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Journal of Applied Mathematics
Volume 2013, Article ID 197628, 15 pages
Research Article

Proposal of Damping Function for Low-Reynolds-Number - Model Applicable in Prediction of Turbulent Viscoelastic-Fluid Flow

Department of Mechanical Engineering, Tokyo University of Science, 2641 Yamazaki, Noda-shi, Chiba 278-8510, Japan

Received 24 June 2013; Revised 12 September 2013; Accepted 13 September 2013

Academic Editor: Mohamed Fathy El-Amin

Copyright © 2013 Takahiro Tsukahara and Yasuo Kawaguchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A low-Reynolds-number k- model applicable for viscoelastic fluid was proposed to predict the frictional-drag reduction and the turbulence modification in a wall-bounded turbulent flow. In this model, an additional damping function was introduced into the model of eddy viscosity, while the treatment of the turbulent kinetic energy (k) and its dissipation rate ( ) is an extension of the model for Newtonian fluids. For constructing the damping function, we considered the influence of viscoelasticity on the turbulent eddy motion and its dissipative scale and investigated the frequency response for the constitutive equation based on the Giesekus fluid model. Assessment of the proposed model’s performance in several rheological conditions for drag-reduced turbulent channel flows demonstrated good agreement with DNS (direct numerical simulation) data.