Search NASA⌕ Search

SEARCH · Search NASA

Results for “SUPERSONIC 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

Flutter and oscillating air-force calculations for an airfoil in two-dimensional supersonic flow

A connected account is given of the Possio theory of non-stationary flow for small disturbances in a two-dimensional supersonic flow and of its application to the determination of the aerodynamic forces on an oscillating airfoil. Further application is made to the problem of wing flutter in the degrees of freedom - torsion, bending, and aileron rotations. Numerical tables for flutter calculations are provided for various values of the Mach number greater than unity. Results for bending-torsion wing flutter are shown in figures and are discussed. The static instabilities of divergence and aileron reversal are examined as is a one-degree-of-freedom case of torsional oscillatory instability.

Garrick, I E↗

Airfoil profiles for minimum pressure drag at supersonic velocities -- general analysis with application to linearized supersonic flow

A theoretical investigation is made of the airfoil profile for minimum pressure drag at zero lift in supersonic flow. In the first part of the report a general method is developed for calculating the profile having the least pressure drag for a given auxiliary condition, such as a given structural requirement or a given thickness ratio. The various structural requirements considered include bending strength, bending stiffness, torsional strength, and torsional stiffness. No assumption is made regarding the trailing-edge thickness; the optimum value is determined in the calculations as a function of the base pressure. To illustrate the general method, the optimum airfoil, defined as the airfoil having minimum pressure drag for a given auxiliary condition, is calculated in a second part of the report using the equations of linearized supersonic flow.

Chapman, Dean R↗

VARIABLE SWEEP AIRCRAFT

Aerodynamic principles of variable sweep aircraft and application to supersonic aircraft

AERODYNAMIC CHARACTERISTICS↗

Stability analysis of nonlinear autonomous systems - General theory and application to flutter

The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).

Smith, L. L.↗

Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.

Weatherill, W. H.↗

Calculation of two-dimensional inlet flow fields by an implicit method including viscous effects: User's manual

Inlet flow fields for airbreathing missiles are calculated by the adaptation of a two dimensional computational method developed for the flow around airfoils. A supersonic free stream is assumed to allow the forebody calculation to be uncoupled from the inlet calculation. The inlet calculation employs an implicit, time marching finite difference procedure to solve the thin layer Navier-Stokes equations formulated in body fitted coordinates. The mathematical formulation of the problem and the solution algorithm are given. Numerical stability and accuracy as well as the initial and boundary conditions used are discussed. Instructions for program use and operation along with the overall program logic are also given.

Biringen, S.↗

A numerical simulation of two-dimensional inlet flow fields

Inlet flow fields for airbreathing missiles are calculated by the adaptation of a two-dimensional computational method developed for the flow around airfoils. A supersonic free stream is assumed to allow the forebody calculation to be uncoupled from the inlet calculation. The inlet calculation employs an implicit, time-marching finite-difference procedure to solve the thin-layer Navier-Stokes equations formulated in body-fitted coordinates. Because the method can be used for a flow field with both subsonic and supersonic regions, it is applicable to subcritical as well as supercritical inlet operation.

Biringen, S.↗

Applications of an adaptive unstructured solution algorithm to the analysis of high speed flows

An upwind cell-centered scheme for the solution of steady laminar viscous high-speed flows is implemented on unstructured two-dimensional meshes. The first-order implementation employs Roe's (1981) approximate Riemann solver, and a higher-order extension is produced by using linear reconstruction with limiting. The procedure is applied to the solution of inviscid subsonic flow over an airfoil, inviscid supersonic flow past a cylinder, and viscous hypersonic flow past a double ellipse. A detailed study is then made of a hypersonic laminar viscous flow on a 24-deg compression corner. It is shown that good agreement is achieved with previous predictions using finite-difference and finite-volume schemes. However, these predictions do not agree with experimental observations. With refinement of the structured grid at the leading edge, good agreement with experimental observations for the distributions of wall pressure, heating rate and skin friction is obtained.

