ML20056E199

Nonproprietary Modelling of Condensation Heat Transfer in Reactor Containment

ML20056E199
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Site:	05200003
Issue date:	01/01/1985
From:	Michael Kim WISCONSIN, UNIV. OF, MADISON, WI
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ML20056E190	List: ET-NRC-93-3945, Forwards Nonproprietary & Proprietary Refs for Basic Research Tests on Condensation Performed at Univ of Wi at Madison in Support of AP600 Design.Affidavit for Withholding Encl.Proprietary Portion of Document Sent to Westinghouse ML20056E195 ML20056E199 ML20056E202 ML20056E204
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5 1

MODELLING OF CONDENSATION EEAT TRANSFER IN A REACTOR CONTAINEENT I

f by IICO-BWEn Ela i

i i

A thesis submitted in partial fuli111 ment of E

the requirement for the degree of I

4 t

a r

DOCTOR OF PEILOSOPHY (Nuclear Engineering) f a

J

.s sh.

l ITNIVERSITY OF YISCONSIN-MADISON 1985 l

h 9308200251 930816

^

DR ADOCK 05200003

,_ PDR__

i l

l iii ACE 30TLEDGEMENT I would like to arpress my best gratitude to my advisor Professor Michael L. Corradini. Eis patient guidance and continuous encouragement vare invaluable for this work.

The academio attitude I learned from him vill be carried along with me throughout my life.

My special tha,nks go to Professor Gregory A. Moses and the RETRAN a.nd EMC research groups for their valuable advice s.nd cooperation.

I am grateful to J.J. Barry for his helpful a,ssistance and continuous inspiration in this resea.rch. Faustino Gonza.las was appreciated for providing good software to type this thesis and draw the figures.

My deep and heartly n=*=

go to my family; my vite, Hyunjoo, for her endless love, sacrifios and continuaas support during this work; two sons, Bunjeon and Hongjoon, for being there.

My parents who sacrifioed themselves for my being away from them, I cannot thank enough.

I gratefully a.cknowledge the finanoisi support from Yisconsin Public Service. Yestinghouse Z1ectric Co. and the scholarahip from Graduate School of University of visconsin-Eadison

)

i i

I 1

l v

1 Containment..................................

48 2.7 Summary and Concluding Ramarks.........'......

55 I

CE/*JTER 3. TEBORETICAL DEVELOFXENT..................

80 l

l 3.1 Simple Mode 1.................................

80 3.1.1 Model Development......................

80 i

3.1.2 Forced Convection Model 1

for Smooth Interface...................

84 1

3.1.3 Forced Convection Model for Yavy Interface.....................

90 3.1.4 Natural Convection Model...............

99 3.2 Two-Dimensional Mode1........................

102 3.2.1 SIMPLER A1goritha......................

102 3.2.2 Nea.: Yall Model for Smocth Interface...

105 3.2.3 Nea.r Yall Model for Yavy Interface.....

106 3.3 Condensate Film Model........................

108 3.3.1 Model for a 12=4*** Condensate Fils....

108 3.3.2 Model for a Tarbulent Condensate Film..

111 L

i CHAPTER 4. COMPARISON YITE EIPERIEENTAL DATA........

121 4.1 Analysis with the Condensation i

Esat Tra.nsfer Model and Verification.........

121 4.1.1 Analysis with the Simple Model.........

121 4.1.2 Condensate F11a........................

123 4.1.3 Verification of Simple Model with f_'=9*=* F1ov......................

125 4.1.4 Verification of Two Dimensional Model with f==1***

F1ov................

127 4.2 Comparison with Da11mayer's Experiment.......

129 4.3 Comparison with CVTR Experiment..............

131 4.3.1 CVTR Experiment........................

131 4.3.2 Flow Field Calculation with I-FII......

132 4.3.3 Comparison of Esat Transfer Coefficient with Experiment............

134

vii LIST OF TABLES PJLg2 Table 2.1 Condensation on a Flat Flate.............

57 Table 2.2 Experimental Results of Mills and Saban [41] and Slagers and Saban [421....

57 Table 2.3 The Velocity Field in the Region of the Large Yave (See Fig.

2.21)........

58 Table 2.4 Theoretical and Experimental Investigation of Condensation............

59 Table 3.1 Analogies between Esat and Mass Transfer at Low Mass Transfer Rate......

113 Table 3.2 Summary of 4, P and S in Eq. (3.2.1-1) for the Cartesian Coordinates...........

114 Table 3.3 Summary of d. T and S in Eq. (3.2.1-1)

~

for the Axisymmetric Cy11erifica.1 I

C oo r111nat e s.............................

115 Table 4.1 Tbs Effect of the Distance of the Nearest Rode to the Yall at the Two-Dimensional Calculation of Asano Experiaant.......... 143 Table 4.2 Comparison of the Calculated Stanton i

Rumber of Esat and Eass between the Simple Model and Two-Dimensional Model..

144 Table 4.3 Injected Steam Condition................

144 Table 4.4 Inflov Steam Condition for E-FII......... 145 Table 4.5 Results of Estimated Velocity from I-FII............................... 145 i

1

l X

Fig. 2.30 BTF Contahment Test Syste.a...............

77 Fig. 2.31 Vertical Cross Section of EDR Containment 0

0 Building along 90 to 270 Disseter.......

78 Fig. 2.32 Absolute Fressure: Erperimetal and Theoretical Results.......................

79 Fig. 3.1 Predicted Turbulent Prandt1 Number.......

116 Fig. 3.2 Comparison between Eq. (3.1.3-17) for the Friction Coefficient and Chu and Dukler Experiment (59,60).................

117 Fig. 3.3 Control Volume for the Two-Dimensional Calculation with SIMPLER Algcrithm........ 118 Fig. 3.4 Mean Gas Velocity Profiles for Interfacial Region.......................

119 Fig. 3.5 Rough Surface Correlation for Gas velocity..................................

119 i

Fig. 3.6 Comparison between the Film Thickness Calculated by the I==4*=? Film Model I

and Tellea and Duker Experiment

[58)......

120 Fig. 4.1 Flow Chart of the Simple Model to Calculate the Condensation Isat Transfer Coefficient with a Noncondensable Gas....

148 j

Fig. 4.2 Calculation Results from the Models Developed and Goodykoonts and Dorsh's Experiment Data at uin = 19.9 m/sec...... 147 Fig. 4.3 Calculation Reruits from the Models Developed and Goodykoonts and Dorsh's Erperizant Data at uin = 35.1 m/seo......

148 Fig. 4.4 Calculation Results from the Models Developed and Goodykoonts and Dorsh's Experiment Data at uin = 47.9 m/seo......

149 Fig. 4.5 Calculation Results from the Models Developed and Goodykoonts and Dorsh's Experi.nent Data at uin - 53.3 m/seo......

150 i

ix Number....................................

67 Fig. 2.14 Probability Density of Substrate Yave Amplitude: Eero Gas Rate..................

68 Fig. 2.15 Froh=M11ty Density of Substrate Yave Amplitude: Nffect of Gas Rate.............

68 Fig. 2.16 Probability Density of Yave Amplitude, Reg - 0: Varying Liquid Rates.............

69 Fig. 2.17 Mean Deviation of Large Yave Amplitude....

69 Fig. 2.18 Theory.vs. Experiment: Yave Amplitude....

70 Fig. 2.19 Longitndinal Change of Critical Reynolds Number....................................

71 Fig. 2.20 Longitndinal Developing Frocess of Interfacial Tave Fora.....................

71 Fig. 2.21 Close-up View of the Yave Calculated.

Three interior strs==1ines are shown. The Pressure is shown (dyne on-2) at points marked with open circles,and velocities are reported in Table 2.3.................

72 Fig. 2.22 The Influence of Vapor Shear on the Average T==4ner Flow Condensation F.est Transfer Rate........................

72 Fig. 2.23 The Function F.,..........................

73 Fig. 2.24 The Year-Tall Nodes Y and F...............

73 l

i Fig. 2.25 Year-s's.11 Two-Layer Mode 1.................

74 Fig. 2.26 Near-Tall Three-Layer Model...............

74 Fig. 2.27 Ratio of Irperimental and Theoretical Stanton Number for Neat and Mass Transfer.

75 Fig. 2.28 Numerical Frediction of the Influence of Film Taves on the Turbulence Energy Distribution in the Boundary Layer for Rey = 95..............................

75 Fig. 2.29 Rumeriet.1 Frediction of the Influence of Film Reynolds Number on Stanton Numbers for Neat and Mass Transfer................

76

l t

x iii

~l l

NOEENCLATURE a

gravitational acceleration l

A vave amplitude A+

Van Driest Constant C

friction ocefficient f

C specifio heat at constant pressure p

DAB :

binary diffusivity for system A-B f

friction factor g

mass-transfer conductance G

mass flux of x direction j

Gr Grashof number h

heat transfer coefficient 1

enthalpy k

turbulent kinetic energy k'

constant in universal velocity profile k,

equivalent " sand grain

• roughness I

thermal conductivity L

length of plate i

m' mass flux of y direction X

molecular weight of A I

Eu Nusselt number Pr Prandtl number turbulent Prandt1 number Prg q'

heat fluz Re Reynolds number So Schmit number So turbulent Schmit number g

Sh Sherwood number St Stanton number T

Tamperature u

velocity x

distance down the plate I

mass fra.otion of species i

1 Chapter 1 INTRODUCTION During a postulated light water rea.otor scoident (e.g.

Loss of Coolant Accident), an important ooneern is hov'to predict the pressu e-temperature response in the containmant building.

This is because the flashing high energy coolant released from the primary system ca.n significantly contribute to a rise in the contsinnent pressure, perhaps threatening its structual integrity. To reduos the steam

pressure, both active and passive ssfeguard syntaas are used in current conta.inment designs.

The active systems include conta.inment

sprays, fan coolers, ice condensers and suppression pool cooling.

The paasive systems, which are the convective heat transfer to the containment vall and interna.1 structural components, have an important role a.s an inherent safety feature.

If the vall surface tanperature is below the devpoint, the heat transfer rate is able to be greatly increased by condensation, which is the subject of this report.

j Even though condensation phenomena can be classified isto dropvise and film condensation modes, dropvise oondensation usually changes quickly to film condensation duing the initial period of condensation and probably would not affect the final containment pressure-temperat us response [1]. In this work we focus on film condensation heat transfer.

Rates of heat transfer for film condensation can be predicted as a function of bulk and suface temperatues, total bulk pressure, surf ace and liquid film characteristics, bulk velocity and the presence of noncondensable gases.

Even though film condensation has been investigated aztensively, the majority of these studies were devoted to lanin=*

film condensation (In=9nn?

bulk flow and laminar film). Since i

3 air flow. The past work in condensation phenomena in a

rea,otor containment are reviewed.

The simple model and two-dimensional model are l

described in chapter 3.

The analyses are presented in chapter 4 by comparing these models to 'saparate effects' experiments and integral test data.

Finally, conclusions and recommendations are presented in chapter 5 l

F 1

I I

5 1

the wavy interface, which is expected for vertically falling film, is investigated.

i The model for the turbulent vapor-air flow and the affect of the tubulent flow on the condensation phenomena are presented, since the vapor-gas flow in the containment and the condensate film are supposed to be turbulent under some conditions.

After the review of

, condensation theories and azperiments, the characteristics of a falling film and the model for the tubulent flow, the previous investigations of condensation phenomena in a reactor containment duing a postulated accident are described.

2.2 Theoretical Developments of Condensation

)

2.2.1 Stationary Pure Vapor i

For f11avise condensation of a

" stationary" satuated vapor. Nusselt [5] presented the first analytical solution for heat transfer on a plane surfmoe with the following assumptions [6):

1) the flow of condensate in the film is laminar,

2) the fluid properties are constant.

3) subcooling of the condensate may be neglected,

4) nomentum convective changes through the film are negligible, 5) the vapor is stationary and exerts no drag on the downward motion of the condsnaate,

6) heat transfer is by conduction only.

From a force balance on an element of-film lying between y and 6 in Fig. 2.1.

du (6 - 7) d2 (Oy-9) a sin 0 = Uy ( dy }

(* *~}

i i

7 Russelt's assumptions.

In ps.rticular,

Bromley

[7]

considered the effects of subcooling within the liquid film and Rohsenov

[8]

also allowed the non-linea.:

distribution of temperature through the film due to energy convection. The results indicated that the latent heat ' of vaporization, ifg, in eq. (2.2.1-6) should be replaced by C

AT i' q = i q 1 + 0.68 (

I

)

(2.2.1-6) fg s

However, it should be noted that is most engineering applications, the value of CpgM/1gg is small (typically less than 0.001) and os.n be neglected.

Sparrow and Gregg

[9]

removed assumption (4) and included inertis forces and a convection term within the condensate film by using a boundary layer treatment for the condensate film.

The governing partial differential equations were reduced to ordinary differentia,1 equations by means of similarity transformations. For common fluids with Prandt1 numbers around and greater than

unity, inertia effects,are negligible for values of C AT/i p1 gg less than 2.0. For liquid metals with very lov Pra,ndt1

numbers, however, the heat trassfer coefficient falls below the Russelt prediction with increasing C

AT/i p1 gg when C AT/1 p1 gg is greater than 0.001.

i Poots and Mills

[10]

have loched at the effect of I

variable physica.1 properties (a.ssumption 2) on vertical plates.

More recently, Koh et al. [11] asd Chen [12] included the influence of the drag azerted by the vapor on the liquid film.

This interfacial shear stress also necessitated consideration of the vapor boundary layer.

Both of them treated the condensate fila asd the vapor layer on the ba. sis of bonnda 7 layer equations with appropriate conditions at the interfs.oe.

Ich at al.

j

i 9

which means that the interfacial shear stress approaches i

the

" frictional" shes.r stress for single-phase flow over an impermeable plate for lov condensation rates, while in the other extrea.e esse of h.igh oondensation rates it approaches the asymptotio value of acaentum transfer rate of condensing vapor, rg.

g " E ( ". ~ "6)

T (2.2.2-3) where ug was a.ssumed to be zero in his own work.

From these solutions, the local Russelt number is given by i

G" v

o Pr i 4

(

)

=(j)'((i) (f)(C

))

a p

where G" : tabulated value as a

function of G.

the y

y suction parameter (14) and the following asymptotic relations similar to Eq.

(2.2.2-1) and (2.2.2-2) were derived

= 0.436[(h)I[h

)))

(v )

(h)I(f)(C[AT) (2.2.2-5) for small fg v

v (h)I(f)(

(v ) = 0.5 for large

)fg (2.2.2-6)

Re v

v

,e i

Cass further ruggested that it.is permissible for CptAT/(Pr igg) << 30 to neglect the inertis forces amd for l

I j

11 1

1 l

i This result corresponds to Eq. (2.2.2-6) which is Cess's

.esult for high oondansation rs,tes when X is much less than 1. (This is ganarelly true for non metallio liquids. )

It means that Cess's assumption (ug = 0) is valid for this i

l case.

{

Statriladze and Gemelsuri a.lso considered the case of a.n isothermal vertica.1 plate with the same assumptions.

l (The effects of inertia forces s.nd energy convection l

within the condensate film vere neglected. In addition, j

the interfsoial velocity ug was assumed to be zero for i

this ca.loulation. ) Only Eq. (2.2.2-7) is changed to du

+ pg = 0 (2.2.2-12) 2 j

d7 with the st=e other equatichs a.nd boundary conditions. The 1

rec its are l~

1 + /(1

)

3 u

film (r) = 1

(

)

g.

(2.2.2-13) h 2

u x 2

g J

]

It was reviewed that the interfs.oia.1 shear stress, l

ry.

has two a.symptotio values Eq. (2.2.2-1), vapor friction on the film, and Eq. (2.2.2-2) which is zozentum drag as

)

the vapor condenses on the slover moving film. Mayhev et.

al. [16,17] attempted to arpasd Russelt's simple approsoh to tahe secount of both forms of drag by usi.ng a very l

simple interpolation formula, i

11 71, (2.2.2-1c 1

1 and I

du

{

u (,, )dr - (6-y)p -0,)adx + T y

pdx + dT(w -u5)

(2.2.2-15)

13 comparison with the experimenta.1 data. It is interesting to note that the result of Shehriladze and Gomelauri corresponds to the osse Dr 0

(

=

1 of Mayhev's

=

calculation.

South ami Denny [19] proposed an interpolation formula of the form for the interfs.ois.1 shear stress.

1 g=(T)+T[

i (2.2.2-19) i i

vs.ere n = 1.375 was suggested to give good agreement with the numerical results for both the flat plate and stagnation point flow over the entire range of the suction i

paranater as shown in Fig. 2.3. However. in view of the fact that the contribution of ry to rg is small except for very lov oondensation

rates, such an interpolation formula would only lead to a small difference in the heat transfer with the result from rg = ry.

Jacobs [20]

used an integral method to solve the boundary layer equation for the condensate film and the vapor bo-@ layer by matching the mass flux, shear

stress, tamperature ami velocity at the interface. The inertia and convection terms in the bouA ary layer equations of the liquid film were neglected. The variation of the physical properties and the thermal resistance at the vapor-liquid interface were also neglooted.

Since Ja. cobs used an incorrect boundary condition for the vapor boundary layer (uy = 0 instead of

= 0 at hik). Fujii au*

g and Uehara [21) solved the same probles with the oorrect bounda.ry condition.

In addition, the velooity profile in the vapor layer was taken as a quadratio formula of (y-8).

They presented the numerical results and their approvi sate expressions for the cases of free convection, forood convootion, and combined" free and forced convection.

The results show good agroement with the

i 15 3

surfaos are restricted within some limitations and where 4

Nun is smaller than 2 x 10. Then the predicted Nu is 4

n larger than 2

x 10, the experimental Nun is a, bout fron l

1.3 to 1.9 times as large as the predicted one except for the cases of amm11 heat fluz as r.;hown in Fig. 2.4. nese i

high Nun experimental data were reported by Goodykoontz and Dorah

[23,24]

and Jacob et al. [22), who performed j

the experiments by condensing steam on the inner surface L

of a cylinder with a ranga of staa.a flow velocity of 10 -

80 m/s [22), 20-70 m/s

[233 and 95-310 m/s

[24).

The 1

3 authors attributed this discrepancy to the turbulence in l

l the liquid film from the very high vapor velocity.

l 2.2.3 Stationary Vapor with a Noncondensable Gas 4

i 1

i F

Air, a noncondensable gas, exists in a containment and

(

leads to a significut reduction in has,t transfer during

[

condensation. An air-vapor boundary layer forms next to 4

the condensate layer and the partial pressures of a.ir and vapor vary through the bounda.ry layer as shown in Fig.

2.5.

The build-up of noncondensable gas near the i

condensate fila inhihits the. diffusion of the vapor from the bulk airture to the liquid film and redsoes the rate of mass and energy transfer. Therefore, it is necessary to solve simultaneously the conservation equations of mass, momentum and snergy for both the condensate film and the vapor-gas bounda:y layer together with the conservation of species for the vapor-gas layer.

At the interfsos, a

oontinuity condition of mass, acaentum and energy has to be satisfied.

I For a stagnant vapor-gas aizture, Sparrow and Ichert

(

[25) and Sparrow and Lin [26] solved the aa.ss, somentua and energy equations for inninar film condensation on an isothermal vertical plate by using a

similarity l

l l

i j

1

17 i

2.2.4 Moving Vapor with a Noncondensible Gas i

t For a laminar vapor-gas mixture case. Sparrow et.

al.

[29] solved the conservation equations for the liquid film l

and the vapor-air boundary layer neglooting inertia and I

convection in the liquid layer and assuming the streaavise velocity component at the interfsoo to be zero in the oosputation of the velocity field in the vapor-gas boundary layer. Also a reference temperature arms used for the evaluation of properties. The results showed that the effect of nonoondensable gas for the moving vapor-gas l

)

mixture osse is such less than for the oorresponding

{

stationary vapor-gas mixture. A moving vapor-gas airture is consi(.qred to have a

' sweeping'

effect, thereby

(

resulting M a lower gas concentration at the interface (compared to the corresponding stationary vapor-gas I

mixture case). Alsc, the ratio of the heat flur with a

noncondensable gu to that without a noncondensable gas was calculated to be independent of the bulk velocity (uB).

The computed results reveal that interfacial l

resistance has a negligible effect on the heat transfer i

and that superheating has much less of an effect than in the cor"1ponding free convection case.

Ech (30] and Fujii et al.

[31]

solved this problem f

without the simplifying assumptions used in [29] except f

for uniform properties and showed good agreement with the j

approximate analysis.

Instead of solving a complJte set of the conservation equations, Rose (32] used the experimental heat transfer result for flow over a flat plate with suotion (33]

s.,t f. C ( 1 +.8%C)-I + 8,Pr (2.2.4-1)

I where

19 simultaneously to

give, for specified free stream conditions, the relationship between the vapor mass fluz to the condensate surface f.nd the composition at the interface. E14=9= ting either E

(=Sh N ) or #g he E

g g

obtained w = [ l + 8, Sc ( 1 + 0.941 S *I'sc.93) j y_1 (2.2.4-5) o or 2, + o.941 sc-o.21( 1 - o l'z.14 l

2

- C/*

• O (2.2.4-e)

The results given by equation (2.2.4-5) were compared with the numerical solutions of Sparrow et.

a,1.

[29]

for 3.

given value of Ag and agreed very well as shown in Ta.ble G.,1. The results given by equation (2.2.4-6) were compared with the aza.ot numerical solutions of Koh [30]

a.nd Pujii et.

al.

[31) as shown in Fig. 2.7. The good agreement between the exact numerical dolutions and equation (2.2.4-

6) confirms the validity of the simplifications made in his work.

Danny et.

al.

[M,US) also considered the case of downwa.rd vapor-gas mixtu:Je A

, callel to a vertical flat plate. They pressisted num 4 % ' solution of similar l

sa.s s,

momentum and emergy equations for a vapor-gas

{

mixture by means of a forward marching technique.

Interfacia.1 boundary conditions at sach step vers artracted frea a locally valid russelt type analysis of the condsasste film.

Locally variable properties in the condensate film vere evaluated by means of the reference I

temperature

conoopt, while those in the vapor-gs.s layer were treated exactly.

Asano et.

al.

