Wing-body Combinations Research Articles

Progress in Finite-Volume Calculations for Wing-Fuselage Combinations

Progress in the application of finite-volume methods to the calculation of transonic potential flows past general wing-body combinations is reviewed. Two different methods of generating boundary-conforming grids are investigated, and the results compared to provide an estimate of solution sensitivity to grid geometry. Both conservative and quasiconservative difference schemes are used in one of the coordinate systems. Results show that the error introduced by the quasiconservative formulation seems to be small, although a one-dimensional analysis suggests that schemes of this type may violate conservation of mass, except in the limit when all shocks are weak. Comparison of calculated results with experimental data for realistic fuselage geometries clearly shows the importance of modeling the effect of fuselage geometry upon the wing pressure distribution.

Comment on "Boundary-Layer- Induced Secondary Flows on Wing-Body Combinations"

Comment on "Boundary-Layer- Induced Secondary Flows on Wing-Body Combinations"

Calculation of wing-body pressures in incompressible flow using Green's function method

\0 0 3 A > /, 0 IV In the present paper, the finite element technique is applied to the calculation of three-dimensi onal steady incompressible potential flow around a wing-body combination, the main emphasis being placed upon the study of the aerodynamic interference effect between the wing and the body. The formulation of the problem is made in the form of an integral equation following Morino's method. By the use of the finite element technique combined with the collocation method, this integral equation is reduced to a set of linear algebraic equations. By solving this set, the pressure distribution over the surface of the wing-body combination is obtained. Wind tunnel experiments have been conducted at National Aerospace Laboratory of Japan in pace with the numerical analysis. It has been found that agreement between the numerical results obtained by the present method and those obtained by the wind tunnel experiments is very encouraging.

Three-Dimensional Flow over Wings with Leading-Edge Vortex Separation

Recent advances in a panel method for the solution of three-dimensi onal flow about wing and wing-body combinations with leading-edge vortex separation are presented. These advances were achieved as par't of an ultimately successful assault on two shortcomings of the method, namely convergence failures in seemingly random cases, and overprediction of lift coefficient for high aspect-ratio wings. Advances include the implementation of improved panel numerics for the purpose of eliminating the highly nonlinear effects of ring vortices around doublet panel edges, and the development of a least-squares procedure for damping vortex sheet geometry update instabilities. A variety of cases generated by the computer program implementing the method are presented. These cases are of two types. The first type consists of numerical studies, which verify the underlying mathematical assumptions of the method and moreover show that the results are strongly invariant with respect to such user dependent input as wing panel layout, initial sheet shape, sheet rollup, etc. The second type consists of cases run for the purpose of comparing computed results with experimental data, and these comparisons verify the underlying physical assumptions made by the method. a A & b B c CD Q

Side-Force Alleviation on Slender, Pointed Forebodies at High Angles of Attack

A new device was proposed for alleviating high angle-of-attack side force on slender, pointed forebodies. A symmetrical pair of separation strips in the form of helical ridges are applied to the forebody to disrupt the primary lee-side vortices and thereby avoid the instability that produces vortex asymmetry. Preliminary wind tunnel tests at Mach 0.3 and Reynolds no. 5,250,000 on a variety of forebody configurations and on a wing-body combination at angles of attack up to 56 degrees, demonstrated the effectiveness of the device.

