Showing papers on "Airfoil published in 1978"

Thin-layer approximation and algebraic model for separated turbulent flows

Abstract: An algebraic turbulence model for two- and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer. Properties of the model are determined and comparisons made with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil. Separation and reattachment points from numerical Navier-Stokes solutions agree with experiment within one boundary-layer thickness. Use of law-of-the-wall boundary conditions does not alter the predictions significantly. Applications of the model to other cases are contained in companion papers.

Design of Subsonic Airfoils for High Lift

Abstract: Nomenclature c = airfoil chord CL = lift coefficient = L/!/2pV00c CLu = upper-surface lift coefficient Cp = pressure coefficient = (p -p^)/ Ap Vx 2 Mx = freestream Mach number p = static pressure Re^ = freestream Reynolds number based on airfoil chord = V^clv sp = location of leading-edge stagnation point V^ — freestream velocity v local velocity on airfoil surface x = distance along chord line F = circulation about the airfoil 7 = ratio of specific heats v = kinematic viscosity p = density () oo = freestream conditions () t e = conditions at the airfoil trailing edge

Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility

Abstract: The hydrodynamic forces due to the motion of a flexible foil in a large amplitude curved path in an inviscid incompressible flow are analysed. A parametric study of large amplitude oscillatory propulsion, with special emphasis on the effect of chordwise flexibility of the fin, is presented. This flexibility was found to increase the propulsive efficiency by up to 2% while causing small decreases in the overall thrust, compared with similar motion with rigid foils.

The unsteady motion of a two-dimensional aerofoil in incompressible inviscid flow

Abstract: A numerical method has been developed for the calculation of the pressure distribution, forces and moments on a two-dimensional aerofoil undergoing an arbitrary unsteady motion in an inviscid incompressible flow. In a discussion of the appropriate Kutta condition(s) it is argued that two Kutta conditions are required to obtain a satisfactory solution. The method is applied to (i) a sudden change in aerofoil incidence, (ii) an aerofoil oscillating at high frequency and (iii) an aerofoil passing through a sharp-edged gust.

Computation of Unsteady Transonic Flows by the Indicial Method

Abstract: The indicial method is investigated for the computation of unsteady transonic force and moment coefficients for use in flutter analyses. This approach has the advantage that solutions for all reduced frequencies for a given mode of motion can be obtained from a single finite-difference flowfield computation. Comparisons of indicial and time-integration computations for oscillating airfoil and flap motions help define limits on the motion amplitude for the applicability of the indicial method to transonic flows. Within these limits, solutions for various motion modes can be superposed to obtain solutions for multiple-degree-of-freedom aeroelastic systems. Also, a simple aeroelastic problem is solved by an alternative approach in which the structural motion and flowfield equations are integrated simultaneously using a time-integration finite-difference procedure.

Dynamic stall experiments on the NACA 0012 airfoil

Abstract: The flow over a NACA 0012 airfoil undergoing large oscillations in pitch was experimentally studied at a Reynolds number of and over a range of frequencies and amplitudes. Hot-wire probes and surface-pressure transducers were used to clarify the role of the laminar separation bubble, to delineate the growth and shedding of the stall vortex, and to quantify the resultant aerodynamic loads. In addition to the pressure distributions and normal force and pitching moment data that have often been obtained in previous investigations, estimates of the unsteady drag force during dynamic stall have been derived from the surface pressure measurements. Special characteristics of the pressure response, which are symptomatic of the occurrence and relative severity of moment stall, have also been examined.

Experimental and Computational Steady and Unsteady Transonic Flows about a Thick Airfoil

Abstract: An experimental and computational investigation of the steady and unsteady transonic flowfields about a thick airfoil is described. An operational computer code for solving the two-dimensional, compressible NavierStokes equations for flow over airfoils was modified to include solid-wall, slip-flow boundary conditions to properly assess the code and help guide the development of improved turbulence models. Steady and unsteady fiowfieids about an 18% thick circular arc airfoil at Mach numbers of 0.720, 0.754, and 0.783 and a chord Reynolds number of 11 x 10 are predicted and compared with experiment. Results from comparisons with experimental pressure and skin-friction distributions show improved agreement when including test-section wall boundaries in the computations. Steady-flow results were in good quantitative agreement with experimental data for flow conditions which result in relatively small regions of separated flow. For flows with larger regions of separated flow, improvements in turbulence modeling are required before good agreement with experiment will be obtained. For the first time, computed results for unsteady turbulent flows with separation caused by a shock wave were obtained which qualitatively reproduce the time-dependent aspects of experiments. Features such as the intensity and reduced frequency of airfoil surface-pressure fluctuations, oscillatory regions of trailing-edge and shock-induced separation, and the Mach number range for unsteady flows were all qualitatively reproduced.

