正冲击波后固壁表面颗粒的上升运动

doi:10.19596/j.cnki.1001-246x.8242

摘要/Abstract

摘要：

为揭示固壁表面颗粒的冲击波夹卷本质，模拟垂直于固壁表面的正冲击波后单个颗粒的上升运动。假定颗粒初始时刻处于气载状态（因波的反射或碰撞离开壁面），受Saffman升力、气动阻力和重力作用。模型方程为波后定常气流边界层方程和颗粒运动常微分方程，分别用单参数法和四阶龙格库塔法求解。计算颗粒速度与轨迹表明：颗粒的冲击波卷扬动力，源于边界层内强剪切流提供的Saffman力；在所考察的冲击波强度和颗粒尺寸范围内，颗粒的上升高度不依赖于冲击波强度；上升高度按颗粒尺寸变化，即尺寸越大，高度越大。比较分析单颗粒和颗粒层的结果，认为实验中颗粒云内大尺寸颗粒少的原因是由于这些颗粒不易从颗粒层中逸出。部分计算结果与实验结果较为符合，验证了所建模型与假设的合理性。

关键词: 冲击波, 颗粒, 边界层, Saffman力

Abstract:

To reveal shock wave entrainment of particles on a wall, simulation is carried out for raising of single particle on a wall behind a shock wave perpendicular to the wall. The particle is assumed air-born(depart from the wall immediately) at initial time, and is acted by gravity, gas resistance, and Saffman force. The model equation is a combination of boundary layer equations of gases behind shock wave and ordinary differential equations describing movement of the particle. A single parameter method and a 4-order Rung-Kutta method are employed to solve boundary layer equations and particle movement equations, respectively. Calculated particle velocities and their tracks show that the basic dynamic of particle entraining is from Saffman force provided by strong shear flows in boundary layer. The raising height of particle is independent of intensity of the shock wave. It changes with size of the particle. Calculated results agree with experimental results in references. It validates the model and the assumptions.

Key words: shock wave, particle, boundary layer, Saffman force

中图分类号:

O359

薛社生, 李守先. 正冲击波后固壁表面颗粒的上升运动[J]. 计算物理, 2021, 38(3): 280-288.

Shesheng XUE, Shouxian LI. Raising of Particles on a Wall Behind a Normal Shock Wave Perpendicular to the Wall[J]. Chinese Journal of Computational Physics, 2021, 38(3): 280-288.

图/表 12

图1 冲击波后边界层流动

Fig.1 Boundary layer flows behind a shock wave

表1 正冲击波后气体参数

Table 1 Parameters of gas behind normal shock waves

Ma	U_s/(m·s^-1)	ρ/(kg·m^-3)	u/(m·s^-1)	T/K	p/MPa
1.15	380.65	1.619	77.35	299.45	0.139 0
1.20	397.20	1.73	101.13	308.00	0.152 8
1.30	430.30	1.995	146.00	325.00	0.182 3
1.80	595.80	3.04	343.20	418.24	0.364 9
2.20	728.20	3.80	481.40	507.07	0.553 5
2.60	860.60	4.45	611.07	611.25	0.779 7
2.97	983.07	4.93	726.35	722.00	1.022 5
3.00	993.00	4.97	735.60	731.50	1.043 7
5.00	1 655.00	6.45	1 324.0	1 583.80	2.929 0

图2 计算网格

Fig.2 Computational mesh

图3 气流的速度分布

Fig.3 Vector of gas velocity

图4 气流水平速度的横向梯度分布

Fig.4 Transverse gradient of gases horizontal velocity

图5 颗粒高度分布

Fig.5 Height of particles

图6 颗粒上升速度随高度变化

Fig.6 Lifting velocity of particles as functions of height

图7 颗粒垂直上升速度随时间变化

Fig.7 Vertical lifting velocity of particles as functions of time

图8 颗粒垂直上升速度随时间变化

Fig.8 Vertical lifting velocity of particles as functions of time

图9 定常冲击波后的颗粒运动轨迹

Fig.9 Tracks of a particle behind stationary shock waves

表2 4种尺寸颗粒垂直方向加速上升期时间(单位：μs)

Table 2 The time (in μs) that particles accelerate to lift

d_p/μm	Ma= 1.3	Ma= 2.2	Ma= 3.0
10	70	25	20
50	140	65	56
100	180	100	80
500	300	280	240

表3 四种颗粒离开边界层外缘的时间(Ma= 1.3)

Table 3 The time that particles leave boundary layer(Ma= 1.3)

d_p/μm	10	50	100	500
τ/μs	71	142	296	833

参考文献 10

1	GERRARD J H. An experimental investigation of the initial stages of the dispersion of dust by shock[J]. Brit J Appl Phys, 1963, 14, 186- 192. DOI
2	FLETCHER B. The interaction of a shock with a dust deposit[J]. J Phys D: Appl Phys, 1976, 9, 197. DOI
3	HWANG C C. Initial stages of the interaction of a shock wave with a dust deposit[J]. Int J Multiphase Flow, 1986, 12 (4): 655- 666. DOI
4	BRACHT K, MERZKIRCH W. Dust entrainment in a shock-induced turbulent air flow[J]. Int J Multiphase Flow, 1979, 5, 301- 312. DOI
5	HWANG C C. Interaction of coal-dust beds with shock-induced air stream[M]//MERZKIRCH W. Flow visualization II, Washington: Hemisphere, 1982, 547-551.
6	FEDOROV A V, FEDOROVA N N, DEDORCHENKO I A, et al. Mathematical simulation of dust lifting from the surface[J]. J Applied Mechanics and Technical Physics, 2002, 43 (6): 877- 887. DOI
7	WANG B Y, XIONG Y, QI L X. Shock-induced near-wall two-phase flow structure over a micro-sized particles bed[J]. Shock Waves, 2006, 15, 363- 373. DOI
8	范宝春, 陆守香, 龚昌超, 等. 激波诱导的燃烧粉尘云边界层的结构[J]. 力学学报, 1995, 27 (6): 653- 662.
9	范宝春, 陆守香, 龚昌超. 激波卷扬的气体粉尘边界层的实验与数值研究[J]. 爆炸与冲击, 1994, 14 (3): 199- 207.
10	汤普森P A. 可压缩流体动力学[M]. 田安久, 等, 译. 北京: 科学出版社, 1986: 456-468.

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