0.622 P" (4)
(o* =
P ,-P ,
With Equation 4, Equation 3 can be rewrinen as
.622 P m 0.622 P, (0)
%s *%s
- pm .p m.1
'y a _p m.n With P. = 14.7 psia, and because AP = Pe P is very small relative to P., Equation 5 can be approximated as 0.622 AP N1 -Ni " N g 4,7 _ p The required difference in the humidity ratios calculated above,0.00479, can now be used to calculate the corresponding difference in saturation pressure and the corresponding temperature increase required to support the increased vapor load. By selecting arbitrary, but reasonable values of temperature,it can be shown that the temperature increase is small enough to be neglected, and thus, the effect of radiation capture by fog in AP600 has a negligible effect on the air temperature. Table 2 presents the values calculated with Equation 6 and the saturation pressure temperature relationship from the steam tables ,
m Table 2 AIR TEMPERATURE INCREASE RESULTING FROM FOG CAPTURING ALL THE VESSEL RADIATION '
Arbitrary AP,,, (psia) Air Temp Increase (F)
Air Temo fF) Equation 6 Steam Table 160 0.0766 0.68 ,
140 0.0909 1.22 120 0.1001 2.13 l 100 0.1058 3.71 1
I l
Note that the lower the air temperature, the less effect the air temperature increase will have on the steam partial pressure difference from the hot (-200 F) wall to the cooler air. The evaporation mass flux which accounts for approximately 90% of the containment heat rejection is proportional to the steam partial pressure difference So, although the air temperature calculation error increases at lower ternperatures, the effect on the mass transfer, the dominant energy transport mechanism, decreases at lower temperatures.
'The net effect on the air temperature is the comblyd e from the low inlet temperature to the hotter outlet temperature In AP600 at 115 F inlet and(,) J et the combined effect of capturing all the radiation, by inspection of Table 2, is less than 2 F.
In summary, the consequence of neglecting the capture by fog of the radiant heat transfer from containment is not significant relative to the overall containment heat rejection, is less than 1 to 2 degrees Fahrenheit on the gap air temperature, and produces an overestimate of the baffle temperature and heat loss to the downcomer air. Only if the baffle ternperature is specifically ofinterest (and an overestimated
ternperature is not acceptable) is it necessary to consider the actual capture of radiant heat transfer by fog.
The actual calculadon of fog capture is quite complicated, requiring the simultaneous calculation of two dimensional velocity, temperature and concentratico fields, with phase change and both molecular and turbulent transport of rnomentum, enthalpy and gas species. The phase change occurs by drop formation, so models are required for the dinneter of drops formed from the homogeneous nucleation of drops from supersaturated air, and for heat and mass transfer to and from the drops. The medel must be valid in the boundary layer, where fog likely forms first, u well as in the bulk flow. The absorption and scatter of the locident radiant energy on the droplets must be modeled, and because t.'e drop diameter is of the sene order as the wave length of the dominant infrared radiadon,2 to 4 mh tcas, a complicated model such as the Mie solution to the Maxwell equation fy: radiation must be used. These formidable analytical i challenges led to the approach of quantifying the effect of neglecting fog, rather than to calculate its minor l effect.
References
- 1. " Simplified Passive Advanced Light Water Reactor Plant Program, AP600 Standard Safety Analysis Report", June 26,1992,
- 2. W. A. Stewart, A. T. Pieczynski, L E. Conway, ' Tests of Heat Transfer and Water film Evaporation on a Heated Plate Simulating Cooling of the AP600 Reactor Containment" WCAP 12665, Westinghouse Proprietary Class 2. .
- 3. " Heavy Water Reactor Facility Large Scale Passive Containment Cooling System Confirmatory Test Data Report," HWRF-RET-93-001, July 15,1993.
- 4. "AP6001/8 Large Scale Passive Containment Cooling System Heat Transfer Test Baseline Data Report", WCAP-13566. Rev 1, Westinghouse Proprietary Class 2.
- 5. R. E. Taylor, H. Groot and J. Ferrier, "Thermophysical Properties of Steel Samples - A Report to Westinghouse Electric Corporation", TPRL 1265, March 1993, Thermophysical Properties Research Laboratory, Purdue University, West Lafayette, Indiana.
- 6. D. R. Spencer, " Emissivity for Contalnment and Test Matedals", ET-RMOI CDBT 92 207, April 29, 1992.
- 7. J. H. Keenan and F. G. Keyes, Thermodynamic Propenies o/ Stear., First Edition, John Wiley,1936.
170 H
160 f
150- c Baffle Surface Uquid Filrn Surface _--am b 140- - -
C
- 130--
2 -
a lii 120 k
g 110-jgg_ .
