Matched asymptotic analysis of steady viscoelastic wake flows

A study is reported on modeling a laminar viscoelastic wake flow in intermediate and far regions behind a cylinder by the matched asymptotic expansion method. With the Oldroyd-B model chosen as the constitutive model, a globally valid, composite, reduced-order solution is constructed up to the third order. When viscoelasticity is disabled in the model, the resultant solution to the Newtonian flow can be favorably compared with previous experimental, analytical, and numerical investigations. Results show that the elastic effect begins to surface at the third order in our expansion scheme. For the flow field, the model predicts that the viscoelasticity has a positive effect on the growth of the longitudinal velocity and that the viscosity ratio has a negative effect. As the inertial effect increases, the longitudinal velocity increases. The elastic effects exerting on the vorticity distribution in the wake flow are also predicted by the theoretical model. For the conformation tensor field, the model dictates that a larger elastic effect leads to a greater extension of the polymer molecules, but predicts no influence of the viscosity ratio on the polymer extension because the solutions are only expanded till the third order. The reduced-order solutions establish a theoretical guidance for the complex viscoelastic wake flow, which is beneficial for the investigation of the drag reduction in the viscoelastic wake flow past a bluff body.