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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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 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. $ 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 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 -
[1] 胥蕊娜, 李晓阳, 廖致远等. 航天飞行器热防护相变发汗冷却研究进展. 清华大学学报(自然科学版), 2021, 61(12): 1341-1352 (Xu Ruina, Li Xiaoyang, Liao Zhiyuan, et al. Research progress in transpiration cooling with phase change. Journal of Tsinghua University (Science and Technology), 2021, 61(12): 1341-1352 (in Chinese) doi: 10.16511/j.cnki.qhdxxb.2020.25.044 Xu Ruina, Li Xiaoyang, Liao Zhiyuan, et al . Research progress in transpiration cooling with phase change. Journal of Tsinghua University (Science and Technology),2021 ,61 (12 ):1341 -1352 (in Chinese) doi: 10.16511/j.cnki.qhdxxb.2020.25.044[2] 栾芸, 贺菲, 王建华. 临近空间飞行器发汗冷却研究进展. 推进技术, 2023, 44(1): 6-20 (Luan Yun, He Fei, Wang Jianhua. Review on transpiration cooling for near-space aircraft. Journal of Propulsion Technology, 2023, 44(1): 6-20 (in Chinese) doi: 10.13675/j.cnki.tjjs.22010020 Luan Yun, He Fei, Wang Jianhua . Review on transpiration cooling for near-space aircraft. Journal of Propulsion Technology,2023 ,44 (1 ):6 -20 (in Chinese) doi: 10.13675/j.cnki.tjjs.22010020[3] Uyanna O, Najafi H. Thermal protection systems for space vehicles: A review on technology development, current challenges and future prospects. Acta Astronautica, 2020, 176: 341-356 doi: 10.1016/j.actaastro.2020.06.047 [4] Van Foreest A, Sippel M, Gülhan A, et al. Transpiration cooling using liquid water. Journal of Thermophysics and Heat Transfer, 2009, 23(4): 693-702 [5] Zhao L, Wang J, Ma J, et al. An experimental investigation on transpiration cooling under supersonic condition using a nose cone model. International Journal of Thermal Sciences, 2014, 84: 207-213 [6] Shen L, Wang J, Dong W, et al. An experimental investigation on transpiration cooling with phase change under supersonic condition. Applied Thermal Engineering. 2016, 105: 549-556 [7] 廖致远, 祝银海, 黄干等. 超声速主流平板相变发汗冷却实验研究. 推进技术, 2019, 40(5): 1058-1064 (Liao Zhiyuan, Zhu Yinhai, Huang Gan, et al. Experimental investigation of transpiration cooling on a porous plate with phase change in supersonic flow tunnel. Journal of Propulsion Technology, 2019, 40(5): 1058-1064 (in Chinese)Liao Zhiyuan, Zhu Yinhai, Huang Gan, et al. Experimental investigation of transpiration cooling on a porous plate with phase change in supersonic flow tunnel. Journal of Propulsion Technology, 2019, 40(5): 1058-1064 (in Chinese) [8] Huang Z, Zhu Y, Xiong Y, et al. Investigation of transpiration cooling for sintered metal porous struts in supersonic flow. Applied Thermal Engineering, 2014, 70(1): 240-249 doi: 10.1016/j.applthermaleng.2014.02.076 [9] 时骏祥. 发散冷却基础问题的理论研究. [博士论文]. 合肥: 中国科学技术大学, 2009 (Shi Junxiang. Theoretic investigation on basic problems of transpiration cooling. [PhD Thesis]. Hefei: University of Science and Technology of China, 2009 (in Chinese)Shi Junxiang. Theoretic investigation on basic problems of transpiration cooling. [PhD Thesis]. Hefei: University of Science and Technology of China, 2009 (in Chinese) [10] Zhang B, Huang H, Lu X, et al. Experimental investigation on transpiration cooling for porous ceramic with liquid water. Acta Astronautica, 2020, 167: 117-121 doi: 10.1016/j.actaastro.2019.11.009 [11] Zhang B, Huang H, Huang J, et al. An experimental investigation on performance of transpiration cooling with liquid water through C/SiC porous ceramic. Applied Thermal Engineering, 2020, 178: 115-526 [12] Cheng Z, Li X, Xu R, et al. Investigations on porous media customized by triply periodic minimal surface: Heat transfer correlations and strength performance. International Communications in Heat and Mass Transfer, 2023, 205: 123862 doi: 10.1016/j.ijheatmasstransfer.2023.123862 [13] Cheng Z, Xu R, Jiang P. Transpiration cooling with phase change by functionally graded porous media. International Journal of Heat and Mass Transfer, 2023, 205: 123-862 [14] Huang G, Zhu Y, Ouyang X, et al. Experimental investigation of transpiration cooling with phase change for sintered porous plates. International Journal of Heat and Mass Transfer, 2017, 114: 1201-1213 [15] 栾芸, 贺菲, 王建华. 