DIRECT NUMERICAL SIMULATION OF SINGLE ABLATIVE PARTICLE DYNAMICS IN NEAR-WALL COUETTE FLOW UNDER AERODYNAMIC LOAD
-
摘要: 高超声速飞行器防热材料在气动载荷下发生机械剥蚀, 进而影响绕流流态、气动性能、热载荷等, 相关颗粒剥离动力学是高超声速热防护系统设计及防热材料体系评价中的共性基础性科学问题. 研究通过近壁流动量纲分析, 将烧蚀颗粒剥离过程模化为单个圆球惯性烧蚀颗粒在Couette流动中的动力学问题, 并采用颗粒解析的直接数值模拟方法开展数值研究, 获得了烧蚀颗粒关键特征参量对颗粒输运动力学的影响规律. 研究发现, 随着颗粒/流体密度比
$ {\rho _r} $ 越大, 颗粒惯性St越大, 则颗粒水平和法向输运速度均减小; 随着颗粒粒径${d_{\text{p}}}$ 越大, 颗粒惯性St越大, 则颗粒水平输运速度减小, 但是, 法向输运速度和位移均因大颗粒受到更大的Saffman升力而增大. 此外, 烧蚀颗粒法向位移远小于水平位移, 颗粒以水平输运为主. 本研究最终建立了颗粒启动速度归一化表达式, 发现归一化颗粒启动速度是颗粒和流体惯性的函数, 即颗粒水平输运速度等于流体微团或中性浮力颗粒的速度减去惯性修正项. 研究结果为烧蚀颗粒调制边界层作用机理研究提供支撑.Abstract: When hypersonic vehicles reenter the atmosphere, the surface thermal protection materials will ablate under the action of high temperature airflow. In the process, the ablative particles will entrance the high temperature airflow and affect boundary-layer transition and turbulence characteristics downstream. Those phenomena will also happen in an arc-heated wind tunnel when conducting material thermal response experiments. Therefore, it is a significant basic scientific problem to study the transport behavior of inertial ablative particles under aerodynamic load. In this article, we analyzed the flow condition and particle exfoliation process very near a hypersonic vehicle wall with dimensional theory. After a series of reasonable assumptions and simplifications, we modelled the ablative particle exfoliation and transport process as one spherical inertial particle in Couette flow and adopted the particle resolved-direct numerical simulation (PR-DNS) method to study it. As a result, the particle exfoliation and transport characteristics were revealed and a normalized expression of particle start-up velocity was obtained, which would provide theoretical basis for accurate prediction of particle mass loss in the future. The research findings show that as the particle fluid density ratio$ {\rho _r} $ increases, the particle inertia St increases, and the horizontal and normal velocities of particle decrease. The larger the particle diameter is, the larger the particle inertia St is, and the horizontal velocity of the particle decreases. However, the normal velocity and displacement of the larger particle are increased. The reason is maybe larger particles receive larger Saffman lift force. Besides, the normal displacement of ablative particles is much smaller than the horizontal displacement, so the particles are mainly transported horizontally. In order to find the unified law underlying all the regularities, we defined the start-up velocity and found that the normalized particle start-up velocity is a function of the particle and fluid inertia, i.e., the particle horizontal transport velocity is the velocity of fluid or neutral buoyant particle minus the inertia correction term.-
Key words:
- ablative particle /
- aerodynamic load /
- PR-DNS /
- transport /
- start-up velocity
-
图 1 纤维增强防热材料在高温气流作用下的机械剥落示意图
Figure 1. Schematic diagram of mechanical spalling of fiber reinforced ablative composite materials under high temperature air flow
图 3 不同压力梯度Falkner-Skan流动速度分布图
Figure 3. Velocity profiles of Falkner-Skan flow at different half cone angles
图 5 Couette流中单个中性颗粒法向速度随颗粒到壁面位移的变化
Figure 5. The normal velocity of a single neutral particle in Couette flow varies with the particle displacement to the wall
