Second-moment turbulence closures for CFD: Needs and prospects

Differential second-moment (Reynolds-stress) turbulence closure models (DSM) have long been expected to replace the currently popular two-equation k - epsilon and similar eddy viscosity models (EVM) as the industrial standard for Computational Fluid :Dynamics (CFD). Yet, despite almost three decades of development and indisputable progress, only a few commercial CFD vendors offer DSM as a modelling option. Even fewer industrial users recognize the natural superiority of the DSM. These models, used and researched mainly within academic community, are still viewed as a development target rather than as a proven and mature technique for solving complex how phenomena. This paper gives an overview of the rationale for employing more advanced models for the computation of complex flows and transport processes. It also discusses reasons for their slow adoption by the CFD community. Physical arguments are briefly given; these illustrate a higher degree of exactness inherent in the second-moment closure approach. The superiority of these models is demonstrated by a series of computational examples, provided by author's co-workers who used either the same or very similar computational methods and model(s). Examples include several nonequilibrium flows, attached and with separation and reattachment, flow impingement and stagnation, longitudinal vortices, secondary motion, swirl, system rotation. The modelling of molecular effects, both near and away from a solid wall and associated laminar-to-turbulent and reverse transition are also discussed in view of the need for an advanced closure approach particularly when wall phenomena are in focus. Numerical aspects associated with the application of second-moment closure are then discussed, together with current practice used to overcome numerical problems and to reconcile the need for advanced models with unavoidably increasing computational challenge. Several examples related to the automotive industry illustrate the applicability of DSM to real complex flows which have industrial relevance.