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The unsteadiness of shock waves propagating through gas-particle mixtures

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Abstract

A shock wave which is incident onto a gas-particle mixture or initiated within such a mixture needs a certain distance to reach a constant velocity. This effect is due to the inertia and the heat capacity of the particles. In general the shock wave is decelerated and the frozen pressure jump is decaying.

A vertical shock tube was used in order to produce a plane shock wave incident onto a homogeneous gas-particle mixture. In addition to measurements of the shock velocity and the pressure history along the total low pressure section, the particle velocity was measured within the relaxation zone far downstream of the diaphragm using a laser-Doppler-velocimeter. Thus a drag law describing the particle acceleration within the relaxation zone was derived from the measurements.

To compare the experiments with theoretical results, calculations were performed by the random-choice method.

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Abbreviations

a :

velocity of sound

c :

specific heat of particles

c p :

specific heat of the gas at constant pressure

c v :

specific heat of the gas at constant volume

c D :

drag coefficient

D p :

particle diameter

F p :

drag force

m p :

particle flow rate

m G :

gas flow rate

\(Ms = \frac{{u_s }}{{a_1 }}\) :

shock Mach number

M s0 :

initial shock Mach number

Nu :

Nusselt number

p :

pressure

Pr :

Prandtl number

Q p :

heat transfer

R :

gas constant

Re :

Reynolds number

t :

time

T :

temperature

u :

flow velocity

u s :

shock wave velocity

χ:

coordinate

γ:

ratio of the specific heats of the gas

δ:

ratio of the specific heats of the particles and the gas

ɛ:

volume fraction of the particles

ν:

loading ratio

μ:

dynamic viscosity

ϱ:

gas density

ϱ p :

density of particle material

σ:

particle density in the mixture

E :

equilibrium

e :

equivalent gas

G :

gas

P :

particles

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Authors and Affiliations

  1. Stoßwellenlabor, Rheinisch-Westfälische Technische Hochschule, Templergraben 55, D-5100, Aachen, Germany

    M. Sommerfeld

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Sommerfeld, M. The unsteadiness of shock waves propagating through gas-particle mixtures. Experiments in Fluids 3, 197–206 (1985). https://doi.org/10.1007/BF00265101

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