The importance of quadrupole sources in prediction of transonic tip speed propeller noise

Abstract: A theoretical analysis is presented for the harmonic noise of high speed, open rotors. Far field acoustic radiation equations based on the Ffowcs-Williams/Hawkings theory are derived for a static rotor with thin blades and zero lift. Near the plane of rotation, the dominant sources are the volume displacement and the rho U(2) quadrupole, where u is the disturbance velocity component in the direction blade motion. These sources are compared in both the time domain and the frequency domain using two dimensional airfoil theories valid in the subsonic, transonic, and supersonic speed ranges. For nonlifting parabolic arc blades, the two sources are equally important at speeds between the section critical Mach number and a Mach number of one. However, for moderately subsonic or fully supersonic flow over thin blade sections, the quadrupole term is negligible. It is concluded for thin blades that significant quadrupole noise radiation is strictly a transonic phenomenon and that it can be suppressed with blade sweep. Noise calculations are presented for two rotors, one simulating a helicopter main rotor and the other a model propeller. For the latter, agreement with test data was substantially improved by including the quadrupole source term.

Steady and unsteady transonic flow

Abstract: An investigation of the transonic flow over a circular arc airfoil was conducted to obtain basic information for turbulence modeling of shock-induced separated flows and to verify numerical computer codes which are being developed to simulate such flows. The investigation included the employment of a laser velocimeter to obtain data concerning the mean velocity, the shear stress, and the turbulent kinetic energy profiles in the flowfield downstream of the airfoil midchord where the flow features are more complex. Depending on the free-stream Mach number, the flowfield developed was either steady with shock-wave-induced separation extending from the foot of the shock wave to beyond the trailing edge or unsteady with a periodic motion also undergoing shock-induced separation. The experimental data were compared with the results of numerical simulations in which a computer code was employed that solved the time-dependent Reynolds' averaged compressible Navier-Stokes equations.

Dynamic stall of an oscillating airfoil

Abstract: Unsteady separated boundary layers and wakes were studied by investigating flow past an oscillating airfoil which in part models the retreating blade stall on the helicopters. The Navier-Stokes equations in terms of the vorticity and stream function for laminar flow were solved to determine the flow field around a modified NACA 0012 airfoil. After a fully developed flow was determined at zero incidence, the airfoil was oscillated in pitch through an angle of attack range from 0 deg to 20 deg. The computed streamlines during this pitch-up motion are in qualitative agreement with the trajectories of air bubbles observed in water tunnel experiments conducted with a NACA 0012 airfoil under the same conditions. During the pitch-down motion of the airfoil, the computed flow patterns cannot be compared with the experiments because the trajectories of air bubbles intersect.

Steady and Unsteady Transonic Flow

Abstract: An investigation of the transonic flow over a circular arc airfoil was conducted to obtain basic information for turbulence modeling of shock-induced separated flows and to verify numerical computer codes which are being developed to simulate such flows. The investigation included the employment of a laser velocimeter to obtain data concerning the mean velocity, the shear stress, and the turbulent kinetic energy profiles in the flowfield downstream of the airfoil midchord where the flow features are more complex. Depending on the free-stream Mach number, the flowfield developed was either steady with shock-wave-induced separation extending from the foot of the shock wave to beyond the trailing edge or unsteady with a periodic motion also undergoing shock-induced separation. The experimental data were compared with the results of numerical simulations in which a computer code was employed that solved the time-dependent Reynolds' averaged compressible Navier-Stokes equations.

Vertical axis wind turbine

Abstract: VERTICAL AXIS WIND TURBINE ABSTRACT OF THE DISCLOSURE Wind turbines are largely divided into vertical axiw wind turbines and propeller (horizontal axis) wind turbines. The present invention discloses a vertical axis high speed wind turbine provided with rotational speed control systems. This vertical axis wind turbine is formed by having blades of a proper airfoil fitted to respective supporting arms provided radially from a vertical rotating shaft by keeping the blade span-wise direction in parallel with the shaft and being provided with aerodynamic control elements operating manually or automatically to control the rotational speed of the turbine.

