Analysis of Saturated Film Boiling Heat Transfer in Reflood Phase of PWR-LOCA

Transcription

1 Jornal of Nclear Science and Technology ISSN: (Print) (Online) Jornal homepage: Analysis of Satrated Film Boiling Heat Transfer in Reflood Phase of PWR-LOCA Masahiro OSAKABE & Ykio SUDO To cite this article: Masahiro OSAKABE & Ykio SUDO (1984) Analysis of Satrated Film Boiling Heat Transfer in Reflood Phase of PWR-LOCA, Jornal of Nclear Science and Technology, 21:2, , DOI: 1.18/ To link to this article: Pblished online: 15 Mar 212. Sbmit yor article to this jornal Article views: 61 View related articles Fll Terms & Conditions of access and se can be fond at Download by: [ ] Date: 2 November 217, At: 1:5

2 Jornal of NUCLEAR SCIENCE and TECHNOLOGY, 21[2], pp (Febrary 1984). 115 Analysis of Satrated Film Boiling Heat Transfer in Reflood Phase of PWR-LOCA Trblent Bondary Layer Model Masahiro OSAKABE and Ykio SUDO japan Atomic Energy Research Institte* Received janary 12, 1983 Rivised jne 22, 1983 Downloaded by [ ] at 1:5 2 November 217 The heat transfer regime jst above the qench front dring the reflood phase in PWR LOCAs is the film boiling. A two-region model is developed for the description of satrated film boiling in this region. It is considered that the violent two-phase flow srronds the vapor film and promotes the transition of laminar to trblent vapor film in the reflood phase. In the model, the vapor film srronded with the two-phase mixtre core is treated with the trblent bondary layer theory. The higher void fraction of the mixtre core gives the lower heat transfer in the model. The reslts obtained by the model are compared with the data of the Slab Core Reflood Tests which cannot be explained with the previos laminar vapor film theory. The data fall between the crves predicted by the models assming zero interfacial shear stress ('ri=o) and zero interfacial velocity (i=o) at the different elevations in the core, different core inlet velocities and different system pressres. These show the applicability of the two-region model for the reflood phase. KEYWORDS: PWR type reactors, loss of coolant, reflood, satrated film boiling, heat transfer, vapor film, trblence, mixtre core, two-region model, zero interfacial shear stress, zero interfacial velocity, two-phase flow Bromley<ll < > I. INTRODUCTION developed a model for satrated film boiling heat transfer on a vertical heated srface assming a laminar vapor film. expressed as, where hsat = C[.l;pg (pt- pg) hj gy/ (z flg.d Tsat) ]1 14 hjg =hjg [1 +.4Cp L1Tsat/hjg] 2,.dTsat = T w- Tsat. The local heat transfer coefficient h is The second term in Eq. ( 1) is the effective radiative heat transfer coefficient. transfer coefficient hn is expressed as, (1) The heat hn=a(t:-t~at)/l1tsat. The heat transfer regime<"> of the satrated film boiling can be observed jst above the qench front in the reflood phase of PWR-LOCA. Sdo<4> proposed C=.94 in Eq. ( 1) based on the PWR-Fll Length Emergency Core Heat Transfer (PWR-FLECHT) Grop I reflood test > as shown in Fig. 1. FLECHT tests ranged between 4. 8 and 25. em/ s. of C as the fnction of core inlet water velocity and propo~ed * Tokai-mra, Ibaraki-ken The core inlet water velocity of the referred PWR -33- Kaminaga et al. < 5 > expressed the vale C=.9 at the core inlet

