Taylor Couette Flow with Imposed Radial and Axial Flows- A Weakly Nonlinear Analysis

Richard M. Lueptow (1) , Denis Martinand (2) , Eric Serre (2)

1 Department of Mechanical Engineering [Evanston]
2 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres

The linear stability analysis of Taylor-Couette flows where axial and radial through-flows are superimposed is extended to consider the weakly nonlinear behavior of convective-type instabilities using a fifth-order amplitude equation and numerical simulations. Special attention is paid to the influence of the radius ratio η, particularly as the gap increases to become very wide (η increases from top to bottom in Figure 1), which magnifies the impact of the radial Reynolds number α. The instabilities take the form of pairs of counter-rotating Figure 1: Modes of instabilities for β = 20 and (a) η = 0.85 and α =-10, (b) η = 0.85 and α = 0, (c) η = 0.85 and α = 10, (d) η = 0.55 and α =-10, (e) η = 0.55 and α = 0, (f) η = 0.55 and α = 10, (g) η = 0.25 and α =-10, (h) η = 0.25 and α = 0, (i) η = 0.25 and α = 10. Isosurfaces of the radial velcoity of the instability are shown at 0.2 (red) and-0.2 (yellow) of the maximum value. The critical Taylor number and wavelength are indicated. Reprinted with permission [1].

Domains: Engineering Sciences [physics]; Chemical and Process Engineering

Richard M. Lueptow, Denis Martinand, Eric Serre. Taylor Couette Flow with Imposed Radial and Axial Flows- A Weakly Nonlinear Analysis. 20th International Couette Taylor Workshop, Jul 2018, Marseille, France. ⟨hal-02121894⟩