Airfoil variable cambering device and method

Abstract: Airfoil device and method providing smooth, continuous, variation in airfoil camber and surface curvature over substantially the entire length of the device by use of a trusslike bendable beam as an airfoil rib having the airfoil skin surfaces flexibly slidable relative thereto. The beam is divided chordwise into upper and lower beam members each formed of a plurality of articulated sections. The beam members are connected by a bendable jackscrew which upon rotation causes one member to move chordwise, and its curvature to be changed, relative to the other thereby effecting deflection of the airfoil with concomitant variation in its camber and the curvatures of its outer skin surfaces.

A new method for designing shock-free transonic configurations

Abstract: A new method for the design of shock-free supercritical airfoils, wings, and three-dimensional configurations is described. Results illustrating this procedure in two and three dimensions are given. They include modifications to part of the upper surface of an NACA 64A410 airfoil that will maintain shock-free flow over a range of Mach numbers for a fixed lift coefficient, and the modifications required on part of the upper surface of a swept wing with an NACA 64A410 root section to achieve shock-free flow. While the results are given for inviscid flow, the same procedures can be employed iteratively with a boundary layer calculation in order to achieve shock-free viscous designs. With a shock-free pressure field the boundary layer calculation will be reliable and not complicated by the difficulties of shock-wave boundary-layer interaction.

Experimental Studies of Unsteady Trailing-Edge Conditions

Abstract: In the prediction of unsteady pressure distributions over airfoils, the steady-state Kutta-Joukowsky condition usually is assumed. Recent experimental investigations show that the pressure differential at the trailing edge approaches zero at lower reduced frequencies (ft 5). This paper describes an investigation to find the range of reduced frequencies over which the classical Kutta-Joukowsky condition is valid and the nature of deviations beyond this range. An NACA 64A010 airfoil with a 15-cm chord is supported between the side wails of a 25- x35-cm low-speed wind tunnel and oscillated over reduced frequencies ranging from 0.05 to 1.2. The experimentally determined loading near the trailing edge is measured and compared with unsteady, incompressible, small-disturbance theory. Experimental data are obtained both with and without a boundary-layer trip. It is observed that application of the Kutta-Joukowsky condition in the theoretical analysis is valid below a reduced frequency of about 0.6 in predicting the loading in the trailing-edge region. At reduced frequencies beyond 0.8, the predicted results underestimate the measured loading near the trailing edge, and the deviations increase further with reduced frequency. Similarly, the experimental phase angle of the loading in the trailing-edge region agrees reasonably with the linear theory up to k = 0.8 but lags the predicted value beyond k - 0.8.

An Investigation of Strut-Wall Intersection Losses

Abstract: A study of the intersection losses associated with the junction of a symmetric airfoil and a planar wall is reported. An experimental program, conducted in a low-speed air tunnel, provided detailed wake total pressure profiles as well as surface flow visualization photographs which define the overall flowfield. The behavior of the intersection losses was examined for dependence on flow incidence angle and strut contour. It was found that the endwall intersection losses were strongly dependent on the thickness of the incident boundary layers-thick boundary layers producing markedly lower losses than very thin incident boundary layers. A heuristic model of the flowfield, which explains marked differences between the thick and thin boundary-layer results, is also presented.

Film cooled airfoil body

Abstract: A film cooled airfoil body is provided wherein radially spaced apart cooling passages discharge cooling air in a thin continuous film of cooling air along the exterior wall surface of the airfoil body.

Fixed geometry self starting transverse axis wind turbine

Abstract: This invention relates to a fixed geometry self starting wind turbine having a blade rotatable about a vertical axis. The blade is of a wide streamlined cambered airfoil shape and has a forward portion that includes a well rounded leading edge and thickness distribution that is conducive to high lift to drag ratios and having a high drag characteristic in reversed flows. The concave curvature of this camber line of said airfoil is directed to the rotational axis. The wide blade in combination with the well rounded leading edge, camber and airfoil thickness gives the turbine improved self-starting characteristics and causes the turbine to have improved acceleration characteristics through the intermediate speed range and up to full operating speed.

