Showing papers on "Airfoil published in 1979"

Aerodynamics for Engineers

Abstract: (NOTE: Each section contains a Summary, Problems, and References) 1. Fluid Properties. Concept of a Fluid. Fluid as a Continuum. Fluid Properties. Pressure Variation in a Static Fluid Medium. The Standard Atmosphere. 2. Fundamentals of Fluid Mechanics. Introduction to Fluid Dynamics. Conservation of Mass. Conservation of Linear Momentum. Applications to Constant-Property Flows. Reynolds Number and Mach Number as Similarity Parameters. Concept of the Boundary Layer. Conservation of Energy. First Law of Thermodynamics. Derivation of the Energy Equation. 3. Dynamics of an Incompressible, Inviscid Flow Field. Inviscid Flows. Bernoulli's Equation. Use of Bernoulli's Equation to Determine Airspeed. The Pressure Coefficient. Circulation. Irrotational Flow. Kelvin's Theorem. Incompressible, Irrotational Flow. Stream Function in a Two-Dimensional, Incompressible Flow. Relation Between Streamlines and Equipotential Lines. Superposition of Flows. Elementary Flows. Adding Elementary Flows to Describe Flow Around a Cylinder. Lift and Drag Coefficients as Dimensionless Flow-Field Parameters. Flow Around a Cylinder with Circulation. Source Density Distribution on the Body Surface. Incompressible, Axisymmetric Flow. 4. Viscous Boundary Layers. Equations Governing the Boundary Layer for a Steady, Two-Dimensional, Incompressible Flow. Boundary Conditions. Incompressible, Laminar Boundary Layer. Boundary-Layer Transition. Incompressible, Turbulent Boundary Layer. Eddy Viscosity and Mixing Length Concepts. Integral Equations for a Flat-Plate Boundary Layer. Thermal Boundary Layer for Constant-Property Flows. 5. Characteristic Parameters for Airfoil and Wing Aerodynamics. Characterization of Aerodynamic Forces and Moments. Airfoil Geometry Parameters. Wing-Geometry Parameters. Aerodynamic Force and Moment Coefficients. Wings of Finite Span. 6. Incompressible Flows around Airfoils of Infinite Span. General Comments. Circulation and the Generation of Lift. General Thin-Airfoil Theory. Thin, Flat-Plate Airfoil (Symmetric Airfoil). Thin, Cambered Airfoil. High-Lift Airfoil Sections. Multielement Airfoil Sections for Generating High Lift. High-Lift Military Airfoils. 7. Incompressible Flows about Wings of Finite Span. General Comments. Vortex System. Lifting-Line Theory for Unswept Wings. Panel Methods. Vortex Lattice Method. Factors Affecting Drag Due-to-Lift at Subsonic Speeds. Delta Wings. Leading-Edge Extensions. Asymmetric Loads on the Fuselage at High Angles of Attack. Flow Fields for Aircraft at High Angles of Attack. 8. Dynamics of a Compressible Flow Field. Thermodynamic Concepts. Adiabatic Flow in a Variable-Area Streamtube. Isentropic Flow in a Variable-Area. Characteristic Equations and Prandtl-Meyer Flow. Shock Waves. Viscous Boundary Layer. 9. Compressible, Subsonic Flows and Transonic Flows. Compressible, Subsonic Flow. Transonic Flow Past Unswept Airfoils. Swept Wings at Transonic Speeds. Forward Swept Wing. Transonic Aircraft. 10. Two-Dimensional Supersonic Flows around Thin Airfoil. Linear Theory. Second-Order Theory (Busemann's Theory). Shock-Expansion Technique. 11. Supersonic Flows Over Wings and Airplane Configurations. General Remarks About Lift and Drag. General Remarks About Supersonic Wings. Governing Equation and Boundary Conditions. Consequences of Linearity. Solution Methods. Conical-Flow Method. Singularity-Distribution Method. Design Considerations for Supersonic Aircraft. Some Comments About the Design of the SST and of the HSCT. Aerodynamic Interaction. Aerodynamic Analysis for Complete Configurations in a Supersonic Stream. 12. Hypersonic Flows. Newtonian Flow Model. Stagnation Region Flow-Field Properties. Modified Newtonian Flow. High L/D Hypersonic Configurations-Waveriders. Aerodynamic Heating. A Hypersonic Cruiser for the Twenty-First Century? Importance of Interrelating CFD, Ground-Test Data, and Flight-Test Data. 13. Aerodynamic Design Considerations. High-Lift Configurations. Circulation Control Wing. Design Considerations for Tactical Military Aircraft. Drag Reduction. Development of an Airframe Modification to Improve the Mission Effectiveness of an Existing Airplane. Considerations for Wing/Canard, Wing/Tail, and Tailless Configurations. Comments on the F-15 Design. The Design of the F-22. 14. Tools for Defining the Aerodynamic Environment. CFD Tools. Establishing the Credibility of CFD Simulations. Ground-Based Test Programs. Flight-Test Programs. Integration of Experimental and Computational Tools: The Aerodynamic Design Philosophy. Appendix A: The Equations of Motion Written in Conservation Form. Appendix B: A Collection of Often Used Tables. Index

