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NASA NTRS1980

An improved panel method for the solution of three-dimensional leading-edge vortex flows. Volume 1: Theory document

An improved panel method for the solution of three dimensional flow and wing and wing-body combinations with leading edge vortex separation is presented. The method employs a three dimensional inviscid flow model in which the configuration, the rolled-up vortex sheets, and the wake are represented by quadratic doublet distributions. The strength of the singularity distribution as well as shape and position of the vortex spirals are computed in an iterative fashion starting with an assumed initial sheet geometry. The method calculates forces and moments as well as detail surface pressure distributions. Improvements include the implementation of improved panel numerics for the purpose of elimination the highly nonlinear effects of ring vortices around double panel edges, and the development of a least squares procedure for damping vortex sheet geometry update instabilities. A complete description of the method is included. A variety of cases generated by the computer program implementing the method are presented which verify the mathematical assumptions of the method and which compare computed results with experimental data to verify the underlying physical assumptions made by the method.

Johnson, F. T.↗

NASA NTRS1984

Application of panel method to wake vortex/wing interaction and comparison with experiment

The ability of a low-order panel method to calculate the aerodynamic loads on wings caused by interaction with wake vortices was studied. The loads were calculated for various positions of a downstream following wing relative to an upstream vortex-generating wing. Calculated vortex-induced span loads and rolling-moment coefficients on the following wing were compared with experimental data. A good agreement with experiment was obtained when the following wing was located more than one following-wing chord length from the tip vortex. The predictions deteriorated as the following wing was placed closer to the vortex. At large downstream distances (approximately 10 generating-wing chord lengths), induced rolling-moment coefficients on the following wing were consistently overestimated. Despite the strong interaction between the wake-vortex filaments and surface doublet panels, the accuracy of the calculations was in most cases independent of the panel distribution and density. A good agreement between theoretical and experimental loads was obtained with a minimum of experimentation with panel arrangements.

Smith, B. E.↗

NASA NTRS1985

A transonic rectangular grid embedded panel method

In this chapter, a description is given of a nonstandard method which has the ultimate goal to provide a routine solution of transonic flow problems about large, complex configurations. For a number of reasons, it is difficult to extend standard methods to the solution of flows about complicated configurations. According to the particular approach of the considered nonstandard method, in the process of solving for linear potential flow via panel methods, a flow everwhere in space is created, taking into account the interior of the aircraft as well as the external flowfield of interest. Attention is given to the solution of flow problems without interior boundaries, the treatment of interior boundaries, and areas of current and future research.

Johnson, F. T.↗

NASA NTRS1979

An improved Woodward's panel method for calculating leading-edge and side-edge suction forces at subsonic and supersonic speeds

Woodward's panel method for subsonic and supersonic flow was improved by employing control points determined by exactly matching two-dimensional pressure at a finite number of points. The results show great improvement in the predicted pressure distribution of a flapped airfoil. With the paneling scheme of cosine law in both chordwise and spanwise directions, the method is shown to accurately predict leading edge and side edge suction forces of various configurations in subsonic and supersonic flow.

Lan, C. E.↗

NASA NTRS1983

Evaluation of a surface panel method coupled with several boundary layer analyses

Three boundary layer models are interacted with an inviscid panel method to evaluate their capabilities to predict aerodynamic performance characteristics. These boundary layer models include two two-dimensional boundary layer models and one three-dimensional boundary layer model. Previously reported discrepancies between the transpiration and surface displacement inviscid boundary layer simulations are discussed and resolved. Results from each of the models are compared with experimental data.

Kjelgaard, S. O.↗

NASA NTRS1988

Evaluation of the constant pressure panel method (CPM) for unsteady air loads prediction

This paper evaluates the capability of the constant pressure panel method (CPM) code to predict unsteady aerodynamic pressures, lift and moment distributions, and generalized forces for general wing-body configurations in supersonic flow. Stability derivatives are computed and correlated for the X-29 and an Oblique Wing Research Aircraft, and a flutter analysis is carried out for a wing wind tunnel test example. Most results are shown to correlate well with test or published data. Although the emphasis of this paper is on evaluation, an improvement in the CPM code's handling of intersecting lifting surfaces is briefly discussed. An attractive feature of the CPM code is that it shares the basic data requirements and computational arrangements of the doublet lattice method. A unified code to predict unsteady subsonic or supersonic airloads is therefore possible.