3 116 ]. Ncl. Sci. Technol., Downloaded by [ ] at 1:5 2 November 217 water velocity of 2.5 cm/s. The higher vale of C were obtained at the higher core inlet velocity in their reflood experiment. When the laminar vapor film theory is applied, the vale of C is.5 at the condition of zero interfacial velocity Ct=O) and.77 at the condition of zero interfacial shear stress Crt=O) as shown in Fig. 1. As the vapor film velocity is mch higher than the water velocity in the reflood phase, the vale of C is actally less than. 77 in the laminar.6 1 Laminar (U; =OJ vapor film theory. These indicate the difficlty to.4 L...-L---L---L.-1---L----L---Jl-.J..._..J._...J express the film boiling heat transfer with the.2.4 laminar vapor film theory in the reflood phase. The violent flid motion in the reflood phase promotes the transition from laminar to trblent flow Distance from qench front z (m J Fig. 1 Vale of C in Eq. ( 1) in PWR FLECHT test and predicted vale in the vapor film. A new model, called the twoin laminar vapor film theory region model, is developed in which the vapor film is treated with the trblent bondary layer theory and is srronded by a two-phase mixtre core. This two-region model is compared with the data from the Slab Core Reflood Test at the Japan Atomic Energy Research Institte. The Slab Core Test Facility< > has a core which is composed of eight 16x16 rod array bndles arranged in a row. ll. DESCRIPTION OF MODEL Film boiling on a vertical isothermal srface, which is at wall temperatre T w and is srronded by a mixtre core, is considered. The following assmptions are made to obtain the local heat flx. (1) The vapor film is evalated by the trblent bondary layer theory. (2) The pressre drops in the vapor film and the mixtre core are the same<7) <sj. (3) Trblent Prandtl nmber is 1.. (4) The physical properties of vapor film are constant and evalated at the film temperatre [(T w+tsat)/2]. (5) The mixtre core and vapor are incompressible. (6) The mixtre core is homogeneos and at the satration temperatre. z (7) The enthalpy of vaporization is expressed with h/ in Eq. ( 1) to compensate the transportation of sensible heat in the vapor film. Interface y (8) The pressre loss de to the acceleration of vapor film is negligible. d=-jz f---l.4.4'-:ll.lj (9) The generated vapor flows in the vapor film. The schematic diagram at zero interfacial shear stress is shown in Fig. 2. Under this condition, the vapor film velocity is the maximm at the interface. The pressre drop in the mixtre core is (z=o} Details of A Qench front de to the static pressre difference. The density Fig. 2 Flow model at zero interfacial of mixtre core is evalated with Pm[ =apg+ shear stress rt = -34-

4 Vol. 21, No. 2 (Feb. 1984) 117 (1-a) p z]. The pressre drop in the vapor film is de to the wall shear stress and the static pressre difference. The force balance abot the flid element described in Details of A in Fig. 2 with the assmption (2) is d (o-y)dz(pm-pg)g=(t-tg+pgcg) dy dz. ( 2) Eqation ( 2 ) is transformed to (o+ -y+)(pm --p g)g =(*)~ /(1Jg) 2 f-tg(1 +sg/ljg) ~~: where + =f, * Y + =-- y* * = Jrw ~ Tw=o(pm-pg)g., IJg pg. Sleicher' 9 > proposed following eddy diffsivity: ( 3) Downloaded by [ ] at 1:5 2 November 217 where b=.91. cg/ljg =b2(y+)2' The sbstittion of Eq. ( 4) to Eq. ( 3) gives where a= 1Jg(pm-pg)U_ (*)3pg (y+ <3-5) ' d+ ij+-y+ dy+ =a 1+b2(y+)2 ' -+ ii* =- IJg Integration of Eq. ( 5) with the bondary condition of +=O at y+=o gives ( 4) ( 5) -a aij+ += 2 b 2 In {b 2 (y+) 2 + 1} + ~b~ arctan (by+). ( 6) The schematic velocity profile obtained with Eq. ( 6) is shown in Fig. 2. flow rate per nit width, r, at a given z is expressed as Sbstittion of Eq. ( 6 ) into Eq. ( 7 ) gives F=pg~:dy=f-tg~:+ +dy+. F!t-tg= : 2 [o+-ij+lnw(ij+) 2 +1}+{bW) 2 - The heat condction eqation in the vapor film is dt Qw=-pgCp(K+sg) dy!}arctan(bij+)]. The vapor mass (7) (8) ( 9) where the trblent Prandtl nmber is assmed as 1.. dt+ l.o=(k/ljg+cg/ljg) dy+ Transformation of Eq. ( 9) gives (1) where T+=pgCp*(Tw- T)fqw. Integration of Eq. (1) with the bondary condition of T+=O at y+=o and by sing Eq. ( 4) gives, 1 J~ b /~ + T+=~ J:'garctan( vljgy ) b K v'k. As the temperatre at ij+ is satration temperatre Tsat in Eq. (11), (11) _ b../k pgcp*(t w-tsat) Qw-. v'ij arctan ( b..;'ljg (j+) g v'k (12) -35-