Flying-Hot-wire Study of Flow Past 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 mad mum 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 deg from the probe ads. A digital computer was used to control synchronized sampling of hot-wire data at closely spaced points along the probe arc. Ensembles of data were obtained at several thousand locations in the flowfield. The data include Intermittency, two components of mean velocity, and twelve mean values for double, triple, and quadruple products of two velocity fluctuations. No Information was obtained about the third (spanwise) velocity component. An unexpected effect of rotor interference was identified and brought under reasonable control. The data are available on punched cards in raw form and also after use of smoothing and interpolation routines to obtain values on a fine rectangular grid aligned with the airfoil chord. The data are displayed In the paper as contour plots.

The Minimum Induced Drag of Aerofoils

Abstract: Equations are derived to demonstrate which distribution of lifting elements result in a minimum amount of aerodynamic drag. The lifting elements were arranged (1) in one line, (2) parallel lying in a transverse plane, and (3) in any direction in a transverse plane. It was shown that the distribution of lift which causes the least drag is reduced to the solution of the problem for systems of airfoils which are situated in a plane perpendicular to the direction of flight.

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.

Potential Flow Analysis of Multielement Airfoils Using Conformal Mapping

Abstract: Conformal mapping techniques are applied to the problem of calculating the two-dimensional potential flow about multielement airfoils. Airfoil geometry is completely arbitrary and, unlike other mapping methods, any number of airfoil elements can be considered. The multiple airfoil elements are transformed to the same number of circles by successive applications of a method for mapping a single body to a unit circle. The flow about the multiple circles is analyzed using multiply-reflected doublets and vortices. All iterative procedures converge rapidly, giving accurate results with considerably better computational efficiency than existing distributedsingularity panel methods.

Experiments on an aerofoil at high angle of incidence in longitudinal oscillations

Abstract: Details of flow visualization, aerodynamic forces and pitching moment, static pressure and skin friction measurements have been carried out on a symmetrical aerofoil at fixed angle of incidence in longitudinal oscillations parallel to the uniform airstream of a wind-tunnel.This investigation shows weak unsteady effects at incidences below that of static stall. For higher incidences, strong unsteady effects appear and depend on the frequency and amplitude of the oscillations. The measurements indicate an overshoot of the instantaneous lift and drag which is explained by a strong vortex shedding process occurring during the dynamic stall encountered by the aerofoil in decelerated motion, as observed for profiles oscillating in pitch through stall. When the aerofoil is going forward in accelerated motion dynamic reattachment may be observed at very high incidence over a short part of the period of oscillation.Dynamic stall and dynamic reattachment contribute to a favourable effect of unsteadiness on the mean lift coefficient, which increases as compared to the steady state one, and which is expressed through an empirical formula involving incidence, frequency and amplitude of oscillations. At given incidence, optimization of this feature is achieved by matching the frequency and the amplitude of oscillation, respectively with the frequency linked with the highest peak of energy in the wake, and with the distance between two consecutive vortices in the mean wake when modelled as a von Karman's vortex street.

