Finite-amplitude Taylor-vortex flow of viscoelastic fluids

The influence of inertia and elasticity on the onset and stability of Taylo r-vortex flow (TVF) is examined for an Oldroyd-B fluid. The Galerkin projec tion method is used to obtain the departure from Couette flow (CF). Only ax isymmetric flow is examined. The solution is capable of capturing the dynam ical behaviour observed experimentally for viscoelastic fluids in the inert io-elastic and purely elastic ranges. For flow with dominant inertia, the b ifurcation picture is similar to that for a Newtonian fluid. However, trans ition from CF to TVF is oscillatory because of fluid elasticity. Steady TVF sets in, via supercritical bifurcation, as Re reaches a critical value, Re -c. The critical Reynolds number decreases with fluid elasticity, and is st rongly influenced by fluid retardation. As elasticity exceeds a critical le vel, a subcritical bifurcation emerges at Re-c, similar to that predicted b y the Landau-Ginzburg equation. It is found that slip along the axial direc tion tends to be generally destabilizing. The coherence of the formulation is established under steady and transient conditions through comparison wit h exact linear stability analysis, experimental measurements, and flow visu alization. Good agreement is obtained between theory and the measurements o f Muller et al. (1993) in the limit of purely elastic overstable TVF.