On the dynamic computation of the model constant in delayed detached eddy simulation

The current work puts forth an implementation of a dynamic procedure to locally compute the value of the model constant CDES, as used in the eddy simulation branch of Delayed Detached Eddy Simulation ( DDES). Former DDES formulations [P. R. Spalart et al., A new version of detached-eddy simulation, resistant to ambiguous grid densities, Theor. Comput. Fluid Dyn. 20, 181 ( 2006); M. S. Gritskevich et al., Development of DDES and IDDES formulations for the k - omega shear stress transport model, Flow, Turbul. Combust. 88, 431 ( 2012)] are not conducive to the implementation of a dynamic procedure due to uncertainty as to what form the eddy viscosity expression takes in the eddy simulation branch. However, a recent, alternate formulation [K. R. Reddy et al., A DDES model with a Smagorinsky-type eddy viscosity formulation and log-layer mismatch correction, Int. J. Heat Fluid Flow 50, 103 ( 2014)] casts the eddy viscosity in a form that is similar to the Smagorinsky, LES ( Large Eddy Simulation) sub-grid viscosity. The resemblance to the Smagorinsky model allows the implementation of a dynamic procedure similar to that of Lilly [D. K. Lilly, A proposed modification of the Germano subgrid-scale closure method, Phys. Fluids A 4, 633 ( 1992)]. A limiting function is proposed which constrains the computed value of CDES, depending on the fineness of the grid and on the computed solution. (C) 2015 AIP Publishing LLC.