Non-axisymmetric Homann stagnation-point flows

Abstract

A modification of Homann's axisymmetric outer potential stagnation-point flow of strain rate a is obtained by adding periodic radial and azimuthal velocities of the form b r sin 2θ and b r cos 2θ , respectively, where b is a shear rate. This leads to the discovery of a new family of asymmetric viscous stagnation-point flows depending on the shear-to-strain-rate ratio γ = b/a that exist over the range −∞ < γ < ∞. Numerical solutions for the wall shear stress parameters and the displacement thicknesses are given and compared with their large-γ asymptotic behaviours. Sample similarity velocity profiles are also presented.

Experimental characterization of water droplet deformation and breakup in the vicinity of a moving airfoil

“…The base flow, very close to the airfoil, as seen from the airfoil reference frame could be characterized as an approximate inviscid potential stagnation flow impinging on a flat surface; see Panton [26], Homan [27] and Weidman [28] for the 2D, axisymmetric and non-axisymmetric configurations respectively. The potential flow solution, regardless of whether the configuration is 2D axisymmetric or non-axisymmetric is characterized by a constant velocity deceleration along the stagnation streamline as the solid surface is approached.…”

Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

“…However, Figure B indicates the opposite results. Weidman also reported such gradual variations of the displacement thicknesses. The displacement thickness δ x ( δ y ) decreases (increases) for smaller values of α , and after certain α , both become parallel (almost) and increase gradually further.…”

“…The solutions exist only in the range −1≤ α ≤0. However, the flow in the 3‐dimensional boundary‐layers is mainly dominated by the mainstream flows U = U ∞ x and V = V ∞ y , which are further superposed onto U ( x , y )= U ∞ x + V ∞ y and V ( x , y )= V ∞ x + U ∞ y so that the constraint on α can be removed (Weidman), and also further extended for the applied magnetic field in the boundary‐layer flow (Kudenatti and Kirsur). Note that in these studies, the shear flows form an irrotational flow outside the boundary layer.…”

A class of exact Navier–Stokes solutions for homogeneous flat-plate boundary layers and their linear stability

“…The other group of solutions obtain their three-dimensionality through two independent ansatz functions for the chordwise and streamwise velocity components, which are both linked to the wall-normal component (e.g . Howarth 1951;Wang 1991;Weidman 2012). These flows obtain their three-dimensionality from a quasi-axisymmetric flow where the chordwise and streamwise axes are merely rescaled in different ways.…”