Thareja, R. R.↗

Subsonic flow over thin oblique airfoils at zero lift

A previous report gave calculations for the pressure distribution over thin oblique airfoils at supersonic speed. The present report extends the calculations to subsonic speeds. It is found that the flows again can be obtained by the superposition of elementary conical flow fields. In the case of the swept-back wing the pressure distributions remain qualitatively similar at subsonic and supersonic speeds. Thus a distribution similar to the Ackeret type of distribution appears on the root sections of the swept-back wing at Mach=0. The resulting positive pressure drag on the root section is balanced by negative drags on outboard sections.

Jones, Robert T↗

Visualization of In-Flight Flow Phenomena Using Infrared Thermography

Infrared thermography was used to obtain data on the state of the boundary layer of a natural laminar flow airfoil in supersonic flight. In addition to the laminar-to-turbulent transition boundary, the infrared camera was able to detect shock waves and present a time dependent view of the flow field. A time dependent heat transfer code was developed to predict temperature distributions on the test subject and any necessary surface treatment. A commercially available infrared camera was adapted for airborne use in this application. Readily available infrared technology has the capability to provide detailed visualization of various flow phenomena in subsonic to hypersonic flight regimes.

Banks, D. W.↗

Flutter and oscillating air-force calculations for an airfoil in a two-dimensional supersonic flow

An account is given of the Possio theory of non stationary flow for small disturbances in a two-dimensional supersonic flow and of its application to determination of the aerodynamic forces on an oscillating airfoil. Further application is made to the problem of wing flutter in the degrees of freedom - torsion, bending, and aileron torsion. Numerical tables for flutter calculations are provided for numerous values of the Mach number greater than unity. Results for bending-torsion wing flutter are discussed. The static instabilities of divergence and aileron reversal are examined as is a one degree of freedom case of torsional oscillatory instability.

Garrick, I E↗

Flat Plate Cascades at Supersonic Speed

A brief review of exact two-dimensional supersonic flow theory and Ackeret's linearized theory are first presented. The lift and drag coefficients of a cascade of flat plates are calculated exactly and compared to those obtained using the linearized theory. The forces on the cascade are determined for unsteady inlet flow. The flat plate cascade theory is extended to compute the efficiency of a supersonic propeller with friction and finite blade thickness.

FLOW - PLATES, FLAT - SUPERSONIC↗

Base Pressure at Supersonic Speeds on Two-dimensional Airfoils and on Bodies of Revolution with and Without Fins Having Turbulent Boundary Layers

An analysis has been made of available experimental data to show the effects of most of the variables that are more predominant in determining base pressure at supersonic speeds. The analysis covers base pressures for two-dimensional airfoils and for bodies of revolution with and without stabilizing fins and is restricted to turbulent boundary layers. The present status of available experimental information is summarized as are the existing methods for predicting base pressure. A simple semiempirical method is presented for estimating base pressure. For two-dimensional bases, this method stems from an analogy established between the base-pressure phenomena and the peak pressure rise associated with the separation of the boundary layer. An analysis made for axially symmetric flow indicates that the base pressure for bodies of revolution is subject to the same analogy. Based upon the methods presented, estimations are made of such effects as Mach number, angle of attack, boattailing, fineness ratio, and fins. These estimations give fair predictions of experimental results. (author)

LOVE EUGENE S↗

Comparisons of two-dimensional shock-expansion theory with experimental aerodynamic data for delta-planform wings at high supersonic speeds

An investigation has been conducted to explore the potential for optimizing airfoil shape at high supersonic speeds by utilizing the two-dimensional shock-expansion method. Theoretical and experimental force and moment coefficients are compared for four delta-planform semispan wings having a leading-edge sweep angle of 65 deg and incorporating modified diamond airfoils with a thickness-chord ratio of 0.06. The wings differ only in airfoil maximum-thickness position and camber. The experimental data are obtained at Mach numbers of 3.95 and 4.63 and at a Reynolds number of 9.84 million per meter. A relatively simple method is developed for predicting, in terms of lift-drag ratio, the optimum modified diamond airfoil at high supersonic and hypersonic speeds.

Jernell, L. S.↗