Late-time turbulent mixing induced by multimode Richtmyer–Meshkov instability in cylindrical geometry

2020 ◽  
Vol 32 (12) ◽  
pp. 124116
Author(s):  
Jin Ge ◽  
Xin-ting Zhang ◽  
Hai-feng Li ◽  
Bao-lin Tian
Keyword(s):  
Turbulent Mixing ◽  
Cylindrical Geometry ◽  
Late Time

scholarly journals Implicit large eddy simulation of shock-driven material mixing

2013 ◽  
Vol 371 (2003) ◽  
pp. 20120217 ◽  
Author(s):  
F. F. Grinstein ◽  
A. A. Gowardhan ◽  
J. R. Ristorcelli
Keyword(s):  
Large Eddy Simulation ◽  
Turbulent Mixing ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Late Time ◽  
Eddy Simulation ◽  
Geometrical Complexity ◽  
Planar Shock ◽  
Large Eddy ◽  
Implicit Large Eddy Simulation

Under-resolved computer simulations are typically unavoidable in practical turbulent flow applications exhibiting extreme geometrical complexity and a broad range of length and time scales. An important unsettled issue is whether filtered-out and subgrid spatial scales can significantly alter the evolution of resolved larger scales of motion and practical flow integral measures. Predictability issues in implicit large eddy simulation of under-resolved mixing of material scalars driven by under-resolved velocity fields and initial conditions are discussed in the context of shock-driven turbulent mixing. The particular focus is on effects of resolved spectral content and interfacial morphology of initial conditions on transitional and late-time turbulent mixing in the fundamental planar shock-tube configuration.

scholarly journals Computing multi-mode shock-induced compressible turbulent mixing at late times

2015 ◽  
Vol 779 ◽  
pp. 411-431 ◽  
Author(s):  
T. Oggian ◽  
D. Drikakis ◽  
D. L. Youngs ◽  
R. J. R. Williams
Keyword(s):  
Mach Number ◽  
Numerical Simulations ◽  
Compressible Flow ◽  
Turbulent Mixing ◽  
Numerical Study ◽  
Mixing Layer ◽  
Suitable Model ◽  
Late Time ◽  
Flow Equations ◽  
Multi Mode

Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late-time behaviour of a single-shocked Richtmyer–Meshkov instability (RMI) and the associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that the RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field, the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible–incompressible solver that removes the low-Mach-number limitations of the compressible solvers, thus allowing numerical simulations of late-time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

scholarly journals Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics

2014 ◽  
Vol 748 ◽  
pp. 113-142 ◽  
Author(s):  
M. Lombardini ◽  
D. I. Pullin ◽  
D. I. Meiron
Keyword(s):  
Turbulent Mixing ◽  
Spherical Surface ◽  
Density Ratio ◽  
Mixing Layer ◽  
Inertial Subrange ◽  
Planar Geometry ◽  
Late Time ◽  
Mean Flow ◽  
Turbulence Statistics ◽  
Decaying Turbulence

AbstractWe present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number $\approx $1.2, the density ratio (precisely $|A_0|\approx 0.67$) and the perturbation shape (dominant spherical wavenumber $\ell _0=40$ and amplitude-to-initial radius of 3 %): the incident shock travels from the lighter fluid to the heavy one, or inversely, from the heavy to the light fluid. In Part 1 (Lombardini, M., Pullin, D. I. & Meiron, D. I., J. Fluid Mech., vol. 748, 2014, pp. 85–112), we described the computational problem and presented results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. In particular, it was shown that both configurations reach similar convergence ratios $\approx $2. Here, turbulent mixing is studied through various turbulence statistics. The mixing activity is first measured through two mixing parameters, the mixing fraction parameter $\varTheta $ and the effective Atwood ratio $A_e$, which reach similar late time values in both light–heavy and heavy–light configurations. The Taylor-scale Reynolds numbers attained at late times are estimated at approximately 2000 in the light–heavy case and 1000 in the heavy–light case. An analysis of the density self-correlation $b$, a fundamental quantity in the study of variable-density turbulence, shows asymmetries in the mixing layer and non-Boussinesq effects generally observed in high-Reynolds-number Rayleigh–Taylor (RT) turbulence. These traits are more pronounced in the light–heavy mixing layer, as a result of its flow history, in particular because of RT-unstable phases (see Part 1). Another measure distinguishing light–heavy from heavy–light mixing is the velocity-to-scalar Taylor microscales ratio. In particular, at late times, larger values of this ratio are reported in the heavy–light case. The late-time mixing displays the traits some of the traits of the decaying turbulence observed in planar Richtmyer–Meshkov (RM) flows. Only partial isotropization of the flow (in the sense of turbulent kinetic energy (TKE) and dissipation) is observed at late times, the Reynolds normal stresses (and, thus, the directional Taylor microscales) being anisotropic while the directional Kolmogorov microscales approach isotropy. A spectral analysis is developed for the general study of statistically isotropic turbulent fields on a spherical surface, and applied to the present flow. The resulting angular power spectra show the development of an inertial subrange approaching a Kolmogorov-like $-5/3$ power law at high wavenumbers, similarly to the scaling obtained in planar geometry. It confirms the findings of Thomas & Kares (Phys. Rev. Lett., vol. 109, 2012, 075004) at higher convergence ratios and indicates that the turbulent scales do not seem to feel the effect of the spherical mixing-layer curvature.

Hairpin vortices and highly elongated flow structures in a stably stratified shear layer

2019 ◽  
Vol 878 ◽  
pp. 37-61
Author(s):  
Tomoaki Watanabe ◽  
James J. Riley ◽  
Koji Nagata ◽  
Keigo Matsuda ◽  
Ryo Onishi
Keyword(s):  
Turbulent Mixing ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Flow Structures ◽  
Late Time ◽  
Large Contribution ◽  
Turbulent Structures ◽  
Hairpin Vortices ◽  
Shear Parameter ◽  
O 10

Turbulent structures in stably stratified shear layers are studied with direct numerical simulation. Flow visualization confirms the existence of hairpin vortices and highly elongated structures with positive and negative velocity fluctuations, whose streamwise lengths divided by the layer thickness are $O(10^{0})$ and $O(10^{1})$, respectively. The flow at the wavelength related to these structures makes a large contribution to turbulent kinetic energy. These structures become prominent in late time, but with small buoyancy Reynolds numbers indicating suppression of turbulent mixing. Active turbulent mixing associated with the hairpin vortices, however, does occur. The structures and the vertical profile of the integral shear parameter show connections between stable stratified shear layers and wall-bounded shear flows.

Turbulent mixing in uniform channels of irregular cross-section

1994 ◽  
Vol 32 (1) ◽  
pp. 67-86 ◽  
Author(s):  
R. I. Nokes ◽  
G. O. Hughes
Keyword(s):  
Cross Section ◽  
Turbulent Mixing
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