On explicit algebraic stress models for complex turbulent flows

Abstract

Explicit algebraic stress models that are valid for three-dimensional turbulent flows in non-inertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope [J. Fluid Mech. 72, 331 (1975)] who based his analysis on the Launder, Reece and Rodi model restricted to twodimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -as well as anistropic eddy viscosity models -is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

Applicability of URANS and DES Simulations of Flow Past Rectangular Cylinders and Bridge Sections

“…It introduces the anisotropy tensor, which offers a more accurate representation of all components of the Reynolds stress tensor and captures rotation and curvature effects, without the drawbacks of high numerical effort and reduced robustness of a full differential stress model. In particular, Rung et al [12] proposed a quadratic model based on the EARSM of Gatski and Speziale [13] with an improved representation of the production-to-dissipation ratio within the stress-strain relation, which does not require any regularization and yields superior predictive capabilities in case of non-equilibrium large-strain-rates conditions. As compared to the Spalart and Allmaras model, where the turbulence production term is based on the second invariant of the vorticity tensor, this EARSM model relies on a formulation based on the second invariant of both strain rate and vorticity rate tensors, which also does not seem to produce excessive turbulence in the stagnation region in front of the body's upstream face.…”

Large-eddy simulation of turbulent flows in a heated streamwise rotating channel

“…The Among the studies of turbulent channel flows subjected to these three types of system rotations, the spanwise rotating turbulent channel flows have been studied extensively through experiments [23,24] and numerical simulations [14,[25][26][27][28][29][30][31][32][33][34][35][36][37]. It is reported that as the rotation number increases, turbulence is gradually enhanced on the pressure side and reduced on the suction side, further resulting in asymmetric distributions in the mean flow and Reynolds stresses [14,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. At the same time, large-scale roll cells come forth as a result of the Taylor-Görtler (T-G) instability [14,23,25,35].…”

Stellar Mixing

“…There is no physical reason why τ/T should be small, which would justify stopping at the first term (2a), and non-perturbative derivations of the Reynolds stresses (Taulbee 1992;Gatski & Speziale 1993) showed there are higher order terms in powers of τ/T . A second consideration is that (1d) requires that the principal axes of the tensor τ i j representing turbulence be aligned with those of S i j representing the mean flow.…”

“…In fact, a complete derivation of (1d) shows the presence of nonisotropic terms that break the "alignment assumption" and that are ultimately responsible for the extra terms discussed above. In other words, in lieu of the first of (1d), one has (Taulbee 1992;Gatski & Speziale 1993) an expression of the type…”