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

Published online by Cambridge University Press:  16 April 2018

M. Parmar ,
S. Annamalai Open the ORCID record for S. Annamalai [Opens in a new window] ,
S. Balachandar Open the ORCID record for S. Balachandar [Opens in a new window]  and
A. Prosperetti Open the ORCID record for A. Prosperetti [Opens in a new window]
M. Parmar
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
S. Annamalai
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
S. Balachandar*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
A. Prosperetti
Affiliation:
Department of Mechanical Engineering, University of Houston, TX 77204-4006, USA Physics of Fluids Group, Department of Science and Technology, J.M. Burgers Centre for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Multiphase flow Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 970 - 993
Copyright
© 2018 Cambridge University Press 

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