A comparison of the pitching and plunging response of an oscillating airfoil

Abstract: An oscillating SC1095 airfoil model was tested for its aerodynamic stability in a rigid body with a single degree of freedom pitch about its quarter chord, and also in a rigid body with single degree of freedom plunge. The ability of pitching data to model plunging motions was evaluated. A one to one correspondence was established between pairs of pitching and plunging motions according to the potential flow transformation formula alpha=ikh. The imposed variables of the experiment were mean incidence angle, amplitude of motion, free stream velocity, and oscillatory frequency. Results indicate that significant differences exist between the aerodynamic responses to the motions, particularly at high load conditions. At high load conditions, the normal force for equivalent pitch is significantly greater than that for true pitch at the geometric incidence angle.

Estimation of Attainable Leading-Edge Thrust for Wings at Subsonic and Supersonic Speeds

Abstract: The factors which place limits on the theoretical leading edge thrust are identified. An empirical method for the estimation of attainable thrust is presented. The method is based on the use of simple sweep theory to permit a two dimensional analysis, the use of theoretical airfoil programs to define thrust dependence on local geometric characteristics, and the examination of experimental two dimensional airfoil data to define limitations imposed by local Mach numbers and Reynolds numbers. Comparisons of theoretical and experimental aerodynamic characteristics for a series of wing body configurations are examined.

An efficient algorithm for numerical airfoil optimization

Abstract: A new optimization algorithm is presented. The method is based on sequential application of a second-order Taylor's series approximation to the airfoil characteristics. Compared to previous methods, design efficiency improvements of more than a factor of 2 are demonstrated. If multiple optimizations are performed, the efficiency improvements are more dramatic due to the ability of the technique to utilize existing data. The method is demonstrated by application to subsonic and transonic airfoil design but is a general optimization technique and is not limited to a particular application or aerodynamic analysis.

A self-deployable air spoiler assembly

Abstract: A self-deployable front air spoiler assembly (10) mounted beneath a vehicle underbody (11) the air spoiler assembly (10) comprising a laterally extending airfoil (19) which in non-deployed condition is situated in a semi- concealed position. The airfoil (19) is supported at each side of the longitudinal center of the vehicle on swingable links (26. 27) each link being pivotally coupled at one end to the airfoil (19) and at the other end to the vehicle underbody. The pivot axes (28, 29, 32, 33) of the links are substantially parallel to the airfoil. Biasing means interposed between the air spoiler assembly (10) and the vehicle underbody (11) normally biases the airfoil (19) toward its deployed condition. As the air pressure against the front face of the airfoil (19) increases as the speed of the vehicle is increased, the airfoil (19) swings downwardly increasing the frontal area impacted by the airstream and restricting the flow of air beneath the vehicle underbody (11).

Applications of Laplace transform methods to airfoil motion and stability calculations

Abstract: This paper reviews the development of generalized unsteady aerodynamic theory and presents a derivation of the generalized Possio integral equation. Numerical calculations resolve questions concerning subsonic indicial lift functions and demonstrate the generation of Kutta waves at high values of reduced frequency, subsonic Mach number, or both. The use of rational function approximations of unsteady aerodynamic loads in aeroelastic stability calculations is reviewed, and a reformulation of the matrix Pade approximation technique is given. Numerical examples of flutter boundary calculations for a wing which is to be flight tested are given. Finally, a simplified aerodynamic model of transonic flow is used to study the stability of an airfoil exposed to supersonic and subsonic flow regions.

Wing sections for hydrofoils--part 1: symmetrical profiles

Abstract: NACA 16-series wing sections have been extensively applied to U.S. hydrofoil craft. However, this series of wing sections was developed around 1940. Since then new airfoil sections have been continuously investigated both theoretically and experimentally. By means of recently developed methods of calculation for boundary-layer and profile theory, it is possible to determine, in a simple way, profiles with fixed characteristics of pressure distributions and to carry out boundary-layer calculations. Three classes of new wing sections with improved hydrodynamic characteristics in terms of cavitation inception have been successfully developed. It is shown that each series of profiles has its own merit. The choice of a wing section can be made only when the operational requirements of the craft are specified.