[36]

treated the condensate film e,s in the Nusselt anr.'71s but assumed the interfa.oial ahear stress was the saae a,s that for single-

.=

I i

21 and for the local vapor-side Sherwood nunber is i

Sh,

=0.332RefSeg(BSc)

(2.2.4-10) g i

where g1(B.So) can be understood as a high mass transfer correction factor which was tabulated to be a function of the dimensionless mass transfer drivi.ng force B.

The numerical results showed good agreement with the numerical solution by Denny at al. for ug - 0.3 m/s. L = 0.05 m.

The analytical model described above was solved using i

1 only a lamin =* vapor-gas (or pure vapor) boundary layer except for Mayhew

[18).

All complete sets of the conservation equations were solved by assuming a laminar l

flow for both a

condensate film and a vapor-gas layer, j

Yhitley [37) proposed a simple method, which uses the i

{

analogy between heat and mass transfer for forced convection condensation of a turbulent mixture boundary layer by neglooting the interfacial velocity and treating the surface of the condensate fila to be smooth. The local I

Russelt number for a turbulent flow over a flat pista is Nu,,, = 0.02% te.8 O

Pr.6 0

(2.2.4-11) i The local Sherwood number and mass transfer conductance are t

0 i

Sh

= 0.0296 Ee.8,0.6 3

r.s z

3 (2.2.4-12) i i

g(x) = 0.02% c' o u, Ref*2Sc[*'

(2.2.4-13) where gg In 1+B)

i 23 Mayhev and Agge,rval (18) experimented with pure steam condensing on a flat surface. To avoid air in-leakage, the experiments were carried out at pressures slightly above atmospherio. Fig. 2.8 shows good agreement between the i

arperimental results and the calculated values by their own theory (Eq. (2.2.2-17)). It is very interesting to note that the results for the counter-current flow cases are appreciably higher than those predicted by the authors' own model and indeed a,1vays higher than the cor m ponding co-current velocity vapor values. The reason was investigated and arplained as follows in the original Paper ;

1 "An obvious explanation was provided by dye-injection

)

tests which shoved that, with counterflow, no laminar film l

flow oculd be schieved. The film was torn off the plate (i.e. flooding occurred) at quite moderate values of vapor velocity.

Similar observations with parallel flov confirmed that the film was alvays both laminar and

]

smooth. From work with noncondensing films it was expected that rippled flow would be encountered over ps.rt of the surface at the higher velocities used. In fact razarkably smooth filma vere observed suggesting that ma,ss transfer, and possi.bly also surface tension effects on the non-isothermal film, must have had a stabilizing effect."

Recently Ass.no et al. [36] reported their data for the condensation of pure saturated vapors on a vertical flat oopper p3, ate and shoved good agreement with the authors' own model (Eqs. (2.2.4-8, 2.2.4-9)).

2.3.3 Stationary vapor with a Nonconddssable Gas Perhaps the earliest definitive experiment of the

i 25 active condensation length.

The tube was mounted in a cylinhical pressure vessel 1.52 a 0.D. by J.35 m

long.

Saturated steam was supplied by an arternal source and allowed to diffuse to the tube resniting in steady-state, natural convection conditions. An arpression, which is a j

function of AT, percent noncondensable gas by volume (n) and total pressure (Ptot),

of the heat transfer coefficient was proposed from the experimental data.

h.149.9 (a)-1 II(1-T/100)2.59(p 0.48 (2.3.3-1) where 0.27 e pgog < 0.70 MPa 0.0

<Y

< 14.0 %

40 C AT

=

C i

Even though this experiment was done over a good range of Pressue for a

containment analysis and showed a

significant effect of pressure, the pipe geometry and length scale male it questionable to apply this correlation to a

reactor containment analysis.

Umfortunately, the experiment results were not compared with any other theoretical model.

2.3.4 Xoving Vapor with a Noncondensable Gas Rauscher, Mills and Danny [49] performed arperi.nents of filavise condensation from staaa-air mixtures undergoing forood flow over a O.74 in. O.D. horizontal tube. The heat tra.nsfer ocefficient at the stagnation point was reported for bull air mass fractions of O - 7 % and onooming vapor velocity of 1 - 6 ft/s. The reduction in heat transfer for the steaa-air mixture was found to be in arcellent agreement with the theoretical analysis of Denny and South (50).

27 turbulence intensity and decreasing the viscous sublayer thickness similarly to the effects of a rough wall.

Therefore, the understanding of the structure of the condensate liquid film and the interfsos on a long vertical vall is important to the study of condensation phenomena on a containment vall.

From the es.rly experimental studies, three different flow regimes have been reported for the falling film on a

vertical vall [513:

1) At Reynolds numbers less than 20 to 30. there arists the usual visoons flow regime.

2) From Reynolds numbers between 30 to 50, a wave regime appears. In this flow regime, the gross flow rate does not deviate appreciably from the laminar parabolio description in spite of the presence of surface waves. Eence, it is sometimes called pseudo-1*=4n=?.

~~

3) At Reynolds number larger than 1500 to

2000, the laminar region is replaced by turbulent motion.

Theoretically, there were many investigations made to obts.in the analytic solution for the structure of the falling film.

For

example, Ben,jamin

[S2]

developed a

linear stability theory and Kapitzt

[53] attempted to solve the nonlinear equation which is derived from the boundary layer equation with kinematio surfsoe condition and tangential and normal shear stress continuity condition.

After. that, many modifications or other attempts [54, 55, 56, 57] vers made.

Even though these theoretical analyses partially agreed with the experimental data, analysis generally can not describe the highly nonlinear wave motion with a.few terms in a Fourier series.

l

t i

29 i

i force causes acceleration and thinning of the waves.

I The following papers by Chu and Dukler (59,60]

concluded that the small waves which oover the substrate i

in the failing film control the fluid resistance and i

transport prooesses in the gas boundary layer since the

{

substrate is present for a large portion of

time, while the large waves control these same processes in the liquid I

film sinoe the large waves otrry a large portion of liquid mass.

Fig.

2.12 shows that the liquid flow rate has a strong effect on the probability density distri.bution of l

substrate thickness and the maximum peak value decreases rapidly with dooressing liquid flow rate.

On the other

hand, the gas flow rate has only a small effect on the pavinum peak value and the spread of the curve. Also, Fig.

t 2.13 shows that increasing gas flow rate dooresses the substrate thickness on the liquid film.

Fig.

2.14 shows that the probability densities of substrate wave amplitude f (A ) is loosted remarkably near s

the same value, within 0.0128 mm, for all liquid rates in I

the absence of gas flow.

From this phenomenon, it was suggested that the waves that are formed are all of same maplitude and that a prooess of dispersion or coalescence generates waves of other sizes.

This dispersion and coalesoonce increases as the flow rate increases. The wave i

amplitude is insensitive to gas flow as shown at Fig.

2.18, even though the average substrate film thickness is sensitive as shown at Fig. 9.15.

On the other hand, probability density functions of large wave amplitudes display well defined multiple peaks except for the lowest film Reynolds number as shown in Fig. 2.18. This suggests the existonoe of several discrete large

waves, At low liquid rates (Ro

'700),

one n

characteristio vsve may11tude was presented with a modal value of about 0.05 mm. If Fig. 2.16 is compared with Fig.

31 strongly on the distance as voll as the liquid and gaseous film Reynolds number.

The critical Reynolds nu=.ber, where the flow is supposed to change from laminar to turbulent, varies with the longit"A4 M1 distance as shown at Fig.

2.19. Fig. 2.20 shows a typical result of the longitnAini effect for Ren - 576. In this figure, small amplitudes of less than 0.1 mm and high frequencies (100 E:)

were reported in the entrance region (0.1 m). This changed to ripple type waves of about 0.3 ma in amplitude and about 50 Ez frequency at 0.3 n. Af ter 0.5 m, large waves (0.5 z=

a=plitude and 10 - 20 En frequency) vere reported. These la.rge waves and the substrates are similar to the two-vave systam which was reviewed before. T*Vrh*M also measured the increase of surface a.rea due to interfacial waves and found that the increment is very small.

This means that the promotion of heat and mass tre.nsfer between the two-phases is not due to an increase of the interfacial surface a.re a but to the disturbance effect of the vavy motion.

Recently, the simulation of a vertical wavy film was solved analytically by using a finite-element method by P.

Bach and J.

Villadsen

[63).

The ocaputed result (Fig.

2.21) shovs the characteristic features (the deep

trough, the steep forefront s' d much smoother receding bach of the n

wave) of a

f ailing film vave which vere reported by the prevj.ons experiment.

Another important result of this calculation is the dramatio increa.se of y

component velocity before the wave fronte (point I at Fig.

2.21 and Table 2.3). It means that a fluid; particle, which is at a position quite close to the v811 at that

point, accelerates very rapidly out ofI.the trough. It is avept towards the surface of the liquid a$d past the crest of the large wave before settling down in the smooth flev behind the wave. This phengrena aust greatly enhance the i

33 intensity and decreasing the viscous sublayer. This effect was correlated by ocaparing drag on the wavy surfaces to that on a roughened surface. As a conclusion, even though the numerical solution by P.

Each and J.

Villadson

recently, shows some possibility for solving for the wave action, experimental oorrelation is still a better tool than numerical solution to represent the characteristics of the falling film and the effect of a wavy interf ace in promoting transport phenomena.

2.5 Turbulent Condensation 2.5.1 Turbulent film condensation For long vertical surfaces, it is possible to obtain condensation rates such that the film Reynolds number aroeeds the critical value at which turbulence begins.

Kirkbride (67] found that the heat transfer coefficient is much greater than the value calculated from Russelt's theory on this turbulent condensate film.

After his experiment, Colburn [68] reviewed the results of Kirkbride and developed the following correlation for the heat transfer coefficient of the turbulent condensate film by using the analogy with the flow of liquids through pipes under conditions where the liquid completely filled the pipe.

In this work the critical film Reynolds number was taken as 2000.

2

[

] = 0.056 Re0.2 Pr (2.5.1-1) 1 1

I D y(o 4,)a g

1 This analysis was extended by Carpenter and Colburn

[69]

to propose the following correlation which included the effect of vapor shear stress, i

35 order of 10,000 with interfacial shear. Therefore, he suggested that neither true laminar nor fully developed turbulent flow exists in the film and the combined mechanisa was considered at all points in the film.

The Deissler equation near a solid boundary and Yon-Karman's equation at the region of y+ larger than 20 for the eddy viscosity were used to model the turbulent motion as follows:

2,7 ( 3,,,, g, n

))

for y+

20 (2.5.1-3) l c=n

• • I

)

for y*

20 (2.5.1-4) i where n and I are numerical constants.

l This model was solved digitally by using a

computer.

It was found that the velocity distribution carve in the liquid film depends both on the interfacial shear and on

)

the film thickness while the universal velocity i

distribution is usual in full pipe flow. The results agree i

j well with Russelt values at very low Reynolds number and l

with Carpenter's experimental data in the turbulent I

region. There is also good agreement with Seban's analysis at high Reynolds numbers and Frandt1 numbers.

Lee [73),

I

however, pointed out that the fal.1-off in the heat j

transfer rate for small Frandt1 numbers was greatly over-l estimated sinoe Dukler neglected the molecular thermal conductivity with respect to the eddy conductivity in i

defining the temperature profile at values of y+ greater f

than 20. He has repeated Dukler's ~ onloulation using an improved velocity profile and oonsidering the molecular conductivity ters and obtained a solution which is very olose to Dukler's results at high Prandt1 numbers and to i

i 37 i

C

- vare celerity i

The analogous dimensionless heat transfer equations are used by Bankoff [75] ss follows:

i f r Re

> 500 (2.5.1-5)

Nu

= 0.25 Re Pr t

t g

=0.7FRefPr5 Nu for Re

< 500 (2.5.1-9) g g

where the turbulent Nusselt number is given by Nu g

hi /k.

He used these correlations with ug = 0.3 ut and is t

8 for the horizontal occurrent steam-vater flow and got a good fit of his own horizontal condensation arperimental data and the value predicted by Eq (2.5.1-9).

E.J.

Kim and S.G.

Bankoff

[76]

presented another

~

correlation as follows for countercurrent steaa-water flow in an inclined nhannel, where the interface is expected to be more agitated by countercurrent flow and the inclined surfs.co than the horizontal occurrent flow.

Ref*I2 Nu

0.061 o.5 Pr (2.5.1-10) g where, ug

fet

/p i

is-A As a conclusion, even though some theoretical predictions before 1970 agree well with the arperimental I

data in some speoitio range, they do not consider the physical structure of the falling film. On the other hand, although the use of a turbulence-oentered model appears to take into account the physical structure of the turbulent i

1 39 l

1. 1

-u.og = p (2.5.2-3) g 3x J

The transport equation for uguj is transformed to the

{

turbulent kinetic energy equation by the contraction, j-1, j

vhich can be expressed as:

l Dk 1 3 "t

k u

t "i

"k ) e"i

{ l + T ax C

+

(~

}

Ft p ax ax

~

r k i

Also, the turbulence dissipation equation can be derived f

in a similar way with some assumptions.

j

" t. Bc )

Lc.13

[

De p 0x k c #*k (2.5.2-5)

Cu c Bu Bu I"i 2

{

3 t g

k } &x c

I

+

-C 2T l

O k ax 8x k

i k

where the turbulent viscosity gg can be calculated by h

2 C

ok u

u

=

(2.5.2-6)

~

t c

The values of the constants appearing in Eqs. (2.5.2-4) f (2.5.2-6) were suggested as follows by Launder et al.

{

[81).

W j

i i

6 l

WESTINGHOUSE CLASS 3 l

41 assigned in the orM na7 k-e model, while C, and C2 are to vary with turbulence Reynolds number according to the formulas:

C

= C, exp[-2.5/(1+Re /50.)]

(2. 5. 2-9)'

g C2 =C2o exp[1.0 - 0.3 exp(-Re2))

(2.S.2-10) where 2

k Re

=7 g

v where C,o and C are the values assumed by C, and 2o C

18 2

the fully turbulent region.

Ya11 Pusetion Method In this method, the effective viscosity near the vall is deduced not from the k-e model described above, but from the laplications of the universal velocity profile.

The fluzes of momentum and heat to the vall are calculated by the following correlations, z

l

}

4 "P

=b C

I

k. in[EyP

]

(2.5.2-11)

(t/c)W u

v kf Pr, Eyp (Cfkp)Y (T -T ) C D C p

y p

In{

]

q" k'

V (2.5.2-12)

+ Pr

( )I (I'

• I' 1)(Pr

)~

t sinw/4 k

g

WESTINGHOUSE CLASS 3 l

43

1) It is econcaical in oosputational time and storage.

{

That is, it produoos relatively accurate results with fewer mode points within the boundary layer, sinoe the wall effect is evaluated only in the numerical cells next to the wall.

For example.

Chiang and Launder

[84]

showed much slower convergence with a fine grid using the low Reynolds I

number model than that by using the near wall I

model on the calculation of turbulent heat transport downstream from an abrupt pipe expansion.

2) It allows the introduction of additional empirical information in special cases (for example; suotion, blowing and rough wall, etc.). The extra espirical information can be expressed by way of the constants

{

or functions k*, I and A+.

i For normal steady flow like pipe flow, the above wall-model showed good results [85]. It is frequently j

1-function observed, however, that a disturbanoe in the main streaa (separated, reattached or recirculating flows) has a

[

significant effect on the wall boundary.

Chieng and I

Launder

[84]

reported a numerical study of flow and heat transfer in the separated flow region orested by an abrupt i

pipe orpansion by using the k-e model and the near wall model.

In this omloulation, a parabolio variation of the

{

turbulent kinetio energy is assumed within,the viscous

sublayer, which means a

j linear increase of fluctuating velocity with distance from the wall.

The turbulent kinetic energy varies linearly toward the outer node

{

points. The turbulenoe shear stress is sero within the viscous sublayer and increases abruptly at the edge of the sublayer while varying linearly over the remainder of the os11.

However, these local variations of turbulence quantities were not incorporated in the evaluation of both i

e-. - + -,

s e

,,-a w

a r

n--

i WESTINGHOUSE CLASS 3 f

45 1

The convective and diffusive terms are negligible near and i

on the wall. This is ensured in Eqs.

(2.5.2-15a.

2.5.2-15b) by i

3k Ti (2.5.2-17)

~

15

-0 ay (2.5.2-18) w i

which corresponds to no d.iffusion of k and e to the wall.

L Yith these distributions, the mean generation and destruction rates in the e equation oan be obtained as follows.

t i

i i

(C P) =

[T*(T A)

+

Ik o

I k' C1y k

I 2

v n

~

v n

(2.5.2-19) t T

-T

" (2(kg - kg) + al)]

+

7, a

v i

+Cy, II v)**

~

( n~ v w

i I

t, i

(C

) = C -I2 -(I"v)2 a

v (2.5.2-20) 1 y'/y"(_a 2 j

yh+b) 2ab

+

C IvT I

-T 7,

y a

n v

l where t

h 1

(k -a )(kY+al) 1 g in[

k (k, - ak)(k,i + aI)-)

for a>0 a

i i

f

WESTINGHOUSE CLASS 3 i

47 low-Reynolds number model described in section 2.5.2 was used to consider the 1==1==iisation near the interface for t

the k-e model. A modified Musselt approximation was used I

j for the liquid film.

I The results show that Cebooi's model agrees best with the measured Stanton number of heat and mass transfer and l

the profiles of velocity, temperature and conoontration in the three version of the Prandt1 m1ving length model. Even

(

though the predicted profiles from the k-e model were in reasonable agreement with the measured value, this model I

underpredicted the condensation rate for the higher condensation rate case.

Rooently, by' ocuparing the ratio.of the experiment va.lue to the computed one with the film Reynolds number se ahown Fig. 2.27. Rens and Odenthal

[92]

attributed '4he

{

discrepancy between the i

experiments and the computation results to the influence of the condensate film waves. The increase in the condensation rate by a wavy interface is supposed to be due to the influence of the waves on the

{

j turbulence structure of the vapor-gas

side, since the contribution of the transfer resistance of the condensate film to the overall resistanoe is calculated

{

to be less t

than 5 percent in this experiment.

i, By assuming the 4

i condensate film as a sinusoidal wave i

form, the instantaneous values of the z and y components i

velocity at the film surface were calculated by Gollan and Sideman's [563 statement. Also, the amplitude of the waves is assumed to be of the order of 30 to 80 peroent of the i

average film thickness. The value of the-turbulent kinetio i

l energy of the gas boundary layer was calculated with these

{

velocities and maplitudes.

Fig. 2.28 shows the distribution of the turbulent i

kinetic energy in the boundary layer. The thickly drawn ourve shows the computed results for an incompressible j

.,-a m

--"~

-e W

T

WESTINGHOUSE CLASS 3 49 typical containment following a loss of coolant tooident can vary by about 4 - 7 psi at the and of blevdown [1] and up to 23 psi at marimum [37] depending on the assumptions made for the condensation heat transfer ooefficient.

An experim nt of condensation phenomena in a

reactor conta.inment was started by Jubb [941. Steam was supplied to a large boiler (8 ft sin dia, 30 ft long).

Both the heat transfer ocefficient for -the forced convection portion (during blevdown) and for the free convection portion (post blevdown) were slaulated.

In the forced conysotion period, Jubb correlated the heat transfer rate as i

o St Pr.5 - 0.0576 / (Re P)0.25 (2.6-1) and in the natural convection portion, the heat transfer rate was correlated as O

h = 0.0152 p AT.25 (2.6-2) in the calculation of the Reynold's number, the velocity is calculated for steam at the end of ths blevdown pipe, and the influence of this velocity on the air-vapor boundary layer is characteristic of this particular boiler. That is, the velocity along the condensing vall is needed to calculate a condensation rate at any position in a conta.inment. Also, the dependence of AT' was presented rather than the fnmiamental condensation theory of the dependonoe of (1/AT).

Kolfist

[981 reported a

conta.inment experiment where the containment was slaulated by a

steel tank 8 feet high and 10.5 feet in diameter.

Steam entered from an external pressure tank at 1000 psia and was injected into the containment through a pipe located under a ba.ffle plate. The authors oonoluded that

l WES TINGHOUSE CLASS 3 51 the time to reach the marimum coefficient decreased, and the nazimum heat fluz increased. The =Arimum heat transfer j

ocefficient was expressed by Slaughterbeck (1) o haaz = C (

)0.62 y

(2.6-3) where haaz : the maximum heat transfer coefficient during blevdown (cal /seo-ca Co or Btu /hr-ft OF)

C

a ocastant equal to 0.185 for metrio units or 72.5 for English units Q

the tota.1 energy relea. sed from the primary during blevdown (cal or Btu)

V

the free volume of the containment vessel t

the time interval until peak pressure (seo).

p and the heat transfer coefficient for the transition period to the =*vinum was recommended to be h-haaz(f)

I (2.6-4)

P where t : time (seo)

Fujii et al. showed the following correlation which was presmanhly derived from same experimental data 0

}1.3 9 p,,a ( ye P

(2.8-5)

WESTINGHOUSE CLASS 3 53 orifice plates of va.rious sizes and types.

The BTF C-series tests involved geometrically complex containment configuration with a blevdown source of saturated liquid i.nat resulted in the introduction of a two-phase blevdown mixture into the containment.

The D-series test configurations were geometrically simpler than the C-series configurations and were characterized by a single-phase blevdown of saturated steam.

The independent variables of both series are the blevdown mass flow

rate, blevdown location, number of compartments involved in the test and the connectivity of the subcomps.rtments.

The EDR experiments are an artension of the containment analysis from the m 11 sosle facility of BTF and should shed more light on the feasibility of extrapolating results to resi pla.nt scale. This facility 3

has a 75 m

reactor which was filled with saturated water and steam at a pressure of 110 bar.

As shown in Fig. 2.31 tota 1 containment consisted of 34 compartments and most of the facility data was presented in terms of these zones.

Kanzleiter

[97]

shoved that the measured mazi=um interna.1 pressure of the BTF test

a. mounted to only 60 percent of the internal pressure calculated without heat transfer to the cold conorate and steel structures.