I go __
80! _
70 , , , , , , ,
0 0.5 1 1.5 2 2.5 3 3.5 4 Distance from Baffle (inches)
Figure 1 PCCS Gap Air Temperature Distribution in Flat Plate Test 10 l
l l
4- W
4 N
5 :s 4.5 -~c Baffle Surface Uquid Film Surface -liiii L bi lir 4- -
---/ f:
m .:
O f\ .I e 3.5 = ,
u f:,
3 Gradient 2 _._
k 8 2.5
. 7f P
y 7
't m Gradient 1 i :
cc -
" ^
2 M i
!\ '
g 1.5-
\\- -
3 ...q.......q.. ... .. y........ ...... ..z . ..Bd k 2 -- q- -- z -- - g -- - q -- - q --
g
.s Fog
\ \ j' -
0.5 .- _
...............................................BWk.1.------.....-.......--.-...-..-- -.
0 , , , , , , ,
0 0.5 1 1.5 2 2.5 3 3.5 4 Distance from Baffle (inches)
Figure 2 PCCS Gap Air Saturation Pressure Distribution in Flat Plate Test 10 4
O -
)
i
.gj h ,
P C
b 5
a 1-Olstance along Baffle (inches)
Figure 3 Vessel, Baffle and PCCS Air Temperatures in Wet Large Scale Tests
LIQUID FILht MODEL VALIDATION by: D. R. Spencer January,1994 1.0 Introduction The AP600 bas two distinct beat transfer regions: inside containment and outside containment. Heat transfer from the contamment atmosphere to the containment inner surface is prtmartly by way of condensation and convective beat transfer. (Radiation is not sigmficant mside containment for design basis accidents.) The process of condensation on the inside of containment produces a thin (0.006 inch cr less) film of liquid water. The liquid fdm develops as a LOCA transient proceeds and the outer surface of the liquid film becomes the surface on which condensation takes place, and to which convective beat transfer occurs. Heat is transferred by conducdon from the containment atmospbere, through the ligid film, to the contamment surface. In terms of reladve magnitude, tbc equivalent beat transfer coefficients for the liquid film, for condensation and for convection are approximately 500 2
Bh-ft'-F,30 Bh ft F and 3 2 B&-ft F, respectively. Using these values, the liquid film accounts for approximately 6% of the thermal resistance between the containment atmosphere and the solid containment surface.
Heat transfer from the containment outer surface to the cooling air annulus is modeled by conducuon through the liquid water fdm, by evaporadon and convecuon from the liquid fdtn to the cooling air, and by radiation from the liquid film surface to the baffic inner surface. When the containment exterior is dry tbc liquid film and evaporadon are not included, Radiadon from containment beats the baffle inner surface which transfers additional beat to the cooling air by convection and transfers beat through the baffic wall by conduedon. The beat transfer to the cooling air induces a natural convection flow in the cooling air annulus which enhances beat removal from contamment. .
2 The equivalent radiation beat transfer coefficient is approximately 0.6 Bh ft F while the convecuve beat transfer I 2
coefficient is 1 B/bs ft 2-F, and the evaporation coefficient is 60 Bh ft -F. The liquid fdm beat transfer coefficient l 2
is 400 Bh ft -F or higher over 93% of the dome and all of the vertical sides. .I Three types of flow instability affect the containment liquid films. Gravitational instability causes the condensate i on the underside of borizontal or near-borizontal surfaces to form large drops which fall as ram, while the j condensare n: mains attached to sloped surfaces and drains downward. The surface area affected by gravitauonal l instability is limited in AP600 and is discussed in Secnon 2.0. l l
Hydrodynamic instability causes flow disturbances to be amplified and leads to a transition from smooth laminar to wayy laminar flow at Reynolds numbers of 10 to 30. Hydrodynamic instability subsequently causes a transidon from wavy laminar flow to turbulent flow at Reynolds numbers on the order of 2000. Both wavy laminar flow and turbulent flow cause a departure of the beat transfer from that fcr smooth hmmar flow. The modeling of wavy laminar flow is presented in Section 2.0.
Wetting instability puts a lower limit on the thickness of a liquid fihn: a fdm which is too thin may separate into two thicker rivuleta, or may contract undl it's thickness is equal to the lower stability limit. This type of fdm instability is presented in Section 3.0. l Another property of liquid fdms is their capability for convecuve enthalpy transport as the liquid flows over a surface. Tbe liquid film can function as either a source or sink for a fraction of the containment surface beat flux.
This fraction is generally only significant when cold water is applied to a warm surface, such as the application of the PCCS cooling water to the central dome region of AP600. The subject of subcooled beat transport by the liquid film is discussed in Section 4.0.
t 2.0 Liquid Film Thickness and Heat Transfer The classical Nusselt model for (be gravity induced laminar flow of liquid down an inclined surface' provides a simple model for smoodi liquid film flows. The correlation for the film thickrx:ss is
1
< vn 3,'3" v2 R e , ,,
m
,4, t g smte),
Robsenow showed that for the low beat fluxes of interest to AP600 (c,aTA < 0.01) the temperature distnbution 2
through the liquid nlm is linear and thus b = k/6. With the reference length defined L = (v /(g sin (0)))'", and the Nusselt number defined by Nu = bL/k, the beat transfer correlation is Nu =
/
4u Re *n (2)
<T >
The term g sin (0) produces a result which is valid for any angle of inclination except borizontal. For boruontal surfaces facing downward, gravitauonal instability causes rain drops to form and fall from the surface. For boruontal surfaces facing upward the liquid will establish a surface gradient as necessary to satisfy the flow rate. Section 2.4 shows that horizontal portions of contamment do not present realistic analytical problems in the overall solution.
