Wind-tunnel investigation of the effects of ventral fins at two positions on lateral-stability derivatives of 45 degree swept high-wing models oscillating in yaw
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Jaquet, Byron M↗
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Algorithm and code development for unsteady three-dimensional Navier-Stokes equations
Aeroelastic tests require extensive cost and risk. An aeroelastic wind-tunnel experiment is an order of magnitude more expensive than a parallel experiment involving only aerodynamics. By complementing the wind-tunnel experiments with numerical simulations, the overall cost of the development of aircraft can be considerably reduced. In order to accurately compute aeroelastic phenomenon it is necessary to solve the unsteady Euler/Navier-Stokes equations simultaneously with the structural equations of motion. These equations accurately describe the flow phenomena for aeroelastic applications. At ARC a code, ENSAERO, is being developed for computing the unsteady aerodynamics and aeroelasticity of aircraft, and it solves the Euler/Navier-Stokes equations. The purpose of this cooperative agreement was to enhance ENSAERO in both algorithm and geometric capabilities. During the last five years, the algorithms of the code have been enhanced extensively by using high-resolution upwind algorithms and efficient implicit solvers. The zonal capability of the code has been extended from a one-to-one grid interface to a mismatching unsteady zonal interface. The geometric capability of the code has been extended from a single oscillating wing case to a full-span wing-body configuration with oscillating control surfaces. Each time a new capability was added, a proper validation case was simulated, and the capability of the code was demonstrated.
Obayashi, Shigeru↗
Analysis of transonic flow about harmonically oscillating airfoils and wings
A finite difference method for analyzing the unsteady transonic flow about harmonically oscillating wings is discussed. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting partial differential equations for small disturbances. Initial solutions were obtained using relaxation procedures, but the solution range proved to be limited in terms of Mach number and reduced frequency. Recent two-dimensional results are presented which have been obtained with direct solution procedures in which the difference equations are solved 'all at once' and these provide reasonable correlation for practical values of Mach number and reduced frequency.
Weatherill, W. H.↗
Transonic steady- and unsteady-pressure measurements on a high-aspect-ratio supercritical-wing model with oscillating control surfaces
A supercritical wing with an aspect ratio of 10.76 and with two trailing-edge oscillating control surfaces is described. The semispan wing is instrumented with 252 static orifices and 164 in situ dynamic-pressure gages for studying the effects of control-surface position and motion on steady- and unsteady-pressures at transonic speeds. Results from initial tests conducted in the Langley Transonic Dynamics Tunnel at two Reynolds numbers are presented in tabular form.
Sandford, M. C.↗
Subsonic and transonic pressure measurements on a high-aspect-ratio supercritical-wing model with oscillating control surfaces
A high aspect ratio supercritical wing with oscillating control surfaces is described. The semispan wing model was instrumented with 252 static orifices and 164 in situ dynamic pressure gases for studying the effects of control surface position and sinusoidal motion on steady and unsteady pressures. Data from the present test (this is the second in a series of tests on this model) were obtained in the Langley Transonic Dynamics Tunnel at Mach numbers of 0.60 and 0.78 and are presented in tabular form.
Sandford, M. C.↗
Algorithm development with applications to aerodynamics and aeroelasticity
The development of a streamwise upwind algorithm is presented. Applications of this algorithm to steady flow over a delta wing and unsteady flow over an oscillating wing, respectively, are covered. An extension to higher order accuracy for upwind methods is discussed. This scheme will use the compatibility relations for the extension. The use of multiple zones in the calculation of unsteady flows is considered. Multiple zones are one way to treat complex configurations, such as complete aircraft. Aeroelastic calculations are discussed. A procedure for aeroelastic calculations is described that simultaneously solves the aerodynamic and structural equations of motion. Sample calculations are given to illustrate the above.
Goorjian, P. M.↗
Linearized compressible-flow theory for sonic flight speeds
The partial differential equation for the perturbation velocity potential is examined for free-stream Mach numbers close to and equal to one. It is found that, under the assumptions of linearized theory, solutions can be found consistent with the theory for lifting-surface problems both in stationary three-dimensional flow and in unsteady two-dimensional flow. Several examples are solved including a three dimensional swept-back wing and two dimensional harmonically-oscillating wing, both for a free stream Mach number equal to one. Momentum relations for the evaluation of wave and vortex drag are also discussed. (author)
Heaslet, Max A↗
An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.
Ehlers, F. E.↗
Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.
Weatherill, W. H.↗
Effect of aspect ratio on undamped torsional oscillations of a thin rectangular wing in supersonic flow
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FLUTTER - WINGS↗
Steady- and unsteady-pressure measurements on a supercritical-wing model with oscillating control surfaces at subsonic and transonic speeds
A high aspect ratio supercritical wing with oscillating control surfaces is described. The semispan wing model was instrumented with 252 static pressure orifices and 164 in situ dynamic pressure gages for studying the effects of control surface position and sinusoidal motion on steady and unsteady pressures. Results from the present test (the third in a series of tests on this model) were obtained in the Langley Transonic Dynamics Tunnel at Mach numbers of 0.60, 0.78, and 0.86 and are presented in tabular form.
Sandford, M. C.↗
Unsteady transonic flow analysis for low aspect ratio, pointed wings.
Oswatitsch and Keune's parabolic method for steady transonic flow is applied and extended to thin slender wings oscillating in the sonic flow field. The parabolic constant for the wing was determined from the equivalent body of revolution. Laplace transform methods were used to derive the asymptotic equations for pressure coefficient, and the Adams-Sears iterative procedure was employed to solve the equations. A computer program was developed to find the pressure distributions, generalized force coefficients, and stability derivatives for delta, convex, and concave wing planforms.
