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Results for “THIN AIRFOIL”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

A unified viscous theory of lift and drag of 2-D thin airfoils and 3-D thin wings

A unified viscous theory of 2-D thin airfoils and 3-D thin wings is developed with numerical examples. The viscous theory of the load distribution is unique and tends to the classical inviscid result with Kutta condition in the high Reynolds number limit. A new theory of 2-D section induced drag is introduced with specific applications to three cases of interest: (1) constant angle of attack; (2) parabolic camber; and (3) a flapped airfoil. The first case is also extended to a profiled leading edge foil. The well-known drag due to absence of leading edge suction is derived from the viscous theory. It is independent of Reynolds number for zero thickness and varies inversely with the square root of the Reynolds number based on the leading edge radius for profiled sections. The role of turbulence in the section induced drag problem is discussed. A theory of minimum section induced drag is derived and applied. For low Reynolds number the minimum drag load tends to the constant angle of attack solution and for high Reynolds number to an approximation of the parabolic camber solution. The parabolic camber section induced drag is about 4 percent greater than the ideal minimum at high Reynolds number. Two new concepts, the viscous induced drag angle and the viscous induced separation potential are introduced. The separation potential is calculated for three 2-D cases and for a 3-D rectangular wing. The potential is calculated with input from a standard doublet lattice wing code without recourse to any boundary layer calculations. Separation is indicated in regions where it is observed experimentally. The classical induced drag is recovered in the 3-D high Reynolds number limit with an additional contribution that is Reynold number dependent. The 3-D viscous theory of minimum induced drag yields an equation for the optimal spanwise and chordwise load distribution. The design of optimal wing tip planforms and camber distributions is possible with the viscous 3-D wing theory.

Yates, John E.↗
NASA NTRS1976

Leading-edge singularities in thin-airfoil theory

If the thin airfoil theory is applied to an airfoil having a rounded leading edge, a certain error will arise in the determination of the pressure distribution around the nose. It is shown that the evaluation of the drag of such a blunt nosed airfoil by the thin airfoil theory requires the addition of a leading edge force, analogous to the leading edge thrust of the lifting airfoil. The method of calculation is illustrated by application to: (1) The Joukowski airfoil in subsonic flow; and (2) the thin elliptic cone in supersonic flow. A general formula for the edge force is provided which is applicable to a variety of wing forms.

Jones, R. T.↗
NASA NTRS1944

On the general theory of thin airfoils for nonuniform motion

General thin-airfoil theory for a compressible fluid is formulated as boundary problem for the velocity potential, without recourse to the theory of vortex motion. On the basis of this formulation the integral equation of lifting-surface theory for an incompressible fluid is derived with the chordwise component of the fluid velocity at the airfoil as the function to be determined. It is shown how by integration by parts this integral equation can be transformed into the Biot-Savart theorem. A clarification is gained regarding the use of principal value definitions for the integral which occur. The integral equation of lifting-surface theory is used a s the starting point for the establishment of a theory for the nonstationary airfoil which is a generalization of lifting-line theory for the stationary airfoil and which might be called "lifting-strip" theory. Explicit expressions are given for section lift and section moment in terms of the circulation function, which for any given wing deflection is to be determined from an integral equation which is of the type of the equation of lifting-line theory. The results obtained are for airfoils of uniform chord. They can be extended to tapered airfoils. One of the main uses of the results should be that they furnish a practical means for the analysis of the aerodynamic span effect in the problem of wing flutter. The range of applicability of "lifting-strip" theory is the same as that of lifting-line theory so that its results may be applied to airfoils with aspect ratios as low as three.

BIBLIOGRAPHY-WINGS↗
NASA NTRS1946

Critical Mach Numbers of Thin Airfoil Sections with Plain Flaps

Critical Mach number as function of lift coefficient is determined for certain moderately thick NACA low-drag airfoils. Results, given graphically, included calculations on same airfoil sections with plain flaps for small flap deflections. Curves indicate optimum critical conditions for airfoils with flaps in such form that they can be compared with corresponding results for zero flap deflections. Plain flaps increase life-coefficient range for which critical Mach number is in region of high values characteristic of low-drag airfoils.

