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Eric Johnsen - One of the best experts on this subject based on the ideXlab platform.
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the role of bulk viscosity on the decay of compressible homogeneous isotropic turbulence
Journal of Fluid Mechanics, 2017Co-Authors: Shaowu Pan, Eric JohnsenAbstract:While Stokes’ Hypothesis of neglecting bulk viscous effects is exact for monatomic gases and unlikely to strongly affect the dynamics of fluids whose bulk-to-shear viscosity ratio is small and/or of weakly compressible turbulence, it is unclear to what extent this assumption holds for compressible, turbulent flows of gases whose bulk viscosity is orders of magnitude larger than their shear viscosities (e.g. ). Our objective is to understand the mechanisms by which bulk viscosity and the associated phenomena affect moderately compressible turbulence, in particular energy transfer and dissipation. Using direct numerical simulations of the compressible Navier–Stokes equations, we study the decay of compressible, homogeneous, isotropic turbulence for ratios of bulk-to-shear viscosity ranging from 0 to 1000. Our simulations demonstrate that bulk viscosity increases the decay rate of turbulent kinetic energy; whereas enstrophy exhibits little sensitivity to bulk viscosity, dilatation is reduced by over two orders of magnitude within the first two eddy-turnover times. Via a Helmholtz decomposition of the flow, we determine that the primary action of bulk viscosity is to damp the dilatational velocity fluctuations and reduce dilatational–solenoidal exchanges, as well as pressure–dilatation coupling. In short, bulk viscosity renders compressible turbulence incompressible by reducing energy transfer between translational and internal degrees of freedom. Our results indicate that for gases whose bulk viscosity is of the order of their shear viscosity (e.g. hydrogen) the turbulence is not significantly affected by bulk viscous dissipation, in which case neglecting bulk viscosity is acceptable in practice. However, in problems involving compressible, turbulent flows of gases like whose bulk viscosities are thousands of times greater than their shear viscosities, bulk viscosity cannot be ignored.
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the role of bulk viscosity on the decay of compressible homogeneous isotropic turbulence
Journal of Fluid Mechanics, 2017Co-Authors: Shaowu Pan, Eric JohnsenAbstract:While Stokes’ Hypothesis of neglecting bulk viscous effects is exact for monatomic gases and unlikely to strongly affect the dynamics of fluids whose bulk-to-shear viscosity ratio is small and/or of weakly compressible turbulence, it is unclear to what extent this assumption holds for compressible, turbulent flows of gases whose bulk viscosity is orders of magnitude larger than their shear viscosities (e.g. $\text{CO}_{2}$ ). Our objective is to understand the mechanisms by which bulk viscosity and the associated phenomena affect moderately compressible turbulence, in particular energy transfer and dissipation. Using direct numerical simulations of the compressible Navier–Stokes equations, we study the decay of compressible, homogeneous, isotropic turbulence for ratios of bulk-to-shear viscosity ranging from 0 to 1000. Our simulations demonstrate that bulk viscosity increases the decay rate of turbulent kinetic energy; whereas enstrophy exhibits little sensitivity to bulk viscosity, dilatation is reduced by over two orders of magnitude within the first two eddy-turnover times. Via a Helmholtz decomposition of the flow, we determine that the primary action of bulk viscosity is to damp the dilatational velocity fluctuations and reduce dilatational–solenoidal exchanges, as well as pressure–dilatation coupling. In short, bulk viscosity renders compressible turbulence incompressible by reducing energy transfer between translational and internal degrees of freedom. Our results indicate that for gases whose bulk viscosity is of the order of their shear viscosity (e.g. hydrogen) the turbulence is not significantly affected by bulk viscous dissipation, in which case neglecting bulk viscosity is acceptable in practice. However, in problems involving compressible, turbulent flows of gases like $\text{CO}_{2}$ whose bulk viscosities are thousands of times greater than their shear viscosities, bulk viscosity cannot be ignored.
Shaowu Pan - One of the best experts on this subject based on the ideXlab platform.