2.1 Liquid Film Thickness and Heat Transfer Equations Liquid fdms bave been categorized into three flow regimes: at the lowest Reynolds numbers the fdm surface is smooth and the Dow is laminar, consistent with the Nusselt model. At a Reynolds number of 10 to 30, the surface 2
of water films begins to exhibit waves. The waves travel at speeds 1.5 to 2 times the average liquid film velocity and can grow to contain a large fraction of the total mass flow'. The wavy fdm is locally thinner than the value given by Equadon 1, except at the waves where it can be much thicker. Waves thus produce an effective thickness for beat transfer which is less than the average film thickness. At Reynolds numbers higher than approximately 2000, the liquid fdm becomes turbulent and the turbulent diffusion causes the beat transfer to become greater than the values given by thermal conduction through the thickness. It is shown in Section 2.3 that tbc Reynolds numbers for AP600 condensing and evaporating liquid fdms are largely those of wavy laminar fdms.
The Chun and Seban' correlation for wavy lanunar films is used in the WGOTHIC code. The film thickness model from Chun and Seban, which accounts for the wavy surface gives an effective beat transfer thickness of f T l /3 6 = 1.216 Re 22 W
g stn(0) ,
The Chun and Seban beat transfer correladon is:
Nu = 0.822 Re-22 @
where
< m h v2 (5)
Nu = T(g sin (e) ,
Note the similarity of the Chun and Seban correlations, Equadons 3 and 4, to the Nusselt correlations, Equadons I and 2. The Chun and Seban equations art equal to the Nusselt equations at Re = 14. At Reynolds numbers greater than 14 the Chun and Seban correladon predicu increased beat transfer due to the wavy nature of the bmmr fihn.
2.2 Experimental Bases for L6 quid Film Equations The large scale tests"" (LST), the Wisconsin condensation tests *", and the paper by Chun and Seban are the bases for the Westingbouse liquid fdm beat transfer model. The LST data are used for integral comparisons.
The Wisconsin tests provide the separate effects data for validating the correladon for condensing liquid film beat transfer and Chun and Seban provide the separate effects data for validating the correlation for evaporating liquid film beat transfer.
4
-l
. l l
Tbc dome condensate was collected and measured in the LST Phase 2 Tests at an internal gutter located approximately 2 feet below the spring line, separately collected and measured from the intemal gutter down to the _1 I
operaung deck, and the ram from the dome collected and measured. De intemal gutter in the 1.ST corresponds to I the polar crane rail support structure in the AP600 which removes all condensate from above. The liquid nlm then builds up on the vertical sbell starting from zero thickness below the crane rail.
The Wisconsin tests provided a measurement of the liquid fdm beat transfer coefncient for a range of surface inclinations from verucal to bonzontal as discussed in Section 2.4. De Wisconsin tests showed that ram occurs on the prototypic inorganic zine surface for angles of one degree from borizontal of less. The liquid remams attached and flows down the surface for larger angles.
The paper by Chun and Seban presents correlations for the liquid fdm thickness, the liquid film Nusselt number and beat transfer coefficient, parameters which characterize tbc transition from laminar to turbulent film How, and comparisons to test data for evaporating laminar and turbulent fdm flow.
2 3 Scaling Both the classical Nusselt model and the Chun and Seban model characterize the laminar liquid film beat transfer i with only two dimensionless groups: the Nusselt and Reynolds numbers. In addition, the Reynolds number for wave incepdon and for transition from laminar to turbulent flow may be characterized by tbc Kapitza number (Reference 4 correlates transiuon with tbc Archimedes number, the inverse of the Kapitza number). De correlation for wave incepdon given by Chun and Seban (attributed to Kapitza)is Re, = 2.43(Kayiin (6) and the correlation for transinon to turbulent flow is Re, = 0.215(Kar'd (7)
The resulting inception and transition Reynolds numbers for water at 200 F are 33 and 2905. Figures i and 2 show the distribuuon of liquid fdm Reynolds numbers on the inside and outside of the AP600 Approximately 97% of the AP600 liquid film Reynolds numbers are within the wavy taminar range. Consequently, only the wavy laminar correlations are included in EGOTHIC, Note that Equations 6 and 7 are not in WGOTHIC, they are presented bere as reasonable standards by which to quantify the limits of validity of Equadon 4 for wavy laminar tiow. The smooth laminar, wavy laminar, and turbulent correlations are compared in Figure 3 for water. Figure 3 shows that the wavy
- laminar correlation gives Nusselt number values wbich are less than those from Equation 2 for smooth laminar Dow, at Reynolds numbers less than 14, and values less than the turbulent values at Reynolds numbers greater than transition.
