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

Cabot, W.; Schilling, Oleg; Zhou, Ye

doi:10.1063/1.1636477

Cited by 16 publications

(9 citation statements)

References 60 publications

(64 reference statements)

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“…Firstly, E c (k, t) may not have the same power law at low wave number (NLg) in (7) and at high wave number (NLν) in (9). In the self similar regime c ′ 2 tends to be a constant [21] which will be denoted c 2 0 .…”

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confidence: 99%

“…The fluctuating part will be denoted with a prime and defined as Φ ′ = Φ − Φ . With the increasing capacity of super computers, many simulations of RT flows in the developed turbulent regime have been performed, which describe the velocity spectrum E(k) [7,8,9], defined in such a way that u ′ 2 = dk E(k), or the concentration spectrum E c (k) [10,11,12,13], defined as c ′ 2 = dk E c (k), or both [14,15]. In the same time, although fewer in number, experimental investigations of E(k) [16] and E c (k) [10,17,18] have been carried out.…”

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confidence: 99%

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Rayleigh-Taylor Turbulence is Nothing Like Kolmogorov Turbulence in the Self-Similar Regime

Poujade

2006

Phys. Rev. Lett.

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An increasing number of numerical simulations and experiments describing the turbulent spectrum of Rayleigh-Taylor (RT) mixing layers came to light over the past few years. Results reported in recent studies allow to rule out a turbulenceà la Kolmogorov as a mechanism acting on a self similar RT turbulent mixing layer. A different mechanism is presented, which complies with both numerical and experimental results and relates RT flow to other buoyant flows.PACS numbers: 52.35. Py, 47.20.Bp, 47.27.eb, 47.27.te A Rayleigh-Taylor (RT) instability [1, 2] occurs whenever a light fluid, ρ 1 , pushes a heavy fluid, ρ 2 , or similarly, when a heavy fluid on top of a lighter fluid is subject to a gravitational acceleration. The understanding of such instability in the developed turbulent regime is of primary interest to many fields of physics and technology since it is an important cause of mixing between two fluids of different density. In astrophysics for instance, it is responsible for the outward acceleration of a thermonuclear flame in type Ia supernovae [3], but it also plays an important role in shaping the interstellar medium so that new stars can be born [4]. The technology of confinement fusion also relies on a good understanding of RT mixing [5] and ways to reduce it [6]. The RT flow of two incompressible fluids in the low Atwood limit, A = (ρ 2 − ρ 1 )/(ρ 2 + ρ 1 ) ≪ 1 (Boussinesq approximation), is governed by a concentration equation (1), the Navier Stokes equation supplemented with a buoyant source term (2) and the incompressibility constraint (3)where g is a stationary and uniform gravitational acceleration vector field (i.e. planar symmetry is assumed). The coefficient κ is the molecular diffusion coefficient and ν is the kinematic viscosity of the mixture. They are both supposed constant. Without loss of generality, g is parallel to the z-axis. This is why, for any generic physical value Φ, the average (so defined numerically and experimentally) will be Φ (z) = 1 S S dx dy Φ throughout this paper. The fluctuating part will be denoted with a prime and defined as Φ ′ = Φ − Φ . With the increasing capacity of super computers, many simulations of RT flows in the developed turbulent regime have been performed, which describe the velocity spectrum E(k) [7,8,9], defined in such a way that u ′ 2 = dk E(k), or the concentration spectrum E c (k) [10,11,12,13], defined as c ′ 2 = dk E c (k), or both [14,15]. In the same time, although fewer in number, experimental investigations of E(k) [16] and E c (k) [10,17,18] have been carried out. A quick inspection of these results shows that no consensus arises concerning the shape of these spectrum. From a theoretical point of view, the situation is not more satisfactory. In [19] it is claimed that the Kolmogorov-Obukhov scheme, E(k) ∼ k −5/3 , holds in 3D RT mixing given that the effect of buoyancy on turbulence, although fundamental at the largest scale, becomes irrelevant at smaller scales. In [20] the particular RT time scale 1/ √ kgA at wave number k has been postu...

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confidence: 99%

Rayleigh-Taylor Turbulence is Nothing Like Kolmogorov Turbulence in the Self-Similar Regime

Poujade

2006

Phys. Rev. Lett.

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“…One of the first investigations of Rayleigh-Taylor instability was done by Rayleigh [43]. Since then, there have been many experimental, theoretical and numerical studies of Rayleigh-Taylor instability (Cabot [44] and Andrews [45]). …”

Section: Simulations Of Rayleigh-taylor Instabilitymentioning

confidence: 98%

Two‐fluid model with interface sharpening

Štrubelj

Tiselj

2010

Numerical Meth Engineering

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SUMMARYTwo-fluid models are applicable for simulations of all types of two-phase flows ranging from separated flows with large characteristic interfacial length scales to highly dispersed flows with very small characteristic interfacial length scales. The main drawback of the two-fluid model, when used for simulations of stratified flows, is the numerical diffusion of the interface. Stratified flows can be easily and more accurately solved with interface tracking methods; however, these methods are limited to the flows, that do not develop into dispersed types of flows. The present paper describes a new approach, where the advantage of the two-fluid model is combined with the conservative level set method for interface tracking. The advection step of the volume fraction transport equation is followed by the interface sharpening, which preserves the thickness of the interface during the simulation. The proposed two-fluid model with interface sharpening was found to be more accurate than the existing two-fluid models. The mixed flow with both: stratified and dispersed flow, is simulated with the coupled model in this paper. In the coupled model, the dispersed two-fluid model and two-fluid model with interface sharpening are used locally, depending on the parameter which recognizes the flow regime.

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“…where the overline denotes …ltering in this case (Smagorinsky 1963;Lilly 1967;Pope 2000). In wavenumber space, the modelling of R ij is accomplished by the calculation or modeling of triadic wave interactions between resolved and …ltered ‡uctuations (Leslie & Quarini 1979;Pope 2000;Cabot et al 2004). This method has the advantage of greater computational e¢ ciency and achieving a greater range of Reynolds numbers than suitable for DNS.…”

Section: Previous Simulationsmentioning

confidence: 99%

An Investigation of the Influence of Initial Conditions on Rayleigh-Taylor Mixing

Mueschke

2004

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Experiments and direct numerical simulations (DNS) have been performed to examine the e¤ects of initial conditions on the dynamics of a Rayleigh-Taylor unstable mixing layer. Experiments were performed on a water channel facility to measure the interfacial and velocity perturbations initially present at the two-‡uid interface in a small Atwood number mixing layer. The experimental measurements have been parameterized for use in numerical simulations of the experiment. Two-and threedimensional DNS of the experiment have been performed using the parameterized initial conditions. It is shown that simulations implemented with initial velocity and density perturbations, rather than density perturbations alone, are required to match experimentally-measured statistics and spectra. Data acquired from both the experiment and numerical simulations are used to examine the role of initial conditions on the evolution of integral-scale, turbulence, and mixing statistics. Early-time turbulence and mixing statistics are shown to be strongly-dependent upon the early-time transition of the initial perturbation from a weakly-nonlinear to a strongly-nonlinear ‡ow.

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

Cited by 16 publications

References 60 publications

Rayleigh-Taylor Turbulence is Nothing Like Kolmogorov Turbulence in the Self-Similar Regime

Rayleigh-Taylor Turbulence is Nothing Like Kolmogorov Turbulence in the Self-Similar Regime

Two‐fluid model with interface sharpening

An Investigation of the Influence of Initial Conditions on Rayleigh-Taylor Mixing

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