Effects of Heat And Mass Transfer of Thin Film Region on the Stability of the Capillary Evaporating Meniscus

34 6 2013 6 Journal of Astronautics Vol. 34 June No. 6 2013 黄晓明 1, 吴江权 1, 刘伟 1 2, 郁伯铭 1. 430074 2. 430074 50% TK124 DOI 10. 3873 /j. issn. 1000-1328. 2013. 06. 019 A 1000-1328 2013 06-0873-08 Effects of Heat And Mass Transfer of Thin Film Region on the Stability of the Capillary Evaporating Meniscus HUANG Xiao-ming 1 WU Jiang-quan 1 LIU Wei 1 YU Bo-ming 1. School of Energy and Power Engineering of Huazhong University of Science and Technology Wuhan 430074 China 2. School of Physics Huazhong University of Science and Technology Wuhan 430074 China Abstract The stability of heated and evaporating capillary meniscus is crucially important for the operation of capillary pumped heat transfer devices. Since more than 50% of the mass transfer by evaporation occurs on a very small region socalled thin film region it is expected that the instability will arise from this region. To explain the stability mechanism of the meniscus effectively a new method that can skillfully combine the linear stability analysis with the numerical analysis of the meniscus is proposed in this paper. Numerical analysis is executed to acquire the characteristic thickness and length of thin film region and a linear stability criteria is calculated by using these two characteristic dimensions. By use of the combination of these two analysis methods the stability mechanism of an evaporating meniscus can be clearly disclosed especially about the effect of the temperature of the meniscus thermophysical properties of the working fluid and the dimensions of the capillary tube on the stability. The effectiveness of this method can be approved by the experimental results of some published references. Key words Capillary evaporating meniscus Linear stability analysis Heat and mass transfer Numerical analysis 0 Heat Pipe LHP 50% - - Microchannel Heat Pipe MHP Loop 2012-07-10 2013-01-01 51106057 2011QN150

874 34 2 thin film region 3 10 7 W /m 2 1 adsorbed region 2-4 Burelbach 5 long-wave evolution equations S. W. Joo 6 D. Pratt 7 CPL Heat Transfer Loop Buffon 8 PIV 1 Fig. 1 Schematic of evaporation meniscus within a cylindrical capillary pore 9 1 16 R 100nm y = h x t h x y t 1 1 1 one-sided model 5 lubrication theory 1 14 1 intrinsic 9 meniscus region h

6 875 ( ) 珘 h τ = - E 珔珘 Π^ 珘 h + K -1 0 h + h - ( ) 1 3 S 珘 h 3 珘 h - 2 E珔 2 D -1 珘 h + K -3 珘 h 3 珘 h 3-1 Ma [ 珘 h + K 2 Pr [ -1 珘 h ] 2 珘 h ] 1 2 珘 h 珘 h = ΔT ΔT cr = 8 珔 Ax c γh 3 0 h /h 0 η x y Hamaker Marangoni Prandtl ΔT cr h 0 x c E 珔 = EX = kδt D = ρνh fg h0 ρ v x c ρ S = σ 0h 3 0 ρν 2 x c Π^ = 珔 A Ma = c pγδth 2 0 P ρν 2 h 0 x c νk r = μc p k k c P ν h fg σ 0 γ 1 σ = σ 0 - γt 珔 A Hamaker Hamaker A 珔 A = A /6π 1 1 2 2 3 Derjaguin 13 Wayner 14 4 5 Young-Laplace 1 2 4 3 5 Kelvin-Clapeyron 1 d σδ 3σδ'δ 2 dx 1 + δ '2 1. 5-1 + δ '2 2. 5 ΔT < 8 珔 Ax c γh 3 0 2 T w ΔT = T w - T v ΔT 2 ΔT cr = x /x c η = y /h 0 h 0 x c x y η τ ΔT cr 2 η τ E珔 E 珔 D S Π^ Ma Pr Marangoni Hamaker 7 9 1 /r 2 δ ( [ ] 3 ) - 3Aδ' δ 4 3ν = - m 3 δ δ' δ 2 ΔT m Schrage 15 T v

876 34 m = 2^σ 2 - ^σ ( ) 珚 M 2πR g ( ) 1/2 P v_equ T lv - P v 4 2 T lv 1/2 T v 1/ ^σ M珚 R g T lv T v P v P v_equ P v_equ T lv = [ ] P sat T lv exp P v_equ T lv - P sat T lv - P d + P c ρ l T lv R g /M [ ( ) ] P sat T lv = P sat_ref T sat_ref exp Mh fg 1 R g T sat_ref - 1 T lv T lv m T lv = - m h fg /k l δ + T w 5 Runge-Kutta 3 ~ 5 2 1nm 2 2 a Pratt 7 2 a 2 Fig. 2 The effect of superheat on the evaporating P d characteristic of the meniscus R = 2500nm T v = 320K 2 b 3 2 c x 3. 1 2 2 Pratt 7 x c

6 877 P d P d P d = 1 /2000P d0 3 x c 2 Fig. 4 4 h 0 Critical superheat variation with temperature of meniscus based on different h 0 Pentane R = 2500nm ΔT = 1K Fig. 3 3 Length of the thin film region with different super heat h 0 h 0_m h 0_T h 0_a T v 4 4 h 0_m 5 5 Fig. 5 The effect of meniscus temperature on the a evaporating characteristic of the thin film region Pentane R = 2500nm ΔT = 1K 4 h 0_T 5 b

878 34 25000nm ΔT = 5K h 0_a ΔT = 10K Pratt 7 Buffone 8 4 1K 3. 2 6 h 0_a 7 Fig. 7 Critical superheat variation with tube radius 0. 1 ~ 0. 2KPratt at different evaporating condition Pentane T v = 300K 10 5 3. 4 K /m 8 Pentane R = 2500nm ΔT = 1K 3. 3 7 h 0_a ΔT = 1K ΔT = 5K ΔT = 10K Buffone Buffone 8 9 6 h 0_a 9 a Fig. 6 Critical superheat variant with temperature of meniscus basing on average film thickness 9 b

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