Theoredcal stability analyses by Benjamin", as well as more recent analyses by Yih", have shown there is no minimum Reynolds number for the unbounded amplification of linear disturbances (onset of wavy flow). However, experimental results by Binnie'* showed that for all practical purposes the amplification of disturbances is not significant at Reynolds numbers below 17.6. He Binnie wave incepdon Reynolds number of 17.6 was determined in water at 66 F. De corresponding wave inception Reynolds number calculated from Equation 6 is 22.1. Figure 3 shows that the exact value of the wave incepdon Reynolds number is not criucal because the smooth and wavy laminar correlations give nearly equal results for 10<Rei<30.
Additional points which are important for the validity of the liquid film correlation as used in EGOTHIC:
1 The gas velocities are so low (<20 ft/sec) both inside and outside containment that the effect of interfacial shear on the liquid fdm is negligible",
" - ne temperature jump at the gas-liquid interface is negligible for condensing steam'*
Rain was observed in the Wisconsin tests on a prototypic surface for angles up to one degree from
203.2 with a total measured condensation rate o( )b/hr).
l The AP600 values in Table r assume (be same normalized beat flux distribuuon as in LU 2 gith a total beat removal rate correspondlag to evaporating the maximum external cooling now rate of g Fos per minute.
Similar to intemal mass transfer, external mass transfer (evaporadon) accounts for over $% of the extemal beat l transfer and is (be product of the evaporated mass flux and the liquid to-gas enthalpy change. Thus, wben transient l cffects are not sigmficant, the intemal condensation rate is approximately equal to the external evaporauon rate. For j the purpose of this companson, all AP600 cooling water was assumed to evaporate before texbing the bouom of I the air baffle. Evaporauon at a higber elevation would reject nearly the same total beat, while evaporauco of less I total flow would remove less total beat. l l
Calculauoos were performed to determine the scositivity of the AP600 intemal and extemal Reynolds numbers to l the normalized beat flux distribution. The second line of AP600 values in Table I show that an assumed umform l beat flux over the dome and side walls produces only modest changes in tbc AP600 Reynolds numbers, and does !
not change other conclusions. l 1
Figure 4 compares the calculated AP600 and LST condensing liquid fdm thickness as a function of the area '
i integrated from the ccoter of the dome to the crane rail or gutter, with tbc area cornulmd to the dome area. The results show the film thickness is quite uniform over most of the surface, even though the film now rate increases significantly with distance from the center. The explanation is the effect of gravity is small near (be ccoter of the dome so the fdm flows slowly and remains thicker. As the slope increases to verucal, the flow velocity increasca, .
but due to tiie accumulation of condensate the flow rate also increases, so the thickness does not change rapidly.
The liquid film thickness is nearly the same fcr both AP600 and the LST because the thickness is related to the-Reynolds number to the 0.22 power. Whereas the AP600 donne Reynolds number is approximately 2.5 times the LST value, the AP600 thickness is only 2.5" or 1.22 times as thick as the LST. The thermal resistance of the alm is proportonal to its thickness, so the fUm resistance to beat transfer differs very little from the prototyp to (be tests.
To put the therinal resistance of the Alm in perspective, the intemal liquid fUm beat transfer coefficients are compared in Figure 5 and the Nusselt numbers are compared in Figure 6.
The calculated AP600 external liquid nlm thickness is compared to the mMmum and minumum calculated LST flow cases in Figure 7. The fdm is thick and tustulent near the PCCS cooling water source, but at a radius of approximately 22 feet (57 degrees above borizootal) transidoos to wavy lammar, and remains lammar over 97.4%
of tbc total evaporanng surface area. The LST external flim is supplied from two header rings": approximately 1/8 of the total flow is applied at a radius of 5.5 inches arul the remamder at a radius of 30.75 inches (54 degrees above horizontal). De manmum and mmunum LST cases envelope the AP600 ft!m thicknesses until part way down the vertical side, due io the assumpdon that all AP600 cooling water evaporates before reaching the bottom of the air baffle. The beat transfer coefficients corresponding to the film thicknesse4 of Figure 7 are shown in Figure 8, and the Nusselt numbers are compared in Figure 9.
In summary, the liquid fUm model used in the W GOTHIC code for AP600 is laminar, criosistent with the expected transinoo Reynolds numbers, and pedicts film thicknesses of 0.005 inches or less in tbc tests and prototype. The Ixiuid fdm constitutes a small fractwo of the thermal resistance for beat transfer to the condensing surface, so any uncertainties have little effect on the local beat transfer. De effect of surface orientation on rain was investigated and docurnented in the Wisconsin tests and was found to affect a negligibly small portion of the surface area. Both the new experimental results and the literature sources cover a range of characteristic dimensionless groups which encompasses the AP600 design.