5 118 ]. Ncl. Sci. Techno!., From conservation of energy in the vapor film, dr d \" qw= ~htg+ dz JopgU Cp T dy. (13a) The last term in Eq. (13a) represents the transportation of sensible heat in the vapor film. An approximation to accont for this is to se the modified vale h j g in place of h 1 rr [assmption (7)], so that Eq. (13a) becomes drh, qw=dz fg (13b) Downloaded by [ ] at 1:5 2 November 217 Differentiation of Eq. ( 8 ) with z gives 1 dr do =ef19 dz dz, where e= a [ o+- { b(a+) 2 } arctan (bo+), J 2 il b 2 b. From Eqs. (12), (13b) and (14), do dz b.jk pgcp*(t w-tsat) Eqation (15) gives the vale of o at a given z. flx qw at a given z. The schematic diagram at zero interfacial velocity is shown in Fig. 3. Under this condition, the vapor film velocity is the 3 maximm at the half width of vapor film. The velocity in o/2~y~o is the mirror image of that in ~ y ~ o /2. The temperatre profile in o/2~y~o is the inverted mirror image of that in O~y~o/2. When the half width of film (O<;;,y<;;.lJj2) is considered, the bondary condition at o/2 is zero shear stress (r=o). This condition is the same with the zero interfacial shear stress ( r; = ) condition. Eqations (12) and (15) are modified to, h ' 1- t (b.jl!go+) 19 f1 9ev lig arc an -;;K.-. (14) (15) The obtained o and Eq. (12) give the heat Center line of vapor film ( T' ) ~ m~ Flid 2 element / vapor Details of 8 Tw z o Qench front (z ') Fig. 3 Flow model at zero interfacial velocity i=o (16) (17) Ths, the heat flx qw at a given z for the zero interfacial velocity is obtained with Eqs. (16) and (17). The vale of C in Eq. ( 1) corresponding to the heat flx qw calclated with the tworegion model is obtained by -36-

6 Vol. 21, No. 2 (Feb. 1984) 119 Downloaded by [ ] at 1:5 2 November 217 C Qw JT sat[a~p g(pt- p g)hj Y /(zpgjt sat)] 114 (18) The effects of wall temperatre T w are shown in Fig. 4. The higher vales of C are obtained at the higher T w The range of T w in Fig. 4 is the typical cladding temperatre at the film boiling regime observed in Slab Core Reflood Tests. The difference of C is very small in spite of the temperatre difference of 2 K. The effects of satration temperatre and pressre are shown in Fig. 5. This also shows a little dependency on the satration temperatre. Shown in Fig. 6 are the effects of void fraction of mixtre core. The vales of C strongly depend on the void fraction of mixtre core. The lower vales of C are obtained at the higher void fraction. When the void fraction of mixtre core is high, the lift force on the vapor film is redced. This cases the thicker vapor film, the lower heat transfer coefficient and then, the lower vale of C< 3 >. Shown in Fig. 7 is the vale of ij+ for ri=o and ij+ /2 for i= as the fnction of the distance above the qench front. The vapor film thickness increases with the increase of the distance above the qench front. In the calclations shown in Figs. 4rv6, y+ is less than 5 and therefore, Sleicher's expression for the eddy diffsivity, Eq. ( 4 ), is applicable. -';' a,.5 ) ---U;'O ( Tsat '393 K. L_L. j j_----..j j.._j J_...L...J...J QO Q2 OA Distance from qench front z ( m) Fig. 4 Effect of wall temperatre T w on vale of C Q)..2 : ;.6 3 f------o(-a =-c:-.c::-5---:)-+ Two 693K. L-...Jl._.l..J j j_...l...l..-'-~..2.4 Distance from qench front z (m) Fig. 5 Effect of satration temperatre Tsat on vale of C 1.2 c/.. =.8 (j. =.5 =. ~.9 t---t-t-:7"'--- "7.-flec Q::--_-l :i.6 fj::_::~~;~~:===v,.3r r;oo Tw' 693 K) --- U;' ( Tsato393 K. L. j----..j j.. j j_...l...l..-1--~..2.4 Distance from qench front z (m) Fig. 6 Effect of void fraction a of mixtre core on vale of C - 'Cj =( ) Uj =( 6i2) Tw=693K. kt393k Vapor film thickness 8, 'b/2 Fig. 7 Vapor film thickness a+ for -ri=o and oi/2 for i=o as fnction of dis tance above qench front -37-

