Kinetic energy transfer in compressible isotropic turbulence

Wang, Jianchun; Wan, Minping; Chen, Song; Chen, Shiyi

doi:10.1017/jfm.2018.23

Cited by 121 publications

(101 citation statements)

References 49 publications

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“…This Gaussian kernel form has been used in several prior studies (e.g. [31,59]) due to advantages in numerical discretization (see [60], page 30). In this work, we purposefully avoid using a sharp-spectral filter which, for density, yields ρ (x), with at the top and bottom boundaries, filtering near the walls is performed by extending the computational domain in accordance with the boundary conditions.…”

Section: Numerical Resultsmentioning

confidence: 99%

Inviscid criterion for decomposing scales

Zhao

Aluie

2018

Phys. Rev. Fluids

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The proper scale decomposition in flows with significant density variations is not as straightforward as in incompressible flows, with many possible ways to define a 'length-scale.' A choice can be made according to the so-called inviscid criterion [1]. It is a kinematic requirement that a scale decomposition yield negligible viscous effects at large enough 'length-scales.' It has been proved [1] recently that a Favre decomposition satisfies the inviscid criterion, which is necessary to unravel inertial-range dynamics and the cascade. Here, we present numerical demonstrations of those results. We also show that two other commonly used decompositions can violate the inviscid criterion and, therefore, are not suitable to study inertial-range dynamics in variable-density and compressible turbulence. Our results have practical modeling implication in showing that viscous terms in Large Eddy Simulations do not need to be modeled and can be neglected. *

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Section: Numerical Resultsmentioning

confidence: 99%

Inviscid criterion for decomposing scales

Zhao

Aluie

2018

Phys. Rev. Fluids

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“…The following dimensionless Navier-Stokes equations in conservative form are solved numerically in this study (Wang et al 2010(Wang et al , 2018a ∂ρ ∂t + ∂(ρu j ) ∂x j = 0, (2.1)…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

“…Two turbulent Mach numbers are considered: M t = 0.2 and M t = 0.6. The Kolmogorov length scale η of compressible turbulence is defined by (Wang et al 2018a) where is the spatial average of the viscous dissipation rate of kinetic energy per unit mass:…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Cascades of temperature and entropy fluctuations in compressible turbulence

et al. 2019

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Cascades of temperature and entropy fluctuations are studied by numerical simulations of stationary three-dimensional compressible turbulence with a heat source. The fluctuation spectra of velocity, compressible velocity component, density and pressure exhibit the $-5/3$ scaling in an inertial range. The strong acoustic equilibrium relation between spectra of the compressible velocity component and pressure is observed. The $-5/3$ scaling behaviour is also identified for the fluctuation spectra of temperature and entropy, with the Obukhov–Corrsin constants close to that of a passive scalar spectrum. It is shown by Kovasznay decomposition that the dynamics of the temperature field is dominated by the entropic mode. The average subgrid-scale (SGS) fluxes of temperature and entropy normalized by the total dissipation rates are close to 1 in the inertial range. The cascade of temperature is dominated by the compressible mode of the velocity field, indicating that the theory of a passive scalar in incompressible turbulence is not suitable to describe the inter-scale transfer of temperature in compressible turbulence. In contrast, the cascade of entropy is dominated by the solenoidal mode of the velocity field. The different behaviours of cascades of temperature and entropy are partly explained by the geometrical properties of SGS fluxes. Moreover, the different effects of local compressibility on the SGS fluxes of temperature and entropy are investigated by conditional averaging with respect to the filtered dilatation, demonstrating that the effect of compressibility on the cascade of temperature is much stronger than on the cascade of entropy.

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“…For isotropic compressible turbulence in supersonic regime, the stronger random shocklets and higher spatial-temporal gradients pose greater difficulties for numerical analyses than other regimes. Currently, the supersonic regime is much less known and reported, and only a very few systematic numerical experiments are available [16,17,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence I: Criterion for direct numerical simulation

Cao

Pan

2019

Computers & Fluids

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In this paper, we intend to address the high-order gas-kinetic scheme (HGKS) in the direct numerical simulation (DNS) of compressible isotropic turbulence up to the supersonic regime. To validate the performance of HGKS, the compressible isotropic turbulence with turbulent Mach number M a t = 0.5 and Taylor microscale Reynold number Re λ = 72 is simulated as a benchmark. With the consideration of robustness and accuracy, the WENO-Z scheme is adopted for spatial reconstruction in the current higher-order scheme. Statistical quantities are compared with the high-order compact finite difference scheme to determine the spatial and temporal criterion for DNS. According to the grid and time convergence study, it can be concluded that the minimum spatial resolution parameter κ max η 0 ≥ 2.71 and the maximum temporal resolution parameter ∆t ini /τ t 0 ≤ 5.58/1000 are adequate for HGKS to resolve the compressible isotropic turbulence, where κ max is the maximum resolved wave number, ∆t ini is the initial time step, η 0 and τ t 0 are the initial Kolmogorov length scale and the large-eddyturnover time. Guided by such criterion, the compressible isotropic turbulence from subsonic regime M a t = 0.8 to supersonic one M a t = 1.2, and the Taylor microscale Reynolds number Re λ ranging from 10 to 72 are simulated. With the high initial turbulent Mach number, the strong random shocklets and high expansion regions are identified, as well as the wide range of probability density function over local turbulence Mach number. All those impose great challenge for high-order schemes. In order to construct compressible large eddy simulation models at high turbulent Mach number, the ensemble budget of turbulent kinetic energy is fully analyzed. The solenoidal dissipation rate decreases with the increasing of M a t and Re λ . Meanwhile, the dilational dissipation rate increases with the increasing of M a t , which cannot be neglected for constructing supersonic turbulence model. The current work shows that HGKS provides a valid tool for the numerical and physical studies of isotropic compressible turbulence in supersonic regime, which is much less reported in the current turbulent flow study.

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Kinetic energy transfer in compressible isotropic turbulence

Cited by 121 publications

References 49 publications

Inviscid criterion for decomposing scales

Inviscid criterion for decomposing scales

Cascades of temperature and entropy fluctuations in compressible turbulence

Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence I: Criterion for direct numerical simulation

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