2.4 Liquid Film Model Validatico The validity of the Chun and Seban correlation for evaporaung, wavy laminar fdms on vertical surfaces was demonstrated in the original paper. Tbc purpose of this section is to use the Wisconsin test data to extend the validity of tbc Chun and Seban corretaboo to condensing wavy laminar flow and to surfaces which are inclined, as in the dome region of the AP600
borizontal. His correspoods to 0.088 percent of the AP600 docne surface area, so the area where raio is expected is negligible. Results from the LST Phase 2 rain collection indicses that the total rain fall is negligible.
Table I compares the AP600' liquid film Reynolds numbers to those in the LST, the Wisconsin tests, and the Chun and Seban paper. The comparuons in Table i show that the manmum condensation Reynolds numbers in the l Wisconsin tests are similar to those in the AP600. Less than 0.8% of the AP600 dome surface area operates with ,
condensed film Reynolds numbers less than the minimum Wisconsin test Reynolds numbers of approximately 40. l Furthermore, the wavy correlauon is expected to slightly underpredict the smooth correlabon at Reynolds numbers l below 14. Derefore, tbc fact ths the AP600 bas local fdtn Reynolds numbers less than the minimimum values for I which there are data is not considered sigmficant and it is concluded that the range of the Wisconsin test results is adequate to support condensation in AP600 he manmum Reynolds number for evaporaung wavy hmmm rdms in the Chun and Seban paper is approximately 3000, with turbulent flow at bigber values. His value is greater than the AP600 and LST values on the verucal wall, and is approximately the same as for the dome at 57 degrees of angle above borizontal. Only 7.0% of the dome area or 2.6% of the total surface area lies between 57 and 90 degrees, and therefore operates in turbulent flow. As noted l earlier, the wavy lammar correlauon underpredicts tbc Nusselt number in turbulent flow. Underpredicting the Nusselt l l
number will result in an underestunation of the beat transfer over a small fraction (7.0%) of the dome surface area.
The minimum AP600 Reynolds numbers are less than the measured Chun and Seban values, but there is no indication that the local evaporating fdm bcs transfer is any different than the local condensing film bem transfer for (be same film thickness at the relatively low mass transfer rates of AP600 and the tests (see Section 2.4). Rus, !
the Wisconsin data are valid for the beat transfer through evaporating films and extend the film Reynolds number I down to 40, which is near the limit of tbc wavy correlation. At lower Reynolds numbers the wavy concladan l
underpredicts beat transfer.
l Table i Scaling Parameters for Liquid Fdms in AP600 Condensint Evaporatina Reynolds Number Prandd Reynolds Number Prandtl Over Dome Vertical Side Number Over Dcxne Vertical Side Number e O N C. j
/ #
AP600 I
AP600 (Uniform Flt a Large Scale Test Wisconsin Tests l
Chun and Seban na na na na 320-21,000 1.77 5.7 ;
. locanon at which the nonnal to tbc dome surface makes an angle of 57 degrees with the horizontal, conesponding to 7.0% of the total dome surface area or 2.6% of the total beat transfer surface area. I Condensation accounts for more than 90% of the localinternal beat transfer to the containment surface. As a first- l order approximanon, the wall beat flux is equal to the product of the condensation mass flux and the steam gas to- l liquid enthalpy change. This approximation was used, with the local beat Oux as a function of position over tbc l dome and side walls of the LST, to give the condensadon mass flux distribution inside the LST (based on LST test l l
l
l i
l l
l Five of the Wisconsin Tests were conducted without a noncondensable gas present. Without a noncondensable gas i I
tbc gas to-liquid beat transfer coefficient is so bigh that the gas to-liquid temperature drop is negligible compared to the temperatue drop across the liquid fdm. Consequently, the temperature of the liquid film surface may be assumed equal to the gas temperature and the liquid fdm beat transfer coefficient is beat flux divided by the liquid film temperature drop. Since the beat flux, solid surface temperature and liquid film surface temperature are measured, the beat transfer coefficient may be dertved directly from the measurements. De Wisconsin tests thus provided a direct measurement of the liquid film beat transfer coefficient for a range of surface inclinations from 2
verucal to borizontal. Equation 7 from Robsenow was used to calculate the beat transfer coefficient. His equation (8) h = m" h*
! +
f 5 375 ,
accounts for the difference between the beat flux to the surface and to the wall.
Figure 10 presents the terms of the mass and energy conservanon equations that were combined to solve for the local condensation mass flux at each of the seven measurmg locations a , 4 " +r%(h,-h,)/A (9) h ,-hy ne enthalpy of t% is evaluated at the average of the surface and mixture temperatures of the measuring station above, and the entahalpy of th ,, is the average of tbc local surface and mixture temperatures. He local mass flux ,
caused the film thickness to increase as the film flowed down the inclined surface, and the liquid fdm Reynolds l number was calculated from the local fdm flow rate. The beat transfer coefficient derived from the beat flux and temperature measurements now had a corresponding Reynolds number and plate inclination angle.