On the added mass of a perforated shell, with application to the generation of aerodynamic sound by a perforated trailing edge

Abstract: This paper examines the theory of oscillatory flow through the perforated surface of a rigid shell. The Reynolds number based on the diameter of a typical perforation is sufficiently large that the flow may be assumed to be irrotational. The case in which the surface apertures are small on a scale of the local radius of curvature of the shell is discussed in detail, and a pair of integral equations is derived whose solutions determine the principal properties of the flow, and in particular the fluctuating inertial drag experienced by the shell. These equations are solvable in closed form only for relatively simple shell geometries. Application of the theory is made to the case of a spherical shell, and to the problem of sound generation by turbulence swept past the trailing edge of a perforated aerofoil. Numerical results are presented which support the view that significant reductions in the level of trailing edge noise are possible, and illustrate the dependence of the attenuation on the distribution of perforations.

Prediction of Viscous Effects in Steady Transonic Flow Past an Aerofoil

Abstract: An account is given of a numerical method for calculating transonic flow past an aerofoil with an allowance for viscous effects, providing that the boundary layer remains fully attached over the aerofoil surface. The method has been developed by combining, in an iterative manner, calculations of the inviscid flow with calculations of the compressible boundary layer and wake. The solution for the inviscid flow is obtained by an iterative scheme, originally established by Garabedian & Korn, which has been modified to give a more realistic representation of shock waves. The boundary-layer development is treated as laminar initially; at a certain transition position a turbulent boundary layer is assumed to develop, and this is determined by the lag-entrainment method of Green et al. Comparisons of the results from the numerical scheme with some experimental measurements are shown for various examples in which shock waves of moderate strength are present. The method predicts, with reasonable accuracy, both the detailed pressure distribution and the variation of drag coefficient with lift coefficient.

Time-Dependent Response of a Two-Dimensional Airfoil in Transonic Flow

Abstract: A procedure is developed for the aeroelastic analysis of a two-dimensional airfoil in transonic flow. The fluid is assumed to be described by the unsteady low-frequency small-disturbance transonic potential equation for which a fully time-implicit integration scheme exists. Structural equations of motion are integrated in time simultaneously with the potential equation in order to predict the unsteady airfoil motion. As a computational example, a three-degree-o f-freedom NACA 64A010 airfoil is considered using representative values of the structural parameters. The method is shown to be both stable and accurate, and the time response for several choices of initial conditions and reduced freest ream density is presented. Oscillations with either growing or decaying amplitudes are indicated depending upon the prescribed initial conditions. OR the case of flow over an airfoil in a freestream at Mach numbers near 1, small amplitude motions of the body surface can produce large variations in the aerodynamic forces and moments acting on the structure. In addition, phase differences between the flow variables and the resultant forces may be great. These characteristics tend to enhance the probability of encountering aeroelastic instabilities in the transonic flow regime, and thus evidence a need for tech- niques of analyzing the coupled unsteady flowfield and resultant structural response in such situations. In the subsonic and supersonic cases, the governing flow equations may be linearized such that the aerodynamic forces depend upon the body motion in a linear fashion. Moreover, the resultant forces acting on the airfoil may be obtained through superposition by summing the contributions due to each of the various types of body motion permitted. This allows the linear structural equations of motion to be solved independent of the governing aerodynamic equations which provide only the force coefficients. Uncoupling of the fluid and structural equations is not, in general, possible for the transonic regime due to its inherent nonlinear nature. Recent advances in computational methods have made several approaches available for computing unsteady tran- sonic flows. While a number of different techniques have evolved and various physical problems have been con- sidered, M6 the unsteady body motion was generally prescribed as a known function of time, thereby precluding the simulation of true aeroelastic behavior. Only more recently have these procedures been applied to actual aeroelastic problems.17'18 It is the intent here to describe a method for obtaining the time-dependent response of a two- dimensional airfoil in transonic flow and to provide a computational example by applying this technique to a physical situation of practical interest. The governing aerodynamic equation of motion is assumed to be the unsteady low-frequency small-disturbance transonic equation for the velocity potential function which is capable of simulating nonlinear flow phenomena including irregular shock wave motions. Solutions to this equation have corn-

Experiments in unsteady transonic flow

Abstract: The static and dynamic response of a 0.5-m-chord airfoil were measured in the NASA-Ames 11- by 11-Foot Transonic Wind Tunnel. The effects of mean angle of attack, Reynolds number, oscillation mode, and frequency were investigated over a range of subsonic and transonic Mach numbers. Unsteady pressure distributions and loads on an oscillating NACA 64A010 airfoil are discussed. The unsteady pressure distributions are compared with classical subsonic theory and with newer unsteady aerodynamic codes. The experimental data are also used to assess the validity of linearity and modal superposition in the transonic-flow regime.