AIRFOILS - NACA 651-208 - CHARACTERISTICS LOW-DRAG↗
NASA NTRS1979

Unsteady thin airfoil theory for transonic flows with embedded shocks

Classical unsteady thin airfoil theory fails for low frequencies at the subsonic freestream Mach number, because of the formation of a shock wave that shields the forward region of the airfoil from aft generated disturbances. In the present paper, the classical thin airfoil theory is modified to account for the presence and induced motion of such shocks. The modification consists of taking the steady local Mach number to be a simple step discontinuity, normal to the undisturbed flow, separating two uniform regions. Predicted regions are shown to correlate well both with the experiment and finite difference calculations.

Williams, M. H.↗
NASA NTRS1982

Solution of the unsteady subsonic thin airfoil problem

The problem of a thin airfoil subject to simple harmonic disturbances in a uniform subsonic free stream is solved by extension of a technique developed earlier for a stationary strip vibrating in a uniform fluid. Explicit expressions are given for the lift and moment, acoustic directivity pattern, and total acoustic power for arbitrary upwash and, in particular, for the 'elementary disturbances': plunge, pitch and a stationary transverse gust. Numerical results for a simple skewed gust are presented and compared to the high-frequency asymptotic theory of Martinez and Widnall.

Williams, M. H.↗
NASA NTRS1989

Numerical solution of periodic vortical flows about a thin airfoil

A numerical method is developed for computing periodic, three-dimensional, vortical flows around isolated airfoils. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Solutions for thin airfoils at zero degrees incidence to the mean flow are presented in this paper. Using an elliptic coordinate transformation, the computational domain is transformed into a rectangle. The Sommerfeld radiation condition is applied to the unsteady pressure on the grid line corresponding to the far field boundary. The results are compared with a Possio solver, and it is shown that for maximum accuracy the grid should depend on both the Mach number and reduced frequency. Finally, in order to assess the range of validity of the classical thin airfoil approximation, results for airfoils with zero thickness are compared with results for airfoils with small thickness.

Scott, James R.↗
NASA NTRS1989

Numerical solution of periodic vortical flows about a thin airfoil

A numerical method is developed for computing periodic, three-dimensional, vortical flows around isolated airfoils. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Solutions for thin airfoils at zero degrees incidence to the mean flow are presented in this paper. Using an elliptic coordinate transformation, the computational domain is transformed into a rectangle. The Sommerfield radiation condition is applied to the unsteady pressure on the grid line corresponding to the far field boundary. The results are compared with a Possion solver, and it is shown that for maximum accuracy the grid should depend on both the Mach number and reduced frequency. Finally, in order to assess the range of validity of the classical thin airfoil approximation, results for airfoils with zero thickness are compared with results for airfoils with small thickness.

Scott, James R.↗
NASA NTRS1941

On the calculation of flow past an infinite screen of thin airfoils

This report deals with the flow past an infinite screen of thin airfoil (two-dimensional problem). The vortex distribution across the profile is established with appropriate expansion in series and the velocity distribution lift, moment, and profile shape deduced. Inversely, the distribution is deduced from the vorticity. The method is the extension of the Birnbaum-Glauert method for the isolated wing.

Pistolesi, E↗
NASA NTRS1978

Unsteady two dimensional airloads acting on oscillating thin airfoils in subsonic ventilated wind tunnels

The numerical calculation of unsteady two dimensional airloads which act upon thin airfoils in subsonic ventilated wind tunnels was studied. Neglecting certain quadrature errors, Bland's collocation method is rigorously proved to converge to the mathematically exact solution of Bland's integral equation, and a three way equivalence was established between collocation, Galerkin's method and least squares whenever the collocation points are chosen to be the nodes of the quadrature rule used for Galerkin's method. A computer program displayed convergence with respect to the number of pressure basis functions employed, and agreement with known special cases was demonstrated. Results are obtained for the combined effects of wind tunnel wall ventilation and wind tunnel depth to airfoil chord ratio, and for acoustic resonance between the airfoil and wind tunnel walls. A boundary condition is proposed for permeable walls through which mass flow rate is proportional to pressure jump.

