Bulk viscosity in the Navier–Stokes equations

Emanuel, George

doi:10.1016/s0020-7225(98)00020-2

Cited by 34 publications

(16 citation statements)

References 22 publications

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“…The theoretical result in (2.16) shows that ζ is proportional to the term pτ , which is consistent with the prediction of the Boltzmann kinetic theory (Emanuel 1998). …”

Section: )supporting

confidence: 84%

“…The static pressure p inside the fluid element is a result of the average molecular thermal motion and reaches equilibrium after a relaxation time τ , whereas the mean pressurep is the average normal surface force imposed by the adjacent fluid elements and changes with a characteristic flow time t c . If t c is much larger than τ , the local thermodynamic equilibrium (LTE) assumption is satisfied, for which the BVC phenomenologically interpreted as a transport coefficient is valid (Thompson 1972;Emanuel 1998;Graves & Argrow 1999). Based on the LTE condition, we deem that the mean pressurep remains unchanged or that the magnitude of change inp is negligible compared with that of the static pressure p during a period of relaxation, i.e.…”

Section: )mentioning

confidence: 99%

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Continuum perspective of bulk viscosity in compressible fluids

Jiang

2017

J. Fluid Mech.

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Kinetic theory and acoustic measurements have proven that the bulk viscosity associated with the expansion or compression effect cannot be ignored in compressible fluids except for monatomic gases. A new theoretical formula for the bulk viscosity coefficient (BVC) ζ is derived by the continuum medium methodology, which provides a further understanding of the bulk viscosity, i.e. ζ is equal to the product of the bulk modulus K and the relaxation time τ (ζ = Kτ ). The continuum and kinetic theories present consistent results from macro-and microperspectives respectively, only differing in terms of a coefficient. The theoretical predictions of the BVC in diatomic molecules, such as N 2 , O 2 and CO, show good agreement with the experimental data over a wide range of temperature. In addition, the vibrational contributions to ζ are controlled by a rapid exponential decrease at high temperatures, while at low temperatures a slow linear increase proceeds for the rotational cases. The relaxation time τ , collision number Z, BVC ζ and ratio of bulk-to-shear viscosities ζ /µ in the vibrational mode are found to be several orders of magnitude larger than those in the rotational mode.

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“…The theoretical result in (2.16) shows that ζ is proportional to the term pτ , which is consistent with the prediction of the Boltzmann kinetic theory (Emanuel 1998). …”

Section: )supporting

confidence: 84%

Section: )mentioning

confidence: 99%

Continuum perspective of bulk viscosity in compressible fluids

Jiang

2017

J. Fluid Mech.

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“…There has always been a lot of debate on bulk viscosity [66], and in particular on the way it should be incorporated in the Navier-Stokes equations [67,68]. In the present study, bulk viscosity b ,which is not expected to be important in plane channel flow (at least for the M 1.5 cases studied in the present work), was set to 0 (Stokes hypothesis [67]). Viscosity follows a Sutherland law [69] and heat-conductivity follows a modified Sutherland law [70] …”

Section: Flow Modelmentioning

confidence: 95%

Performance of very‐high‐order upwind schemes for DNS of compressible wall‐turbulence

Gerolymos

Senechal

Vallet

2009

Numerical Methods in Fluids

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“…A plane acoustic wave of wave-vector 2 k π λ′ = and angular frequency at . Then the analytical velocity is given by [47]…”

Section: B Attenuation-driven Acoustic Streamingmentioning

confidence: 99%

Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices

Luo

et al. 2012

Phys. Rev. E

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In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard two-dimensional nine-velocity (D2Q9) lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small. Meanwhile, the simple structure and general features of the DDF LB approach are retained. The model is tested by numerical simulations of thermal Couette flow, attenuation-driven acoustic streaming, and natural convection in a square cavity with small and large temperature differences. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.

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Bulk viscosity in the Navier–Stokes equations

Cited by 34 publications

References 22 publications

Continuum perspective of bulk viscosity in compressible fluids

Continuum perspective of bulk viscosity in compressible fluids

Performance of very‐high‐order upwind schemes for DNS of compressible wall‐turbulence

Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices

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