Detached Eddy Simulations of Incompressible Turbulent Flows Using the Finite Element Method

摘要

An explicit Galerkin finite-element formulation of the Spalart-Allmaras (SA) 1 - equation turbulent transport model was implemented into the incompressible flow module of a parallel, multi-domain, Galerkin finite-element, multi-physics code, using both a RANS formulation and a DES formulation. DES is a new technique for simulating/modeling turbulence using a hybrid RANSkES formulation. The turbulent viscosity is constructed from an intermediate viscosity obtained from the transport equation which is spatially discretized using Q1 elements and integrated in time via forward Euler time integration. Three simulations of plane channel flow on a RANS-type grid, using different turbulence models, were conducted in order to validate the implementation of the SA model: SA-RANS, SA-DES and Smagorinksy (without wall correction). Very good agreement was observed between the SA-RANS results and theory, namely the Log Law of the Wall (LLW), especially in the viscous sublayer region and, to a lesser extent, in the log-layer region. The results obtained using the SA-DES model did not agree as well with the LLW, and it is believed that this poor agreement can be attributed to using a DES model on a RANS grid, namely using an incorrect length-scale. It was observed that near the wall, the SA-DES model acted as an RANS model, and away from the wall it acted as an LES model.