Application of frequency-domain-method to rotorcraft aerodynamics

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering


V. R. Murthy


Frequency-domain method, Aerodynamics, Helicopter rotors, Harmonic balance, Computational fluid dynamics, Multiblade coordinates

Subject Categories

Aerospace Engineering | Engineering | Mechanical Engineering


A formulation is developed to compute the flow around a helicopter rotor in the frequency domain combined with computational fluid dynamics software. The solution in frequency domain is obtained using a harmonic balance method. This approach is found to be very suitable for problems involving periodic flow like oscillating airfoils and wings. Helicopter rotor in forward flight encounters periodic flow variation around the azimuth and therefore lends itself very well to frequency-domain-based solution methods. In the frequency-domain approach, the periodicity is enforced in the solution methodology as opposed to traditional time-domain approaches, where periodicity evolves after transients are damped out during the solution procedure. This leads to a huge leap in efficiency for the frequency-domain approach as compared to the time-domain approach. The solution can also be obtained using a single blade with phase-shifted periodic boundary conditions. This reduction in domain leads to an increase in efficiency by a factor equal to the number of blades in the rotor. In the current work, the feasibility as well as potential advantages of obtaining helicopter flow solution in multiblade coordinates is also explored. The process of transformation of flow equations from a conventional rotor coordinate system to a multiblade coordinate system leads to the cancellation of harmonics other than those at the blade passage frequencies. Therefore, a reduced number of time locations per revolution are required to capture the retained harmonics. This further reduces the processing time and storage memory requirements. Another advantage of multiblade coordinate system is the simplicity of coupled aeroelastic formulation due to a direct relation between rotor aerodynamic forces and rotor motion parameters. The developed software implements the formulation based on Euler equations and incorporates a structured grid generation method. A distributed programming technique is implemented to manage the memory storage requirements. The complete framework is validated for a number of cases including steady and unsteady cases for two-dimensional airfoils and three-dimensional wings and helicopter rotors in hovering and forward flight for various nonlifting and lifting cases. Comparisons are made against available experimental data or results from previous numerical calculations and show excellent agreement.