Showing papers on "Airfoil published in 1974"

A Quasi-Vortex-Lattice Method in Thin Wing Theory

Abstract: A quasi-continuous method is developed for solving thin-wing problems. For the purpose of satisfying the wing boundary conditions, the spanwise vortex distribution is assumed to be stepwise-constant, while the chordwise vortex integral is reduced to a finite sum through a modified trapezoidal rule and the theory of Chebyshev polynomials. Wing-edge and Cauchy singularities are acounted for. The total aerodynamic characteristics are obtained by an appropriate quadrature integration. The two-dimensional results for airfoils without flap deflection reproduce the exact solutions in lift and pitching moment coefficients, the leading edge suction, and the pressure difference at a finite number of points. For a flapped airfoil, the present results are more accurate than those given by the vortex-lattice method. The three-dimensional results also show an improvement over the results of the vortex-lattice method. Extension to nonplanar applications is discussed.

An assessment of airfoil design by numerical optimization

Abstract: A practical procedure for optimum design of aerodynamic shapes is demonstrated. The proposed procedure uses an optimization program based on the method of feasible directions coupled with an analysis program that uses a relaxation solution of the inviscid, transonic, small-disturbance equations. Results are presented for low-drag, nonlifting transonic airfoils. Extension of the method to lifting airfoils, other speed regimes, and to three dimensions if feasible.

Review of NASA supercritical airfoils

Abstract: NASA supercritical airfoils are characterized by a substantially reduced curvature of the midcord region of the upper surface together with increased camber near the trailing edge. The basic aerodynamic phenomena associated with the airfoils and representative wind tunnel results are discussed. The results indicate that the drag rise Mach numbers for NASA supercritical airfoils are 0.1 higher than for comparable NACA 6-series airfoils. A recent analytic method for predicting the aerodynamic characteristics of supercritical airfoils is described. The flight demonstration programs of three applications of supercritical airfoils utilizing the F-8, T-2C and F-111 as test beds are summarized.

Passage of a Swept Airfoil through an Oblique Gust

Abstract: An analysis is presented which yields an approximate solution for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained.

A finite difference method for the solution of the transonic flow around harmonically oscillating wings

Abstract: A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.

A streamline curvature method for design of supercritical and subcritical airfoils

Abstract: 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.

Oblique-wing supersonic aircraft

Abstract: An aircraft including a single fuselage having a main wing and a horizontal stabilizer airfoil pivotally attached at their centers to the fuselage. The pivotal attachments allow the airfoils to be yawed relative to the fuselage for high speed flight, and to be positioned at right angles with respect to the fuselage during take-off, landing, and low speed flight. The main wing and the horizontal stabilizer are upwardly curved from their center pivotal connections towards their ends to form curvilinear dihedrals.

Unsteady Aerodynamic Response of a Two-Dimensional Airfoil at High Reduced Frequency

Abstract: An experimental technique is described which corroborates the predictions of several new analyses of the unsteady response of an airfoil to high frequency flow fluctuations. The periodically fluctuating flowfield was produced by the natural shedding of vortices from a transverse cylinder to yield a reduced frequency of 3.9 based on airfoil semichord. Unsteady pressure measurements were made on an instrumented airfoil mounted downstream and above the turbulent wake of the cylinder. These unsteady pressures were found to be in good agreement with current compressible theories and show a chordwise variation of pressure phase angle which is not predicted by the incompressible analysis of Sears. Large reductions of the unsteady lift and phase angle were also observed for large airfoil incidence angles.

Development of a Fowler flap system for a high performance general aviation airfoil

Abstract: A two-dimensional wind-tunnel evaluation of two Fowler flap configurations on the new GA(W)-1 airfoil was conducted. One configuration used a computer-designed 29-percent chord Fowler flap. The second configuration was modified to have increased Fowler action with a 30-percent chord flap. Force, pressure, and flow-visualization data were obtained at Reynolds numbers of 2.2 million to 2.9 million. Optimum slot geometry and performance were found to be close to computer predictions. A C sub L max of 3.8 was achieved. Optimum flap deflection, slot gap, and flap overlap are presented as functions of C sub L. Tests were made with the lower surface cusp filled in to show the performance penalties that result. Some data on the effects of adding vortex generators and hinged-plate spoilers were obtained.