Appa, Kari↗

NASA NTRS1993

Unsteady panel method for flows with multiple bodies moving along various paths

A potential flow based three-dimensional panel method was modified to treat time dependent conditions in which several submerged bodies can move within the fluid along different trajectories. This modification was accomplished by formulating the momentary solution in an inertial frame-of-reference, attached to the undisturbed stationary fluid. Consequently, the numerical interpretation of the multiple-body, solid-surface boundary condition and the viscous wake rollup was considerably simplified. The unsteady capability of this code was validated by comparing computed and experimental results for a finite wing undergoing pitch oscillations. In order to demonstrate the multicomponent capability, computations were made for two wings following closely intersecting paths (e.g., to avoid mid air collisions) and for a flow field with relative rotation (e.g., helicopter-rotor/fuselage interaction). Results were compared to experimental data when such data was available.

Richason, Thomas F.↗

NASA NTRS1994

Unsteady panel method for flows with multiple bodies moving along various paths

A potential flow based three-dimensional panel method was modified to treat time-dependent conditions in which several submerged bodies can move within the fluid along different trajectories. This modification was accomplished by formulating the momentary solution in an inertial frame of reference, attached to the undisturbed stationary fluid. Consequently, the numerical interpretation of the multiple-body, solid-surface boundary condition and the viscous wake rollup was considerably simplified. The usteady capability of this code was calibrated and validated by comparing computed results with closed-form analytical results available for an airfoil, which was impulsively set into a constant speed forward motion. To demonstrate the multicomponent capability, computations were made for two wings following closely intersecting paths (i.e., simulations aimed at avoiding mid-air collisions) and for a flowfield with relative rotation (i.e., the case of a helicopter rotor rotating relative to the fuselage). Computed results for the cases were compared to experimental data, when such data was available.

Richardson, Thomas F.↗

NASA NTRS1986

Application of a low order panel method to complex three-dimensional internal flow problems

An evaluation of the ability of a low order panel method to predict complex three-dimensional internal flow fields was made. The computer code VSAERO was used as a basis for the evaluation. Guidelines for modeling internal flow geometries were determined and the effects of varying the boundary conditions and the use of numerical approximations on the solutions accuracy were studied. Several test cases were run and the results were compared with theoretical or experimental results. Modeling an internal flow geometry as a closed box with normal velocities specified on an inlet and exit face provided accurate results and gave the user control over the boundary conditions. The values of the boundary conditions greatly influenced the amount of leakage an internal flow geometry suffered and could be adjusted to eliminate leakage. The use of the far-field approximation to reduce computation time influenced the accuracy of a solution and was coupled with the values of the boundary conditions needed to eliminate leakage. The error induced in the influence coefficients by using the far-field approximation was found to be dependent on the type of influence coefficient, the far-field radius, and the aspect ratio of the panels.

Ashby, D. L.↗

NASA NTRS1984

Applicability of a panel method, which includes nonlinear effects, to a forward-swept-wing aircraft

The ability of a lower order panel method VSAERO, to accurately predict the lift and pitching moment of a complete forward-swept-wing/canard configuration was investigated. The program can simulate nonlinear effects including boundary-layer displacement thickness, wake roll up, and to a limited extent, separated wakes. The predictions were compared with experimental data obtained using a small-scale model in the 7- by 10- Foot Wind Tunnel at NASA Ames Research Center. For the particular configuration under investigation, wake roll up had only a small effect on the force and moment predictions. The effect of the displacement thickness modeling was to reduce the lift curve slope slightly, thus bringing the predicted lift into good agreement with the measured value. Pitching moment predictions were also improved by the boundary-layer simulation. The separation modeling was found to be sensitive to user inputs, but appears to give a reasonable representation of a separated wake. In general, the nonlinear capabilities of the code were found to improve the agreement with experimental data. The usefullness of the code would be enhanced by improving the reliability of the separated wake modeling and by the addition of a leading edge separation model.

Ross, J. C.↗

NASA NTRS1987

Steady and unsteady aerodynamic forces from the SOUSSA surface-panel method for a fighter wing with tip missile and comparison with experiment and PANAIR

The body surface-panel method SOUSSA is applied to calculate steady and unsteady lift and pitching moment coefficients on a thin fighter-type wing model with and without a tip-mounted missile. Comparisons are presented with experimental results and with PANAIR and PANAIR-related calculations for Mach numbers from 0.6 to 0.9. In general the SOUSSA program, the experiments, and the PANAIR (and related) programs give lift and pitching-moment results which agree at least fairly well, except for the unsteady clean-wing experimental moment and the unsteady moment on the wing tip body calculated by a PANAIR-predecessor program at a Mach number of 0.8.

