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

本研究的目的是建立亚网尺度（SGS）估计模型，该模型可用于大涡模拟（LES）方法在实际工程流中的应用。在2000财政年度，我们首先比较了SGS估算模型的几种公式的性能。为此，我们生成了不可压缩均匀各向同性湍流的直接数值模拟（DNS）数据。通过对DNS数据进行过滤得到的SGS应力张量精确值与SGS模型得到的应力估计值之间的相关性，对模型进行了直接评价。SGS估计模型的一个重要过程是网格上的速度估计，其间隔是LES网格的一半。在此过程中，利用Navier-Stokes （N-S）方程的动力学特性，即将N-S方程中非线性项的作用纳入到速度场的修正中。通过对在网格尺度和SGS之间产生能量传递的湍流结构进行分类来进行评估。发现J.A. Domaradzki等人(Phys.；流体11(1999)，模型1)高估了应变主导涡度的区域的贡献。通过使用亥姆霍兹分解（模型2）将估计的速度场投影到螺线线空间，可以避免模型1的这一缺点。通过使用N-S方程（Truncated Navier-Stokes （TNS）模型，模型3）推进估计速度，进一步提高了速度。我们将三种模型应用于旋转作用下不可压缩均匀各向同性湍流的实际LES计算中，对三种模型进行了评价，结果表明，模型2和模型3的性能优于以往的SGS模型和模型1。在2001财年，尝试将SGS估计模型应用于实际工程流程中，采用有限差分法作为数值方法。有限差分法应用的一个重要过程是对滤波后的速度场进行反滤波（反卷积）。研究表明，使用近似反卷积过程可以有效地完成这种去过滤(horuti （1999)， Stolz等人（1999））。然而，在提高有限差分法的精度时，由于存在混叠误差，导致了数值的不稳定性。结果表明，这种不稳定性可以通过加入松弛项来消除（Stolz et al.）。（1999）>到反褶积过程。结合近似反褶积过程和加入松弛项的SGS估计模型进行了LES计算，并证明了该模型在LES实际应用中的有效性。利用本财年DNS数据产生的较高雷诺数，我们对模型进行了与2000年相同的几何评估，结果表明，使用模型3预测涡度占主导的应变区域的精度高于使用模型2。当考虑SGS应力张量和网格尺度应变速率张量特征向量的对中性时，DNS数据显示出这两个特征向量的强烈非对中性，而模型2和模型3的结果与DNS数据吻合较好，表明SGS涡动黏度模型存在局限性。少

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