Potential flow through a cascade of aerofoils: direct and inverse problems

Area of Science:

• Fluid dynamics
• Aerodynamics
• Applied mathematics

Background:

• Potential flow analysis is crucial for understanding fluid behavior around aerofoils.
• Infinite cascades of aerofoils present complex flow challenges.
• Perturbation expansion offers a method for analyzing such flows.

Purpose of the Study:

• To investigate potential flow through infinite aerofoil cascades.
• To solve both direct (flow field calculation) and inverse (geometry determination) problems.
• To develop analytical expressions for flow characteristics and aerofoil geometry.

Main Methods:

• Perturbation expansion about a uniform flow background.
• Recasting the direct problem as a Riemann-Hilbert problem.
• Solving a singular integral equation for the inverse problem.

Main Results:

• Analytical expressions for surface velocity, lift, and deflection angle derived.
• Convergence of cascade solution to single aerofoil solution as spacing increases.
• Good agreement between analytical and numerical results.

Conclusions:

• The perturbation method effectively analyzes potential flow in aerofoil cascades.
• The study provides a framework for both direct and inverse problems in this context.
• Derived analytical solutions offer valuable insights into aerofoil cascade aerodynamics.