Relaxation drag history of shock accelerated microparticles
Abstract
Experimental measurements of the displacements of shock accelerated microparticles from shortly after shock interaction to the particle relaxation time show timedependent drag coefficients ($$C_{D}$$) that are much higher than those predicted by quasisteady and unsteady drag models. Nylon particles with mean diameter of $$4~\unicode[STIX]{x03BC}\text{m}$$, accelerated by onedimensional normal shocks (Mach number$$M_{s}=1.2$$, 1.3 and 1.4), have measured$$C_{D}$$values that follow a powerlaw behaviour. The drag is a function of the timedependent Knudsen number,$$Kn^{\ast }=M_{s}/Re_{p}$$, where the particle Reynolds number ($$Re_{p}$$) is calculated using the timedependent slip velocity. Also, some portion of the drag can be attributed to quasisteady 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 quasisteady 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$$Re_{p}\rightarrow 0$$. Finally, 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.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA10)
 OSTI Identifier:
 1369203
 Report Number(s):
 LAUR1722125
Journal ID: ISSN 00221120
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Fluid Mechanics
 Additional Journal Information:
 Journal Volume: 823; Journal ID: ISSN 00221120
 Publisher:
 Cambridge University Press
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; highspeed flow; multiphase and particleladen flows; shock waves
Citation Formats
Bordoloi, Ankur D., Martinez, Adam A., and Prestridge, Katherine. Relaxation drag history of shock accelerated microparticles. United States: N. p., 2017.
Web. doi:10.1017/jfm.2017.389.
Bordoloi, Ankur D., Martinez, Adam A., & Prestridge, Katherine. Relaxation drag history of shock accelerated microparticles. United States. doi:10.1017/jfm.2017.389.
Bordoloi, Ankur D., Martinez, Adam A., and Prestridge, Katherine. Wed .
"Relaxation drag history of shock accelerated microparticles". United States. doi:10.1017/jfm.2017.389. https://www.osti.gov/servlets/purl/1369203.
@article{osti_1369203,
title = {Relaxation drag history of shock accelerated microparticles},
author = {Bordoloi, Ankur D. and Martinez, Adam A. and Prestridge, Katherine},
abstractNote = {Experimental measurements of the displacements of shock accelerated microparticles from shortly after shock interaction to the particle relaxation time show timedependent drag coefficients ($C_{D}$) that are much higher than those predicted by quasisteady and unsteady drag models. Nylon particles with mean diameter of $4~\unicode[STIX]{x03BC}\text{m}$, accelerated by onedimensional normal shocks (Mach number$M_{s}=1.2$, 1.3 and 1.4), have measured$C_{D}$values that follow a powerlaw behaviour. The drag is a function of the timedependent Knudsen number,$Kn^{\ast }=M_{s}/Re_{p}$, where the particle Reynolds number ($Re_{p}$) is calculated using the timedependent slip velocity. Also, some portion of the drag can be attributed to quasisteady 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 quasisteady 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$Re_{p}\rightarrow 0$. Finally, 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.},
doi = {10.1017/jfm.2017.389},
journal = {Journal of Fluid Mechanics},
number = ,
volume = 823,
place = {United States},
year = {2017},
month = {6}
}
Web of Science
Works referenced in this record:
Drag Coefficients of Spheres in Continuum and Rarefied Flows
journal, June 1976
 Henderson, Charles B.
 AIAA Journal, Vol. 14, Issue 6
Design of a fast diaphragmless shock tube driver
journal, July 2015
 MejiaAlvarez, R.; Wilson, B.; Leftwich, M. C.
 Shock Waves, Vol. 25, Issue 6
Drag coefficient of a sphere in a nonstationary flow: new results
journal, September 2007
 Jourdan, G.; Houas, L.; Igra, O.
 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 463, Issue 2088
Dust suspensions accelerated by shock waves
journal, April 2000
 Geng, J. H.; Groenig, H.
 Experiments in Fluids, Vol. 28, Issue 4
Some Properties of Shock Relaxation in Gas Flows Carrying Small Particles
journal, January 1964
 Rudinger, George
 Physics of Fluids, Vol. 7, Issue 5
On the Passage of a Shock Wave Through a DustyGas Layer
journal, January 1983
 Miura, H.; Glass, I. I.
 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 385, Issue 1788
SubKolmogorov resolution partical image velocimetry measurements of particleladen forced turbulence
journal, January 2010
 Tanaka, Tomohiko; Eaton, John K.
 Journal of Fluid Mechanics, Vol. 643
Compressibility and Rarefaction Effects on Drag of a Spherical Particle
journal, September 2008
 Loth, E.
