Showing papers on "Vortex lattice method published in 1976"

Nonlinear prediction of the aerodynamic loads on lifting surfaces

Abstract: A numerical procedure is used to predict the nonlinear aerodynamic characteristics of lifting surfaces of low aspect ratio at high angles of attack for low subsonic Mach numbers. The procedure utilizes a vortex-lattice method and accounts for separation at sharp tips and leading edges. The shapes of the wakes emanating from the edges are predicted, and hence the nonlinear characteristics are calculated. Parallelogram and delta wings are presented as numerical examples. The numerical results are in good agreement with the experimental data.

A vortex-lattice method for the mean camber shapes of trimmed noncoplanar planforms with minimum vortex drag

Abstract: A new subsonic method has been developed by which the mean camber surface can be determined for trimmed noncoplanar planforms with minimum vortex drag. This method uses a vortex lattice and overcomes previous difficulties with chord loading specification. A Trefftz plane analysis is utilized to determine the optimum span loading for minimum drag, then solved for the mean camber surface of the wing, which provides the required loading. Sensitivity studies, comparisons with other theories, and applications to configurations which include a tandem wing and a wing winglet combination have been made and are presented.

A quadrilateral vortex method applied to configurations with high circulation

Abstract: A quadrilateral vortex-lattice method is briefly described for calculating the potential flow aerodynamic characteristics of high-lift configurations It incorporates an iterative scheme for calculating the deformation of forcefree wakes, including wakes from side edges The method is applicable to multiple lifting surfaces with part-span flaps deflected, and can include ground effect and wind-tunnel interference Numerical results, presented for a number of high-lift configurations, demonstrate rapid convergence of the iterative technique The results are in good agreement with available experimental data

Optimization and design of three-dimensional aerodynamic configurations of arbitrary shape by a vortex lattice method

Abstract: A new method based on vortex lattice theory has been developed which can be applied to the combined analysis, induced drag optimization, and aerodynamic design of three-dimensional configurations of arbitrary shape. Geometric and aerodynamic constraints can be imposed on both the optimization and the design process. The method is compared with several known analytical solutions and is applied to several different design and optimization problems, including formation flight and wingtip fins for the Boeing KC-135 tanker airplane. Good agreement has been observed between the theoretical predictions and the wind tunnel test results for the KC-135 modification.

Historical Evolution of Vortex-Lattice Methods

Abstract: A review of the beginning and some orientation of the vortex-lattice method were given. The historical course of this method was followed in conjunction with its field of computational fluid dynamics, spanning the period from L.F. Richardson's paper in 1910 to 1975. The following landmarks were pointed out: numerical analysis of partial differential equations, lifting-line theory, finite-difference method, 1/4-3/4 rule, block relaxation technique, application of electronic computers, and advanced panel methods.

Some applications of the quasi vortex-lattice method in steady and unsteady aerodynamics

Abstract: The quasi vortex-lattice method is reviewed and applied to the evaluation of backwash, with applications to ground effect analysis. It is also extended to unsteady aerodynamics, with particular interest in the calculation of unsteady leading-edge suction. Some applications in ornithopter aerodynamics are given.

Extended applications of the vortex lattice method

Abstract: The application of the vortex lattice method to problems not usually dealt with by this technique is considered It is shown that if the discrete vortex lattice is considered as an approximation to surface-distributed vorticity, then the concept of the generalized principal part of an integral yields a residual term to the vortex-induced velocity that renders the vortex lattice method valid for supersonic flow Special schemes for simulating non-zero thickness lifting surfaces and fusiform bodies with vortex lattice elements are presented Thickness effects of wing-like components are simulated by a double vortex lattice layer, and fusiform bodies are represented by a vortex grid arranged on a series of concentric cylindrical surfaces Numerical considerations peculiar to the application of these techniques are briefly discussed

Investigations of the Rolling-Up of the Vortex Wake and Calculation of Non-Linear Aerodynamic Characteristics of wings.

Abstract: : This report investigates the rolling-up of vortices over and behind wings of low and high aspect ratios, and simultaneously the evaluation of the aerodynamic characteristics including the spanwise and chordwise pressure distributions on the wings. The present method is based on the extension of the Vortex Lattice concepts also to low aspect ratio wings and the rolled-up vortex which is established over as well as behind the wings. The computer program, which was developed, is capable of reproducing the results of the Vortex Lattice Method (VLM) for linear aerodynamic coefficients for high aspect ratio wings. The wake effect is included in the modified VLM program. This wake calculation showed that the center of the tip vortex is very near the wings' tip for the high aspect ratios wings. The non-linear aerodynamic characteristics are evaluated when the vortices are shed over the wing and begin the rolling-up process from the leading edges. This effect is particularly important for wings of low aspect ratios.

