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At least 937 records · Page 52

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NASA NTRS1975

Computer simulation of transonic flow past airfoils with boundary layer correction

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.

Bauer, F.↗

NASA NTRS1975

Design of low-speed airfoils by numerical optimization

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.

Hicks, R. M.↗

NASA NTRS1975

Adaptation of the Theodorsen theory to the representation of an airfoil as a combination of a lifting line and a thickness distribution

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.

Barger, R. L.↗

NASA NTRS1975

Force and pressure measurements on an airfoil oscillating through stall, part 2

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.

Parker, A. G.↗

NASA NTRS1976

Airfoil section drag reduction at transonic speeds by numerical optimization

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.

Hicks, R. M.↗

NASA NTRS1976

The compressibility rule for drag of airfoil noses

It is shown that the drag of any semi-infinite airfoil section in purely subsonic inviscid flow follows precisely the Prandtl-Glauert compressibility rule. The result for the parabola has application to leading edge corrections in thin airfoil theory.

Jones, R. T.↗

NASA NTRS1976

Pressure distributions on a rectangular aspect-ratio-6, slotted supercritical airfoil wing with externally blown flaps

An investigation was made in the 5.18 m (17 ft) test section of the Langley 300 MPH 7 by 10 foot tunnel on a rectangular, aspect ratio 6 wing which had a slotted supercritical airfoil section and externally blown flaps. The 13 percent thick wing was fitted with two high lift flap systems: single slotted and double slotted. The designations single slotted and double slotted do not include the slot which exists near the trailing edge of the basic slotted supercritical airfoil. Tests were made over an angle of attack range of -6 deg to 20 deg and a thrust-coefficient range up to 1.94 for a free-stream dynamic pressure of 526.7 Pa (11.0 lb/sq ft). The results of the investigation are presented as curves and tabulations of the chordwise pressure distributions at the midsemispan station for the wing and each flap element.

Johnson, W. G., Jr.↗

NASA NTRS1976

Transonic airfoil design using Cartesian coordinates

A numerical technique for designing transonic airfoils having a prescribed pressure distribution (the inverse problem) is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that inverse boundary conditions and Cartesian coordinates are used. The method is a direct-inverse approach that controls trailing-edge closure. Examples show the application of the method to design aft-cambered and other airfoils specifically for transonic flight.

Carlson, L. A.↗

NASA NTRS1976

The passage of a distorted velocity field through a cascade of airfoils

An analysis has been developed to predict the unsteady force and moment generated by the passage of a timewise periodic total pressure distortion through an arbitrary cascade of airfoils. The mathematical formulation of this analysis is based on the assumption that the magnitudes of the timewise fluctuations of the variables which describe the flow field are small compared to their time average values. This assumption permits the development of a linear unsteady perturbation analysis about a steady flow field. In addition to this linearization assumption the fluid medium is assumed to be incompressible and inviscid. The mathematical development begins by decomposing the velocity field surrounding an infinite cascade of airfoils into its irrotational and rotational components. The rotational component is associated with an upstream unsteady total pressure distortion and is defined in terms of the vorticity field associated with the distortion pattern. The irrotational component is further decomposed into a steady and unsteady part. A combined analytical and numerical procedure has been developed to solve the field equations which govern the rotational and irrotational velocity fields. Results of this analysis show a strong influence of mean loading on the unsteady force generated by the passage of a one dimensional gust through a cascade of compressor blades.

