Stress relation for three-dimensional turbulent flows

Abstract

In this Brief Communication, the nonlinear stress–strain model for three-dimensional turbulent flows, as given by Taulbee [Phys. Fluids A 4, 11 (1992)], is expanded upon. That relation represents a closed form solution to the algebraic Reynolds stress model equation set which is obtained from the modeled transport equation for the Reynolds stress. The parameter values, which appear in the linear pressure–strain closure, that were suggested by Taulbee to obtain a simplified stress relation for three dimensions, are justified in this Brief Communication. A stress solution is also presented for a wider range of pressure–strain model parameter values.

Progress in Favré–Reynolds stress closures for compressible flows

“…Several permutations of quasi-explicit algebraic Reynolds stress expressions exist: [20,21,22,23,24,25,26,27,28]. The qualifier "quasi-explicit" is used to indicate that, as the fixed point equations are nonlinear, the solution is given implicitly.…”

“…Closures for the unclosed terms involving the mean acceleration are also constructed. In as much as most engineering calculations [in this country] are done with lower order closures this article therefore also includes the additional development of the secondorder moment closure into an algebraic Reynolds stress closure, suitable for flows in structural equilibrium, following established procedures [20,21,22,23,24,25,26,27,28].…”

Explicit algebraic scalar‐flux models for turbulent reacting flows

“…The improvement is due to an extended range of validity; the model is valid in both small and large mean strain fields and time scales of turbulence. The nonlinear stress-strain relation for 3-D mean flows is of the form (Taulbee, 1992;Taulbee et al, 1993) where P = -( k)aijSj, is the production of the turbulent kinetic energy; the invariants of the strain rate and rotation rate tensors cr2 = (SijSji), w 2 = ( f l i j f l i j ) ; and the model coefficients of the pressure-strain correlation and the modeled dissipation equation.…”

“…The objective of this work is to expand upon the formulation developed by Taulbee (1992) (also see Taulbee et al, 1993) for predictions of turbulent flows involving scalar quantities (Brodkey, 1981). The specific objective is to provide explicit algebraic relations for the turbulent flux of scalar vari-ables.…”

New explicit algebraic stress and flux model for active scalar and simulation of shear stratified cylinder wake flow

“…i j u u Pope [8] first presented the two-dimensional explicit relation for the Reynolds stress tensor from the implicit algebraic stress model, and pointed out that the three-dimensional Reynolds stress tensor could be represented by ten independent tensors and five invariants; Taulbee et al [9,10] simplified the implicit algebraic stress model, and then obtained explicit algebraic expressions for three-dimensional Reynolds stress tensors by using partial independent tensors; Gatski and Speziale [11] extended the work of Pope [8] , and obtained the explicit Reynolds stress expression by these ten tensors; Wallin [12] considered the ratio of turbulent kinetic energy term and dissipation rate term as an unknown quantity, and proposed the explicit Reynolds stress algebraic expression with the ten tensors; Gatski and Wallin [13] further extended the work for additional considerations taking into account the flow rotation and curvature. While solving the implicit algebraic equations of the scalar flux , i u θ the ill-conditioned problems are similar to the implicit algebraic Reynolds stress models.…”