Lift Prediction Research Articles

Method for the prediction of wing maximum lift

This article describes the development of a semiempirical three-dimensional method for the prediction of maximum lift for complex multielement wing geometries. The method is a combination of cost effective and reliable CFD technology (a surface panel method), and an empirically observed phenomenon occurring at maximum lift conditions that is introduced here as the pressure difference rule. The panel method solutions used in conjunction with the pressure difference rule yield surprisingly accurate predictions of maximum lift for both clean wings as well as multielement wings. Comparisons with experimental data are presented for increasingly complex high-lift wing geometries including full transport aircraft configured for landing.

カプセル形状物体の空力性能に及ぼす閉塞率の影響

Low-speed aerodynamic characteristics and effects of the blockage ratio of an axisymmetric capsule configuration are experimentally investigated. The flow conditions in a closed-type test section with high blockage ratio are obtained by setting a circular duct coaxially in the open-type test section of the wind tunnel. The aerodynamic loads of similar scale model of three kinds with body diameter of 100, 180 and 240mm are measured in both open-type and closed-type test sections. Also the pressure distributions along the model surface and along the duct wall are measured. From the investigations of experimental results, the following major conclusions are obtained on aerodynamic characteristics of such capsule-type configurations: (1) It is expected that the drag force of capsule-type configuration is strongly affected by blockage ratio effects. (2) The usual method of the wind tunnel wall effect correction is applicable to prediction of lift and pitching moment coefficients, but not sufficient to drag coefficient. (3) The velocity profiles in the closed type test section are much different from those in the open-type test section. In case of the high blockage ratio, the flow which has been accelerated because of the decrease of the section area, is bent by the curvature of the model tail and separates at the trailing edge. Such phenomena make the flow field complicated and result in the increase of drag force.

Biology, natural selection and the prediction of maximal wave-induced forces

Appropriate interpretation of body form often requires knowledge regarding the maximal force that an organism is likely to encounter in its lifetime. In many situations, prediction of maximal forces is nearly impossible, but the statistical distribution of ocean waves allows prediction of the maximal lift and drag to which a benthic plant or animal is subjected. These predictions can, in turn, be used to provide quantitative estimates of the severity of natural selection on specific attributes of body form.

Convergence of lift and drag predictions by a Morino panel method (VSAERO)

CONVERGENCE results from both two-dimensional and three-dimensional versions of a Morino-type code are presented an analyzed. In both two and three dimensions it is found that reasonably accurate lift and moment predictions are obtained using modest numbers of nominally uniform-sized panels, but induced drag predictions are seriously inaccurate and converge at best very slowly with increasing density. Two ways are found to improve accuracy and convergence of drag predictions: 1) use cosine spacing for chordwise distribution of panels on foil sections, or 2) deduce lift and drag from the far-field wake by a classical Trefftzplane analysis. Of the two methods, the far-field has superior accuracy and convergence properties and, indeed, produces highly accurate and stable drag predictions even from quite coarse panelizations. It is also shown that large benefits in accuracy and/or savings in computational effort are possible by use of Richardson extrapolation applied to results from two or more relatively coarse (but systematically related) panelizations. Contents Although methods have been extensively employed and validated for aerodynamic lift and moment calculations, they have a reputation for being inaccurate or unreliable with respect to drag. The work reported here was stimulated by attempts to apply the code VSAERO to calculate the lift and induced drag of complex wing-body configurations representing sailboat hull, keel, and rudder geometries,1 for which induced drag (effective span) is the characteristic that most strongly impacts performance. (Note that there exist various versions of VSAERO. The three-dimensional code used in this study, a public-domain version obtained directly from NASA in 1984 and currently distributed by COSMIC, may differ from commercial versions.) Conventional VSAERO drag predictions were found to be highly sensitive to details and density of panelization and in poor agreement with experiments. These studies, undertaken to discover the sources and magnitude of the errors, led eventually to usably accurate drag predictions by two methods that are believed to be applicable to most three-dimensional codes. Any code is a discrete approximation to a continuous flow: a mostly smooth body surface is approximated by an assemblage of triangular or quadrilateral panels, and continuous flow quantities (e.g., singularity strengths and pressure) are approximated by simple distributions over each panel. As the subdivision of the body is made successively finer, the discretized model approximates the true body geometry and the continuous flow more closely and so, presumably, computed flow quantities such as lift and drag will converge toward the exact continuous solution. The rate of convergence is of considerable practical interest because the computational effort of a method increases rapidly with the number TV of panels. Using a finer panelization than necessary is, therefore, very expensive in terms of time and computer resources. Also, if reliable rates of convergence can be established for some systematic way of subdividing the panels, a projection to infinite density is possible from two or more relatively coarse panelizations using Richardson extrapolation. VSAERO2'3 is a low-order three-dimensional subsonic code for general configurations. In common with many current production codes, for its potential-flow calculations it adopts the Morino formulation4 with constant known source and unknown doublet panels. In the solution phase, a Morino code sets up and solves a large system of linear equations for the unknown doublet densities on the panels. In the phase, surface velocities, hence pressures, are obtained by local differencing of the doublet densities; these pressures are multiplied by areas and normals and summed to obtain total forces. This near-field force calculation is referred to in the sequel as panel pressure analysis (PPA). A principal tool for investigating the sources of drag error was VSA2D, a two-dimensiona l incompressible code based on the same singularity model, the same integral equation, and the same pressure, force, and moment calculations as VSAERO. VSA2D alternatively evaluates lift and drag from a far-field (FFA), which is extremely simple in two dimensions. Numerical results are given for two airfoils for which exact analytic results are available for comparison: a biconvex section and a Joukowsky section. Some lift and drag results are plotted in Fig.l against I/TV, for both uniform and cosine spacings on the 10% biconvex section, with TV ranging from 6 to 80.

