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Keywords
(6)
Kinetic Theory
knudsen number
Laminar Flow
Thermal Fluctuation
Turbulence Model
Higher Order
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Expanded analogy between Boltzmann kinetic theory of fluids and turbulence
Expanded analogy between Boltzmann kinetic theory of fluids and turbulence,10.1017/S0022112004001211,Journal of Fluid Mechanics,Hudong Chen,Steven A.
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Expanded analogy between Boltzmann kinetic theory of fluids and turbulence
(
Citations: 17
)
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Hudong Chen
,
Steven A. Orszag
,
Ilya Staroselsky
,
Sauro Succi
We demonstrate that the effects of turbulent fluctuations have a striking resemblance to those of microscale (thermal) fluctuations in laminar flows, even to
higher order
in the Knudsen number. This suggests that there may be a good basis for understanding turbulence in terms of Boltzmann kinetic theory. If so, turbulence may be better described in terms of `mixing times' rather than the more classical `mixing lengths'. Comparisons are made to Reynoldsstress turbulence models.
Journal:
Journal of Fluid Mechanics  J FLUID MECH
, vol. 519, pp. 301314, 2004
DOI:
10.1017/S0022112004001211
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Citation Context
(9)
...Discrete kinetic theory, and in particular the LBM, has recently been employed to a priori derive turbulence models based on a meanfield approximation [36,37,
38
] and lattice kinetic turbulence models have found much success [39]...
Kannan N. Premnath
,
et al.
Dynamic subgrid scale modeling of turbulent flows using latticeBoltzm...
...Indeed, based on a ChapmanEnskoglike analysis, one can show that 6 N ≥ is necessary to realize the correct NavierStokes level thermohydrodynamics or Burnett level (in the framework of kinetictheorybased hydrodynamics) isothermal fluid physics [6,
10
, 21, 22]...
...Both NavierStokes thermal energy fluxes or higherorder nonequilibrium moment fluxes require isotropy to at least 6th order [
10
]...
Hudong Chen
,
et al.
Discrete Rotational Symmetry, Moment Isotropy, and Higher Order Lattic...
...In Sects. 3 and 4 the analogy between molecular and turbulent motion [32,
33
] will then be used for the construction of equations for turbulent motion...
...It is of interest to note that the same nonlinear stress model can be derived from the stress transport equation by adopting the Chapman–Enskog expansion technique, which accounts for small deviations of F from the equilibrium PDF Feq [
33
]...
Stefan Heinz
.
Unified turbulence models for LES and RANS, FDF and PDF simulations
...First we use the hydrodynamic approximation, derived from kinetic equation by Chen et. al..[
6
] in the limit ωτ ≪ 1. Then, derivation of equations valid in an infinite range 0 < ωτ < ∞ is presented and it is shown that in the highfrequency limit ωτ → ∞, the dissipation rate W → const...
...remarkable paper, Chen et. al. [
6
], based on thequation (1)(2), formulated the ChapmanEnskog expansion in powers on dimensionless relaxation time ǫ = τ∂xiuj...
Victor Yakhot
,
et al.
Stokes' second flow problem in a highfrequency limit: application to ...
...This procedure was used in [
19
] for constructing a quadratic model for the Reynolds stresses in singlephase turbulence by solving a simple kinetic equation with a relaxation “collision term”...
V. M. Alipchenkov
,
et al.
Differential and algebraic models for the second moments of particle v...
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Citations
(17)
Macroscopic description of arbitrary Knudsen number flow using BoltzmannBGK kinetic theory. Part 2
Hudong Chen
,
Steven A. Orszag
,
Ilya Staroselsky
Journal:
Journal of Fluid Mechanics  J FLUID MECH
, vol. 658, pp. 294309, 2010
Dynamic subgrid scale modeling of turbulent flows using latticeBoltzmann method
(
Citations: 5
)
Kannan N. Premnath
,
Martin J. Pattison
,
Sanjoy Banerjee
Journal:
Physica Astatistical Mechanics and Its Applications  PHYSICA A
, vol. 388, no. 13, pp. 26402658, 2009
Primitive turbulence: kinetics, Prandtl's mixing length, and von Karman's constant
Helmut Z. Baumert
Published in 2009.
Discrete Rotational Symmetry, Moment Isotropy, and Higher Order Lattice Boltzmann Models
(
Citations: 1
)
Hudong Chen
,
Isaac Goldhirsch
,
Steven A. Orszag
Journal:
Journal of Scientific Computing
, vol. 34, no. 1, pp. 87112, 2008
What Does Kinetic Theory Have to Do with Hydraulics?
(
Citations: 1
)
Mohamed S. Ghidaoui
Journal:
Journal of Hydraulic Engineeringasce  J HYDRAUL ENGASCE
, vol. 134, no. 7, 2008