图 6 网格无关性验证算例(ρr = 10000, rp = 0.25,
$ OX \times OY \times OZ{\text{ = 5}}{r_{\text{p}}} \times {\text{5}}{r_{\text{p}}} \times 2.{\text{5}}{r_{\text{p}}} $ )Figure 6. Grid independent verification(ρr = 10000, rp = 0.25,
$ OX \times OY \times OZ{\text{ = 5}}{r_{\text{p}}} \times {\text{5}}{r_{\text{p}}} \times 2.{\text{5}}{r_{\text{p}}} $ )
图 7 不同密度比颗粒输运轨迹 (dp/δ = 1)
Figure 7. Particle transport trajectories with different density ratios (dp/δ = 1)
图 8 不同密度比颗粒水平速度沿流向变化规律 (dp/δ = 1)
Figure 8. The horizontal velocity of particles with different density ratios varies along the flow direction (dp/δ = 1)
图 9 不同密度比颗粒水平滑移速度沿流向变化规律 (dp/δ = 1)
Figure 9. The horizontal slip velocity of particles with different density ratios varies along the flow direction (dp/δ = 1)
图 10 不同密度比颗粒法向速度沿流向变化规律(dp/δ = 1)
Figure 10. Normal velocity of particles with different density ratios varies along the flow direction (dp/δ = 1)
图 11 不同密度比颗粒法向位移随时间变化规律(dp/δ = 1)
Figure 11. The normal displacement of particles with different density ratios varies with time (dp/δ = 1)
图 12 不同直径颗粒水平速度沿流向变化规律(
$ {\rho _r}{\text{ = }}10\;000 $ )Figure 12. The horizontal velocity of particles with different diameters varies along the flow direction (
$ {\rho _r}{\text{ = }}10\;000 $ )
图 13 不同直径颗粒水平滑移速度沿流向变化规律(
${\rho _r}{\text{ = }}10\;000$ )Figure 13. The horizontal slip velocity of particles with different diameters varies along the flow direction (
$ {\rho _r}{\text{ = }}10\;000 $ )
图 14 不同直径颗粒法向速度沿流向变化规律(
$ {\rho _r}{\text{ = }}10\;000 $ )Figure 14. The normal velocity of particles with different diameters varies along the flow direction (
$ {\rho _r}{\text{ = }}10\;000 $ )
图 15 不同直径颗粒的运动轨迹 (
$ {\rho _r}{\text{ = }}10\;000 $ )Figure 15. Trajectories of particles of different diameters (
$ {\rho _r}{\text{ = }}10\;000 $ )
图 17 不同密度比颗粒的非定常归一化启动速度随颗粒雷诺数变化规律
Figure 17. Dimensionless unsteady start-up velocity of particles along the particle Reynolds number for different density ratios
表 1 激波前后来流参数范围
Table 1. Flow parameters beside the shock
Before shock After shock density/(g·m−3) $ \rho _1^* $ 18 $ \rho _2^* $ O (0.1) temperature/K $ T_1^* $ 226.5 $ T_2^* $ O (103) inflow velocity/(m·s−1) $ U_1^* $ 6034 $ U_2^* $ O (103) coefficient of kinematic viscosity/(m2·s−1) $ \nu _1^* $ 8.3 × 10−4 $ \nu _2^* $ O (10−4) 
下载: 导出CSV
表 2 数值计算参数设置
Table 2. Numerical calculation parameters settings
Dimensional
parameters
(superscript *)Reference quantity
(subscript ∞)Dimensionless
parametersDimensionless values validation numerical experiment shear rate ${B^*}$ ${B_\infty }$ $ B = {{{B^*}} \mathord{\left/ {\vphantom {{{B^*}} {{B_\infty }}}} \right. } {{B_\infty }}} $ 0.5 1 fluid density $ \rho _{\text{f}}^{\text{*}} $ $ \rho _\infty ^{} $ $ \rho _{\text{f}}^{}{\text{ = }}{{\rho _{\text{f}}^{\text{*}}} \mathord{\left/ {\vphantom {{\rho _{\text{f}}^{\text{*}}} {\rho _\infty ^{}}}} \right. } {\rho _\infty ^{}}} $ 1 1 particle density $ \rho _{\text{p}}^{\text{*}} $ $ \rho _\infty ^{} $ $ \rho _{\text{p}}^{}{\text{ = }}{{\rho _{\text{p}}^{\text{*}}} \mathord{\left/ {\vphantom {{\rho _{\text{p}}^{\text{*}}} {\rho _\infty ^{}}}} \right. } {\rho _\infty ^{}}} $ 1 10000
20000