A direct viscid-inviscid interaction scheme for the prediction of two-dimensional aerofoil lift and pitching moment in incompressible flow

SummaryThis paper presents a method for assessing two-dimensional aerofoil lift and pitching moment characteristics including trailing edge and gross laminar separation. The model used is a direct viscid-inviscid interaction scheme based on a vortex panel method with boundary-layer corrections and an inviscidly modelled wake. The integral boundary-layer methods adopted behave well in the region of separation and thus, good comparisons with measured separation characteristics are obtained. Generally the predictions of lift and pitching moment may be considered to be within the experimental error, but where this is not the case, the applicability of the modelling technique is discussed.

Prediction of vortex lift of non-planar wings by the leading-edge suction analogy

SummaryA three-dimensional panel method has been used to calculate edge-suction forces for thin sharp-edged wings in incompressible flow. The suction forces have been used to estimate the vortex lift on the wings by means of the leading-edge suction analogy due to Polhamus.The results for planar wings are in acceptable agreement with other methods based on the suction analogy. A limited comparison with results from experiments for non-planar wings revealed good prediction of lift and drag increments associated with the deflection of leading and trailing edge flaps for ‘conventional’ wings of high sweep, but only moderate agreement for a grossly non-planar configuration.

Efficient self-consistent viscous-inviscid solutions for unsteady transonic flow

An improved method is presented for coupling a boundary layer code with an unsteady inviscid transonic computer code in a quasi-steady fashion. At each fixed time step, the boundary layer and inviscid equations are successively solved until the process converges. An explicit coupling of the equations is described which greatly accelerates the convergence process. Computer times for converged viscous-inviscid solutions are about 1.8 times the comparable inviscid values. Comparison of the results obtained with experimental data on three airfoils are presented. These comparisons demonstrate that the explicitly coupled viscous-inviscid solutions can provide efficient predictions of pressure distributions and lift for unsteady two-dimensional transonic flows.

An assessment of the use of low-order panel methods for the calculation of supersonic flows

SummaryThree low-order panel methods developed for the analysis of supersonic flows have been used to make calculations for a number of test configurations, with the aim of establishing the range of problems for which this class of computational method yields adequate solutions. The programs investigated were the Woodward USSAERO/C program, the related NLRAERO program, and the British Aerospace Warton supersonic panel program. Results obtained using these programs have been evaluated against theoretical and experimental data for a number of test cases covering wing-alone, body-alone and wing-body geometries. It is concluded that low-order panel methods can provide adequate solutions for supersonic flows about wings, bodies and wing-body combinations, provided the assumptions implicit in the linearised potential flow model are not violated. Examples show that the prediction of lift and pitching moment curve slopes for quite complex configurations may be acceptable, but that the detailed pressure distributions are not always predicted satisfactorily. In particular, serious problems are encountered in calculating the flow about wings with rounded supersonic leading edges due to the linearised flow model which is used.

