Abstract
We propose a modified low-Reynolds-number k-ε turbulence model, in which anisotropy of the Reynolds normal stresses is considered, for viscoelastic fluids and have tested it to predict the drag-reduced turbulent channel flow. In order to obtain the constitutive stresses more accurately, we solved numerically the averaged constitutive equation based on the Giesekus model. This equation includes several terms that pertain to the correlation between velocity and constitutive-stress fluctuations and require to be modeled. We employ a model, in which the Reynolds stress and the viscoelastic stress were used to estimate the correlation terms, and hence it is important to predict the Reynolds normal stress precisely. In this study, we propose an algebraic equation to model the anisotropic Reynolds normal stresses using a damping function of the eddy viscosity. The present proposal allows the constitutive stresses to be predicted well.
