Ashok Gopalarathnam

Poststall Prediction of Multiple-Lifting-Surface Configurations Using a Decambering Approach

A novel scheme is presented for an iterative decambering approach to predict the post-stall characteristics of wings using known section data as inputs. The new scheme differs from earlier ones in the details of how the residual is computed. With this scheme, multiple solutions at high angles of attack are brought to light right during the computation of the residual for the Newton iteration. As with earlier schemes, multiple solutions are obtained for wings at high angles of attack and the resulting converged solution depends on the initial conditions used for the iteration. In general, the new scheme is found to be more robust at achieving convergence. Results are presented for a rectangular wing with two different airfoil lift curves and for a wing-tail configuration.

Low-Speed Natural-Laminar-Flow Airfoils: Case Study in Inverse Airfoil Design

A systematic study of the trends in low-speed natural-laminar-eow airfoils for general aviation applications is presented. The airfoils have been designed using a multipoint inverse airfoil design method, which allows for specie cation of velocity and boundary-layer properties over different portions of the airfoil. A panel method with a coupled boundary-layer scheme is used to analyze the characteristics of the resulting airfoils. By systematically adjusting the speciecations, families of airfoils have been designed with different lift, drag, and pitching-moment characteristics. Parametric studies are presented to study the tradeoffs involved in designing laminar-e ow airfoils for general aviation. Although the results of the study are speciec to the class of airplanes considered, the design philosophies and the design approach used inthestudy areapplicable toa widerangeof airplanes. In addition, the examples presented in the paper form an excellent case study to demonstrate the power of modern inverse design techniques in controlling the performance of an airfoil to a ene degree and in generating a custom database of airfoils suitable for airplane multidisciplinary optimization and trade studies.

Investigations of Lift-Based Pitch-Plunge Equivalence for Airfoils at Low Reynolds Numbers

The limits of linear superposition in two-dimensional high-rate low-Reynolds-number aerodynamics are examined by comparing the lift-coefficient history and flowfield evolution for airfoils undergoing harmonic motions in pure pitch, pure plunge, and pitch―plunge combinations. Using quasi-steady airfoil theory and Theodorsens formula as predictive tools, pitching motions are sought that produce lift histories identical to those of prescribed plunging motions. It follows that a suitable phasing of pitch and plunge in a combined motion should identically produce zero lift, canceling either the circulatory contribution (with quasi-steady theory) or the combination of circulatory and noncirculatory contributions (with Theodorsens formula). Lift history is measured experimentally in a water tunnel using a force balance and is compared with two-dimensional Reynolds-averaged Navier―Stokes computations and Theodorsens theory; computed vorticity contours are compared with dye injection in the water tunnel. Theodorsens method evinces considerable, and perhaps surprising, resilience in finding pitch-to-plunge equivalence of lift-coefficient―time history, despite its present application to cases in which its mathematical assumptions are demonstrably violated. A combination of pitch and plunge motions can be found such that net lift coefficient is nearly identically zero for arbitrarily high reduced frequency, provided that amplitude is small. Conversely, cancellation is possible at large motion amplitude, provided that reduced frequency is moderate. The product of Strouhal number and nondimensional amplitude is therefore suggested as the upper bound for when superposition and linear predictions remain valid in massively unsteady two-dimensional problems.

Design of low Reynolds number airfoils with trips

A design philosophy for low Reynolds number airfoils that judiciously combines the tailoring of the airfoil pressure distribution using a transition ramp with the use of boundary-layer trips is presented. Three airfoils with systematic changes to the shape of the transition ramp have been designed to study the effect of trips on the airfoil performance. The airfoils were wind-tunnel tested with various trip locations and at Reynolds numbers of 100,000 and 300,000 to assess the effectiveness of the design philosophy. The results show that the design philosophy was successfullyusedin integratinga boundary-layertrip from theoutsetin theairfoildesignprocess.FortheReynolds numbers and the range of airfoil shapes considered, however, airfoils designed with trips do not hold any clear advantage over airfoils designed for good performance in the clean condition.