Perturbation of a Discontinuous Transonic Flow

Abstract: The main difficulty in perturbing a discontinuous transonic How is in the representation of the shift in the location of the discontinuity (shock wave). Herein presented is a method of overcoming this difficulty by using a distorted airfoil as the initial case rather than the real physical airfoil; the distortion is chosen such that the shock location is unchanged by the perturbation. The distorted airfoil is obtained by the use of a strained coordinate system. A direct consequence of the theory is the derivation of an algebraic similarity relation between related airfoils with shock waves at different locations. Results for simple examples are shown. N important problem in aerodynamics is the accurate prediction of the pressures on an airfoil that is oscillating with small amplitude in a transonic flow; this prediction is necessary for the satisfactory estimation of flutter parameters. An important physical feature of such flows can be the presence of an oscillating shock wave, which should be accurately represented in any solution procedure because of the relatively large pressure fluctuations in the region bounded by the extremities of the shock motion. It is therefore desirable to represent the shock wave by the correct discontinuity rather than by the rapid compression exhibited by the commonly used "shock capture" finite-difference methods.' Such a discontinuous representation of the shock can be obtained in steady flow by using either a finite- difference method with shock fitting,2 or by the integral equation method.3 The shock fitting technique has recently been applied4 to unsteady flows. The present work is ultimately directed toward the development of a method of treating oscillating shock waves mainly through the integral equation approach. In the limit of zero frequency, the problem of computing the flow around an oscillating airfoil reduces to a steady perturbation problem with the airfoil geometry perturbed by an amount proportional to the amplitude of the oscillation. The feature of a shock increment is retained in this problem since it is unlikely that the perturbed airfoil will have a shock wave in the same location as the initial airfoil. The steady perturbation case is therefore a good starting point for deriving a fundamental approach for computing oscillatory flows, and it is this problem that is considered in this paper. In addition, a perturbation solution is useful in other ways; for example, when the flow over a given airfoil for a range of freestream Mach numbers is required, since once one nonlinear result is obtained, the other required results can be . obtained from the linear perturbation solution. As suggested earlier, the main difficulty in perturbing a discontinuous transonic flow is in the representation of the shift in the position of the discontinuity (shock wave), because for most small perturbations the physical aspects of the flow require that there be the same number of shock waves in both the initial and perturbed states but at different locations. An examination of the usual form for a perturbation solution indicates that this physical feature cannot be correctly represented except in the trivial case where no shock movement occurs. In the method herein presented, the

Inflated wing aircraft

Abstract: An aircraft is constructed of an airfoil shaped inflated involucrum of lightweight gas-impervious plastic film. The airfoil is maneuverable to attain forward self-propulsion upon ascent as well as descent. The gases contained in the involucrum are heated by solar radiation to reduce craft density with the upper surface of the airfoil being translucent and the lower surface of the airfoil interior mirrored for concentration of the radiant energy upon an interior cylindrical black spar. A honeycomb reradiation barrier is provided beneath the translucent surface. In one embodiment a large volume involucrum is changeable in camber to maximize forward propulsion. The craft may be utilized to suspend a large fog broom for the purpose of condensation of water vapor. In a further embodiment a manpowered inflatable craft is formed with a flexible longitudinal medial fold which separates the airfoil into wing segments. Each segment includes a passive trailing zone. When the wing segments are oscillated about the medial fold, the craft is propelled by ciliary thrust.

Turbulent Airfoils for General Aviation

Abstract: Several new airfoils are presented which have short pieces of steep favorable pressure gradient followed by an early pressure recovery which is a compromise between the Stratford distribution and soft stall. The drag polars are computed by a mathematical model, which is briefly described. For comparison, NACA 652 - 415 and NASA GA(W)-1 airfoils are evaluated using the same model; in this case the results are also compared with experimental drag polars.

