Raising of Particles on a Wall Behind a Normal Shock Wave Perpendicular to the Wall

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

Abstract

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

CLC Number:

O359

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.

Figures/Tables 12

Fig.1 Boundary layer flows behind a shock wave

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

Fig.2 Computational mesh

Fig.3 Vector of gas velocity

Fig.4 Transverse gradient of gases horizontal velocity

Fig.5 Height of particles

Fig.6 Lifting velocity of particles as functions of height

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

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

Fig.9 Tracks of a particle behind stationary shock waves

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

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

References 10

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