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 vendor s offer DSM as a modelling option. Even fewer industrial users recognize th e 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. Th is paper gives an overview of the rationale for employing more advanced mod els for the computation of complex flows and transport processes. It also d iscusses reasons for their slow adoption by the CFD community. Physical arg uments are briefly given; these illustrate a higher degree of exactness inh erent in the second-moment closure approach. The superiority of these model s is demonstrated by a series of computational examples, provided by author 's co-workers who used either the same or very similar computational method s and model(s). Examples include several nonequilibrium flows, attached and with separation and reattachment, flow impingement and stagnation, longitu dinal vortices, secondary motion, swirl, system rotation. The modelling of molecular effects, both near and away from a solid wall and associated lami nar-to-turbulent and reverse transition are also discussed in view of the n eed for an advanced closure approach particularly when wall phenomena are i n focus. Numerical aspects associated with the application of second-moment closure are then discussed, together with current practice used to overcom e numerical problems and to reconcile the need for advanced models with una voidably increasing computational challenge. Several examples related to th e automotive industry illustrate the applicability of DSM to real complex f lows which have industrial relevance.