Kutateladze Zuber C 0 C 1 r eq
q CHF A v /A w A v /A w q CHF [1] [2] q CHF A v /A w [3] [4]
A v : A w : A : g : H fg : Q : q : q CHF : T : T 1 : T 2 : T 3 : c 100 T 4 : c 100 T b : T sat : T w : t : V : v 1 : T sat : (=T w T sat ) T sub : (=T sat T b ) c : : : D : Taylor H : Helmholtz ( ) 11 : = l : v : : d : 16 eq :
l : sat : sub : v : w :
Kutateladze Zuber
C 0 C 1 r eq
q CHF A v /A w A v /A w q CHF
[1]
[2] q CHF A v /A w
[3]
[4]
(CHF) CHF CHF
1950 Kutateladze[1] (1.2.1) q CHF 1 4 σg ( ρ ) l ρv = K1ρ vh fg 2 (1.2.1) ρv K 1 K 1 = 0.130.19 1959 Zuber[2] Taylor Helmholtz CHF (1.2.2) q CHF 1 4 σg ( ρ ) l ρv = 0.131ρ vh fg 2 (1.2.2) ρv Vapor Steam Fig. 1.2.1 Zuber
Kutaterladze Zuber CHF 1960 Gartner & Westwater[3] 1968 [4] CHF CHF (1.2.3) d q CHF ρδ l ch fg 1 A τ (1.2.3) = v Aw (1.2.3) 1976 [5] Davidoson [6] d (1.2.4) 1 ( ξρl + ρv ) ( ρ ρ ) 3 5 1 v 5 1 3 5 4 d 4 g τ = (1.2.4) π l v =11/16 v 1 V q = v1 t, v1 = Aw (1.2.5) ρv H fg
1983 [7] Helmholtz Helmholtz H 1/4 (1.2.6) c 2 ρ 2 v + ρl Av 2 δ = 0.5 ( ) c πσ ρv H fg q (1.2.6) CHF ρvρl Aw d (1.2.4) (1.2.7) q v = 1 ρ H (1.2.7) λ 2 D v fg D Taylor 1 σ λ 3 2 ( ) D = π 2 (1.2.8) g ρl ρv (1.2.4) (1.2.6) (1.2.8) (1.2.3) q CHF (1.2.9) q CHF 4 π = 11 2 3 2 1 16 A A v w 5 8 1 A A v w 5 16 ρl ρv + 1 11 ρl 16 ρv + 5 3 5 1 16 ρ H v fg gσ ρ 1 ( ρ ρ ) 4 l 2 v v (1.2.9) (1.2.9) A v /A w (1.2.9)Zuber (1.2.2) A v /A w (1.2.10) A A v w 11 ρl = 0.0654 16 ρv + 1 3 5 ρl ρv + 1 1 2 (1.2.10) v / l 1 (1.2.10)
A A v w ρ v = 0.0584 ρl 0.2 (1.2.11) (1.2.9) (1.2.11) Vapor Bubble c Fig. 1.2.2
CHF
Fig.2.1.1Fig.2.1.2 Fig.2.1.1 Fig.2.1.2
Fig.2.1.3
High Speed Video Camera Universal Scanner Digital Multi Meter Computer Ice Box V Flow Meter Cooling Water Outlet Condenser High Speed Video Camera Fixed Thermocouple Movable Thermocouples Auxiliary Heater Light PID controller AC100V Copper Block Catridge Heater Ice Box Select Switch Slidac Multi-Point Recorder Digital Multi Meter AC100V Fig. 2.1.3
160mm 160mm 180mm [1] 45 10mm 4mm 0.6mm [1] 100V, 500W5 0.5mm CA 3
PID 8mm 1mm 110mm 7 6mm 1mm 50mm 9 1.6mm CA 1 SHIMADEN SR64 SHIMADEN PAC15P 30A CA x = 0mm, 5mm, 10mm, 20mm, 30mm, 40mm Scanner CA 0.2mm Scanner Takeda Riken TR7200 7562 NEC PC-9801RA
CHF ER6 10 500W 1 PHOTRON
CHF CHF CHF 0, 2/0, 3/0, 4/0 CHF 0 30
PID 10 1. 20V 5V CHF CHF 1V 2. CHF 10V 2V CHF CHF 1V 10 3 2 2 648 0.001 6 z = 0.5mm, 1mm, 2mm, 3mm, 5mm, 10mm, 15mm, 20mm, 22mm 1 20
