Investigation for the one-equation-type subgrid model with eddy-viscosity expression including the shear-damping effect

The model expression for the subgrid-scale (SGS) Reynolds stress and the transport equation of the SGS energy are theoretically derived using a two-scale direct-interaction approximation (TSDIA), Applying the model to three-type flows, i.e. a homogeneous decaying turbulence, a mixing layer and a channel flow, the model constants are optimized and the results are compared with those of the Smagorinsky model in detail. Consequently, it is found that this one-equation model has two deficiencies. One is that the model-constants are dependent on flow fields like the Smagorinsky model. The other is that an exact asymptotic-behavior of the SGS energy in the vicinity of the wall is not satisfied by this one-equation model, Therefore, for the purpose of improving the near-wall profiles for the SGS quantities in this model, a new model for the SGS dissipation rate is suggested on the basis of a low-Reynolds-number K-epsilon model. Moreover, using the model including a high-order term of the SGS Reynolds stress, a new one-equation model which is applicable to several flows with fixed model-constants is proposed.