Progress in the development of a Reynolds-stress turbulence closure
TL;DR: In this article, the authors developed a model of turbulence in which the Reynolds stresses are determined from the solution of transport equations for these variables and for the turbulence energy dissipation rate E. Particular attention is given to the approximation of the pressure-strain correlations; the forms adopted appear to give reasonably satisfactory partitioning of the stresses both near walls and in free shear flows.
Abstract: The paper develops proposals for a model of turbulence in which the Reynolds stresses are determined from the solution of transport equations for these variables and for the turbulence energy dissipation rate E. Particular attention is given to the approximation of the pressure-strain correlations; the forms adopted appear to give reasonably satisfactory partitioning of the stresses both near walls and in free shear flows. Numerical solutions of the model equations are presented for a selection of strained homogeneous shear flows and for two-dimensional inhomogeneous shear flows including the jet, the wake, the mixing layer and plane channel flow. In addition, it is shown that the closure does predict a very strong influence of secondary strain terms for flow over curved surfaces.
Citations
More filters
TL;DR: The second-moment turbulent closure hypothesis has been applied to geophysical fluid problems since 1973, when genuine predictive skill in coping with the effects of stratification was demonstrated as discussed by the authors.
Abstract: Applications of second-moment turbulent closure hypotheses to geophysical fluid problems have developed rapidly since 1973, when genuine predictive skill in coping with the effects of stratification was demonstrated. The purpose here is to synthesize and organize material that has appeared in a number of articles and add new useful material so that a complete (and improved) description of a turbulence model from conception to application is condensed in a single article. It is hoped that this will be a useful reference to users of the model for application to either atmospheric or oceanic boundary layers.
6,488 citations
Journal Article•
01 Jun 1978TL;DR: In this paper, the authors evaluated the applicability of the standard κ-ϵ equations and other turbulence models with respect to their applicability in swirling, recirculating flows.
Abstract: The standard κ-ϵ equations and other turbulence models are evaluated with respect to their applicability in swirling, recirculating flows. The turbulence models are formulated on the basis of two separate viewpoints. The first perspective assumes that an isotropic eddy viscosity and the modified Boussinesq hypothesis adequately describe the stress distributions, and that the source of predictive error is a consequence of the modeled terms in the κ-ϵ equations. Both stabilizing and destabilizing Richardson number corrections are incorporated to investigate this line of reasoning. A second viewpoint proposes that the eddy viscosity approach is inherently inadequate and that a redistribution of the stress magnitudes is necessary. Investigation of higher-order closure is pursued on the level of an algebraic stress closure. Various turbulence model predictions are compared with experimental data from a variety of isothermal, confined studies. Supportive swirl comparisons are also performed for a laminar flow case, as well as reacting flow cases. Parallel predictions or contributions from other sources are also consulted where appropriate. Predictive accuracy was found to be a partial function of inlet boundary conditions and numerical diffusion. Despite prediction sensitivity to inlet conditions and numerics, the data comparisons delineate the relative advantages and disadvantages of the various modifications. Possible research avenues in the area of computational modeling of strongly swirling, recirculating flows are reviewed and discussed.
5,396 citations
TL;DR: In this article, a new k -ϵ eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscous formulation, is proposed.
4,648 citations
TL;DR: The implementation of various types of turbulence modeling in a FOAM computational-fluid-dynamics code is discussed, and calculations performed on a standard test case, that of flow around a square prism, are presented.
Abstract: In this article the principles of the field operation and manipulation (FOAM) C++ class library for continuum mechanics are outlined. Our intention is to make it as easy as possible to develop reliable and efficient computational continuum-mechanics codes: this is achieved by making the top-level syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Object-orientation techniques enable the creation of data types that closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modeling in a FOAM computational-fluid-dynamics code is discussed, and calculations performed on a standard test case, that of flow around a square prism, are presented. To demonstrate the flexibility of the FOAM library, codes for solving structures and magnetohydrodynamics are also presented with appropriate test case results given. © 1998 American Institute of Physics.
