Spectra and statistics in compressible isotropic turbulence

Wang, Jianchun; Gotoh, Toshiyuki; Watanabe, Takeshi

doi:10.1103/physrevfluids.2.013403

Cited by 57 publications

(54 citation statements)

References 42 publications

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“…if the leading coefficients (i.e., A and B) and power-law exponents (i.e., a-h) were known with a high degree of certainty. In fact, previous numerical and theoretical studies of inert and [20,40,59], and citations therein) have found that a should be exactly 2. However, A and B can be expected to depend on the initial chemical mixture and thermally-perfect equations of state, and no previous studies have sought a scaling law for |∇T | rms .…”

Section: Physical Setup Of the Simulationsmentioning

confidence: 95%

Detonation initiation by compressible turbulence thermodynamic fluctuations

Towery

Poludnenko

Hamlington

2020

Combustion and Flame

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Theory and computations have established that thermodynamic gradients created by hot spots in reactive gas mixtures can lead to spontaneous detonation initiation. However, the current laminar theory of the temperature-gradient mechanism for detonation initiation is restricted to idealized physical configurations. Thus, it only predicts conditions for the onset of detonations in quiescent gases, where an isolated hot spot is formed on a timescale shorter than the chemical and acoustic timescales of the gas. In this work, we extend the laminar temperature-gradient mechanism into a statistical model for predicting the detonability of an autoignitive gas experiencing compressible isotropic turbulence fluctuations. Compressible turbulence forms non-monotonic temperature fields with tightly-spaced local minima and maxima that evolve over a range of timescales, including those much larger than chemical and acoustic timescales. We examine the utility of the adapted statistical model through direct numerical simulations of compressible isotropic turbulence in premixed hydrogen-air reactants for a range of conditions. We find strong, but not conclusive, evidence that the model can predict the degree of detonability in an autoignitive gas due to turbulence-induced thermodynamic gradients.

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Section: Physical Setup Of the Simulationsmentioning

confidence: 95%

Detonation initiation by compressible turbulence thermodynamic fluctuations

Towery

Poludnenko

Hamlington

2020

Combustion and Flame

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“…We observe that p rms /p 0 increases rapidly with the turbulent Mach number, while ρ rms /ρ 0 , T rms /T 0 and s rms are insensitive to the change of turbulent Mach number. Previous studies showed that if the compressible velocity component is dominated by acoustic waves, there are equipartition relations between pressure and the compressible velocity component in weak and strong forms (Sarkar et al 1991;Sagaut & Cambon 2008;Jagannathan & Donzis 2016;Wang et al 2017;Chen et al 2018;Wang et al 2018b). The weak acoustic equilibrium can be expressed as…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

“…By an asymptotic analysis, Bayly, Levermore & Passot (1992) predicted that temperature, entropy and density have k −5/3 power spectra in the inertial range of weakly compressible turbulent flows with some heat source. Wang, Gotoh & Watanabe (2017) performed numerical simulations of solenoidally forced compressible isotropic turbulence without any heat source at turbulent Mach numbers, M t , from 0.05 to 1.0. The spectra of pressure, density and temperature exhibit a k −7/3 scaling for M t 0.3 and a k −5/3 scaling for 0.5 M t 1.0.…”

Section: Introductionmentioning

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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“…As an improvement, it has been suggested that the solenoidal part of the energy spectra (∇ · u s = 0) does scale according classical Kolmogorov scaling; the basis for this claim comes from solenoidally forced DNS [5,7]. However, this result does not hold when the forcing has a strong dilatational component, as shown in Fig.…”

Section: Pacs Numbers 4727mentioning

confidence: 99%

“…1). Existing work [5,7,30,31] which makes this claim concerns the velocity field under solenoidal forcing and decaying turbulence.…”

Section: Pacs Numbers 4727mentioning

confidence: 99%

Solenoidal Scaling Laws for Compressible Mixing

2019

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Mixing of passive scalars in compressible turbulence does not obey the same classical Reynolds number scaling as its incompressible counterpart. We first show from a large database of direct numerical simulations that even the solenoidal part of the velocity field fails to follow the classical incompressible scaling when the forcing includes a substantial dilatational component. Though the dilatational effects on the flow remain significant, our main results are that both the solenoidal energy spectrum and the passive scalar spectrum scale assume incompressible forms, and that the scalar gradient aligns with the most compressive eigenvalue of the solenoidal part, provided that only the solenoidal components are used for scaling in a consistent manner. Minor modifications to this statement are also pointed out.

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Spectra and statistics in compressible isotropic turbulence

Cited by 57 publications

References 42 publications

Detonation initiation by compressible turbulence thermodynamic fluctuations

Detonation initiation by compressible turbulence thermodynamic fluctuations

Cascades of temperature and entropy fluctuations in compressible turbulence

Solenoidal Scaling Laws for Compressible Mixing

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