Numerical study of a partial differential equation as an extension to the classical solution to oscillating wall problems

• Main Author: Zhan, Mengke
• Other Authors: Martin Skote
• Format: Final Year Project
• Language: English
• Published: 2017
• Subjects: DRNTU::Engineering::Aeronautical engineering
• Online Access: http://hdl.handle.net/10356/71150
• Institution: Nanyang Technological University

Drag Reduction (DR) can bring significant economical savings for machinery operations. Many studies have been conducted to deepen the understanding of the mechanism behind the DR. Thus far, the main approaches used include direct numerical simulations (DNSs) and experiments. Analytical methods have also been sought to solve the complex governing equations associated with the flow. However, the current approaches are still faced by problems like high computational cost. The objective of the project is to develop an effective numerical scheme with a high accuracy to computational cost ratio to study the turbulent boundary layer flow with spatial spanwise oscillating walls. The central finite difference scheme was applied to the governing spanwise momentum equation. Together with the boundary conditions, the mathematical model of the flow was set up as a matrix system, from which solutions to spanwise velocity in the computational region were obtained. Spanwise shear and spanwise velocity profiles were analysed and compared with those obtained from the DNS data and the analytical solutions. It is observed that for spanwise shear, the solutions obtained from the finite difference method follow the DNS data very closely except at the beginning where solutions from the finite difference method are lower than the DNS data. Unlike the analytical solutions which show a sharp increase towards the end of the computational region, the solutions from the finite difference method display the same gradual change as the DNS data. For spanwise velocity profiles beyond one wavelength, the solutions from the finite difference method, the DNS data and the analytical solutions are very close together. However, for spanwise velocity profiles within one wavelength, the solutions from the finite differenceii method show closer agreement with the DNS data than the analytical solutions. In terms of the computational time, the finite difference method requires a significantly lower time as compared to the DNS method.