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On the method of indirectly measuring gas and particulate phase velocities in shock induced dusty-gas flows

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Abstract

A method of indirectly measuring the temporally varying velocities of the gas and particulate phases in the nonequilibrium region of a shock wave moving at constant speed in a dusty-gas flow is described, and this method is assessed by using experimental data from shock-induced air flows containing 40-μm-diameter glass beads in a dusty-gas shock-tube facility featuring a large horizontal channel (19.7-cm by 7.6-cm in cross-section). Simultaneous measurements of the shock-front speed with time-of-arrival gauges, particle concentration by light extinctiometry and gas-particle mixture density by beta-ray absorption are used in conjunction with two mass conservation laws to obtain the indirect velocity measurements of both phases. A second indirect measurement of the gas-phase velocity is obtained when the gas pressure is simultaneously recorded along with the particle concentration and shock-front speed when used in conjunction with the conservation of mixture momentum. Direct measurements of the particulate-phase velocity by laser-Doppler velocimetry are also presented, as a means of assessing the indirect velocity measurement method.

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Abbreviations

a f :

frozen speed of sound

D :

particle diameter

d f :

LDV interference fringe spacing

d m :

LDV probe-volume diameter

l m :

LDV probe-volume length

M sf :

frozen shock Mach number

M se :

equilibrium shock Mach number

Ñ(D) :

probability density distribution by number

p :

pressure

R :

gas constant

t :

time

T :

temperature

S :

LDV-signal amplitude

v g :

gas velocity in laboratory frame of reference

v p :

particle velocity in laboratory frame of reference

V s :

shock-front velocity

δ :

ratio of specific heats of particles and gas

γ :

ratio of specific heats of gas

Γ:

equilibrium specific heats ratio

η :

particle-to-air loading ratio

θ :

half-angle between incident laser beams

λ :

laser light wavelength

ϱ g :

gas density

ϱ p :

particle material density

σ g :

gas concentration

σ m :

mixture concentration

σ app m :

apparent mixture concentration

σ p :

particle concentration

ζ :

particle volume fraction

\(\bar \zeta\) (D) :

probability density distribution by volume

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Author notes

  1. G. D. Lock

    Present address: St. Anne's College and, Dept. of Engineering Science, Oxford University, OX2 6HS, England

Authors and Affiliations

  1. Institute for Aerospace Studies, University of Toronto, 4925 Dufferin St., M3H 5T6, Downswiew, Ontario, Canada

    G. D. Lock

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Lock, G.D. On the method of indirectly measuring gas and particulate phase velocities in shock induced dusty-gas flows. Experiments in Fluids 15, 1–9 (1993). https://doi.org/10.1007/BF00195589

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  • DOI: https://doi.org/10.1007/BF00195589

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