Adamczyk, J. J.↗

NASA NTRS1976

Airfoil section drag reduction at transonic speeds by numerical optimization

Hicks, R. M.↗

NASA NTRS1976

A numerical solution of the flow field over a transonic airfoil including strong-shock-induced flow separation

An approximate numerical method has been developed for computing the entire transonic flow field over an airfoil, including the boundary layer, the shock-wave/boundary-layer interaction, and the shock-induced-separation. The inviscid flow, the turbulent boundary layer in the weak interaction zone, and the strong interaction elliptic region are solved separately. The inviscid flow is represented by the solution of the transonic small-disturbance equation, while the boundary layer is solved by the generalized Galerkin method, and the strong interaction region (including the wake) is computed from the time-averaged Navier-Stokes equations. A second-order interaction is computed iteratively using the inviscid pressure distribution as a boundary condition for the boundary layer and Navier-Stokes codes, and the viscous displacement thickness to modify the airfoil geometry for the inviscid computation. The computed pressure distributions and shock-wave profiles are compared with experimental data. Agreement is very good except that the pressure recovery on the trailing edge is greater than the experimental data.

Seginer, A.↗

NASA NTRS1976

A systematic method for computer design of supercritical airfoils in cascade

A computer code has been developed for the direct calculation of shockless transonic airfoils whose pressure distributions can be assigned within reasonable limits. The partial differential equations of two-dimensional inviscid gas dynamics are solved by analytic continuation into the domain of two independent complex characteristic coordinates. The domain of integration is mapped conformally onto the unit circle in the hodograph plane of one of these coordinates. It is possible to formulate a boundary value problem on this circle for the stream function that is well posed in the case of transonic flow. This enables the formulation of a procedure for the calculation of an airfoil on which the speed is prescribed as a function of the arc length

Garabedian, P.↗

NASA NTRS1976

Force and pressure measurements on an airfoil oscillating through stall

Details of force, moment, and pressure distributions on a two-dimensional, 4-ft 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 steady 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.

Parker, A. G.↗

NASA NTRS1976

Transonic flow theory of airfoils and wings

There are plans to use the supercritical wing on the next generation of commercial aircraft so as to economize on fuel consumption by reducing drag. Computer codes have served well in meeting the consequent demand for new wing sections. The possibility of replacing wind tunnel tests by computational fluid dynamics is discussed. Another approach to the supercritical wing is through shockless airfoils. A novel boundary value problem in the hodograph plane is studied that enables one to design a shockless airfoil so that its pressure distribution very nearly takes on data that are prescribed.

Garabedian, P. R.↗

NASA NTRS1976

A nonlinear theory for airfoils with trailing-edge jet flap

A nonlinear procedure for computing the pressure distribution on an airfoil with a trailing edge jet flap is described. The method is not restricted to thin airfoils or shallow jet-deflection angles. Correlation with experiment indicates that the characteristics of the pressure distribution are predicted by the theory, but the effect of entrainment is overpredicted with the entrainment coefficient used.

Barger, R. L.↗

NASA NTRS1975

Low-speed aerodynamic characteristics of a 13-percent-thick airfoil section designed for general aviation applications

Wind-tunnel tests were conducted to determine the low-speed section characteristics of a 13 percent-thick airfoil designed for general aviation applications. The results were compared with NACA 12 percent-thick sections and with the 17 percent-thick NASA airfoil. The tests were conducted ovar a Mach number range from 0.10 to 0.35. Chord Reynolds numbers varied from about 2,000,000 to 9,000,000.

Mcghee, R. J.↗

NASA NTRS1977

An analytical model for highly seperated flow on airfoils at low speeds

A computer program was developed to solve the low speed flow around airfoils with highly separated flow. A new flow model included all of the major physical features in the separated region. Flow visualization tests also were made which gave substantiation to the validity of the model. The computation involves the matching of the potential flow, boundary layer and flows in the separated regions. Head's entrainment theory was used for boundary layer calculations and Korst's jet mixing analysis was used in the separated regions. A free stagnation point aft of the airfoil and a standing vortex in the separated region were modelled and computed.

Zunnalt, G. W.↗

NASA NTRS1977

TRANDES: A FORTRAN program for transonic airfoil analysis or design

A program called TRANDES is presented that is used for the analysis of steady, irrotational transonic flow over specified two-dimensional airfoils in free air or for the design of airfoils having a prescribed pressure distribution, including the effects of weak viscous interaction. Instructions on program usage, listings of the program, and sample cases are given.

Carlson, L. A.↗