A Pedagogical Example for STEM using the Glauert Inflow Equation, Mathematica and Python
Ranjan Ganguli · AIAA Scitech 2019 Forum · 2019
The prediction of inflow velocity through the rotor disk is an important problem for helicopters. In forward flight, the resulting Glauert inflow equation is an irrational algebraic equation which is typically solved using the Newton-Raphson numerical method. We present a closed form solution of the Glauert inflow equation by using the theory of equations in algebra to convert the irrational equation to the rational form. Superfluous or extraneous roots introduced into the rational form are then eliminated and the inflow velocity is obtained in forward flight for a given thrust coefficient, flight speed and rotor disk angle of attack. This problem is solved using the symbolic programming language Mathematica and the results are verified by writing a Python code. The problem is useful as a benchmark solution in helicopter aerodynamics for comparing numerical solutions of the Glauert inflow equation. It can also be used as an example problem for STEM education to illustrate algebra, numerical methods and symbolic and scientific computer programming. © 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.