 AIAA Journal, Vol. 46, Issue 9
Shock wave interaction with a cloud of particles
journal, October 1997
 Boiko, V. M.; Kiselev, V. P.; Kiselev, S. P.
 Shock Waves, Vol. 7, Issue 5
A new experiment to measure shocked particle drag using multipulse particle image velocimetry and particle tracking
journal, November 2014
 Martinez, Adam A.; Orlicz, Gregory C.; Prestridge, Katherine P.
 Experiments in Fluids, Vol. 56, Issue 1
Modeling of the unsteady force for shock–particle interaction
journal, May 2009
 Parmar, M.; Haselbacher, A.; Balachandar, S.
 Shock Waves, Vol. 19, Issue 4
The Motion of HighReynoldsNumber Bubbles in Inhomogeneous Flows
journal, January 2000
 Magnaudet, J.; Eames, I.
 Annual Review of Fluid Mechanics, Vol. 32, Issue 1
Particle response and turbulence modification in fully developed channel flow
journal, October 1994
 Kulick, J. D.; Fessler, J. R.; Eaton, J. K.
 Journal of Fluid Mechanics, Vol. 277
Measurement of instantaneous Eulerian acceleration fields by particle image accelerometry: method and accuracy
journal, December 2002
 Christensen, K.; Adrian, R.
 Experiments in Fluids, Vol. 33, Issue 6
Shock Tube Study of the Drag Coefficient of a Sphere in a NonStationary Flow
journal, August 1993
 Igra, O.; Takayama, K.
 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 442, Issue 1915
The effect of an unsteady drag force on the structure of a nonequilibrium region behind a shock wave in a gasparticle mixture
journal, October 2007
 Saito, T.; Saba, M.; Sun, M.
 Shock Waves, Vol. 17, Issue 4
Flow past a sphere with an oscillation in the freestream velocity and unsteady drag at finite Reynolds number
journal, April 1992
 Mei, Renwei; Adrian, Ronald J.
 Journal of Fluid Mechanics, Vol. 237
The unsteadiness of shock waves propagating through gasparticle mixtures
journal, July 1985
 Sommerfeld, M.
 Experiments in Fluids, Vol. 3, Issue 4
The Unsteady, Subsonic Motion of a Sphere in a Compressible Inviscid Fluid
journal, January 1952
 Longhorn, A. L.
 The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 5, Issue 1
On Virtual mass and Transient Motion in Subsonic Compressible flow
journal, January 1951
 Miles, John W.
 The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 4, Issue 4
Effective Drag Coefficient for GasParticle Flow in Shock Tubes
journal, March 1970
 Rudinger, George
 Journal of Basic Engineering, Vol. 92, Issue 1
Unsteady drag on a sphere by shock wave loading
journal, June 2005
 Sun, M.; Saito, T.; Takayama, K.
 Shock Waves, Vol. 14, Issue 12
Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the freestream velocity
journal, December 1991
 Mei, Renwei; Lawrence, Christopher J.; Adrian, Ronald J.
 Journal of Fluid Mechanics, Vol. 233
Improved Drag Correlation for Spheres and Application to ShockTube Experiments
journal, June 2010
 Parmar, M.; Haselbacher, A.; Balachandar, S.
 AIAA Journal, Vol. 48, Issue 6
Shock tube investigation of quasisteady drag in shockparticle interactions
journal, December 2012
 Wagner, Justin L.; Beresh, Steven J.; Kearney, Sean P.
 Physics of Fluids, Vol. 24, Issue 12
On the unsteady inviscid force on cylinders and spheres in subcritical compressible flow
journal, March 2008
 Parmar, M.; Haselbacher, A.; Balachandar, S.
 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 366, Issue 1873
Generalized BassetBoussinesqOseen Equation for Unsteady Forces on a Sphere in a Compressible Flow
journal, February 2011
 Parmar, M.; Haselbacher, A.; Balachandar, S.
 Physical Review Letters, Vol. 106, Issue 8
Effect of particle size on modulating turbulent intensity
journal, April 1989
 Gore, R. A.; Crowe, C. T.
 International Journal of Multiphase Flow, Vol. 15, Issue 2
Equation of motion for a small rigid sphere in a nonuniform flow
journal, January 1983
 Maxey, Martin R.
 Physics of Fluids, Vol. 26, Issue 4
Particle Breakup in Shock Waves Studies by single Particle Light Scattering
journal, June 1994
 Strecker, Jörgt J. F.; Roth, Paul
 Particle & Particle Systems Characterization, Vol. 11, Issue 3