Supercritical flow about a thick circular-arc airfoil

Abstract: The supercritical flow about a biconvex circular-arc airfoil is being thoroughly documented at Ames Research Center in order to provide experimental test cases suitable for guiding and evaluating current and future computer codes. The effects of angle of attack, effects of leading and trailing-edge splitter plates, additional unsteady pressure fluctuation (buffeting) measurements and glow-field shadowgraphs, and application of an oil-film technique to display separated-wake streamlines were studied. Computed and measured pressure distributions for steady and unsteady flows, using a recent computer code representative of current methodology, are compared. It was found that the numerical solutions are often fundamentally incorrect in that only strong (shock-polar terminology) shocks are captured, whereas experimentally, both strong and weak shock waves appear.

Real Flow Limitations in Supersonic Airplane Design

Abstract: angle of attack for this example i s found to be approximately 15 degrees. Experience indicates that the airstream normally Experimental studies, including pressure measurements, will not be able to flow around the leading edge at this large force measurements and flow visualization techniques, have angle of attack without flow separation. This i s particularly shown that predicted aerodynamic performance levels of supertrue for the thin airfoils that are characteristic of supersonic sonic wings can be achieved only when the flow remains wing designs. This leading.edge flow separation completely attached over the entire wing surface. alters the character o f the flow pattern over the wing. The nature of the breakdown of potential flow on supersonic wings is discussed and illustrated with experimental f low visualization pictures and wind-tunnel data. Various types of flow breakdown are examined. Simplified flow analogies that explain these flow phenomena are developed. Practical procedures that ensure design for attached flow at prescribed con. ditions are described. Flow analogies are used to explore the impact of various airplane design parameters on the breakdown of attached flow. 1.0 Introduction The design of efficient, very highly swept supersonic wings is one of the more difficult problems in aeronautics. These highly swept wings are of interest because they have the potential, according to theory, o f having relatively low drag a t super. sonic lifting conditions. LWell known supersonic wing theory' indicates that the leading edge of a wing must be a t an angle of sweepback greater than the angle weak shockwaves make with the free stream a t corresponding Mach numbers to achieve low drag a t lifting conditions. Sweepback angles of 70 to 75 degrees are necessary for Mach numbers in the range of 2.0 to 3.0 Theoretical predictions indicate that an airplane with a wing of such high sweep would have an advantage of approximately 15 to 20 percent in liftldrag ratio when compared to an airplane having a much lower sweepback angle (for example, 50 degrees). When i t was first attempted to substantiate these very encouraging predictions with wind-tunnel models, it was found that the experimental results did not confirm them a t all. Subsequent examinations revealed that the low drag predicted by theory was not achieved because the flow pattern around the wings, implicit in theory, did not occur in practice. Viscosity, which normally has a relatively small effect on the overall f low over wings a t normal cruise lift conditions, had a rather substantial effect on these highly swept wings. Consider as an example a wing a t Mach 3.0 and a t an angle of attack of 4 degrees-typical supersonic conditions. With the wing swept 75 degrees to achieve low drag, the Mach number component normal t o the leading edge i s 0.78. Hence near the wing leading edge, a recognized subsonic flow condition i s produced. The leading edge flow is governed by the angle normal to the leading edge. Using simple sweep theory. the normal !d Leadingedge flow separation i s only one of the reasons why the predicted low drag levels o f highly swept wings could not be obtained. The flow over the wing, which i s a t a relatively low pressure, must adjust t o freestream pressure through a shock wave at the trailing edge. If the theoretical f low requires too large a pressure rise, trailing-edge separation occurs. Again the flow pattern postulated by theory cannot occur and the theoretical drags cannot be achieved. Similar problems can occur on other partsof sucha highly swept wing. The establishment o f a f low consistent with theoretical low drag is, therefore, contingent on the response of the boundary layer to potentially severe conditions a l l over the wing. The development and behavior of highly swept wing boundary layers under complicated three-dimensional flow conditions is not amerable to theoretical calculations. Necessary wing design limitations cannot be defined strictly on the basis of analytical studies, and therefore had t o be developed from experimental test programs. This paper presents a comprehensive set o f design conditions that can be used to define efficient, highly swept super. sonic wings. I f these conditions are applied as constraints to theoretical calculations, the flow pattern resulting from analysis would not have a very large effect on the wing boundary layers and the theoretical flow, and drag, could be expected to be obtained in practice. The results presented in this paper are based on work that began in the la te 1950s and was carried through the U.S. SST program until cancellation of the program in 1971. The object of the work was to develop methods for the design of efficient supersonic wings. More recently. interest in the design of such wings has been renewed both for eventual commercial' and military3 applications. For the latter case, not only does the designer require low drag a t cruising conditions, but he also requires a reasonable flow at higher l i f t coefficients associated with military maneuvers. A review of design methods to accomplish this is therefore timely and appropriate, and forms the subject of this paper. In Section 2 the basic characteristics of supersonic wing planforms are discussed, pointing out the advantages of highly swept wings in supersonic flow. This i s followed by a review of experimental results illustrating the basic flow problems of highly swept wings. The potential effects of warping the sur. face of such wings, (e.g., camber and twist) are discussed in

