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An airfoil design procedure, applicable to both subcritical and supercritical airfoils, is described. The method is based on the streamline curvature velocity equation. Several examples illustrating this method are presented and discussed.
The Theodorsen theory of airfoil design for incompressible flow can be used with the modifications proposed in this paper to design airfoils that satisfy a much wider variety of pressure variations than are permitted by the original Theodorsen procedure. Several examples illustrating this method are computed and discussed.
A computer program was developed to produce the ordinates for airfoils of any thickness, thickness distribution, or camber in the NACA 6- and 6A-series. For the 6-series and for all but the leading edge of the 6A-series, agreement between the ordinates obtained from the new program and previously published values is generally within .00005 chord. Near the leading edge of the 6A-series airfoils, differences up to .00035 chord are found.
Airfoil has least amount of drag under given restrictions of boundary layer transition position, lift coefficient, thickness ratio, and Reynolds number based on airfoil chord. It is suitable for use as wing and propeller aircraft sections operating at subsonic speeds and for hydrofoil sections and blades for fans, compressors, turbines, and windmills.
Low-speed wind-tunnel tests have been conducted to determine the two-dimensional aerodynamic characteristics of the NACA 65 sub 1-213, a = 0.05, airfoil. The results were compared with data from another low-speed wind tunnel and also with theoretical predictions obtained by using a viscous subsonic method. The tests were conducted over a Mach number range from 0.10 to 0.36. Reynolds numbers based on the airfoil chord varied from about 3 million to 23 million.
A practical procedure for the optimum design of low-speed airfoils is demonstrated. The procedure uses an optimization program based on the method of feasible directions coupled with an aerodynamic analysis program that uses a relaxation solution of the inviscid, full potential equation. Results are presented for airfoils designed to have small adverse pressure gradients, high maximum lift, and low pitching moment.
Wind-Tunnel tests were conducted in the Lockheed-Georgia Company's compressible flow facility to determine the transonic two-dimensional aerodynamic characteristics of a NACA 65 sub 1-213 a = 0.50 airfoil. The results are correlated with data obtained in the NASA-Langley 8-foot transonic pressure tunnel and the NAE high Reynolds number 15x60-inch two-dimensional test facility. The tests were conducted over a Mach number range from 0.60 to 0.80 and an angle of attack range from -1 deg to 8 deg. Reynolds numbers, based on the airfoil chord, were varied.
Two-dimensional wind-tunnel tests were conducted to determine effectiveness of spoilers applied to the GA(W)-1 airfoil. Tests of several spoiler configurations show adequate control effectiveness with flap nested. It is found that providing a vent path allowing lower surface air to escape to the upper surface as the spoiler opens alleviates control reversal and hysteresis tendencies. Spoiler cross-sectional shape variations generally have a modest influence on control characteristics. A series of comparative tests of vortex generators applied to the (GA-W)-1 airfoil show that triangular planform vortex generators are superior to square planform vortex generators of the same span.
The effects of temperature gradients, cooling-hole rim and bulk metal temperatures, and mechanical stress were investigated by using a finite-element structural analysis of a symmetrical airfoil with and without leading-edge holes. The results indicate that leading-edge film cooling is beneficial when large chordwise temperature gradients exist and if the cooling-hole rim temperatures are above the bulk metal temperature. The effects of film cooling at other locations on the airfoil were not considered, and the relative merits of convection or film cooling at the leading edge, in terms of allowable turbine inlet temperature or coolant flow requirements, were not evaluated.
A theory is developed, for the inviscid, incompressible flow past a thin airfoil equipped with a thin, part-span jet flap, by treating the induced flowfields of the jet and the wing separately and by obtaining the fully coupled solution in an iterative manner. Spanwise variation of the jet vortex strength is assumed to be elliptical in the analysis. Since the method considers the vorticity associated with the jet to be positioned on the computed locus of the jet, the downwash aft of the wing is evaluated as well as forces and moments on the wing. A lifting-surface theory is incorporated for the aerodynamics of the wing. Computational results are presented for a rectangular wing at momentum coefficients above 2.0 and compared with existing linear theories and experimental data. Good agreement is found for small angles of attack, jet-deflection angles, and jet-momentum coefficients where the linear theories and experimental data are applicable. Downwash data at a point in the vicinity of a control surface, the load distribution on the airfoil, and the jet, and the jet location are also presented for representative flight conditons.
