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This paper deals with topology optimization of body shapes in fluid flows, where some new ideas for drag minimization and lift maximization problems are proposed. For drag minimization problems, the objective function is expressed as a body force integration in the flow domain. Also a similar expression of objective function is given for lift maximization problems. Employing those objective function expressions, optimum shapes of bodies in incompressible axisymmetric and two-dimensional flows are numerically investigated.

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A new subgrid-scale (SGS) model for practical large eddy simulation (LES) is proposed. The model is constructed with the concept of mixed time-scale, which makes it possible to use fixed model-parameters and to dispense with the distance from the wall. The model performance is tested in plane channel flows, and the results show that this model is able to account for near-wall turbulence without an explicit damping function as in the dynamic Smagorinsky model. The model is also evaluated in a backward-facing step flow and in a flow around a circular cylinder. The calculated results using the consistent model-parameters show good agreement with experimental data, while the results obtained using the dynamic Smagorinsky model show less accuracy and less computational stability. Furthermore, to confirm the validity of the present model in practical applications, the three-dimensional complex flow around a bluff body (Ahmed et al., SAE paper no. 840300) is also calculated with the model. The agreement between the calculated results and the experimental data is quite satisfactory. These results suggest that the present model is a refined SGS model suited for practical LES to compute flows in a complicated geometry.