Optimum lattice arrangement developed from a rigorous analytical basis

Abstract: The spanwise vortex-lattice arrangement is mathematically established by lattice solutions of the slender wing which are shown to be analogous to the chordwise vortex-lattice thin wing solution. Solutions for any number N of panels wing theory lift and induced drag and thin wing theory lift and moment are predicted exactly. As N approaches infinity, the slender wing elliptic spanwise loading and thin wing cotangent chordwise loading are predicted, which proves there is mathematical convergence of the vortex-lattice method to the exact answer. Based on this planform spanwise lattice arrangement, an A-vortex-lattice spanwise system is developed for an arbitrary aspect ratio A. This A-lattice has the optimum characteristic of predicting lift accurately for any value of N.

Application of the vortex-lattice technique to the analysis of thin wings with vortex separation and thick multi-element wings

Abstract: Two techniques for extending the range of applicability of the basic vortex-lattice method are discussed. The first improves the computation of aerodynamic forces on thin, low-aspect-ratio wings of arbitrary planforms at subsonic Mach numbers by including the effects of leading-edge and tip vortex separation, characteristic of this type wing, through use of the well-known suction-analogy method of E. C. Polhamus. Comparisons with experimental data for a variety of planforms are presented. The second consists of the use of the vortex-lattice method to predict pressure distributions over thick multi-element wings (wings with leading- and trailing-edge devices). A method of laying out the lattice is described which gives accurate pressures on the top and part of the bottom surface of the wing. Limited comparisons between the result predicted by this method, the conventional lattice arrangement method, experimental data, and 2-D potential flow analysis techniques are presented.

Propulsion Characteristics Affecting the Aerodynamic Performance of an Externally Blown Flap Transport Model

Abstract: Two wind-tunnel investigations were conducted at Langley Research Center to determine the effect of dif- ferent wake characteristics on the performance of two separate externally blown flap transport configurations. In both cases, the thrust removed lift coefficient could be directly related to the proportion of momentum cap- tured by the flap system. In another investigation of an externally blown flap transport configuration, tufts were used to measure the upwash angles ahead of the wing. Using the thrust-removed lift coefficient, a simple vortex- lattice method provided a good approximation of these angles away from the nacelle inlets. Nomenclature = total area of jet wake which impinges flap m2 = incremental area of jet wake which impinges flap m2 = total area of jet wake at flap m2 = local wing chord m = lift coefficient, lift/^s1 = thrust removed lift coefficient = thrust coefficient, thrust/qs = engine-exhaust-flap impingement parameter = free-stream dynamic pressure N/m2 = incremental portion of jet which impinges flap, N/m2 = jet dynamic pressure at flap location, N/m2 = upper-half radius of nacelle, m = wing area, m2 = static thrust, N = vertical distance, m = angle of attack, degrees = nominal flap deflection angle, degrees =jet exhaust deflection (measured from body axis), tan;1 (normal force/axial force), degrees = inflow angle, with respect to model horizontal axis, degrees = static thrust recovery efficiency, ((normal force)2 + (axial force)2 ) 1/2/T = upflbw angle, with respect to freestream degrees = bypass ratio = externally blown flap The present paper describes the results of a relatively simple analysis based on an engine exhaust flap area impingement parameter, which is a function of the distribution of dynamic pressure impingement on the flap, the area of the flap im- pingement, the total area of the engine exhaust, and the thrust. Isolated engine wake surveys were conducted to define this parameter for one of the EBF models for which aerodynamic performance data were available.2 A uniform dynamic pressure profile was assumed to determine this parameter for the other EBF model correlation with aerodynamic performance data. n A high-lift system, such as an EBF, induces large upflow angles in front of the wing in the region of the nacelle inlets. These flowfields must be defined in order that the nacelles be properly designed to minimize flow distortion at the engine face. This paper also presents the results of an investigation to measure the flow angle near the engine inlets of a represen- tative EBF model. The vortex-lattice method14 was used to calculate these upflow angles, to determine if they could be predicted.

Sample wings for study

Abstract: Two simple wings were selected for study using the various implementations (old and new) of the vortex lattice method. These are: (1) a rectangular wing with an aspect ratio of 2, and (2) a tapered wing with an aspect ratio of 5, a taper ratio of 0.5, a leading sweep of 3.317 deg., and a trailing edge sweep of 1-11.308 deg. This was done in order to gain an appreciation for the accuracy of the various implementations. References were given where force, moment, and pressure data could be found for these wings.