3,987 citations
TL;DR: In this article, a dynamic renormalization group (RNG) method for hydrodynamic turbulence was developed, which uses dynamic scaling and invariance together with iterated perturbation methods, allowing us to evaluate transport coefficients and transport equations for the large scale (slow) modes.
Abstract: We develop the dynamic renormalization group (RNG) method for hydrodynamic turbulence. This procedure, which uses dynamic scaling and invariance together with iterated perturbation methods, allows us to evaluate transport coefficients and transport equations for the large-scale (slow) modes. The RNG theory, which does not include any experimentally adjustable parameters, gives the following numerical values for important constants of turbulent flows: Kolmogorov constant for the inertial-range spectrumCK=1.617; turbulent Prandtl number for high-Reynolds-number heat transferPt=0.7179; Batchelor constantBa=1.161; and skewness factor¯S3=0.4878. A differentialK-\(\bar \varepsilon \) model is derived, which, in the high-Reynolds-number regions of the flow, gives the algebraic relationv=0.0837 K2/\(\bar \varepsilon \), decay of isotropic turbulence asK=O(t−1.3307), and the von Karman constantκ=0.372. A differential transport model, based on differential relations betweenK,\(\bar \varepsilon \), andν, is derived that is not divergent whenK→ 0 and\(\bar \varepsilon \) is finite. This latter model is particularly useful near walls.
3,342 citations
References
More filters
Book•
01 Jan 1972
TL;DR: In this paper, the authors present a reference record created on 2005-11-18, modified on 2016-08-08 and used for the analysis of turbulence and transport in the context of energie.
Abstract: Keywords: turbulence ; transport ; contraintes ; transport ; couche : limite ; ecoulement ; tourbillon ; energie Reference Record created on 2005-11-18, modified on 2016-08-08
8,276 citations
TL;DR: In this article, a general, numerical, marching procedure is presented for the calculation of the transport processes in three-dimensional flows characterised by the presence of one coordinate in which physical influences are exerted in only one direction.
5,946 citations
TL;DR: In this article, the rate constants of 60 typical electron donor-acceptor systems have been measured in de-oxygenated acetonitrile and are shown to be correlated with the free enthalpy change, ΔG23, involved in the actual electron transfer process.
Abstract: Fluorescence quenching rate constants, kq, ranging from 106 to 2 × 1010 M−1 sec−1, of more than 60 typical electron donor-acceptor systems have been measured in de-oxygenated acetonitrile and are shown to be correlated with the free enthalpy change, ΔG23, involved in the actual electron transfer process
in the encounter complex and varying between + 5 and −60 kcal/mole. The correlation which is based on the mechanism of adiabatic outer-sphere electron transfer requires ΔG≠23, the activation free enthalpy of this process to be a monotonous function of ΔG23 and allows the calculation of rate constants of electron transfer quenching from spectroscopic and electrochemical data.
A detailed study of some systems where the calculated quenching constants differ from the experimental ones by several orders of magnitude revealed that the quenching mechanism operative in these cases was hydrogen-atom rather than electron transfer.
The conditions under which these different mechanisms apply and their consequences are discussed.
3,485 citations
01 Jan 1972
TL;DR: In this article, the authors discuss the Reynolds equations and estimate of the Reynolds stress in the kinetic theory of gases, and describe the effects of shear flow near a rigid wall.
Abstract: This chapter contains sections titled: The Reynolds equations, Elements of the kinetic theory of gases, Estimates of the Reynolds stress, Turbulent heat transfer, Turbulent shear flow near a rigid wall
3,270 citations
01 Jan 1972
TL;DR: In this article, the probability density, Fourier transforms and characteristic functions, joint statistics and statistical independence, Correlation functions and spectra, the central limit theorem, and the relation functions are discussed.
Abstract: This chapter contains sections titled: The probability density, Fourier transforms and characteristic functions, Joint statistics and statistical independence, Correlation functions and spectra, The central limit theorem
3,260 citations