Research Papers: Fundamental Issues and Canonical Flows

An Investigation Into Nonlinear Growth Rate of Two-Dimensional and Three-Dimensional Single-Mode Richtmyer–Meshkov Instability Using an Arbitrary-Lagrangian–Eulerian Algorithm

[+] Author and Article Information
Mike Probyn

Centre for Fluid Mechanics and
Scientific Computing,
School of Engineering,
Cranfield University,
Bedfordshire MK43 0AL, UK
e-mail: m.g.probyn@cranfield.ac.uk

Ben Thornber

School of Aerospace Mechanical and
Mechatronic Engineering,
Faculty of Engineering and
Information Technologies,
University of Sydney,
Sydney NSW 2006, Australia
e-mail: ben.thornber@sydney.edu.au

Dimitris Drikakis

Centre for Fluid Mechanics and
Scientific Computing,
School of Engineering,
Cranfield University,
Bedfordshire MK43 0AL, UK
e-mail: d.drikakis@cranfield.ac.uk

David Youngs

Aldermaston Reading,
Berkshire RG7 4PR, UK
e-mail: david.youngs@awe.co.uk

Robin Williams

Aldermaston Reading,
Berkshire RG7 4PR, UK
e-mail: robin.williams@awe.co.uk

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 27, 2013; final manuscript received March 17, 2014; published online July 9, 2014. Assoc. Editor: Stuart Dalziel.

J. Fluids Eng 136(9), 091208 (Jul 09, 2014) (7 pages) Paper No: FE-13-1196; doi: 10.1115/1.4027367 History: Received March 27, 2013; Revised March 17, 2014

This paper presents an investigation into the use of a moving mesh algorithm for solving unsteady turbulent mixing problems. The growth of a shock induced mixing zone following reshock, using an initial setup comparable to that of existing experimental work, is used to evaluate the behavior of the numerical scheme for single-mode Richtmyer–Meshkov instability (SM-RMI). Subsequently the code is used to evaluate the growth rate for a range of different initial conditions. The initial growth rate for three-dimensional (3D) SM Richtmyer–Meshkov is also presented for a number of different initial conditions. This numerical study details the development of the mixing layer width both prior to and after reshock. The numerical scheme used includes an arbitrary Lagrangian–Eulerian grid motion which is successfully used to reduce the mesh size and computational time while retaining the accuracy of the simulation results. Varying initial conditions shows that the growth rate after reshock is independent of the initial conditions for a SM provided that the initial growth remains in the linear regime.

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Grahic Jump Location
Fig. 1

Development of the density field with time for the sod-shock tube test case comparing stationary and moving grid algorithms

Grahic Jump Location
Fig. 2

Schematic of the simulation based on the Collins and Jacobs experiment. The end wall is at x = 0 while the opposite x boundary is an extended domain to allow outflow without additional pressure waves polluting the solution. The remaining boundary conditions are treated as inviscid (slip) walls. The domain is 89 mm in the transverse direction and the single-mode perturbation has a wavelength of 59 mm with an initial amplitude of 2 mm.

Grahic Jump Location
Fig. 3

Results of 2D grid study comparing stationary and moving grid techniques for mixing layer width development as a function of time

Grahic Jump Location
Fig. 9

Study of the effect of initial amplitude of the perturbation on the mixing layer width. Initial amplitudes are expressed as a function of the initial wavelength.

Grahic Jump Location
Fig. 4

Comparison of contour plots of volume fraction for the 2D results for the highest and lowest resolution case at 9 ms. The large scale vortical structures can be seen in the lowest resolution case and the additional smaller scale vortices arising from KHI are visible at the higher resolution.

Grahic Jump Location
Fig. 5

Comparison of the development of the mixing layer width as a function of time for different initialization techniques for the Collins and Jacobs test case in 3D

Grahic Jump Location
Fig. 6

Volume fraction isosurfaces (1%, 50%, and 99%) immediately prior to reshock (t = 5 ms), (a) shows the results when a 2D initialization is used, no substantial instability arises in the third direction and (b) is the results when initialized in 3D with superposition of low amplitude multimodal perturbation (diffuse interface)

Grahic Jump Location
Fig. 7

Volume fraction isosurfaces (1%, 50%, and 99%) immediately after reshock (t = 8 ms), initial conditions as in Fig. 6

Grahic Jump Location
Fig. 8

Slices through the central plane of the 3DPM-diffuse simulations, the upper row (a)–(d) has 128 cells/wavelength, middle row (e)–(h) has 256 cells/wavelength, and the lower row (i)–(l) is the experimental image of Collins and Jacobs [6]. The computational results show the gradient of the volume fraction.



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