A novel method for boundary layer flow that uses asymptotics and the Wiener-Hopf technique

Adamu, Hamid

Abstract

We consider the theory by (Chadwick, 2019) on the applications of Navier-Stokeslets (NSlets) by a Green’s integral distribution of fundamental solutions in boundary layer flow which we call BL-lets. This research investigates the application of the theory to the problem of uniform flow past a semi-infinite flat plate, which results
in the determination of the unknown strength function of a Wiener-Hopf type integral. The research first reviews Imai’s method describing the far-field wake and shows that it approximates to an Oseenlet representation to leading order (Adamu& Chadwick, 2019). The BL-lets are given as an expansion where the first term is given by the Oseenlet with Imai’s approximation applied. The research reviews
two existing approaches that are used in determining the strength function of the BL-lets, and also develops a new approach. The existing approaches are the one that uses BL-lets (Chadwick, 2019) and the one that uses Wiener-Hopf technique with Oseenlet as the kernel (Gautesen, 1971). While the newly developed approach is called degenerate approach that evaluates the integral straight away in transform space. All approaches agree for the strength function of the first approximation and the expression for the velocity agrees with Kusukawa’s and Chadwick’s solutions. However, the BL-lets representation is only valid in the far-boundary layer and so this solution is a first approximation and not accurate. By relaxing the boundary condition at the leading edge, equivalent to assuming the BL-lets approximation breaks down there, enables us to consider a strength function expansion and consequently a velocity expansion. The resulting velocity expansion is continued into the boundary layer and shown to give a good representation of the flow even with just
three terms (Adamu et al., 2023), and is compared to the numerical Blasius shooting method and Kusukawa’s boundary layer expansion. Hence the NSLet successfully models the problem of uniform flow past a semi-infinite flat plate.

Citation

Adamu, H. (2024). A novel method for boundary layer flow that uses asymptotics and the Wiener-Hopf technique. (Thesis). University of Salford

• Thesis Type: Thesis
• Deposit Date: Jan 2, 2024
• Award Date: Jan 26, 2024