Fig.2.3.1 r eq r 1 R r 2 r 3 Copper Block Fig.2.3.1 T q = λ (2.3.1) T q A = const (2.3.3) 2 T r = const r (2.3.3) (2.3.4) C T = + r 0 C1 (2.3.2) (2.3.3) (2.3.4) q w T w r eq (2.3.5) C0 Tw = + C1 (2.3.5) r eq (2.3.1) (2.3.5) (2.3.6) C0 qw = qeq = λ 2 r eq (2.3.6)
3 1, 2, 3 r 1, r 2, r 3 T 1, T 2, T 3 (2.3.4) C 0, C 1 (2.3.7), (2.3.8) C 3 i i= 1 0 = 3 ( x x)( T T) 2 ( xi x) i= 1 C1 0 i (2.3.7) = T C x (2.3.8) 3 3 1 1 1 xi = x = x i T = r 3 3 i i= 1 T i i= 1 r 1 =16.17mm, r 2 =20.15mm, r 3 =24.14mm
Q w = Q eq (2.3.9) Q = A q (2.3.10) w eq w eq w Q = A q (2.3.11) eq (2.3.9)(2.3.10)(2.3.11) (2.3.12) A w = A eq (2.3.12) 2 A w = πr (2.3.13) (2.3.14) A eq = 2πr eq 1 cos 2 2 θ (2.3.14) (2.3.12)(2.3.13)(2.3.14) (2.3.15) R r eq = (2.3.15) θ 2sin 4 =45 (2.3.15) (2.3.16) r eq = 2. 563R (2.3.16) (2.3.5)~(2.3.8), (2.3.16) [2]
Tsub 0 K 20 K 40 K 60 K App.2
073 10 5 CHF CHF CHF CHF CHF CHF 4% CHF CHF 0K~73K CHF I. II. T sub =0, 10, 15K Fig.3.1.1~Fig.3.1.3 T sub =20, 25, 35, 45, 55K Fig.3.1.4~Fig.3.1.8 III. T sub =65, 73K Fig.3.1.9~Fig.3.1.10
[5] A A a A A A B A a A T sub = 0K T sub = 10K T sub = 15K A, a B a A B a A B
T sub =0, 10K
CHF d d d d Fig.3.2.1 State 1 State 2 State 3 State 4 State 5 Fig.3.2.1 d [5] [5]
Fig.3.2.2 d T 2 State 1 State 2 State 6 Former Bubble Former Bubble State 3 State 4 Study Object State 5 Study Object Study Object T 1 T 1 T 2 T T Waiting Time Macro-layer Consuming Time Cycle T 2 Fig.3.2.2 A Time Dividing Method in CHF Analysis Using Macrolayer Thinning Model State 1 State 2 State 3 State 4 State 5 State 6 T 1 T 2 T=T 1 +T 2 [4]
d d A a B A a B Fig.3.3.1 A d A c A a B t Fig.3.3.1 A a B a B A CHF A a B A d t 2 3.3.1 T, T 1, T 2 Fig.3.3.2~Fig.3.3.4 3.3.1 T sub (K) 0 10 15 20 25 35 45 55 15 19 20 35 34 33 56 50
Fig.3.3.2
Fig.3.3.3
Fig.3.3.4
+ = fg sub p v l sat CHF sub CHF H T C q q 0.8,, 0.065 1 ρ ρ + = fg sub p v l sat CHF sub CHF H T C q q 4 3,, 0.102 1 ρ ρ
Fig.4.1.1
(1.2.4)(1.2.5) (1.2.3) (4.2.1) l v v q = ( ) 3 CHF 0.00171πσH fg 1 + ρ ρv H ρv fg 2 1 ρ 0.0584 ρl 0.2 ρ ρl 0.4 1 3 1 τd (4.2.1) (4.2.1) d CHF Fig.4.2.1 [2] Fig.4.2.1 T sub = 45K 2 (1.2.3) (1.2.4) (1.2.5)Zuber (1.2.5) A v /A w v/ l
Experimental Calculated Fig.4.2.1 CHF in pool boiling as a function of liquid subcooling. Result for water
