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Title: Differential formulation of the viscous history force on a particle for efficient and accurate computation

Abstract

It is well known that the computation of the Basset-like history force is very demanding in terms of CPU and memory requirements, since it requires the evaluation of a history integral. We use the recent rational theory of Beylkin & Monzón (Appl. Comput. Harmon. Anal., vol. 19, 2005, pp. 17–48) to approximate the history kernel in the form of exponential sums to reformulate the viscous history force in a differential form. This theory allows us to approximate the history kernel in terms of exponential sums to any desired order of accuracy. This removes the need for long-time storage of the acceleration histories of the particle and the fluid. The proposed differential form approximation is applied to compute the history force on a spherical particle in a synthetic turbulent flow and a wall-bounded turbulent channel flow. Particles of various diameters are considered, and results obtained using the present technique are in reasonable agreement with those achieved using the full history integral.

Authors:
; ORCiD logo; ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
Univ. of Florida, Gainesville, FL (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1538910
DOE Contract Number:  
NA0002378
Resource Type:
Journal Article
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 844; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
Mechanics; Physics

Citation Formats

Parmar, M., Annamalai, S., Balachandar, S., and Prosperetti, A. Differential formulation of the viscous history force on a particle for efficient and accurate computation. United States: N. p., 2018. Web. doi:10.1017/jfm.2018.217.
Parmar, M., Annamalai, S., Balachandar, S., & Prosperetti, A. Differential formulation of the viscous history force on a particle for efficient and accurate computation. United States. doi:10.1017/jfm.2018.217.
Parmar, M., Annamalai, S., Balachandar, S., and Prosperetti, A. Mon . "Differential formulation of the viscous history force on a particle for efficient and accurate computation". United States. doi:10.1017/jfm.2018.217.
@article{osti_1538910,
title = {Differential formulation of the viscous history force on a particle for efficient and accurate computation},
author = {Parmar, M. and Annamalai, S. and Balachandar, S. and Prosperetti, A.},
abstractNote = {It is well known that the computation of the Basset-like history force is very demanding in terms of CPU and memory requirements, since it requires the evaluation of a history integral. We use the recent rational theory of Beylkin & Monzón (Appl. Comput. Harmon. Anal., vol. 19, 2005, pp. 17–48) to approximate the history kernel in the form of exponential sums to reformulate the viscous history force in a differential form. This theory allows us to approximate the history kernel in terms of exponential sums to any desired order of accuracy. This removes the need for long-time storage of the acceleration histories of the particle and the fluid. The proposed differential form approximation is applied to compute the history force on a spherical particle in a synthetic turbulent flow and a wall-bounded turbulent channel flow. Particles of various diameters are considered, and results obtained using the present technique are in reasonable agreement with those achieved using the full history integral.},
doi = {10.1017/jfm.2018.217},
journal = {Journal of Fluid Mechanics},
issn = {0022-1120},
number = ,
volume = 844,
place = {United States},
year = {2018},
month = {4}
}

Works referenced in this record:

Effect of the history term on the motion of rigid spheres in a viscous fluid
journal, June 1994


The Forces on a Body Placed in a Curved or Converging Stream of Fluid
journal, September 1928

  • Taylor, G. I.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 120, Issue 785
  • DOI: 10.1098/rspa.1928.0148

Generalized Basset-Boussinesq-Oseen Equation for Unsteady Forces on a Sphere in a Compressible Flow
journal, February 2011


Equation of motion for a drop or bubble in viscous compressible flows
journal, May 2012

  • Parmar, M.; Balachandar, S.; Haselbacher, A.
  • Physics of Fluids, Vol. 24, Issue 5
  • DOI: 10.1063/1.4719696

Velocity measurement of a settling sphere
journal, November 2000

  • Mordant, N.; Pinton, J. -F.
  • The European Physical Journal B, Vol. 18, Issue 2
  • DOI: 10.1007/PL00011074

A novel way of computing the Basset term in unsteady multiphase flow computations
journal, July 1992

  • Michaelides, Efstathios E.
  • Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 7
  • DOI: 10.1063/1.858430

The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number
journal, November 1993


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

  • Longhorn, A. L.
  • The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 5, Issue 1
  • DOI: 10.1093/qjmam/5.1.64

A scaling analysis of added-mass and history forces and their coupling in dispersed multiphase flows
journal, December 2013


Work-based criterion for particle motion and implication for turbulent bed-load transport
journal, November 2012

  • Lee, Hyungoo; Ha, Man Yeong; Balachandar, S.
  • Physics of Fluids, Vol. 24, Issue 11
  • DOI: 10.1063/1.4767541

Equilibrium expansion for the Eulerian velocity of small particles
journal, June 2002


A fast Eulerian method for disperse two-phase flow
journal, July 2001


Development and validation of a reduced order history force model
journal, October 2016


Efficient calculation of the history force at finite Reynolds numbers
journal, August 2007


Advection of inertial particles in the presence of the history force: Higher order numerical schemes
journal, December 2013


Computation of the Particle Basset Force with a Fractional-Derivative Approach
journal, October 2008


On approximation of functions by exponential sums
journal, July 2005


A scaling analysis for point–particle approaches to turbulent multiphase flows
journal, September 2009


A locally implicit improvement of the equilibrium Eulerian method
journal, June 2003


Investigation of Saltating Particle Motions
journal, July 1994


On the unsteady forces during the motion of a sedimenting particle
journal, September 2007


An efficient, second order method for the approximation of the Basset history force
journal, February 2011

  • van Hinsberg, M. A. T.; ten Thije Boonkkamp, J. H. M.; Clercx, H. J. H.
  • Journal of Computational Physics, Vol. 230, Issue 4
  • DOI: 10.1016/j.jcp.2010.11.014

Equation of motion for a small rigid sphere in a nonuniform flow
journal, January 1983


Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number
journal, April 1992


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
  • DOI: 10.1098/rsta.2008.0027

Equation of motion for a sphere in non-uniform compressible flows
journal, April 2012

  • Parmar, M.; Haselbacher, A.; Balachandar, S.
  • Journal of Fluid Mechanics, Vol. 699
  • DOI: 10.1017/jfm.2012.109

Direct numerical simulation of bedload transport using a local, dynamic boundary condition
journal, April 2003


History force on a sphere due to a step change in the free-stream velocity
journal, June 1993


Turbulent Dispersed Multiphase Flow
journal, January 2010