Computational Simulation of Supersonic Delta-wings: Computational Simulation of Supersonic Delta-wings Mentor: Dr. Sritharan, Chairman of Department of Mathematics Presenter: Jingling Guan Department of Mathematics


Introduction: Introduction A delta-wing is a wing whose shape looks like a triangle when viewed from above. Delta-wings are very efficient in high-speed flight. What are Delta-wings?


Introduction: Introduction Several Popular Delta-wings Delta wings were used on several military aircrafts that had a need for speed. YF 102


Introduction: Introduction Several Popular Delta-wings Concorde


Introduction: Introduction Several Popular Delta-wings


Introduction: Introduction What is Supersonic Speed? Supersonic Speed is the speed faster than the speed of the sound.


Introduction: Introduction What are Shock Waves? A shock wave is a very strong pressure wave in air, produced by supersonic crafts, that creates sudden, huge changes in pressure. Shock waves are very important in designing an aircraft, because the change of pressure will influence the performance of aircrafts.


Introduction: Introduction Design Requirements - Transonic leading edge ---cross flow shocks - Attached flow ---shock free or contains only weak shocks Hence, it would be very helpful if we can find a numerical method to study the behavior of the cross-flow around the wing.


Coordinate Systems: Coordinate Systems Source: Nonlinear Aerodynamics of Conical Delta Wings, Dr. S. S. Sritharan To find such a numerical method, first, the intersect of the wing is modeled in the spherical coordinate system. Intersect of an elliptic wing


Coordinate Systems: Coordinate Systems


Coordinate Systems: Coordinate Systems A 3D plot of the grids in the spherical coordinate system.


Coordinate Systems: Coordinate Systems Stereographic Projection A B O


Coordinate Systems: Coordinate Systems A plot of the grids on a plane after stereographic projection


Transformation of the Coordinate Systems: Transformation of the Coordinate Systems Joukowski’s transformation


Coordinate Systems: Coordinate Systems By a simple shearing, the circular computational domain will be transformed into a rectangular region.


Transformation of the Coordinate Systems: Transformation of the Coordinate Systems The first Fundamental Form Cartesian system Any coordinate system α,β=1, 2


Transformation of the Coordinate Systems: Transformation of the Coordinate Systems The first Fundamental Form (continued) Metric Tensor


Governing PDE: Governing PDE The Governing Partial Differential Equation Source: Nonlinear Aerodynamics of Conical Delta Wings, Dr. S. S. Sritharan


Governing PDE: Governing PDE The density Source: Nonlinear Aerodynamics of Conical Delta Wings, Dr. S. S. Sritharan


Governing PDE: Governing PDE Also, we have the velocity defined on the unit sphere Source: Nonlinear Aerodynamics of Conical Delta Wings, Dr. S. S. Sritharan


Governing PDE: Governing PDE By substituting the previous equations, we get: Source: Nonlinear Aerodynamics of Conical Delta Wings, Dr. S. S. Sritharan


Sonic Line: Sonic Line Sonic Line Source: Nonlinear Aerodynamics of Conical Delta Wings, Dr. S. S. Sritharan On the sonic line, the governing PDE changes type between elliptic and hyperbolic.


Numerical Method: Numerical Method The geometric quantities at the center of primary cells 1. metric tensor in the spherical coordinate system Source: Nonlinear Aerodynamics of Conical Delta Wings, Dr. S. S. Sritharan


Numerical Method: Numerical Method The geometric quantities at the center of primary cells 2. metric tensor in the mapped coordinate system Source: Nonlinear Aerodynamics of Conical Delta Wings, Dr. S. S. Sritharan


Numerical Method: Numerical Method The geometric quantities at the center of primary cells 3. Source: Nonlinear Aerodynamics of Conical Delta Wings, Dr. S. S. Sritharan 1 2 3 4


Numerical Method: Numerical Method The flow quantities Source: Nonlinear Aerodynamics of Conical Delta Wings, Dr. S. S. Sritharan


Numerical Method: Numerical Method The flow quantities (continued) Source: Nonlinear Aerodynamics of Conical Delta Wings, Dr. S. S. Sritharan


Computational Results: Computational Results 3-D Plot of the Sonic Line angle of attack=10o


Computational Results: Computational Results 3-D Plot of the Sonic Line angle of attack=10o


Computational Results: Computational Results 3-D Plot of the Sonic Line angle of attack=20o


Computational Results: Computational Results 3-D Plot of the Sonic Line angle of attack=20o


Computational Results: Computational Results 3-D Plot of the Sonic Line angle of attack=10o, elliptic wing


Computational Results: Computational Results 3-D Plot of the Sonic Line angle of attack=10o, elliptic wing


Summary: Summary Transformation of Coordinate Systems Governing PDE Numerical Method 3-D Numerical Results Many things can be done based on the research results. This research project is based on Nonlinear Aerodynamics of Conical Delta Wings, by Dr. S. S. Sritharan


Special Thanks to:: Special Thanks to: Dr. Sritharan Wyoming EPSCoR Dr. Lynne Ipina Mr. John Spitler Regent Thanks everybody for coming!


Questions?Comments?: Questions? Comments?