NUMERICAL INVESTIGATION ON DOUBLE-LAYER POROUS PLATE OF TRANSPIRATION COOLING WITH PHASE CHANGE
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摘要: 为了提高相变发汗冷却的冷却性能, 提出不同孔隙率组合的双层多孔板结构设计代替传统的单层多孔板结构. 以液态水作为冷却剂, 使用修正后的局部热非平衡两相混合流模型, 数值研究了不同孔隙率组合的多孔板内流−固耦合传热和冷却剂流动输运特性. 数值模拟结果表明存在可以降低结构表面温度的双层多孔板设计, 并且在冷却剂流量较大、液体水相变发生在上层多孔板内时, 该新型结构相较于传统结构的表面温度降低更为明显. 与此同时, 冷却剂的注射压力被重点关注. 由于水蒸气的运动黏度远高于液体水, 研究中发现当冷却剂相变发生在多孔板内时, 冷却剂的注射压力主要取决于水蒸气所集中的上层多孔板孔隙率. 因此基于多孔介质内的渗流特性, 采用孔隙率较大的上层多孔板有助于降低结构内的水蒸气压力, 从而实现多孔板板底冷却剂注射压力的降低, 在某一孔隙率组合中冷却剂注射压力的最大降幅可以达到65%. 如果采用相反的孔隙率设计, 即下层多孔板的孔隙率较大, 虽然也可以在一定程度上降低表面温度, 但是注射压力将会数倍增加, 不利于相变发汗冷却的实际应用.Abstract: In order to improve the cooling performance of the transpiration cooling with phase change, a new structure, double-layer porous plate with different porosity combination is suggested as replacement for the conventional single-layer porous plate. Using liquid water as coolant, the modified two phase mixture model which considers local thermal non-equilibrium is adopted to study the fluid-solid coupled heat transfer and coolant flow transport characteristics in the porous plate with varied porosity combination. The simulation results reveal that there exists the structure of double-layer porous plate that can reduce the surface temperature on the hot side. Specially, the surface temperature decrease for the double-layer porous plate is more pronounced when the coolant mass flux is greater and coolant phase change occurs in the upper porous plate. At the same time, the injection pressure of coolant is taken into consideration. Because the kinematic viscosity of vapor is much higher than that of liquid water, it is found that when coolant phase change occurs in the porous plate, the coolant injection pressure mainly depends on the porosity of the upper porous plate where the vapor is gathered. Therefore, based on the seepage effect in the porous media, the upper plate with larger porosity than lower porous plate can greatly reduce the vapor pressure in the structure, so as to reduce the coolant injection pressure at the bottom of the porous plate. In a certain porosity combination, the maximum reduction of the coolant injection pressure can reach 65%. If the opposite porosity design is adopted, where the porosity of the lower porous plate is greater than that of the upper porous plate, although the surface temperature can be reduced to some extent, the injection pressure will be several times increased, which is not conducive to the practical application of transpiration cooling with phase change.
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Key words:
- transpiration cooling /
- water phase change /
- porous medium /
- thermal protection
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图 1 双层多孔板发汗冷却示意图
Figure 1. Schematic diagram of transpiration cooling with double-layers
图 2 3种不同网格下多孔介质内固体温度分布
Figure 2. Solid temperature distribution in porous plate under three different meshes
图 4 case1 ~ case4多孔板内沿y轴的温度分布
Figure 4. The temperature distributions in porous plate of case1−case4
图 5 case1, case2和 case5多孔板内沿y轴的温度分布
Figure 5. The temperature distributions in porous plate of case1, case2, and case5
图 6 不同冷却剂质量流量下case1, case2和case5的表面温度
Figure 6. The surface temperature of case1, case2 and case5 under different coolant mass flux
图 7 不同冷却剂质量流量下, case1, case2和case5的注射压力
Figure 7. The injection pressure of case1, case2 and case5 under different coolant mass flux
图 8 case1, case2和case5中多孔板沿y轴的压力分布
Figure 8. The pressure distributions in porous plate of case1, case2, and case5