The good agreement was achieved between the results of this experiaant (subcompartment R9 of experiment 01) and calculations using a constant heat transfer coefficient of 1300 v/m2oI as shown in Fig. 2.32. The author attributed the big difference in the pressure to the higher ratio of inner surfaos area to volume and that the influence of heat transfer to the cold structure is much greater in a

sea.le model oonta.inment than in a full scale plant. Sohvan and Aust

[98]

presented the experiment for the break compartment with high steam flow.

The heat tranfer coefficient vs.s reported to be the order of 104 v/m2og

WESTINGHOUSE CLASS 3 55 cold vall and other time dependent effects,

however, the condensation heat transfer coefficient data have not been systematically arnmined for these arperiments.

2.7 Summary and Concluding Remarks Condensation phenomena can be classified by the presence of noncondensable gas, the ga.s mixture velocity, the flow characterization (laminar or turbulent) of the gas mixture and the condensate film and the interface condition as shown in Table 2.4, which shows the summ a 7 of the theoretical and experimental investigations reviewed.

For all cases except the turbulent vapor-air nizture bonno ag layer and the wavy interface of both the pure vapor and the vapor-air mirture

case, it is seen that extot numerical solutions of the conservation equations and approximate solutions agree well with the corresponding experimental work.

For the analysis of

~

condensation phenomena in a re&ctor containment,

however, the effect of the turbulent vapor-air flow and the vavy interfs.co is supposed to be important, since the structure of a falling film is covered by very unsymmetrio waves and this wavy interfaos is supposed to have some effect on the transport phenomena through both the gor-air bonnd a 7 layer and the condensate film. Yhitley's model for the turbulant vapor ~ air mixture boundary layer was only applied to a coattinsent analysis assuming the velocity of vapor-air flow and comparing the calculated containment pressure response with the arperimental data.

As a

conclusion, theoretical development and experiments for turbulent flow with a wavy interface are needed to predict condensation phenomena in a

reactor

WESTINGHOUSE CLASS 3 57 i

Table 2.1 Reproduced from Rose (32]

TeMe L Coedsammien se a Amt pinen. F, h of emmenad solumens of 5panee a at (3) for se las me h g m byegename m i

i I.

Synnse Egn m 6B25 E951 '

- 4951 ta$

LSOS 1905 4875 taa) 4863 11 4223 A324 1 125 1787 1 738 i

1 13 GL752 R733 4 175 E72 E721 SJ

&AGO tett 4.225 4462 0A&3 425 SA33 0437 13 1357 83as 1 35 S.543 4345 13 1438 R4N E75 L319 1318 1A R241 42 4 l

!J List 114 la 1500 1100 2J 40717

&#713 si tas32 tes32 18 60214 6a217 i

i i

t Table 2.2 Experimental Results of Mills and. Seban (41]

a and Siegers and Seban (42]

i Investigator fluid 7.('C)

AT('t) h"(kw/m) faff.4,,

2

[41]

senas 7.2 - 10.0 4.4 - 6.1 31.4 - 34.6 0.9 - 1.1

[42) n-butyl 29.5 - 38.2 3.9 - 5.6 25.1 - 34.6 0.98 -1.02 alcohol

+

0 s

l 1

v'r'

WESTINGHOUSE CLASS 3 59 l

h I !

I i

-o

.e a

g g

1

=

J t

2 i 2 r

}

} }

i s

o u

2 I

=

j

.3 i

s ii p.

2 n

.i

^

=

-g i 1

r t

3 J jjj.3 j

0. 5 8

e 1.

31

_j i L

?! E i

5:: E !

i.

t s.

n. l.

i gi.

I I ;.,

: c y

• . g*.l. 3 3 ; b t

e g-ld j ::g,,

l 5

I:(

! ll!I 3

u I 3 4[ - 2

=

2i

_ =. _

, ~.

t u

~

I

.=

a.

.I w

a 3

t' w

3:t

.1 r

i t

J

[ }

1.

}. _.

Ji i !.

e a

r i:I, 2 j j j jjf.<. '.i

[.! 521 i

~

I 1

l is

=

_=

=..

4 u

=. g,

o g

a 1

1 I

1.

6 3

J.

8..!.I 3

g.

3.

N 3

I ':s [:

a.I 3

3 I

I S a 1] f I d

3 s

r j

I.

1}2}14 1

I'

=

,3 2

i 11-i 3 1 1

]

.r

-i 2: 2-i t

1 4!

)i.

(

3 el J

h v

h

- - - -. -, ~ -

a

WESTINGHOUSE CLASS 3 61 i

g

\\

u Gm t

~

Fig. 2.3 Comparison of Dimensionless Shear 1(

vith Numerical Results for Laminar Film Condensation down a Vertical Flat Plate and a Horizontal Cylinder.

u

.h Reproduced from South and Denny [19) u -

\\

\\,

.,,,,s w;

a J

i

=.

n,

,.s c

i s

s ww.

n r

' Cav r(M

/

a.,,.

..n

. =,, tes

-m,o

• 9t.s-er f0)

)g i

cs E,,.

• a'*

as s

i i

i

/

f

t ANNN 8

I IN NA.

_l T =$39:69"1 i

-Ix h'

'i e

i *-

+h,0 l

e

. 10

• 20

[0 -

E

$N f~

i (T.. T ),

'r

~ ~~

e g

3 g

~

. Ti r. 12 f f..l.i.c.~.t of 's7pe~b o u..s.s. g (o r variou s p r e s c ribe d vad e e s of 8

I

.T an.d for W e 0.005 (no taterfac2a.1 resistsace)

---e

(

l Fig. 2.6 Reproduced from Minkovycz [27]-

3

WESTINGHOUSE CLASS 3 l

?

65 t

1 I

I I

Large Wave on Film I

}

I i

l

/ Small Vave on large Wave I

I l

I Substrate l

Sas11 Vave on Substrate I

I Mean Thickness of Film

!I lI Mean Thickness of Substrate

/

I

~

I I

i I

i e

l 4

I i

I f

l I

I 3

l k

l I

l i

\\

Fig. 2.9 Identification of the Structure of a Falling

Film, s

Reproduoed from Chu and Duk.ler [59) 1 i

i I

i

WESTINGHOUSE CLASS 3

~

I i

a 67 t

6

=00 0 s

s

~

f

• *h j.

...$.7 0 O

=

\\

300 0.

g gese Re,

• O c

I

(

1

.e. :oo o.

?

t

[

eso.o.

i I

A OO i

CD 64 4.

i a

Fig. 2.12 Frobability Density of Substrate Thickness:

Iffeet cf the Film Reynolds Number, i

Reproduced from Chu and Dakler [59]

[

g I

==.

==.

ee.

i 2

rt.:

r

%~

o j

m m.

l d

i I

i

[e.a..

j i

l

,[

/

i

\\

1 l

_.i

.\\.

1 u

Fig. 2.13 Probability Density of Substrate Thickness:

s Iffoct of the Gas Reynolds Number, i

Reproduced from Chu and Dukler [59]

j 1

l

5 WESTINGHOUSE CLASS 3 i

~

I 1

69 i

i g3 e

e 5

{

1 to #

• =,

• e N

• • g

~

e 370 e

ecLS ao

=

4 a

see i

3 383

{

cc n.

3. -

ss=*

I

~

l O

~

go N h k* %.

cN~~N -

l

~

i e

m i

Fig. 2.16 Probability Density of Tave Amplitude.-Re i

Varying Liquid Rates I

i

- 0:

Reproduoed from Chu and Duller [60]

i i'

d i

==

u=

i 4

?

v y '*

v e

/

c a.us o

u.s:

..ue.

s

,, b e

i 3.

==

.cs.

=o 1

Fig. 2.17 Mean Deviation of Large'Yave Amplitude Reproduced from Chu and Dukler [60]

u 4

1

WESTINGHOUSE CLASS 3 i

t i

71 i

s10' t

t 6m g

tur bLient cc fl ow 6

tamina flaw L

~

i a

0 R

12 16 = 102 a mm Fig. 2.19 LongitnA4 n=1 Change of Critical Reynolds Number.

Reproduced from Takah===[62]

se.57s to as ;_ -- _: :

a. ai, I

.=-

e i

s w/%. W m d i o.s c 0

[

I

a. 0.5 m h

C y

a. 0.3 m c

3" u

C t.'

s e t.7 m 3 3

[

bb I

o at n2 a3 u

os 48 time, sec Fig. R.20 LongitnAinal Developing Process of Interfacial Yave Form.

Reproduoed from Takahamm[62]

l l

I

WESTINGHOUSE CLASS 3 i

)

c 73

,I s -

.f.

3>

i s

e t =2..........

e es en e.

es e.

er se se

.e e.v r i

Fig. 2.23 he Function F.

i Reproduced frca Brumfield [74]

i MF

\\

1, I

I flI w

/

/

i l

i Fig. 2.24 he Near-Yall Rodas T and P j

l 1

WESTINGHOUSE CLASS 3 75 n.;-l

n

1

~

e s-a f"L1 y

..*e o.

La o

s to is

o ts o

s to

s

s

s ser a*r Fig. 2.27 Ratio of Erperimr2tal a.nd Theoretical Stanton Rua.ber for Esat m.ui Mass Transfer.

Reproduced from Rees and Odenthal [92) 10 E

L6

=e j

/

/

1.*

/

=

\\\\*

{

/

t J

ns

/

t k

s 04

/

/

s t

t e

5 0

10' 10' IC 10' 10' I

r' Fig. 2.28 Numerical Prediction of the Influence of Film Yaves on the Turbulence Energy Distribution in the Boundary Layer for R-e

- 95.

( - Inocapressible Bo Layer. -- Boundary Layer with Condensation and Yave-Free Film, Boundary Layer with Condensation and Yavy Film

('A/ 6 = 0.8)

Measurement's of Archsya [93].

Incompressible BonMn?7 Layer),

Reproduced from Rahs a.nd'Odenthal [92]

i

s WESTINGHOUSE CLASS 3 i

77 i

i

?

v ma nue.e su.

l N

A

.N%

• O l

P E.Kalaifg ry:q

~

A-com w

4 @ >

dut 8

i Y

Y!

Mumme summmme g

g aQ s A

?

-v* C ? A L~s.* " c,,,

q 7

h O{;ww.-i' et P*

I W

g-a t

,o r-s l

o-

-s 3

S a

+v k

.o E m

• p 8

(

@*/,*y,.

..T* h *.

as %

gggg..I M

• . ey a..........'.

i I

Fig. 2.30 BTF Containment Test System 1

?

1

WESTINGHOUSE CLASS 3 4

i i

79 f

t 1

i i

i I

i

.0, l /,. e ~ a.

• 68<

l

-/./.-#,~~.

w.

u.

.a i

m.

,9,/

/

r s

?

u.

.r u.

=

=

=

m e.

aa Fis.10. Absolute presure; expenmental and theoretial results.

't t

r b

Fig. 2.32 Reproduced from Kanzleiter [54]

tj t

P l

1 l

y

,4

WESTINGHOUSE CLASS 3 i

i 81

{

[fl(#1 ~ 'g} "1 h

film o,943 19 4

(3.1.1-3) a L (7I.7y w

where L is the vertical leogth of the cold surface and

hfty, is the average heat tra.nsfer coefficient.

As mentioned previously, a number of modifications were suggested to this model. In addition, the surface of the liquid film vill eventually become vavy and the liquid film vill be turhalent as the vall length increases and as obstacles on the vall tiisturb the film flow. The data.iled model for the condensa,te film with these conditions is to be presented in section 3.3. However, when noncondensable gs.ses are present the film heat transfer coefficient is larger than that of the vapor-air layer coefficient, and therefore is usually negligible or can be estimated by l

Nusselt's method with little error on the overa.ll heat transfer coefficient ezoopt under special conditions, which will be explained in section 4.3.3. If the filn beoones turbulent, this assumption becomes even more valid.

The heat tra.nsfer coefficient in the vapor-air boundary layer is ocaposed of three contributions:

1) convective heat transfer from the vapor-air mixture to the film, hoonv'

2) condensation of the steam onto the liquid film,

hoog,

3) radiation heat transfer from the air-vapor airture, hre-hg g, hoony + hoond + hrad (3 1 1-4)

)

WESTINGHOUSE CLASS 3 i

83 condition (vertical-horizontal, piste-tube, forced-natural and im=4"m*-turbulent),

the condensation heat transfer coefficient could be calculated easily without any specific condensation experiment correlation.

For the turbulent flow, the above equations become 30* - p u, c' (3.1.1-10) t = v

-K

+pC 7 U' (3,1,1_11) q

=

3X

-ag A+og U-(3.1.1-12) j

=

The bar is omitted for simplicity arcept for the correlation t e rr.s.

In analogy to molecular transport ocefficients, Ec asinesq suggested the introduction of eddy diffusivities by the definitions au*

u,' U '

g,y (s,1,1_1s)

=

y

~%h (3.1.1-14)

U' y

y

_g (3.1.1-15) ge v' I

Now the Reynolds shear stress is replaced by the eddy i

diffusivity eg for aczentum and Reynolds heat and aass

WESTINGHOUSE CLASS 3

~

f i

85 of meters per second

[2.96].

If the length of the containment wall and some obstacles to disturb the flow I

were considered with the above

velocity, the vapor-air j

boundary layer has to be considered as turbulent.

Simos the Chilton-Colburn analogy applies for fully

[

turbulent flow inside tubes, and for flow parallel to plane surfaces at low mass transfer rates [106), it can be f

3 used to calculate the convective heat transfer coefficient near the contain= ant vall, h

j

,Yk p C u 9 P 9 (3.1.2-1)

-2/3 k*N~

" Pr e

(3.1.2-2) where E is the ratio of the turbulent eddy diffusivity of E

i heat eg to momentum eg.-This analogy cannot apply to any other. geometry (e.g. streamline tubes or flow across tube-and tube bank) however. Now, for a wall the local skin-friction factor is given by [107]

i f=0.0296no, (3.1.2-3) for Reynolds numbers between 5 x 105 7

and 10. Then this is combined with Eq.

(3.1.2-1),

the resultant local convective heat transfer coefficient is i

i h, x 1/3 0.02% no,0.8 "x

=

h K

(3.1.2-4)

)

81noe the Reynolds number is a function of x, the average turbulent convective heat transfer coefficient for the j

WESTINGHOUSE CLASS 3 87

&=. 9 (3.1.2-11) 1-g and the condensation heat transfer coefficient is then given by h ' h (1 9

2 _ b-3-i) g 3

(3.1.2-12) cud (T -T) g g

Recently, a lot of effort has been given to predict the turbulent Frandt1/Schmidt number (108).

The most interesting analytinal results were derived from transport equations for the turbulent kinetic

anergy, for the turbulent heat flux, s.nd the turbulent mass flux by Jischa and Rieke [109).

~

C2 Pr

=C t

2 + p-(3.1.2-13) r se

.g+

(3.1.2-14)

The two constants C2 and C2 vare fitted on experimental data C3 0.85 (3.1.2-15)

C2 0.012 to 0.05 for Re ='2x104 j

i i

WESTINGHOUSE CLASS 3 89 the same functional form.

Since Eqs.

(3.1.2-13) and (3.1.2-14) agree well with the experimenta.1 data for a vide range of Prs =dtl and Schmidt

number, these equations are to be implemented in Eqs. (3.1.2-2) and (3.1.2-7). The resultant local heat a.nd mass transfer ocefficients are ca.lculated from 0.8 0.0296 Re Pr

• (0.85 + 0.01/Pr)

(3.1.2-20) x 0.8 0.0296 Re Pr Sh, = (0.85 + 0 01/Sc)

(3.1.2-21)

As the mass transfer rate (ocndensation rate) increases, the

momentum, thermal and mass transfer boundary layers vill be reduced in size because of the apparent suction effect of the condensation process. This reduction in the bounds.ry layer thickness will further increase the temperature and concentration gradients near the vall and increase the heat and mass transfer coefficients.

To

{

consider this

effect, the following correction factors

[112, 113] can be used In (1 + B,) g g

Momentum transfer: my- =

3 7

(3.1.2-22) f m" / G B

= -

g 2

In(1+sg)St (3.1.2-23)

Heat transfer:

st ah In* l G <

i 5=

3t.

1

WESTINGHOUSE CLASS 3 t

l 91 l

uk T*

k=

(3 1 3-1)

Re v

where u, is the ahear velocity.

For the solid rough

surfsos, three regimes are identified as smooth surfaos (Reg < 5.0), transitional roughness (5.0 < Rok < 70.0) and i

fully rough region (Reg

• 70.0). Since the interface of a

fa.lling film changes quickly to be a highly unsynnetrio vave, it is hard to define and model the transitional region for the wavy int erf a.ce.

Therefore, the vavy interface is assumed to be the fully rough region if a

wave is formed.

Collier (6) presented that the shear stress increases progressively by the wavy interface at a

film Reynolds number greater than 100, which will be used for the critical Reynolds number for the wavy interface in this work.

In the fully rough

regime, the visoons sublayer is expected to disappear entirely and the momentum is transmitted to the, vall (liquid falling film) by the l

impact or pressure drag on the rough element (vave).

Therefore, the oddy diffusivity and =1 ring length must be finite at the vall surface (interfa.ce) and can be represented as

~

i = k (y + 67,)

(3.1.3-2) rather than the =1 ring length model for smooth surfaces:

g.g y (3.1.5-3) where i goes to zero at the vall.

In Eq (3.1.3-2),

87o can be correlated to k,

a.s a

nondimensional form

WESTINGHOUSE CLASS 3 93

+

v

=

(3.1.3-8o) dp "I dx )

+

(3.1.3-8d)

P

( g 3) w This equation is reduced for the case of no pressure gradient and mass transfer to the vall o"

D (V

+C T

g)

(3.1.3-9)

For the fully turbulent region, ther molecular viscosity can be neglected relative to the eddy viscosity eg.

T, oc

- 01 2(

)2

=

g (3.1.3-10) ok.2 g7

+ (6 y,)+]2 (

)2

+

By introducing the nondimensional fora, we obts.in du+

1 dy k* [y+ + (67o)*}

(3'1'3~11}

9 Since there is no viscous subicyer in the fully rough

region, the lower limit of

~ integration of this differential equation must be extended to y+ = 0.

)

+

WESTINGHOUSE CLASS 3 95 bonMm7 layer, the friction coefficient becomes 68 (3.1.3-15)

=

in (864 6 /k,)2 2

2

Now, it is worthwhile to notice that the friction coefficient depends only on boundary layer thichess and the roughness size, not on the viacosity or velocity of the fluids. nis friction ocefficient is used to calculate the shear stress on the interfa.ca and the film thickness.

ne effective roughness k

is correlated by using g

Yallis's suggested correlation (65) as described in section 2.5.

k 48 g

(3.1.3-16) where 6 is the mean film thichess, which is calculated by the model for the condensate liquid film presented in section 3.3. As de(cribed in section 2.4 the substrate in a

f all i ng film plays an important role in the transport phenomena through the vapor-air boundary layer.

ne substrate film thickness or the wave amplitude of the substrate, therefore, seems to be more plausible for the correlation of the friction coefficent for a falling film than the average film thickness. no experimental data of the friotion oosfficient for a falling film by Chu and Dukler (59, 60) was compared with the ratio of the substrate film thichess to *he diameter. Fig. 3.2 shows a very similar correlation with Eq. (2.4-1) 6

~

(C )y = 0.005 * (1 + 750 g)

(3.1.3-17) g It means that the substrate film thichess is proportional

WESTINGHOUSE CLASS 3 97 correlations for the heat and mass transfer are required for the wavy interface. For the thermal boundary layer at the vall without pressure gradient and mass transfer, the dimensionless temperature profile is expressed from the conservation equation of energy with the Couette flow approximation as follows:

}

+

'T dv*

T+ -

(3,1,s_19) 1/Pr + c /v g

vbere

(

} !

~

T+.

(3.1.3-20) q" / o C, f

Since there is no viscous sublayer at the rough wall, the eddy conductivity eg is assumed to be much larger than the molecular conductivity for all the way down to y+ - 0 l

axcept very small Prandt1 numbers.

The temperature i

difference across the interface by conduction is

. represented by in Thus Eq. (3.1.5-20) becomes

+

d',

T* -

T*o.

(3.1.3-21) l

<a C H/W l

To calculate eg the turbulent Prandt1 number and Eq.

(3.1.5-2) are used H

1 "M

k C

7 = Pr

• Pr (I+* OI+)

(3.1.3-22) v o

t t

I

WESTINGHOUSE CLASS 3 99 where Eq. (3.1.3-15) is used to calculate C /2. Since St f

g is a function of Prandtl number, the racistance for heat transfer by the molecular conduction is included.

The Russelt number for the convective heat transfer is calculated from the following equation.

C /2 Re Pr Nu =.

f

(

~

Pr

+ /C /2 t

f

/ St k Stanton number for the mass transfer is derived by a.nalogy between the heat and ma.ss transfer.

C /2 7

3*AB *

(3,1,3-29)

Sc, + /C /2 73 f

ABk where ABk - C Re-0.2 3c-0.44 (3.1.3-29a)

St k

The Sherwood number for the condensation heat transfer is i

correlated as:

C /2 Re Sc Sh =

g Sc

+ /C /2 (3.1.3-30) g jgg These equations will be used to compute the heat and mass transfer through the vapor-gas bonnon7 layer with a wavy interface.

3.1.4 Natural Convection Model

WESTINGHOUSE CLASS 3 i

101 (104 < Gr Pr < 10 )

8 Nu - O.13 (Gr Pr)1*'3: Transition flow range (5.1.4-4)

(108 < Gr Pr < 1010)

Nu - 0.021(Gr Pr)2/5: Turbulent flow range (3.1.4-5)

(1010 < Gr Pr)

Ye have generalized the original condensation mass transfer model by using a

similar approach. Table 3.1 shows the analogies between heat and mass transfer at lov mass transfer rates. For the la=4"=* flow range, the mass t

transfer correlation was derived by merely substituting Sh for Nu and So for Pr. For the other range, one can derive simple fo: mulation by using the Chilton-Colburn analogy l

a which is valid for turbulent flow.

St.,-

Eh - 0.56 (Gr ff)1/4 t==4"=*

flow range (3.1.4-6)

(104 < Gr Pr < 10 )

8 Eh - O.13 (Gr

@#3: Transition flow range (3.1.4-7)

(108 < Gr Pr < 1010)

Sh = 0.021(Gr /5 21/3 2

l Pr /15).