Kimble, K. R.↗
General airfoil theory
On the assumption of infinitely small disturbances the author develops a generalized integral equation of airfoil theory which is applicable to any motion and compressible fluid. Successive specializations yield various simpler integral equations, such as Possio's, Birnbaum's, and Prandtl's integral equations, as well as new ones for the wing of infinite span with periodic downwash distribution and for the oscillating wing with high aspect ratio. Lastly, several solutions and methods for solving these integral equations are give.
Kussner, H G↗
Air forces and moments on triangular and related wings with subsonic leading edges oscillating in supersonic potential flow
This analysis treats the air forces and moments in supersonic potential flow on oscillating triangular wings and a series of sweptback and arrow wings with subsonic leading edges and supersonic trailing edges. For the wings undergoing sinusoidal torsional oscillations simultaneously with vertical translations, the linearized velocity potential is derived in the form of a power series in terms of a frequency parameter. This method can be useful for treatment of similar problems for other plan forms and for wings undergoing other sinusoidal motions. For triangular wings, as many terms of such a series expansion as may be derived can be determined; however, the terms after the first few become very cumbersome. Closed expressions that include the reduced frequency to the fifth power, an order which is sufficient for a large class of practical application, are given for the velocity potential and for the components of chordwise section force and moment coefficients. These wings are found to exhibit the possibility of undamped torsional oscillations for certain ranges of Mach number and locations of the axis of rotation. The ranges of these parameters are delineated for triangular wings.
Watkins, Charles E↗
Comparison of theory with experiment in the phenomenon of wing flutter
Direct measurements were undertaken at the Aeronautics Laboratory in Turin of the aerodynamic actions on an oscillating wing. The tests conducted had as their essential object the examination of the operation of apparatus designed for this measurement. The values experimentally obtained for the aerodynamic coefficients are in good agreement with the theory of oscillatory motion of the wing of finite span and show clear deviation from the values obtained by theory of plane motion.
Cicala, P↗
On the stability of oscillations of an airplane wing
During a flight with a Van Berkel W. B. seaplane it was observed that the wing could perform violent oscillations. A theoretical and experimental investigation led to the conclusion, that in some cases an unstable oscillation of the wing-aileron system under the influence of the elastic and aerodynamic forces is possible without further external causes.
FLUTTER - WINGS - VAN BERKEL W B↗
Test Cases for a Rectangular Supercritical Wing Undergoing Pitching Oscillations
Steady and unsteady measured pressures for a Rectangular Supercritical Wing (RSW) undergoing pitching oscillations have been presented. From the several hundred compiled data points, 27 static and 36 pitching oscillation cases have been proposed for computational Test Cases to illustrate the trends with Mach number, reduced frequency, and angle of attack. The wing was designed to be a simple configuration for Computational Fluid Dynamics (CFD) comparisons. The wing had an unswept rectangular planform plus a tip of revolution, a panel aspect ratio of 2.0, a twelve per cent thick supercritical airfoil section, and no twist. The model was tested over a wide range of Mach numbers, from 0.27 to 0.90, corresponding to low subsonic flows up to strong transonic flows. The higher Mach numbers are well beyond the design Mach number such as might be required for flutter verification beyond cruise conditions. The pitching oscillations covered a broad range of reduced frequencies. Some early calculations for this wing are given for lifting pressure as calculated from a linear lifting surface program and from a transonic small perturbation program. The unsteady results were given primarily for a mild transonic condition at M = 0.70. For these cases the agreement with the data was only fair, possibly resulting from the omission of viscous effects. Supercritical airfoil sections are known to be sensitive to viscous effects (for example, one case cited). Calculations using a higher level code with the full potential equations have been presented for one of the same cases, and with the Euler equations. The agreement around the leading edge was improved, but overall the agreement was not completely satisfactory. Typically for low-aspect-ratio rectangular wings, transonic shock waves on the wing tend to sweep forward from root to tip such that there are strong three-dimensional effects. It might also be noted that for most of the test, the model was tested with free transition, but a few points were taken with an added transition strip for comparison. Some unpublished results of a rigid wing of the same airfoil and planform that was tested on the pitch and plunge apparatus mount system (PAPA) showed effects of the lower surface transition Strip on flutter at the lower subsonic Mach numbers. Significant effects of a transition strip were also obtained on a wing with a thicker supercritical section on the PAPA mount system. Both of these flutter tests on the PAPA resulted in very low reduced frequencies that may be a factor in this influence of the transition strip. However, these results indicate that correlation studies for RSW may require some attention to the estimation of transition location to accurately treat viscous effects. In this report several Test Cases are selected to illustrate trends for a variety of different conditions with emphasis on transonic flow effects. An overview of the model and tests is given and the standard formulary for these data is listed. Sample data points are presented in both tabular and graphical form. A complete tabulation and plotting of all the Test Cases is given. Only the static pressures and the real and imaginary parts of the first harmonic of the unsteady pressures are available. All the data for the test are available in electronic file form. The Test Cases are also available as separate electronic files.
Bennett, Robert M.↗
Effect of aspect ratio on the air forces and moments of harmonically oscillating thin rectangular wings in supersonic potential flow
This report treats the effect of aspect ratio on the air forces and moments of an oscillating flat rectangular wing in supersonic potential flow. The linearized velocity potential for the wing undergoing sinusoidal torsional oscillations simultaneously with sinusoidal vertical translations is derived in the form of a power series in terms of a frequency parameter. The series development is such that the differential equation for the velocity potential is satisfied to the required power of the frequency parameter considered and the linear boundary conditions are satisfied exactly. The method of solution can be utilized for other plan forms, that is, plan forms for which certain steady-state solutions are known.
Watkins, Charles E↗