Flying-hot-wire study of two-dimensional turbulent separation of an NACA 4412 airfoil at maximum lift

Abstract: Hot-wire measurements have been made in the boundary layer, the separated region, and the near wake for flow past an NACA 4412 airfoil at maximum lift. The Reynolds number based on chord was about 1,500,000. Special care was taken to achieve a two-dimensional mean flow. The main instrumentation was a flying hot wire; that is, a hot-wire probe mounted on the end of a rotating arm. The probe velocity was sufficiently high to avoid the usual rectification problem by keeping the relative flow direction always within a range of ±30 degrees to the probe axis. A digital computer was used to control synchronized sampling and storage of hot-wire data at closely spaced points along the probe arc. Data were obtained at several thousand locations in the flow field. These data include intermittency, two components of mean velocity, and mean values for three double, four triple, and five quadruple products of two velocity fluctuations. No information was obtained about the third (spanwise) velocity component. The data are available on punched cards in raw form and also in processed form, after use of smoothing and interpolation routines to obtain values on a fine rectangular mesh aligned with the airfoil chord. The data are displayed as contour plots of the fifteen variables.

An implicit algorithm for the conservative transonic full potential equation using an arbitrary mesh

Abstract: A new, implicit approximate factorization (AF) algorithm designed to solve the conservative full-potential equation for the transonic flow past arbitrary airfoils has been developed. The new algorithm uses an upwind bias of the density coefficient to provide stability in supersonic regions. This allows the simple two- and three-banded matrix form of the AF scheme to be retained over the entire flow field, even in regions of supersonic flow. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Airfoil pressure distributions have been computed and are in good agreement with independent results.

Turbine engine blade with airfoil projection

Abstract: A turbomachinery blade, which includes an airfoil and a projection from the airfoil for the purpose of abutting contact with the surface of an adjacent member is provided with a surface means having an improved combination of adhesive wear resistance and impact toughness through the attachment to the contact surface of a discreet wear pad. The pad comprises a substantially fully dense, compacted, sintered member of a material selected from carbides, nitrides and borides, with or without a suitable binder, the pad being of a thickness of at least about 0.01 inches and having thermal expansion characteristics compatible with the projection over the range of intended operating temperature.

Small Unsteady Perturbations in Transonic Flows

Abstract: The effects of very small, low-frequency perturbations on steady transonic flows, in the context of twodimensional flows described by the small perturbation equation, are investigated. Previous time-linearized studies failed to account for the shock wave motions that are known to occur. A method is provided that allows one to correctly account for shock wave motions due to arbitrary but small unsteady changes in the boundary conditions. Consequently, both harmonic and indicia! responses may be determined. Time-linearized results for the transonic flow past an NACA 64A006 airfoil experiencing harmonic motions in one of several modes are presented. Selected results are compared with those obtained from nonlinear calculations using a shock-fitting algorithm.

Convergence of the Adaptive-Wall Wind Tunnel

Abstract: Analytical functional relationships for exterior and interior regions with respect to the control surface inside a two-dimensional wind tunnel are used to investigate the iteration procedure for an adaptive-wall wind tunnel. Convergence to interference-free conditions is proven for any symmetric model in subsonic flow. Also, formulas are presented for determining interference-free conditions directly from two measured flow variables at the measuring plane, thus enabling an adaptive-wall wind tunnel to achieve unconfined flow in a single adjustment. A wavy-wall model and an NACA 0012 airfoil are used as examples to examine the convergence and validate the derivation. In addition, a numerical solution to the transonic small disturbance equation is used to demonstrate the convergence of the adaptive-wall iterative procedure for supercritical flow on an airfoil.

Experimental investigation of the subwing tip and its vortex structure

Abstract: A better understanding of the subwing's vortex structure relative to a square tip for several angles of attack and yaw angles is provided. This comparison included subwings of various chord size and airfoil thickness. Flow visualization, together with performance and wake measurements, provided a comparison between the square tip and subwing tips during both a semi-span wind-tunnel test and a small-scale rotor hover-stand test.

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

Abstract: 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.

Vertical axis type wind power turbine

Abstract: Wind power turbines are largely divided into vertical axis type wind power turbines and propeller type (horizontal axis type) wind power turbines. The present invention discloses a vertical axis type wind power turbine. The airfoil of blades in this vertical axis type wind power turbine is formed in such manner that, denoting a proper position on the airfoil chord line as a camber reversing position, a camber having a downward convex curvature is given between said position and a leading edge and a camber having an upward convex curvature is given between said position and a trailing edge so as to be a mean line and a rational thickness distribution is given to this mean line. This vertical axis type wind power turbine is formed by keeping the spanwise direction of the above mentioned blade parallel with a vertical rotary axis and fitting a plurality of blades at regular intervals at a distance to the vertical rotary axis through respective supporting arms.