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A GNF framework for turbulent flow models of drag reducing fluids and proposal for a $$k-\varepsilon$$ type closure. (English) Zbl 1058.76030
Author’s summary: Based on a generalised Newtonian fluid (GNF) model, modified to account for strain-thickening of the extensional viscosity, this paper derives transport equations for mass, momentum, Reynolds stresses, turbulent kinetic energy and its rate of dissipation. An analysis of order of magnitude identifies the relevant new terms, and suggestions are made to model those terms needed to ensure closure in the perspective of a low Reynolds number $$k-\varepsilon$$ model. Specifically, a closed model for the time-average viscosity is proposed which takes into account its nonlinearity and dependence on the second and third invariants of the fluctuating rate of deformation tensor. The turbulence model is qualitatively shown to increase the rate of decay of turbulent kinetic energy in isotropic grid turbulence for certain rheological conditions. The performance of the turbulence model in a pipe flow is assessed in a companion paper by D. O. A. Cruz and F. T. Pinho [J. Non-Newton. Fluid Mech. 114, No. 2–3, 109–148 (2003; Zbl 1042.76533)].

##### MSC:
 76F60 $$k$$-$$\varepsilon$$ modeling in turbulence 76F70 Control of turbulent flows 76A05 Non-Newtonian fluids
##### Keywords:
single-point closure; transport equations
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