Unsteady flow of a Herschel-Bulkley fluid over a stationary, smooth circular cylinder is studied numerically. The effects of fluid parameters such as the Oldroyd number, Od, and the flow index, n, on the flow morphology and various dynamic coefficients are examined. It is found that for shear-thinning fluids (high modified Reynolds numbers) and high Oldroyd numbers (high yield-stress), the flow parameters such as drag and skin-friction coefficients exhibited rather complicated behavior, often with bi- and tri-frequencies. Strouhal number dependence on these parameters was quantified and found to be consistent with recent reported results in the lower Re regime; its qualitative behavior mirrored for the most part what Newtonian fluids did in the range of Re investigated. Physical explanations are given as to why the departure from Newtonian, or simple non-Newtonian fluid, behavior is observed — mainly the combined effect of shear-thinning and the presence of regions of unyielded fluid.

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