Effects of Dynamic Aeroelasticity on Aircraft Handling Qualities

Body Combinations, Discussions by J.P. Giesing, Analytic Methods in Aircraft Aerodynamics, NASASP-228, 1969. Hink, G.R., Bills, G.R., and Dornfeld, G.M., A Method for Predicting the Characteristics of Control Configured Vehicles. Vol. H-Flexstab User's Manual, Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio, Rept. AFFDL-TR-74-91,Nov. 1974. Dillenius, M.F.E. and Nielsen, J.N., Prediction of Aerodynamics of Missiles at High Angles of Attack in Supersonic Flow, Nielsen Engineering and Research, Inc., Mountain View, Calif., Rept. NEAR TR-99, Oct. 1975. Lan, C.E., Calculation of Lateral-Directional Derivatives for Wing-Body Combinations With and Without Jet Interaction Effects, NASA CR-145251,1977. Lan, C.E., A Quasi Vortex-Lattice Method in Thin Wing Theory, Journal of Aircraft, Vol. 11, Sept. 1974, pp. 518-527. Lan, C.E. and Mehrotra, S.C., An Improved Woodward's Panel Method for Calculating Leading-Edge and Side-Edge Suction Forces, The University of Kansas Center for Research, Inc., Lawrence, Kansas, Tech. Rept. CRINC-FRL-266-3, Feb., 1979. Lamar, J.E., Extension of Leading-Edge-Suction Analogy to Wings with Separated Flow Around the Side Edges at Subsonic Speeds, NASA TR R-428, Oct. 1974. Margolis, K., Theoretical Calculations of the Lateral Force and Yawing Moment Due to Rolling at Supersonic Speeds for Sweptback Tapered Wings with Stream wise Tips. Subsonic Leading Edges, NACATN 2122, June 1950. Harmon, S.M., Stability Derivatives at Supersonic Speeds of Thin Rectangular Wings with Diagonals Ahead of Tip Mach Lines, NACA Rept. 925, 1949. flying qualities, such effects should not be overlooked in calculations or analyses directed toward investigation of compliance with the requirements of this specification. The specification is concerned mainly with desirable ranges of values on rigid body static and dynamic response parameters. There are methods available for estimating static aeroelastic corrections to rigid body aerodynamic stability derivatives; however, these are then used in rigid aircraft equations of motion. It seems quite possible that the desirable ranges of parameter values could be significantly affected by elastic mode degrees of freedom—particularly when some of the modes have natural frequencies of the same order of magnitude as the frequencies of the rigid body alone. It is not clear at all that the handling qualities should be specified by rigid body dynamic parameters when such mode interaction is present. In fact, the pilot would find it difficult to tell, for example, how much of a given pitch angle response to command input is due to rigid body and how much to lowfrequency elastic modes.

Incompressible Flow Past a Wing-Body Combination Using General Curvilinear Coordinates

SummaryIt is shown, by the successive application of coordinate transformations involving complex analytic functions, how a general curvilinear coordinate system can be constructed which is suitable for geometries consisting of a finite surface together with two semi-infinite cylinders. A typical example of such a geometry is considered which comprises a wing-body combination in which two semi-infinite unswept wings are attached to a finite body. The potential problem associated with non-lifting incompressible flow past the wing-body combination is formulated in the general curvilinear coordinate system and is solved numerically. The distribution of the pressure coefficient over the wing-body surface is presented.

Synthesis of Aerodynamic Transfer Functions for Elastic Flight Vehicles

This paper presents a method of generating the reasonable approximations to aerodynamic transfer functions on general configurations of elastic wings or wing-body combinations. The transfer functions are specified by asymptotic expansions in which either the polynomial or rational function approximation is applied. Procedures are described for incorporating a variety of quantitative and qualitative information concerning the unsteady aerodynamic behavior in both subsonic and supersonic flow regimes. Two types of power series approximations, power series with real coefficients and the other with complex coefficients, are applied. Consideration of the hereditary effect of wake vortices on the wing-bound vortices and the analogy with the behavior of a feedback control system provide useful guidance in selecting the form of approximation in both subsonic and supersonic flows. By relaxing the restriction imposed in the first-order piston theory, a limit as co^oo is discussed. Both the standard and extended Fade approximates s = # and s = R are studied in order to improve their accuracy at high k values. The above procedures are programmed in conjunction with the lifting surface theory, doublet lattice, and advanced Mach box scheme and demonstrated for the determination of AGARD wing aerodynamics and the flutter stability boundary for advanced aircraft configurations. The results appear to be satisfactory.

