Numerical simulation of viscoelastic flow past a cylinder

Abstract

The flow of an upper-convected Maxwell fluid past a circular cylinder is simulated numerically using the algorithn SIMPLER, which is based on a finite volume discretization on a staggered grid of the governing equations and an iterative solution to the nonlinearly coupled equations. The effect of the viscoelasticity of the fluid on the flow is examined. The drag force on the cylinder and the heat transfer from the cylinder to the surrounding fluid are calculated and compared with those obtained in experiments. One feature seen in the experiments is the existence of a critical velocity across which the variation of the drag and heat transfer changes from a characteristic Newtonian variation to a flat response. This feature is interpreted as a change of type when the critical speed U c of flow becomes greater than the material wave speed c = ▪. The numerical computation is completely consistent with this interpretation. Using an Einstein-type formula for the relaxation and λ = Aø with A independent of ø we find that the experiments follow a scaling law U cø 1 2 =constant, where ø is the mass fraction of polymers in water in the regime of extreme dilution, the drag reduction range, consistent with the interpretation that U c = c.