Numerical simulations of high density ratio lock-exchange flows

Jocelyn Étienne,Pierre Saramito,Emil J Hopfinger

doi:10.1063/1.1849800

Abstract

In this paper direct numerical simulations of exchange flows of large density ratios are presented and are compared with experiments by Gröbelbauer et al. [J. Fluid Mech. 250, 669 (1993)]. These simulations, which make use of a dynamic mesh adaptation technique, cover the whole density ratio range of the experiments and very good agreement with the experimental front velocities and the Froude number variations is obtained. Moreover, in order to establish more definitely the Froude number dependency on density ratio, the simulations were carried up to ratios of 100 compared with 21.6 accessible in experiments. An empirical law for the dense front Froude number as a function of the density parameter is proposed. The mathematical difficulty of the problem is discussed. This difficulty arises because, when the density ratio is large, the existence of a solution is dependent on a compatibility condition between the diffusion and viscous terms model. Moreover, a specific numerical technique is required to treat the finite, nonuniform divergence of the mass-averaged velocity field described by the continuity equation.

Highlights

Numerical simulations of gravity driven flows are relatively rare compared with the number of experiments which considered various aspects of gravity currents and of density intrusions.1 Recent numerical simulation2,3 of gravity currents are limited to small density differences where the Boussinesq approximation is applicable.4 In certain geophysical flows, such as avalanches or pyroclastic flows, and in industrial applications related with heavy gases, the density change across the current fronts is, no longer small.Since theoretical models or experimental results which hold for small density ratios can, in general, not be extrapolated to these flows, large density ratio flows need specific attention.Direct numerical simulations of gravity currents of large density ratios seem to be nonexistent
The direct numerical simulations presented in this paper are, to our knowledge, the first simulations of exchange flows of miscible fluids of very large density ratios
A finite element discretization is used, allowing a dynamic mesh adaptation which is an essential feature in the simulations of this type of flow

Summary

Introduction

Numerical simulations of gravity driven flows are relatively rare compared with the number of experiments which considered various aspects of gravity currents and of density intrusions. Recent numerical simulation of gravity currents are limited to small density differences where the Boussinesq approximation is applicable. In certain geophysical flows, such as avalanches or pyroclastic flows, and in industrial applications related with heavy gases, the density change across the current fronts is, no longer small.Since theoretical models or experimental results which hold for small density ratios can, in general, not be extrapolated to these flows, large density ratio flows need specific attention.Direct numerical simulations of gravity currents of large density ratios seem to be nonexistent. Recent numerical simulation of gravity currents are limited to small density differences where the Boussinesq approximation is applicable.. In certain geophysical flows, such as avalanches or pyroclastic flows, and in industrial applications related with heavy gases, the density change across the current fronts is, no longer small. Since theoretical models or experimental results which hold for small density ratios can, in general, not be extrapolated to these flows, large density ratio flows need specific attention. Direct numerical simulations of gravity currents of large density ratios seem to be nonexistent. Gröbelbauer et al. conducted lock-exchange flow experiments with gases of density ratios up to 21.6.

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Conclusion