Abstract
A low-Reynolds-numberk-εmodel 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 (ε) 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.
Highlights
It is known that minute amount of additives, such as polymer and surfactant, can reduce the frictional drag in wallbounded turbulent flows at high Reynolds numbers
Since the direct numerical simulation (DNS) is one of the important tools to investigate turbulence phenomena qualitatively and quantitatively, DNSs of viscoelastic flows have been increasingly performed by a number of researchers after the pioneering works in 1997-1998 [1, 2]: see reviews [3, 4]
The numerical solutions of the proposed model equations were obtained using the secondorder central-difference scheme for discretization, while convergence calculation was performed by the successive overrelaxation (SOR) method
Summary
It is known that minute amount of additives, such as polymer and surfactant, can reduce the frictional drag in wallbounded turbulent flows at high Reynolds numbers. The development of mathematical and computational models for viscoelastic flow is not sufficiently well advanced to allow RANS simulation to be undertaken With this background, it is a matter of interest to build more physically-based turbulence closures for the prediction of flows with drag-reducing additives with the aid of the DNS database and the already-proposed mechanism of DR. Their closure models were calibrated well on the basis of DNS database, Iaccarino et al [15] employed the V2-f approach to treat the intensed wall damping of wall-normal turbulence in the drag-reduced flow They modelled directly the Reynolds-averaged polymer stress without solving the constitutive equation for the conformation tensor, resulting in less coefficients and functions. The proposed model will be tested in comparison with DNS results
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