323,910 research outputs found
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
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
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
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
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Richtmyer-Meshkov instabilities in stratified fluids
No full textWe present an analytic theory of Richtmyer-Meshkov instabilities in an arbitrary number N of stratified fluids subjected to a shock. Following our earlier work on Rayleigh-Taylor instabilities, the theory assumes incompressible flow in which a shock is treated an impulsive acceleration, g = ..delta.. v delta(tau/sub s), ..delta..v being the jump velocity induced in the system by a shock at time tau/sub s/. We discuss the special cases N = 2 and N = 3, and illustrate both Rayleigh-Taylor and Richtmyer-Meshkov instabilities by examples patterned after inertial confinement fusion implosions
Implicit large eddy simulation for unsteady multi-component compressible turbulent flows
No full textNumerical methods for the simulation of shock-induced turbulent mixing have been
investigated, focussing on Implicit Large Eddy Simulation. Shock-induced turbulent
mixing is of particular importance for many astrophysical phenomena, inertial confinement
fusion, and mixing in supersonic combustion. These disciplines are particularly
reliant on numerical simulation, as the extreme nature of the flow in question makes
gathering accurate experimental data difficult or impossible.
A detailed quantitative study of homogeneous decaying turbulence demonstrates that
existing state of the art methods represent the growth of turbulent structures and the decay
of turbulent kinetic energy to a reasonable degree of accuracy. However, a key observation
is that the numerical methods are too dissipative at high wavenumbers (short
wavelengths relative to the grid spacing). A theoretical analysis of the dissipation of
kinetic energy in low Mach number flows shows that the leading order dissipation rate
for Godunov-type schemes is proportional to the speed of sound and the velocity jump
across the cell interface squared. This shows that the dissipation of Godunov-type
schemes becomes large for low Mach flow features, hence impeding the development
of fluid instabilities, and causing overly dissipative turbulent kinetic energy spectra.
It is shown that this leading order term can be removed by locally modifying the reconstruction
of the velocity components. As the modification is local, it allows the
accurate simulation of mixed compressible/incompressible flows without changing the
formulation of the governing equations. In principle, the modification is applicable to
any finite volume compressible method which includes a reconstruction stage. Extensive
numerical tests show great improvements in performance at low Mach compared
to the standard scheme, significantly improving turbulent kinetic energy spectra, and
giving the correct Mach squared scaling of pressure and density variations down to
Mach 10−4. The proposed modification does not significantly affect the shock capturing
ability of the numerical scheme.
The modified numerical method is validated through simulations of compressible,
deep, open cavity flow where excellent results are gained with minimal modelling
effort. Simulations of single and multimode Richtmyer-Meshkov instability show that
the modification gives equivalent results to the standard scheme at twice the grid resolution
in each direction. This is equivalent to sixteen times decrease in computational
time for a given quality of results. Finally, simulations of a shock-induced turbulent
mixing experiment show excellent qualitative agreement with available experimental
data
Nonlinear theory of classical cylindrical Richtmyer-Meshkov instability for arbitrary Atwood numbers
No full textA nonlinear theory is developed to describe the cylindrical Richtmyer-Meshkov instability (RMI) of an impulsively accelerated interface between incompressible fluids, which is based on both a technique of Pade approximation and an approach of perturbation expansion directly on the perturbed interface rather than the unperturbed interface. When cylindrical effect vanishes (i.e., in the large initial radius of the interface), our explicit results reproduce those [Q. Zhang and S.-I. Sohn, Phys. Fluids 9, 1106 (1996)] related to the planar RMI. The present prediction in agreement with previous simulations [C. Matsuoka and K. Nishihara, Phys. Rev. E 73, 055304(R) (2006)] leads us to better understand the cylindrical RMI at arbitrary Atwood numbers for the whole nonlinear regime. The asymptotic growth rate of the cylindrical interface finger (bubble or spike) tends to its initial value or zero, depending upon mode number of the initial cylindrical interface and Atwood number. The explicit conditions, directly affecting asymptotic behavior of the cylindrical interface finger, are investigated in this paper. This theory allows a straightforward extension to other nonlinear problems related closely to an instable interface. (C) 2014 AIP Publishing LLC
q-deformed variational study of the Lipkin-Meshkov-Glick model via coherent states
No full textWe show that the ground-state energy of the q-deformed Lipkin-Meshkov-Glick Hamiltonian can be estimated by q-deformed coherent states. We also use these coherent states to analyse qualitatively the suppression of the second order ground-state energy phase transition of this model. © 1993.Instituto de Fisica Teórica Universidade Estadual Paulista, Rua Pamplona 145, 01405-900 São Paulo, SPInstituto de Fisica Teórica Universidade Estadual Paulista, Rua Pamplona 145, 01405-900 São Paulo, S
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