Study on the subgrid-scale model taking into account of the viscoelastic effect

我们从生成衰减和强迫均匀各向同性湍流的DNS数据开始我们的研究。使用了高达512^3的网格点，我们使用了位于大阪大学网络媒体中心的SX-5超级计算机，其用户费用由该补助金支付。下一步，我们利用DNS数据研究了沿涡片的涡管结构的形成过程。我们已经证明，这些管是通过双涡旋片的相互作用形成的，它们彼此相交形成τ形构型。结果表明，根据两个薄片上涡量矢量的相对排列，存在三种构型模式。当两张片上的涡量矢量相互垂直放置时，两张片附近的应变率张量在拉伸方向上产生压缩。因此，在这种构型下产生的涡管轴线方向与沿涡片的涡度矢量方向是横向的。随着这一转化过程发生频率的增加，湍流能量梯级的强烈产生。然后，我们利用Oldroyd本构方程研究粘弹性对这一转变过程发生的影响。利用该方程的稳态解表明，粘弹性效应主要作用于涡片上，消除了涡片向管内转变的发生，湍流的产生明显减少。结果表明，稳态解类似于牛顿流体中使用的非线性模型，但要考虑非牛顿流体中的粘弹性效应，应将一项的符号反转。

We begun our study with the generation of the DNS data for the decaying and forced homogeneous isotropic turbulence. Grid points up to 512^3 were employed, and we utilized the SX-5 supercomputer located at the Cyber-media Center, Osaka University, and its user fee was paid by this grant-in aid. In the next step, we investigated on the process of formation of the vortex tube structures along the vortex sheets using the DNS data. We have shown that the tubes are formed through the interaction of the dual vortex sheets, which intersect to each other forming the τ shaped configuration. It was shown that three modes of configuration exist depending on the relative alignment of the vorticity vectors on the two sheets. When the vorticity vectors on the two sheets were placed perpendicular to each other, compression of the strain-rate tensor in the stretching direction arose in the vicinity of the dual sheets. Thus the direction of the axis of the vortex tube generated in this configuration was in the transverse direction against the vorticity vector along the vortex sheet. As the frequency of occurrence of this transformation process increased, intense generation of turbulent energy cascade took place. Then, we investigated the effect of viscoelasticity on the occurrence of this transformation process using the Oldroyd constitutive equation. Using the steady state solution of this equation, we have shown that the viscoelastic effect is primarily exerted on the vortex sheet, and occurrence of its transformation into the tube was annihilated, and the turbulence generation was markedly reduced. It was shown that the steady solution is similar to the nonlinear model which is used in LES of the Newtonian fluid, but to take into the viscoelastic effect in the non-Newtonian fluid, a sign of the one specific term should be reversed.