Robust Wake Rollup Modelling Using Dyes

This project report gives details on a modification of VAPTOR, a program that can predict the aerodynamic performance of aircrafts using a potential flow method with a relaxed wake model. In VAPTOR the wake is modelled using distributed vorticity elements (DVEs). DVEs can induce velocities at certain points used to relax the wake. A DVE has inbuilt singularity protections i.e. prevents the calculated velocity to approach infinity, but when two adjacent DVEs have a very low relative angle, these protections lead to an error in the calculation of the velocity at its shared midpoint during the relaxation process. In most cases these errors are negligible until a rotor is analysed during hover or vortex ring state. In these special cases the wake rollup is more intense leading to relatively small angles. The subsequent errors caused by the singularity protections cannot be ignored since they cause the solutions to be erratic and not smooth. It also causes the wake DVEs to deform disproportionally which is a visual indication of the errors. The modification uses a method that involves splitting the DVE in order to eliminate the errors when calculating the velocity at the junction of two adjacent DVEs. The splitting is temporary and only applied during the calculation of the velocity at the junction. The algorithm for the splitting of the DVE and its implementation into MATLAB is provided in this report. The implementation is tested by ensuring that all conditions are kept the same except when splitting is enabled or disabled. A number of test runs were conducted, and an index called the Smoothness Index was created in order to quantify the improvements of the DVE splitting method. The results shown are promising as the solution with splitting enabled is twice as smooth as when the splitting is disabled. There is also a noticeable improvement during visual comparison of the wake diagrams when splitting is enabled and disabled. The results combined with the fact that the extra computation required to execute the DVE splitting method is negligible, the author recommends it be enabled in all cases. Having said that, the end user has full control whether he or she would like to use it or not. They can also change the parameters of splitting to suit their needs.