Cunningham, Herbert J.↗

NASA NTRS1982

A transonic rectangular grid embedded panel method

A method is presented that has the potential for solving transonic flow problems about the same complex aircraft configurations currently being analyzed by subsonic panel methods. This method does not require the generation of surface fitted grids. Instead it uses rectangular grids and subgrids together with embedded surface panels on which boundary conditions are imposed. Both the Euler and full potential equations are considered. The method of least squares is used to reduce the solution of these equations to the solution of a sequence of Poisson problems. The Poisson problems are solved using fast Fourier transforms and panel influence coefficient techniques. The overall method is still in its infancy but some two dimensional results are shown illustrating various key features.

Johnson, F. T.↗

NASA NTRS1984

The application of a low-order panel method - program VSAERO to powerplant and airframe flow studies

Results from the application of VSAERO, a low-order panel method, to three practical aircraft configurations are presented. The Grumman 698-411 tilt-nacelle V/STOL model is analyzed with particular emphasis on the inlet pressures and the nacelle/fuselage interference effects. Excellent correlation with experiment is reported for the inlet pressure ratio and the inlet operational boundaries. Analysis of an inlet designed for a tilt-rotor/nacelle aircraft is presented. The code was used in a design environment for this configuration to determine an inlet geometry that maintained attached flow for three design flight conditions: hover, hover-transition and cruise. VSAERO is also used to examine the prop-slipstream induced loading for the Langley prop-fan configuration. The versatility and economy of the aerodynamic modeling program, VSAERO, is demonstrated.

Strash, D. J.↗

NASA NTRS1982

Unsteady rotor aerodynamics using a vortex panel method

The problem of the potential incompressible flow about a helicopter rotor blade is solved using an unsteady vortex-panel method where the mutual interaction between the blade and the distorting free wake is taken into account. The present method alleviates the need to rely upon measured-wake geometries or p5escribed-wake models in order to calculate the airloads. A computer program has been developed which is capable of predicting the geometry of the time-dependent three-dimensional (3-D) wake and the instantaneous loadings for a single blade in hover, climb, and forward flight. The solution is obtained by using a time-accurate step-by-step procedure. The complex-wake geometry at any time is presented graphically with a computer graphics system. Calculated results are compared with published data for a rotor blade in both hover and forward flight. The code has also been applied to the study of the effect of changing blade tip geometry.

Crispin, Y.↗

NASA NTRS1988

A panel method procedure for interference assessment in slotted-wall wind tunnels

This paper describes a method for three-dimensional wind tunnel interference assessment developed specifically for slotted-wall tunnels. The method is an adaptation to the assessment problem of a previously published high-order panel method procedure for simulating the flow in slotted-wall tunnel test sections. The method uses a mixed outer boundary condition, primarily a Neumann condition, with measured pressure constraints used to control only those boundary phenomena which can not be specified accurately a priori. Assessment results are illustrated from a calibration test with variations in wall geometry, and from tests of a generic subsonic transport aircraft configuration.

Kemp, William B., Jr.↗

NASA NTRS1985

A theoretical basis for extending surface-paneling methods to transonic flow

The surface integral terms in Green's third identity are often used to solve the Prandtl-Glauert (linear potential-flow) equation with panel methods. This can be done, as in the PAN AIR code, for either subsonic or supersonic flow about complete aircraft. The extension to transonic flow is suggested by the volume integral terms of Green's third identity. The mathematical basis for this extension, without the use of body-fitted grids, is presented. Supercritical transonic results computed from a two-dimensional transonic PAN AIR research code demonstrate the method.

Erickson, L. L.↗

NASA NTRS1985

Calculation of compressible flow about three-dimensional inlets with auxiliary inlets, slats and vanes by means of a panel method

An efficient and user oriented method was constructed for calculating flow in and about complex inlet configurations. Efficiency is attained by: (1) the use of a panel method; (2) a technique of superposition for obtaining solutions at any inlet operating condition; and (3) employment of an advanced matrix iteration technique for solving large full systems of equations, including the nonlinear equations for the Kutta condition. User concerns are addressed by the provision of several novel graphical output options that yield a more complete comprehension of the flowfield than was possible previously.

Hess, J. L.↗

NASA NTRS1985

Calculation of compressible flow about three-dimensional inlets with auxiliary inlets, slats and vanes by means of a panel method

An efficient and user-oriented method has been constructed for calculating flow in and about complex inlet configurations. Efficiency is attained by: the use of a panel method, a technique of superposition for obtaining solutions at any inlet operating condition, and employment of an advanced matrix-iteration technique for solving large full systems of equations, including the nonlinear equations for the Kutta condition. User concerns are addressed by the provision of several novel graphical output options that, taken together, yield a more complete comprehension of the flowfield than had been possible previously. Examples of these features are presented for some complicated configurations, and where possible, comparisons are made between calculation and experiment.

Hess, J. L.↗