Browsing by Author "Dr. Xiao-Biao Lin, Committee Member"

Now showing 1 - 2 of 2

Dafermos Regularization of a Modified KdV-Burgers Equation
(2010-03-19) Taylor, Monique Richardson; Dr. Xiao-Biao Lin, Committee Member; Dr. Pierre Gremaud, Committee Member; Dr. Michael Shearer, Committee Member; Dr. Stephen Schecter, Committee Chair
This project involves Dafermos regularization of a partial differential equation of order higher than 2. The modified Korteweg de Vries-Burgers equation is u_T + f(u)_X = alpha u_XX +beta u_XXX, where the flux is f(u) = u^3, alpha> 0, and beta is nonzero. We show the existence of Riemann-Dafermos solutions near a given Riemann solution composed of shock waves using geometric singular perturbation theory. When beta > 0, there is a possibility that the Riemann solution is composed of two shock waves as opposed to one. In addition, we use linearization to study the stability of the Riemann-Dafermos solutions.
On the Use of Wing Adaptation and Formation for Improved Aerodynamic Efficiency
(2005-05-11) King, Rachel Marie; Dr. Ashok Gopalarathnam, Committee Chair; Dr. Hassan Hassan, Committee Member; Dr. Jack Edwards, Committee Member; Dr. Xiao-Biao Lin, Committee Member
There is a continuous effort to improve the performance and efficiency of today's aircraft, and the reduction of aircraft drag has been the primary focus of many aerodynamicists. In the current research, two different and innovative approaches for aircraft drag reduction are examined. These approaches are: (1) multiple spanwise trailing-edge flaps, and (2) formation and ground-effect flight. The main goal of this dissertation was to assess the drag benefits of the two approaches, in an effort to explore their potential for use on future aircraft. The first approach of using multiple trailing-edge flaps has the potential for application on aircraft in the near future. By using multiple trailing-edge flaps along the wing span, it is possible to redistribute the spanwise lift distribution to suit the flight condition. For this research, a numerical approach was developed for determining optimum lift distributions on a wing with multiple trailing-edge flaps for various flight conditions. The objective of the approach was to determine the flap angles that will reduce the drag at 1-g flight conditions, and constrain the wing root-bending moment at high-g conditions to not exceed a specified value. The approach uses the concept of additional and basic lift distributions, and the proper use of a trailing-edge flap for redistributing the aerodynamic loads to bring about a minimum in profile and induced drag. The results for the flap-angle distributions are presented for a planar and a nonplanar wing, along with post-design analysis and aircraft performance simulations used to validate the optimum flap-angle distributions determined using the numerical approach. It is shown that the approach is effective in determining optimum flap angles for reducing both profile and induced drag over a wide range of flight conditions. Performance benefits due to using the optimum flap angles are shown when compared to the zero-flap case. In addition, the trailing-edge flaps were found to be successful in relieving the wing root-bending moment at high-g flight conditions, which can be used to reduce wing weight. When examining formation and ground-effect flight as another approach for aircraft drag reduction, an optimum-downwash approach using a vortex-lattice implementation was used to study formations of wings loaded optimally for minimum induced drag with roll trim. An exact approach was also developed to examine the drag of elliptically-loaded wings in formation. The exact approach allows for decomposition of the benefits by considering the mutual-interference contributions from different pairs of wings in a formation. The results show that elliptically-loaded wing formations have nearly the same drag as optimally-loaded wing formations. For a formation of planar wings, in or out of ground effect, the optimum lateral separation corresponds to a 9%-span overlap of wing tips. At this optimum lateral separation, a formation of 25 elliptically-loaded wings flying out of ground effect experiences an 81% drag reduction compared to 25 wings flying in isolation. For large formations, in or out of ground effect, multiple local optima are seen for the lateral separation. Large formations experience small additional benefits due to ground effect even at relatively large ground clearances of four wing spans. The shape of vee-formations, for equipartition of drag benefits, is found to be nearly independent of flight in or out of ground effect. Overall, both approaches for aircraft drag reduction show potential for significant drag savings. It is believed that the presented research will further increase interest in such flight techniques, and thus advance their progression toward becoming viable solutions for drag reduction on future aircraft.