Overall aerodynamic performance of an annular flat-plate airfoil cascade
Previously cited in issue 05, p. 588, Accession no. A83-16824
Bergsten, D. E.↗
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Aerodynamic characteristics of several airfoils of low aspect ratio
This paper presents the results of wind-tunnel tests of several airfoils of low aspect ratio. The airfoils included three circular Clark Y airfoils with different amounts of dihedral, two Clark Y airfoils with slots in their portions, and three flat-plate airfoils. Lift, drag, and pitching-moment characteristics of the slotted airfoils with slots open and closed; pitching moment characteristics of one of the slotted airfoils with slots open and closed; and lift characteristics of the flat-plate airfoils are included. The results reveal a definite improvement of lift, drag, and pitching-moment characteristics with increase in dihedral of the circular Clark Y wing. Lift characteristics near the stall were found to depend markedly on the shape of the extreme tip but were not greatly affected by slots through the after portion of the airfoils. Changes in plan form of the flat-plate airfoils gave erroneous indications of the effect to be expected from changes in plan form of an airfoil of Clark Y section. The minimum drag characteristics of the circular Clark Y airfoils were found to be substantially the same as for a Clark Y airfoil of conventional aspect ratio.
Zimmerman, C H↗
Unsteady airfoils
Progress towards successful modelling of unsteady flows past two-dimensional oscillating airfoils is examined. Linearized, thin airfoil theory is reviewed with special regard to the vortex shedding which occurs when either the body or the flow fluctuates. A sinusoidally oscillating flat-plate airfoil is considered in terms of noncirculatory components, including boundary conditions and bound and wake vortices, respectively. Applications of linear theory to vertical airfoil oscillations and to oscillating control surfaces are described, and oscillating airfoils in subsonic and supersonic flows are investigated. Perturbations in linear solutions are explored for the occurrence of second-order effects, and trailing edge and wake effects. The effects of unsteady transonic flows are broken into nearly inviscid and strongly viscous cases, and analyses of dynamic stall and stall flutter are presented.
Mccroskey, W. J.↗
Study of Flow Over Oscillating Airfoil Models at a Mach Number of 7.0 in Helium
A wind-tunnel study of unsteady flow at a Mach number of 7 in helium has been conducted on several sting-mounted wedge, double-wedge, and flat-plate airfoil models with three different leading-edge radii. The data were obtained by taking high-speed schlieren motion pictures of the decaying motion of the model as it was released from an initial deflection. The shock-wave position observed on the sharp-leading-edge models during the oscillation was compared with that obtained by use of unsteady flow theory as well as steady-state theory. Comparison of theoretical results indicated that no unsteady-flow effects exist over the range of reduced frequencies k, 0.007 less than equal than k less than or equal 0.030, studied experimentally. The experimental results confirmed this finding as no unsteady-flow effects were detected in this reduced-frequency range. Comparison of shock-wave positions measured for the blunt models with those calculated by steady-state methods indicated fair agreement.
Arman, Ali↗
Aerodynamic performance of an annular classical airfoil cascade
Results are presented for a series of experiments that were performed in a large-scale subsonic annular cascade facility that was specifically designed to provide three-dimensional aerodynamic data for the verification of numerical-calculation codes. In particular, the detailed three-dimensional aerodynamic performance of a classical flat-plate airfoil cascade is determined for angles of incidence of 0, 5, and 10 deg. The resulting data are analyzed and are correlated with predictions obtained from NASA's MERIDL and TSONIC numerical programs. It is found that: (1) at 0 and 5 deg, the airfoil surface data show a good correlation with the predictions; (2) at 10 deg, the data are in fair agreement with the numerical predictions; and (3) the two-dimensional Gaussian similarity relationship is appropriate for the wake velocity profiles in the mid-span region of the airfoil.
Bergsten, D. E.↗
Experimental evaluation of trailing edge and incidence fluctuation noise theories
Tests were conducted to evaluate conflicting theories for trailing edge noise and for incidence fluctuation noise. A flat-plate airfoil with flush-mounted surface pressure transducers was tested in an anechoic wind tunnel at velocities from 31.5 to 177 m/sec and nominal 4 and 6% grid-generated turbulence levels. In one series of runs, the airfoil was faired into the tunnel nozzle and extended beyond the nozzle lip for studies of trailing edge noise without a leading edge and with flow on only one side. Such noise was found to vary with velocity to the fifth power and turbulence level squared as predicted by Ffowcs Williams and Hall (1970) and by Chase (1972). Power spectral density at high frequencies decayed approximately inversely with frequency to the 10/3 power as predicted by Chase. The data were poorly predicted by Hayden's correlation (1969, 1972).
