1,063 research outputs found
On the Richtmyer-Meshkov Instability in Magnetohydrodynamics
No full textThe Richtmyer-Meshkov instability is important in a wide variety of applications including inertial confinement fusion and astrophysical phenomena. In some of these applications, the fluids involved may be plasmas and hence be affected by magnetic fields. For one configuration, it has been numerically demonstrated that the growth of the instability in magnetohydrodynamics is suppressed in the presence of a magnetic field. Here, the nature of this suppression is theoretically and numerically investigated.
In the framework of ideal incompressible magnetohydrodynamics, we examine the stability of an impulsively accelerated, sinusoidally perturbed density interface in the presence of a magnetic field that is parallel to the acceleration. This is accomplished by analytically solving the linearized initial value problem, which is a model for the Richtmyer-Meshkov instability. We find that the initial growth rate of the interface is unaffected by the presence of a magnetic field, but for a finite magnetic field the interface amplitude asymptotes to a constant value. Thus the instability of the interface is suppressed. The interface behavior from the analytical solution is compared to the results of both linearized and non-linear compressible numerical simulations for a wide variety of conditions.
We then consider the problem of the regular refraction of a shock at an oblique, planar contact discontinuity separating conducting fluids of different densities in the presence of a magnetic field aligned with the incident shock velocity. Planar ideal MHD simulations indicate that the presence of a magnetic field inhibits the deposition of vorticity on the shocked contact, which leads to the suppression of the Richtmyer-Meshkov instability. We show that the shock refraction process produces a system of five to seven plane waves that may include fast, intermediate, and slow MHD shocks, slow compound waves, 180° rotational discontinuities, and slow-mode expansion fans that intersect at a point. In all solutions, the shocked contact is vorticity free and hence stable. These solutions are not unique, but differ in the type of waves that participate. The set of equations governing the structure of these multiple-wave solutions is obtained in which fluid property variation is allowed only in the azimuthal direction about the wave-intersection point. Corresponding solutions are referred to as either quintuple-points, sextuple-points, or septuple-points, depending on the number of participating waves. A numerical method of solution is described and examples are compared to the results of numerical simulations for moderate magnetic field strengths. The limit of vanishing magnetic field at fixed permeability and pressure is studied for two solution types. The relevant solutions correspond to the hydrodynamic triple-point with the shocked contact replaced by a singular structure consisting of a wedge, whose angle scales with the applied field magnitude, bounded by either two slow compound waves or two 180° rotational discontinuities, each followed by a slow-mode expansion fan. These bracket the MHD contact which itself cannot support a tangential velocity jump in the presence of a non-parallel magnetic field. The magnetic field within the singular wedge is finite and the shock-induced change in tangential velocity across the wedge is supported by the expansion fans that form part of the compound waves or follow the rotational discontinuities. To verify these findings, an approximate leading order asymptotic solution appropriate for both flow structures was computed. The full and asymptotic solutions are compared quantitatively and there is shown to be excellent agreement between the two.</p
Study of the turbulent mixing zone induced by the Richtmyer-Meshkov instability using Laser Doppler Velocimetry and Schlieren visualizations
No full textAn experimental study of the compressible mixing generated by the Richtmyer-Meshkov instability (RMI) is carried out in a vertical shock tube by means of two-components Laser Doppler Velocimetry (2C-LDV) measurements and Time-resolved Schlieren visualizations. An attempt is made to quantify the RMI-induced air/sulphurhexafluoride (SF6) mixing by measuring turbulence levels inside the mixing zone at a given stage of its development and by extracting the growth rate of the mixing zone from the Schlieren images
The influence of initial conditions on turbulent mixing due to Richtmyer-Meshkov instability
No full textThis 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 x 10(9) 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 theta
approximate to 0.26 at low Atwood and theta approximate to 0.3 at high Atwood
numbers. The broadband case uses a perturbation power spectrum of the form P(k)
proportional to k(-2) with a proposed theoretical growth rate of theta = 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
Low-mach number effects and late-time treatment of Richtmyer-Meshkov and Rayleigh-Taylor instabilities
No full textThe Richtmyer-Meshkov instability appears when the mixing between two fluids is triggered
by the passage of a shock wave. It occurs in a range of different applications,
such as astrophysics, inertial confinement fusion and supersonic combustion. Due to
the extreme complexity of this phenomenon to be reproduced in a controlled environment,
its study heavily relies on numerical methods. The presence of a shock wave
as a triggering factor requires the use of compressible solvers, but once the shock has
started the mixing process, the flow field freely decays and becomes incompressible.
The dynamics of this instability is still to be fully understood, especially its long-time
behaviour. One of the hypothesis is that the mixing layer achieves a self-similar development
at some point during its evolution. However, the low-Mach flow at late-times
does not always allow to push compressible simulations so far in time and when it is
possible, they become extremely demanding from a computational point of view. In
fact, it is known that standard compressible methods fail when the Mach number of
the numerical field is low and moreover they lose time-marching efficiency.
In this thesis, a new approach to the study of the very late-stage of the instability
through the use of ILES is presented. The technique consists in starting the simulation
by using the compressible model and to initialise the incompressible solver when
the compressibility of the numerical field becomes sufficiently low. This allows to bypass
the issues previously mentioned and study the very late-stage of the instability
at reasonable computational costs. For this purpose, a new incompressible solver that
employs high-resolution methods and which is based on the pressure-projection technique
is developed. A number of different Riemann-solvers and reconstruction schemes
are tested against experiments using the incompressible, impulsive version of RMI as
test case. Two alternative methods are considered for triggering the mixing: velocity
impulse and gravity pulse. Excellent results were obtained by using the former, whereas
discrepancies were noticed when the latter was employed. Comparisons against numerical
simulations in the literature allowed to identify the inviscid nature of the solver as
the cause of these differences. However, this did not affect the capability of the solver
to correctly compute multi-mode cases, in which viscosity is negligible. A preliminary
study on the compressibility of the numerical field in time proved the feasibility of
the numerical transition and a switching criterion based on the Mach number was established.