30000coefficient of kinematic viscosity $ {\nu ^{\text{*}}} $ $ {\nu _\infty } $ $ \nu {\text{ = }}{{{\nu ^{\text{*}}}} \mathord{\left/ {\vphantom {{{\nu ^{\text{*}}}} {{\nu _\infty }}}} \right. } {{\nu _\infty }}} $ 1 1 characteristic length $ {\delta ^{\text{*}}} $ $ {\delta _\infty }{\text{ = }}\sqrt {{\nu _\infty }{\text{/}}{B_\infty }} $ $ \delta {\text{ = }}\sqrt {\nu {\text{/}}B} $ $\sqrt 2 $ 1 characteristic velocity ${U^*}$ ${U_\infty } = \sqrt {{B_\infty }{\nu _\infty }} $ $U = \sqrt {B\nu } $ $\sqrt {0.5} $ 1 characteristic time ${t^*}$ ${t_\infty } = {{{\delta _\infty }} \mathord{\left/ {\vphantom {{{\delta _\infty }} {{U_\infty }}}} \right. } {{U_\infty }}}$ $t = {\delta \mathord{\left/ {\vphantom {\delta U}} \right. } U}$ 2 1 particle diameter $d_{_{\text{p}}}^*$ $ {\delta _\infty }{\text{ = }}\sqrt {{\nu _\infty }{\text{/}}{B_\infty }} $ ${{{{d_{\text{p}}} = d_{\text{p}}^*} \mathord{\left/ {\vphantom {{{d_{\text{p}}} = d_{\text{p}}^*} \delta }} \right. } \delta }_\infty }$ 2 0.5, 0.75, 1, 1.5, 2, 4, 6, 8, 10, 12, 14
下载: 导出CSV
-
[1] Zhang S, Li X, Zuo J, et al. Research progress on active thermal protection for hypersonic vehicles. Progress in Aerospace Sciences, 2020, 119: 100646 doi: 10.1016/j.paerosci.2020.100646 [2] 韩杰才, 张杰, 杜善义. 细编穿刺碳/碳复合材料超高温氧化机理研究. 航空学报, 1996, 17(5): 577-581 (Han Jiecai, Zhang Jie, Du Shanyi. Oxidation behavior of 3 D fine weaver pierced carbon/carbon composites at ultra-high temperatures. Acta Aeronautica Et Ast Ronautica Sinica, 1996, 17(5): 577-581 (in Chinese) doi: 10.3321/j.issn:1000-6893.1996.05.014Han Jiecai, Zhang Jie, Du Shanyi. Oxidation Behavior of 3 D fine weaver pierced carbon/carbon composites at ultra-high temperatures. Acta Aeronautica Et Ast Ronautica Sinica, 1996, 17(5): 577-581(in Chinese)) doi: 10.3321/j.issn:1000-6893.1996.05.014 [3] Barrios-Lobelle A, Davuluri R, Fu R, et al. Surface oxidation of carbon/carbon composites in hypersonic environments. AIAA Scitech 2021 Forum, 2021: 1173 [4] Wang Z, Wang J, Song H, et al. Laser ablation behavior of C/SiC composites subjected to transverse hypersonic airflow. Corrosion Science, 2021, 183: 109345 doi: 10.1016/j.corsci.2021.109345 [5] 陈卫, 伍越, 黄祯君等. 基于TDLAS的电弧风洞流场Cu组分监测. 航空学报, 2019, 40(8): 96-103Chen Wei, Wu Yue, Huang Zhenjun, et al. Monitoring copper species in flow of arc-heated wind tunnel based on TDLAS. Acta Aeronautica Et Ast Ronautica Sinica, 2019, 40(8): 96-103 (in Chinese)) [6] Dong Y, Pan B. In-situ 3D shape and recession measurements of ablative materials in an arc-heated wind tunnel by UV stereo-digital image correlation. Optics and Lasers in Engineering, 2019, 116: 75-81 doi: 10.1016/j.optlaseng.2018.10.022 [7] Li W, Huang H, Tian Y, et al. Nonlinear analysis on thermal behavior of charring materials with surface ablation. International Journal of Heat and Mass Transfer, 2015, 84: 245-252 doi: 10.1016/j.ijheatmasstransfer.2015.01.004 [8] Mortensen CH, Zhong X. Real-gas and surface-ablation effects on hypersonic boundary-layer instability over a blunt cone. AIAA Journal, 2016, 54(3): 980-998 doi: 10.2514/1.J054404 [9] 国义军, 代光月, 桂业伟等. 碳基材料氧化烧蚀的双平台理论和反应控制机理. 