飞行器鼻锥凹腔-发散组合冷却数值模拟. 航空学报, 2021, 42(2): 9 (Luan Yun, He Fei, Wang Jianhua. Transpiration cooling of nose-cone with forward-facing cavity: Numerical simulation. Acta Aeronautica et Astronautica Sinica, 2021, 42(2): 9 (in Chinese) Luan Yun, He Fei, Wang Jianhua . Transpiration cooling of nose-cone with forward-facing cavity: Numerical simulation. Acta Aeronautica et Astronautica Sinica,2021 ,42 (2 ):9 (in Chinese)[16] Wu N, Wang J, Dong W, et al. An experimental investigation on combined sublimation and transpiration cooling for sintered porous plates. International Journal of Heat and Mass Transfer, 2018, 116: 685-693 [17] Jiang P, Huang G, Zhu Y, et al. Experimental investigation of combined transpiration and film cooling for sintered metal porous struts. International Journal of Heat and Mass Transfer, 2017, 108: 232-243 [18] 丁锐. 发散冷却在高超声速飞行器上的应用可行性研究. [博士论文]. 合肥: 中国科学技术大学, 2020 (Ding Rui. Investigations on the application feasibility of transpiration cooling on hypersonic vehicles. [PhD Thesis]. Hefei: University of Science and Technology of China, 2020 (in Chinese)Ding Rui. Investigations on the application feasibility of transpiration cooling on hypersonic vehicles. [PhD Thesis]. Hefei: University of Science and Technology of China, 2020 (in Chinese) [19] Shen B, Liu W. Insulating and absorbing heat of transpiration in a combinational opposing jet and platelet transpiration blunt body for hypersonic vehicle. International Journal of Heat and Mass Transfer, 2019, 138: 314-325 [20] Shen B, Yin L, Liu H, et al. Thermal protection characteristics for a combinational opposing jet and platelet transpiration cooling nose-tip. Acta Astronautica, 2019, 155: 143-152 [21] 贺菲. 发散冷却基础问题的理论和实验研究. [博士论文]. 合肥: 中国科学技术大学, 2014 (He Fei. Theoretical and experimental investigations on basic problems of transpiration cooling. [PhD Thesis]. Hefei: University of Science and Technology of China, 2014 (in Chinese)He Fei. Theoretical and experimental investigations on basic problems of transpiration cooling. [PhD Thesis]. Hefei: University of Science and Technology of China, 2014 (in Chinese) [22] Reimer T, Esser B, Gülhan A. Arc jet testing of CMC samples with transpiration cooling//44th AIAA Thermophysics Conference, 2013: 2904 [23] Reimer T, Kuhn M, Gülhan A, et al. Transpiration cooling tests of porous CMC in hypersonic flow//17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2011: 2251 [24] Su H, Wang J, He H, et al. Numerical investigation on transpiration cooling with coolant phase change under hypersonic conditions. International Journal of Heat and Mass Transfer, 2019, 129: 480-490 [25] Xiao X, Zhao G, Zhou W. Numerical investigation of transpiration cooling for porous nose cone with liquid coolant. International Journal of Heat and Mass Transfer, 2018, 121: 1297-1306 [26] Hu H, Jiang P, Ouyang X, et al. A modified energy equation model for flow boiling in porous media and its application to transpiration cooling at low pressures with transient effect. International Journal of Heat and Mass Transfer, 2020, 158: 119-745 [27] Chen Y, Shen D, Dong L, et al. Numerical investigation of transient phase-change transpiration cooling based on variable properties of coolant. Applied Thermal Engineering, 2021, 184: 116204 [28] Huang G, Liao Z. Self-pumping transpiration cooling with a protective porous armor. Applied Thermal Engineering, 2019, 164: 114485 [29] Huang G, Zhu Y. Biomimetic self-pumping transpiration cooling for additive manufactured porous module with tree-like micro-channel. International Journal of Heat and Mass Transfer, 2018, 131: 403-410 [30] Wang C, Beckermann C. A two-phase mixture model of liquid-gas flow and heat transfer in capillary porous media—I. Formulation. International Journal of Heat and Mass Transfer, 1993, 36: 2747-2758 [31] Wang C. A fixed-grid numerical algorithm for two-phase flow and heat transfer in porous media. Numerical Heat Transfer Part B-Fundamentals, 1997, 32: 85-105 [32] Wang J, Shi J. Discussion of boundary conditions of transpiration cooling problems using analytical solution of LTNE model. Journal of Heat Transfer, 2008, 130(1): 014504 doi: 10.1115/1.2780188 -