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The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability†

Published online by Cambridge University Press:  12 May 2010

B. THORNBER ,
D. DRIKAKIS ,
D. L. YOUNGS  and
R. J. R. WILLIAMS
B. THORNBER*
Affiliation:
Fluid Mechanics and Computational Science Group, Aerospace Sciences Department, Cranfield University, Cranfield MK43 0AL, UK
D. DRIKAKIS
Affiliation:
Fluid Mechanics and Computational Science Group, Aerospace Sciences Department, Cranfield University, Cranfield MK43 0AL, UK
D. L. YOUNGS
Affiliation:
AWE, Aldermaston, Reading RG7 4PR, UK
R. J. R. WILLIAMS
Affiliation:
AWE, Aldermaston, Reading RG7 4PR, UK
*
‡Email address for correspondence: b.j.r.thornber@cranfield.ac.uk
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Abstract

This paper investigates the influence of different three-dimensional multi-mode initial conditions on the rate of growth of a mixing layer initiated via a Richtmyer–Meshkov instability through a series of well-controlled numerical experiments. Results are presented for large-eddy simulation of narrowband and broadband perturbations at grid resolutions up to 3 × 109 points using two completely different numerical methods, and comparisons are made with theory and experiment. It is shown that the mixing-layer growth is strongly dependent on initial conditions, the narrowband case giving a power-law exponent θ ≈ 0.26 at low Atwood and θ ≈ 0.3 at high Atwood numbers. The broadband case uses a perturbation power spectrum of the form P(k) ∝ k−2 with a proposed theoretical growth rate of θ = 2/3. The numerical results confirm this; however, they highlight the necessity of a very fine grid to capture an appropriately broad range of initial scales. In addition, an analysis of the kinetic energy decay rates, fluctuating kinetic energy spectra, plane-averaged volume fraction profiles and mixing parameters is presented for each case.

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Type
Papers
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Journal of Fluid Mechanics , Volume 654 , 10 July 2010 , pp. 99 - 139
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

†

Contains material ©British Crown Copyright 2009/MoD.

References

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