Based on an optimization formulation, a procedure has been developed to evaluate Mach number and angle-of-attack corrections. The Euler equations are assumed to be the flow governing equations. To obtain efficient solutions for the optimization problem, the iterative solutions for the flow variables and the design parameters are simultaneously updated. In addition to the model lift and geometry, the procedure requires pressure measurements near the tunnel walls. The tunnel boundary conditions are based on the introduction of Reimann invariants for a one-dimensional flow normal to the boundary. Computations are performed to verify that the errors introduced by this approximate boundary-condition formulation are acceptably small. The correction scheme is applied to an aircraft configuration in an open jet. The results indicate that the optimization scheme is highly efficient with the rate of convergence of the flow solution nearly equal to the corresponding rate of a regular analysis problem.

A scheme is developed for solving constrained optimization problems in which the objective function and the constraint function are dependent on the solution of the nonlinear flow equations. The scheme updates the design parameter iterative solutions and the flow variable iterative solutions simultaneously. It is applied to an advanced propeller design problem with the Euler equations used as the flow governing equations. The scheme's accuracy, efficiency and sensitivity to the computational parameters are tested.

Based on an optimization formulation, a procedure has been developed to evaluate Mach number and angle- of-attack corrections. The Euler equations are assumed to be the flow governing equations. To obtain efficient solutions for the optimization problem, the iterative solutions for the flow variables and the design parameters are simultaneously updated. This is done by using a scheme that eliminates the limitations of a previously developed scheme. In addition to the model lift and geometry, the procedure requires pressure measurements near the tunnel walls. The accuracy and efficiency of several optimization techniques are investigated. The effect of perturbing certain test conditions on the residual interference is investigated. IRCRAFT models are tested in wind tunnels to study their aerodynamic properties and to estimate their perfor- mance qualities. Because of wall interference effects, however, the properties observed in the wind tunnel differ from those observed under free-air conditions. To estimate correctly the free-air performance of the tested models and to achieve the maximum benefit from wind-tunnel tests for design improve- ments, it is necessary to determine the wall interference effects and to correct for them accurately. The classical procedure1 for correcting wall interference effects is based on linear theory. Although it provides insight into the features of wall interference, it does not produce sufficiently accurate formulas for practical use. A major source of error in the classical approach has been eliminated by wall interference correction procedures that replace the inaccurate homogeneous wall boundary conditions with measured flow properties. Procedures that require pressure measurements along a contour neighboring the tunnel walls,2 measurements of a single flow quantity along two contours,3 and measurements of two flow variables at a single contour4 have been developed. These and other methods summarized in Ref. 5 are applicable to linear, subsonic flows. Two-dimen- sional transonic wall interference correction procedures have been developed by Kemp^' 7 and Murman.8 These procedures use measured pressures near the tunnel walls and on the model surface. Solutions of the transonic small-disturbance equations are obtained and used to determine Mach number and arigle-of-attack corrections. The two-dimensional correction procedure presented here is formulated as an optimization problem. The Euler equations are assumed to be the flow governing equations, and the limitations of using the small-disturbance assumption are removed. Body-fitted coordinates are used to apply accurately the surface boundary conditions. The three-dimensional tran- sonic correction procedure developed in Ref. 9 includes a

: Modifications are introduced to Code TUNCOR to allow its use in determining wall interference corrections in the AEDC 1T tunnel. The modifications include conversion to cylindrical coordinates and converting the measured pressure data to a form acceptable by the code. Keywords: Wind tunnel corrections; Transonic flow; Wall interference.

The feasibility of designing propellers by an optimization procedure is investigated. A scheme, which solves the full potential flow equation about a propeller by line relaxation, is modified so that the iterative solutions of the flow equation and the design parameters are updated simultaneously. Some technical problems in using optimization for designing propellers with maximum efficiency are identified. Approaches for overcoming these problems are presented.

A single-cycle approach has been developed to solve optimization problems in which the objective and constraint functions are dependent on the solution of a set of partial differential equations. This approach is very suitable for solving transonic aerodynamic design problems. The procedure simultaneously updates the solutions of the flow equations and the design parameters and, thus, presents an efficient alternative to the costly innerouter iterative procedures currently used in transonic aerodynamic design. The procedure is applied here to examples in which the Euler equations are assumed to be the flow governing equations.

A procedure for the evaluation of wall interference corrections for three-dimensional models is presented. In addition to Mach number and angle-of-attack corrections, the procedure provides an estimate of the accuracy of the corrections. Lift, pitching moment, and pressure measurements near the tunnel walls are required by the correction method. The method is demonstrated by application to an isolated wing model and to a wing-body-tail configuration.

A new approach to solving optimization problems that involve nonlinear partial differential equations is presented. The approach eliminates the need for an inner-outer iterative procedure, solving the partial differential equation only once, thereby reducing the cost of computation to an extent which would allow its use as a practical tool in optimization problems. The approach is tested on a single design parameter problem through the use of a specially developed scheme. The results indicate comparable convergence properties for the present iterative process and the standard iterative scheme. The presented ideas are also applicable to multidesign parameter problems.

A second-order theory including camber effects in wind tunnel wall interference corrections is described. Changes in the geometrical configuration of the model tested are avoided by introducing the camber correction as an equivalent angle-of-attack correction. Tabular and graphic data are presented which indicate improved accuracy for second-order over first-order theory.

An inviscid model for the interaction between a thin wing and a nearly uniform propeller slipstream is presented. The model allows the perturbation velocities due to the interaction to be potential although the undisturbed slipstream velocity is rotational. A finite difference scheme is used to solve the governing equation. Numerical examples indicate that the slipstream has a strong effect on the aerodynamic properties of the wing section within the slipstream and lesser effects elsewhere. The slipstream swirling motion strongly affects the wing load distribution, however, its effect on the wing's total lift and wave drag is small. The axial velocity increment in the slipstream has a small effect on the wing lift, however, it causes a large increase in wave drag.

A simplified model is used to describe the interaction between a propeller slipstream and a wing in the transonic regime. The undisturbed slipstream boundary is assumed to coincide with an infinite circular cylinder. The undisturbed slipstream velocity is rotational and is a function of the radius only. In general, the velocity perturbation caused by introducing a wing into the slipstream is also rotational. By making small disturbance assumptions, however, the perturbation velocity becomes nearly potential, and an approximation for the flow is obtained by solving a potential equation.