Unsteady Lift and Radiated Sound from a Wake Cutting Airfoil

Abstract: An experimental study of the transient response of an airfoil to a passing wake, commonly known as "wake cutting," has been carried out in order to contribute to the basic understanding of interaction between successive blade rows in turbomachinery. An open jet was traversed periodically by moving circular rods in pinwheel fashion and a periodic row of oblique wakes was created. An instrumented airfoil was placed in the jet and microphones were used to obtain the radiated field. By using periodic sampling and averaging technique on all signals, the random, turbulent portion was suppressed, and only the periodic component was extracted. The periodic component of the instantaneous chordwise surface pressure distribution on the airfoil and the radiated sound field from the airfoil were measured and compared with the existing theories.

The passage of an infinite swept airfoil through an oblique gust

Abstract: An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

Laser velocimeter measurements of the helicopter rotor-induced flow field

Abstract: The use of a two-color laser velocimeter to measure the flow velocities in the wake of a helicopter rotor is discussed, including methods for obtaining two components of both instantaneous and time-averaged velocities Results are presented from an experiment using a 213 m diameter model helicopter rotor operating at a tip speed ratio of 018 in a wind tunnel The location of the tip vortex from the preceding blade was determined on the advancing side, and the diameter of the vortex core was found to be 15 percent of the blade chord (15 percent of the radius) The effects of the airfoil's bound vorticity were observed in the velocity distributions vry near the blade These effects suggest that the laser velocimeter may be used to determine the aerodynamic loading (circulation) at a spanwise station on the blade Also, the structure and boundary of the time-averaged wake were investigated

Laminar Viscous-Inviscid Interactions at Transonic Speeds

Abstract: Some aspects of the laminar viscous-inviscid interaction at transonic speeds are discussed by examining data obtained on a 6% thick biconvex circular-arc airfoil and comparing the results with the predictions of Klineberg and Steger (1972). The results obtained from experiments are compared for Re = 140,000 and for Re = 40,000. It is clear that the theoretical results overestimate the effects of viscosity and consequently predict values for the pressure coefficient which lie below the experimental data over the range of Mach numbers given.

Wall Interference on Two-Dimensional Supercritical Airfoils, Using Wall Pressure Measurements to Determine the Porosity Factors for Tunnel Floor and Ceiling.

Abstract: The effects of unequal porosity factors, ascribed to the floor and ceiling of two-dimensional wind tunnel test sections, are investigated with a simplified mathematical model that utilizes a point vortex and a point doublet placed mid-way between the two walls. Closed form solutions are derived, using the method of images, for wall pressure distributions, and corrections to Mach number and model angle of attack. The predicted wall pressure distributions are compared with experimental results obtained in the National Aeronautical Establishment 15x60 inch high Reynolds number two-dimensional test facility for three airfoils with thickness-chord ratios from 0.10 to 0.17 and chords of 10 and 15 inches. Agreement is shown to be markedly better than is possible with equal porosity factors. Reasonable agreement continues up to tunnel mainstream Mach numbers of about 0.82, providing confidence in the derived blockage and angle of attack corrections.

Hingeless in-plane rotor blade design

Abstract: A hingeless rotor wing system having a relatively stiff in-plane blade which has a one-piece spar of substantially rectangular cross section which is untwisted at the mean blade angle and airfoil defining structure surrounding the spar, the blade angle of the structure relative to the spar being preset to the mean operating angle of the blade in order to reduce the variation of the in-plane natural frequency during operation.

Analysis of oscillatory pressure data including dynamic stall effects

Abstract: The dynamic stall phenomenon was examined in detail by analyzing an existing set of unsteady pressure data obtained on an airfoil oscillating in pitch. Most of the data were for sinusoidal oscillations which penetrated the stall region in varying degrees, and here the effort was concentrated on the chordwise propagation of pressure waves associated with the dynamic stall. It was found that this phenomenon could be quantified in terms of a pressure wave velocity which is consistently much less than free-stream velocity, and which varies directly with frequency. It was also found that even when the stall region has been deeply penetrated and a substantial dynamic stall occurs during the downstroke, stall recovery near minimum incidence will occur, followed by a potential flow behavior up to stall inception.

Development of a computer program to obtain ordinates for NACA-6 and 6A-series airfoils

Abstract: 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.

On the Unsteady Supersonic Cascade With a Subsonic Leading Edge—An Exact First Order Theory—Part 1

Abstract: This paper presents, in two parts, the theoretical predictions of the aerodynamic forces acting on slowly oscillating airfoils in a supersonic cascade with a subsonic leading edge. The analysis is based on the assumption of an inviscid, two-dimensional and linearized flow. In the first part of the paper, the flow field ahead of the cascade is considered. An initial value problem is posed and, from the periodicity requirement in the cascade, the problem is reformulated in terms of integral equations. Solution of the integral equations, accurate to the first order of a frequency parameter, are obtained in closed form. In the limit of the steady flow, the unsteady flow analysis yields a mathematical verification of the unique incidence effect. Based on this proof, a simple rule is presented for the airfoil suction surface contour satisfying steady flow requirement ahead of the cascade. The complete aeroelastic problem, including the solution for the flow field between the blades and the trailing interference zone, is treated in Part 2.

