Buoyancy-Generated Variable-Density Turbulence

Sandoval, David; Clark, Timothy T.; Riley, James J.

doi:10.1007/978-94-011-5474-1_22

Cited by 9 publications

(13 citation statements)

References 5 publications

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“…Time evolution of the mean pressure gradient normalized by the pressure head. Sandoval et al (1996). After the initial moment, most of energy resides in the solenoidal component (see below) and the pressure plays a role similar to that in incompressible flows: it reduces the velocity magnitude in the direction driven by gravity by transferring energy to the other two components.…”

Section: Resultsmentioning

confidence: 99%

“…The mean pressure gradient in VD turbulence is not hydrostatic as it is for a Boussinesq fluid; it is a dynamically evolving quantity. The mean pressure gradient is intimately coupled to material mixing through the specific volume pressure correlation (Sandoval et al 1996;. Once enough mixing has taken place so that vp, i is negligible, the fluid becomes a Boussinesq fluid and the mean pressure gradient is hydrostatic.…”

Section: Discussionmentioning

confidence: 99%

“…The first two terms dominate the right-hand side of (2.17); thus the VD deviation of the pressure gradient from hydrostatic is set by the specific volume pressure gradient correlation. The same mean pressure gradient was used by Sandoval et al (1996). Equation (2.17) shows that, unlike the Boussinesq case, the mean pressure is a dynamical quantity.…”

Section: Well-posedness and The Mean Pressure Gradientmentioning

confidence: 99%

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Buoyancy-driven variable-density turbulence

Livescu¹,

Ristorcelli²

2007

J. Fluid Mech.

105

165

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Buoyancy-generated motions in an unstably stratified medium composed of two incompressible miscible fluids with different densities, as occurs in the variable-density Rayleigh–Taylor instability, are examined using direct numerical simulations. The non-equilibrium homogeneous buoyantly driven problem is proposed as a unit problem for variable density turbulence to study: (i) the nature of variable density turbulence, (ii) the transition to turbulence and the generation of turbulence by the conversion of potential to kinetic energy; (iii) the role of non-Boussinesq effects; and (iv) a parameterization of the initial conditions by a static Reynolds number. Simulations are performed for Atwood numbers up to 0.5 with root mean square density up to 50% of the mean density and Schmidt numbers, 0.1 ≤ Sc ≤ 2. The benchmark problem has been designed to have the largest mass flux possible and is, in this configuration, the maximally unstable non-equilibrium flow possible. It is found that the mass flux, owing to its central role in the conversion of potential to kinetic energy, is probably the single most important dynamical quantity to predict in lower-dimensional models. Other primary findings include the evolution of the mean pressure gradient: during the non-Boussinesq portions of the flow, the evolution of the mean pressure gradient is non-hydrostatic (as opposed to a Boussinesq fluid) and is set by the evolution of the specific volume pressure gradient correlation. To obtain the numerical solution, a new pressure projection algorithm which treats the pressure step exactly, useful for simulations of non-solenoidal velocity flows, has been constructed.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Well-posedness and The Mean Pressure Gradientmentioning

confidence: 99%

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Buoyancy-driven variable-density turbulence

Livescu¹,

Ristorcelli²

2007

J. Fluid Mech.

105

165

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“…The current VD problem was first addressed in Sandoval (1995) and Sandoval, Clark & Riley (1996); their study focused on the hydrodynamics statistics of the flow. Our interest is: (i) in the statistics of the active scalar field; (ii) useful measures of the state and rate of the material mixing; and (iii) changes in the structure of the flow induced by the differential accelerations.…”