Hypersonic Flow Over Conical Wing-Body Combinations

SummaryThis paper shows how thin shock layer theory may be applied to wing-body combinations and also to yawed wings of caret and diamond section. The common feature of these cases is the interaction of the crossflow with the body slope discontinuity and the manner in which the resulting disturbances propagate through the shock layer. Practical computation of surface pressures is straightforward and comparison with experiment appears to be fairly good for the limited results available.

Aerodynamic Design of a Mach 2.2 Supersonic Cruise Aircraft

The McDonnell Douglas Corporation has conducted numerous Mach 2.2 supersonic aircraft design and in- tegration studies in support of the NASA Supersonic Cruise Aircraft Research (SCAR) program. This program traces the evolution of a baseline study configuration and an improved performance configuration through several aerodynamic design and trade study cycles. The impact of real-world constraints on configuration design is discussed. Previous studies have not addressed the Mach 2.2 cruise design condition and this work has resulted in a structurally feasible configuration capable of achieving £/D's in excess of 9 at this cruise Mach number. The purpose of this paper is to present the resulting design and wind-tunnel test results for two configurations. The wind-tunnel test results are compared to the analysis methods. N 1972, interest was renewed both at NASA and in the industry in conducting technology assessment studies on supersonic cruise aircraft. The NASA Supersonic Cruise Aircraft Research (SCAR) program emerged late in 1972, charged with the task of identifying, through aircraft design studies, key technologies whose pursuit would lead to im- proved aerodynamic efficiency, reduced operating costs, and environmental compatibility for typical next-generation supersonic cruise configurations. McDonnell Douglas (MDC) reassessed the entire spectrum of supersonic travel beginning with a market analysis and a review of technology available at various design Mach numbers. Results of these preliminary design studies indicated that a 273-passenger, Mach 2.2 aircraft offered the best mix of low operating costs, productivity, near-term technology materials, and reduced program risk for typical supersonic transport con- figurations. 1 Using this as a starting point, McDonnell Douglas conducted numerous aerodynamic studies, trade studies, and sizing studies in support of the SCAR program.2'3 A baseline study configuration, shown in Fig. 1, emerged, which was a structurally feasible arrow-wing configuration promising good cruise L/D's. Subsequent studies indicated that improved performance was available through wings optimized to reduce configuration trim drag. In 1975, a cooperative MDC-NASA wind-tunnel test program was conducted in which the performance of the study baseline configuration and an improved-perf ormance configuration was substantiated, and the analytical techniques used in their design were validated. Methods of Analysis The primary analytical tools used in the aerodynamic design and analysis of the McDonnell Douglas advanced supersonic cruise aircraft configuration have been the Woodward program4 and the Douglas Arbitrary Body Wave Drag Program.5 The McDonnell Douglas version of the Woodward program has been extensively modified to im- prove its versatility. In the SCAR studies it was used in both the inverse (optimization) and direct (analysis) modes. Wings were designed by optimizing the wing camber distributions for minimum drag due to lift at specified CL's, with and without specified pitching moments. Wings were primarily optimized as wings alone extended to the fuselage centerline, but some optimizations were done in the presence of the fuselage. Drag due to lift and wing-body pitching moments were computed by direct analysis of wing-body combinations including wing thickness effects. Wing panels were spaced equally spanwise and chordwise on both wings alone and wings exterior to the fuselage. All wings were represented by 9 spanwise and 12 chordwise panels, which is sufficient for converged solutions. Biquadratic interpolation was used to determine exterior wing camber distributions from wing-alone optimizations, and vice versa. A typical Woodward wing-body paneling scheme is shown in Fig. 2. Although not depicted on Fig. 2, the Woodward program was used in the full configuration mode to calculate wing-body pitching moments, including the ef- fects of forebody lift. Configuration zero-lift wave drag was calculated using the McDonnell Douglas-developed Arbitrary Body Wave Drag Program which calculates, based on the area rule theory,6'7 the wave drag of completely arbitrary configurations. All analyses were performed on full wing-body and wing-body- nacelle configurations at their cruise attitudes. While the program can accept cambered fuselages with exact cross sections, it has been determined that cambered fuselages with