(1.2.5) A v /A w (1.2.4) (1.2.3) (4.3.1) A A v w 2 1 A A v w = πσh fg 2τ q 1 + d ρ ρ l v 3 ( ρ H ) 2 v fg (4.3.1) (4.3.1) H fg v l d T 2 q State 1 State 2 State 6 Former Bubble Former Bubble State 3 State 4 Study Object State 5 Study Object Study Object q 1,T 1 q CHF,T q 2,T 2 Fig.4.3.1 Relationship between q 1, q 2, and experimentally measured q CHF Fig4.3.1 q 1 T 1 q 2 T 2 q CHF q 1 q 2 T1 T2 q CHF = q1 + q2 (4.3.2) T T (4.3.1) q (4.3.2)q 2 (4.3.1)q q CHF q 2
100 c 100 c 100 c c c T1 T b T b T b 100Front Line T w 100Front Line c c c q 3,T 3 q 4,T 4 q 1,T 1 Fig.4.3.2 A guessed macro-layer evaporation mechanism T 3 100 c T 4 100 c T 3 +T 4 T 1 T 3 q 3 T 4 q 4 q 2 q CHF T3 = q3 + T T3 = q3 + T T3 = q3 + T T4 T2 q4 + q T T T4 T2 q2 + q T T T T3 q2 T 2 2 (4.3.3)
q q 2 CHF q T qchf T T T T = 3 3 1 (4.3.4) 3 q 3 T 3 q 3 T 3 q 2 /q CHF 4.3.1 4.3.1 q 2 /q CHF t sub =10K q 2 q CHF (4.3.1) 10% (4.3.1)q q CHF A v /A w Fig4.3.3 Fig.4.3.3 A v /A w A v /A w q CHF Fig.4.3.3 q CHF A v /A w q CHF (4.3.4)
4.3.1
T sub 0K 10K 15K 20K 25K 35K 45K 55K Haramura-Katto [4] Fig.4.3.3 A v /A w as a function of CHF in subcooled pool boiling
Fig.4.3.3 A v /A w q CHF (1.2.4) c q CHF c q -2 CHF c q CHF T sub = 0K 25K Fig.4.4.1 T sub = 25K T sub = 0K T sub = 0K T sub = 25K q CHF,Tsub= 0K = 1.483 MW/m 2 q CHF,Tsub= 25K =2.772 MW/m 2 c,tsub= 25K c,tsub= 0K 13.5 13.5 T sub = 0K Fig.4.4.2 T sub = 25K B C T sub = 25K t = 4.6 ms, t = 6.2 ms D,E T sub = 0K A t = 0 t = 0 T sub = 0 K T sub = 0K T sub = 25K 1 c δc q 2
In The Case of Saturate Boiling A D E C B Calculated Value With Haramura- Katto Model Fig.4.4.1 Bubble volume growing with time
Tsub=0~73 K () T sub 55K ) A v /A w q CHF ) CHF ) CHF a) b) () T sub 55K (1),) CHF
[1] S.S.Kutateladze, Zh. Tekh. Fiz.,20,p.1389,1950 [2] N.Zuber, USAEC Report AECU 4439, 1959 [3] R.F.Gaertner and J.W.Westwater, Chem. Eng. Prog. Symposium Ser., No.30, Vol.56, pp.39, 1960 [4] Y.Katto and S.Yokoya, Int.J.Heat Mass Transfer, Vol.11, No.6, pp.993-1002, 1968 [5] Y.Katto and S.Yokoya, Heat Transfer-Japanese Research, Vol.5, No.2, pp.43 65, 1976 [6] J.F.Davidson and B.O.G.Schueler, Trans. Inst. Chem. Engr., Vol.38, pp.335, 1960 [7] Y.Haramura and Y.Katto, Int.J.Heat Mass Transfer, Vol.26, No.3, pp.389-399, 1983 [8] S.S.Kutateladze, Isv.Akad.Nauk, S.S.S.R, Otd.Tekh.Nauk, No.4, p.529, 1951 [9] H.J.Ivey and D.J.Morris, UKAEA Report No.AEEW-R 137, 1962 [10] M.Shoji, S.Yokoya and Z.L.Huang, Trans. JSME, Vol.58, No.551, pp174-180, 1992