Section: Introductionmentioning

confidence: 99%

Variable-density mixing in buoyancy-driven turbulence

Livescu¹,

Ristorcelli²

2008

J. Fluid Mech.

109

123

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The homogenization of a heterogeneous mixture of two pure fluids with different densities by molecular diffusion and stirring induced by buoyancy-generated motions, as occurs in the Rayleigh–Taylor (RT) instability, is studied using direct numerical simulations. The Schmidt number, Sc, is varied by a factor of 20, 0.1 ≤ Sc ≤ 2.0, and the Atwood number, A, by a factor of 10, 0.05 ≤ A ≤ 0.5. Initial-density intensities are as high as 50% of the mean density. As a consequence of differential accelerations experienced by the two fluids, substantial and important differences between the mixing in a variable-density flow, as compared to the Boussinesq approximation, are observed. In short, the pure heavy fluid mixes more slowly than the pure light fluid: an initially symmetric double delta density probability density function (PDF) is rapidly skewed and, only at long times and low density fluctuations, does it relax to a Gaussian-like PDF. The heavy–light fluid mixing process asymmetry is relevant to the nature of molecular mixing on different sides of a high-Atwood-number RT layer. Diverse mix metrics are used to examine the homogenization of the two fluids. The conventional mix parameter, θ, is mathematically related to the variance of the excess reactant of a hypothetical fast chemical reaction. Bounds relating θ and the normalized product, Ξ, are derived. It is shown that θ underpredicts the mixing, as compared to Ξ, in the central regions of an RT layer; in the edge regions, θ is larger than Ξ. The shape of the density PDF cannot be inferred from the usual mix metrics popular in applications. For example, when θ, Ξ ≥ 0.6, characteristic of the interior of a fully developed RT layer, the PDFs can have vastly different shapes. Bounds on the fluid composition using two low-order moments of the density PDF are derived. The bounds can be used as realizability conditions for low-dimensional models. For the measures studied, the tightest bounds are obtained using Ξ and mean density. The structure of the flow is also examined. It is found that, at early times, the buoyancy production term in the spectral kinetic energy equation is important at all wavenumbers and leads to anisotropy at all scales of motion. At later times, the anisotropy is confined to the largest and smallest scales: the intermediate scales are more isotropic than the small scales. In the viscous range, there is a cancellation between the viscous and nonlinear effects, and the buoyancy production leads to a persistent small-scale anisotropy.

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“…The CFDNS code also uses a mixed spectral-compact finite differences scheme. DNS of HRT are reported in references [1,[90][91][92][93] (A up to 0.5) for the unsteady case and reference [16] for the stationary case (A up to 0.9). LES of incompressible RTI using explicit subgrid modelling were performed with the MIRANDA code in reference [94] at A = 0.5 and of stationary HRT using the stretched vortex model of Pullin [95] in reference [16] at A up to 0.9.…”

Section: (I) Direct Numerical Simulations Of Rayleigh-taylor Instabilmentioning

confidence: 99%

Numerical simulations of two-fluid turbulent mixing at large density ratios and applications to the Rayleigh–Taylor instability

Livescu

2013

Phil. Trans. R. Soc. A.

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A tentative review is presented of various approaches for numerical simulations of two-fluid gaseous mixtures at high density ratios, as they have been applied to the Rayleigh–Taylor instability (RTI). Systems exhibiting such RTI behaviour extend from atomistic sizes to scales where the continuum approximation becomes valid. Each level of description can fit into a hierarchy of theoretical models and the governing equations appropriate for each model, with their assumptions, are presented. In particular, because the compressible to incompressible limit of the Navier–Stokes equations is not unique and understanding compressibility effects in the RTI critically depends on having the appropriate basis for comparison, two relevant incompressible limits are presented. One of these limits has not been considered before. Recent results from RTI simulations, spanning the levels of description presented, are reviewed in connection to the material mixing problem. Owing to the computational limitations, most in-depth RTI results have been obtained for the incompressible case. Two such results, concerning the asymmetry of the mixing and small-scale anisotropy anomaly, as well as the possibility of a mixing transition in the RTI, are surveyed. New lines for further investigation are suggested and it is hoped that bringing together such diverse levels of description may provide new ideas and increased motivation for studying such flows.

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Buoyancy-Generated Variable-Density Turbulence

Cited by 9 publications

References 5 publications

Buoyancy-driven variable-density turbulence

Buoyancy-driven variable-density turbulence

Variable-density mixing in buoyancy-driven turbulence

Numerical simulations of two-fluid turbulent mixing at large density ratios and applications to the Rayleigh–Taylor instability

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