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the role of bulk viscosity on the decay of compressible homogeneous isotropic turbulence
Journal of Fluid Mechanics, 2017Co-Authors: Shaowu Pan, Eric JohnsenAbstract:While Stokes’ Hypothesis of neglecting bulk viscous effects is exact for monatomic gases and unlikely to strongly affect the dynamics of fluids whose bulk-to-shear viscosity ratio is small and/or of weakly compressible turbulence, it is unclear to what extent this assumption holds for compressible, turbulent flows of gases whose bulk viscosity is orders of magnitude larger than their shear viscosities (e.g. ). Our objective is to understand the mechanisms by which bulk viscosity and the associated phenomena affect moderately compressible turbulence, in particular energy transfer and dissipation. Using direct numerical simulations of the compressible Navier–Stokes equations, we study the decay of compressible, homogeneous, isotropic turbulence for ratios of bulk-to-shear viscosity ranging from 0 to 1000. Our simulations demonstrate that bulk viscosity increases the decay rate of turbulent kinetic energy; whereas enstrophy exhibits little sensitivity to bulk viscosity, dilatation is reduced by over two orders of magnitude within the first two eddy-turnover times. Via a Helmholtz decomposition of the flow, we determine that the primary action of bulk viscosity is to damp the dilatational velocity fluctuations and reduce dilatational–solenoidal exchanges, as well as pressure–dilatation coupling. In short, bulk viscosity renders compressible turbulence incompressible by reducing energy transfer between translational and internal degrees of freedom. Our results indicate that for gases whose bulk viscosity is of the order of their shear viscosity (e.g. hydrogen) the turbulence is not significantly affected by bulk viscous dissipation, in which case neglecting bulk viscosity is acceptable in practice. However, in problems involving compressible, turbulent flows of gases like whose bulk viscosities are thousands of times greater than their shear viscosities, bulk viscosity cannot be ignored.
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the role of bulk viscosity on the decay of compressible homogeneous isotropic turbulence
Journal of Fluid Mechanics, 2017Co-Authors: Shaowu Pan, Eric JohnsenAbstract:While Stokes’ Hypothesis of neglecting bulk viscous effects is exact for monatomic gases and unlikely to strongly affect the dynamics of fluids whose bulk-to-shear viscosity ratio is small and/or of weakly compressible turbulence, it is unclear to what extent this assumption holds for compressible, turbulent flows of gases whose bulk viscosity is orders of magnitude larger than their shear viscosities (e.g. $\text{CO}_{2}$ ). Our objective is to understand the mechanisms by which bulk viscosity and the associated phenomena affect moderately compressible turbulence, in particular energy transfer and dissipation. Using direct numerical simulations of the compressible Navier–Stokes equations, we study the decay of compressible, homogeneous, isotropic turbulence for ratios of bulk-to-shear viscosity ranging from 0 to 1000. Our simulations demonstrate that bulk viscosity increases the decay rate of turbulent kinetic energy; whereas enstrophy exhibits little sensitivity to bulk viscosity, dilatation is reduced by over two orders of magnitude within the first two eddy-turnover times. Via a Helmholtz decomposition of the flow, we determine that the primary action of bulk viscosity is to damp the dilatational velocity fluctuations and reduce dilatational–solenoidal exchanges, as well as pressure–dilatation coupling. In short, bulk viscosity renders compressible turbulence incompressible by reducing energy transfer between translational and internal degrees of freedom. Our results indicate that for gases whose bulk viscosity is of the order of their shear viscosity (e.g. hydrogen) the turbulence is not significantly affected by bulk viscous dissipation, in which case neglecting bulk viscosity is acceptable in practice. However, in problems involving compressible, turbulent flows of gases like $\text{CO}_{2}$ whose bulk viscosities are thousands of times greater than their shear viscosities, bulk viscosity cannot be ignored.
K S Shruti - One of the best experts on this subject based on the ideXlab platform.