Turbulant flow range (3.1.4-8)

- 0.021(Gr Pr)2/5 (golo, Gr Pr)

(3.1.4-9) f Since (So/Pr)1/15 of vapor-air is almost 1.0 Eq.

(3.1.4-9) could be used instead of Eq. (3.1.4-8) for a simpler i

consistent form.

P The high mass transfer correction factors can also be used with this natural convection model.

r

WESTINGHOUSE CLASS 3 103 i

A staggered grid system is associated with every grid t

node, while the vector quantities (velocity components) are displaced in space relative to the scalar quantities.

This grid system has advantages.in solving the velocity field since the pressure gradients are easy to evaluate and velocities are conveniently located for the calculation of the convective fluzes.

The discretization equation of eq (3.2.1-1) can be written for the two-i dimensional geometry as shown in Fig.3.3, a e

=a 0

pp E E * "V V + *N'N * "S*S + b (3.2.1-3) where E = D,A(lP,l) + MAI(-F,,0)

(3.2.1-sa) a y = D,A(lP,l) + MAI(-F,,0)

(3.2.1-3b) a g = D,A(lP,l) + MAI(-F,,0)

(3.2.1-3c) a g - D,A(lP,l) + MAI(-F,,0)

(3.2.1-3d) a "P * *E + "V * *N + *S + a

- S 4xay (3.2.1-3a) b = ScAx47+.04 0 PP (3.2.1-3f)

,o,

(3.2.1-3g)

P t

and(jandp refer to the known values at time t,

while all other valun are unknown at time. t+At. Also the flow rates F and conductances D are defined by F, = (ou), ay (3.2.1-ta)

WESTINGHOUSE CLASS 3 105 field to correct the velocity field.

After that, the remaining d's a.re solved and the whole process is repeated until convergence.

3.2.2 Near Yall Model for Smooth Interface As described at section 2.5.2, the effective viscosity near the vall is calculated by using the universal velocity profile of turbulent flow ever a flat plate a.s follows (113):

+

u

= 2.44 in y

+ 5.0 (3.2.2-1) which corresponds to the Eqs.

(2.5.2-11) and (2.5.2-12) with 1* - 0.41 (3.2.2-2)

~

E

- 7.76 (3.2.2-3)

Also, the Van Driest's constant is reccamended ss 25.0 for the external bonndary layer over the flat plate.

The 1

effective d.iffusivities are calculated from Eqs (2.5.2-11) and (2.5.2-12) u 6v+

for u and v (3.2.24) u,gg = k, in(E 6,)

7

+

'If u 67 for T (3.2.2-6)

=

i C

Pr

[k' In(E 6 +) + PTN) p g

7 Y

DD for m*

(3. 2. 2-8 )

• II = Sc, [k' in(E 6 +) + STN]

7

WESTINGHOUSE CLASS 3 107 (3.1.3-23),

the second term of Eq.

(2.5.2-12). which contains A+, can be replaced by the second term of Eq.

(3.1.5-23) with the modification of k* and E described above. It corresponds to the change of PFN in Eq.

(3.2.2-

5) to 0.2 o.44 Re Pr k

PFN =

Pr (3.2.3-3) t The analogy between heat and mass transfer is used again for the oddy diffusivity for mass. SFN in Eq. (3.2.2-6) becomes O.2 Re g,0.44 STN -

e (3.2.3-4) t

~~

Akai at al. [119) used a k-e turbulence model with near vall model to solve a horizontal stratified two-phase flov i

system.

Fig.

3.4*

shows the velocity profile shifted i

downward nearly parallel with incressing gas phase Reynolds number, which is expected for the horizontal flov l

at section 2.5.

The universal velocity profile for near vall model, therefore, vs.s modified to match their own arperimental velocity profile with the wavy interface as follows

"

• 0.4 I"8 6,+

+

1 A+

(3.2.3-5) where A+

dimensionless vava amplitude and showed good agreements a.s shown at Fig.

3.5. Also, the

WESTINGHOUSE CLASS 3 I

109 For the laminar condensate

film, the velocity

{

distribution is calculated from the balance of forces 1

(3.3.1-1)

(6-y)(o -o ) a dx +T dx + @ da y

6 (u,-u6 i

=

vhere each term of the right side represents the. forces arising from

gravity, friction at the

surface, and acaentum drag by mass transfer through the interface and i

$ is a multiplying factor. This factor was suggested to be 0.75 by Mayhew, since the vapor crossing at the interface is not supposed to be at exactly the same velocity as the main vapor. Even though this factor seems to vary with the

'l condition of the gas flow pattern and interface, the j

suggested value.

0.75, will be used.

Since the j

condensation

rate, da must be same as the heat transfer rate through the condensate film as shown i

1 I (T -T )

y y

ij,6 (3.3.1-2) l

-l Eq. (3.3.1-1) can be rewritten with the assumption of J

1. 1 pg.

3 l

I (T -T )(u,-uk) d y (3.3.1-3)

- i a

oy T

7 y

du =

(6-y)dy + - Edy +

u u

uij,6 i

Integrating this equation with respect to y, with u = 0 at y = 0, gives 1

1

WESTINGHOUSE CLASS 3 111 i

interface at film Reynolds numbers less than the critical value.

Yith the mean film thickness calculated from the above

equation, the heat transfer coefficient through the condensate film can be ca.lculated by h=

(*

• ~0 6

3.3.2 Model for a Turbulent Condensate Film The condensate film is supposed to change from lasinar flow to turbulent flow at the critical Reynolds number, which is widely suggested to lie between 1000-3000.

T*ht**e,

however, reported it as a function of the longitnd4"=1 distance without gas fl,ov.

In the current work. 2000 is te=porarily chosen for the critical Reynolds number.

The universal velocity profile for the arternal boundary layer is used, since the ahear stress on the interfs.oe is large due to the large vapor-gas velocity and wavy surface.

+

+

• I for y+ < 10.8 (3.3.2-1) u

= 2.44 in y* + 5.0 for y*

• 10.8 (3.3.2-2)

Tith these distributions, the mass flev rate can be calculated by using Eq. (3.3.1-5) for y+ < 10.8 r, v6 2 (3.3.2-3) 2 for y+ > 10.8

WESTINGHOUSE CLASS 3 l

113 i

Table 3.1 Analogies between Heat and Mass Transfer

}

i i

at Low Mass-Transfer Rates Heat-Transfer Binary Mass-Transfer Profiles T

n, k

Diffusivity

• "Z

1. d8 Transfer rate 0

Yl* -'d@f' + YI')

l Transfer a.0 a,. We* -

• dye * + Ys9 i

coefficient Aar A ans e

D Yo DG D Yr DG Dimensionless "T*7 e

p groups which y,

y, are the same in Fr - #

Fr = #

both correlations L

L 3

3 AD

&,D i

Nu= 7 Nues = Y l

A5 l

Basic dimensionless Pr b I

= _ '

sc = # 8 groups which d

d8 are different g, Wrsat Wyc an, g

Ne k " g,p, g&

se,= No,

a

- a p

,y Special N = R4Pr = DYrC*

DY N as = R45c = g combinations of dimenaionless ja = NMM fo = Not,Rs-8Sc-w groups

" C,Y(ef)w ar a,

, tw T

~ 'T' e

r v

=

1 i

. WESTINGHOUSE CLASS 3

\\

115 l

Table 3.3 Summary of 4, r and S in Eq. (3.2.1-1).

for the Ax1 symmetric Cylindrical Coordinate i

Equation 6

u,fg S

l Continuity 1

0 0

u,ff

+h(u,gf I Momentum u

)+

r(ru,ff

)

3P 3

Bu la av Y Momentum v

u,f f p + p( u,f fp) + rar(ru p) 2 u,f f v I

2 K

l Energy T

D C

l P

Mass f

Concentration I pD,ff 0

l

}

Turbulent u

Energy k

d O P - oc j

g k Energy u

2 t

oc p pc Dissipation c

C

-C

-g 1k 2k l

c 4

I where i

P=v

[(h + E)2 + 2(h)2 + 2(h)2 + 2(')2 t

Br ax 3x 3r r

i

?

I

WESTINGHOUSE CLASS 3 i

i f

117 f

r 4

v 2.93

~

r t

O

~

^

h 4U O

v r

• 9. 02-t c

i s

t u

s 4s O

A

~

'~

D

~

EO.el O

Reg = E25GG u

~

O Rag = S2900 L

k t

O Reg = 113000 t

9.00 GE+000 2E-003 4E-003 GE-OO3 Dimens ion less Subs trate FI Ja Th ic kness (ds/D) t Fig. 3.2 Comparison between Eq. C 3.1. 3-17 )

for the Fr ic t ion Coef f ic ien t and Chu and Dukler Experiment C59.603 i

+

1

[

t

t WESTINGHOUSE CLASS 3 l

{

I19 l

1 l

I t

zo 44

+ 4 %'*L*

• r I

io

. *.

• l *g.

j

... : *:' s.

l io io' i s'

\\

l Fig. 3.4 MeanGasVelocityProfilesforInte5';'e'**Re

• • 81 "

3 (Reg = 8.04x10 ;

o, Re g - 8.54x103; g = 1.32x10 ;

.g = 6.52x10 A. Re Universal Velocity Profile) 1 20 8

t 4

a i

uj=hinM+52 j

15

+ oc D

i i

10 I

I 5

i I

i 1

10 100 (r- ) / A

~

Fig. 3.5 Rough Surface Correlation for Gas Velocity (Reg = 8.04x103; o, Reg = 6.52x103; e, Reg = 8.54x103 A. Reg = 1.32x10';

, Correlation Line)

WESTINGHOUSE CLASS 3 121 Chapter 4 COEPARISON YITE EIPERIXENTAL DATA 4.1 Analysis with the Condensation Esat Transfer Model and Verification 4.1.1 Analysis with the Simple Model The condensation heat tra.nsfer models were incorporated into a computer program to compare with the experimenta1 data.

This program separately calenistes the heat flu through the liquid film by using the model dese 1 bed in section 3.3 and the heat flu through the air-vapor boundary layer by using the model in section 3.1 with an assumed interfa.ca temperature (T ).

The program then 7

iterates on the heat flu by modifying Ty until the heat l

fluss converge within a specified aocuracy a.s shown in Fig 4.1.

Since the shear stress is a function of the distance along the va.11 and the characteristics of the condensate fil: change along the vall, the vall is divided into a

finite number of control nodes a.nd the condensate rate and the other values sre calculated at each node a.long the dirsotion of the condensate film flow. For countercurrent

flow, the momentum boundary thickness of the vapor-air flow is guessed at the sta.rting point of the condensate film s.nd is subtracted at each node. At the end of the calculation for the whole length, the momentum boundary thickness is checked and vill be iterated to obtain the proper acaentum boundary layer thickness.

Then these heat and mass transfer coefficients were calculated, the transport properties at the vapor-air boming layer vere evaluated at a reference tenperature and mass fraction suggested by Spa.rrow at al. [29) as

i WESTINGHOUSE CLASS 3 i

i l

1 t

123 t

(7 -T )

(4,1,1 7) 7 9

y TR1 = Ty+

t 3

t 4

t 4.1.2 Condensate Fila i

I J

The model for the condensate film was compared with the i

c pure vapor experimental data of J.E. Goodykoontz and R.G.

l Dorah

[23).

One should remember that for pure vapor the oondensate film controls the heat transfer. The purpose of oonparison to this data is to verify that the model for the condensate is reasonable when ocapared to tests in vhich the film controls the heat transfer.

This data I

showed that the experimental heat transfer ooefficient is j

1.3 to 1.9 times as large as the value predicted by the j

laat nar model of Fujii and Uehara as shown in Fig. 2.4.

{

Pujii and Uehara attributed this disorepancy to the j-turbulence in the film due.to the very high vapor velocity.

The effect of the wavy interface and the j

turbulent model of the condensate film were, therefore.

{

investigated. The following values of k', I and A+

were f

chosen from the expeimental data for pipe flow in a tube, 4

where the experiments were done, and were used with Eqs.

1 4

(2.6.2-11) and (2.8.2-12) k* - O.4 (4.1.2-1) 8 j

E

- 9.0 (4.1.2-2) l A+ - 26.0 (4.1.2-3)

This experiment was done with a range of the steam inlet j

velocity from 10 to 80 m/seo and the oondensate film should change from a 1 pinar film to a turbulent film with j

j W

a gn4

-r.

r v,.

WESTINGHOUSE CLASS 3 125 ne dimensionless shear stress at the high inlet velocity, however, is calculated to be auch higher than 10 and in this case the critical film Reynolds 1

number is considered to be less than 100 in Fig.

2.22. Derefore, two criteria vill be used for.the change from 1m=1*sr flow to turbulent flow as I

follows :

a) A critical Reynolds number : 2000 b) A dimensionless critical shear stress of 10 with the critical film Reynolds number of 100.

3) ne wavy interfa,ce affects the heat transfer rate by increasing the shear stress and decreasing the film thickness. ne calculation ahovs about a

10 percent increase in the heat transfer coefficient at the entrance region for the immi"*r flow. In this model, for 1**in=2 flow, although the wavy interface reduces the film thickness by incree. sing the shear

stress, it is not considered that it increases the heat transfer by the turbulent motion of the wavy layer.

It results in a nall increase of the heat transfer rate by the vavy interface for in4 war flow.

nis effect seems to disappear at the end of the tube, since more vapor was condensed at the entrance region and the velocity at the end region is calculated to be much slover than that of the case of a

smooth interface.

In addition to the decrease of the condensate film thichness, the eddy diffusivity of heat for the turbulent flov is modelled to increa.se with the shea.r stress.

no effect of the wavy interface is, therefore, la.rger than that on the la=4 *s? flow a.s ahovn by Figs.

4.2 and 4.5.

4.1.3 Verification of Simple Xodel with in tnar Flov I

WESTINGHOUSE CLASS 3 127 Asano cones from the high mass transfer correction factor, since Asano used a ta.bulated value from mass transfer azperiments rather than the valte calculated from Eq.

(3.1.2-24).

The origin of Asano's tabulated values for high mass transfer was not given in the original paper. nor referenced in the bibliography.

4.1.4 Verification of Two-Di.nensional Model with Laminar Flow A two dimensional calculation was done with the SIMPLER algorithm for the vapor-air phase and cra.2 lated the condensation rate on the assumed interfsom temperature.

The perpendicular velocity (y direction velocity) at the condensate interface is assigned as the bonnom y condition from the condensate rate calculated.

v g - n' /p (4.1.4-la) g The other boundary conditions for the condensate interface are u g - ut (8)

(4.1.4-lb) g Tgg - T1 (8)

(4.1.4-lo)

P

• M

'I Iyz =

(4.1.4-Id)

P,7+M, + P og vI v

where the partial pressure of the steam at the interfa.oe is set equal to the saturation pressure at the interface temperature calculated. The following bonMag conditions for the other side vall are imposed

WESTINGHOUSE CLASS 3 i

i 129 l

I Since the perpendiculai-velocity is set at the t

interface, the correction term for high mass transfer rates is not needed and is included within the theory of the two-dimensional calculation. The

results, therefore, show very good agreement with the experiments for the vide range of the vapor mass fractions as shown in Fig. 4.8.

i 4.2 Comparison with Dallmeyer's Erperiment i

The Dallmeyer experiment was -also compared with the i

calculated results from the simple model developed for turbulent vapor-gas flow and with the two dimensional k-e model.

This experiment was chosen because it was the only i

forood convection ' separate effects' test avsilable for turbulent flow of the vapor-gas airture. The condensate film is considered to be in 1 W nar flow with a

smooth interface, sinoe the film was maints.ined to be laminer by sucking off the condensate at intervals of 100 and 200 f

as i

along the plate.

Moreover, the film Reynolds number without considering the suction is calculated to be less than 100.

'f CCL4 were evaluated The thermophysical properties o

from tabulated values

[121].

In' the two dimensional i

calculation, the boundary oonditions for

velocity, temperature and mass fraction at the interface were evaluated by Eqs.

(4.1.4-la) -

(4.1.4-14) and the l

turbulent kinetic energy and dissipation were omloulated by the local equilibrium condition of Eqs. (2.5.2-13) and

[

(2.5.2-14). The following boundary conditions for the oentarline of the apparatus are imposed i

i u-u s (4+2-1)

J i

i l

WESTINGHOUSE CLASS 3 131 l

l l

l l

4.3 Comparison with CVTR Erperiment 4.3.1 CVTR Experiunt The only large scale integral containment arperiments which have been performed in the United States, are the Carol han Virginia Tube Reactor (CVTR) test series, where slightly superheated steam was injected from a nearby l

fossil power plant into a fu.I.1 scale containment of a

I decommissioned nuclear reactor.

This steam was injected through a diffuser which oonsisted of a 10 ft section of 10 inch diameter pipe acunted vertically with 126 1 inch diameter holes drilled in its vall. The base elevation of 1

the diffuser was 335 ft, which was 10 ft higher than the operating floor. Only one arperiment of the three in the test series (Test 3) was conducted without an active spray

system, which was used for the-other two experiments.

Table 4.3 shows the injected steam condition of Test 3.

The CVTR cont'a hant is a

reinforced conorate cyli

• ical structure v.'.th a hemispherical top done, i

having an internal diamator of 17.66 m.

The operating floor is also of reinforced concrete (see Fig. 4.12). The oomannication betvean the operating region and basement is via the circumferential space between the containment vall and the edge of the operating floor and through the ste.irways [122].

The most reliable method of measuring the heat tra.nsfer ocefficient through the containment vall utilized two heat transfer assemblies (heat plugs), which were installed in 1

the operating floor (elevation of 330' ft and 350 )

and 0

Esat Plug 2

some 23 ft higher on the vall (elevation of 0

546 ft and 318 ). These measured the temperature profile l

l l

l

1 WESTINGHOUSE CLASS 3 133 n e I-FII computer code (123]

which calculates the transient dynamics of two-diat a,onal, two-fluid flow with interfacial

exchange, was used to obtain an estimate of the velocities along the surfmoe of the heat plugs.

The six field equations for the two fluids couple through aa,ss, momentum, and energy exchange and are solved using an Euleria.n finite difference technique [124].

For the velocity field calculation of the CVTR test, air was treated as one fluid and ' team was assumed as the s

othe.?. No condensation or evaporation for either phase was assumed and the same velocity and temperature for air and steam was calculated by setting a large interfa.oial friction coefficient and heat transfer coefficient. As shown in Fig. 4.14, the total conta9 = ant (total volume 3

64.8 m,

height

= 25.9 m, radius - 8.83 m) was divided into 358 oells by using the axis of symmetry; i.e. the r-direction was diveided into 20 nodes, the x-direction was done by 21 nodes and 62 oells were used for the internal i

obstacles which simulated the hemispherical done and the operating floor. ne communication between the operating i

region and the basement is allowed only via the oircumferential gap between the containment vall and the i

1 edge of the operating floor. ne steam was assumed to be injected homogeneously and horizonta,lly through a

10 ft high inflow boundary opening as an approximaticu to the horizontally oriented holes in the diffuser. The injected steam conditions at the inflow opening vere estimated by using choked flow calculations as shova in Table 4.4.

Since a rum 11 time step was required (2

maec),

the velocity fields in the containment could not be simulated during the whole blevdown period (166.4 soo).

ney were calculated at the beginMng of steam injection (BOSI) and the end of steam injection (EOSI) by assuming a quasi steady-state.

This method is a good assumption given the

WESTINGHOUSE CLASS 3

)

135 model, the vapor-air boundary layer is developed fron 340 ft for both directions and the counterou rent effect is considered.

n o heat transfer ooefficient along the wall at 110 sec after the blowdown was calculated and is shown in Fig 4.18.

no omlonistion estimated that the oondensate fils develops waves at 365 ft, where the film Reynolds number exceeded 100. D e effect of the wavy interfaos is expected-to increase the heat transfer coefficient about 10 percent at the position of Beat Plug 2 and agrees well with the experimental data.

Figue 4.19 shows that the heat resistance through the condensate film cannot be neglected for this condition, even though the early investigators

[37, 116] insisted that the condensate film oonid be i

t neglected in computing the total heat transfer coefficient

+

for condensation with a noncondensable gas. De conditions are different as follows:

~

1)

Asano's experiment and analysis (36]

was done in i

imm4*** vapor-air flow, where the heat and mass 1

transfer rates through the vapor-sir boundary laya.

{

are much lower than that in tubulent vapor-air flow.

2)

Even though the tubulent - vapor-air flow is considered by CorrmAini's analysis, he neglected the vapor mass fraction at interface (I

at Eq.

3 g

(3.1.2-12))

to caloniste the heat transfer by condensation. At 110 see after a blowdown, however, i

the temperatue of the contatsmant wall rises to l

l the satuation temperatue of the atmosphere and

{

the vapor mass fraction is not negligible at the interface. Figu e 4.20 shows that the heat transfer i

ooefficient with Ig is almost 1.6 times as large as j

that without it.

3) ne velocity of the vapor-air mixture is higher

WESTINGHOUSE CLASS 3 137 oundensation vill not occur any more given this condition, and only forced convection heat transfer ooonra at the surfa,oe. his transition is not represented in the present j

model.

The results of the heat transfer coefficients calculation at Heat Plug 1 (lower plug) overestimated the j

experiment data with the parallel velocity calculated by K-FII as shown in Fig. 4.24.

i

Finally, the two -dimensional model results for the vapor-air flows are ocapared as shown in Fig. 4.25 to the arperimental data.

he vapor-air flow conditions calculated from E-FII are used as the boundary condition in the two-dimensional calculation as shown in Fig. 4.26, The ca.loulation results show the following discrepancies with that of the simple model:

1) The two dimensional calculation estimated a lover heat transfer ocefficient than the simple model near the stagnation point. This seems to be reasonable, since it is supposed to come from the la= %=rization by the strong stabilization effect of acceleration.

This same effect was found in the turbulent impinging, jet arperiment on a plate by C. O.

Popiel i

al. [125] for the ratio of the distance from the et nozzle to the nozzle dia. meter (z/d) less than 4 (at this calculation s/d

- 1). By a limitation of the vall function model, which is that the nearest node should be remote from the vall for y+ to be larger than 10.8 the calonistion result is not arpected to be accurate at the node of the stagnation

point, where y+

is less than 10.8. This is because the ry is calculated to be very small.due to the small parallel m'.coity to the vall.