Rapid finite-difference computation of subsonic and transonic aerodynamic flows

Abstract: Rapid iterative (or semidirect) computation methods are developed for the finite-difference solution of the nonlinear equations of subsonic and transonic aerodynamics. At each iteration, a fast, direct elliptic algorithm solves the entire computation field. In an application to subsonic flow over a lifting airfoil, the full nonlinear stream-function equation is solved. Finally, a direct Cauchy-Riemann solver is used for the nonlinear transonic small-disturbance equations for a biconvex airfoil. At M = 0.7, t/c = 0.1 (subcritical), three iterations on a 39 x 32 mesh (totaling 2.45 sec on an IBM 360/67 computer) obtain convergence within 0.1%. A slightly supercritical case requires seven iterations (6.75 sec) for convergence within 1%.

The passage of an infinite swept airfoil through an oblique gust. [approximate solution for aerodynamic response

Abstract: An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

Numerical calculations of two dimensional, unsteady transonic flows with circulation

Abstract: The feasibility of obtaining two-dimensional, unsteady transonic aerodynamic data by numerically integrating the Euler equations is investigated. An explicit, third-order-accurate, noncentered, finite-difference scheme is used to compute unsteady flows about airfoils. Solutions for lifting and nonlifting airfoils are presented and compared with subsonic linear theory. The applicability and efficiency of the numerical indicial function method are outlined. Numerically computed subsonic and transonic oscillatory aerodynamic coefficients are presented and compared with those obtained from subsonic linear theory and transonic wind-tunnel data.

Methods for the Design and Analysis of Jet-Flapped Airfoils

Abstract: Methods for solving both the direct and inverse jet flap airfoil potential flow problems are described. The direct airfoil analysis method is a completely nonlinear iterative method which is applicable to either thick or thin airfoils of arbitrary shape. The very general surface singularity formulation has been extended to include multielement airfoils, ground effects, nonuniform freestreams, inlet flows, jet entrainment effects, etc. Comparisons are given with the results of previous linear and nonlinear methods as well as with experimental data. The inverse (design) method is a more approximate method in which camber and thickness distributions are designed separately. Section shapes are shown for several airfoils designed to have only very small regions of adverse pressure gradient. Nomenclature c = length of airfoil chord cp = coefficient of pressure d = coefficient of lift cu = coefficient of jet momentum h = height of airfoil leading edge above ground plane R = radius of curvature of the jet sheet s = coordinate along the jet sheet t = airfoil thickness V = local flow speed V = average flow speed across a vortex sheet Vj - jet flow speed Vn = component of velocity normal to a surface V = freestream flow speed x = coordinate parallel to the freestream = coordinate perpendicular to the freestream = jet deflection angle at the trailing edge relative to the airfoil chord line 7 = strength of a vortex sheet 0 = local angle of inclination of the jet sheet relative to the freestream 0 = velocity potential

Some Measurements on Dynamic Stall

Abstract: Details of a flow oscillation device and of force and moment measurements on a 2 ft chord twodimensional NACA 0012-64 airfoil in the oscillating flow and oscillated in pitch in a steady flow through stall are presented. Results indicate that both methods give essentially the same description of the dynamic stall process. It is apparent from peaks in the pressure distributions and in the pitching moment traces that more than one vortex is shed from the leading edge during the stall process. This, coupled with the very rapid changes that occur during stall, requires very close scrutiny of force and moment data that has not been recorded continuously. Understanding of dynamic stall overshoot will not be complete until detailed measurements are obtained in the region of the laminar separation bubble near the nose.

A generalized-capacity-matrix technique for computing aerodynamic flows

Abstract: A numerical generalized-capacity-matrix technique is developed for application to aerodynamic flow computations. This technique allows the very fast direct (noniterative) numerical elliptic solvers to be used in problems with arbitrary internal boundaries and with a wide class of boundary conditions, including numerical application of the Kutta condition on an airfoil without iteration. Accuracy, speed, and usefulness of the technique are demonstrated with linear problems for potential flows over airfoil shapes. The method's main advantages, however, can be exploited within iterative procedures for a variety of complex flow problems governed by systems of equations not necessarily elliptic or linear.