Application of TVD scheme in numerical simulation of water droplet field

WANG Zhaoli; ZENG Tao; ZHOU Zhihong; CHEN Yu

doi:10.7527/S1000-6893.2022.27010

ACTA AERONAUTICAET ASTRONAUTICA SINICA >

2022 , Vol. 43 >Issue 12: 627010 - 627010

DOI: https://doi.org/10.7527/S1000-6893.2022.27010

Special Topic of Numerical Simulation of High Speed Vehicles in Near Space

Application of TVD scheme in numerical simulation of water droplet field

WANG Zhaoli ,
ZENG Tao ,
ZHOU Zhihong ,
CHEN Yu

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1. College of Architecture and Environment, Sichuan University, Chengdu 610065, China;
2. Yibin Industrial Technology Research Institute of Sichuan University, Yibin 644000, China

Received date: 2022-01-28

Revised date: 2022-03-07

Online published: 2022-05-19

Supported by

National Natural Science Foundation of China (12072213); National Science and Technology Major Project (J2019-III-0010-0054); National Numerical Windtunnel Project (NNW2019-JT01-023)

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Abstract

Aircraft icing endangers the safety of aviation, while numerical calculation is a major method to research icing. The iterative solving process of the water droplet field in the numerical calculation of aircraft icing tends to easily diverge due to the discontinuity in the distribution of water content and the singularity of the velocity in the Euler method. Aiming at this problem and considering the hyperbolic conservation law equation, we present five TVD schemes for the calculation of the water droplet field. The main idea is to develop a monotonic linear reconstruction function for the variables on each unit based on the first-order upwinding scheme, and the time discretization adopts the fourth-order Runge-Kutta method. The accuracy and convergence of the method are analyzed by calculation, and the calculation results of the NACA0012 airfoil, NACA23012 airfoil and three-element airfoil 30P30N show that the method is successful. It improves the spatial accuracy in solving the water droplets field using Eulerian method and provides reference for the application of TVD scheme in two-phase flow.

Key words： icing; droplet impingement; Euler method; discretion of convection; TVD scheme; flux limiter

Cite this article

WANG Zhaoli , ZENG Tao , ZHOU Zhihong , CHEN Yu . Application of TVD scheme in numerical simulation of water droplet field[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022 , 43(12) : 627010 -627010 . DOI: 10.7527/S1000-6893.2022.27010