7 12 ]. Ncl. Sci. Technol., m. COMPARISON WITH DATA OF SLAB CORE TESTS The major test conditions of Slab Core Tests are listed in Table 1. Test Sl-1 is the base case test and Test Sl-9 is a high core inlet velocity test. Test Sl-SHl is a high system pressre test and Test Sl-2 is a low system pressre test. In the satrated film boiling dration in this stdy, the core inlet velocity V in is 2.5 or 4 cm/s de to the Low Pressre Coolant Injection (LPCI) after the Accmlator (Ace) Injection. Table 1 Test conditions of forced flooding in Slab Core Tests Test No. Sl-SH2 Sl-1 Sl-2 Sl-9 Downloaded by [ ] at 1:5 2 November 217 System pressre (MPa) Core inlet velocity Vin Ace for -1 s (cm/s) LPCI after Ace (cm/s) Max. core inlet sbcooling (K) Max. cladding temp. at start of refiooding (K) The estimation of void fraction in the core is important to clarify the film boiling heat transfer. In the Slab Core Test Facility, the effective heated length of simlated heater rods is m which is the same as an actal PWR. The mean void fractions in the core can be obtained with the differential pressres LIP measred at the spans DP1, DP2, DP3, DP4 and DP5 in Fig. 8. The void fraction a is obtained by a=1-lip/(p 1 g L), (19) ~.6 ~ "C.4 "i5 >.2 where the frictional loss is neglected and L is the length of span. Shown in Fig. 8 are the transient profiles of void fraction in the base case test (Test Sl-1) and the high core inlet velocity test (Test SI-9) when the qench front comes to the three elevations. 95, and m above the bottom of core. By sing these transient profiles, the void fractions at qench front are estimated as Test 51-1 ( Vin= 2.5 cm/s ) b. Test 51-9 ( Vjn= 4 cm/s ) Elevation ( m) Fig. 8 Transient profile of void fraction in core.j:: c:: "' C" ~ c:: ~ ~ f----1 t----1 Test 51-1 ( Vin=2.5 cm/s) b. Test 51-9 "C a ( Vin=4cm/s > Elevation ( m l Fig. 9 Void fraction at qench front