The approach was therefore tested on a single-mode perturbation case and
compared against compressible simulation. Very good agreement was found in the prediction
of the growth of the instability and the analysis of the divergence of velocity of
the numerical field proved the incompressibility of the solution generated by the hybrid
solver. Finally, the approach was applied to multi-mode test cases. Excellent agreement
with the theory was found. The turbulent kinetic energy presented a modified
subinertial range and the growth exponent was very close to fully compressible predictions
and experiments. Deeper results analysis showed against compressible simulations
showed very good agreement on the flow physics. In fact, the instability settled to a
self-similar regime with the same time-scale predicted by compressible analysis, but
the simulated time reached by the hybrid solver was three times longer. The results
obtained proved the applicability of the approach, opening to new possibilities for the
study of the instability
Effects of initial conditions and Mach number in the evolution of Richtmyer-Meshkov instabilities
No full textWe present an experimental study of the effects of shock intensity and initial conditions on the evolution of Richtmyer-Meshkov Instabilities (RMI). This study is carried out in a vertical shock tube with a single interface of sulfur-hexafluoride and air. We use combined particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) to obtain simultaneous measurements of velocity and density. These measurements enable us to determine single- and multi-point statistics of vector, scalar, and combined fields. We use these statistical descriptors to study the evolution of turbulence mixing in RMIs under different Mach numbers and initial conditions
Modeling and simulation of compressible multi-material interface instabilities
No full textThis work was partially funded by the DGA.We aim to simulate the interactions at the material interface of two compressible media. These interactions are modeled by a single fully Eulerian system of conservation laws. The materials differ by their constitutive laws, that can reproduce the mechanical characteristics of fluids or elastic solid. We illustrate the model with simulations of shock waves impinging on undulated interfaces, generating instabilities such as Richtmyer-Meshkov instabilities
Large-eddy simulation of multi-component compressible turbulent flows using high resolution methods
No full textThe ability of a finite volume Godunov and a semi-Lagrangian large-eddy
simulation (LES) method to predict shock induced turbulent mixing has been
examined through simulations of the half-height experiment [Holder and Barton.
In: Proceedings of the international workshop on the physics of compressible
turbulent mixing, 2004]. Very good agreement is gained in qualitative
comparisons with experimental results for combined Richtmyer-Meshkov and Kelvin-
Helmholtz instabilities in compressible turbulent multi-component flows. It is
shown that both numerical methods can capture the size, location and temporal
growth of the main flow features. In comparing the methods, there is variability
in the amount of resolved turbulent kinetic energy. The semi-Lagrangian method
has constant dissipation at low Mach number, thus allowing the initially small
perturbations to develop into Kelvin-Helmholtz instabilities. These are
suppressed at the low Mach stage in the Godunov method. However, there is an
excellent agreement in the final amount of fluid mixing when comparing both
numerical methods at different grid resolutions
Direct Numerical Simulation Of Three-Dimensional Richtmyer-Meshkov Instability
No full textDirect numerical simulation (DNS) is used to study flow characteristics after interaction of a planar shock with a spherical media interface in each side of which the density is different. This interfacial instability is known as the Richtmyer-Meshkov (R-M) instability. The compressible Navier-Stoke equations are discretized with group velocity control (GVC) modified fourth order accurate compact difference scheme. Three-dimensional numerical simulations are performed for R-M instability installed passing a shock through a spherical interface. Based on numerical results the characteristics of 3D R-M instability are analysed. The evaluation for distortion of the interface, the deformation of the incident shock wave and effects of refraction, reflection and diffraction are presented. The effects of the interfacial instability on produced vorticity and mixing is discussed
Numerical Investigation of Richtmyer-Meshkov Instability Driven by Cylindrical Shocks
No full textIn this paper, a numerical method with high order accuracy and high resolution was developed to simulate the Richtmyer-Meshkov(RM) instability driven by cylindrical shock waves. Compressible Euler equations in cylindrical coordinate were adopted for the cylindrical geometry and a third order accurate group control scheme was adopted to discretize the equations. Moreover, an adaptive grid technique was developed to refine the grid near the moving interface to improve the resolution of numerical solutions. The results of simulation exhibited the evolution process of RM instability, and the effect of Atwood number was studied. The larger the absolute value of Atwood number, the larger the perturbation amplitude. The nonlinear effect manifests more evidently in cylindrical geometry. The shock reflected from the pole center accelerates the interface for the second time, considerably complicating the interface evolution process, and such phenomena of reshock and secondary shock were studied
Effects of adiabatic exponent on Richtmyer-Meshkov instability
No full textWe present a systematical numerical study of the effects of adiabatic exponent gamma on Richtmyer-Meshkov instability (RMI) driven by cylindrical shock waves, based on the gamma model for the multi-component problems and numerical simulation with high-order and high-resolution method for compressible Euler equations. The results show that the RMI of different gamma across the interface exhibits different evolution features with the case of single gamma. Moreover, the large gamma can hold back the development of nonlinear structures, such as spikes and bubbles
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