Boundary layer measurements on a two-dimensional wing with flap and a comparison with calculations

Abstract: Measurements were performed on a wing flap configuration, which was so designed that flow separations occur nowhere, apart from a small laminar separation bubble on the wing nose. The measurements comprise surface pressure measurements, boundary layer and wake traverses at 16 stations, and flow visualization tests to establish the presence of separation bubbles and boundary layer transition regions. The data resolve the various flow phenomena sufficiently well to provide a significant test case for calculation methods for the flow around multi-element airfoils. Comparison with such a calculation method showed satisfactory agreement in many respects. A need for improved modelling was found to exist in some regions, particularly for the wing wake above the flap. The investigation has been performed under contract with the National Agency for Aerospace Programs (NIVR, contract numbers 1738 and 1812). Paper presented for the AGARD Symposium on "Turbulence boundary layers: experiments, theory and modelling", 24-25 September 1979, The Hague, The Netherlands.

Computation of subsonic and transonic flow about lifting rotor blades

Abstract: An inviscid, nonconservative, three-dimensional potential flow code has been developed for computing the quasi-steady flow about an isolated lifting rotor blade. Calculations from the code were compared with chordwise pressure measurements obtained in a wind tunnel on a nonlifting rotor at transonic tip speeds at advance ratios from 0.40 to 0.55. The overall agreement between theoretical calculations and experiment was good. To illustrate the early capability of the program, the flow about a hypothetical lifting rotor blade having twist, airfoil thickness taper, and a 20 deg sweptback tip was analyzed at azimuthal positions of 60, 90, and 120 deg for an advance ratio of 0.342. A typical run on a CDC 7600 computer required about 5 min for one rotor position at transonic tip speeds.

Shapes for rotating airfoils

Abstract: This invention is an airfoil which has particular application to the blade or blades of rotor aircraft and aircraft propellers. The airfoil thickness distribution, camber and leading edge radius is shaped to locate the airfoil crest at a more aft position along the chord, and to increase the freestream Mach number at which sonic flow is attained at the airfoil crest. The upper surface of the airfoil has a general reduction in the surface slope back to the maximum ordinate which is about 40 percent of the airfoil chord. The reduced slope causes a reduction in velocity at the airfoil crest at lift coefficients from zero to the maximum lift coefficient. The leading edge radius is adjusted or shaped so that the maximum local Mach number at 1.25 percent chord and at the designed maximum lift coefficient is limited to about 0.48 when the Mach number normal to the leading edge is approximately 0.20. The lower surface leading edge radius is shaped so that the maximum local Mach number at the leading edge is limited to about 0.29 when the Mach number normal to the leading edge is approximately 0.20 and the lift coefficient is in the range of 0.0 to -0.2. This design moves the drag divergence Mach number associated with the airfoil to a higher Mach number over a range of lift coefficients resulting in superior aircraft performance.

