Research on Development of Engineering-Application Oriented Subgrid-Scale Estimation Model

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The aim of the present study was to develop the subgrid-scale (SGS) estimation model which can be used for application of large-eddy simulation (LES) method in practical engineering flows.In the fiscal year of 2000, we began with the comparison of the performance of several formulations for the SGS estimation model. For this purpose, we generated the Direct numerical simulation (DNS) data for the incompressible homogeneous isotropic turbulence. We carried out direct assessment of the models by measuring the correlation between the exact value for the SGS stress tensor, which was obtained by filtering the DNS data, and the estimate of the stress derived using the SGS models. One of important processes involved with the SGS estimation model is the estimation of the velocities on the grids, the interval of which is half of that for the LES grids. In this process, corrections were incorporated into the velocity fields, which were obtained using the interpolation of the velocity fields on t … More he LES grids, utilizing the dynamics of the Navier-Stokes (N-S) equations, i.e., incorporating an action of the nonlinear terms in the N-S equations. The assessment was carried out by classifying the turbulent structures which are responsible for generation of energy transfer between the grid scale and the SGS. It was found that the method proposed by J.A. Domaradzki et al. (Phys. Fluids 11 (1999), Model 1) yields the overestimate of the contribution of the region in which the strain predominates the vorticity. This drawback of Model 1 was circumvented by applying the projection of the estimated velocity fields onto the solenoidal space using the Helmholtz decomposition (Model 2). Further improvement was achieved by advancing the estimated velocity in time using the N-S equations (Truncated Navier-Stokes (TNS) model, Model 3). We carried out assessment of the three models by applying the models to actual LES calculations of incompressible homogeneous isotropic turbulence which was subjected to rotation, and showed that the performances of Models 2 and 3 is better than those of previous SGS models as well as Model 1.In the fiscal year of 2001, attempts were made to apply the SGS estimation model to practical engineering flows, in which the finite difference method was used as for the numerical method. An important process involved with the application of the finite difference method is the defiltering (deconvolution) of the filtered velocity field. It was shown that this defiltering can be efficiently done using the approximate deconvolution procedure (Horiuti (1999), Stolz et al.(1999)). When the accuracy of the finite difference method was raised, however, it was found that numerical instability arises due to occurrence of the aliasing errors. It was shown that this instability can be eliminated by adding the relaxation term (Stolz et'al.(1999)> to the deconvolution procedure. We carried out LES calculations using the SGS estimation model in conjunction with the approximate deconvolution procedure and addition of the relaxation term, and showed the effectiveness of the proposed model for LES of practical applications. Taking advantage of the higher Reynolds number at which the DNS data was generated in this fiscal year, we conducted the same geometrical assessment of the models as was done in the year 2000, and showed that the accuracy for prediction of the region in which the vorticity predominates the strain obtained using Model 3 was higher than that obtained using Model 2.When the alignment of the eigenvectors for the SGS stress tensor and the grid-scale strain rate tensor was considered, the DNS data showed strong non-alignment of these two eigenvectors, whereas the results obtained using Models 2 and 3 were in good agreement with the DNS data, revealing a limitation of the SGS eddy viscosity model. Less