2) The velocity at Esat Plug 2 is used as the velocity along the vall for the whole upper vall (from 340 ft

WESTINGHOUSE CLASS 3 139 coefficient agrees well with the experimental data and the two-dimensional calculation at the point of Rest. Plug 1

+

(9.2 m). Even though this velocity may not be oorrect, it l

is used for the whole period of the experiment to include the effect of the two dimensional flow and stair way. Fig j

4.24 shows good agreement for the whole period. After 110

sec, the upper wall is not expected to have a condensate

{

2 film, and the condensate film is assumed to start at 340 ft (stagnation point).

Also, near the time of the steam shutoff, the temperature difference between the bulk and i

the wall surfaos are 0

small (5-10 C). Basil temper'sture l

difference unoertainties, which were estimated to be about l

0 1.1 C in the report [2], result in large heat transfer l

coefficient unoertainties from Eq. (4.3.2-1) (see error bar in Fig. 4.24). These two reasons cause the difference t

between the model and experiment after 110 sec.

As a

conclusion, the calculated results of the simple model agree fairly well with the experimental data and the j

detailed two-dimensional calculation eroept for the narrow j

stagnation area. Sinoe the velocity of the vapor-air flow i

is one of the most important factors in estimating the j

j heat transfer ooefficient, a more reliable computing j

)

method for predicting the vapor-air flow in a containment, i

4 which may consider the effect of three dimensional j

If

]

geometry and turbulent vapor-air flow, is required to make j

j more reliable estimates.

1 i

)

1 4.4 Natural Convootion Model with Tagami Experiment 4.4.1 Tagami Experiment

~

j The Tagami experiment, which measured the condensation heat transfer coefficient at the steady-state, was g

~ ~ - -

' ' - - -"~~

WESTINGHOUSE CLASS 3 141 condensation heat transfer va.s measured to be slightly dependent on the surface height [3]. It agrees well with 3

the natural convection model of the transition region, where the heat transfer ooefficient is independent of the surfeoe length.

Therofore.

Tagani's experiment. was i

analyzed by using the natural convection model. Figs. 4.27 and 4.28 show good agreement of the calculated heat transfer ocefficients with experiment. Also, the results of the turbulent and im=9 "a" model calculation show that the turbulent region model is useful to predict results for the case beyond this transition region.

From this

analysis, it is concluded that the developed natural convection models are useful to predict a post-blevdovn a,ocident by choosing the appropriate model from the (Gr Pr) number.

l 4.5 Precalculation of the Future Experiment I

Using the simple model, parametrio studies were done to predict the result of the condensation arperiment with a

noncondensable gas, which is under way in this laboratory.

i The dimensions of the apparatus are shown at Fig. 4.29.

The turbulent vapor-air flow is injected into the rectangular flow nh="nel (100 mm x 100 mm) and the water is injected onto the surface to model the thick film condition, which is expected from a long containment vall.

No condensation is a,ssumed in the inlet section (1.245 m) but the bonMm7 layer of the vapor-a.ir is developed in 1

this section. The tamperature of the condensing vall is 0

about 20 C and the total pressure is un4ntained to be y

a. bout atmospherio. The maas ratio of the air to the vapor is controlled by cha.nging the bulk temperature, which is the saturation temperature at the partial vapor pressure.

i 4

1 4

N m

Table 4.1 The Effect of the Distance of the Nearcat Node to the Wall the Two-Dimenafo,nal Calculation of Anano Experleent h

at I

C)

T (oC)

(Q/QNu}Exp Two-Dimenalonal Calculation (Q/QNu)

C:

IvB B

fg 2.0E-4" 1.0E-4 5.0e-5 2.7e-5 1.2e-5 5.0e-6 0

0.97 65.0 0.7 0.471 0.517 0.550 0.564 0.575 0.578 5;

0.95 65.0 0.5 0.345 hh 0.400 0.410 0.417 0.420 0.85 37.0 0.23 0.189 0.207 0.218 0.224 0.227 G3 0.80 37.0 0.19 0.150 0.173 0.171 0.70 17.0 0.13 0.115 0.118 0.!!9 0.50 17.0 0.047 0.062 0.064 0.40 17.0 0.037 0.047 0.047 The Diatance of the Nearcat Node to the Wall i

Not Calculated l

1 bl

WESTINGHOUSE CLASS 3 I

1/. 5

)

j 2

i Table 4.4 Inflow Steam Condition for K-FIX

.i I

5 Pressure (MPa) 0.6307 (1.1660) [a]

Temperature ( C) 122.08 (186.67)

{

Density (kg/m3) 3.4972 (5.5570)

Mass Flow Rate (kg/sec) 47.879

[

Velocity (m/sec) 214.58 Inflow Area (m ) [b]

0.0638 i

[a] () repersents the values before choked,

[b] Inflow area is calculated by summation of the areas of 126 1 inch disseter hole.

7 l

1 Table 4.5 Results of Estimated Yelocity from K-FIX i

i j

BOSI (0-- 10 see) EOSI (160 - 166 sec)

Heat Plug 1 (m/sec) 7.9 6.1 i

Heat Plug 2 (m/sec) 10.2 8.0 1

i j

4 1

i i

i l

l I

1 e

d w

e

WESTINGHOUSE CLASS 3 147 40000 a I i

I m

f I

{j O

Experimental Data n

300002 Turbulent Fala and Wavy Interface

{

- -- Lam i n ar F i l m an d Wav y Interface v

'g

-- - Lam i n ne F i l m an d Smo o t h Interface g

e

~

\\

u 5

1

~

w 20000 s

O U

1

~

L

~

W

-)

c

,g o

,N L10000-H

~. s

'.s

\\

O

~

0..'~ 4: ::'

\\

~

8 j

- c..

,c a -

. ~...

O

~

O

.........i.......

3........

4.........

0.00 0.50 1.00 1.50 2.00 Leng th (m)

Fig. 4.2 Calculat lon Resul ts from the Mode is i

Developed and Goodgkoontz and Dorsh's Exper imen t Data at Uin 19.9 m/sec

=

i i

WESTINGHOUSE CLASP 3 149 80000 4

a t'

m O

Exp e r i me n t a l Data (600002 Turbulent Fi lm and 14avy Interface 2

w

-- - Lam i n ne F i l m an d Linv y Interface

~

c s

u 4w 400002 s

o

(

o

\\

y w

4

\\

c 0

L 20000-

\\

o s

s a

o w

~

z

~

~.o ' ' & ~ y _

~_

~

O

............................i... i.ii G.00 0.50 1.00 1.50 2.00 Lang th C m)

FI D.

4.4 CalcuIntion Results from the Modeis Developed and Goodgkoont2 and Dorsh's Experiment Data at Uin = 47.9 m/sec T

1

WESTINGHOUSE CLASS 3 151

[

l l

5000 t

~

4000 r

53.3 unsc'

/

l Uin a

/

~

j s.

p w

a n

/ /Uin = 47.9 usec I

~

{ 3000-l' /

~

,/ /

a

• /

D

/

Uln = 35.1 us e c l' /

/

O

,'/

a

$ 2GGB.~

j/

7

• /

E

/

/

~

1.

/

l E

l'/

~

/?

'/

~

1000 l?/

uin 1s.s usee

,1

~

t 9"....

...i..................

9.99 9.50 1.00 1.50 2.00 Leng th (m) 4 1

Fig. 4.6 Calcu lated Fl im Reyno lds Number 1

e i

h I

i I

n e

.e, n

WESTINGHOUSE CLASS 3 153 I E+ BB Q

~

o N.:,' ;:

s..

3 i*

8

.1 i.'.

\\

\\.

N. *.

o

• \\, *

~

o As an o Exp e r i me n t

i. *.

y' Asano Calcu lat ion gg Simpte Modei

-- e Teo-D i men s l ona l Modei

,g)

.,'i i

.31

.1 JE+BI Xu (Air Mass Fraction at Bulk) i Fig. 4.8 Calculation Results of Simple Model and Two-Olsensional Model mith Asano Experimental Data C3SJ j

. - - i

~

WESTINGHOUSE CLASS 3 i

i 155 i

l 1.00

o

/

O I

0 0

l O

~

/

W O. 80 --

o j

p O

d

^

E

/

l O.50, p

/

v 9

x O

^

- 0. 40-F 0

I g

lj mb J

{

O Experiment 0.20-ui = e.e j

)

--e-UI = rian s Flux / De n s i t v l

0.003:.........

2.0 4.0 8.0 12.O Leng th f rom Wal l (mm)

Fig. 4.10 Comparison of the Tamperature Prof I le I

between the Two-Dimensinnal Calculation Results and Dalimever Experimental Data i

l t

t

i WESTINGHOUSE CLASS 3 i

~

1 l

t 1

157 1

I i

l l

l i

l W 3" i

vr se.e L.

Seae Leme h

d EL-360' i

St- 0

• 00 C enerene l

Ortmart=s ersics,

$8 *-0* 0 0

(

ye* swa L.aer

{

Grouse Lovet l

EL - Ste' i

fg ep *. g*

i r

arrowspiart arseon i

?

CLattn' 8Ettestwt at040s I

Oe.eem meer l

EL trS*

(

i'ifd%BR SR-59./GF4EGE'.Sif e

i

\\

\\.-- r..

i.e, i

e i

1 b

?

e..-..

i i

t Fig. 4.12 CVTR Containment Structure 1

i l

I h

i I

f I

l l

r t

.. - ~

WESTINGHOUSE CLASS 3 159 t

32.004 Illll v

6 A

A s

< < e.

. < < T e r s 3 v

v v k

k

' 4 4 4 T

P P

P ^ ^

N'43 4

v v v v L 4

A

< c e e e o A A e

v v v v

& u t

t c c < t r e r 3 A d v v v v v u

s u s < <

< s r v v n s

22.860 V

V V V

b b

M E

E ' 4 4 4 T-T T T

T TfD i

v u

> uu u

u u u r r

< r e n n n m

y k

k 4

L k

k k

V V

4 y

3 4

4 4

E 18.288

> l>

2 4 2 2

7 y 4 H

v i

=

2,

> > i>

> > > > > :s > >

_s x

2 0

^

A v v e e r e t

c. c t

e <

> v v v v W 13.716 I

a o w r e v A

s v v

Operating Floor W

9.144 r < r e w.. 4 4

, r e 4

T T

T T

T T

T T

v t v g

V

- +

4.572 v v u t

<! < ( 4 4

4 4

5 6

• v k

k 4

4 4

4 4

h b

W D

W L

o O

2.207 4.415 6.622 8.830 RADIUS (m)

Fig. 4.14 Flow Dietribution Calculated from I-FII at 5 sec for CVTR test I

l

WESTINGHOUSE CLASS 3 161

.5 I

~ fl 8-in i II Ii i

i

^

u 8,8 q

'; }: i 1

Ii e

/j v

Heat Plug 2

s i

u

..5 y

IA i

i D

\\

a 11 1[: A.,

-1.B Y t \\l"ij'\\{\\{\\hj\\/\\

Heat Plug 1 I

-1.5 BB 2.8 4.8 6.8 8.0 2 Time (sec )

FI D. 4.16 Radlui UalocIty Calculated at BOSI C O-8 sec )

1 l

l 1

WESTINGHOUSE CLASS 3 163 1

l l

2500 s

e n

~

a 2eea:

=

e N

2

,e j

.~

(. ~~.... "

e

." 1500-u s

s,

~

OU

~

1000.

L c

w i,

~

4 e

c c

g

~,

500-O 2

--- - W i t h tio de l f or Wavy Interface w

~

Without Model for Wavy Interface t

0 i

G.9 4.B B.9 12.O Leng th (m)

Fig. 4.18 Haut Transfer Coefficient along the Mali at 110 sac af ter a i

Blowdown i

i

+

~ ~

~ ~ --

l WESTINGHOUSE CLASS 3 i

i

!65 2500 t

f W

n 2000 a

s 2

c 3 15002 u

s-s o

u 1000;q,............

t c

u s

s.

o

~,'~.

n t

c g

u 500-

)

U Simple Model l

1 Corradini ModeI C1153 O

~

0.0 4.0 8.0 12.0 Leng th (m)

Fig. 4.20 Compar ison be tman the Simple ModeI and Corradini ModeI l

O y

y

-~

WESTINGHOUSE CLASS 3 167 i

l 2000

~

$ Experiment

" S i mp l e Mo d e l with Wug Interface

~ S i mp l e Mo d e l without Wug Interface

^

M O

N O

?15G3:

p 2

v

/

i

~

/l

~

c f,A e

/,l u

p s

S 1000-

/

l w

,4 o

p U

,4 L

~

m 4

e c

a L

500-F i

t

,L' e

t 5

Y i

/

G i.........

O.9 50.0 100.0 150.0 200.0 Time (sec )

I Fig. 4.22 Condensation Heat Transfer t

Coefficient at Haut Plug 2 t

~

WESTINGHOUSE CLASS 3

~

169 i

l 2000 j

l Y Experiment

- 6 S i mp l e Mo de l w i t h U = S.1 - 7. S m/s e c

[

-@ Simp le Mode i elth U = 4.5 m/sec

^

O A

m

,e s1500-

,L E

2

/

v

/

c

,4 u

Ph 1000

/

3

=

j a

g~

u

~

,$ )a/ /

c

=

,e s

e p

c a

g M

L 500-

\\

e

,/

a

~

6 x

\\

e G.............................................

0.0 50.0 100.0 150.0 200.0 250.0 l

Time (sec )

Fig. 4.24 Condensetion Haut Transfer Coefficient at Haut Plug 1

WESTINGHOUSE CLASS 3 171 32.004 Heat Plug 2 21.336 Boundary Conditions r*--

Calculated by I-FIX l

.Two-Dimensional l Calculation

, Region l

in

~

/

Heat Plug 1 y

Operating Floor 9.144 0.0 0.0 5.7462 8.830 Radius (a)

Fig. 4 '.' 2 6 The nodes used at Two-Dimensional Calculation of CVTR Test-with the i

Boundary Conditions Calculated by K-FII l

l I

WESTINGHOUSE CLASS 3 173 1E+B3 L = 8.9 m a

?

N

/

~

2

/

}

.V P,, -

g/,

%IE+B2 g-m

,@g, OU

~

t

- 0;/

sa C

U

---

Tu r b u l e n t tio d e I

- - - Lam i n ar tio d e l e.

O Translant tio d e l w

I O

Tana=1 Experimene i

3g i

t t t t tit t

t t t t t t9 1E+E9 1E+1B 1E+11 Gr Pr Fig. 4.28 Natural Convection Model vs.

Tagaml Experiment ( L = 0. 9 m )

i i

WESTINGHOUSE CLASS 3

~

I

~

i i

175 1

1200

~.... U i n = 10 usec Cleaug In terf ace >

..... _~~..... -........

n 1000~

=

o

~

N a

l

\\

2 v

800~

c m

u S

600-in = 5 us e c C leavy Interface)

U m

3 Uin = 5 us ec C Smoo th Interface)

L

~

.s 4

400~

e c

O L

Uin = 2 usec Cleavy In terf ace )

p

~

e.

a 200-E b

l

=

g

.................si....

gg g.2 g.4 g,g g,g Langth from Condensing WalI Cm)

Fig. 4.39 The Effect of Inlet Uelocity (Mass Ratio of Air to Unpor 0.584 )

=

C Injec ted Fi lm Th ickness 0.5 mm)

=

CTemperature Difference = 70 cC )

4 1

I 3

WESTINGHOUSE CLASS 3

~

i

?

P 1

f I

177 I

4 j

i E00 i

i k

Tbulk = Se C Crtantu

= 0.684)

{

^

i 1

o e

N c

f a

i s2 i

t v

i 400-3 c

e

.u 1

~

s i

l w

w l

OU t

3.54)

L Thulk = 7e C (Manto

=

s i

1 4 200-l

=

c I

0 l

~

i Thulk = Se

=

C C M 11.4) i i

~

\\

8.

Thulk = 3 e C Cria n su = ss.25) i 5

0 G.9 9.2 9.4 G.S G.8

)

Langth from Condensing WalI (m)

Fig. 4.72 The Ef f ec t of Mass Ratto of Air to Unpor C In Jac tad Fila Th ic kness = 0. 5 mm )

C InJac ted Sas Ua loc i ty = 5 m/ sac) s e

I 4

WESTINGHOUSE CLASS 3 179

- Asa.no arperiment (Inninar vapor-air flow)

- Dalizeyer arperiment (turbulent vapor-air flow with laminar condansate film and smooth interface)

- CVTR arperiment (Esat Plug 2)

(turbulent vapor-air flow with IniMr condensate film and vary interface)

- Tagami arperiment (natural convection)

2) The effect of the wavy interface on the vapor-air boundary layer shows about a. 10 percent increase in the heat tranefer rate at East Plug 2 for the CVTR test.

The increased rate is a function of the wave height as shown in the prediction of the future arperiments.

3)

Usually, the heat transfer resistance through the condensate film in the presence of noncondensable ga.s is auch smaller than that through the vapor-air bonMan layer and oss be neglected.

The heat transfer coefficient of the condensate

film, however, should be considered under the following conditions:

(a)

The temperature difference between the bulk and the vall is email, (b) The heat transfer coefficient of the vapor-a.ir boundary is large enough due to the high velocity of the vapor-air or the high va.11 temperature, sinoe the high vall tamperature causes the vapor mass fra,otion at the interface to be is.rge.

4)

The two-dimensional calculation with a k-e model shows good agreement with the separate effects' data and the simple model. In pt.rticular the computations i

i

WESTINGHOUSE CLASS 3 181 vapor.

No experiment of condensation with noncondensable gas which investigated the structure of the interfmos, the critical condition for the q

generation of a wavy interface or the structure of the tubulent condensate film, has been reported.'

j 4)

The correlation for a rough wall surfsoe is used to model the effoot of a wavy laterfsoe.

Sinos the strsoture of a wavy surfmoe is apparently different than that of sand roughness or a rough solid wall.

l the correlation can be modified from future condensation experimental data.

5) Two dimensional calculations with a k-e model for the turbulent flow and a vall function model for the wavy interface can be' oonbined with a multi-dimensional turbulent containment analysis code for a

better overall estimate of the pressure-j temperature response after a postulated accident.

t i

1 j

4 I

1 l

l 1

i i

i i

i 4

h 4

l l

4 i

i d

i

WESTINGHOUSE CLASS 3 183 M

C l DOCm17710N or PA4AastTERS (II UNITS)

I sf C l I

sa C I Acra a re CTIon Cotrr Crorf I

ee C 1 AKA

TntRMAL CoseuCT!vtTY Or AIR AT Tref l

st C l AKS

TWERhtAL CSeuCT!v!TY Sr STtAss AT Tref I

en C l ALose

Lasm erTurmAn l

sa C I ALsmoo LtueTu or Tur for mAu com Twt CowTswous CAu:utation l

4A C l AasrA 3 88483 rRACTtou er A A AT Trot l

l Es C l Mars a tehs: rRACTIou Or $T828 AT Tref I

se C l 4etiA v!SCOS!?Y tr AIR AT That StrDDeCE TOFERATURE (Trot) l of C l AnaJo a VISCOSITY er utstD WAPoe (AIR a sTEAas) AT Trer l

[

68 C I Aas7L VISCostTY er Llouls (mATOt) AT Tror l

Se C l AnanA e sottcutAA WateMT tr AIR l

Te C-l Assrs

adottcubAR stleHT or aAftR l

j Yt C l CI IsoLAR ConCOtTRAffoM or :TtAss AT INTO FACE I

T2 C l CosetTE : ConsTAss? In fut uutvet$AL vtLacITY Peor1LE (E tu touATIow) l l

T3 C i coutfit : ConsTAstT tu TW UnivDtsAL vtLOCITV peoFILE (he tu touAfton) I To C 1 CouSTV : COMBTANT Foe TME CowfamleuTIon or TWC anAss TRAsesrtR I

{

T5 C l TO TMC 98 TAR STRtsS IN Tht Llou!D r1Las CALcutATIon To C 1 CarTrt rLAs rom fue CowTtessous CAtcutAf ton i

j TT C l

• • • CONTIseucus CALcuLATIOne eee l

Ts C l l

Te C I vAron-Ate rLow Co e tusAft rtos I

se C l 1

at C l CALeutAfton t up ooun I

i 42 C 1 CALCuLAfloM 2 Samu Domu l

a3 C l I

i H

C l CouMTC : rLAS rom TMC CouwTDCURRDIT rLos I

i Ss C l CPA

W'EttrIC setAT er AIR AT Trof I

i to C I CPS

SPEC!rtC setAT er STEAas AT Trot l

87 C l CstTRtt : CRITICAL r1Lal ACThoLDS IEastR PoR TMC tub 9ULDrf FILM (2ees) l

,~

sa C 1 Catata : Cn!TICAL rikas arvuoLas nuetR TM sntAn : Tats: (CnTTau)

I i

as C 1 rom Tur TwouttnT rim (see) t l

to C I CmTTau Cn TICAL 9taansrantts: metAa stress stTw arTata l

l st C l rom Test Tumuttut r!Las (to)

I 93 C l CRWUtt : CRITICAL FILal RiftsotDS same5t roA The aAvY INTERFAct l

{

$3 C l CB teLAA CesCDaTRATIml Or SYRAa8 AT DuLat l

l e4 C l CsTAa CotrrtCterf con uten inAss TRasesrtR aatt i

es C 1 sAs strruster Cotrr C orf I

se C l DEL 2

memortw soueAer LAvst Tn Csosass or varon-Ata rLos I

eT C I DELTAx : InCRoses? (Lassfn or sACm moot)

{

e4 C l DOsSA : DE*SITT or Alt AT Tref I

De C l DDeSAS : DEP43?T er AIR AT Thef t r

I see C l DOsSL DesSITY OF LIgiftD (aAftR)

I j

tel C l doe 8 Dee!TY OP 5120 VApost AT Trof I

to:

C l Dossos DosstTV or stuG varon AT Theim i

sta C I 9 0s88

DesSt77 er BTRAas AT Tret j

1 i64 C l DeeBSS : DENSITY er STEAAB AT TheIh

)

• l inAss rLas natt er Coeossa t poi utf wrofw i

~

tee C 1 eAm tee C 1 eaaas eaAvtfattenAL ACCrLaRATime cocpr:Cient i

teT C i serILm CoeDesAf tou saAT TRAsertR Cottr. Temouen CoseossAf t rtus t

ies C I asAs

Cae cesaftou utAT TaAser R Cotrr. Twnouen varon-Ata e. L.

l l

tee C l sovet total CoeosAfton wtAT TRAsesrpt Cotrf tCtorf I

t sie C 1 eretu crfnALrf strrenoect ettwens varon Ase CaecesAft mAftR l

t r,----

v -

WESTINGHOUSE CLASS 3 185 iss oPen(te.r:LE-rm at.rtArus ots-)

187 c

isa umstr(..*(As)') ourPur r Lt uut ran PAaAuciotst-i ise atAc(..-(A)*) runt 17e cPEN(21.FILterWmt.sTAtuse*MDr')

171 C

172 tstift(..'(A\\)*)' talTPVT FILc mAsst FoR cDetAAL RCsULTS !?'

