Jiangang Cai

Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Mathematics



First Advisor

Chaoqun Liu


The wing tip vortex is very important because of its effects on the noise generation, blade/vortex interactions on helicopter blades, propeller cavitations on ships, and other fields. The objective of this work is to use the numerical simulation with high order accuracy and high resolution to investigate the formation and the near field evolution of a wing tip vortex at high Reynolds number. The computational domain includes a rectangular half-wing with a NACA 0012 airfoil section, a rounded wing tip and the surrounding boundaries. The wing has an aspect ratio of 0.75. The angle of attack is 10 degrees. The Reynolds number based on free-stream velocity and the chord length is 4.6106. In the simulations, the free-stream Mach number is set to 0.2. The flow field is solved by a fully-implicit time-marching N-S solver with 6th order compact scheme and 8th order filter. Non-reflecting boundary conditions with buffer are also utilized in the code to avoid non-physical reflection. The code uses MPI parallel computation whose performance scales almost linearly over a large number of processors. The numerical simulation showed that the turbulent shear layer and the interaction between the primary and the secondary vortices are the major sources of turbulent activity in the vortex core. The information about the phenomena provided by the simulation can be used in various engineering applications at high Reynolds numbers.


Mathematics | Physical Sciences and Mathematics


Degree granted by The University of Texas at Arlington

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Mathematics Commons