8 Vol. 21, No. 2 (Feb. 1984) 121 shown in Fig. 9. The heat transfer coefficients are measred cs> at the elevations. 95, and m. The vale of C in Eq. ( 1 ) is experimentally obtained from the measred vales Of the heat transfer coefficient h, the wall sperheat 11T sat and the distance from qench front z when the qench front is within.4 m below the measred point. The location Of the qench front is estimated with the qench times of the 1 thermocople elevations.on the heater rods cs>. The vale of C is obtained by (2) Downloaded by [ ] at 1:5 2 November 217 where the radiative heat transfer coefficient is assmed to be described with 3/4 hr as in Eq. ( 1 ). The mean void fractions a at the corresponding elevations.55 to.95, to and 2.36 to 2.76 m are shown in Fig. 9. In Fig. 9 the void fractions at qench front are lower at the higher core inlet velocity. Shown in Fig. lo(a)"-'(c) are obtained reslts in Slab Core Tests and the predicted crves from the two-region model. The vales of C in the tests are between.6 and 1.2, which cannot be explained with the previos laminar vapor film theory in which the vale.of C shold be between.5 and. 77. In the application of the model, the following are taken into accont : (1) The void fraction of mixtre core is eqal to the void fraction at the qench front and is represented by the mean void fraction a. (2) The range of wall temperatre T w in this stdy is between 793 and 593 K when the qench front is within.4 m below the measred point. As the effect of T w is small as shown in Fig. 4, the constant vale of T w =693 K is sed. (3) The satration temperatre T sat at each system pressre is sed. Shown in Fig. 1 (a) are the vales of C measred in the base case test (Test Sl-1) and the high core inlet velocity test (Test Sl-9) at elevation.95 m above the bottom of core. Shown in Fig. 1 (b) and (c) are the vales of C at elevations and m, respectively. In Fig. 1 (a)"-'( c), the mean void fractions a in Fig. 9 are sed as the void fractions of mixtre core in the model. In the two-region model, the generated vapor flows in the vapor film. The void fraction in the core increases with the increase of the distance above the qench front as shown in Fig. 8, and is larger than the void fraction of mixtre core becase the vapor film velocity is mch higher than the velocity of mixtre core and the actal interfacial shear stress is not considered to be always zero. The maximm increase of void fraction obtained by the differential pressre measrement, de to the interfacial shear stress in the model assming i=o is abot.15 from the qench front to.4 m above the qench front. The increase of the void fraction of mixtre core above the qench front is not so large as shown in Fig. 8. The error by sing a instead of the local void fraction of mixtre core is considered to be small. The amont of vapor which is a part of the generated vapor and flows into the mixtre core, is negligible compared to that in the vapor film becase the vapor velocity in the vapor film is considered to be mch higher than that in the mixtre core. The decrease of the vapor film thickness de to a part of the generated vapor which flows in the mixtre core can ths be neglected. The acceleration loss in the vapor film is neglected in the model. The maximm acceleration loss can be estimated with the calclated vapor film velocity in the model. The acceleration loss increases as the increase of the distance z above the qench front. The vale of C decreases a maximm 1% at z=.4 m by sing the maximm acceleration loss obtained by the model. The ac- -39-

9 122 ]. Ncl. Sci. Techno!., 1.5 Test S1-1 Test Si Q)..=! > Ti=O --- Uj= Distance from qench front z (m J Q) ::> ~. 6 r-----=""'--=-::::_ '..2.4 Distance from qench front z (m J Downloaded by [ ] at 1:5 2 November 217 Q) ::> > (a) Elevation.95 m Test S1-1 Test S Vin=2.5cm/s Ele m Q) :::> Ti=O > Uj= Distance from qench front z (m) Distance from qench front z (m} (b) Test S1-1 Vin=2.5 cm/s Ele m l---- Elevation m Vin=L.cm/s Ele.2.76m l Test S1-9 - ~. 6 ~...::!..:"----"-,J.::;..,.l.L --J > f------=:7""1"''---=--;'---1. L-...:'----l l l...j...-l--l--'--l ~ ~2.4 Distance from qench front z (m J Fig. lo(a)~(c). L_,;L-J-----l-----l.l. J.. j_--l...j..._j..2.4 Distance from qench front z ( m l (c) Elevation 2.76 m Vale of Cat elevation.95, and 2.76m obtained from Slab Core Tests and two-region model -4-

