## Vortex shedding in cylinder flow of shear-thinning fluids. I: Identification and demarcation of flow regimes.(English)Zbl 1024.76505

Summary: 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, $$Re^{\ast}$$.

### MSC:

 76-05 Experimental work for problems pertaining to fluid mechanics 76A10 Viscoelastic fluids
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