173 NEA0(..*(A)') Pm Mt 174 oP CW (22. FI Li=#Wut. sTA TWs*

• NC3r ' )

17s sa!TE(22.640) 173 ote FoamAt(*

ale.g'. 4E. 'e.first'.

wave fe.ine'. 3r. *tesle'.

177 82

• refile'. ss.

'ti'. es. 'se4*. SX. 'reau.k'. sI.

17

• n file'. ex. *mes *, fr. se.o r*)

17s e

see sa Tr(..*(A\\)*)* oWTPV7 FILc met FoR ScWERAL ACsULTs !!?*

is atAc(..*(A)*) rW at I

ist art >(22.rttt-enAmt. status ats')

tas untit(22. set) is4 4et roam t(-

rLoss*. ar. 'rucas', ex. rotoso*. sr. counte.

tas is. Cumtr *. ir.

• nous, ex. 'xxsa. fr. ocL2,

ses fr. *cr2*.

ex. 'vttstr')

i ist c

iss c

Lee,for en este est iss c

ise c

ist c a..e s.%t este e.e eet tmo sea t s : eu ests.

ist c

tes tai ava (ie..) scAst. PfotAL. TuALL. Ts. v6..%DC. Ifkoot. ImTW is*

umstr(22.21) IcAsc. PtotAL. TsALL. Ts vs iss ti ronut(int.

• 1 cast.*. Is.

• ProtA w Eta.s.

• Tmau= *.

tes t

tit.s.

Ts *. tia.s.

vom *

. Et2.s.//)

1:7 tr (IcAst.co. tes) twem iss ao to is tes ce ir see tr (Aes(! cast).to. Aas(Icasto)) Twcn l

291 CowtFI e o t11UC.

Se2 ELst 2s3 Ctaffr! *.FALat.

See De IF t

Its LSTOP =.FALst.

296 T!ast e IcAst. s.s 297 CALL SAT (Ts. PB. DPs) 264 PA = Pro 7AL - PB 20e RAT!o e AmeA. PA / (Amers. Ps) 219 DELTAE e ALDes / (i..!Twoct) 2:1 ICc!TE = 9 1

212 e

i 213 c !.itleilsett.e for seestre.t ft.e 214 c

i Sts IF (ICASC.LT. 8) THEN tis couwre e.rALst.

2t?

LaTOP =. faut.

s 21s T!ast = -t.. TIME i

2t9 IF (CearTFI) fMDI 229 YttatF = V6 - VDCLTA i

0

WESTINGHOUSE CLASS 3 l87 278 ELLDeG = rLDs0 277 20LDec = ALDQ - ELDe:

278 CLS E 279 rLLDe0 = RLDeG

[

24#

CLDs0 = 1LDs3 181 DdD IF 182 IF (CONTFI) TMDI 2S3 rLLDeo = ALDeco e rLDeo 284 De IF 185 C

238 C First geese of the Interf ace tosperature et eesh nose 257 C

2S8 IF (ICCITE.mt.1) TMDI 2RS

?! = Titl(IM30t) ase CLst Ir (IM3ec.co. 1) Tn D 1st TI = (7 TALL eTS) / 2.

2:2 ELs t 18 3 71 = T1 29e DC IF 195 ITcR = 1 294 TLos = TRALL 297 THICM = T3 288 C

299 C

369 C

llorettee f ees f or the laterfose temperstere 341 C

382 C

3e3 C Casoulete the meet treaefer eestfleleet thr eegn t he esper-el t 30s C

beendery sayer and esaseneste file 305 C

Jet 20e CALL FAAAaf 3e7 THETAS = T1. ftALL 368 RDsJhd = DDtSC8 e VELDIF e ICLDas / AMuo 349 IF (teFIRTT) THD ate DEL 2 = DELc2 311 Drut2 = 0.6 312 CALL FomCt(WAvt.C3 xTC) 313 CALL FILasta(CouwtC) 31e to TU ttS 318 DED IF 3t8 CEL = CELI 317 DEL 2 = CEL21 314 DELM2 = trut21 319 VDCLTA = WDELTI 32s IF (LAutha) TW D 321 CALL FILasLA(WAvt.CouwTC) i at2 ELSE 313 CALL FILuTV(CouwTC) 324 DC IF 325 CALL Fostet(tavt.C3mTC) 328 C

l 327 C Celeulete the es, Interfeee toeperstere to metah the boet fles 325 C

three1h t he es pe r-o l t benadery leyer end the eensemeets file 129 C

33e 285 0FILas = leFILas e (T!-TRALL) e DELTAx i

s.

t WESTINGHOUSE CLASS 3 l

189 344 WRITC(23.464) ELDee. 30LEMs. ELLEMO. CoustTC. COMTFI.

347 1

REMuu. XK3. DEL 2, ACF2. WCLDIF 348 Ds0 IF

{

34e ELDes = ELDes + DCLTAx 394 ser!RST =.FALat.

3tt 10s00t = ItsOOC + t I

ast IF (LSTOP) Tutu 363 IF. (IN00t.LE. !Th00t) YMEN 394 40 TO 293 j

Jos etSt Jos et To te?

3sf Os0 tf ELSt IF (In00t.Lt. ITwoot) TwDe i

3os see oO To 2s3

• • e De IF

• et 4e3 F0ma4T(ete.s. 3Ls. s(ete.3. is))

ee2 444 roma4T(3(rte.s. tu). 2Ls s(cle.3.13))

44 3 C

i 44 4 C Ene of the saleetellea for the seese leegth ees C

aos IF (COatTC) TWDs

+47 Ot0tL2 = ABS ((DELM2 - SELO2) / Stutt) 6ee IF (Dr0CL2.LE.1.St-3) TMD 4es ust!TE(20.e) *CONvt>Gr twLETCLY AssD 00 TO Twt utXT TIbst STEP' 41e CALL ouTWT(CouMTC. CouTFI) 45t LSTOP =.TWWE.

412 DEL 2 = DCLet2 6

413 CL3t IF (navt) TwtM 414 DCL2 = e.T*0tLQ2

• 9.3ectLM2 41S EL$t l

41s DEL 2 = DCLM2 417 De0 IF 418 ICCITE = ICCITE + 1 419 00 TO 2e2 I

r 420 De IF 421 C End of the eeleeletten of +as sete set 422 287 IF (CountTC) TMDI 423 CLSE i

424 CALL SUTPUT(COWETC CONTFI) 423 De IF 42e ALDs00 = ALDs0 427 ICASto = ICASE 420 to TO Ret i

42e 199 WRITr(e.e) 'CEstvpCE FAIL F0ft FINDiseg TMC INTDFAct TDdP.'

434 WRITr(e.e) *perIW. peGAS. OFILaf. OsAS. EPS'.

431 1

MFIW. seGAS. OFILM. SGAS. EPS 432 10 STOP 433 De I

434 C

t 434 C

438 SWOROWT!ast FOAct(aAvt. COWtTC) 437 C

434 C

i TMIS summeWTlast CALCULAfts That CemetSAT10ss MtkT TRAmsFER CotFFICIDtt 438 C

444 C

OF TMC VAP04-4IR 30WsDARY LAYER 37 ugIsse Tht AseALOGY StttrtDe N.

i I

+

.4

. - - ~...

WESTINGHOUSE CLASS 3 i

4 i

191 l

40s RETURN 497 D80 498 C

l ett C

S9esupWTINC NATu Set C

set C

r Sc3 C THis supouTint CALCULAfts THE COMODesATION MEAT TRAseSFER CotFFICIDtf see C 97 usIMS THE isDDat DtvttaPED POR Tset unfuRAL CowytCTION Ses C

f Set SINCLuet: 'Caus.Ches*

Se7 tr (enLMt.Lt. s.ets) Twos Set A8 = 0.84. (88L e Scenas) ee (1./4.) e SAS / ALages See MCOuv e 0.88 e (GRL e Manas) ee (t./4.) e Amt / ALDeS sie ELst Ir (enLMt.Lt. t.ette) Tutu sit A8 = 0.13 * (eRL e soeum)== (1./3.) e SAS / ALDet sit 8ECONY = 0.13 e (Gab e Musas) ee (1./3.) e Asic / ALDeG sis ELst i

st4 As = s.e:S. (Cat e scenas) ee (s./s.) e aAs / Altho

}

sis eav - e.est e (ent e naam).. (1./S.) e Asco / ALDec sie De ir sit socce. As e Ansse. (Cs - Cs) e (etrr + servAP) / (Ts - TsALL) sie e

+ AMC0wv sie nCoe - CsTAm. ecosso i

s2e nCowy. CsTAa.esoowy sat usAs - MCm0 + escowv sz3 aETunu 313 DeO

(

s24 C

~

s1s C

1

$2s suBRWT1pt r!Lattes(CouwfC) s27 C

s28 C

s2s C TMis sus 40uTINC 15 P9004AastD TO CALCutAft TMC MEAT TRAMSFDt S3e C Cottr!CIDrf 0F flat ComeDDeSATE FILas AT TMC FIRST scot, S31 C

{

S32

$1NCLUDE:

• Cuess. Chat S33 400! CAL serItsi, savt. LAastua. 00WuffC. CONTr!

S34 Ae6AKTM e Ame/L e AstL e THETAS 6

S3ssw otust..z. e omavo e separu e xLLDec. 3. / (4..AssAKTM)

S34 ACF2 = 0.9294 / RDeuhe ee.2 S3T tr (CouwTC) TMEN I

S38 Acr2. -Act S39 EMD tr l

See Det

• DoesL e Acr2 e 00:30s e vs. 3 e pratu e NLLDee.e2. / AnaAKTM i

set ktTP = DDesk a CosesTV e VS e ILLDes / Assut

$42 IITDt. t 4

a 543 IF (ITDt.30.1) TMDe 544

. 1.et-T 548 De IF S44 44 Y = De e I.e4 + Set e N.e3 / 3. + RETF e Xe.1 / 4. = 1.

547 sRY = Aes (Y)

Sea DDtiv = 4..pe.E*e3 + Da.x..I + RETP.E/2.

DE = Y /.DDtIV Set 1

j n.

WESTINGHOUSE CLASS 3 5

193 644 DEL = DEL + DELTAS I

set HTufts ses ce see c

I' sit C

Sit SUBROUTlast FILWTU(CouwfC) sit c

I sta c

sie e

Twas sue =0UTsut is Pn00RatD TO CALevLAft Tut atAT TunsrtR sis c

CotrFicient er Tnt Twouumf comossAft rius

.j

.i.

e st?

$1McLUDE: "cuses.Cass' sit LOGICAL seFIR$7. Savt. LAssthA. Couw?C. COWTF1 1

?

Sit 101 ODEL = DEL I

829 OTAus e TAue 421 OYDELT = WDCLTA

$12 ITDt e ITER + 1 813

• IF (CDUNTC) THDs 424 vtLDIF = VC + VDELTA 813 ELSE r

828 vtLDIF = VO - VDELTA sti ce ir 825 ACF2

• 9.188 / (ALOG(844.eDEL2/IKS))eet.

829 IF (CouwfC) THOs 439 ACF2 = -ACF2 Est DED IF i

632 TAul0 = AcF2 e 908808 e vtLDIreet I

833 TAUIC = DELTAas

• Coss87V e VELDIF E34 TAuf = TAuts + tau!C 433 TAU!A = ORAv0 e (DOESL-DOESCS)

• Ott 83s TAus a TAU!A + TAUT 637 YTAU e (TAUG/ dos 5L) +e.S 634 DELP = DEL e DOESL / AmeJL e (TAue/DoesL)eet.5 639 00tLP e DELP l

s44 set tr (DELP.Lts to.s) Two Set DELP = (Saaset./AaduL)ese.5 Ret (Lat

)

643 MLP = (SAas/AsiL+32.64)/(2.44eAL40(DCLP)o2.86) 644 De IF 643 Dinge = (DELP== #Et#) / DCLP See ODELP = DELP 647 IF (ASS (Dutolt).87.1.tt-4) 80 70 tot 544 DEL = DELP / DDISL e AMAL / (Taut /DOsSL)e*4.3 s4e tr (Dets.Lt. to.s) Tutu Ese VDELTA e (TAue/AaduL) e DEL asi ELst 882 VDELTA e (2.44 o ALSS(DELP) + $.9) e VTAU SSJ De IF S84 Otnoe = ASS (CEL - ODEL) / Dtt 445 1F (ERROR.81.1.98-4) to 70 194 854 IF (DELP.LT.19.8) Twos

&$7 AKTL = AEL 654 ELSE ESS MesasL = CPL e Ansst / AKL See PRTL e S.S$ + 0.01 / PIbsas(

)

WESTINGHOUSE CLASS 3 195 i

i l

71s CALL sat (ratrt. PsRets. DesAt) 717 C

718 C Celeutete seesity 719 C

729 OtNSS = 1. / SYSO (TRCT1) 721 Otwrsa = 1. / sys0(Ts) 722 DDesA = (PTOTAL-esRtrtlet.ets e AunA / (t3 4.e(TRui + 273.))

713 DDtSAS = (PTOTAL-PS) e t. stb e ApuA / (8314 (78 + 273.))

e 724 CDtSO = CDt35 + DDr&A 713 CDtSC8 = CDc358 + CDr5A8 728 DEMSL = 1. / 4.991 727 C

728 C Celselete eleseelty 729 C

728 Ass /5 = 5.84E-4 + 4.07t-4

• Tref t = Otk13 + (1.ESS E-7 = 5.St-t e 731 1

ofREFI) 732 AmuA = Aa4A0(TREF 1) 733 P!1A = (1 + (AMUS / AMuA)eet.8 e (A&stA / Anar$) set.13)eet /

734 i

(a e (1 + amars / AassA))ees.s 733 PIAS = (1 + (AMUA / AaAlf)*et.S e (Anart / AaaNA)eet.23)oet /

738 1

(5 e (1 + AnasA / Amers))ees.3 737 Aasr3 = PSRETt e Amart / (PSRtyt e Anars + (PTOTAL = PSREF1) e AnarA) 734 AasfA = 1 = AnaF3 73s AMotts e Aa#3 / Anars 748 AMOLEA = AMFA / AadBA 748 E3 = AMOLES / (AMcLES + AMDLEA) 742 1A = AMOLEA / (Ans0Lt3 + Aas2LtA) 743 AasJC = Es e AAAJS / (r3 + EAeptsA) + KA e Anna / (EA + rseet AS) 744 AMUL = Ana/LD (TRE/2) 743 C

744 C Celeelete seedsetibity 747 C

744 AKS = AKSD (TREFt) 74s AKA = Au0 (rRcF1) 73e AKO = rs e Ar3 / (x + xA e Pl$A) + KA e AKA / (IA + E3 e PIAS) 731 AKL = AKLO(TRCT2) 732 C

753 C Celeelete ePeelple meet 754 C

735 CPS = CP50 (TRtft) 758 CP A = CP AD (TR EF t )

737 CPC = Aasr$ e CPS + AasFA e CPA 754 CPL = CPLO (TREF 2) 759 C

788 C Celeelete dif f aelea esof fielent 7s1 C

782 TCA = 132.

75.3 PCA = 24.4 744 TCS = 647.3 7ES PCS = 218.81 784 P = Pf0tAL e 9.8882 j

787 SAS = 3.84t-4 e ( ( TR CF t +273. )/(TCA e tC3 ).+ 0. S ) e e t.334 * (PCA ePCB )

1 768 1

==(1./3.) e (TCAetCS)ee(5./12.) e (t/AnasA + 1/Anars)ese.3 / P 789 C

770 C Celeetete eethelpA differesee

WESTINGHOUSE CLASS 3 l

i i

i 197

)

i i

s2s c

fut$ Suer 0uting calcut.Af t1 THE CORRECTIDW FACTOR Cr MICH MASS TRMrSFER f

s*?

c s2s sincLuOt cune.Cm' tas c

I S38 AasrSS = PS e Aasr3 / (PS e Aasr8 + (FTOTAL - PS) e AMRA)

S31 AasrAS = 1 - AasrSe

{

432 AssDLESS e AasrSS / Aasr3

{

833 AesoLEAS = AasrAs / AasmA 434 ISS = AasDLESS / (Ass 0LESS + Ass 0 LEAS) 835 XA8 = AacLtAs / (Ans0LESS + AssoLEA4)

}

436 Aasr$1 = P! e Andet / (P! e AaRr3 + (PTOTAL - PI)

• AaseA)

[

437 AasrAI = 1 - Aasr$1 r

E3B Ans0Lts! = Aasr$I / Anset Est AssOLtAl e AasrAl / AnsBA I

see xst. Aas0Ltst / (AacLES! + Ass 0 LEAL)

{

set mat. AssottAt / (AacLESI + Ans0LEAI) 442 R = (Est - ESs) / (t - ISI) l 463 CSTAR = ALOC(Ret)/R s **

c i

ses IF (ICCITE.te. 1.AssO. IMODE.re t. Ase. ITER.ts. t) THEM i

844 tutITr(21. tee) ICASE. RATIO. Pf0TAL. TWALL. DELTAE

]

e47 sRift(21.2 eel vs. Attwo. Anar$r. AasrSe See est1TE(21.300) ISI. KSS. R. CSTAR oc ir SSG t ee FOReakf( * !.*, 12.

• RA710 **. (15.7.

• PTOTAL=*. Its.7 ast t

TmALL.*. ris.7.

• stLTAs.*. Its.7) as:

See r0smeAT(sr. *vo

.*, ris.r.

• ALose.* tis.r.

[

ts3 1

Aanr$3.*. Ets.7.

• Aasrls =*. (13,7)-

i 434 300 FORMAT (SI. *ISI

• • . Ets.7 ESS **. I:5.7 ass t

A

.*. Ets.7 CSTAm.* ris./)

sse RETuRm

&s7 De i

r SSS C

I ase c

888 SuSROWTINE SAT (TSAT. PSAT. DPSAT)

{

881 C

.3 e

843 C THIS SueROUT!WE CALCULAft3 SAfuRAT!oss PRESSURt v!TW RESPECT 70 ese c

SATuRAf!ON TO rtRAfutt.

ses c

l ses cruosstom r(s) -

4 457 DATA F / -741.9242. =29.721. -11.18288. -0.8644448. 4.1994098 888 1

8.439983. 9.23298Ss. 0.est:8444 /

l See Stas = 0.

879 DSUW = 0.

a7t I o 0.04 - 0.01 e 75Af s72 TAU = tete. / (TSAT + 273.18) 873 DELT = 374.13e - TSAT 874 D0 t ! - f. 8 E7s 4

s-t s7s tr (4.es.

) oo To t i

v77 esum - osw.

+ (4 - 1) e r(J) i s7s t sum - suu e

+ r(s) 873 Rt3 = tau e 1.t-48 e DELT etum i

see PSAT. ExP(RtS) e 22.ees I

l t

?

a s

~

WESTINGHOUSE CLASS 3 t

i 199 (A(!$US+1) - A(ISUS))

938 1

m 837 RCTURN 035 DC

$39 C

544 FUNCTION AKSO(TEW )

set C

942 C CALCULATION OF THENL CO@uCTIVITY OF 2TCAW 943 C

844 O!WDcSION A(15) 845 OATA A

/ 10.9 te.G.

15.2(-3. 14.8E-3. 13.S[=3.

See 1

It.2E-3. 28.st-3. 21.st-3. 22.4E-3.13.2C-3.

847 2

24.9t-3. 24.st-3. 23.8E-3. 25.TE-3. 27.8E-3 /

964 Isue = 3. + (TDsP -A(2)) / A(t) 548 8 = ISuS - 3 354 TLDe a A(2) + 3 e A(.;

981 TMICM = TLow e A(1) 952 AKSD = A(!$ug) * (TDdP - TLDs) / (TMICM - TLC 9)

(A(13uS+1) - A(Isus))

953 1

e 954 RCTURN SSS DC 958 C

337 F1, pct 10N AaduAD(T D#)

ss8 C

SS9 C

CALCULATION OF VISCOSITY OF AIR 988 C

981 O!MDt3104 A(11) tot DATA A/29..

0.

0.81718, 8.81813. 8.81948, 4.01999. 0.02987 su t

e.ettT3. e.ez2ss, s.e234, e.e2428/

864 18u8 = 3. + (TDdP -A(2)) / A(t) ess a = sus - 3 see TLow = A(2) + 3 e A(t) 987 TWIGN = TLow + A(1) est AnduAD = A(Isul) + (TDdP - TLDs) / (TNIG4 - TLoe)

(A(FJUS+1) - A(ISut))

989 1

e 970 AMGAA = Ahaya e 1.pt-3 871 RCTURN

$72 DC 973 C

974 FLpeCT10m AWum (TOdP) 878 C

978 C CALCULATION OF VISCOSITY OF L23f!D (sAfDt}

er7 C

978 OlndDeSIQ4 A(St) 879 SATA A/29..

4.

1.787.1.9418. 4.ES3. 8.48E5. e.3544, 6.2821 see i

s.23te, e.tset,e.t 77/

est ISue = 3. + (TDr -A(2)) / A(t) sS2 e = rsus - 3 ss3 TLow = A(2) + s

• A(t) 964 THIGrt = TLOw + A(1)

SE5 AndVm = A(15ue) + (TC# - TLDs) / (TMIGM - TLce) s&s t

. (A(ssus 1) - ARIsue))

ss?