The surface temperatures presented in Reference 10 were calculated for the surface of the aluminum plate, and do not account for the inorganic zine coating. Measurements of the coating thickness performed subsequent to the tests give a coating thickness of 0.0049 2 0023 0 inches. Because the fdm does not flow ca the borizontal plate it is expected that all of the values of beat transfer coefficient for the bo:izontal plate sbould be equal. His was nearly true for all values except the bottom point which has an unexpectedly high value which cannot be explained. Small adjustments were made to the local coating thickness to produce the same beat transfer coefficient for each measuring location, except the bottom location which could not be completely corrected The adjusted thickness was used with an average thermal conductivity of 1.21 BTU /br ft F from the coatmg vendor and the measured beat flux to calculate the temperature at the wet coatmg surface. j The Wisconsin data are presented in Figure 11 and show b values between C)0 and 2000 B/hr-ft' F. The major variables in Figure 11 are the angle of the plate and the Reynolds number of the liquid fihn. The beat transfer coefficients tend to be greater for the more vertical angles of 45 and 88 degrees at the top of the plate where the hquid film is thinter.
The data are compared to the Chun and Seban laminar correlation and data in Figure 12. The correlation seems to predict nearly best estimate values over the full Reynolds number range of data.
De effect of small slope angles on the beat transfer coefficient is shown in Figure 11 where the values at zero I degrees inclination are all greater than or equal to the values at six degrees. Figure 13 shows the dependence of the i predicted to measured Nusselt numbers on the angle and suggests that the correlation may underpredict beat transfer at smaller angles.
The Nusselt number is not defined for borizontal surfaces, because the value of sin (0) in the denominator of the Nusselt definition goes to zero as 0 goes to zero. For surface inclinations from borizontal to one degree, an underestimated value of the beat transfer coefficient may be achieved by inputting an angle of one degree to WGOTHIC. In the Wisconsin tests, the condensate was removed by rain for angles up to one degree, and by fdm flow for angles greater than one degree, la practice. the fraction of tbc surface area of a 2:1 ellipsoid contained l l
between zero and one degree,is 8.8xt(y'. The nodauzauon of tbc dome region normally results in that surface area bemg lumped into a node with an angle greater than one degree, so the concern with bortzontal surfaces is not a pracucal one.
Figure 14 shows that there are no significant unaccounted dependence of the Nusselt number on the distance from the entrance.
2.5 Summary ne dimensionless Chun and Seban correladon chosen for the liquid film beat transfer is valid for any water rdm with a Reynolds number less than approximately 3000. The fracbon of the AP600 surface which operates with ftim flows outside this range of Reynolds numbers is insignificant. Comparisons of the correlation to condensing and evaporating data sbow that the Chun and Seban correlation is a good, best estimate representation of the data.
Comparison of liquid rdm Reynolds numbers for the tests and AP600 shows that the data adequately cover the range of Reynolds numbers, for both verucal and inclined surfaces, expected in AP600.
3.0 Liquid Film Stability To be supplied later 4.0 Liquid Film Enthalpy Trarnport Model To be supplied later.
5.0 References
- 1. R. B. Bird. W. E. Stewart. E. N. Lightfoot. Tran.rport Phenomena, John Wiley & Sons,1960,
- 2. W. M. Rohsenow, " Heat Transfer and Temperature Distilbution in Iaminar-Fdm Condensation", Transactions of the ASAfE, November,1956, pp.16451648.
- 3. M. L. Jackson,
- Liquid F11ms in Viscous Flow", American Institute of Chemical Engineering Journal, June 1955.
Vol.1, No. 2, pp 231240.
- 4. S. S. Kutateladze, L L Gogonin, N.1. Grigor*eva. A. R. Dorokbov, "Determinanon of Heat Transfer Coefficient with Film Condensanon of Stationary Vapour on a Vertical Surface" Thermal Engineering,27 (4),1980, pp 184-186.
- 5. K. R. Chun and R. A. Seban, " Heat Transfer to Evaporating Liquid Fdms*, Journal of Heat Transfer, November, 1971, pp 391396.
- 6. WCAP 13566, *AP6001/8th Large Scale Passive Containment cooling System Heat Transfer Test Baseline Data Report", Rev. O, Westinghouse Proptietary.
- 7. Letter, N. J. Liparulo to R. W Borchardt (NRC), "AP600 Design and Design Certification Test Program Overview", Table 4. Revision 3. August 13,1993.
- 8. " Heavy Water Reactor Facility Large Scale Passive Containment Cooling System Baseline Test Data Report,'
HWRF.RPT 92-0(M. Rev.1. February,1993. -j
- 9. " Heavy Water Reactor Facility Large Scale Passive Containment Cooling System Confirmatory Test Data Report." HWRF.RPT 93 001, July 15,1993. !
- 10. WCAP 13307, *Conde,osanon la the Presence of a Noncondensable Gas Expenmental Investiganon*,
Wesungbouse Proprietary.