Fink, M. R.↗
Bifurcation analysis of aircraft pitching motions near the stability boundary
Bifuraction theory is used to analyze the nonlinear dynamic stability characteristics of an aircraft subject to single degree of freedom pitching-motion perturbations about a large mean angle of attack. The requisite aerodynamic information in the equations of motion is represented in a form equivalent to the response to finite-amplitude pitching oscillations about the mean angle of attack. This information is deduced from the case of infinitesimal-amplitude oscillations. The bifurcation theory analysis reveals that when the mean angle of attack is increased beyond a critical value at which the aerodynamic damping vanishes, new solutions representing finite-amplitude periodic motions bifurcate from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solutions are stable (supercritical) or unstable (subcritical). For flat-plate airfoils flying at supersonic/hypersonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop.
Hui, W. H.↗
Critical evaluation of the unsteady aerodynamics approach to dynamic stability at high angles of attack
Bifurcation theory is used to analyze the nonlinear dynamic stability characteristics of an aircraft subject to single-degree-of-freedom. The requisite moment of the aerodynamic forces in the equations of motion is shown to be representable in a form equivalent to the response to finite amplitude oscillations. It is shown how this information can be deduced from the case of infinitesimal-amplitude oscillations. The bifurcation theory analysis reveals that when the bifurcation parameter is increased beyond a critical value at which the aerodynamic damping vanishes, new solutions representing finite amplitude periodic motions bifurcate from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solutions are stable or unstable. For the pitching motion of flat-plate airfoils flying at supersonic/hypersonic speed and for oscillation of flaps at transonic speed, the bifurcation is subcritical, implying either the exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop.
Hui, W. H.↗
Distribution of wave drag and lift in the vicinity of wing tips at supersonic speeds
The point-source-distribution method of calculating the aerodynamic coefficients of thin wings at supersonic speeds was extended to include the effect of the region between the wing boundary and the foremost Mach wave from the wing leading edge. The effect of this region on the surface velocity potential has been determined by an equivalent function, which is evaluated over a portion of the wing surface. In this manner, the effect of angles of attack and yaw as well as the asymmetry of top and bottom wing surfaces may be calculated. As examples of the method, the pressure distribution on a thin plate wing of rectangular plan form as well as the lift and the drag coefficients as a function of Mach number, angle of attack, and aspect ratio are calculated. The equations for the surface velocity potential of several other plan forms are also included. (author)
AIRFOILS, FLAT-PLATE↗
Theoretical lift distribution and upwash velocities for thin wings at supersonic speeds
Explore the source record for details and available documents.
UPWASH↗
Volterra's solution of the wave equation as applied to three-dimensional supersonic airfoil problems
Explore the source record for details and available documents.
WINGS, INFINITE-SPAN↗
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↗
Wind-tunnel experiments on divergence of forward-swept wings
An experimental study to investigate the aeroelastic behavior of forward-swept wings was conducted in the Langley Transonic Dynamics Tunnel. Seven flat-plate models with varying aspect ratios and wing sweep angles were tested at low speeds in air. Three models having the same planform but different airfoil sections (i.e., flat-plate, conventional, and supercritical) were tested at transonic speeds in Freon 12. Linear analyses were performed to provide predictions to compare with the measured aeroelastic instabilities which include both static divergence and flutter. Six subcritical response testing techniques were formulated and evaluated at transonic speeds for accuracy in predicting static divergence. Two "divergence stoppers" were developed and evaluated for use in protecting the model from structural damage during tests.
Ricketts, R. H.↗
Flutter Tests of Some Simple Models at a Mach Number of 7.2 in Helium Flow
Hypersonic flutter tests on rectangular flat-plate models and double-wedge airfoils in helium flow
FLUTTER ANALYSIS↗
Wind-Tunnel Investigation of a Rectangular NACA 2212 Airfoil with Semispan Ailerons and with Nonperforated, Balanced Double Split Flaps for Use as Aerodynamic Brakes
Flat-plate flaps with no wing cutouts and flaps having Clark Y sections with corresponding cutouts made in wing were tested for various flap deflections, chord-wise locations, and gaps between flaps and airfoil contour. The drag was slightly lower for wing with airfoil section flaps. Satisfactory aileron effectiveness was obtained with flap gap of 20% wing chord and flap-nose location of 80 percent wing chord behind leading edge. Airflow was smooth and buffeting negligible.