Subsonic Wing-Body Interference for Missile Configurations at Large Angles of Attack

SummaryAn approximate method is presented for estimating the normal-force and pitching-moment characteristics (including the effects of wing-body interference) of wings mounted on bodies. A pair of wings placed side by side can be specified which, when operating at a certain angle of attack different from the geometrical angle of attack, have the same aerodynamic properties as the wings in the presence of the body. The equivalent wings and effective angle of attack are determined, and these enable the wing-body normal force and pitching moment to be estimated for wing-body combinations at angles of attack up to 90°. Comparisons made with the results of a specially conducted series of experiments on rectangular and delta planform wing-body combinations have provided gratifying supporting evidence for the theory.Estimates are also made of the normal force and pitching moment produced by two cone-cylinder bodies over the angle of attack range 0° to 90°. These estimates, when added to the wing-body normal-force and pitching-moment estimates, have resulted in a set of longitudinal aerodynamic characteristics which are generally close to those found experimentally. The method appears to have application in the preliminary design phase for slewing missiles.

Study of Low-Aspect Ratio Swept and Oblique Wings

Experimental forces and moments for two wing-body combinations having a) a swept wing and b) an oblique wing are compared. At all Mach numbers, the oblique wing (at its optimum sweep angle) had higher maximum lift-to-drag ratios than the fixed, swept wing. At high angles of attack, the direction of the pitching or rolling tendencies of the oblique wing was a function of the spanwise distribution of wing bend or washout for the two bends being investigated. At low angles of attack, linear theory gave satisfactory predictions of the subsonic liftcurve slope, the aerodynamic-center travel with Mach number, and the maximum lift-to-drag ratio.

Steady and Oscillatory Subsonic and Supersonic Aerodynamics around Complex Configurations

A general formulation for steady and oscillatory, subsonic and supersonic, potential linearized aerodynamic flows around complex configurations is presented. A linear integral equation relating the unknown potential on the surface of the body to the known downwash is used. The formulation is applied to the analysis of flowfields around wings and wing-body combinations. The surface is divided into small quadrilateral elements which are approximated with hyperboloidal surfaces. The potential is assumed to be constant within each element. This yields a set of linear algebraic equations. The coefficients are evaluated analytically. Numerical results for steady and oscillatory, subsonic and supersonic flows indicate that the method, is not only more general and flexible than other available methods, but is also fast, accurate, and in excellent agreement with existing results.

Comment on "Correlation of Wing-Body Combination Lift Data"

Comment on "Correlation of Wing-Body Combination Lift Data"

Comment on ''Simplification of the Wing-Body Problem"

THE formula for the total lift, including interference effects, for a wing mounted on a circular cylindrical body, in terms of the lift which would be experienced by the exposed wing alone, presented as Eq. (4) by Graham and McDowell was apparently first given by Ward in 1949. Ward also surmised that the formula might have much broader application than its origin in slenderbody theory would suggest. The same formula may be inferred from the results obtained by Spreiter, and it has earlier antecedents in the classical work on wing-body combinations of minimum induced drag. Since Spreiter's and Ward's work, a vast literature on the subject of wing-body interference has come into being, including many heuristic and empirical methods built on extensions of slender-body theory results. Ward's formula was presented or utilized in many subsequent papers. For example, it appears in the survey paper by Lawrence and the writer and, explicitly in the interference factor notation used in Ref. 1, in the book by Nielsen. The main purpose of this Comment, however, is not to set forth the historical development of the particular formula presented in Ref. 1. Rather it is, in view of the approach taken in Ref. 1, to point out again that the total forces and moments of aerodynamically interfering wingbody combinations can almost always be more readily obtained in simple closed form than the forces and moments of components. This can be done by a variety of methods, closely related in principle, but differing in convenience for particular applications. These methods include farfield contour integration as used by Ward, direct application of conformal and mapping to the integral expressions for total force as used by Lawrence and the writer, and Bryson's apparent mass methods, which he applied extensively in the determination of stability derivatives. Utilizing these methods, relatively simple closed-form expressions for the total forces and moments on the various wing-body combinations of considerably more general configurations than the one considered in Ref. 1 have been obtained in the cited references and many other papers. The formulas for slender-body theory interference ratios are usually applied to configurations which are not slender enough for the theory to apply with high precision, the aspect-ratio effects being taken into account through the ex-