空气动力学学报, 2014, 32(6): 755-760 (Guo Yijun, Dai Guangyue, Gui Yewei, et al. A dual platform theory for carbon-based material oxidation with reaction-diffusion rate controlled kinetics. ACTA Aerodynamica Sinica, 2014, 32(6): 755-760 (in Chinese)Guo Yijun, Dai Guangyue, Gui Yewei, et al. A dual platform theory for carbon-based material oxidation with reaction-diffusion rate controlled kinetics. A dual platform theory for carbon-based material oxidation with reaction-diffusion rate controlled kinetics. ACTA Aerodynamica Sinica, 2014, 32(6): 755-760(in Chinese)) [10] Bacik KA, Canizares P, Colm-cille PC, et al. Dynamics of migrating sand dunes interacting with obstacles. Physical Review Fluids, 2021, 6(10): 104308 doi: 10.1103/PhysRevFluids.6.104308 [11] Alvarez CA, Franklin EM. Force distribution within a barchan dune. Physics of Fluids, 2021, 33(1): 013313 doi: 10.1063/5.0033964 [12] D’Alessandro G, Hantsis Z, Marchioli C, et al. Accuracy of bed-load transport models in eddy-resolving simulations. International Journal of Multiphase Flow, 2021, 141: 103676 doi: 10.1016/j.ijmultiphaseflow.2021.103676 [13] Fonias EN, Grigoriadis DGE. Large eddy simulation of particle-laden flow over dunes. European Journal of Mechanics-B/Fluids, 2022, 91: 38-51 doi: 10.1016/j.euromechflu.2021.09.007 [14] Balachandar S, Eaton JK. Turbulent dispersed multiphase flow. Annual Review of Fluid Mechanics, 2010, 42: 111-133 doi: 10.1146/annurev.fluid.010908.165243 [15] Yu Z, Shao X. A direct-forcing fictitious domain method for particulate flows. Journal of Computational Physics, 2007, 227(1): 292-314 doi: 10.1016/j.jcp.2007.07.027 [16] Cox RG, Brenner H. The slow motion of a sphere through a viscous fluid towards a plane surface—II Small gap widths, including inertial effects. Chemical Engineering Science, 1967, 22(12): 1753-1777 doi: 10.1016/0009-2509(67)80208-2 [17] 尹健, 张红波, 熊翔. C/C复合材料烧蚀性能的研究进展. 粉末冶金材料科学与工程, 2004, 9(1): 54-59 (Yi Jian, Zhang Hongbo, Xiong Xiang. Research and development of ablative performance of C/C composites. Materials Science and Engineering of Powder Metallurgy, 2004, 9(1): 54-59 (in Chinese) doi: 10.3969/j.issn.1673-0224.2004.01.009Yi Jian, Zhang Hongbo, Xiong Xiang. Research and development of ablative performance of C/C composites. Materials Science and Engineering of Powder Metallurgy, 2004, 9(1): 54-59(in Chinese)) doi: 10.3969/j.issn.1673-0224.2004.01.009 [18] 俞继军, 马志强, 姜贵庆等. C/C复合材料烧蚀形貌测量及烧蚀机理分析. 宇航材料工艺, 2003, 1(1): 36-39 (Yu Jijun, Ma Zhiqiang, Jiang Guiqing, et al. Pattern surface measure and ablation analysis for C/C composite material. Aerospace Materials & Technology, 2003, 1(1): 36-39 (in Chinese) doi: 10.3969/j.issn.1007-2330.2003.01.009Yu Jijun, Ma Zhiqiang, Jiang Guiqing, et al. Pattern surface measure and ablation analysis for C/C composite material. Aerospace Materials & Technology, 2003, 1: 36-39(in Chinese)) doi: 10.3969/j.issn.1007-2330.2003.01.009 [19] Zhang YL, Li HJ, Yao XY, et al. Oxidation protection of C/SiC coated carbon/carbon composites with Si-Mo coating at high temperature. Corrosion Science, 2011, 53(6): 2075-2079 doi: 10.1016/j.corsci.2011.02.024 [20] Huang HM, Huang Wu LZ, Du SY, et al. Thermochemical ablation of spherical cone during re-entry. Journal of Harbin Institute of Technology, 2001, 18(1): 18-22 [21] 任金翠. 化学气相沉积HfC纳米线增韧HfC基抗烧蚀涂层研究. [博士论文]. 西安: 西北工业大学, 2018Ren Cuiping. HfC nanowire-toughened HfC-based ablation resistance coatings synthesized by chemical vapor deposition. [PhD Thesis]. Xi’an: Northwestern Polytechnical University, 2018 (in Chinese)) [22] 丁杰. 耐高温抗烧蚀无机颗粒改性碳/酚醛复合材料的制备与性能研究. [博士论文]. 