Showing papers on "Vortex lattice method published in 1977"

A generalized vortex lattice method for subsonic and supersonic flow applications

Abstract: If the discrete vortex lattice is considered as an approximation to the surface-distributed vorticity, then the concept of the generalized principal part of an integral yields a residual term to the vorticity-induced velocity field. The proper incorporation of this term to the velocity field generated by the discrete vortex lines renders the present vortex lattice method valid for supersonic flow. Special techniques for simulating nonzero thickness lifting surfaces and fusiform bodies with vortex lattice elements are included. Thickness effects of wing-like components are simulated by a double (biplanar) vortex lattice layer, and fusiform bodies are represented by a vortex grid arranged on a series of concentrical cylindrical surfaces. The analysis of sideslip effects by the subject method is described. Numerical considerations peculiar to the application of these techniques are also discussed. The method has been implemented in a digital computer code. A users manual is included along with a complete FORTRAN compilation, an executed case, and conversion programs for transforming input for the NASA wave drag program.

A subvortex technique for the close approach to a discretized vortex sheet

Abstract: The close-approach problem associated with flow calculation methods based on vortex-lattice theory was examined numerically using two-dimensional discretized vortex sheets. The analysis first yields a near-field radius of approximately the distance apart of the vortices in the lattice; only within this distance from the sheet are the errors arising from the discretization significant. Various modifications to the discrete vortices are then considered with the objective of reducing the errors. This leads to a near-field model in which a vortex splits into an increasing number of subvortices as it is approached. The subvortices, whose strengths vary linearly from the vortex position, are evenly distributed along an interpolated curve passing through the basic vortices. This subvortex technique can be extended to the three-dimensional case and is efficient because the number of vortices is effectively increased, but only where and when needed.

Formation flying benefits based on vortex lattice calculations

Abstract: A quadrilateral vortex-lattice method was applied to a formation of three wings to calculate force and moment data for use in estimating potential benefits of flying aircraft in formation on extended range missions, and of anticipating the control problems which may exist. The investigation led to two types of formation having virtually the same overall benefits for the formation as a whole, i.e., a V or echelon formation and a double row formation (with two staggered rows of aircraft). These formations have unequal savings on aircraft within the formation, but this allows large longitudinal spacings between aircraft which is preferable to the small spacing required in formations having equal benefits for all aircraft. A reasonable trade-off between a practical formation size and range benefit seems to lie at about three to five aircraft with corresponding maximum potential range increases of about 46 percent to 67 percent. At this time it is not known what fraction of this potential range increase is achievable in practice.

Oscillatory Subsonic Piecewise Continuous Kernel Function Method

Abstract: Theme T WO main methods currently are employed in the prediction of the aerodynamic forces acting on lifting surfaces at subsonic flow. These methods inlcude the subsonic kernel function approach, which assumes pressure polynomials to describe the pressure field over the wing, and the finite-element approach, such as the doublet lattice method (DLM) or the vortex lattice method (VLM). The kernel function method (KFM), when based on orthogonal polynomials and carefully determined collocation points, shows a rapid convergence of its solution (with a small number of pressure polynomials) provided that the pressure field over the wing is smooth. Pressure discontinuities, such as those arising from control surface rotations, can be treated successfully using the KFM only when the exact shape of the singularity is known. The overlooking of pressure singularities using the KFM leads to a rapid deterioration in the convergence of the solution and to a general loss in the effectiveness of the method. The finite-element methods (FEM) can cope successfully with unknown pressure singularities provided that their location is known. The FEM, however, require a relatively large number of unknowns for convergence, leading at times to a relatively large residual error at the converged values. In the present paper a method is presented, similar to the one described in Ref. 4 in connection with mixed transonic flow, which combines the rapid convergence characteristics of the KFM with the ability of the FEM to treat discontinuities without having to determine their exact form. The method is tested using a two-dimensional airfoil problem (with control surfaces and gaps) with the intention of establishing its merits before embarking on its extension to the three-dimensional flow case.