Fromme, J.↗
NASA NTRS1931

An extended theory of thin airfoils and its application to the biplane problem

The report presents a new treatment, due essentially to von Karman, of the problem of the thin airfoil. The standard formulae for the angle of zero lift and zero moment are first developed and the analysis is then extended to give the effect of disturbing or interference velocities, corresponding to an arbitrary potential flow, which are superimposed on a normal rectilinear flow over the airfoil. An approximate method is presented for obtaining the velocities induced by a 2-dimensional airfoil at a point some distance away. In certain cases this method has considerable advantage over the simple "lifting line" procedure usually adopted. The interference effects for a 2-dimensional biplane are considered in the light of the previous analysis. The results of the earlier sections are then applied to the general problem of the interference effects for a 3-dimensional biplane, and formulae and charts are given which permit the characteristics of the individual wings of an arbitrary biplane without sweepback or dihedral to be calculated. In the final section the conclusions drawn from the application of the theory to a considerable number of special cases are discussed, and curves are given illustrating certain of these conclusions and serving as examples to indicate the nature of the agreement between the theory and experiment.

Millikan, Clark B↗
NASA NTRS1990

Acoustic radiation from a thin airfoil in nonuniform subsonic flows

Noise resulting from the interaction of a three dimensional gust is modeled directly from unsteady aerodynamic codes. This paper provides bench mark results for the case of a thin airfoil for comparison with the more complex case of a loaded airfoil. It is shown that the acoustic pressure pattern strongly depends on the value of a certain reduced frequency. The effects of an oblique gust are examined and shown to significantly reduce the acoustic power for certain gust parameters range. The Acoustic power versus the gust frequency exhibits a maximum. High frequency and non-compact source effects are also investigated.

Atassi, H. M.↗
NASA NTRS1980

Aerodynamic coefficients in generalized unsteady thin airfoil theory

Two cases are considered: (1) rigid body motion of an airfoil-flap combination consisting of vertical translation of given amplitude, rotation of given amplitude about a specified axis, and rotation of given amplitude of the control surface alone about its hinge; the upwash for this problem is defined mathematically; and (2) sinusoidal gust of given amplitude and wave number, for which the upwash is defined mathematically. Simple universal formulas are presented for the most important aerodynamic coefficients in unsteady thin airfoil theory. The lift and moment induced by a generalized gust are evaluated explicitly in terms of the gust wavelength. Similarly, in the control surface problem, the lift, moment, and hinge moments are given as explicit algebraic functions of hinge location. These results can be used together with any of the standard numerical inversion routines for the elementary loads (pitch and heave).

Williams, M. H.↗
NASA NTRS1950

The reversibility theorem for thin airfoils in subsonic and supersonic flow

A method introduced by Munk is extended to prove that the light-curve slope of thin wings in either subsonic flow or supersonic flow is the same when the direction of flight of the wing is reversed. It is also shown that the wing reversal does not change the thickness drag, damping-in-roll parameter or the damping-in-pitch parameter.

Brown, Clinton E↗
NASA NTRS1985

Technology for pressure-instrumented thin airfoil models, phase 1

A network of channels was chemically milled into one surface of a pair of matched plates having bond planes which were neither planar or profiled to match the contour of the trailing edge of a supercritical airfoil for testing in cryogenic wind tunnels. Vacuum brazing bonded the plates together to create a network of pressure passages without blockages or cross leaks. The greatest success was achieved with the smaller samples and planar bonding surfaces. In larger samples, problems were encountered due to warpage created by the relief of residual stresses. Successful bonds were formed by brazing A286, Nitronic 40 and 300 series stainless steels at 1065 C using AMS 4777B brazing alloy, but excessive grain growth occurred in samples of 200 grade 18 nickel maraging steels. Good bonds were obtained with maraging steel using a 47 percent Nickel-47 percent Palladium-6 percent Silicon alloy and brazing at 927 C. Electro-Discharge-Machining was an effective method of cutting profiled bond planes and airfoil contours. Orifices of good definition were obtained when the EDM wire cut passed through predrilled holes. Possible configurations for joints between small segments and the larger main wing were also studied.

Wigley, D. A.↗