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K-epsilon turbulence model
About: K-epsilon turbulence model is a research topic. Over the lifetime, 13914 publications have been published within this topic receiving 509292 citations.
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TL;DR: Using renormalization-group methods and the postulated equivalence between the inertial-range structures of turbulent flows satisfying initial and boundary conditions and of flows driven by a random force, the Kolmogorov constant and Batchelor constant are evaluated and the skewness factor and power-law exponent are evaluated.
Abstract: Using renormalization-group methods and the postulated equivalence between the inertial-range structures of turbulent flows satisfying initial and boundary conditions and of flows driven by a random force, we evaluate the Kolmogorov constant (1.617) and Batchelor constant (1.161), skewness factor (0.4878), power-law exponent (1.3307) for the decay of homogeneous turbulence, turbulent Prandtl number (0.7179), and von K\'arm\'an constant (0.372). This renormalization-group technique has also been used to derive turbulent transport models.
1,569 citations
01 Jan 1991
TL;DR: In this article, the velocity components at each point P = (xi, x2, x3, t) of the region G under consideration belonging to the four-dimensional space were regarded as random variables in the sense of probability theory.
Abstract: §1. We denote by ua(P) = ua(xl, x2, x3, t), a= 1,2,3, the velocity components at time t at a point with rectangular Cartesian coordinates xi, x2, x3. When studying turbulence it is natural to regard the velocity components ua(P) at each point P = (xi, x2, x3, t) of the region G under consideration belonging to the four-dimensional space (xi, x2i X3, t) as random variables in the sense of probability theory (for this approach, see the paper by Millionshchikov [1]).
1,538 citations
01 Aug 1994
TL;DR: In this article, a new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscous formulation, is proposed.
Abstract: A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.
1,524 citations
TL;DR: In this article, a review of scale-invariance properties of high-Reynolds-number turbulence in the inertial range is presented, focusing on dynamic and similarity subgrid models and evaluating how well these models reproduce the true impact of the small scales on large scale physics and how they perform in numerical simulations.
Abstract: ▪ Abstract Relationships between small and large scales of motion in turbulent flows are of much interest in large-eddy simulation of turbulence, in which small scales are not explicitly resolved and must be modeled. This paper reviews models that are based on scale-invariance properties of high-Reynolds-number turbulence in the inertial range. The review starts with the Smagorinsky model, but the focus is on dynamic and similarity subgrid models and on evaluating how well these models reproduce the true impact of the small scales on large-scale physics and how they perform in numerical simulations. Various criteria to evaluate the model performance are discussed, including the so-called a posteriori and a priori studies based on direct numerical simulation and experimental data. Issues are addressed mainly in the context of canonical, incompressible flows, but extensions to scalar-transport, compressible, and reacting flows are also mentioned. Other recent modeling approaches are briefly introduced.
1,395 citations
TL;DR: In this paper, the scale of turbulence is defined in terms of the correlation between the velocity of a particle at one time and that of the same particle at a later time, or between simultaneous velocities at two fixed points.
Abstract: Since the time of Osborne Reynolds it has been known that turbulence produces virtual mean stresses which are proportional to the coefficient of correlation between the components of turbulent velocity at a fixed point in two perpendicular directions. The significance of correlation between the velocity of a particle at one time and that of the same particle at a later time, or between simultaneous velocities at two fixed points was discussed in 1921 by the present writer in a theory of “Diffusion by Continuous Movements.” The recent improvements in the technique of measuring turbulence have made it possible actually to measure some of the quantities envisaged in the theory and thus to verify some of the relationships then put forward. The theory has also been developed in several directions which were not originally contemplated. The theory, as originally put forward, provided a method for defining the scale of turbulence when the motion is defined in the Lagrangian manner, and showed how this scale is related to diffusion. It is now shown that it can be applied either to the Lagrangian or to the Eulerian conceptions of fluid flow.
1,367 citations