Vortex shedding in cylinder flow of shear-thinning fluids. I: Identification and demarcation of flow regimes.

*(English)*Zbl 1024.76505Summary: An experimental study on the flow of non-Newtonian fluids around a cylinder was undertaken to identify and delimit the various shedding flow regimes as a function of adequate non-dimensional numbers. The measurements of vortex shedding frequency and formation length (\(l_{\text f}\)) were carried out by laser-Doppler anemometry in Newtonian fluids and in aqueous polymer solutions of CMC and tylose. These were shear thinning and elastic at weight concentrations ranging from 0.1 to 0.6%. The 10 and 20 mm diameter cylinders (\(D\)) used in the experiments had aspect ratios of 12 and 6 and blockage ratios of 5 and 10%, respectively. The Reynolds number (\(Re^{\ast}\)) was based on a characteristic shear rate of \(U_{\infty}/(2D)\) and ranged from 50 to \(9\times 10^3\) thus encompassing the laminar shedding, the transition and shear-layer transition regimes. Increasing fluid elasticity reduced the various critical Reynolds numbers (\(Re_{\text{etr}}^{\ast}\), \(Re_{\text{lf}}^{\ast}\), \(Re_{\text{bbp}}^{\ast}\)) and narrowed the extent of the transition regime. For the 0.6% tylose solution the transition regime was even suppressed. On the other end, pseudoplasticity was found to be indirectly responsible for the observed reduction in \(Re_{\text{otr}}^{\ast}\): it increases the Strouhal number which in turn increases the vortex filaments, precursors of the transition regime. Elasticity was better quantified by the elasticity number \(Re'/We\) than by the Weissenberg number. This elasticity number involves the calculation of the viscosity at a high characteristic shear rate, typical of the boundary layer, rather than at the average value \((U_{\infty}/(2D))\) used for the Reynolds number, \(Re^{\ast}\).