10 Vol. 21, No. 2 (Feb. 1984) 123 Downloaded by [ ] at 1:5 2 November 217 celeration loss can be neglected near the qench front or for the model assming <;=. The vapor film thickness increases with the increase of the distance above the qench front in the model. The maximm vapor film thickness at z=.4m is abot.72 to.85mm in the model assming <;= and is.86 to 1.1 mm in the model assming ;=O. The rod diameter is 1.7 mm and the minimm gap between rods is 3.6 mm in the Slab Core Test Facility. It is considered that the interference among the vapor films on the rods can be neglected. The two-region model adopted in this stdy describes the two-dimensional vapor film. The vale of C at z=.4 m increases a maximm 6% for the models assming <;= and ;=O de to the three-dimensionality of the vapor film on the rods as shown in APPENDIX. As the vapor film is very thin near the qench front, this effect can be neglected. When the atove reslts are considered, it is well nderstood that the Slab Core Test reslts fall between two crves predicted by the models assming <;= and ;=O. Shown in Fig. 11 are the vales of C obtained in the high system pressre test (Test Sl-SH2) and the Test MPa.4 MPa Ete m 1.2 Ete m Q) Q) ::l ~ > > Test S1-SH2 - T;=O 3 Ti = ---- U; = U; = Distance from qench front z (m) Distance from qench front z (m) Fig. 11 Vale of C at different system pressres obtained from Slab Core Tests and two-region model low system pressre test (Test Sl-2). The void fraction in the mixtre core is estimated to be a=.63 for Test Sl-SH2 and a=.6 for Test Sl-2 with the same method as mentioned above. The data fall between the two crves even for the different system pressre tests. These show the applicability of the two-region model for the reflood phase. The lower vales of C are obtained at the higher elevation in the core and at the lower core inlet velocity. One of the reasons is to be the higher void fraction of mixtre core as predicted by the model. Shown in Fig. 12 is the vale of C at z=.1 m. The vale of C decreases with the increase of the void fraction as predicted by the model assming <;=. IV. CONCLUSION E 1.25r-----c: , -'tj = Tw =693K N 1. 1ii --,~~rl~" I RANGE OF TEST RESULTS Void fraction ix Fig. 12 Vale of C at z=.1 m obtained by model assming 'Z';=O (1) The satrated film boiling model called as the two-region model was developed. In the model, the vapor film srronded with the two-phase mixtre core is treated with -41-

11 124 ]. Ncl. Sci. Techno/., the trblent bondary layer theory. The model gives the lower heat transfer with the higher void fraction of the mixtre core. {2) The reslts by the model are compared with the data of Slab Core Reflood Tests. The vales of C in the tests are between.6 and 1.2, which cannot be explained with the previos laminar vapor film theory in which the vale of C shold be between.5 and. 77. The data fall between the predicted vales by the model assming zero interfacial shear stress (r;=o) and zero interfacial velocity (;=O) at the different elevations in the core, the different core inlet velocities and the different system pressres. These show the applicability of the two-region model for the reflood phase. {3) The lower vales of C are obtained at the higher elevation in the core and at the lower core inlet velocity. One of the reasons for this is considered to be the higher void fraction in the mixtre core as predicted by the model. Downloaded by [ ] at 1:5 2 November 217 [NOMENCLATURE] C: Constant in Eq. (1) : Vapor film velocity (m/s) h Heat transfer coefficient (WI (m 2 K)) Y: Distance from wall (m)..! : Thermal condctivity (W/(m K)) a: ljg (pm- p 9 )Y![(*) 3 pg] p: Density (kg/m 3 ) *: Friction velocity ( = v'rw! p) (m/s) hfg: Latent heat (Jjkg) +: j* hjg: Modified latent heat defined y+: y*j" by Eq. (I) (J;kg) a+: o*j)) z Distance from qench front (m) r: Vapor mass flow rate per nit p.: Dynamic viscosity (Pa. s) width (kg/(s m)) lj: Kinematic viscosity ( = p./ p) (m 2 /s) LITsat: Wall sperheat (=Tw-Tsatl (K) T: Temperatre (K) V;n: Core inlet water velocity (m/s) Cp: Specific heat CJ1 (kg K)) a: Void fraction (Sbscript) a: Stefan-Boltzmann constant (W/(m 2 K 4 )) Y: Vapor Y: Accerelation de to gravity (m/s 2 ) m Mixtre ii: Vapor film thickness (m) w: Wall : Eddy diffsivity (m 2 /s) sat: Satration r: Shear stress (N/m 2 ) l : Liqid K Thermal diffsivity (=J./Cp p) (m 2 /s) i: Interface q: Heat flx (W/m 2 ) ACKNOWLEDGMENT The athors are mch indebted to Drs. S. Katsragi, M. Ishikawa, K. Hirano, H. Adachi and Y. Mrao for their gidances and encoragements. They wold like to express their appreciations to Dr. P. ]. Schally, Messrs. D.H. Miyasaka and Y. Abe for their sefl discssions. (1) BROMLEY, L.A.: Chern. Eng. Prog., 46, 221 (195). (2) idem: Ind. Eng. Chern., 44, 22 (1952). (3) OsAKABE, M., Soo, Y. : ]. Ncl. Sci. Techno!., 2(7], 559 (1983). (4) SUDO, Y. : ibid., 17(7], 516 (198). (5) KAMINAGA, F., et al.: Nihon-Kikai-Gakkai Ronbn.Sh (Trans. ]pn. Soc. Mech. Engrs.), (in Japanese), 44(388], 4263 (1978). (6) ADACHI, H., et at. : ] AERI-M 83-8, (1983). (7) MRAO, Y., et al.: ]. Ncl. Sci. Techno/., 18(4], 275 (1981). (8) CHAN, K. C., et al.: 19th National Heat Transfer Con/., ASME, Orlando, Florida, Jly, (198). (9) SLEICHER, Jr., C. A.: Trans. ASME, 8[3], 693 (1958). (lo) CERMAK, ].., et al.: PWR-FLECHT Grop I test report, WCAP-7435, (197). -REFERENCES- -42-

