Mark D. Maughmer

Multipoint Inverse Airfoil Design Method Based on Conformal Mapping

A method of multipoint inverse airfoil design for incompressible potential flow is presented. Multipoint design is handled by dividing the airfoil into a number of desired segments. For each segment, the velocity distribution is prescribed together with an angle of attack at which the prescribed velocity distribution is to be achieved. In this manner, multipoint design objectives can be taken into account in the initial specification of the velocity distribution. In order for the multipoint inverse airfoil design problem to be well posed, three integral constraints and several conditions arise that must be satisfied

Generalized Multipoint Inverse Airfoil Design

In a rather general sense, inverse airfoil design can be taken to mean the problem of specifying a desired set of airfoil characteristics, such as the airfoil maximum thickness ratio, pitching moment, part of the velocity distribution, or boundary-layer development. From thie information, the corresponding airfoil shape is determined. We present a method that approaches the design problem from this perspective. In particular, the airfoil is divided into segments along which, together with the design conditions, either the velocity distribution or boundary-layer development may be prescribed

Design of winglets for high-performance sailplanes

Although theoretical tools for the design of winglets for high-performance sailplanes were initially of limited value, simple methods were used to design winglets that gradually became accepted as benefiting overall sailplane performance. To further these gains, an improved methodology for winglet design has been developed. This methodology incorporates a detailed component drag buildup that includes the ability to interpolate input airfoil drag and moment data across operational lift coefficient, Reynolds number, and flapsetting ranges. Induced drag is initially predicted using a relatively fast multi- lifting line method. In the final stages of the design process, a full panel method, including relaxed-wake modeling, is employed. The drag predictions are used to compute speed polars for both level and turning flight. The predicted performance is in good agreement with flight-test results. The straight and turning flight speed polars are then used to obtain cross-country performance over a range of thermal strengths, sizes, and shapes. Example design cases presented here demonstrate that winglets can provide a small, but important, performance advantage over much of the operating range for both span limited and span unlimited high-performance sailplanes.

Experimental Investigation of Gurney Flaps

The aerodynamics of a Gurney-flap-equipped airfoil has been explored by means of low-speed wind-tunnel experiments performed at a chord Reynolds number of 1:0 10. Various chordwise locations and sizes of Gurney flaps were tested. Surface-pressure distributions and the wake momentum deficit were measured and used to determine lift, pitching moment, and drag. Compared with the clean airfoil, the measured maximum lift coefficient can be increased by nearly 30%with these simple devices. The amount of lift increase has a nearly linear dependency on the chordwise location and size of the Gurney flap. Minimum drag is primarily affected by the flap size and, to a lesser extent, by the chordwise location. The Gurney flap increases in maximum lift are obtained by increasing the lower-surface pressures over the aft part of the airfoil. At the same time, themagnitude of pressure peak on the upper surface near the leading edge is reduced such that the upper-surface pressures over themiddle parts of the airfoil are reduced and the separation point is moved aft by the reduced pressure-recovery gradients. As expected, this increases the aft loading and results in an increased nose-down pitchingmoment. As the angle of attack is decreased, the influence of a Gurney flap extending from the lower surface likewise decreases as the flap is increasingly immersed in the thickening boundary layer. A Gurney flap mounted to the upper surface behaves in the opposite way: increasing the negative lift at low angles of attack and having less and less influence as the angle of attack is increased. AlthoughGurney flaps result in significantly higher drags for airfoils with extensive runs of laminar flow, this disadvantage disappears as the amount of turbulent boundary-layer flow increases, as is the case with fixed transition near the leading edge of the airfoil.

Relaxed-Wake Vortex-Lattice Method Using Distributed Vorticity Elements

A lifting-surface method is presented that uses elements having distributed vorticity to model lifting surfaces and their shed wakes. Using such distributed vorticity elements allows the representation of a force-free continuous wake-vortex sheet that is free of numerical singularities and is thus robust in its numerical rollup behavior. Unlike other potential-flow methods that use discrete vortex filaments having solid-core models at their centers to avoid problems with the singularities, the numerical robustness of the new method is achieved without the subsequent solution being dependent on the choice of a cutoff distance or core size. The computed loads compare well with results of classical theory and other potential-flow methods. Its numerical robustness, computational speed, and ability to predict loads accurately make the new method ideal for the investigation of applications in which the loadings on a lifting surface depend strongly on the influence of the wake and its shape, as is the case for the two application examples presented: formation flight and rotating-wing systems.