An investigation was conducted regarding the issue of deviation from two-dimensionality in flowfield studies of a supercritical airfoil. It was found that significant three-dimensional effects occur in transonic airfoil tests, even for an aspect ratio of four. This is especially true at the supercritical Mach numbers, for which lateral propagation of disturbances is effective.
A method based on the Navier-Stokes equations was developed for analyzing the unsteady incompressible viscous flow around oscillating airfoils at high Reynolds numbers. The Navier-Stokes equations have been integrated in their classical Helmholtz vorticity transport equation form, and the instantaneous velocity field at each time step was determined by the solution of Poisson's equation. A refined finite element was utilized to allow for a conformable solution of the stream function and its first space derivatives at the element interfaces. A corresponding set of accurate boundary conditions was applied; thus obtaining a rigorous solution for the velocity field. The details of the computational procedure and examples of computed results describing the unsteady flow characteristics around the airfoil are presented.
An experimental and theoretical study of transonic flow over a thick airfoil, prompted by a need for adequately documented experiments that could provide rigorous verification of viscous flow simulation computer codes, is reported. Special attention is given to the shock-induced separation phenomenon in the turbulent regime. Measurements presented include surface pressures, streamline and flow separation patterns, and shadowgraphs. For a limited range of free-stream Mach numbers the airfoil flow field is found to be unsteady. Dynamic pressure measurements and high-speed shadowgraph movies were taken to investigate this phenomenon. Comparisons of experimentally determined and numerically simulated steady flows using a new viscous-turbulent code are also included. The comparisons show the importance of including an accurate turbulence model. When the shock-boundary layer interaction is weak the turbulence model employed appears adequate, but when the interaction is strong, and extensive regions of separation are present, the model is inadequate and needs further development.
A computer program has been developed to solve the compressible flow equation for the velocity potential. The exterior of the airfoil is mapped onto the unit circle and the flow is computed on a grid in the circle plane. A relaxation method using backward differencing in the flow direction at supersonic points permits solutions for large supersonic areas. The pressure distribution resulting from the flow becomes the input to the von Karman momentum equation which when integrated gives the displacement thickness. This displacement thickness is smoothed and added to the airfoil to account for the turbulent boundary layer. The boundary layer correction is computed iteratively with the flow. Results from this program and test data agree well.
A practical procedure for the optimum design of low-speed airfoils is demonstrated. The procedure uses an optimization program based on a gradient algorithm coupled with an aerodynamic analysis program that uses a relaxation solution of the inviscid, full-potential equation. The analysis program is valid for both incompressible and compressible flow, thereby making optimum design of high-speed, shock-free airfoils possible. Results are presented for the following three constrained optimization problems at fixed angle of attack and Mach number: (1) adverse pressure-gradient minimization, (2) pitching-moment minimization; and (3) lift maximization. All three optimization problems were studied with various aerodynamic and geometric constraints.
The theory provides a direct method for resolving an airfoil into a lifting line and a thickness distribution as well as a means of synthesizing thickness and lift components into a resultant airfoil and computing its aerodynamic characteristics. Specific applications of the technique are discussed.
Details of force, moment, and pressure distributions on a two dimensional, four foot chord, NACA 0012 airfoil, oscillating in pitch through stall, in a 7 ft. x 10 ft. low speed wind tunnel, are presented. Tests were run with the airfoil in a closed test section and also in a test section having four longitudinal slots in each sidewall set to provide minimum tunnel interference on the wing in steady flow. In unsteady flow, differences between the results for the closed and 2% open case are small. The dynamic stall process is not triggered by the bursting of a laminar separation bubble but rather by the separation of the turbulent boundary layer downstream of the bubble.
A practical procedure for the design of low drag, transonic airfoils is demonstrated. The procedure uses an optimization program, based on a gradient algorithm coupled with an aerodynamic analysis program, that solves the full, non-linear potential equation for transonic flow. The procedure is useful for the design of retrofit modifications for drag reduction of existing aircraft as well as for the design of low drag profiles for new aircraft. Results are presented for the modification of four different airfoils to decrease the drag at a given transonic Mach number.