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

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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.