. 11. I. K. Huhtiniemi, "Condensadon in the Presence of Noncondensable Gas: Effect of Surface Orientadon*, August 1991, Univenity of Wisconsin Madison, PhD Thesis.
- 12. T. B. Benjamin, " Wave Formadon in Laminar Flow Down an inclined Plane" Journal of Fluid hfechanics,2:
554-574.
- 13. Chia Shun Yib, Fluid Afechanics, West River Press,1977.
- 14. A. M. Binnie, Experiments on the Onset of Wave Formatice on a Fihn of Water Rowing Dow11 a Verucal Plane *, Journal of Fluid hiechanics,2: 55l 553.
- 15. R. A. Gater and M. R. L*ccuyer , " A Fundamental Investigadon of the Phenomena tha Characterize LiquidEdm Cooling *, International Journal of Heat and hiass Transfer, Vol. t3, pp 19251939.
- 16. E. M. Sparrow, W. J. Minkowycz, " Condensation Heat Transfer in the Presence of Noncondensables Interfacial Resistance, S uperbeating, Variable Properties, and Diffusion *, insernational Journal of Heat and Afass Transfer,1966 9 (10) 1125 1144. .
- 17. Westingbouse drawing 2021E31, Sheet 11. PCCS Test Pressure vessel Water Film Distributcr "As Built *, Jan 13,1993.
f 1
'l l
i I
l 1
I l
l i
l
NONENCLATURE c, is the liquid film specific beat, B/lbm F.
2 g is the gravitauonal acceleration,32.2 ft/sec ,
2 b is the liquid fdm beat transfer coefficient, B/ht ft F,4 = b(T Tu) k is the liquid Alm thermal conductivity, B/sec ft-F, L is the reference length, ft. L = (v2 /g s n(0))",
2 4 is the local beat flux., B/br-ft .
Tu is the temperature of the liquid fdm free surface, F.
T is the temperature of the solid wall the liquid film is attached to, F.
Greek Letters F is the liquid fdm now rate per unit width, Ibm /hr ft, 6 is the liquid fdm thickness, ft.
O is the angle of inclinauon tocasured frotn bonzontal, .,
p is tbc liquid fdm viscosity, Ibm /sec ft, v is the liquid fdm kinematic viscosity, ft'/sec, v = p/p p is the liquid Olm density, Ibm /ft'.
o is the liquid nlm surface tension under air, Ibf/ft.
Dirnensionless Groups Ka is the liquid fdm Kapitza Number = p'g/po',
Nu is the liquid Olm Nusselt Number = hlA, Pr is the liquid film Prandtl Number = pc,/k.
Re is the liquid film Reynolds Number = 4r/p. I i
l l
1
4 <
- 4 1
is .
1 1
Iw "
koa Normaized to Dome koa -
\
1 Figure 1. Calculated AP600 and LST Internal Uquid Film Reynolds Numbers 1 l
l e
1 l
1 m ew w ---t+ m y v w'
~
k w
~ w i
z cf '
s u
i W l koa Normaized to Dome hea '
1 Figure 2. Calculated AP600 and LST External Uquid Film Reyndds Numbers i
1 I
1
~
4 1
l l
4:.
t f .
10_ - , ,
Wavy Laminar (Chun and Seben) 3 Smooth Lammar <
z 3_s (Nunson)
~'%,,,,,'- Turbulent : 100 F
- (Chun and Soban) 1*
Smooth-Wavy S Transition: 100 F ..**..
t
- u. ue wavy Turbuient 10.1: -
Transition: 100 F
- FJo F 0.01 i '
i iiiiiu i i i11 , i i , i i i i ii i . . ..... , ,iiiiii .
1 10 100 1000 10000 100000 l Uquid Fkn Reynokie Number, Re l Figure 3. Sn:coth, Wavy and Turbulent Uquid Film Nusselt Number j Correlations For Water I 1
l l
1
$ I 1
.l 1
0.008 m Large Scale Test + AP600 0.007-0.006- i-
_ j! Large Scale Test Gutter i:
jj ~i! +
} 0.0052'- 4 +.+.+'+'+ j..
0.004"g, ..
5 AP800 Crane Rail !
- /
0.003-T , /
9 I i
i 0.002-
.i!! ! l/
l 0.001- !j q Dome ; qi T verscaiwe ; y 0 i
- /!/
0 0.5 1 1.5 2 2.5 3 3.5 4 Area Normalized to Dome Area Figure 4. Calculated Internal Liquid Film Thickness frorn Dome Center to Air Annulus Bottom in LST and AP600 1
J y --- -. .r
)
1 l
1 2000 m Larp Scale Test + AP600 1800-1600- !
IN i g.
W 1400-g li \,\
8 I
- ! k..
] 1200 is E
' % .. _ + .
h 1000-
[++'+-+-+ +......h t' tary seal. Ten ovner
+
4 300- '
} AP600 Crane Rail i
I So -
U 400-i 200- Dome 4 ? qj VerticalWe ? O I
O i i . . , i 0 0.5 1 1.5 2 2.5 3 3.5 4 Area Normdzed to Dome Area Figure 5. Calculated Internal Liquid Film Heat Transfer Coefficient from the Dome Center to the Air Annulus Bottom in the LST and in AP600.
