FULLY DEVELOPED FREE SURFACE 2-D FLOW LIQUID LAYER ENCOUNTERING A 3-D OBSTACLE

Abstract

This thesis investigates the steady two-dimensional incompressible liquid layer flow over a shallow three-dimensional obstacle. The fluid is driven by gravity and the solid surface underneath the flow is inclined. The liquid layer is considered to be thin and fully developed, such that the whole flow is affected by the viscosity of fluid near the solid surface. A double-decked structure is utilized to analyze the problem, and a partial differential equation problem is obtained to describe the flow. A sample two-dimensional problem is generated and solved by three different numerical methods. The efficiency and accuracy of these three methods are evaluated and compared. The fastest numerical method is extended to three-dimensional form and solves the three-dimensional problem. The analytical results for the linearized problem are computed for the validation of numerical results. Comparisons between our numerical method and methods from previous research are also made for further validation. All comparisons show good agreement. The characteristics of the flow are analyzed for different Weber numbers and angles of inclination. The most striking feature is wave patterns on the free surface at large Weber numbers or large angles of inclination. Furthermore, the stability of the liquid layer flow on an inclined plane is also investigated. The analysis directly gives the conditions of stability, and the numerical results for instability are consistent with the analysis.

Date of Award	31 Dec 2023
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Jitesh Gajjar (Supervisor) & Richard Hewitt (Supervisor)