Prediction of vortex lift on interacting delta wings in incompressible flow

Vortex flow modeling is used to calculate the steady inviscid incompressible flow past one, two and three delta wing configurations. The wings are modeled with vortex lattices and the leading and trailing-edge sheets are modeled by segmented straight vortex filaments. Aerodynamic characteristics are obtained for a range of geometry and angle of attack.

Aerodynamic design optimization trim analysis of canard conventionalconfigurations

A design study has been conducted to optimize trim cruise flight of high performance general aviation canard aircraft which achieve minimum drag. In order to investigate the advantages and disadvantages of canard configured aircraft, corresponding conventional tail-aft aircraft were designed and used for comparison. Two-dimensional coupled lift and drag coefficient predictions of the canard and wing airfoil shapes were obtained by coupling inviscid results from a vortex panel multielement program to a momentum integral boundary layer analysis. By using the results of the two-dimensional vortex panel analysis, a vortex lattice method was employed to predict the finite wing results. The analysis utilized a turbulent airfoil and a natural laminar airfoil, which are two NASA state-of-the-art airfoil sections. The canard aircraft designs give quantitative results of wing and canard loadings, wing-to-canard moment arm ratios, and aspect ratio effects for trim cruise flight for a wide range of wing-to-canard area ratios. Both canard and baseline aircraft achieved a 25-30% improvement in performance over typical current technology aircraft, but high canard loading necessary for trim resulted in slightly poorer cruise performance of the canard aircraft for equal fuel as compared to the baseline designs. However, when takeoff gross weight was held the same by reducing the fuel payload, the canard designs achieved longer ranges than the baselines. The required positive decalage angle between the canard and the wing guarantees that the canard will stall first, thereby preventing the wing from stalling, and thus having a stall- and, hence, spin-proof configuration.

On the Application of Linearized Theory to Multi-Element Aerofoils Part I: Tandem Flat Plate Aerofoils

SummaryA linearized two-dimensional incompressible potential flow theory for two-element uncambered tandem aerofoil sections is developed. It leads to formulas for lift and moment which can be calculated rapidly on a programmable hand calculator, and which reduce, when the two aerofoil elements come together, to the familiar thin-aerofoil formulas for an aerofoil with a simple flap. The theory is shown to give lift and moment predictions which are in good agreement with predictions of numerical potential flow theory.

Quasi‐2‐D Forces on a Vertical Cylinder in Waves

Prediction of the total force on a vertical cylinder in waves has been investigated. Drag and inertia coefficients on a small section of span have been measured for a range of orbital shapes. There is considerable scatter but rms in-line force is in reasonable agreement with U-tube data unless orbital shape approaches circular when local and total force is markedly overestimated on a quasi-2-D basis. For surface Kc less than about 12 lift is predominantly at twice the wave frequency. A quasi-2-D calculation using U-tube data underestimates total force for deep-water waves and in general lift prediction is somewhat unreliable.

Comment on "Analytical Prediction of Vortex Lift"

S comments are warranted concerning the paper by J.W. Purvis entitled Analytical Prediction of Vortex Lift, which appears in the April 1981 issue of the Journal of Aircraft. The first comment is relative to the use of singular loadings in the design of mean camber shapes for wings experiencing leading-edge-vortex separated flow. By comparison, Ref. 1 outlines a low-drag, separated-flow design procedure which uses a more appropriate attached-flow initial loading that is nonsingular. There the final solution for the mean camber surface is obtained by iterating to find the shape-yielding minimum separated-flow drag at the required lift coefficient. The second comment is that the section-induced drag, see Eq. (12), does not have an elliptical distribution over the wing as proposed, but only in the Trefftz plane. This is well known (e.g., Ref. 2), and means that for most wings of interest the section-induced drag has to be determined in the near field. The consequence of this wrong assumption leads to an error in Eq. (26) and, hence, in the magnitude of the leading-edge suction force and vortex flow aerodynamics for wings with varying leading-edge sweep. The third comment deals with the missing multiplication by 2 in Eqs. (27), (30), (33), and (34), the missing division by 2 in Eqs. (28) and (37), and the typographical error in Eq. (32). Equation (32) should read