. _ . _ . _ _ _ _ . . .~ ....
\
O.gb-t 1
5 u.
T M
_i
,d, . ... _
Area Normdzed to Dome Area Figure 6. Calculated AP600 and LST Internal Uquid Film Nusselt Numbers l
= w w w ne 1~ ~ - v
1 4
1
. 4 0.008-
- a i a Min Row LST + AP600 M Max Row LST 0.007- ;m s
- 0.006- "N**y
'm 2
n-y '
- v - x -- .-... .~ m- -- - ~y . _ _ g_ _
0.005- *~
o g w ,- . . . ..
j . t - s _ . ,. , ~ ~ ~ a y 0.004-F .;
5
' O 003-T
.P
_t r 0.002-0.001- i
< oom. ;>< v.coes wd 4 y 0 , , , , , ,
2 0 0.5 1 1.5 2 2,5 3 3.5 4 koa Normdz.d to Dome koa ,
y l
Figure 7. Calculated Extemal Uquid Film Thickness from Dome Center to Air Annulus Bottom in LST and AP600
'l l
1 l
'I J l
4 I
1
1 i
2000 s Min Flow LST + APG00 M Max Flow LST
, 1800-1600- M 1400- +
1200- -
~~"" .... .m .
._........m.
m 8 "'
g1000-g 800-a " ...wm. ,,. g x .._...w.-..- *-~~--~'M- "*~~~"""~~#
- 600-1 I
400*i f i.
200H-g Dome 3 4 Vertkal WM ?
O , . , , i i 0 0.5 1 1,5 2 2.5 3 3.5 4 koa Normdzed to Dome koa Figure 8. Calculated External Liquid Film Heat Transfer Coefficient from the Dome Center to the Air Annulus Bottom in the LST and in AP600.
t e
4 i
a l
-l
~
IP 4)b l
I a
l i
l
.6 '
koa Normaized to Dome koa Figure 9. Calculated AP600 and LST Extemal Uquid Film Nusselt Numbers
1 1
'1 i
1 I
/
/
/ 9 mA q" is the Wisconsin measured heat flux, AA is the control volume surface area ,
' 6,is the Sim flow into the control volume,
__y
/ m,is the 81m flow out of the control volume, !
q" ' l; A
I h, &" is the condensing mass flux, !
T[ l I T Tw. Tu is the temperature of the liquid Sim, -l j &" h, Tu is the measured bulk gas temperature, f
fj Tu is the Wisconsin measured surface temperature, !
f - hwistheliquidenthalpyof Aevaluatedat(TsT y2 !
l
/ h,is the vapor enthalpy at T.,
/ h, is the convective heat transfer coefBcient. .- i
/ V Ahr j l
Energy Balance: Mass Balance:
AAQ* + Q = thA + th"AAh, + AAh,(T -Ty A = A + 2"AA ~
The mass and energy equations were combined and solved for &". The term containing h, was neglected because at I to 3 B/hr-ft' F the convective heat transfer is 3 to 4 orders of magnitude smaller than- .)
convective mass transfer without noncondensable gas present. The resulting equation is g n ,, N " * $(A/ .ar'A/ M j As4/as !
l l
1 F1gure 14. Mass and Energy Balmace on the Liquid Filan . .
I 1
I
e.
r 5000 4500- ,
4000- E Surface Angle = 0 + Surface Angle = 8
- Surface Angle = 12 O Surface Angle = 46 X Surfme Angie = 88 8
g %%- ,
4 2500-5 m
2000- 5 a 1 x 1500- , ;
E = E =
- j 1000 R
- *
- W y i 500- l 1
0 . , , . . . . . . l 0.7 0.8 0.9 1
0 0.1 0.2 0.3 0.4 0.5 0.6 1 Namdzed Distance from Entrance xA.
Figure 11. Wisconsin Condensation Test Measured Liquid Film ,
Heat Transfer Coefficient
,.m-, ,
~ _ _ __
9 y
~ ~
)
E 1
Ji w
s i
I
--. ~
ugud Rm Reynch Numbw, Re Figure 12. Chun and Seban Liquid Film Nusselt Number Correlation .
Comparison to the Local Condensation and Evaporation Test Data 4
. 1
.l 4
T 1 J
i
-Q (
2 R
I -
1<
l<
.g
~
Angle from Horizonte (Degrees)
Figure 13. Chun and Seban Uquid Film Nusselt Number Correlation j Comparison to the Wisconsin Condensation Test Local Data '
)
. i 1
-i
'?
, j .-
Y)O 3
kz 3
3 1 .
i ,
e
'- ~ ~
Mal Distance frorn Entrance. x/1.
. Figure 14. Wisconsin Condensation Test Measured Liquid Film Nusselt Number Dependence on Axial Position 4