Stabilization of the turbulent flows in anisotropic viscoelastic tubes

Abstract

Abstract Flow around the aircrafts and marine vehicles is turbulized that increases the skin-friction drag and fuel consumption. Here stability of the fully developed turbulent flow of an incompressible fluid in the viscoelastic tube is considered. The eddy viscosity concept is considered to be adequate and the flow velocity, wall displacement and pressures in the fluid and solid wall are timeaveraged quantities. Continuity conditions for the components of the velocity and stress tensor at the fluid-wall interface and no displacement condition at the outer wall of the tube are considered. Solution of the coupled system has been found in the form of the normal mode and the obtained system has been studied using the numerical technique described in [1,2]. The temporal and spatial eigenvalues and the dependencies of the temporal and spatial amplification rates on the rheological parameters of the wall have been computed. It was shown stability of the modes can be increased by a proper choice of the wall parameters. Successful combinations of the wall thickness, elasticity and viscosity have been found for a large variety of materials. It was shown a substantial reduction in the viscous wall shear stress accompanied by a decrease in the turbulence production or Reynolds stress can be reached via using the viscoelastic coating on the rigid surface. The obtained results are in a good agreement with recent direct numerical computations [3].