Abstract
Abstract
Highlights
The three-dimensional boundary layer induced by a cone rotating in otherwise still fluid has been studied where the flow geometry is defined by the half-apex angle ψ
The results consistently show that the instability development depends on the Görtler number rather than the Reynolds number and that transition starts at a well-defined Görtler number, whereas the transition Reynolds number depends on the rotational rate
We evaluate the flow on a slender cone (ψ = 30◦) at different rotational rates based on a Görtler number G, which has been used for flows dominated by centrifugal instability, e.g. the boundary layer on a concave wall (Floryan 1986; Schrader, Brandt & Zaki 2011; Méndez et al 2018)
Summary
The three-dimensional boundary layer induced by a cone rotating in otherwise still fluid has been studied where the flow geometry is defined by the half-apex angle ψ (figure 1). We evaluate the flow on a slender cone (ψ = 30◦) at different rotational rates based on a Görtler number G (in addition to x), which has been used for flows dominated by centrifugal instability, e.g. the boundary layer on a concave wall Modal analysis of the velocity components and pressure in the form (u, v, w, p) ∝ (u, v, w , p)(z) exp[i(αx + nθ − ωt)] is performed to transform the perturbation equations to a set of ordinary differential equations with the eigenfunctions and eigenvalue α = αr + iαi as unknowns This eigenvalue problem was solved at several x-locations to account for the change of the base velocity profile.
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