Steady flow and static stability of airfoils in extreme ground effect

Steady flow over a thin airfoil-like body in close proximity to a plane ground surface is analysed on the basis of a one-dimensional, but non-linear, gap-region flow, matched to the outside via a trailing edge which may possess significant flap-like appendages. The resulting lift and moment predictions are used to estimate quasisteady stability derivatives in heave and pitch. The results are applied to longitudinal stability of tail-less uncambered airplanes, and to manoeuvring of ships near to a bank, indicating instability in both cases.

A Numerical Study of Vortex Shedding From One and Two Circular Cylinders

SummaryA discrete-vortex representation of the wake of a circular cylinder, in which vortices are convected in a potential-flow calculation and maintain their identities unless they approach one another or a surface closely, predicts many of the unsteady flow features and is computationally more efficient than other schemes. The mean rate of shedding of vorticity is adjusted to be compatible with experiments at a high subcritical Reynolds number of 3 × 104 and the model gives reasonable predictions of separation, drag, lift, Strouhal number and vorticity loss in the formation region. The method is extended to accommodate a second cylinder and many of the surprising features which have been observed experimentally with two cylinders in a side-by-side arrangement are reproduced.

An Aerodynamic Analysis of Several Hypersonic Research Airplane Concepts from M= 0.2 to 6.0

Several conceptual hypersonic research airplanes, designed within the constraints of a B-52 launch aircraft, have been studied experimentally and analytically at Mach numbers from 0.2 to 6.0. Vehicles built to these criteria for Mach 6 cruise were shown to be feasible, if careful attention was paid to the low speed lift, drag, and high angle of attack stability to assure successful landings and transonic pitch angle maneuvers. The integrated scramjet engine drag was high at subsonic speeds and appears to be constant with Reynolds number. The variable geometry airfoil used previously to improve directional stability was shown to be equally adaptable to the improvement of longitudinal stability. The vortex lattice theory gave good subsonic predictions of lift, drag due to lift, and pitching moments. Wind tunnel tests must be relied on for the drag at zero lift, trim, static margins and lateral-directional stability. The Gentry Hypersonic Arbitrary Body Program gave good predictions of the trends of lift, drag, and pitching moments with angle of attack at Mach numbers above 3, but the level of the values were not consistently predicted. No currently available theory or program gave accurate predictions of directional stability or dihedral effects at hypersonic speeds.

Rolling Moments in a Trailing Vortex Flowfield

Rolling Moments in a Trailing Vortex Flowfield

Lift and Moment Prediction For an Oscillating Airfoil With a Moving Separation Point

An analytical method for predicting the perturbed aerodynamic reactions of a harmonically oscillating flat plate airfoil with time dependent point of separation is presented. It is shown that this method in conjunction with an empirical knowledge of the time history of the separation point can predict stall-flutter. Numerical results are presented and compared with existing theoretical and experimental results with special emphasis on torsional mode of oscillation.

Effects of Leading-Edge Vortex Flow on the Roll Damping of Slender Wings

The leading-edge suction analogy of Polhamus, which has proven useful for lift and drag predictions, has been extended in an effort to understand the vortex-flow effects on the roll damping of slender wings at subsonic speeds. Comparisons with experiment indicate that the method can be useful in the prediction of the large increase in roll damping with angle of attack associated with leading-edge vortex flow of highly swept, low-aspect-ratio wings. In addition, the newly developed forced-oscillation roll mechanism, suitable for testing at subsonic and transonic Mach numbers, has been used to obtain subsonic roll damping data on a series of 74° leading-edge sweep wing planforms. These data illustrate the effects of vortex flow on the damping-in-roll parameter of delta, arrow, and diamond planforms.

Severity comparisons of specified and actual impulse tests

problem. Errors in pressure prediction will affect drag predictions much more than lift predictions because leading edge suction is an important factor in resultant pressure drag. In conclusion, it is shown that good estimates of pressure distributions can be derived from the combination of calculation procedures presented here. Also accurate lift and drag predictions can be made up to moderate angles of attack in transonic mixed flow.