Anna m = Adarm a t.sc-3

$44 RCTURN 989 DeD tse C

r i

e e

WESTINGHOUSE CLASS 3 201 r

P 1648 BATA A / 5..

S..

2488.8. 2477.7. 24E3.9. 2484.1 I

1947 1

2442.3. 2439.5. 2418.8. 2448.7. 2394.8. 2382.7 1944 2

1370.7. 2388.3. 2J48.2. 2333.8.1321.4 2368.8.

tese 3

2194.0. 2283.2. 2279.2. 2137.0, 22s3.7. 1238.2.

tess 4

22s t.s. 22:2.8. 2ies.S. 2 74.2. ItSe.e. 2144.7 1981 8

2129.8/

1932 Isus = 3. + (TDP -A(2)) / A(1) j tels a. Isus - 3

~

1834

? LOW = A(2) + B e A(1) tesS tut 0x - TLow + A(t) teSS MCVAPO e A(ISUS) + (TDr - TLow) / (fN10M - TLor) 1937 i

• (A(ISUS+1) - A(ISUS))

)

1958 MCVAPD e MCVAPD o 1969.8 teSS RETURN i

1980 DID test C

1882 FuMCTION MSTCAM(TDeP) tes3 C

j 1984 C

CALCULAf!ON OF STEAM ENTMALPT 1963 C

1888 DIWOst!04 A(38) 1987 DATA A/S.,

S.

2319.8. 28 t 9.8. 2228. 3. 2134.1. 2347.2. 2338. 3 1968 1

1383.3 2374.3. 154J.2. 138 2.1. 260s.8. 2649. 8. 28 t t. 3.

test 2

2828.8 2438.3. 2443.7. 2881.9. 2644.5. 2684.1. 2878.t.

te7s 3

2843.8 2001.5. 2409.8. 2798.3. 2713.3. 2728 S. 2727.3.

isti 4

2723.s. 276e.3. 274s.S. 2782.4 27st.i. 27s3.S. 27se.7/

1972 ISUS = 3. + (TDeP -A(2)) */ A(t) 1973 3 = 1 sus - 3 1874 TLOW = A(2)

• B e A(1) 1878 THIGH = TLos + A(t) i ts78 METEAM e A(ISUS) + (TDP - TLow) / (Th!OM - TLOW) 1977 1

e (A(15US+1) - A(1 sus))

i.78 rrcA...stcA.. it..

i.7.

.crun-test CMD 1881 C

1982 MasCTIou syS0(TDF) 1683 C

1944 C CALDiLATIOu 0F SPECIFIC YOLUWC OF STEAM 1648 C

1688 DlWCM810N A(37) 1687 BATA A

/ 5..

S.,

208.14 147.12. 198.30. 77.83. 87.79 1968 1

43.38, 22.99 28.12, 10.82 18.28, 12.83. 0.884 1888 1

7.t71 8.187 5.682 4.t31, 3.447, 2.828 i

1H.

3 2.383

...n.

i.872.

1..

4 1.2i st. 1. u.8 tH1 4

9.9919. 9.7798. 4.8843, f.$422. 0.3999. 8.4483 ies2 s

e.3s28. e.34as, e.3e71, e.2727. e.2428/

tM3 ISuS e 3. + (TDP -A(2)) / A(t) tese e - ! sus - 3 tesS TLos e A(2) + B e A(t) s ees fNton - YLos + A(t) tes7 SY30 = A(1 Sue) + (TDP - TLow) / (TWION - TL0s) iHS i

. (A(tsus+i) - A(1 sus))

1M9 8CTURN 110e Os0 l

.._.. _,,.. _._.. --.----= - - - - - - - ' ' ' - " ' '

" " ' ' ~ ~ ~ '

WESTINGHOUSE CLASS 3 217 828 MttTd(IMttr.Jpetr}

327 to 63 det.ut 828 90 S3 !=t.Lt 829 83 P(1.J)d(1.J)-Mttr 7

834 90 CEurtissJC sat c

j S32 WtITE(14.SG)

E33 1De=e

)

834 381 IF(IDec.to.Lt) 90 TO 319 63s recent De+1 838 1D80=1D0+7 637 IDEMe:Me(IDS.L1) ase tuttTE.( t e.H) 630 settTE(14.St) (l. !=IBte. IDS)

)

864 IF(ac0t.ta.3) 90 To att set un t TE(14.S2) (X(1).1=Ists. IDED)

M2 NNM j

643 302 salTE(14.83) (R(1).t=l985.3080)

M4 343 80 19 30t 848 31e JDe=4 M4 uitITE(14.SG) l 847 311 IF(JDIO.te.ut) 80 TO 320 pa Jeto=4 De.1 S4e J DeaJ De*7 l

SSe JDe etM*(JDe.ut) est umITE(14.84) 452 WetITE(14.64) (J.4=d8CO. joe) ass uRITE(14.ss) (Y(J).Jadets.JDED) 884 80 TO 311 1 -

su

• • • ConTtet l

ese e

as7 oc pos wei.Mam ass Irt.sof.wstrut(w)) e0 to as ase ultt:(t e.w) 864 uRITE(14.te) YtTLE(MF) est IF57=t 842 Jr57=1 j

843 IF(ser.EB.t.OR.MF.CO.3) IFTT=2 664 IF(MF.ER.2.OR.MF.EO.3) JF5T=2 848 I989=1FST-7 Est 119 Couttuut I

847 1989= t Ste?

tes IDe=tDES+4 See IDeNetMB(IDS.L1) 878 15t tTE(14.94) 871 ERITE(14.2e) (I.I=IStc.IDED) 872 ut!TI(14.30) 873 JFLas FST+ert

T4 so its de=JrTT.ut j

1. 7s w rt-JJ ffe uR ITE (14. 40) J. (F(I. J.seF). t e t Sta. ! EMD )

j 877 115 Coutleast 578 IF(IDe.LT.L1) 0010110 i

s7s ete cerftMut See RETWfts i

l l

.I I

l J

c-

i WESTINGHOUSE CLASS 3 l

i 4

219 i

o i

S36 BATA 6. SETA. FACTOR /9.8. 8.44347. e.3/

l

$37 BATA FRATIO. CRWERE /S.S.190.0/

sas c

'I 838 OffitY GRID He C

Mt MDDE = 2 i

Set vt = 8.83 i

H3 EL = 0.t44 944 mRITE(e.e) *PLS TvPt 1.ASTwt. GAamu FOR uc0C SPACINCT' f

948 REA0(e. ) LASTwl. SAmA

{

He Lt = 33 l

H7 tr( u m.. to. i) flaan s+a CALL uoR!o He CLst I

see vv(s) s.tes est so e t - 3. s j

942 vv(t) = W(1-1) + 0.4418 es3 s coutlet sse soe

.s7 sss vv(t). vv(1-1) + e. sets /s.

i ese e c orri e t es7 ao le - a;1e ese vv(t). vv(1-1) + e.441s/3.

ese te comTt=t too v3 PACE. (0.441s) e ( CAaenA-1. ) / ( Saamma e e ( LA37wi )- 1. )

l Det uRITE(14.*) 'LASTut, v5 PAC (='. LASTW1. v3 Pact 1

982 v3 PACE. v3PACte(GAmenAee(LAETut-t))

esa ao it : - 11. to+i.Astus e**

vv(t). vv(1-1) + vsPAct ess vsPAct. vsPAct/oAnanA eos it corflaut es7 wt - to + LAsTwt ses su(2). e.

oss su(3). 3.s t-2 are su - e.3e+a 07 De 13 e 4.Lt s72 uu(1). au(I-1) + or 973 13 CowTruut t

974 NL e Nu(Lt) 973 De IF 978 RETURN r

977 C

r 870 Drfir? START 879 C

Dee 3 RITE (e.e) 'PL1 TvPC LAST. LASQUT*

941 READ (e.e) LAST. LA90VT 642 TRALL = 97.4 943 TS = t H.S see it = 98.8 DSS PTOTAL = 0.t838 At CALL SAT (78.PS.3PS) 987 PA = Pf9fAL - PS See AMPSS = (PS*AMNE)/(PS* AMWS+PA* AMnA)

&#9 WRITE (14.100) 7 TALL. 73. f t. vtu. PTOTAL. LAST. LASCUT 994 190 FomeAT (

• terVT SATA * /.

• TRALW, (13.3.*

T5='.t12.3

.. - +

~

l

+

WESTINGHOUSE CLASS 3 l

221 i

l i

f 5He 57 CONTIMUC 1047 T CAL (i) e TWALL te*e C

• ^LCULATE TMt Raft 0F IMPLOW AND OutrLOW teos C

Ape NATCM THE thrLOW Raft TO THE ObrTrLOW Raft te$e r!Y e e.e 1081 r1x = e.0 tes so its 3.is za seS3 1 e FIY = r!Y + RM0(1.1)ev(1.2)eECY(1)eR(1) 1M4 30 t t e J..ast tMs tis rix. rix + m 0(i.4) U(s.4)+YCYR(J) tese oO tre. 2.

a test tse rix rix + aM0(s.t).v(s.2)e Cv(I).att) tess ao tat I. 13. La r

toes sat rtz. rix + me(t.1) v(s.2).sCv(t)en(s)

.i' iMe rev. e.

seet P0x. e.

See 90 122 1 2.La 1943 11: FOf = r0Y + AM0(I.ut)ev(I.ut)eICv(1}ea(ut) iM4 et 123 *.ast i

tMS 113 P0x e rox + me0(Lt.J) U(Lt.J)evCvm(J) l 5Me r1N = rIY iMT rouf - rea-rtr+ rov tMe Atma. rout /rtu iMe so tse t - ts. 2 tore v(s.2) - v(I.2). ALMA l

sort 14Ceufswa ters so tsa ut.ut I

ters oO 12s 1-1.Lt sete me(r.4). ocMsCe iets Tut (s.J) - e.eest a w(s.njeet.

~

se7e tas sis (I.J) - e.1 e int (I.J)eet.

ten TICAL(t). TuALL te7e to - e.oo te7e Cs - 1.+4 i

SMe Ca. i.es 1esi PUtf a e.88 + e.et/MtMLas 1942 SCT = e.88 + e.et/SCMbas 1043 P4WC = i.

1004 P W = 1.3 I

1e48 m e Musuu I

1Me SC e SCsaas test paperf = PR/Pett IMe PPete a 9.*(P4PftT-t.}/Perstfe g.23 1Me SCSCT = SC/SCT tese SSFN = 9.e(SCSCT-1.)/SCSCTees.24 seet CD4 = CDeee.38 i

tes:

90 13e ! = 1. L1 I

fee 3 PrW(1) = PPett I

tee 4 S m (!) e SSrts tMe ACON (!) = e.

teos 534 COBfTINWC tes?

WRITE (e.e) *DO YOW sAaff 70 etAS twt RESULT OF THE PREVIOUS CALT*

I teet WRITC(e.o) *(YES e t.

Ise = 2)*

+

tese READ (e.e) 1RCAD i

ties Ir (IREAS.50. t) TMO l

I

=

i i

WESTINGHOUSE CLASS 3 223 l

11se w (1.1). Aurse 11s7 TEt(I.1) = 0.9901*V(I.1)*e2.

i 1954 015(1.1) - 8.1 e TEE (!.t)se2.

11at 231 CONT!satt 1164 C

• LCULAft THC 90LACJJrf Cosclflom FOR TOP suRFAct inst 00 2s J = 2. u2 11t2 T(Lt.J). T(u J) itss ir(d.Lt.e)T(u J).Ts its4 w(u.J) w(u.J) its:

Ir (4.u. 9) w(u.J) = mrta tiss Tuttu.J). Tuttu.J) 11st SIS (Lt.J)

DIS (L2.J) its 1st CizrTimut stGB 1976

• ^LCULAft TMt RATE Or Isertos A#C Oitfrtf-It78 ROT. 0.9 t i tt no tse. 2. u 157:

tss ref. ref + me(1.wi).v(1.ul)erev(t).R(wt) 1T4 Ir (A$s(r07/r13t).LE. 1.0) TMOS ttis r!N. rIY tifs r01/7. FOI - rII + FUT iiTT ALPMA = FOUT/rIN 1 Ts 00 1se I is. 22 tifs v(I.2). u0atett) e AtenA tese 2se Cowrtosur inst ELst list untTt(e.e) 'rer, rtu*, rey, rim itss talTE(12..) *sdJtMINtas FUT IS LARCCR TMAn t.sercitT*

stse De Er Stas unt Ttt e. e)

• rov.*.ref. rta.* rtu. *v(s.wa)..v(s.u2 ).

• ALPMA.'. ALPMA itse ua:Tr(e.e) av(u.us).. v(u. ass) sis?

C 11s4 C

CALCULAft Tt*C SQLMDAJtY CoselTIcos FOR RICNT (CoseDesATE FILM) titt C

SURrACC AT TMt DG OF 18esnt CALCULAftCat 1994 C

tiet Ir (170t. set. LAtT) RETURN 11:2 90 290 I

2. U tiss IF (EPLus(!).LE. 15.8) THOs l

its.

Agre. Ass Ites cLsc ies Arts. Cro e Amuo.xPLus(t) itst i

/ (Pete(2.s*Los(Acom(t)exPLus(t)herm(t)))

itse De Ir slet 1st O(I). MPittise(MecT(!))edETGe(f(f.ht2}-T(f.W1))eECv(I)/rD!r(wl) 12 e CALL riusin 1291 CALL FILheLA 12e2 so tot 3.s.u 1253 CALL SAT (TICAL(!). Pft. DPSI) 52S4 pat. PTOTAL - Ps!

tres AkerstC(I) = (P5teAhers) / (PSIeAssuSeFAteAnasA) tree w(t.rt). Aurs C(t) 1287 tot f(I.ut). ?! CAL (1) stos s w. s.e 1299 90 282 1 2.L2 1250 rot (I) = 4.* DCL(I) e CDe+4.2seTKt(1 W2)**0.s

WESTINGHOUSE CLASS 3 l

(

225 1

t 1264 90 331

= 2. L2 1267 IF (EPWs(t).Lt. ft.s) TMDI 1264 AKTS. AKS i

tase ELst l

137e AKTe. CPO. AmaJ0.EPLus(!)

l Int i

/ (pat (s.s.Los(Acom(t).urtus(!)).Prm(t)))

i 1272 De Ir ins e(I). watw.(Ameof(t))+Aufs.(T(1.wa)-T(t.ut)).ucv(t)/vstrtut) i tus asas. (scust.(ocust-oDesos).(s).wals. Ant. 3/(4..Anast.n(!)

i ins 1

e(Ts-TuAtL}..(e.as) i tus ont seas (Ts-ftaALL). sev(t) tan otof eTot + o(t) { i Ts asufof. ensfoT + ens t 127: essas = o(t) / mev(t) / (Ts-T(s.ut)) j taas wtw = e(t) / mcv(1) / (T(1.ut)-tmALL) j 1:st sovsa - witu.usAs / (sertianesAs) l t st um Tttis.333) x(t), o(I). nrttu, escAs. novan. Pws(!) l 1283 malTE(te..) X(1). Novpt + 12s4 331 Cowfieupt ( 12n* 333 restaAT(etts.7) l 1234 RTof grof / earTOT 1247 malTE (13..)

• MATE or THE TOTAL CALCULAftB 70 musstLT=*, RTot ties aut!TE (13..)
• TOTAL estAT TaAsesrtRED ST MusstLT CAL.* esuf0T 12ee so 33: J. 1. ut tzte sa:Tr(23..) T(J). T(ts.J)

{ 1 12st sa Tr(s3..) T(J) Aasrtis.J) l 12e2 ma:TE(24..) T(J) U(1s.J) 1293 333 CowTtenst 1294 untTE(13.334) 12es 334 PandAT(///.s2 'I(t )*. s tE. 'TICAL(1) *. TX. *vDELTA(t)'. l 12es t ex. 'vtAvott)*. n. AmooT(t)'. ex *ocL(t)*) tast so 33s. s. La 1294 us!Yt(13.333) E(I).T CAL (1).vDELTA(1),vtAv0(1).AmecT(I).ptL(1) ' 129s 3&s CowTtesWE l t3ee un TE(1a.33e) taat 33s ruansT(/// sa. *s(t)* str. *ntz(t)*. er. acrtw(1)* er. J taes t

• Acom(t), an. prm(t).. ex.sen(t) )

i taas so an !

s. L3 13++

ua:Tr(ts.333) x(t), asx(t), acrtw(t). Acom(s), erw(s), srm(s) 13es 337 cowf tenst 1300 MITE (13.334) i 1347 334 PostaAT(///.sr. 'N(t)'.11K. 'APLus(!)', SK. *1ertus(t)*) S3e8 30 330 1

2. LI 13ee aut!7t(tt.3301) x(t). APLus(I). lasrLus(t) tate 330 cowftssut tatt 330t FolmeAT(3tts.7) 1312 selft(13.3303) 1313 3393 FolthAT(tet. 'T(J)*. 181. 'YPLus(J)')

i 1314 30 3383 J. 3. Ist ' tais untTE(tt.3394) T(J). TPLUS(J) 1314 3363 cowf! Inst 1317 3364 PUsanAT(2(Ele.8. tX)) 131s C CITT, THE Rt3 ULT Fest TMC tt37AAT OPTIC 1319 30 344 1

1. Lt 132s 90 304 4 a* 1. art

WESTINGHOUSE CLASS 3 i 227 i 137s ao To ese tan 4se cowituut 1s73 De oss J. 3. 9 tan so to (432.4s2.433.4s3.4s4.431.4st) nr tsee est e m (i.J)-e. l ses ao to ass tsa ass wuas(J)-amo(s.J). sort (Tur(s.J)).cos.xotr(s)/ sense isas em(i.J) anase 13e4 tr(wuas(J).of.it.s) am(t.J) ame.wLus(J)/(z.s. l tsas itme(s.o.vrtus(J))) -taas en to ass l tas7 4s3 sans(t.J).aanse/Ps isse t r (vPuss ( J ).st. i t. s ) sm( s. J )-aasas/ Pat. wuss ( J )/( s. s. isee itos(s.e.fruas(J)}.ePrm) i 1sse eo To esa i 1ast 434 &ase(1 J)-anass/sc tas tr(veuss(J).st.it.s) em(n.J)-4assc/ set.wt.us(J)/(z s. tass 1Los(0.e.vPuss(J))+5SFW) j tas4 es to ess ises 4ss cartsmut j tsee tr (ur.mt. ) ao to see tas7 to 44e J. 3.us tase so +4e f s.t2 l tase com(1.J)-(sm(1.J) (v(1+i.J)-e(1.J))/sev(t)- 1**e s aane( 1-i. J ).(v( I. J )-v( 1-i. J ) )/nev ( I-s ) ) /xo t r ( s ) i test emp.sans( t. 4+ i ).saas( -l. a. i ). ne t r ( s )/ ( cm( 1. u i ). tae quev(1).em( -t.ai).scv(1-s)+s.s-se) seas emp-sane.om( t. J ).saas( 1-t. J ). S t r ( I )/( sm( I. J ). t4*4 1 ev(t).eans(1-i.J).ucv(1:.i>+t.s-se) t teos sanna.eans( s. 4-s ).sm( 1-1.4-t ).us t r( s )/(sm( s. J-s ). t*** t aev( t ).em( 1-i.4-s ). mev( I-1 )+ t. s-se) 14e7 . ---(f.J).om( -i.4).mtr(I)/(em(I.J). sees inev(t)+saas(I-t.4).scv( -s)+i.s-se) 14es com(f 4)-com(1.J)+(ines(J+s).sa.a.(v(t.at)-v(1-i.4+t)) i soie 1-dess( J ) =4aans. (v( t. J )-v ( I-i. J ) ) )/(vcVR ( J ). @ t r ( I )) toit ose testlanat i 141 actuant j t41s 40s tr(nr.ast.3) e9 to 41e 14 4 to see 4-a.us 14ts so 4es 1 3.t2

• 41e ccasti.J).(m(J). sass (t.J).(v(s at).v(.J))/vev(4)-a(4-t).

