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Planar piston motion in dilute granular-gaseous mixture

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Abstract

This paper investigates the one-dimensional planar piston problem in dilute granular-gaseous mixture using both analytical and numerical approaches. Starting from the Euler equations of the two-fluid model, a one-way coupling model for dilute granular flow was derived assuming that the piston speed is higher than the sound speed of the granular phase, but much smaller than that of the gaseous phase—which results in a shock wave propagating in the granular phase. It was shown that the dissipation terms of this model—the drag force and inelastic collisions—affect the shock wave structure. A reference analytical solution for fully elastic particles assuming that the linear drag is the only dissipation mechanism predicted a shock wave structure that is similar to ideal molecular gas but decays exponentially with time. The nonlinear drag component resulted in decreasing velocity and density behind the shock while the temperature increases, in an opposite trend to the effect of inelastic collisions. It was shown that the combined effects of both nonlinear drag and inelastic collisions could result in either two regimes depending on the values of their corresponding parameters.

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  1. Department of Mechanical Power Engineering, Faculty of Engineering, Mansoura University, Mansoura, 35516, Egypt

    Yahia M. Fouda

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  1. Yahia M. Fouda
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Correspondence to Yahia M. Fouda.

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Fouda, Y.M. Planar piston motion in dilute granular-gaseous mixture. Granular Matter 23, 85 (2021). https://doi.org/10.1007/s10035-021-01145-y

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