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Journal ArticleDOI

Expanded analogy between Boltzmann kinetic theory of fluids and turbulence

25 Nov 2004-Journal of Fluid Mechanics (Cambridge University Press)-Vol. 519, pp 301-314
TL;DR: In this article, 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.
Abstract: 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 Reynolds-stress turbulence models.
Citations
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Journal ArticleDOI
TL;DR: This work reviews many significant developments over the past decade of the lattice-Boltzmann method and discusses higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number.
Abstract: With its roots in kinetic theory and the cellular automaton concept, the lattice-Boltzmann (LB) equation can be used to obtain continuum flow quantities from simple and local update rules based on particle interactions. The simplicity of formulation and its versatility explain the rapid expansion of the LB method to applications in complex and multiscale flows. We review many significant developments over the past decade with specific examples. Some of the most active developments include the entropic LB method and the application of the LB method to turbulent flow, multiphase flow, and deformable particle and fiber suspensions. Hybrid methods based on the combination of the Eulerian lattice with a Lagrangian grid system for the simulation of moving deformable boundaries show promise for more efficient applications to a broader class of problems. We also discuss higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number. Additionally, the remarkable scalability of the LB method for parallel processing is shown with examples. Teraflop simulations with the LB method are routine, and there is no doubt that this method will be one of the first candidates for petaflop computational fluid dynamics in the near future.

1,585 citations

Journal ArticleDOI
TL;DR: In this paper, the Navier-Stokes order continuum theory is used for CFD simulation of the hydrodynamics of gas-solid fluidization, without taking the effects of heat and mass transfer as well as chemical reactions into consideration.

179 citations

Journal ArticleDOI
TL;DR: The GLBE approach exhibited markedly better stability characteristics and avoided spurious near-wall turbulent fluctuations on coarser grids when compared with the single-relaxation-time (SRT)-based approach and its implementation showed excellent parallel scalability on a large parallel cluster with over a thousand processors.
Abstract: In this paper, we present a framework based on the generalized lattice Boltzmann equation (GLBE) using multiple relaxation times with forcing term for eddy capturing simulation of wall-bounded turbulent flows. Due to its flexibility in using disparate relaxation times, the GLBE is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near-wall turbulent fluctuations. The subgrid scale (SGS) turbulence effects are represented by the standard Smagorinsky eddy viscosity model, which is modified by using the van Driest wall-damping function to account for reduction of turbulent length scales near walls. In order to be able to simulate a wider class of problems, we introduce forcing terms, which can represent the effects of general nonuniform forms of forces, in the natural moment space of the GLBE. Expressions for the strain rate tensor used in the SGS model are derived in terms of the nonequilibrium moments of the GLBE to include such forcing terms, which comprise a generalization of those presented in a recent work [Yu et al., Comput. Fluids 35, 957 (2006)]. Variable resolutions are introduced into this extended GLBE framework through a conservative multiblock approach. The approach, whose optimized implementation is also discussed, is assessed for two canonical flow problems bounded by walls, viz., fully developed turbulent channel flow at a shear or friction Reynolds number (Re) of 183.6 based on the channel half-width and three-dimensional (3D) shear-driven flows in a cubical cavity at a Re of 12 000 based on the side length of the cavity. Comparisons of detailed computed near-wall turbulent flow structure, given in terms of various turbulence statistics, with available data, including those from direct numerical simulations (DNS) and experiments showed good agreement. The GLBE approach also exhibited markedly better stability characteristics and avoided spurious near-wall turbulent fluctuations on coarser grids when compared with the single-relaxation-time (SRT)-based approach. Moreover, its implementation showed excellent parallel scalability on a large parallel cluster with over a thousand processors.

161 citations

Proceedings ArticleDOI
11 May 2009
TL;DR: In this paper, the Lattice-Boltzmann method is applied to the propagation of planar acoustic waves to determine the resolution dependence of numerical dissipation and dispersion.
Abstract: Numerical simulations are performed to investigate the fundamental acoustics properties of the Lattice–Boltzmann method. The propagation of planar acoustic waves is studied to determine the resolution dependence of numerical dissipation and dispersion. The two setups considered correspond to the temporal decay of a standing plane wave in a periodic domain, and the spatial decay of a propagating planar acoustic pulse of Gaussian shape. Theoretical dispersion relations are obtained from the corresponding temporal and spatial analyses of the linearized Navier–Stokes equations. Comparison of theoretical and numerical predictions show good agreement and demonstrate the low dispersive and dissipative capabilities the Lattice–Boltzmann method. The analysis is performed with and without turbulence modeling, and the changes in dissipation and dispersion are discussed. Overall, the results show that the Lattice–Boltzmann method can accurately reproduce time-explicit acoustic phenomena.

127 citations

Journal ArticleDOI
TL;DR: In this paper, the authors describe a numerical reproduction of the 22-in source diagnostic test fan rig of the NASA Glenn Research Center and perform numerical flow simulations for three different rotor configurations.
Abstract: The present work describes a numerical reproduction of the 22-in source diagnostic test fan rig of the NASA Glenn Research Center. Numerical flow simulations are performed for three different rotor...