tot 7 t em( f. 4-i ). (v t l. J )-v ( 1. 4-1 ) )/rev( 4-t ) )/(smas ( J ).vo t r ( J ) ) tats ~ rr( +t.J).s m(t+t.4-1). verr (J)/(e m(t+t.J).vev(J)+ i4ie te m( +1.J-t).vey(J-t)+i.s-se) tese sano-eame+eanst i. J ).saas( t. 4-t ). vo t r ( J )/( sm( s. J ).vev ( J ). sent t em(1.4-s ).vev(4-t)+s.s-se) 4 tes: saman eass(1-t. J ) =am(1-t.4-t ).vo t r (J )/(s=( t-1. 4 ). to J trev(J).4m(1-i.4-i).vev(4-1)+t.s-se) 1434 eanam eanas.em( s. J ).saast s. 4-t ).vo t r(J )/(em( s. 4).vev ( J ). tens tam (t.4-t).vev(J-s)+t.s-se) tems com(s.J)-costi.J)+(sane.(v(tet.J)-e(I+i.4-s))-eana (v(1.4) ) 1427 t-e(I.4-s)))/(mev(I).votr(J)) i 14:s tr(amot.so.2) aP(t.4)-AP(1.J)-4..sm(t.J).eanett.4-s). j 14:e s vo t r (s )/(sm( 1. 4 ).vcv(J )+am( t. 4-t ).vev( As )+ t. s-se ) 143* s/imme(J)..: J a 1 l ) i l l

f WESTINGHOUSE CLASS 3 229 i I l 144s 41s tr(Wr.ast.T) etTustM

• i4eT 90 49e M.us t445 De ese !=2.L2 149e Cape ( I.J )=C t.40s ( I. J ).c0.stMc ( f. J ).TKt ( t. J )

toes w ( 1. J )=-C2 *8tMC ( I. J ).e l s ( f. J )/(TKt ( 1. J )+ t. E-38 ) I seet see courTIMut I seen so set t = 3. La j 14e3 s i ss.co.txt( f.uz ).. t. s/(e. 4.coe.ro t r (ut ) ) sees coit s.uz).(s.t+3e).e t s: - sees w(t.uz)-i.t+3e toss 4st courttuut toef 90 *e2 J = 2. e toes siss-co. Tut (2.J)..t.s/te..co4.zotr(s)) j 14ee c0m(z.J)-(s. t+3e).e t ss l isee AP(2.J)==i.E+34 iset des cowitwc iset so sie J = 1.w tss3 3r(J.st. to.Ase. w.to. 4) sAu(Lt.J) - e.e tso4 tr(4.st. Se.Ase. w.se. s) sam (Lt.J). e.e tses tr(J.et. is.Ase. nr.sa. :) sm(tt.J) - e.e tsee sto ccertswt tse7 so sit . s.tz tsee ir (w.so i) Can(s.1) - e.e tsee sin coutz w t iste so sia - 34 Lt 1 sit Ir (ter.tO. t) sam (I.9) = e.e esta sta cowT:ssut ist3 no ses J - to, we ist4 tr (w.ut. ) sam (s.4). e.e tsis ses CowTs wt iaie ertusse t ist? De iste C ists susecutant,r:Luin tste e iszt C 1822 C TWIs suetouTINC Is PR00stAnstD TO CALCULAft TMC MEAT TsuJesrtR 1:13 C CotrriCItwf 0F TMC CoeDesArt rILas AT Twt FIItsT es00C. is24 C ists ItPLICIT DCESLE,Pe CI:10st(het,twZ) 18:e FAAAndCTtst (sen. tee) 3817 Cohes04 r(ses. set.s).P(tes. sos). pnp (Me. sos).sAas(set.ses). Con (NN.ses). ists t A t P (mu. sos). ATN(MM. Iso. AJP(fee set).MW(pet.NN ). AP (ses. Iti), tste 1 (aso.sutsen.netr(ses).nCv(ier).zCvs(ses), tase 3 T(sen ).Tv(uw).vs t r (un).vcv(ses). vers (ses), t&3t 4 TCvst ( son ).vevets (ins). Aax (iew). Anza (ses). AnxJP (ses). 1E33 & e(188).shet(let),sI(les),sIbad(tel).3CVI(Ist).ICVIP(tot) 1833 e f! set /w. prwAX. IP. setM0. pseAaf. L t. L2. L2. W1. ast. us. 1834 1 Isf.JST.ITElt.LAST. TITLE (13) RELAR(13).T!tst.07.rL.TL. t&&s 1 IPWtT.JPetr.LsoLyt(s t) LPetgarT(13).as00C.WT!ssts(t t).ItMcc04 t&3e CthesOut /900P/ TBALL. Ts. Tatrt. f t. Aesrae. Aasrst. DDese. DDesk. 1837 1 Assue. AWL Ases. AstL. SAS. cps. cps. CPA. CPL. 1834 2 8 Pet!M. PTOTAL. Atess. AnasA. DDeSOS AtsuGS. t&3e 3 Pes &As. scesai 1644 CChesosi /rIL81/ TICAL(ses). wDELTA(ses). 0(ses). AJ(les). AMDCT(Ist). I e

WESTINGHOUSE CLASS 3 l 4 h a 231 i tsee vottia(u) = stust.cstavC/aauL.otL(L2). 2/2. + TAuott j ise7 t /aasut.on(L2) l ins C 2 + mL.(TICAL(u)-tmLL).vtu/(assit.wstru) tsee vtave(u) = -ocust.eaave/(s..aaset).ontu).. sees t + (penst.eaave.on(u)+Tauott). ett(u)/(z..anseL) i test ust TE(...) *TICAL(L2)='. 7 CAL (Lt). *vDELTA(L2)='. YetLTA!L2). [ 1842 1

• DCL(L2)='. DEL (L2). 'FXt='. F3s. ' DELTAS *. DELTA 2 1s43 2
• ! !Tt3t= *. ItttR i

tsee RCTunes ises eMD j ises C 1847 C 1see suesouT! Int FlusLA j tsee C l isis e 1811 C Twls suenouTI#t Is P*DosuastD TO CALCVLAft TMt McAT TRANsrtst ist3 C COtF7tCtDat OF The LAastman CosetMsATE Flus tsis C ista C isis tw L:Ctf pouett entCtston (A-ei. e.I) i tais P m ant at (ie tee)

a17 Casson r ( ses. sos. e ). P Oes. m ). nno Ose. sos ). saas ( mm. cos ). Con t e. seq.

tots t AI P oes. seq. a t w Oes. seq. asp Ost. ses). AJu pes. ssu ).aP Oes. sed. tsis a :(m). sv(sam ). xo t r(m.:). zCv oe0. nCys ( m ). ists 3 Toeq.vv oss).vo t rusi).vCv(see).vCvs pes). tsai s TCve(m) vCvasOes),anzoso.AaxJoaq.asexaPoss). ista s a(mm) nodes).szOsw).sune: Dei).zCvipes).xCv:POen 3 1s13 CoWWDR/186K/MF. esruAr.W. setMO assamf. Lt. L2. L3.ws.tst. as3.. l tese t1 7.Jsf. Itta. tAst.T t TLt( t s ) acLAx ( t a ).flast.sf.zt.TL. 1s25 2 IPREF. JPerf. LsoLvt(i t ). LPit l asT(13 ).NOOC.stT rists ( t t ). 80socose tats Cassoup /Paarf TmLL. Ts. TWtrt. ?!. maar:3 assFst. DOssC. DENsL. 1 27 i masse. assub. ass. aKL. SAs. CPS. cps. CPa. CPL. 1sts 1 MPRIM. PTUTAL. means. AsseA. posses asados, 1823 3 Papaas, scusas isse Canason /rtus/ TICALOen. vonTAOed opes). Adoso, anecTOso, isst onpos), ractea. xPtuspes), etxpos), atrtuspoo, tas: 1 ACoupes). PrmOes) sFw( m ). vtAvcDeq. Inavt, vtm tass stuosstou voor.ses).voss sse).PCoos. sos) tasa courvAtosettr(i.t.1).v(1.1)).(r(t.t.3).v(t.t)),(r(t.t.3).PC(1,1)) iass enAve. -4.s isse so see II..u Is37 I = L1-II is:s acous? = coast.... saave / (aanit.) Is3s tr (nruss( ).Lt. t1.s) Tuoi is4e asuts = amass is41 ELst 164: ess Ts = amass. xPuss(t)/(2.s.Los(acos:(1).urtus(t) ) i tses ce tr 1644 TanetL = Anarfs. (v(1.ist) - v(t.ut))/fotr(wt) 1ses WCasst = DessL. TAUCCL / Ana#L 1s44 C oconest = DessL.AKL.(ftCAL(!)-TRALL). vim /(2..aasuLorR!u) is47 CConst? = s.s is4e scnom - (acoust. ort (1.t).. + scoust.ott(t+1) Ccmert) ie4s ettTAs = -assocT(1) / ocuou tsee ett(s) e otL(1+t) + pcLTao

~ WESTINGHOUSE CLASS 3 l ~ i 'l 233 $7ee esNsse - 1. / syso(ts) 17e7 otNsA. (PtotAL esmat).t.ets. AnssA / (sale..(tttri + 2n.)) . (Ts + 273.)) 3 17e4 DENsAS = (PTOTAL +s). l.ets. AsseA / (s314 570e DEMOS = DEMes + 9tMs4 l 17te DENSOS = DEN 555 + DEMBAS l 17tt DENsL = 1. / e.eet 1712 C 1713 C CAu:ULAft visteeITY Jt 1714 C 1 17t3 AnsJs - S.e4E-6 + 4. eft-4. TRtrt - CDess. (t.sset s.st-t o 171s t .tatrt) 17t7 AnnaA = AssaAo(terri) 17ts PISA - (t + (Anais / AnnaA)..e.s. (AsseA / Assrs)..e.as). 3 / j 17te 1 (s. (t + Asses / AssnA))..e.s sne pas. (1 + (AssaA / Anna)..e.s. (Aams / AamA). 2s). 3 / f int 1 (e. (s + AmeA / Anas))..e.s 1722 AssFs = PERUt. Aams / (Petri. Assus + (PTOTAL - Psttf t). AssuA) t723 AssFA = 1 = AssPs l 1724 AnspLgs = Aasrs / Assus 5 t?25 Ass 0 LEA e AasrA / AssaA 1728 Es. AacLts / (AmeLES + AmeLEA) 1727 u. AnettA / (Ametas + Anet A) f ins Annas - rs. Assis / (as + u.PtsA) + u. AnnaA / (u. xseP!As) t?to Aedut Ame#La (TREF 1) l 173e C VIsC0517Y OF Gas AT SULK 173 Annes. s.ees-e + 4.s7t-e ts - oossse. (t.asse s.st-te l inz .?s) in3 AnasAs. AnnaAccis) ins Ptsas. (1 + (Assuse / AnnaAs)..e.s. (AssmA / Anos)..e.2s). 3 / l Ins t (s. (t Assus / AsmA))..e.s j tus PtASB e (1 + (AaAaA8 / Asasse). 3. (Assus / AamA)..e.2S). 3 / in7 (s. (1 + Anna / Aams))..e.s l Ina Aasrse. Ps. Aams / (Ps. Aams + (PtotAL - Ps). AamA) ins Aasras - t - Aarse 1744 Ass 0LW = Aarst / Aams 1741 Ass 0LAS = AaFAS / AAAA l 1742 M e AaSLN / (AsOLN + AnsgLAS) 1763 MAS e AdsDLAS / (As@LM + AaOLAS) 1744 Asaf08 e M. Anha53 / (IM + sAS PtsAS) + IAS. AsRana 1744 1 / (EAR + EN.#tASO) 17se C l 1747 C CALCULATE comeuCT!v!?T 1744 C 174e Afts e AsCM (TWtrt) 1794 AstA = AKAS (TRtrt) t?st Ass - as. Asts / (as + u. Ptsa) + u. AKA / (n + us. PIAs) 17s2 AftL e AdEL8(Tktr2) i t?s3 C 1734 C CALCULATE SP:CtPIC estAT i7ss C i im cps - eP= (retrt) 17s? CPA e CPAS (TRCrt) 1794 CPS = Aars. cps

• AasrA. CPA e

1790 GPL = tPLS (Tatr2) i tree-C 1 l 't ~- ~ c,, -

f WESTINGHOUSE CLASS 3 i 235 im = =... i.if

u....

im s.... -... e m f 1.i. u p. i . / ( m f + m.iS) l i.a nu. m.in-fuf isti so 1 :. s. s '{ lett 4.e-I ieu ir o.se. i) f i 1824 00W e DSW e N + (J = 1) e F(J) 1825 t has = Stas e E + F(J) 1828 at3 e TAU e t.t-48 e DELT emas f 1827 PSAT e EXP(RES) e 22.088 [ t ' 1828 SSW = = 0.91 e Smas 1829 983 e -l.E45 e (TAueet

• DCLT e SuW / 1904. + TAU e Suu - TAU t439 1
• DELT e Deuw) f tSat SPSAT PSAT e aED 1832 atfumet 1833 De 1834 C

1838 C 1838 mem0WTint SATEP (PSAT. m t) 1837 C t&&S C 1839 C TMIS SuSROWflNE CALCULATE SAfullAf!Ott TOrtRAtuRC WITM 01vth 1840 C SAfteAf test PRESSURE. 1841 C 1642 thrLICIT ScueLE PRECISION ( M. 9 Z) 1843 ACCURA = 1.DE-6 1844 TSAT = 398. 1648 2 CALL SAT (TSAT. PSATA. DPSAT) 1644 DCLP = PSAT - PSATA 1647 tr (Ass (DEW /PSAT).LT. ACCURA) 00 to 3 f 1846 TSAT = TSAT + DELP / BPSAT 8 teet IF (TSAT.tf.3fe.134) TSAT = 374.138 l tase ao To 2 1&St 3 Rtfulgt 1882 De tS&3 C 1864 PlaeTime AKA0(TDF) s taas C 1864 C CAUllULAf!Out OF TML 00seutf!v!TY OF AIR 1887 C 1884 IMPLICIT DeuBLE PRECIS 10N (6 88. 0=I) i isse DruDeten A(1s) 1944 SATA A / 14.0 10.0 0.9249. 0.92SS. 9.9284 IM1 1 0.82f1. 0.0278. S.9288. 9.4292. 0.8299 .j isat 2 e.aSee, e.e313. e.e32e. e.s327. o.one / i 1943 Isus = 3. + (TDIP -A(2)) / A(1) l 1944 5 = 128 - 3 'i 1984 TLLL m A(2) + 3 e A(1) t846 TNISt e TLSB + A(l) 1987 AEAS e A(ire) + (TDr - TLOW) / (TMIOM - TLOW) 1988 1 e (A(Isutet) - A(19ug)) 1M9 Mftset 1870 De r N l 1 ll [

l WESTINGHOUSE CLASS 3 h 237 taas nascT10m Anasta(Tor) 1927 C 1928 C CALCULATICDs OF VISC081TT OF L30ul0 (BATER) m. C itse tuPLICIT a0ueLK Pescistas ( w. o-z) 1 sat stueesten A(st) im .ATA un..... i.m. i. .... =3.. 4en... u 4.... t. in3 i ..uie...i.4i...i m / 1834 IR S = 3. + (TOP -A(1)) / A(1) { iaas s - tsue - 3 1934 TLSE = A(2) + B e A(1) t iss? Tw Gu. TLos + A(t) 1934 Ana#LB e A(!$LS) + (TEMS - TbWr) / (TM10M - TLOW) 1930 1 e (A(ISUD+1) - A(ISO 9)) 1948 AnasLS e Anasta e 1.9C-3 i.41

cTu=

1942 De ( is43 C 1944 FWMCTION CPAO(TOF) teos C 1944 C CALCULATIQu 0F SPECIFIC Mf.AT OF AIR iser C 1944 IteLICIT DouSLE PRECIIIcel (A-*I. 0-Z) te4s simoes On A(te) tese mATA A / 10.9 29.8 1964.0. 1908.8 1968.0. test t tese.e. toes.o. Seit.o. sets.o. sets.e / 1982 19ut = 3. * (TDr =A(2)) / A(1)* tes3 e. Isus ' 1954 TLOW = A(2) + s e A(t) 19SS TM10Bt e TLOW + A(1) i 1954 CPAS e A(Isug) + (tor - TLOW) / (TM10M - TLOW) 1987 1 e (A(13uS*1) = A(ISuS)) I 1984 RETUNE 1998 DS 1944 C 196f MasCTIWI CPW(Thr) issa C 4 19e3 C CALCULAf tast OF PSCIFIC NEAT OF STRAes tese C 19e4 fuPLICIT 90ueLK Pattittom (M. 6-!) isee stuoss On A(ts) 19e7 SATA A / 10.0 10.0 1879. 1989. 1999. 1998.. 1944 1 1912. 1934.. 1944. 1979. 1999. 3844.. 2 tese a sets., stas., ates. / ten tsue = 3. + (TDr.A(2)) / A(1) is71 e - tsus - 3 t ten Tu m. A(s) + s e A(t) ion Tween. TLas + A(s)- is74 erso - A(Isus) + (Tar - TLae) / (Tm:0n - TLOe) ten t . (A(tam +t) - A(tous)) 1978 RETkNum ten De 1978 C 1979 PUNCT!0It CPLS(TDeP) 190s C I

WESTINGHOUSE CLASS 3 239 2938 setTEAas = M87tAal.10ee.g 2437 ACTustes e 2034 EMD 2638 C - 2D44 fuusCTIOss SYSO(TEW ) 204 C 1942 C CALcutAT!ces GF SPECIFIC woonant OF ttEAas 2643 C 2644 IW LICIT 00ueLE PRECISI0s: (A*. O-Z) 2948 8 ttsDES101s A(37) 2044 BATA A / S.. 9.. 20s.14 147.12. 196.34. 77.83. 87.79. 2647 1 43.36 32.99. 28.22. 18.82 18.28 12.83. S.858 2044 2 7.571 8.187 8.942. 4;131 3.447, 2.828 2See 3 2.341 i.st2 1.8729. t.4194 1.2182. 1.8348 29S4 4 8.8919. 0.77et. 0.8488. 0.5822. e.Sett. e.4443 i test s e.3ess e.34es, e.3e71, e.2727. e.242s/ r ISS2 Isus = 3. * (TDsP -A(2)) / A(t) tes3 e = sus - 3 2es4 TLow. A(2) s. A(t) Ross tutosi = tLos. A(1) 2058 Sys0 = A(Isus) + (TDP - TLOur) / (TNIcet - TLour) Best 1 . (A(tsue.1) - A(tsus)) 2ess atTwas ress EMo e l J

WESTINGHOUSE CLASS 3 241 Transf er, Vol. 10, pp. 1677-1892, (1967). [11] J.C. Koh, I.M. Sparrow and J.O. Eartnett, "The Two-Fhase Boundary Layer in T*=1nne Film Condensation," y Int. J. Esat Mass Transfer Vol. pp. 69-82, (1961). [12] M.M. Chan. *An Analytical Study of f*=inar Film Condensation Part I - Flat Plates.* J. Esat j Transfer. Vol. 83 Series C pp. 48-55, (1961). [13] R.D. Cess, "T*=4 nar Film Condensation on a Flat Plat x in the absence of body force," Esitschrift fur Angewandte und Physik, 11, pp. 426-433, (1960). [14] E.Y. Emmons and D.C. Leigh, " Tabulation of the Blasius Function with Bloving and Suction.* Fluid Motion Sub-committee. Aeronaut. Res. Coun., Report No. FM 1915 (1953). [15] I.G. Shakriladze and V.I. Gomelauri, " Theoretical Study of t==inar Film Condensation of Flowing Vapor," Int. J. Esat Mass Transfer, Vol. 9, pp. 581-591, (1966). [16] Y.R. Mayhew, D.J. Griffiths and J.Y. Phillips, "Effect of. Vapor Drag on Lani.nar Film Condensation X on a vertical Surface," Froo. Instn. Mech. Engrs., Vol. 180, Part 3J. pp. R80-289 (1968-1966). [17] Y.R. Mayhew, " Comments on the paper ' Theoretical Study of i==inne Film Condansation of Flowing Vapor' (by I.G. Eheir11adze and V.I. Gomelauri)," Int. J. Esat Mass Transfer Vol. 10, pp. 107-108, (1967). [18] Y.R. Mayhev and J.K. Aggarval.

• Laminar Film Condensation with Vapor Drag on a Flat Surface,"

Int. J. Esat Mass Transfer, Vol. 16, pp. 1944-1949, (1973). [19] V. South III and 7.2. Danny, "The Vapor Shear Boundary Condition for 72=4"me Film Condensation," Trans. ASEE, 94, pp. 248-249,- (1972). [20] E.R. Jacobs, "An Integral Treatment of Combined Body

I ~ WESTINGHOUSE CLASS 3 ~ l 243 i of a Noncondensing Gas

• Int. E. East Mass Transfer.

Vol. 12, pp. 233-237, (1969) [29] I.M. Sparrow T.J. Minkovyos and M. Saddy " Forced { xi Convection in the Presanoe of Noncondensables and Transfer. Vol. 10, pp. 1829-1848, (1967). l Interfacial Resistanoe " Int. E. Rest Mass l [30] J.C.Y. Koh, " Y==1 mar Film Condensation of Condensable Gases and Gaseous Mixture on a Flat Plate,* Froo. 4th U.S.A. Nat..Cong. Appl. Mech., 2, pp. 1327-1336, (1962). l [31] T. Fujii I. Uehara, E. Mihara and Y. Esto ' Forced Convection in the Presanoe of Non-condensables - a. I Theoretical Treatment for Two-phase imminne Boundary Layer (In Japanese)," University of Kyushu Research l Institute of Industrial Scianoe, Report No. 66, pp l 83-80 (1977). [32] J.T. Rose,

• Approximate Equations for Forced -

i i Convootion Condensation in the Presence of a l 9 Noncondensing Gas on a Flat Flate and Borizontal l Tube " Int. E. Esat Mass Transfer, Vol. 23,-pp. 539-l 546, (1980). [33] J.T. Rose

• Boundary Layer Flow with Transpiration on an Isothermal Flat Plate,*

Int. E. Esat Mass l Transfer, Vol. 22 pp. 1243-1244 (1979). [34] Y.E. Denny, A.F. Mills and V.E. Jusionis, "==4"e? Film Condensation from a Steaa-Air Mirture W Undergoingforood Flow Down a Vertical Surface," J. Reat Transfer, Vol. 95, pp. 297-304, (1971). I t [35] V.I. Danny and V.E. #ousionis, " Effects of j noncondensable gas and forood flow on laminar film YJ oondsasation.* Int. E. Esat Mass Transfer, Vol. 15, pp. 818-326 (1972). [36] E. Asano and Y. Nakano, *Fored Convection Film i W Condensation of Vapors in the Presanoe of i l l 4

- ~ ^ ~ -^ } WESTINGHOUSE CLASS 3 ~ l 245 l [46] L. 81eger and R. A. Baban, "'=4 a** Film Condensation of Steam Containing Small Conoentrations of Air," Int. E. Beat Mass Transfer. Vol. 13, pp. 1941-1947, (1970). t (47] I.E. Al-Diwany and E.T. Rose " Free Convection Film l Condensation of Steam in the Presence of l Noncondensing Gases

• Int. J. Beat Mass Transfer.

Vol. 16, pp. 1359-1369, (1973). i [48] A.C. De?uono and R.E. Christensen, "Erperimental Investigation of the Pressure Effects on Film i I Condensation of Sten-Air Mixtures at Fressure above Atmospherio," Pnadamentals of Phase Change; Boiling and Condensation. The Tinter Annual Meeting of ASME, New Orleans, Louisians, ITD-Vol. 36, (1984). j [49] J.T. Rauscher A.F. Mills and V.E. Denny, l

• Experimental Study of Film Condensation fron l

l Stesa-Air Kiztures Flowing Downward over a Borizontal Tube,* 7. Rest transfer, Vol. 96, pp. 83-

88. (1974).

i [50] V.E. Danny and Y. South III, " Effects of Forced Flow, Nonoondensable and Variable Properties on Film 'i Condensation of Pure and Einary Yapors 'at the i Forward Stagnation Foint of n Borizontal Cylinder," Int. i. Esat Mass Transfer Vol. 15, pp. 2133-2142 (1972). [51] Y.G. Levich, Phyminocha=4n 1 mvdrodym

4es, Prentios-Eall. Inc.

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