A Study on the Mechanism of Reduction of Turbulence Generation in Viscoelastic Fluid

我们研究了粘弹性流体中非亲和性对旋涡结构形成过程和减少湍流产生的影响。我们处理了均匀各向同性湍流和管道流动中的湍流，并利用直接数值模拟方法生成的数值数据。非仿射对聚合物应力的影响使用Johnson-Segalman本构方程（Johnson and Segalman 1977， JS模型）进行近似。在各向同性和管状流动中，湍流产生的减小程度不是单调的。当非仿射效应最大时，即Oldroyd-A方程，湍流产生减少量最大；当非仿射效应最小时，即Oldroyd-B方程，湍流产生减少量最小。通过观察旋涡结构的形成，研究了这种还原的机制。结果表明，在Oldroyd-B方程中，聚合物应力在管核区域的集中最大，涡流管核区域的生长被减弱，而在Oldroyd-A方程中，聚合物应力在涡片区域的集中最大，从而使涡片向涡流管的转变被湮灭。利用模型的代数近似稳态解对JS模型进行了理论分析。结果表明，2^<和>阶解不会产生湍流产生减小的非单调增长。这个缺点在3^<rd>或更高阶的解决方案中得到缓解。

We studied the effect of non-affinity in the viscoelastic fluid on the process of the vortical structure formation and reduction of turbulence generation. We dealt with the homogeneous isotropic turbulence and the turbulence in the pipe flow, and utilized the numerical data which were generated using the direct numerical simulation method. The non-affine effect on the polymer stress was approximated using the Johnson-Segalman constitutive equation (Johnson and Segalman 1977, JS model). In both isotropic and pipe flows, the degree of reduction of the turbulence generation was not monotonic on the strength of the non-affinity. The largest reduction of turbulence generation was achieved when the non-affine effect was largest, i.e., the Oldroyd-A equation, and the smallest reduction when the non-affine effect was smallest, i.e., the Oldroyd-B equation. Mechanism of this reduction was examined by looking into the formation of the vortical structures. It was shown that the concentration of the polymer stress was largest in the tube core region in the Oldroyd-B equation and the growth of the vortex tube core region was attenuated, whereas the concentration was largest in the vortex sheet region in the Oldroyd-A equation, thus the transformation of the vortex sheet into the vortex tube was annihilated. A theoretical analysis on the JS model was carried out using the algebraic approximate steady solution of the model. It was shown that the 2^<nd>-order solution does not yield a non-monotonic growth of the turbulence generation reduction. This drawback was mitigated in the solutions with 3^<rd> or higher orders.