Differential formulation of the viscous history force on a particle for efficient and accurate computation. (16th April 2018)

• Record Type: Journal Article
• Authors: Parmar, M.; Annamalai, S.; Balachandar, S.; Prosperetti, A.
• Is Part Of: Journal of fluid mechanics. Volume 844(2018)
• Page Start: 970
• Page End: 993
• Publication Date: 2018-04-16
• Subjects: multiphase and particle-laden flows, -- multiphase flow, -- particle/fluid flow; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2018.217
• Languages: English
• ISSNs: 0022-1120

Abstract

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.