12 Vol. 21, No. 2 (Feb. 1984) 125 [APPENDIX] In the two-region model, the vapor film is treated as the two-dimensional bondary layer theory. The maximm vapor film thickness at the distance.4 m above the qench front is.85mm by the model assming rt=o and 1.1 mm by the model assming Ut=O. The following are the consideration abot the applicability of the two-region model to the film boiling on the rods of which diameter is 1.7 mm. For the model assming ri=o, Eq. ( 2) for the vapor film on the rod becomes d (3(o-y)dz(pm-pg)g=(p+Pcg) dy dz, (A1) Downloaded by [ ] at 1:5 2 November 217 where o-y. tb=l+ 2 ( ), ro: Rod radms =1.7/2mm. ro+y When the vapor film thickness o is.85 mm, the average of (3 in the vapor film is abot 1.4. Therefore, the vapor velocity is abot 4% larger than that of the two-dimensional model. On the other hand, Eq. ( 7 ) is transformed to T= pg 2 ~ 2rr(y+ro)U dy~(1+- 2 )p/ U dy. rrro Jo r Jo When o is.85 mm, oj2ro is abot.8 and the mass flow rate r becomes abot 8% higher than that of the two-dimensional model. As the reslts, r becomes abot 12% higher than the two-dimensional model at the same vapor film thickness o. Eqations (14) and (15) become _l_.!!_( _)-e!!j_ f.l dz dz, do dz by'k pgcp+(t w-t,at) 1.12h!f.1ev'varctan(h~;/+) Eqation (A4) gives 12% smaller do/dz than Eq. (15) in the two-dimensional model. the vapor film thickness o increases with the increase of the distance from the qench front, the decrease of o at z=.4 m de to the three-dimensionality is considered to be abot half of 12%. Therefore, for the model assming ri=o, the maximm decrease of o is abot 6%. The maximm increase of heat transfer is less than abot 6% becase the decrease of o means the decrease of the mean eddy diffsivity in the vapor film. By sing the same method, the maximm increase of heat transfer is less than abot 6% for the model assming i=o when o is 1.1 mm. (A2) (A3) (A4) As -43-