武汉: 武汉理工大学, 2016Ding Jie. Preparation and performance of heat-resistant and ablation-resist inorganic particles modified carbon/phenolic composites. [PhD Thesis]. Wuhan: Wuhan University of Technology, 2016 (in Chinese)) [23] Prata KS, Schwartzentruber TE, Minton TK. Air-carbon ablation model for hypersonic flight from molecular-beam data. AIAA Journal, 2022, 60(2): 627-640 doi: 10.2514/1.J060516 [24] Balaji R, Jeyan JVML, Singh VK. Review on influence of radiating and aerodynamic shock at hypersonic vehicle. Journal of Physics: Conference Series, 2020, 1473(1): 012004 doi: 10.1088/1742-6596/1473/1/012004 [25] Carmichael R. Properties of the US standard atmosphere 1976//The US Standard Atmosphere, 2014 [26] 吴望一. 流体力学. 北京: 北京大学出版社, 1983Wu Wangyi. Fluid Mechanics. Beijing: Peking University Press, 1983 (in Chinese) [27] Mehrabadi M, Horwitz JAK, Subramaniam S, et al. A direct comparison of particle-resolved and point-particle methods in decaying turbulence. Journal of Fluid Mechanics, 2018, 850: 336-369 doi: 10.1017/jfm.2018.442 [28] Jin G, Wang Y, Zhang J, et al. Turbulent clustering of point particles and finite-size particles in isotropic turbulent flows. Industrial & Engineering Chemistry Research, 2013, 52(33): 11294-11301 [29] Glowinski R, Pan TW, Periaux J. A fictitious domain method for Dirichlet problem and applications. Computer Methods in Applied Mechanics and Engineering, 1994, 111(3-4): 283-303 doi: 10.1016/0045-7825(94)90135-X [30] Yu ZS, Shao XM, Anthony W. A fictitious domain method for particulate flows. Journal of Computational Physics. 2007, 227: 292-314 [31] Vasseur P, Cox RG. The lateral migration of a spherical particle in two-dimensional shear flows. Journal of Fluid Mechanics, 1976, 78(2): 385-413 doi: 10.1017/S0022112076002498 [32] Ho BP, Leal LG. Inertial migration of rigid spheres in two dimensional unidirectional flows. Journal of Fluid Mechanics, 1974, 65(2): 365-400 [33] Wang GQ. Modulation of wall-bounded turbulent flows by large particles: effect of concentration, inertia, and shape. [PhD Thesis]. Institut de Mécanique des Fluides de Toulouse, 2017 [34] Saffman PG. The lift on a small sphere in a slow shear flow. Journal of Fluid Mechanics, 1965, 22: 385-400 [35] Crowe C, Schwarzkopf J, Sommerfeld M, et al. Multiphase Flows with Droplets and Particles. CRC Press of Taylor & Francis Group, 2011 [36] Legendre D, Magnaudet J. The lift force on a spherical bubble in a viscous linear shear flow. Journal of Fluid Mechanics, 1998, 368: 81-126 doi: 10.1017/S0022112098001621 [37] Auton TR, Hunt JCR, Prud'Homme M. The force exerted on a body in inviscid unsteady non-uniform rotational flow. Journal of Fluid Mechanics, 1988, 197: 241-257 doi: 10.1017/S0022112088003246 [38] Bagchi P, Balachandar S. Inertial and viscous forces on a rigid sphere in straining flows at moderate Reynolds numbers. Journal of Fluid Mechanics, 2003, 481: 105-148 doi: 10.1017/S002211200300380X [39] Magnaudet J, Abbas M. Near-wall forces on a neutrally buoyant spherical particle in an axisymmetric stagnation-point flow. Journal of Fluid Mechanics, 2021, 914: A18 doi: 10.1017/jfm.2020.398 [40] Magnaudet J. Small inertial effects on a spherical bubble, drop or particle moving near a wall in a time-dependent linear flow. Journal of Fluid Mechanics, 2003, 485: 115-142 doi: 10.1017/S0022112003004464 -
下载:
点击查看大图
计量
- 文章访问数: 433
- HTML全文浏览量: 148
- PDF下载量: 92
- 被引次数: 0
