A discrete vortex method application to low Reynolds number aerodynamic flows

Date of Award


Degree Name

M.S. in Aerospace Engineering


Department of Mechanical and Aerospace Engineering


Advisor: Aaron Altman


Although experiments and CFD are very powerful tools in analyzing a niche of fluid dynamics problems relevant to developing Micro Aerial Vehicles (MAVs), reduced order methods have shown to be very capable in helping researchers achieve a basic understanding of flow physics with application to highly iterative design processes due to the less computationally expensive nature of the low order models. The current study used one low order method, the Discrete Vortex Method, to model the aerodynamic flow fields and forces around a thin airfoil undergoing a variety of flows, as well as parametric studies to determine the important factors that had to be adjusted to make the results more representative of the physical phenomenon being modeled. Initial investigations validated the code's use in steady flow and low amplitude unsteady flow cases by comparing it with circulation distributions of various airfoil shapes, the Wagner function, and Theodorsen's function. The results showed a strong dependency on bound vortex number and time step size. The code was then used to capture the flow behavior around the airfoil for various AIAA Fluid Dynamics Technical Committee Low Reynolds iv Number Working Group (FDTC-LRWG) canonical cases. Implementing the Uhlman method in the Discrete Vortex Method allowed for the calculation of the pressure at the airfoil surface and in the flow field during high angle attack maneuvers. This method proved very capable in calculating the pressures, forces, and force coefficients around the airfoil post-flow separation in the canonical cases where other methods (such as the Unsteady Bernoulli Method) fall short. The code was also tuned with respect to the results with respect to vortex size, leading edge separation strength factor, desingularization function, wake radius size factor, and in the Uhlman method itself to yield an optimal comparison with experimental and CFD results. The study found a bound vortex number of 30, a leading edge separation strength factor of 1.0, the planetary desingularization function, a wake radius size factor of 1.0, and using just the volume integral term on the RHS of the Uhlman method gave the best results for the geometry analyzed. An investigation then determined the dependency of reduced frequency on the lift and drag coefficients for the canonical cases. Finally, the code was used to model a true perch" by implementing a curve fit function which caused the horizontal free stream velocity to decrease to zero. In this context, the forces were of more interest than the force coefficients since the coefficients experienced anomalous behavior as the free stream velocity approached zero. It was also interesting to find that the code modeled behavior very similar to shear layer instabilities in the LE and TE shear layers, caused by a rippling effect as the bound circulation changed in strength and sign as the LEV and TEV interacting with it. Recommendations were then made to apply the code to airfoils with either fixed or variable camber since camber acts as a high lift device and could prove very beneficial in the design and development of MAVs"


Aerodynamic load Mathematical models, Aerofoils Mathematical models, Micro air vehicles Design and construction, Lift (Aerodynamics)

Rights Statement

Copyright 2011, author