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Damping-in-roll coefficients for a series of triangular plan-form wings and two rectangular plan-form wings have been obtained from supersonic-tunnel tests. The wings were mounted on a body of revolution and tested at Mach numbers of 1.62 and 1.92.
Sonic boom in near field and far field of nonlifting rectangular wing
The stall flutter response of a rectangular wing in a low speed wind tunnel is modelled using a nonlinear difference equation description. Static and dynamic tests are used to select a suitable model structure and basis function. Bifurcation criteria such as the Hopf condition and vibration amplitude variation with airspeed were used to ensure the model was representative of experimentally measured stall flutter phenomena. Dynamic test data were used to estimate model parameters and estimate an approximate basis function.
A new incompressible lifting-surface theory is developed for thin rectangular wings. The solution requires the downwash equation to be in the form of Cauchy-type integrals. Lan's method is employed for the chordwise integrals since it properly accounts for the leading-edge singularity, Cauchy singularity and Kutta condition. The Cauchy singularity in the spanwise integral is also accounted for by using the midpoint trapezoidal rule and theory of Chebychev polynomials. The resulting matrix equation, formed by satisfying the boundary condition at control points, is simpler and quicker to compute than other lifting surface theories. Solutions were found to converge with only a small number of control points and to compare favorably with results from other methods.
An experimental research study to determine the effectiveness of spoiler surfaces in suppressing flutter onset for a low-aspect-ratio, rectangular wing was conducted in the Langley Transonic Dynamics Tunnel (TDT). The wing model used in this flutter test consisted of a rigid wing mounted to the wind-tunnel wall by a flexible, rectangular beam. The flexible beam was connected to the wing root and cantilever mounted to the wind-tunnel wall. The wing had a 1.5 aspect ratio based on wing semispan and a NACA 64A010 airfoil shape. The spoiler surfaces consisted of thin, rectangular aluminum plates that were vertically mounted to the wing surface. The spoiler surface geometry and location on the wing surface were varied to determine the effects of these parameters on the classical flutter of the wing model. Subsonically, the experiment showed that spoiler surfaces increased the flutter dynamic pressure with each successive increase in spoiler height or width. This subsonic increase in flutter dynamic pressure was approximately 15 percent for the maximum height spoiler configuration and for the maximum width spoiler configuration. At transonic Mach numbers, the flutter dynamic pressure conditions were increased even more substantially than at subsonic Mach numbers for some of the smaller spoiler surfaces. But greater than a certain spoiler size (in terms of either height or width) the spoilers forced a torsional instability in the transonic regime that was highly Mach number dependent. This detrimental torsional instability was found at dynamic pressures well below the expected flutter conditions. Variations in the spanwise location of the spoiler surfaces on the wing showed little effect on flutter. Flutter analysis was conducted for the basic configuration (clean wing with all spoiler surface mass properties included). The analysis correlated well with the clean wing experimental flutter results.
Flow field approximation for sonic boom shock wave generation by thin nonlifting rectangular wing
A theory is described for predicting sonic boom pressure signatures emitted by nonlifting rectangular wings. Comparisons are made with previous (Whitham) theory and with experimentally determined near field signatures. Although both theories agree with experiment for low aspect ratio wings, Whitman's theory seriously overpredicts signature length for high aspect ratio wings. No experiments were conducted in the far field, but the two theories predict nearly identical results in this region.
This paper introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing-edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio, and number of control surfaces. Using this information, the generalized forces are computed using the doublet-lattice method. Using Roger's approximation, a rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. All parameters can be easily modified if desired. The focus of this paper is on tool presentation, verification, and validation. These processes are carried out in stages throughout the paper. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool, therefore, the flutter speed and frequency for a clamped plate are computed using damping-versus-velocity and frequency-versus-velocity analysis. The computational results are compared to a previously published computational analysis and wind-tunnel results for the same structure. A case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to damping-versus-velocity and frequency-versus-velocity analysis, including the analysis of the model in response to a 1-cos gust.
This paper introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio and number of control surfaces. A doublet lattice approach is taken to compute generalized forces. A rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. Although, all parameters can be easily modified if desired.The focus of this paper is on tool presentation, verification and validation. This process is carried out in stages throughout the paper. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool. Therefore the flutter speed and frequency for a clamped plate are computed using V-g and V-f analysis. The computational results are compared to a previously published computational analysis and wind tunnel results for the same structure. Finally a case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to V-g and V-f analysis. This also includes the analysis of the model in response to a 1-cos gust.
This report introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing-edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio, and number of control surfaces. Using this information, the generalized forces are computed using the doublet-lattice method. Using Roger's approximation, a rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. All parameters can be easily modified if desired. The focus of this report is on tool presentation, verification, and validation. These processes are carried out in stages throughout the report. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool, therefore, the flutter speed and frequency for a clamped plate are computed using damping-versus-velocity and frequency-versus-velocity analysis. The computational results are compared to a previously published computational analysis and wind-tunnel results for the same structure. A case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to damping-versus-velocity and frequency-versus-velocity analysis, including the analysis of the model in response to a 1-cos gust.
