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Title: Faxén form of time-domain force on a sphere in unsteady spatially varying viscous compressible flows

Journal Article · · Journal of Fluid Mechanics
DOI:https://doi.org/10.1017/jfm.2017.77· OSTI ID:1534391
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An explicit expression for the time-dependent force on a stationary, finite-sized spherical particle located in an unsteady inhomogeneous ambient flow is presented. The force expression accounts for both viscous and compressible effects. Towards this end, a time-harmonic plane travelling wave of a given frequency propagating in a viscous compressible flow over a sphere is considered. Linearized compressible Navier–Stokes equations are solved to obtain an analytical expression for the force exerted on the particle in the frequency domain. The force obtained in the Laplace space due to a travelling wave of a given frequency and wavenumber is then generalized to any arbitrary incoming flow. This is achieved by relating the radial and tangential velocity components in the Laplace space to the surface-averaged radial velocity and volume-averaged velocity vectors respectively in the time space. Moreover an expression relating the surface-averaged radial velocity and volume-averaged velocity vector has been provided. The total force is written as a summation of the undisturbed and disturbed force (quasi-steady, inviscid-unsteady and viscous-unsteady) contributions. The force contributions thus obtained are expressed as comprising of two parts – that arising due to spatial variation in the ambient flow and the other arising due to temporal variation. The current formulation is applicable to inhomogeneous ambient flows, however in the limit of negligible Reynolds and Mach numbers. The results are applicable even for particles of sizes larger than the acoustic wavelength. The accuracy of the explicit time-domain force expression is first tested by computing the force on an 80 mm diameter particle due to a weak planar expansion fan. Extension of this formulation when nonlinear effects become important is also proposed and tested by considering strong expansion fans. The results thus obtained are compared against corresponding axisymmetric numerical simulations.

Research Organization:
Univ. of Florida, Gainesville, FL (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
DOE Contract Number:
NA0002378
OSTI ID:
1534391
Journal Information:
Journal of Fluid Mechanics, Vol. 816; ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English

References (29)

A generalization of Faxén's theorem to nonsteady motion of a sphere through an incompressible fluid in arbitrary flow journal September 1974
Acoustic Radiation Pressure on a Rigid Sphere in a Viscous Fluid journal December 1994
Acoustic radiation force on a sphere in a quasistationary wave field—theory journal January 1979
Approximate Riemann solvers, parameter vectors, and difference schemes journal October 1981
Steady planar straining flow past a rigid sphere at moderate Reynolds number journal September 2002
Forces on bodies moving unsteadily in rapidly compressed flows journal January 1999
Der Widerstand gegen die Bewegung einer starren Kugel in einer zähen Flüssigkeit, die zwischen zwei parallelen ebenen Wänden eingeschlossen ist journal January 1922
Inviscid flow around bodies moving in weak density gradients without buoyancy effects journal December 1997
The force on a sphere in a uniform flow with small-amplitude oscillations at finite Reynolds number journal November 1993
The Unsteady, Subsonic Motion of a Sphere in a Compressible Inviscid Fluid journal January 1952
A generalization of faxén's theorem to nonsteady motion of a sphere through a compressible fluid in arbitrary flow journal December 1974
Improved Drag Correlation for Spheres and Application to Shock-Tube Experiments journal June 2010
On the equation for spherical-particle motion: effect of Reynolds and acceleration numbers journal July 1998
Equation of motion for a sphere in non-uniform compressible flows journal April 2012
The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number journal November 1993
A novel way of computing the Basset term in unsteady multiphase flow computations journal July 1992
The added mass of an expanding bubble With an Appendix by A. Prosperetti, C. D. Ohl, A. Tijink, G. Mougin J. Magnaudet. journal May 2003
Generalized Basset-Boussinesq-Oseen Equation for Unsteady Forces on a Sphere in a Compressible Flow journal February 2011
Elements of Gasdynamics journal October 1957
Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number journal April 1992
Shock interaction with deformable particles using a constrained interface reinitialization scheme journal February 2016
The Motion of High-Reynolds-Number Bubbles in Inhomogeneous Flows journal January 2000
Acoustic‐Radiation Force on a Solid Elastic Sphere journal November 1969
A WENO Reconstruction Algorithim for Unstructured Grids Based on Explicit Stencil Construction conference June 2012
The Forces on a Body Placed in a Curved or Converging Stream of Fluid journal September 1928
Equation of motion for a small rigid sphere in a nonuniform flow journal January 1983
Hydrodynamic Theory of the Velocity Correlation Function journal November 1970
Compressibility and Rarefaction Effects on Drag of a Spherical Particle journal September 2008
On the unsteady inviscid force on cylinders and spheres in subcritical compressible flow
  • Parmar, M.; Haselbacher, A.; Balachandar, S.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 366, Issue 1873 https://doi.org/10.1098/rsta.2008.0027
journal March 2008

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