AIRFOILS - NACA 2212 - CHAR & MOMENTS - WING FLAPS↗
Considerations of Methods of Improving Helicopter Efficiency
Recent NASA helicopter research indicates that significant improvements in hovering efficiency, up to 7 percent, are available from the use of a special airfoil section formed by combining an NACA 632A015 thickness distribution with an NACA 230 mean line. This airfoil should be considered for flying-crane-type helicopters. Application of standard leading-edge roughness causes a large drop in efficiency; however, the cambered rotor is shown to retain its superiority over a rotor having a symmetrical airfoil when both rotors have leading-edge roughness. A simple analysis of available rotor static-thrust data indicates a greatly reduced effect of compressibility effects on the rotor profile-drag power than predicted from calculations. Preliminary results of an experimental study of helicopter parasite drag indicate the practicability of achieving an equivalent flat-plate parasite-drag area of less than 4 square feet for a rotor-head-pylon-fuselage configuration (landing gear retracted) in the 2,000-pound minimum-flying-weight class. The large drag penalty of a conventional skid-type landing (3.6 square feet) can be reduced by two-thirds by careful design. Clean, fair, and smooth fuselages that tend to have narrow, deep cross sections are shown to have advantages from the standpoint of drag and download. A ferry range of the order of 1,500 miles is indicated to be practicable for the small helicopter considered.
Dingeldein, Richard C.↗
Analysis and Evaluation of Supersonic Underwing Heat Addition
The linearized theory for heat addition under a wing has been developed to optimize wing geometry, heat addition, and angle of attack. The optimum wing has all of the thickness on the underside of the airfoil, with maximum-thickness point well downstream, has a moderate thickness ratio, and operates at an optimum angle of attack. The heat addition is confined between the fore Mach waves from under the trailing surface of the wing. By linearized theory, a wing at optimum angle of attack may have a range efficiency about twice that of a wing at zero angle of attack. More rigorous calculations using the method of characteristics for particular flow models were made for heating under a flat-plate wing and for several wings with thickness, both with heat additions concentrated near the wing. The more rigorous calculations yield in practical cases efficiencies about half those estimated by linear theory. An analysis indicates that distributing the heat addition between the fore waves from the undertrailing portion of the wing is a way of improving the performance, and further calculations appear desirable. A comparison of the conventional ramjet-plus wing with underwing heat addition when the heat addition is concentrated near the wing shows the ramjet to be superior on a range basis up to Mach number of about B. The heat distribution under the wing and the assumed ramjet and airframe performance may have a marked effect on this conclusion. Underwing heat addition can be useful in providing high-altitude maneuver capability at high flight Mach numbers for an airplane powered by conventional ramjets during cruise.
wings↗
Flutter Tests of Some Simple Models at a Mach Number of 7.2 in Helium Flow
Results of hypersonic flutter tests on some simple models are presented. The models had rectangular plan forms of panel aspect ratio 1.0, no sweepback, and bending-to-torsion frequency ratios of about 1/3. Two airfoil sections were included in the tests; double wedges of 5-, 10-, and 15-percent thickness and flat plates with straight, parallel sides and beveled leading and trailing edges. The models were supported by a cantilevered shaft. The double-wedge wings were tested in helium at a Mach number of 7.2. An effect of airfoil thickness on flutter speed was found, thicker wings requiring more stiffness to avoid flutter. A few tests in air at a Mach number of 6.9 showed the same thickness effect and also indicated that tests in helium would predict conservative flutter boundaries in air. The data in air and helium seemed to be correlated by piston-theory calculations. Piston-theory calculations agreed well with experiment for the thinner models but began to deviate as the thickness parameter MT approached and exceeded 1.0. A few tests on flat-plate models with various elastic-axis locations were made. Piston-theory calculations would not satisfactorily predict the flutter of these models, probably because of their blunt leading edges.
Morgan, Homer G.↗