123 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the authors present a review of the applicability and applicability of numerical predictions of turbulent flow, and advocate that computational economy, range of applicability, and physical realism are best served by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy k and its dissipation rate ϵ, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour.

11,866 citations


"Expanded analogy between Boltzmann ..." refers background in this paper

  • ...Significant efforts in turbulence modelling have been directed to deriving expressions for νturb (Launder & Spalding 1974)....

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Book
01 Jan 1993
TL;DR: In this paper, the authors proposed a compressible ecoulement for compressible ECCs, based on the disquette reference record created on 2005-11-18, modified on 2016-08-08.
Abstract: Keywords: ecoulement : compressible Note: + disquette Reference Record created on 2005-11-18, modified on 2016-08-08

7,023 citations


"Expanded analogy between Boltzmann ..." refers result in this paper

  • ...Indeed, simple estimation reveals that the effective mean-free path of eddies (i.e. the Prandtl (1925) mixing length) is at least comparable to the characteristic scales of the mean flow (Wilcox 1993)....

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  • ...the Prandtl (1925) mixing length) is at least comparable to the characteristic scales of the mean flow (Wilcox 1993)....

    [...]

01 Jan 1954
TL;DR: In this article, a kinetic theory approach to collision processes in ionized and neutral gases is presented, which is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high pressure limit where the aerodynamic equations are valid.
Abstract: A kinetic theory approach to collision processes in ionized and neutral gases is presented. This approach is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high-pressure limit where the aerodynamic equations are valid. It is also possible to satisfy the correct microscopic boundary conditions. The method consists in altering the collision terms in the Boltzmann equation. The modified collision terms are constructed so that each collision conserves particle number, momentum, and energy; other characteristics such as persistence of velocities and angular dependence may be included. The present article illustrates the technique for a simple model involving the assumption of a collision time independent of velocity; this model is applied to the study of small amplitude oscillations of one-component ionized and neutral gases. The initial value problem for unbounded space is solved by performing a Fourier transformation on the space variables and a Laplace transformation on the time variable. For uncharged gases there results the correct adiabatic limiting law for sound-wave propagation at high pressures and, in addition, one obtains a theory of absorption and dispersion of sound for arbitrary pressures. For ionized gases the difference in the nature of the organization in the low-pressure plasma oscillations and in high-pressure sound-type oscillations is studied. Two important cases are distinguished. If the wavelengths of the oscillations are long compared to either the Debye length or the mean free path, a small change in frequency is obtained as the collision frequency varies from zero to infinity. The accompanying absorption is small; it reaches its maximum value when the collision frequency equals the plasma frequency. The second case refers to waves shorter than both the Debye length and the mean free path; these waves are characterized by a very heavy absorption.

6,004 citations

Journal ArticleDOI
TL;DR: In this article, a two-equation model and Reynolds stress transport model are developed for turbulent shear flows and tested for homogeneous shear flow and flow over a backward facing step.
Abstract: Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986)] with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (η≡SK/■) is the ratio of the turbulent to mean strain time scale. While low‐order expansions appear to provide an adequate description for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of η suffices−terms of all orders must be retained. Based on these ideas, a new two‐equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

2,347 citations


"Expanded analogy between Boltzmann ..." refers background in this paper

  • ...There have also been attempts to go beyond the eddy-viscosity models in order to better describe turbulence, including secondary flow structures and flows subject to sudden distortions (Yakhot et al. 1992)....

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Journal ArticleDOI
01 Dec 1939-Nature
TL;DR: Chapman and Cowling as mentioned in this paper showed that the ultimate scope of the descendent of the kinetic theory of gases must be the whole field of the properties of matter in bulk, derived from the atomic constitution of matter and from properties of atoms and their interactions.
Abstract: SINCE the days when the kinetic theory of gases was founded by Clausius, Maxwell and Boltzmann, great changes have taken place in the scope and bearing of the descendent theory. Taking a wide view of its present field, the qualification “of gases” has become a misnomer. One can see that the ultimate scope of the descendent of the kinetic theory of gases must be the whole field of the properties of matter in bulk, derived from the atomic constitution of matter and from the properties of atoms and their interactions. The present scope of the theory falls short of such inclusiveness, but not so far short as to leave any doubts for the future. The Mathematical Theory of Non-Uniform Gases An Account of the Kinetic Theory of Viscosity, Thermal Conduction, and Diffusion in Gases. By Prof. Sydney Chapman and Dr. T. G. Cowling. Pp. xxiii + 404. (Cambridge: At the University Press, 1939.) 30s. net.

1,346 citations


"Expanded analogy between Boltzmann ..." refers methods in this paper

  • ...On the other hand, if K is treated as a small number, we can use a Chapman– Enskog-like expansion technique (Chapman & Cowling 1990) to obtain deviations from equilibrium at various orders of K: f = f (0) + Kf (1) + K2f (2) + · · · (2.4) where f (0) ≡ f eq....

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