Numerical optimization procedures have been employed for the design of airfoils in transonic flow based on the transonic small-disturbance (TSD) and Euler equations. A sequential approximation optimization technique was implemented for solving the design problem of lift maximization with wave drag and area constraints. A simple linear approximation was utilized for the approximation of the lift. Accurate approximations for sensitivity derivatives of the wave drag were obtained through the utilization of Nixon's coordinate straining approach. A modification of the Euler surface boundary conditions was implemented in order to efficiently compute design sensitivities without recreating the grid. Our design procedures experienced convergence problems for some TSD solutions, where the wave drag was found not to vary smoothly with the design parameters and consequently create local optimum problems. A procedure interchanging the role of the objective function and constraint, initially minimizing drag with a constraint on the lift was found to be effective in producing converged designs, usually in approximately 10 global iterations. This procedure was also shown to be robust and efficient for cases where the drag varied smoothly, such as with the Euler solutions. The direct lift maximization with move limits which were fixed absolute values rather than fractions of the design variables, was also found to be a reliable and efficient procedure for designs based upon the Euler equations. / Ph. D.

Investigations of the three-dimensional flow around a 6:1 prolate spheroid model 1.37 m long were conducted in the separation and near wake regions along the leeward side. Mean velocity flow field measurements, at α = 10∘ and 15∘ , and at Re = 1.3 x 10⁶ (U_re= 15.2 mls) and 4.0x 10⁶ (Ure=45.7 m/s), were obtained at four axial locations along the afterbody. Boundary layer profiles and Reynolds shear stress measurements were obtained at two axial locations, with a = 100 and Re=4.0 X 10⁶. Results of the flow field measurements indicate vortical flow along the surface of the body, growing in strength with increasing Reynolds number and increasing angle of attack. Skewing of the three-dimensional boundary layer is seen in the boundary layer profiles, with the surface shear stress direction lagging the local free-stream velocity direction. Growth of the boundary layer is evident circumferentially and axially along the body. Results of the turbulence measurements show that the distribution of Reynolds stress quantities is different from that of a two-dimensional flow over a flat plate, due to the three-dimensional flow and separation that is present. Estimates of x and z eddy viscosities show that the eddy viscosity is not isotropic. Estimates of the mixing length compared to values for a two-dimensional flow model indicate that the model predicts high values for the mixing length. Comparisons made with results obtained at DFVLR in West Germany show good agreement for the mean velocity and Reynolds normal stress values; however, the agreement of the Reynolds shear stresses is not as good. / Master of Science

This investigation studies the mixing in a shear layer developed from helium slot injection into a parallel supersonic airstream and compares the results to those of previous slot-injection tests. The objectives of this study include documenting the helium slot-injection flowfield; providing a baseline for use as a reference for future work; contributing representative and consistent data to the general database; and increasing understanding of shear layer dynamics, especially as a result of foreign-gas injection. The helium injectant exits the slot at y = 1.67, M₋₁ = 1.78, P_u = 0.892 atm, and T_u = 287° K tangentially to an airstream at y = 1.4, M_∞= 3, P_t∞= 6.5 atm, and T_t∞= 282° K. The freestream has Re/cm = 5.4x10⁵ and a boundary-layer thickness of (δ_au/H) = 0.58. The pertinent ratios are (P₁/P_∞) = 0.838, (U₁/U_∞) = 2, and (P₁/P_∞) = 0.1. The slot height H is 1.21 cm. Along with short-duration Schlieren and Shadowgraph photography, concentration, Pitot, cone-static, and stagnation-temperature measurements are taken at each of four streamwise stations (x H = 0.3, 4.2, 10.5, 21.1) to document the development of the mixing layer. ln light of the binary-gas mixture, local concentration information is required to reduce the data to pertinent mean-flow variables (M, p, U, pU, P, and T). As expected, slot injection in general shows poor initial penetration of the injectant into the freestream, and, thus, poor initial mixing. Nevertheless, the helium case shows better mixing than a similar air injection case of a previous experiment, as the mixing shear layer grows 25 percent larger than that in the air case by the last station. Also, about 30 percent more freestream air is entrained into the shear layer in the helium case and is confined mainly to the top third of the mixing layer. The higher mixing rate stems from larger gradients in velocity and density and lower pU values which result in more active transport mechanisms in the helium injection test / Master of Science