Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence

Chung, Daniel; Pullin, D. I.

doi:10.1017/s0022112009992801

Cited by 61 publications

(45 citation statements)

References 34 publications

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“…Similar results were achieved with the WENO-TCD scheme (Hill & Pullin 2004). Using the same SGS model and the Fourier pseudospectral method, Chung & Pullin (2010) performed DNS and LES of statistically stationary buoyancy-driven turbulent mixing, showing that both the resolved-scale and SGS-extended components of the LES velocity spectra and velocity-density cospectra accurately capture important features of the DNS. Comparisons between LES and DNS initiated by the Taylor-Green vortex (Drikakis et al 2007) demonstrated that a variety of explicit SGS models and implicit LES models (Grinstein, Margolin & Rider 2007) can consistently capture the physics of turbulence decay.…”

Section: Methodssupporting

confidence: 53%

Transition to turbulence in shock-driven mixing: a Mach number study

Lombardini¹,

Pullin²,

Meiron³

2011

J. Fluid Mech.

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Large-eddy simulations of single-shock-driven mixing suggest that, for sufficiently high incident Mach numbers, a two-gas mixing layer ultimately evolves to a late-time, fully developed turbulent flow, with Kolmogorov-like inertial subrange following a −5/3 power law. After estimating the kinetic energy injected into the diffuse density layer during the initial shock-interface interaction, we propose a semi-empirical characterization of fully developed turbulence in such flows, based on scale separation, as a function of the initial parameter space, as, which corresponds to late-time Taylor-scale Reynolds numbers 250. In this expression, η 0 + represents the post-shock perturbation amplitude, u the change in interface velocity induced by the shock refraction, ν the characteristic kinematic viscosity of the mixture, L ρ the inner diffuse thickness of the initial density profile, A + the post-shock Atwood ratio, and C (A + , η 0 + /λ 0 ) ≈ 0.3 for the gas combination and post-shock perturbation amplitude considered. The initially perturbed interface separating air and SF 6 (pre-shock Atwood ratio A ≈ 0.67) was impacted in a heavy-light configuration by a shock wave of Mach number M I = 1.05, 1.25, 1.56, 3.0 or 5.0, for which η 0 + is fixed at about 25 % of the dominant wavelength λ 0 of an initial, Gaussian perturbation spectrum. Only partial isotropization of the flow (in the sense of turbulent kinetic energy and dissipation) is observed during the late-time evolution of the mixing zone. For all Mach numbers considered, the late-time flow resembles homogeneous decaying turbulence of Batchelor type, with a turbulent kinetic energy decay exponent n ≈ 1.4 and large-scale (k → 0) energy spectrum ∼ k 4 , and a molecular mixing fraction parameter, Θ ≈ 0.85. An appropriate time scale characterizing the Taylor-scale Reynolds number decay, as well as the evolution of mixing parameters such as Θ and the effective Atwood ratio A e , seem to indicate the existence of low-and high-Mach-number regimes.

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Section: Methodssupporting

confidence: 53%

Transition to turbulence in shock-driven mixing: a Mach number study

Lombardini¹,

Pullin²,

Meiron³

2011

J. Fluid Mech.

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“…Although RT turbulence is of great importance and has been studied for many decades, there are still some open issues 10,11 . Specifically, for the past decade, many studies [12][13][14][15][16][17][18][19][20][21][22][23][24][25] have focused on small-scale turbulent fluctuations in both two-(2D) and three-dimensional (3D) RT turbulence. In two dimensions, Chertkov 15 proposed a phenomenological theory.…”

