Bulk viscosity of a dilute polyatomic gas

Emanuel, George

doi:10.1063/1.857813

Cited by 90 publications

(39 citation statements)

References 9 publications

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“…In the limiting situation of fast relaxation, we recover the classical one-temperature model including the volume viscosity coefficient. Theoretical models as well as experimental measurements of the volume viscosity have confirmed that this coefficient is of the order of the shear viscosity for polyatomic gases [11,12,13,14,15] and the impact of volume viscosity in fluid mechanics-especially for fast flows-has been established [16,17,18,19,20].…”

Section: Introductionmentioning

confidence: 87%

“…Finally, we note that theoretical models as well as experimental measurements of the volume viscosity have confirmed that this coefficient is of the order of the shear viscosity for polyatomic gases [11,12,13,14,15] and the impact of volume viscosity in fluid mechanics-especially for fast flows-has been established [16,17,18,19,20]. More generally, recent numerical investigations have brought further support for the importance of accurate transport property in various multicomponent reactive flows calculations [47,48,49,50,51,52,53].…”

Section: So That the Two-temperature Entropy Governing Equation Finalmentioning

confidence: 93%

“…After some algebra, the entropy S is found in the form 17) where the translational entropy per unit volume S tr and the translational partition function Z tr are given by 18) whereas the internal entropy per unit volume S int is given by…”

Section: Translational and Internal Entropiesmentioning

confidence: 99%

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Relaxation of internal temperature and volume viscosity

Bruno

Giovangigli

2011

Physics of Fluids

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We investigate the relaxation of internal temperature and the concept of volume viscosity in nonequilibrium gas models derived from the kinetic theory. We first investigate a nonequilibrium gas model with two temperatures-translational and internal-where the volume viscosity is absent. We establish that, in a relaxation regime, the temperature difference becomes proportional to the divergence of the velocity fields and define a nonequilibrium, multitemperature, volume viscosity coefficient. We next analyze the convergence of the two temperature model towards the one temperature model when the relaxation is fast. We then investigate a nonequilibrium two temperature gas model with a fast and a slow internal energy mode. We establish that, in a relaxation regime, there are four contributions to the volume viscosity, namely the fast internal mode volume viscosity, the slow internal mode volume viscosity, the relaxation pressure and the perturbed source term. In the thermodynamic equilibrium limit, the sum of these four terms converges toward the one-temperature two-mode volume viscosity. We finally perform Monte Carlo simulations of spontaneous fluctuations near thermodynamic equilibrium. The numerical results obtained from the Boltzmann equation are compared to the predictions of the one and two temperature fluid models and the agreement between theory and calculations is complete.

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Section: Introductionmentioning

confidence: 87%

Section: So That the Two-temperature Entropy Governing Equation Finalmentioning

confidence: 93%

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Relaxation of internal temperature and volume viscosity

Bruno

Giovangigli

2011

Physics of Fluids

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“…Approximate values of the ratio κ/η for CH 4 , CO, H 2 , O 2 and N 2 at temperatures of 300 and 1,000 K are given in Table 1 [13,24,44], together with their species volume (κ) and shear (η) viscosities. Even larger values have been reported for CO 2 and N 2 O (see for instance [11] and references therein). From Table 1 it is clear that volume viscosity is at least of the same order of magnitude as the shear viscosity at 300 K and even larger at 1,000 K, with the ratio κ/η for pure hydrogen as high as 52 at a temperature of 1,000 K [13].…”

Section: Introductionmentioning

confidence: 87%

Impact of Volume Viscosity on the Structure of Turbulent Premixed Flames in the Thin Reaction Zone Regime

Fru

Janiga

Thévenin

2011

Flow Turbulence Combust

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Direct Numerical Simulations (DNS) of turbulent premixed flames burning hydrogen, synthetic gas and methane have been performed, relying on detailed chemical and transport models and taking into account volume viscosity. In this manner, it becomes possible to quantify the impact of this last contribution. It is shown that laminar flames are not modified by volume viscosity, while the local structure of turbulent flames may differ considerably when taking it into account. A noticeable impact is even observed on global flame properties. The modifications induced by the volume viscosity transport term are extremely small at first, but are sufficient to lead to completely different realizations at a later time due to the chaotic nature of turbulence. Noticeable modifications induced by volume viscosity are found for syngas as well as for hydrogen flames. For such hydrogen-containing fuels, the differences appear to remain unchanged when increasing the turbulent Reynolds number. On the other hand, turbulent flames burning methane show no significant impact due to volume viscosity. Since an accurate computation of the volume viscosity transport term is possible on available supercomputers, it is thus recommended to take it into account for detailed studies of turbulent flames burning hydrogen-containing fuels, in particular for DNS, while this term can be safely neglected for higher hydrocarbon flames.

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“…IV lead us to conclude that there will be some non-zero contribution of the vibrational mode to the total bulk viscosity of CH 4 at 300 K. Nevertheless, in this section we will present our results for the rotational contribution to the bulk viscosity of CH 4 without a detailed consideration of μ b v . The data for the bulk viscosities of CO and CH 4 were taken directly from the results reported by Prangsma, Alberga, and Beenakker 28 and, following Emanuel,39 fit to the following power-law representation:…”

Section: Fluids Having Moderate Bulk Viscositymentioning

confidence: 99%

Numerical estimates for the bulk viscosity of ideal gases

Cramer

2012

Physics of Fluids

168

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We estimate the bulk viscosity of a selection of well known ideal gases. A relatively simple formula is combined with published values of rotational and vibrational relaxation times. It is shown that the bulk viscosity can take on a wide variety of numerical values and variations with temperature. Several fluids, including common diatomic gases, are seen to have bulk viscosities which are hundreds or thousands of times larger than their shear viscosities. We have also provided new estimates for the bulk viscosity of water vapor in the range 380–1000 K. We conjecture that the variation of bulk viscosity with temperature will have a local maximum for most fluids. The Lambert-Salter correlation is used to argue that the vibrational contribution to the bulk viscosities of a sequence of fluids having a similar number of hydrogen atoms at a fixed temperature will increase with the characteristic temperature of the lowest vibrational mode.

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Bulk viscosity of a dilute polyatomic gas

Cited by 90 publications

References 9 publications

Relaxation of internal temperature and volume viscosity

Relaxation of internal temperature and volume viscosity

Impact of Volume Viscosity on the Structure of Turbulent Premixed Flames in the Thin Reaction Zone Regime

Numerical estimates for the bulk viscosity of ideal gases

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