References

[1] 桂业伟, 周志宏, 李颖晖, 等. 关于飞机结冰的多重安全边界问题[J]. 航空学报, 2017, 38(2):520734. GUI Y W, ZHOU Z H, LI Y H, et al. Multiple safety boundaries protection on aircraft icing[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(2):520734(in Chinese).
[2] 卜雪琴, 李皓, 黄平, 等. 二维机翼混合相结冰数值模拟[J]. 航空学报, 2020, 41(12):124085. BU X Q, LI H, HUANG P, et al. Numerical simulation of mixed phase icing on two-dimensional airfoil[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(12):124085(in Chinese).
[3] 杨倩, 常士楠, 袁修干. 水滴撞击特性的数值计算方法研究[J]. 航空学报, 2002, 23(2):173-176. YANG Q, CHANG S N, YUAN X G. Study on numerical method for determining the droplet trajectories[J]. Acta Aeronautica et Astronautica Sinica, 2002, 23(2):173-176(in Chinese).
[4] 易贤, 朱国林, 王开春, 等. 翼型积冰的数值模拟[J]. 空气动力学学报, 2002, 20(4):428-433. YI X, ZHU G L, WANG K C, et al. Numerically simulating of ice accretion on airfoil[J]. Acta Aerodynamica Sinica, 2002, 20(4):428-433(in Chinese).
[5] BOURGAULT Y, HABASHI W, DOMPIERRE J, et al. An Eulerian approach to supercooled droplets impingement calculations[C]//35th Aerospace Sciences Meeting and Exhibit. Reston:AIAA, 1997.
[6] BOURGAULT Y, BOUTANIOS Z, HABASHI W G. Three-dimensional eulerian approach to droplet impingement simulation using FENSAP-ICE, part 1:Model, algorithm, and validation[J]. Journal of Aircraft, 2000, 37(1):95-103.
[7] IULIANO E, BRANDI V, MINGIONE G, et al. Water impingement prediction on multi-element airfoils by means of eulerian and Lagrangian approach with viscous and inviscid air flow[C]//44th AIAA Aerospace Sciences Meeting and Exhibit. Reston:AIAA, 2006.
[8] TONG X, LUKE E A. Robust and accurate eulerian multiphase simulations of icing collection efficiency using singularity diffusion model[J]. Engineering Applications of Computational Fluid Mechanics, 2010, 4(4):483-495.
[9] 张大林, 杨曦, 昂海松. 过冷水滴撞击结冰表面的数值模拟[J]. 航空动力学报, 2003, 18(1):87-91. ZHANG D L, YANG X, ANG H S. Numerical simulation of supercooled water droplets impingement on icing surfaces[J]. Journal of Aerospace Power, 2003, 18(1):87-91(in Chinese).
[10] 杨胜华, 林贵平, 申晓斌. 三维复杂表面水滴撞击特性计算[J]. 航空动力学报, 2010, 25(2):284-290. YANG S H, LIN G P, SHEN X B. Water droplet impingement prediction for three-dimensional complex surfaces[J]. Journal of Aerospace Power, 2010, 25(2):284-290(in Chinese).
[11] 易贤, 王开春, 桂业伟, 等. 结冰面水滴收集率欧拉计算方法研究及应用[J]. 空气动力学学报, 2010, 28(5):596-601, 608. YI X, WANG K C, GUI Y W, et al. Study on Eulerian method for icing collection efficiency computation and its application[J]. Acta Aerodynamica Sinica, 2010, 28(5):596-601, 608(in Chinese).
[12] 陈希, 招启军. 考虑遮蔽区影响的旋翼三维水滴撞击特性计算新方法[J]. 航空学报, 2017, 38(6):120745. CHEN X, ZHAO Q J. New method for predicting 3-D water droplet impingement on rotor considering influence of shadow zone[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(6):120745(in Chinese).
[13] 李浩然, 段玉宇, 张宇飞, 等. 结冰模拟软件AERO-ICE中的关键数值方法[J]. 航空学报, 2021, 42(S1):726371. LI H R, DUAN Y Y, ZHANG Y F, et al. Numerical method of ice-accretion software AERO-ICE[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(S1):726371(in Chinese).
[14] 涂国华, 袁湘江, 陈陆军. 适用于超声速的一种通量限制型紧致格式[J]. 航空学报, 2004, 25(4):327-332. TU G H, YUAN X J, CHEN L J. A limited flux compact scheme suited to supersonic flows[J]. Acta Aeronautica et Astronautica Sinica, 2004, 25(4):327-332(in Chinese).
[15] 刘君, 韩芳, 魏雁昕. 应用维数分裂方法推广MUSCL和WENO格式的若干问题[J]. 航空学报, 2022,43(3):125009. LIU J, HAN F, WEI Y X. Some problem of MUSCL and WENO schemes generated by dimension-by-dimension approach[J]. Acta Aeronautica et Astronautica Sinica, 2022,43(3):125009(in Chinese).
[16] 张涵信. 无波动、无自由参数的耗散差分格式[J]. 空气动力学学报, 1988, 6(2):143-165. ZHANG H X. Non-oscillatory and non-free-parameter dissipation difference scheme[J]. Acta Aerodynamica Sinica, 1988, 6(2):143-165(in Chinese).
[17] 任伟杰, 谢文佳, 田正雨, 等. 高超声速数值激波失稳的网格依赖性[J]. 航空学报, 2021, 42(S1):726376. REN W J, XIE W J, TIAN Z Y, et al. Grid dependence of hypersonic numerical shock instability[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(S1):726376(in Chinese).
[18] 张帝. 高精度有限体积格式及新型VOF自由界面捕捉算法[D]. 北京:清华大学, 2015. ZHANG D. High resolution finite volume method and a refined VOF algorithm[D]. Beijing:Tsinghua University, 2015(in Chinese).
[19] HARTEN A. High resolution schemes for hyperbolic conservation laws[J]. Journal of Computational Physics, 1983, 49(3):357-393.
[20] SWEBY P K. High resolution schemes using flux limiters for hyperbolic conservation laws[J]. SIAM Journal on Numerical Analysis, 1984, 21(5):995-1011.
[21] VAN LEER B. Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme[J]. Journal of Computational Physics, 1974, 14(4):361-370.
[22] ROE P L. Characteristic-based schemes for the Euler equations[J]. Annual Review of Fluid Mechanics, 1986, 18:337-365.
[23] VAN LEER B. Towards the ultimate conservative difference scheme[J]. Journal of Computational Physics, 1997, 135(2):229-248.
[24] WATERSON N P, DECONINCK H. Design principles for bounded higher-order convection schemes-A unified approach[J]. Journal of Computational Physics, 2007, 224(1):182-207.
[25] MORENCY F, TEZOK F, PARASCHIVOIU I. Anti-icing system simulation using CANICE[J]. Journal of Aircraft, 1999, 36(6):999-1006.
[26] 曹广州. 迎风表面三维积冰的数学模型与计算方法研究[D]. 南京:南京航空航天大学, 2011. CAO G Z. Investigation of mathematic model and calculational methodology for 3D ice accretion on the up-wind surfaces[D]. Nanjing:Nanjing University of Aeronautics and Astronautics, 2011(in Chinese).
[27] PAPADAKIS M, RACHMAN A, WONG S C, et al. Water impingement experiments on a NACA 23012 airfoil with simulated glaze ice shapes[C]//42nd AIAA Aerospace Sciences Meeting and Exhibit. Reston:AIAA,2004.

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