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roles of bulk viscosity on rayleigh taylor instability non equilibrium thermodynamics due to spatio temporal pressure fronts
Physics of Fluids, 2016Co-Authors: Tapan K Sengupta, Aditi Sengupta, Nidhi Sharma, Soumyo Sengupta, Ashish Bhole, K S ShrutiAbstract:Direct numerical simulations of Rayleigh-Taylor instability (RTI) between two air masses with a temperature difference of 70 K is presented using compressible Navier-Stokes formulation in a non-equilibrium thermodynamic framework. The two-dimensional flow is studied in an isolated box with non-periodic walls in both vertical and horizontal directions. The non-conducting interface separating the two air masses is impulsively removed at t = 0 (depicting a heaviside function). No external perturbation has been used at the interface to instigate the instability at the onset. Computations have been carried out for rectangular and square cross sections. The formulation is free of Boussinesq approximation commonly used in many Navier-Stokes formulations for RTI. Effect of Stokes’ Hypothesis is quantified, by using models from acoustic attenuation measurement for the second coefficient of viscosity from two experiments. Effects of Stokes’ Hypothesis on growth of mixing layer and evolution of total entropy for the Rayleigh-Taylor system are reported. The initial rate of growth is observed to be independent of Stokes’ Hypothesis and the geometry of the box. Following this stage, growth rate is dependent on the geometry of the box and is sensitive to the model used. As a consequence of compressible formulation, we capture pressure wave-packets with associated reflection and rarefaction from the non-periodic walls. The pattern and frequency of reflections of pressure waves noted specifically at the initial stages are reflected in entropy variation of the system.
Tapan K Sengupta - One of the best experts on this subject based on the ideXlab platform.
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roles of bulk viscosity on rayleigh taylor instability non equilibrium thermodynamics due to spatio temporal pressure fronts
Physics of Fluids, 2016Co-Authors: Tapan K Sengupta, Aditi Sengupta, Nidhi Sharma, Soumyo Sengupta, Ashish Bhole, K S ShrutiAbstract:Direct numerical simulations of Rayleigh-Taylor instability (RTI) between two air masses with a temperature difference of 70 K is presented using compressible Navier-Stokes formulation in a non-equilibrium thermodynamic framework. The two-dimensional flow is studied in an isolated box with non-periodic walls in both vertical and horizontal directions. The non-conducting interface separating the two air masses is impulsively removed at t = 0 (depicting a heaviside function). No external perturbation has been used at the interface to instigate the instability at the onset. Computations have been carried out for rectangular and square cross sections. The formulation is free of Boussinesq approximation commonly used in many Navier-Stokes formulations for RTI. Effect of Stokes’ Hypothesis is quantified, by using models from acoustic attenuation measurement for the second coefficient of viscosity from two experiments. Effects of Stokes’ Hypothesis on growth of mixing layer and evolution of total entropy for the Rayleigh-Taylor system are reported. The initial rate of growth is observed to be independent of Stokes’ Hypothesis and the geometry of the box. Following this stage, growth rate is dependent on the geometry of the box and is sensitive to the model used. As a consequence of compressible formulation, we capture pressure wave-packets with associated reflection and rarefaction from the non-periodic walls. The pattern and frequency of reflections of pressure waves noted specifically at the initial stages are reflected in entropy variation of the system.
Miltiadis Papalexandris - One of the best experts on this subject based on the ideXlab platform.
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on the applicability of Stokes Hypothesis to low mach number flows
Continuum Mechanics and Thermodynamics, 2020Co-Authors: Miltiadis PapalexandrisAbstract:Stokes’ Hypothesis states that the bulk viscosity of a Newtonian fluid can be set to zero. Although not valid for many fluids, it is common practice to invoke this Hypothesis in the study of low-Mach-number, variable-density flows. Based on scaling arguments, we provide a necessary condition for neglecting the bulk viscous pressure from the governing equations. More specifically, we show that the Reynolds number defined with respect to the bulk viscosity must be very large. We further show that even when this condition is not satisfied, the bulk viscous pressure does not need to be taken explicitly into account in the computation of the velocity field because it can be combined with the hydrodynamic pressure.