Thin-Walled Beams in Frame Synthesis

References 1 Yang, H. T., Lift of Wing-Body Combination, AIAA Journal, Vol. 10, No. 11, Nov. 1972, pp. 1535-1536. 2 Miles, J. W., On Interference Factors for Finned Bodies, Journal of the Aeronautical Sciences, Vol. 18, No. 4, April 1952, p. 287. 3 Spreiter, J. R., Aerodynamic Properties of Slender Wing-Body Combinations at Subsonic, Transonic, and Speeds, TN1662, July 1948, NACA. 4 Ward, G. N., Supersonic Flow Past Slender Pointed Bodies, Quarterly Journal of Mechanics and Applied Mathematics, Vol. II, Pt. I, 1949, pp. 76-97.

Comment on "Lift of Wing-Body Combination"

References 1 Yang, H. T., Lift of Wing-Body Combination, AIAA Journal, Vol. 10, No. 11, Nov. 1972, pp. 1535-1536. 2 Miles, J. W., On Interference Factors for Finned Bodies, Journal of the Aeronautical Sciences, Vol. 18, No. 4, April 1952, p. 287. 3 Spreiter, J. R., Aerodynamic Properties of Slender Wing-Body Combinations at Subsonic, Transonic, and Speeds, TN1662, July 1948, NACA. 4 Ward, G. N., Supersonic Flow Past Slender Pointed Bodies, Quarterly Journal of Mechanics and Applied Mathematics, Vol. II, Pt. I, 1949, pp. 76-97.

Prediction of the lift and moment on a slender cylinder-segment wing-body combination

The design of a vehicle with cruise capability which can be packaged in a volume limited space, such as a cylindrical tube, centres around the problem of folding the lifting and control surfaces in such a manner that their deployment is simple and reliable. Several folding schemes are illustrated in Fig. 1. A wing fabricated of a flexible material and suspended by lines from the fuselage (parawing, Fig. 1a) can be folded to occupy only a small volume. These wings, however, are difficult to deploy at high forward speeds and have characteristically poor lift/ drag ratios unsuitable for high performance cruise capability. Another concept which allows storing the wing in a volume-limited space is the “scissor” wing (Fig. 1b) which, when deployed, swings out from a cavity in the fuselage.

Correlation of wing-body combination lift data.

Correlation of wing-body combination lift data.

Slowly oscillating lifting surfaces at subsonic and supersonic speeds.

The paper presents an unsteady aerodynamic influence coefficient method based on the low-frequency approximation. The influence coefficients are of a type which have been used to compute steady flow about wing-body combinations; therefore, the new method may be extended readily to low-frequency unsteady flow about wing-body combinations. The validity of the method is demonstrated by comparisons with numerical results from conventional, unsteady lifting surface methods. The method is valid for arbitrary wings in supersonic flow and for wings of finite span in subsonic flow. The method, when extended to include wing-body-tail interactions, will have important applications for predicting stability, control, and gust response characteristics of large airplanes. Dynamic stability derivatives and pressure distributions are given for several planforms. The comparison with either analytical or other well established numerical methods shows good agreement.-