表 1 双层多孔板孔隙率组合设计
Table 1. Different double-layer porous plate combinations
Case εA εB case1 0.5 0.5 case2 0.4 0.6 case3 0.3 0.7 case4 0.2 0.8 case5 0.6 0.4 
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Variables/coefficients Constitutive relationships mixture density $ \rho = \rho_{1} {{s}} + \rho_{{v}}(1-{s}) $ mixture kinetic viscosity $ v-\dfrac{1}{k_{rl} / v_{l} + k_{rv} / v_{v}} $ relative permeability $ k_{rl} = s^{3}, k_{rv} = (1-s)^{3} $ relative mobility $ \lambda_{l} = v k_{rl}/v_{l}, \lambda_{v} = v k_{rv}/v_{v} $ mixture velocity $ u = ({\rho _l}{u_l} + {\rho _v}{u_v})/\rho $ mixture enthalpy $ h_{f}-\left[\rho_{l} s h_{l} + \rho_{v}(1-s) h_{v}\right] / \rho $ mixture dynamic viscosity $ \mu-\rho v $ specific surface area $ \alpha_{sf}-6(1-\varepsilon ) / d_{p} $ advection coefficient $\gamma_h=\dfrac{\dfrac{\rho_l h_{l, {\mathrm{s a t}}}}{\mu_l} k_{r l}+\dfrac{\rho_v h_{v, \text {sat}}}{\mu_v} k_{r v}}{\dfrac{\rho_l h_{l, {\mathrm{s a t}}}}{\mu_l} s+\dfrac{\rho_v h_{v, \text {sat}}}{\mu_v}(1-s)} $ convective heat transfer coefficient $h_{s i}=\left(\dfrac{k_i}{d_P}\right)\left(2.0+1.1 {Pr}_i^{0.33} {Re}^{0.6}\right), i=l, v $ solid-fluid heat transfer in pores $q_{{sf}}=\left\{\begin{aligned}&h_{sl} \alpha_{s f}\left(T_s-T_l\right), \qquad \text { in liquid region } \\&q_{{\mathrm{boil}}}+(1-s) h_{sv} \alpha_{sf}\left(T_s-T_{{\mathrm{s a t}}}\right), \qquad \text { in two-phase region } \\&h_{sv} \alpha_{sf}\left(T_s-T_v\right), \qquad \text { in vapor region }\end{aligned}\right. $ heat transfer of nucleate boiling $q_{{\mathrm{b o i l}}}=s \alpha_{s f} \mu h_{f g}\left[\dfrac{g\left(\rho_l-\rho_v\right)}{\sigma}\right]^{0.5}\left[\dfrac{c_{p, l}\left(T_s-T_{{\mathrm{s a t}}}\right)}{c_{s, f} h_{f g} {Pr}_l}\right]^3 $ mixture pressure $\nabla P=\lambda \nabla P_l+(1-\lambda) \nabla P_v $ capillary pressure $P_v-P_l=P_c=\left(\dfrac{\varepsilon}{K}\right)^{1 / 2} \sigma J(s) $ capillary pressure function $J(s)=1.417(1-s)-2.120(1-s)^2+1.26 $ capillary diffusion coefficient $D(s)=\dfrac{K}{v(s)} \lambda(1-\lambda)\left(\dfrac{\varepsilon}{K}\right)^{0.5} \sigma\left[-J'(s)\right] $ diffusion coefficient $\varGamma_h= \left\{\begin{aligned}&\varepsilon k_l, \qquad T_M \leqslant T_{{\mathrm{s a t}}} \\&c_{p, l} D(s) \frac{{\mathrm{d}} s}{{\mathrm{d}} \lambda}, \qquad T_{{\mathrm{s a t}}} < T_M < T_{{\mathrm{s a t}}}+\frac{h_{f g}}{c_{p, l}} \\&\varepsilon k_v \frac{c_{p, l}}{c_{p, v}}, \qquad T_M \geqslant T_{{\mathrm{s a t}}}+\frac{h_{f g}}{c_{p, l}}\end{aligned}\right. $
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Property Liquid Vapor density/(kg·m−3) 960 ideal gas law specific heat/(103 J·kg−1·K−1) 4.21 2.03 conductivity/
(10−3 W·m−1·K−1)680 −21.994433 + 0.11842T viscosity/(10−3 kg·m−1·s−1) 24.141 × 10247.8/(T−140) −2.77567 + 0.04035T Prandtl number $\boldsymbol{u}_l c_{p, l} / k_l $ 0.984
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A1 符号表
A1. Table of symbols
Symbol Representation T temperature, K P pressure, Pa u velocity, m/s cp specific heat, J/(kg·k) dp average particle diameter, m h specific enthalpy, J/kg hfg latent heat of evaporation, J/kg s liquid saturation Pr Prandtl number Re Reynolds number ρ density, kg/m3 ε porosity ν kinematic viscosity, m2/s μ dynamic viscosity, N·s/m2 λ relative mobility σ interfacial tension, N/m L porous plate thickness, mm subscript l, v liquid, vapor f fluid s solid eff effective sat saturated A upper porous plate B lower porous plate
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