Relaxation of internal temperature and volume viscosity

Bruno, D.; Giovangigli, Vincent

doi:10.1063/1.3640083

Cited by 43 publications

(66 citation statements)

References 59 publications

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“…The theory for this case is applied to two-atomic and linear molecules (N 2 , O 2 , CO 2 ). The procedure for generalizing to the case of many degrees of freedom, with account taken of energy transport between internal modes and the quantization of levels, can be found in [3,20].…”

Section: Bulk Viscositymentioning

confidence: 99%

Effect of bulk viscosity in supersonic flow past spacecraft

Чикиткин

Rogov

Tirsky

et al. 2015

Applied Numerical Mathematics

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Section: Bulk Viscositymentioning

confidence: 99%

Effect of bulk viscosity in supersonic flow past spacecraft

Чикиткин

Rogov

Tirsky

et al. 2015

Applied Numerical Mathematics

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“…The kinetic theory of polyatomic gases shows that the volume viscosity coefficient is related to the time required for the internal and translational temperatures to come to equilibrium [6,16,35,36,3,4,5]. We establish in this paper local in time error estimates between the solution of an out of equilibrium two-temperature model and the solution of a one-temperature equilibrium model-including volume viscosity terms-when the relaxation time goes to zero.…”

Section: Introductionmentioning

confidence: 94%

Volume viscosity and internal energy relaxation: Error estimates

Giovangigli

Yong

2018

Nonlinear Analysis: Real World Applications

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We investigate the fast relaxation of internal energy in nonequilibrium gas models derived from the kinetic theory of gases. We establish uniform a priori estimates and existence theorems for symmetric hyperbolic-parabolic systems of partial differential equations with small second order terms and stiff sources. We prove local in time error estimates between the out of equilibrium solution and the one-temperature equilibrium fluid solution for well prepared data and justify the apparition of volume viscosity terms.

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“…Many efforts have been devoted to the derivation of relationships between the bulk viscosity and fundamental fluid properties [16,17]. If we consider a single polyatomic gas with a unique internal energy mode, the internal energy relaxation time τ int can be related to the bulk viscosity [4,18]:…”

Section: Mathematical Description and Computational Modelmentioning

confidence: 99%

On the role of bulk viscosity in compressible reactive shear layer developments

Boukharfane

Ferrer

Mura

et al. 2019

European Journal of Mechanics - B/Fluids

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a b s t r a c tDespite 150 years of research after the reference work of Stokes, it should be acknowledged that some confusion still remains in the literature regarding the importance of bulk viscosity effects in flows of both academic and practical interests. On the one hand, it can be readily shown that the neglection of bulk viscosity (i.e., κ = 0) is strictly exact for mono-atomic gases. The corresponding bulk viscosity effects are also unlikely to alter the flowfield dynamics provided that the ratio of the shear viscosity µ to the bulk viscosity κ remains sufficiently large. On the other hand, for polyatomic gases, the scattered available experimental and numerical data show that it is certainly not zero and actually often far from negligible. Therefore, since the ratio κ/µ can display significant variations and may reach very large values (it can exceed thirty for dihydrogen), it remains unclear to what extent the neglection of κ holds.The purpose of the present study is thus to analyze the mechanisms through which bulk viscosity and associated processes may alter a canonical turbulent flow. In this context, we perform direct numerical simulations (DNS) of spatially-developing compressible non-reactive and reactive hydrogen-air shear layers interacting with an oblique shock wave. The corresponding flowfield is of special interest for various reactive high-speed flow applications, e.g., scramjets. The corresponding computations either neglect the influence of bulk viscosity (κ = 0) or take it into consideration by evaluating its value using the EGlib library. The qualitative inspection of the results obtained for two-dimensional cases in either the presence or the absence of bulk viscosity effects shows that the local and instantaneous structure of the mixing layer may be deeply altered when taking bulk viscosity into account. This contrasts with some mean statistical quantities, e.g., the vorticity thickness growth rate, which do not exhibit any significant sensitivity to the bulk viscosity. Enstrophy, Reynolds stress components, and turbulent kinetic energy (TKE) budgets are then evaluated from three-dimensional reactive simulations. Slight modifications are put into evidence on the energy transfer and dissipation contributions. From the obtained results, one may expect that refined large-eddy simulations (LES) may be rather sensitive to the consideration of bulk viscosity, while Reynolds-averaged Navier-Stokes (RANS) simulations, which are based on statistical averages, are not. (A. Mura). structure of the fluid as well as the flowfield conditions. However, acoustic absorption measurements performed at room temperature have shown that the ratio of the volume to the shear viscosity κ/µ may be up to thirty for hydrogen at room temperature [2], and recent analyses of reactive multicomponent high-speed flows have confirmed that it is not justified to neglect it, except for the sake of simplicity [3]. The dilatational viscosity is important in describing sound attenuation in gaseous media, and the absorption o...

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Relaxation of internal temperature and volume viscosity

Cited by 43 publications

References 59 publications

Effect of bulk viscosity in supersonic flow past spacecraft

Effect of bulk viscosity in supersonic flow past spacecraft

Volume viscosity and internal energy relaxation: Error estimates

On the role of bulk viscosity in compressible reactive shear layer developments

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