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Relaxation drag history of shock accelerated microparticles

Published online by Cambridge University Press:  21 June 2017

Ankur D. Bordoloi Open the ORCID record for Ankur D. Bordoloi [Opens in a new window] ,
Adam A. Martinez  and
Katherine Prestridge Open the ORCID record for Katherine Prestridge [Opens in a new window]
Ankur D. Bordoloi*
Affiliation:
Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Adam A. Martinez
Affiliation:
Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Katherine Prestridge
Affiliation:
Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
*
†Email address for correspondence: [email protected]
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Abstract

Experimental measurements of the displacements of shock accelerated microparticles from shortly after shock interaction to the particle relaxation time show time-dependent drag coefficients ($C_{D}$) that are much higher than those predicted by quasi-steady and unsteady drag models. Nylon particles with mean diameter of $4~\unicode[STIX]{x03BC}\text{m}$, accelerated by one-dimensional normal shocks (Mach number $M_{s}=1.2$, 1.3 and 1.4), have measured $C_{D}$ values that follow a power-law behaviour. The drag is a function of the time-dependent Knudsen number, $Kn^{\ast }=M_{s}/Re_{p}$, where the particle Reynolds number ($Re_{p}$) is calculated using the time-dependent slip velocity. Some portion of the drag can be attributed to quasi-steady forces, but the total drag cannot be predicted by current unsteady force models that are based on the Basset–Boussinesq–Oseen equation and pressure drag. The largest contribution to the total drag is the unsteady component ($C_{D,us}$) until the particle attains $Kn^{\ast }\approx 0.5{-}1.0$, then the unsteady contribution decays. The quasi-steady component ($C_{D,qs}$) increases almost linearly with $Kn^{\ast }$, intersects the $C_{D,us}$ at $Kn^{\ast }\approx 2$ and becomes the primary contributor to the drag towards the end of the relaxation zone as $Re_{p}\rightarrow 0$. There are currently no analytical models that are able to predict the nonlinear behaviour of the shock accelerated particles during the relaxation phase of the flow.

JFM classification

Aerodynamics: High-speed flow Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Compressible Flows: Shock waves
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 823 , 25 July 2017 , R4
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Copyright
© 2017 Cambridge University Press 

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