Aerodynamic loads near cranks, apexes, and tips of thin, lifting wings in incompressible flow

Abstract: The calculation of the incompressible and irrotational flow in the vicinity of tips and corners of thin, lifting wings is considered. It is shown that the important characteristics of the flow are governed by an eigenvalue problem, which is nonlinear at the trailing edge because of the shed wake (assumed to be in the wing plane). A new solution method was devised because either the existing methods were not valid for the trailing edge case or they would have required excessive amounts of computer time. The new method, which is fundamentally different than the previous ones, was used to calculate solutions for a number of cases, including some for which correct answers had not previously been obtained. Two of these solutions were used to determine the validity of drag and leading-edge-suction distributions near the tips of a delta wing and a swept wing as calculated by using both the vortex lattice method and a kernel function method. The calculations for the swept wing resolved the question of whether or not the induced drag should be zero at the wing tip.

Computer program for calculating aerodynamic characteristics of upper-surface-blowing and over-wing-blowing configurations

Abstract: The program is based on the inviscid wing-jet interaction theory of Lan and Campbell, and the jet entrainment theory of Lan. In the interaction theory, the flow perturbations are computed both inside and outside the jet, separately, and then matched on the jet surface to satisfy the jet boundary conditions. The jet Mach number is allowed to be different from the free stream value (Mach number nonuniformity). These jet boundary conditions require that the static pressure be continuous across the jet surface which must always remain as a stream surface. These conditions, as well as the wing-surface tangency condition, are satisified only in the linearized sense. The detailed formulation of these boundary conditions is based on the quasi-vortex-lattice method of Lan.

Vortex lattice prediction of subsonic aerodynamics of hypersonic vehicle concepts

Abstract: The vortex lattice method introduced by Lamar and Gloss (1975) was applied to the prediction of subsonic aerodynamic characteristics of hypersonic body-wing configurations. The reliability of the method was assessed through comparison of the calculated and observed aerodynamic performances of two National Hypersonic Flight Research Facility craft at Mach 0.2. The investigation indicated that a vortex lattice model involving 120 or more panel elements can give good results for the lift and induced drag coefficients of the craft, as well as for the pitching moment at angles of attack below 10 to 15 deg. Automated processes for calculating the local slopes of mean-camber surfaces may also render the method suitable for use in preliminary design phases.

Theoretical and experimental analysis of longitudinal and lateral aerodynamic characteristics of skewed wings at subsonic speeds to high angles of attack

Abstract: The effects of sweep and aspect ratio on the longitudinal and lateral-directional aerodynamic characteristics of low-aspect-ratio skewed (oblique) wings having separation-induced vortex flows along leading and side edges were investigated in the Langley high-speed 7- by 10-foot tunnel at a low-subsonic Mach number. The theoretical analysis used the vortex-lattice method for estimating attached-flow aerodynamic characteristics and the leading-edge suction analogy of Polhamus for estimating separation induced vortex-flow effects. Experimental results were compared with asymmetric, separated, vortex flow theory.

Theoretical prediction of over-wing-blowing aerodynamics

Abstract: A theoretical method is developed for predicting the aerodynamic characteristics of wings with over-wing-blowing jet. The method allows the jet to stay above the wing surface as well as to wash the surface. It accounts for the wing-jet interaction due to differences between the jet and freestream dynamic pressures and Mach numbers, in addition to the jet entrainment. For the former effect, the quasi-vortex-lattice method is used to satisfy the jet and wing boundary conditions. For the latter, a new theory was developed to calculate the jet entrained flow for given jet properties. Comparison of predicted results with available data of various configurations shows reasonably good agreement. Further theoretical analysis indicates that it is aerodynamically advantageous to locate the jet exit near and ahead of the wing leading edge, and that the camber shape has significant effect on the induced drag.

Wind Tunnel Wall Corrections for Arbitrary Planforms and Wind Tunnel Cross-Sections.

Abstract: : A computer program was developed to obtain the wind tunnel wall corrections for wing angle of attack, induced drag, and pitching moment in incompressible flow The vortex lattice method is used for computation of these correction factors The program can be applied to wind tunnels of arbitrary cross-sectional shape, and wings of any desired planform, subject to the constraint of straight leading and trailing edges (Author)