Section: Introductionmentioning

confidence: 99%

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence

Zhou

2013

Physics of Fluids

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We report a high-resolution numerical study of two-dimensional (2D) miscible Rayleigh-Taylor (RT) incompressible turbulence with the Boussinesq approximation. An ensemble of 100 independent realizations were performed at small Atwood number and unit Prandtl number with a spatial resolution of 2048 × 8193 grid points. Our main focus is on the temporal evolution and the scaling behavior of global quantities and of small-scale turbulence properties. Our results show that the buoyancy force balances the inertial force at all scales below the integral length scale and thus validate the basic force-balance assumption of the Bolgiano-Obukhov scenario in 2D RT turbulence. It is further found that the Kolmogorov dissipation scale η(t) ∼ t 1/8 , the kinetic-energy dissipation rate ε u (t) ∼ t −1/2 , and the thermal dissipation rate ε θ (t) ∼ t −1 . All of these scaling properties are in excellent agreement with the theoretical predictions of the Chertkov model [Phys. Rev. Lett. 91, 115001 (2003)]. We further discuss the emergence of intermittency and anomalous scaling for high order moments of velocity and temperature differences. The scaling exponents ξ r p of the pth-order temperature structure functions are shown to saturate to ξ r ∞ ≃ 0.78 ± 0.15 for the highest orders, p ∼ 10. The value of ξ r ∞ and the order at which saturation occurs are compatible with those of turbulent Rayleigh-Bénard (RB) convection [Phys. Rev. Lett. 88, 054503 (2002)], supporting the scenario of universality of buoyancy-driven turbulence with respect to the different boundary conditions characterizing the RT and RB systems.

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“…All DNS solutions satisfied standard convergence criteria [15] (with grid spacing l , the Kolmogorov scale). The subgridscale model in the LES was based on a dynamic eddy viscosity and eddy diffusivity (with l 10), as previously shown to be accurate for convection [16][17][18][19] (the detailed algorithms are found in [20,21]). The LES solutions were also validated against the DNS solutions at Ra 6 Â 10 8 and showed no significant differences (in heat transport, volume integrals and vertical profiles of energy conversion terms, and dissipation spectra).…”

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confidence: 99%

Completing the Mechanical Energy Pathways in Turbulent Rayleigh-Bénard Convection

2013

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A new, more complete view of the mechanical energy budget for Rayleigh-Bénard convection is developed and examined using three-dimensional numerical simulations at large Rayleigh numbers and Prandtl number of 1. The driving role of available potential energy is highlighted. The relative magnitudes of different energy conversions or pathways change significantly over the range of Rayleigh numbers Ra $ 10 7 -10 13 . At Ra < 10 7 small-scale turbulent motions are energized directly from available potential energy via turbulent buoyancy flux and kinetic energy is dissipated at comparable rates by both the largeand small-scale motions. In contrast, at Ra ! 10 10 most of the available potential energy goes into kinetic energy of the large-scale flow, which undergoes shear instabilities that sustain small-scale turbulence. The irreversible mixing is largely confined to the unstable boundary layer, its rate exactly equal to the generation of available potential energy by the boundary fluxes, and mixing efficiency is 50%. Introduction.-Flow in a horizontal layer of fluid heated uniformly from below and cooled from above-RayleighBénard convection (RBC)-is an idealized problem from which much can be learned about the nature of convective flow and heat transfer. Recent attention has focused on the relative importance of the boundary layer and interior behavior, including flow structures, at very large Rayleigh numbers [1][2][3][4][5][6]. The salient features of the flow can be usefully interpreted in terms of the energy budget, and previous work has considered the kinetic and thermal energy [2,3,7,8]. However, the existing framework is incomplete and provides limited insight into the exchange of mechanical energy among different forms or between fluid motions of different scales. In particular, the nature of the turbulent energy cascade in RBC is still not fully understood [3] and improved models are needed.Convection is caused by the generation of mechanical energy in the form of available potential energy (APE) by boundary buoyancy fluxes. APE is a subset of the total gravitational potential energy (GPE) and is the form essential for motions [9][10][11]. A complete mechanical energy framework has been recently developed for the case of horizontal convection forced by differential heating at one horizontal boundary [12,13] and recently extended to RBC [14]. In RBC there is a release of APE from thermal boundary layers adjacent to the top and bottom boundaries, driving flow at various scales, while complex feedbacks further distribute the potential and kinetic energy among the different scales or, through mixing, to the background potential energy. The role of APE in RBC was recognized in quantifying the overall rate of irreversible mixing [14]. Here we show that an account of GPE, its partition into available and background forms, and its links to kinetic energy at various scales are essential in a full understanding of the turbulent energy cascade and the relative roles of the boundary layer and the interior.

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Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence

Cited by 61 publications

References 34 publications

Transition to turbulence in shock-driven mixing: a Mach number study

Transition to turbulence in shock-driven mixing: a Mach number study

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence

Completing the Mechanical Energy Pathways in Turbulent Rayleigh-Bénard Convection

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