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Research Papers: Fundamental Issues and Canonical Flows

Simulations and Analysis of the Reshocked Inclined Interface Richtmyer–Meshkov Instability for Linear and Nonlinear Interface Perturbations

[+] Author and Article Information
Jacob A. McFarland

Department of Mechanical Engineering,
Texas A&M University,
College Station, Texas 77843
e-mail: jacmcfar@tamu.edu

Jeffrey A. Greenough

Weapons and Complex Integration,
Lawrence Livermore National Laboratory,
Livermore, CA 94550
e-mail: greenough1@llnl.gov

Devesh Ranjan

Mem. ASME
Assistant Professor
Department of Mechanical Engineering,
Texas A&M University,
College Station, Texas 77843
e-mail: dranjan@tamu.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 24, 2013; final manuscript received January 23, 2014; published online May 6, 2014. Assoc. Editor: Ye Zhou.

J. Fluids Eng 136(7), 071203 (May 06, 2014) (11 pages) Paper No: FE-13-1260; doi: 10.1115/1.4026858 History: Received April 24, 2013; Revised January 23, 2014

A computational study of the Richtmyer–Meshkov instability (RMI) is presented for an inclined interface perturbation in support of experiments being performed at the Texas A&M shock tube facility. The study is comprised of 2D, viscous, diffusive, compressible simulations performed using the arbitrary Lagrange Eulerian code, ARES, developed at Lawrence Livermore National Laboratory. These simulations were performed to late times after reshock with two initial interface perturbations, in the linear and nonlinear regimes each, prescribed by the interface inclination angle. The interaction of the interface with the reshock wave produced a complex 2D set of compressible wave interactions including expansion waves, which also interacted with the interface. Distinct differences in the interface growth rates prior to reshock were found in previous work. The current work provides in-depth analysis of the vorticity and enstrophy fields to elucidate the physics of reshock for the inclined interface RMI. After reshock, the two cases exhibit some similarities in integral measurements despite their disparate initial conditions but also show different vorticity decay trends, power law decay for the nonlinear and linear decay for the linear perturbation case.

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Figures

Grahic Jump Location
Fig. 1

Density contour showing the initial conditions for a 30 deg inclination interface

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Fig. 2

Density contour plots for incident Mach number of 2.5 and interface inclination angle of 30 deg at three times: (a) late time prior to reshock (3 ms), (b) early time after onset of reshock (4 ms), and (c) late time after onset of reshock (6.5 ms). The scale is unique for each time.

Grahic Jump Location
Fig. 3

Vorticity contour plots for incident Mach number of 2.5 and interface inclination angle of 30 deg at three times: (a) late time prior to reshock (3 ms), (b) early time after onset of reshock (4 ms), and (c) late time after onset of reshock (6.5 ms). The scale is uniform for all times.

Grahic Jump Location
Fig. 4

Chi contour plots for incident Mach number of 2.5 and interface inclination angle of 30 deg at three times: (a) late time prior to reshock (3 ms), (b) early time after onset of reshock (4 ms), and (c) late time after onset of reshock (6.5 ms). Here, white shows areas of high molecular mixing. The scale is uniform for all times.

Grahic Jump Location
Fig. 5

Density contour plots for incident Mach number of 2.5 and interface inclination angle of 80 deg for three times: (a) late time prior to reshock (3 ms), (b) early time after onset of reshock (4 ms), and (c) late time after onset of reshock (6.5 ms). The scale is unique for each time.

Grahic Jump Location
Fig. 6

Vorticity contour plots for incident Mach number of 2.5 and interface inclination angle of 80 deg at three times: (a) late time prior to reshock (3 ms), (b) early time after onset of reshock (4 ms), and (c) late time after onset of reshock (6.5 ms). The scale is uniform for all times.

Grahic Jump Location
Fig. 7

Chi contour plots for incident Mach number of 2.5 and interface inclination angle of 80 deg at three times: (a) late time prior to reshock (3 ms), (b) early time after onset of reshock (4 ms), and (c) late time after onset of reshock (6.5 ms). Here, white shows areas of high molecular mixing. The scale is uniform for all times.

Grahic Jump Location
Fig. 8

Schematic of the interface showing the interface wavelength and mixing width. The shaded lower portion of the figure is a representative reflection of the simulation domain to illustrate the full interface wavelength.

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Fig. 9

Plot of scaled mixing width over time for selected linear and nonlinear initial perturbation cases. The data set grouping is highlighted by labels showing the linear, transition, and nonlinear groupings. This data is reproduced from the authors' previous work [42].

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Fig. 10

Scaled mixing width to late scaled times for selected linear and nonlinear initial perturbation cases. Data sets are described in the key as follows: the number following the M is the Mach number multiplied by 10, the number following the a in the interface inclination angle in degrees. The effect of reshock is visible as a late time decrease in mixing width followed by a rise again for cases where the data extends to sufficiently large times. This data is reproduced from the authors' previous work [42].

Grahic Jump Location
Fig. 11

Scaled reshock mixing width versus scaled time for selected linear and nonlinear initial perturbation cases. Data sets are described in the key as follows; the number following the M is the Mach number multiplied by 10, the number following the a in the interface inclination angle in degrees. Linear cases are represented by gray (solid) lines. No trend or difference in the linear and nonlinear cases is visible suggesting the initial condition have had little effect on the post reshock growth rates.

Grahic Jump Location
Fig. 12

Mix mass plot over time. The lighter line represents the nonlinear case, and the darker line represents the linear case. The dashed line approximates the time at which reshock occurs.

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Fig. 13

Plot of circulation over time. The darker and lighter lines represent the linear and nonlinear interface cases, respectively. The solid lines show the positive and negative circulation components, and the dotted lines show the sum of these, the total circulation. The dashed black line approximates the time at which reshock occurs.

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Fig. 14

Enstrophy plot over time. The lighter line represents the nonlinear case, and the darker line represents the linear case. The dashed line approximates the time at which reshock occurs.

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Fig. 15

Annotated vorticity equation showing production terms

Grahic Jump Location
Fig. 16

Plot of positive and negative circulation production terms over time for the nonlinear case. The lightest lines are the circulation diffusion plotted on the right axis. The middle intensity and darkest lines are the baroclinic and compressible stretching production terms plotted on the left axis. The dashed line approximates the time at which reshock occurs.

Grahic Jump Location
Fig. 17

Plot of positive and negative circulation production terms over time for the linear case. The lightest lines are the circulation diffusion plotted on the right axis. The middle intensity and darkest lines are the baroclinic and compressible stretching production terms plotted on the left axis. The dashed line approximates the time at which reshock occurs.

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