Pressure distributions were measured over rectangular wings of aspect ratio 2 and triangular wings of aspect ratios 2 and 4 at Mach numbers of 1.45 and 1.97. The investigation includes some comparison of the effects of Reynolds number and of thickening the wing root sections on the loading.
Pressure distributions were measured over rectangular wings of aspect ratio 2 and triangular wings of aspect ratios 2 and 4 at Mach numbers of 2.46 and 3.36. The investigation includes some comparison of the effects of Mach number, Reynolds number, and thickening the wing root sections on the loading.
The Structural Dynamics Division at NASA LaRC has started a wind tunnel activity referred to as the Benchmark Models Program. The primary objective of the program is to acquire measured dynamic instability and corresponding pressure data that will be useful for developing and evaluating aeroelastic type CFD codes currently in use or under development. The program is a multi-year activity that will involve testing of several different models to investigate various aeroelastic phenomena. The first model consisted of a rigid semispan wing having a rectangular planform and a NACA 0012 airfoil shape which was mounted on a flexible two degree-of-freedom mount system. Two wind-tunnel tests were conducted with the first model. Several dynamic instability boundaries were investigated such as a conventional flutter boundary, a transonic plunge instability region near Mach = 0.90, and stall flutter. In addition, wing surface unsteady pressure data were acquired along two model chords located at the 60 to 95-percent span stations during these instabilities. At this time, only the pressure data for the conventional flutter boundary is presented. The conventional flutter boundary and the wing surface unsteady pressure measurements obtained at the conventional flutter boundary test conditions in pressure coefficient form are presented. Wing surface steady pressure measurements obtained with the model mount system rigidized are also presented. These steady pressure data were acquired at essentially the same dynamic pressure at which conventional flutter had been encountered with the mount system flexible.
An experimental investigation of the flowfield in the near-wake of an aspect ratio 4 rectangular wing was conducted, providing a complete detailed set of data for use in the validation of computational methods. An angle of attack of 8 degrees and two Reynolds numbers 530,000 and 391,000 were investigated using pitot and six-hole probes. In addition, two types of flow visualization were employed. The data presented includes contours of total pressure, mean velocity, flow angularity, and vorticity distribution data at five chordwise stations of the near-wake ranging from 0.167 to 5.00 chord lengths aft of the trailing edge. The experimental results were compared to the predicted results of a 2-D Euler numerical method. The results predicted by an Euler method failed to accurately define the flowfield. Tangential velocities remained relatively constant over the range of X/C considered though increased in angle of attack and Reynolds number did bring about corresponding increases. Axial velocities also increased with angle of attack and Reynolds number but showed greater sensitivity to increases in X/C. Graphic displays and contours of the total pressure data indicate that roll-up of the wing tip vortex is essentially complete one and one half chords downstream of the trailing edge.
A method is presented for determining the time-dependent flow over a rectangular wing moving with a supersonic forward speed and undergoing small vertical distortions expressible as polynomials involving spanwise and chordwise distances. The solution for the velocity potential is presented in a form analogous to that for steady supersonic flow having the familiar "reflected area" concept discovered by Evvard. Particular attention is paid to indicial-type motions and results are expressed in terms of generalized indicial forces. Numerical results for Mach numbers equal to 1.1 and 1.2 are given for polynomials of the first and fifth degree in the chordwise and spanwise directions, respectively, on a wing having an aspect ratio of 4.
An investigation of the nature of the flow field behind a rectangular wing of circular arc cross section has been conducted in the Langley 9-inch supersonic tunnel. Pitot- and static-pressure surveys covering a region of flow behind the wing have been made together with detailed pitot surveys throughout the region of the wake. In addition, the flow direction has been measured by means of a weathercocking vane. Theoretical calculations have been made to obtain the variation of both downwash and sidewash with angle of attack by using the superposition method of Lagerstrom, Graham, and Grosslight. In addition, the effect of wing thickness on the sidewash with the wing at 0 degree angle of attack has been evaluated.
The transonic similarity rules have been applied to the correlation of experimental data for a series of 22 rectangular wings having symmetrical NACA 63A-series sections, aspect ratios from 1/2 to 6, and thicknesses from 2 to 10 percent. The data were obtained by use of the transonic bump technique over a Mach number range from 0.40 to 1.10, corresponding to a Reynolds number range from 1.25 to 2.05 million. The results show that it is possible to correlate experimental data throughout the subsonic, transonic, and moderate supersonic regimes by using the transonic similarity parameters in forms which are consistent with the Prandtl-Glauert rule of linearized theory. The multiple families of basic data curves for the various aspect ratios and thickness ratios have been summarized in single presentations involving only one geometric variable - the product of the aspect ratio and the l/3 power of the thickness ratio.
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