NASA low- and medium-speed airfoil development

Abstract: The status of NASA low and medium speed airfoil research is discussed. Effects of airfoil thickness-chord ratios varying from 9 percent to 21 percent on the section characteristics for a design lift coefficient of 0.40 are presented for the initial low speed family of airfoils. Also, modifications to the 17-percent low-speed airfoil to reduce the pitching-moment coefficient and to the 21-percent low speed airfoil results are shown for two new medium speed airfoils with thickness ratios of 13 percent and 17 percent and design-lift coefficients of 0.30. Applications of NASA-developed airfoils to general aviation aircraft are summarized.

AGARD two-dimensional aeroelastic configurations

Abstract: The development of reliable, efficient methods for the calculation of unsteady aerodynamic forces in the frequency-critical transonic speed regime can be enhanced by the availability of a limited number of test cases for the comparison of competing methods. Seven test cases are presented for airfoils with thickness from 6.0% to 16.5%: a biconvex parabolic arc airfoil, three conventional airfoils, and three cambered supercritical airfoils. The aerodynamic conditions such as Mach number, mean angle of attack, and oscillation amplitude and frequency are also given. Recommendations are made for uniformity in definition and reporting to enhance desired comparison for the aeroelastician.

On sound radiation from the trailing edge of an isolated airfoil in a uniform flow

Abstract: An experimental investigation has been conducted to determine the physical process of the noise production from the trailing edge of an isolated two-dimensional airfoil embedded in a low turbulence uniform mean flow. The Reynolds number of the airfoil based on chord was greater than 1,000,000 and that the boundary layer was fully turbulent at the trailing edge. Smoke injection technique and spark shadowgraphy were used to study the structural features of the boundary layer. Two point joint statistical analyses were made on the surface pressure, the radiated sound and the relationship between the two quantities. Operating conditions included two free stream velocities and two angles of attack for both a naturally developed and an artificially tripped boundary layer. Flow visualizations revealed the existence of large scale coherent motions in the outer region of the boundary layer. The observed coherent motions had scales of the order of boundary layer thickness and a convection velocity near the free stream velocity. The production process of the airfoil trailing edge noise was determined to be the convection of the large scale coherent eddies over the trailing edge of the airfoil. The noise field so generated was found to be rather coherent and dipole-like.

Numerical Solution for Airfoils near Stall in Optimized Boundary-Fitted Curvilinear Coordinates

Abstract: Boundary-fitted curvilinear coordinate systems are optimized for viscous flows about arbitrary airfoils at angles of attack such that boundary-layer-dependent grid systems for high Reynolds numbers are generated efficiently. The grid systems are utilized in implicit finite-difference solutions. Solution of a one-dimensional model equation is compared with the theoretical solution. The unsteady Navier-Stokes equations are solved for the incompressible flow around a cylinder and around NACA airfoils approaching stall. The predicted flows around a NACA 6412 airfoil near stall at Reynolds numbers of 4x 10 and 2x 10 are compared with the experimental observations obtained in a smoke tunnel.

Effects of turbulence model selection on the prediction of complex aerodynamic flows

Abstract: Numerical simulations of viscous transonic flow over a circular-arc airfoil and in a diffuser are described. The simulations are made with a new computer program designed to serve as a tool in the development of improved turbulence models for complex flows. The program incorporates zero-, one-, and two-equation eddy viscosity models and includes a variety of subsonic and supersonic boundary conditions. The airfoil flow contains a shock-separated boundary-layer interaction that has resisted previous attempts at simulation. The diffuser flow also contains a shock-boundary-layer interaction, which has not been simulated previously. Calculations using standard turbulence models, developed originally for incompressible unseparated flows, are described. Results indicate that although there are interesting differences in predictions between the various models, none of them predict the flows accurately. Suggestions for improved turbulence models are discussed.