Stability of flow in a channel with repeated flow-facing wedge-shaped protrusions

Abstract

Motivated by an interest in inciting instabilities and mixing for heat transfer enhancement in ducts, flow in a channel with repeated wedge-shaped protrusions is considered for various blockage ratios (wedge height to duct height), pitch (distance between wedges) and wedge angles. The stability of the two-dimensional base flow and its dependence on the geometric parameters is elucidated through a global linear stability analysis. A linearly unstable two-dimensional mode was found, contrasting similar confined flow set-ups. However, the primary instability is a three-dimensional mode manifesting as counter-rotating streamwise vortices over the wedge tip. Analysis of the kinetic energy budget indicates a lift-up mechanism leading to instability, with the dominant energy gain of the global three-dimensional mode due to shear in the base flow. Structural sensitivity and receptivity of the instability to momentum forcing identifies the core of the instability and locations important for flow control. An endogeneity approach is used to show that the local perturbation pressure gradient component dominates the distribution of the local contribution to the growth rate of the linear global eigenmode in most cases considered, despite its net contribution being identically zero. Weakly nonlinear Stuart–Landau analysis reveals that the primary bifurcation is supercritical across all tested geometric parameter combinations. This is consistent with the finding of low linear transient growth amplifications at subcritical Reynolds numbers, being orders of magnitude lower than in similar channel flow set-ups.