Method for time-dependent simulations of viscoelastic flows: vortex shedding behind cylinder

Abstract In this paper, a comprehensive description of a finite-volume method for the simulation of time-dependent viscoelastic flows is given. It is applied to simulate the flow of a particular type of elastic fluid, having constant viscosity, but shear-thinning relaxation time, as it passes around a circular cylinder, forming and shedding vortices along its wake. Careful attention is given to the accuracy of the method, which is second-order in both the spatial and the temporal discretisation. Frequency of vortex shedding is shown to be attenuated by elasticity of the fluid, while the size of the formation zone behind the cylinder is elongated. These results are in agreement with recent experimental observations, as are further results showing a reduction in the root mean square (rms) fluctuating velocities compared with Newtonian flow. Consideration is also given to the effects of Reynolds number, extensibility parameter in the constitutive model, and Deborah number. In all cases, an increase on those two latter parameters leads to a delay, or a strong hindrance, of shedding formation. The mean drag coefficient decays with the Reynolds number, but it is smaller for the viscoelastic fluid.

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