The dynamics of variable-density turbulence

Sandoval, Donald Leon

doi:10.2172/270823

Cited by 25 publications

(33 citation statements)

References 38 publications

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“…Hence, as far as large scales are concerned, small Mach number high density contrast flows stand apart from Boussinesq and fully compressible flows and require a study of their own. In this respect, a vast literature provides an in depth analysis of their statistical properties [24][25][26][27][28][29]. Unfortunately, most of these works do not address the behavior of large scales, save for brief comments in Refs.…”

Section: Introductionmentioning

confidence: 99%

Permanence of large eddies in Richtmyer-Meshkov turbulence with a small Atwood number

et al. 2018

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In this work, we study the large-scale structure of homogeneous flows displaying high density contrasts and small turbulent Mach numbers. Following Batchelor & Proudman [1], we draw an analogy between this configuration and that of a single isolated eddy displaying density non-uniformities. By doing so, we are able to highlight the crucial role played by the solenoidal component of the momentum in the preservation of initial conditions. In particular, we show that the large-scale initial conditions of the spectrum of the solenoidal momentum are preserved provided its infrared exponent is smaller than 4. This condition is reminiscent of the one usually derived in constant density flow, except that it does not apply to the velocity spectrum. The latter is actually shown to be impermanent for infrared exponents larger or equal to 2. The consequences of these properties on the self-similar decay of the flow are discussed. Finally, these predictions are verified by performing large eddy simulations of homogeneous isotropic turbulence.

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Section: Introductionmentioning

confidence: 99%

Permanence of large eddies in Richtmyer-Meshkov turbulence with a small Atwood number

et al. 2018

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“…For nonreactive Newtonian flows or nonmiscible media, η can be assumed to be zero, and consequently the viscosity μ also follows a transport equation [10,55] like α and ρ, with adequate initial and boundary conditions. In some works, μ is directly assumed to be a function of ρ, and/or reciprocally ρ a function of μ.…”

mentioning

confidence: 99%

A Hybrid Grid-Particle Method for Moving Bodies in 3D Stokes Flow with Variable Viscosity

Chatelin¹,

Poncet²

2013

SIAM J. Sci. Comput.

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This article presents a new approach for the resolution of large three-dimensional Stokes equations with variable viscosity fluids, coupled with transport equations. After building the model, we will write these equations in the context of highly viscous flows and penalization, in order to consider complex geometries moving in a fluid. From a mathematical point of view, the solutions show nonlinear dynamics. Beside the use of standard tools such as finite differences and staggered grids, we have built a new methodology based on large three-dimensional simulations, including operators splitting for an efficient use of fast solvers, multi-index fixed point methods, Lagrangian methods with fast and accurate grid-particle transfers, and the multiresolution description of variables. Among the main original aspects of this method, both accurate incompressibility and variable viscosity are treated in the same fixed point. Hence the computation costs for variable and constant viscosity flows are similar. Several examples are given to validate the order of convergence and conservation rates. Such models are used, among other examples, in biological computing at the cellular scale. The present article eventually describes the ciliated epithelium cells covering a mammal's lungs, beating in a mucus film. This study of human lung diseases explores the efficiency of the mucociliary clearance, a challenging problem in health sciences, especially for the investigation of cystic fibrosis and various chronic obstructive pulmonary diseases.

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“…The equations governing the mixing of two miscible, stratified fluids are the continuity, Navier-Stokes, and mass fraction equations, 13,35 ‫ץ‬…”

Section: A the Evolution Equations For Two Miscible Fluidsmentioning

confidence: 99%

“…The algorithm consists of first solving for the density at the next time step, then the half-time step momentum ͑not including pressure effects͒, and finally the density at the next time step is used in a projection step to solve a Poisson equation for the pressure and the momentum. 35,40 The right side of Eq. ͑9͒ and the last two terms in Eq.…”

Section: Spatial and Temporal Discretizationmentioning

confidence: 99%

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Influence of subgrid scales on resolvable turbulence and mixing in Rayleigh–Taylor flow

2004

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The energy transfer process and the interaction of different scales in a flow induced by the variable-density Rayleigh-Taylor instability in miscible fluids is investigated using a three-dimensional direct numerical simulation database with a spatial resolution of N x ϫN y ϫN z ϭ512ϫ512ϫ2040. The method used to study the transfer of energy between the supergrid and subgrid scales in the homogeneous planes, determined by partitioning the modes into resolved and unresolved scales defined by a two-dimensional cutoff wave number k c in Fourier space, is applied to the kinetic energy evolution equation. The treatment of the flow inhomogeneity in the direction z parallel to the acceleration is analogous to that used in the analysis of incompressible wall-bounded flows, including channel flow and Rayleigh-Bénard convection ͓J. A. Domaradzki et al., Phys. Fluids 6, 1583 ͑1994͒; J. A. Domaradzki and W. Liu, ibid. 7, 2025 ͑1995͔͒. Using a sharp Fourier cutoff filter, the kinetic energy transfer is decomposed into ͑1͒ the resolved part; ͑2͒ a part corresponding to the interaction between resolved and unresolved scales; and ͑3͒ a part corresponding to the interaction between unresolved scales. The sum of these last two contributions is the subgrid-scale kinetic energy transfer, which is studied in the present work. These z-dependent spectra are computed for three different cutoff wave numbers to investigate the dependence of the transfer process on the scales contributing to the subgrid interactions. The kinetic energy transfer is further decomposed into its positive and negative components corresponding to the forward and backward cascades of energy, respectively, that arise from the nonlinear modal interactions. The decomposition into resolved and unresolved scales is used to define an effective eddy viscosity and backscatter viscosity. The principal conclusions of the analysis are ͑1͒ the transfer spectra and eddy viscosities exhibit a strong dependence on the wave number cutoff; ͑2͒ the contributions from the interaction between resolved and unresolved scales dominate the contribution to the total subgrid eddy viscosities and are responsible for the cusp at large k/k c ; ͑3͒ the contributions from the interaction between unresolved scales dominate the contribution to the total subgrid eddy viscosities at small k/k c and are responsible for the small, negative contribution ͑associated with an inverse energy transfer͒, and ͑4͒ backscatter is strongest in the regions near the boundaries of the mixing layer. The physical implications of these results for subgrid-scale modeling in a large-eddy simulation of Rayleigh-Taylor instability-induced turbulence are discussed.

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The dynamics of variable-density turbulence

Cited by 25 publications

References 38 publications

Permanence of large eddies in Richtmyer-Meshkov turbulence with a small Atwood number

Permanence of large eddies in Richtmyer-Meshkov turbulence with a small Atwood number

A Hybrid Grid-Particle Method for Moving Bodies in 3D Stokes Flow with Variable Viscosity

Influence of subgrid scales on resolvable turbulence and mixing in Rayleigh–Taylor flow

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