Design and experimental results for a high-altitude, long-endurance airfoil

Currently, there is interest in the development of high-altitude, long-endurance vehicles for a number of missions including communications relaying, weather monitoring, and provision of targeting information for cruise missiles. The preliminary design of such aircraft is complicated, however, by the lack of suitable airfoils. This is due to the fact that such vehicles, unlike those for which the majority of airfoils have been developed in the past, operate at fairly high lift coefficients and at relatively low Reynolds numbers. Thus, to provide realistic airfoil performance information for preliminary design efforts, an airfoil has been designed for an aircraft with missions similar to those noted. The airfoil is unflapped and has a thickness of 15% chord. The design Reynolds number range is 7 x 10 to 2 x 10. Low drag is predicted for lift coefficients ranging from 0.4, which corresponds to a high-speed dash, to 1.5, the maximum endurance condition. Further, the airfoil is designed specifically such that the maximum lift coefficient is unaffected by surface contamination. Consequently, takeoff and landing in rain or with insect residue on the wings should present no special difficulties. The airfoil has been tested in the NASA Langley Low-Turbulence Pressure Tunnel and, with the exception of the maximum lift coefficient prediction, the results generally confirm the theoretical predictions.

THE DESIGN AND TESTING OF A WINGLET AIRFOIL FOR LOW-SPEED AIRCRAFT

The PSU 94-097 airfoil has been designed for use on winglets of high-performance sailplanes. The design problem is difficult because the airfoil must operate over a wide range of Reynolds numbers, and this range includes values that are relatively low. To validate the design tools, as well as the design itself, the airfoil was tested in the Penn State Low-Speed, Low-Turbulence Wind Tunnel from Reynolds numbers of 2.4 × 10 5 to 1.0 × 10 6 . In addition to transition-free measurements, potential drag reductions using artificial turbulators were explored, although the benefits were found to be limited for this application. Finally, performance predictions from two well-known computer codes are compared to the data obtained experimentally, and both are found to generate results that are in good agreement with the wind-tunnel measurements. Nomenclature CP pressure coefficient, (pl - p∞ )/q∞ L. lower surface R Reynolds number based on free-stream conditions and airfoil chord S. boundary-layer separation location, xS/c T. boundary-layer transition location, xT/c U. upper surface c airfoil chord cd profile-drag coefficient cl section lift coefficient cm section pitching-moment coefficient about the quarter-chord point p static pressure, Pa (lbf/ft 2

Computational Fluid Dynamics Compatible Transition Modeling Using an Amplification Factor Transport Equation

A new laminar–turbulent transition model for low-turbulence external aerodynamic applications is presented that incorporates linear stability theory in a manner compatible with modern computational fluid dynamics solvers. The model uses a new transport equation that describes the growth of the maximum Tollmien–Schlichting instability amplitude in the presence of a boundary layer. To avoid the need for integration paths and nonlocal operations, a locally defined nondimensional pressure-gradient parameter is used that serves as an estimator of the integral boundary-layer properties. The model has been implemented into the OVERFLOW 2.2f solver. Comparisons of predictions using the new model with high-quality wind-tunnel measurements of airfoil section characteristics confirm the predictive qualities of the model, as well as its improvement over the current state of the art in computational fluid dynamics transition modeling at approximately half the computational expense.

Simplified linear stability transition prediction method for separated boundary layers

An existing transition prediction method for attached, two-dimensional, incompressible boundary layers based on linear stability analysis is extended to separated, two-dimensional, incompressible boundary layers such as those found in laminar (transitional) separation bubbles. It is shown why the present method, which tracks the growth of disturbances at many different frequencies, is more accurate than the so-called envelope methods for nonsimilar boundary-layer developments. Reliance on a database of precalculated stability characteristics of known velocity profiles makes this method much faster than traditional stability calculations of similar accuracy. The Falkner-Skan self-similar profiles are used for attached flow, and a new, very general family of profiles is used for separated flow. Comparisons with measured transition locations inside the bubble show good agreement over the range of chord Reynolds numbers and airfoil angles of attack of interest.

Numerical Investigation on the Aerodynamics of Oscillating Airfoils with Deployable Gurney Flaps

To assess their application to rotorcraft, the two-dimensional aerodynamics of deployable Gurney flaps, referred to as miniature trailing-edge effectors, are explored using computational fluid dynamics. These deployable devices have a height of only a few percent of the airfoil chord and deploy normal to the airfoil surface near the trailing edge. Their small size, low inertia, and small added mass make them well suited for deployment in high-frequency applications such as those needed for rotorcraft. A combination of wind-tunnel measurements using airfoils fitted with Gurney flaps and unsteady circulatory theory are used to validate the computational fluid dynamics, and grid and time-resolution studies are used for code verification. Qualitative and quantitative agreement of the effects of a Gurney flap with experiments and theory suggest that the computational fluid dynamics results are valid. These investigations examine the effects of the chordwise positioning and deployment frequency of the miniature trailing-edge effectors. In doing so, their operation on both static and dynamically pitching airfoils is considered. Through these studies, a number of physical insights into miniature trailing-edge effectors and Gurney flap aerodynamics have been obtained. These insights have led to the introduction of a scaling parameter that easily accounts for compressibility effects, an understanding of the aerodynamic consequences due to positioning miniature trailing-edge effectors upstream of the trailing edge, and an assessment on the benefits of using of miniature trailing-edge effectors for active stall alleviation on an airfoil oscillating in pitch.