Two-Dimensional Boundary Surfaces for Planar External Transonic Flows
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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The small perturbation, two-dimensional transonic equation is manipulated with a separation-of-variables approach to obtain two ordinary, nonlinear, differential equations. Numerical integration of these differential equations results in new transonic boundary surfaces for planar external flows. A key ingredient in these solutions is the identification of dependence of two integrations constants, Alpha and Beta, on the parameter 1-M 2 . The anticipated behavior for both the Mach number and the pressure coefficient is used as a guide in the actual selection of the adjustable constants in the problem. The physical reality of our boundary surfaces is examined by displaying the boundary conditions they satisfy. The strictly sonic flow M 1.0 has an analytic representation corresponding to a divergent surface which goes supersonic. This sonic solution is compared with an Euler-CFD approach confirming the validity of our results over the region where small perturbations apply. Solutions are also shown for MO.8,0.9,1.1, and 1.2 . These results are consistent with known behavior for both subsonic and supersonic external flow. Since the results of this work yield actual transonic contours, we can examine shockless surfaces for design applications. The possibility of starting with transonic surface is of interest to present day CFD approach. Finally an entire transonic upper surface is presented for MO.8, by patching a subsonic Mach number, which reaches a plateau at M1.0, with a sonic flow. This patching requires the careful interpretation of a nondimensional reference length, called Y0, which is a function of M. Small perturbation transonic equation, boundary surfaces.
- Fluid Mechanics