Semi-Analytical Method for Unsymmetrical Doublet Flow Using Sink- and Source-Dominant Formulation

Abstract

Potential flow formed by doublet flow has been well applied in environmental applications and geothermal designs such as reservoir and fuel injectors. Most of the doublet flow is assumed based on the sink and source with equivalent strength and distance from the origin, forming the well-known Rankine oval structure when a far-field flow is superposed. A semi-analytical method is formulated to systematically investigate the unsymmetrical doublet flow with different strengths of sink and source. The general mathematical expression for unsymmetrical doublet flow is derived analytically before the streamline and the potential line can be visualised via a numerical approach. The results revealed that the doublet flows altered the Rankine oval structure to form aerofoil-like geometry. When the far-field flow interferes with the general Doublet configuration, unique flow structures such as convex, concave, and various wing shapes could be generated. The current study provides new insight on producing aerodynamic curves for the design of bio-inspired structures.

Keywords

• potential flow
• doublet flow
• Rankine oval
• stream function
• superposition of flow