Computation vs. Experiment for High-Frequency Low-Reynolds Number Airfoil Pitch and Plunge

For a set of pure-pitch and pure-plunge sinusoidal oscillations of the SD7003 airfoil, phase-averaged measurements using particle image velocimetry in a water tunnel are compared with computations using an Immersed Boundary Method and an unsteady Reynolds-Averaged Navier Stokes solver. Re = 40,000 and Re = 10,000, based on free stream velocity and airfoil chord, were chosen as representative values for, respectively, a case where transition in attached boundary layers would be of some importance, and a case where transition would not be expected to occur in attached boundary layers. The two computational approaches were compared for capacity to resolve shed vortical structures near the airfoil and in the wake, and for capacity to resolve the mean streamwise momentum balance in the wake. The plunge and pitch were each at reduced frequency k = 3.93 and with kinematically equivalent amplitudes of effective angle of attack, with the pivot point at the quarter chord. For the plunge cases, agreement between computation and experiment was qualitatively excellent and quantitatively acceptable, but for the pitch cases, the wake structure in the experiment was markedly different from that predicted by both computations, which were however similar among one another. This result was not appreciably altered by whether or not the test section walls were modeled in the computation. In all cases, Reynolds number effects were found to be negligible. Experimental-computational agreement for plunge, but lack of agreement for pitch, is presently left unresolved.

An Iterative Decambering Approach for Post-Stall Prediction of Wing Characteristics using known Section Data

An iterative decambering approach for the post stall prediction of wings using known section data as inputs is presented. The method can currently be used for incompressible flow and can be extended to compressible subsonic flow using Mach number correction schemes. A detailed discussion of past work on this topic is presented first. Next, an overview of the decambering approach is presented and is illustrated by applying the approach to the prediction of the two-dimensional Cl and Cm curves for an airfoil. The implementation of the approach for iterative decambering of wing sections is then discussed. A novel feature of the current effort is the use of a multidimensional Newton iteration for taking into consideration the coupling between the different sections of the wing. The approach lends itself to implementation in a variety of finite-wing analysis methods such as lifting-line theory, discrete-vortex Weissinger’s method, and vortex lattice codes. Results are presented for a rectangular wing for α from 0t o 25 deg. The results are compared for both increasing and decreasing directions of α, and they show that a hysteresis loop can be predicted for post-stall angles of attack.

Ideal Lift Distributions and Flap Angles for Adaptive Wings

An approach is presented for determining the optimum flap angles and spanwise loading to suit a given flight condition. Multiple trailing-edge flaps along the span of an adaptive wing are set to either reduce drag in rectilinear flight conditions or to limit the wing bending moment at maneuvering conditions. For reducing drag, the flaps are adjusted to minimize induced drag, while simultaneously enabling the wing sections to operate within their respective low-drag ranges. For limiting wing bending moment, the flaps are used to relieve the loading near the wing tips. An important element of the approach is the decomposition of the flap angles into a distribution that can be used to control the spanwise loading for induced-drag control and a constant flap that can used for profile-drag control. The problem is linearized using the concept of basic and additional lift distributions, which enables the use of standard constrained-minimization formulations. The results for flap-angle distributions for different flight conditions are presented for a planar and a nonplanar wing. Postdesign analysis and aircraft-performance simulations are used to validate the optimum flap-angle distributions determined using the current approach.

Automated cruise flap for airfoil drag reduction over a large lift range

A small trailing-edge e ap, often referred to as a cruise e ap or camber-changing e ap, can be used to extend the low-drag range of a natural-laminar-e ow airfoil. Automation of such a cruise e ap is likely to result in improved aircraft performance over a large speed range without an increase in the pilot work load. An important step in achieving the automation is to arrive at a simple approach for determination of the optimum e ap angle for a given airfoil lift coefe cient. This optimum e ap angle can then be used in a closed-loop control system to set the e ap automatically. Two pressure-based schemes are presented for determining the optimum e ap angle for any given airfoil lift coefe cient. The schemes use the pressure difference between two pressure sensors on the airfoil surface close to the leading edge. In each of the schemes, for a given lift coefe cient, this nondimensionalized pressure difference is brought to a predetermined target value by dee ecting the e ap. It is shown that the drag bucket is then shifted to bracket the given lift coefe cient. This nondimensional pressure difference, therefore, can be used to determine and set the optimum e ap angle for a specie ed lift coefe cient. The two schemes differ in the method used for the nondimensionalization. The effectiveness of the two schemesisverie ed using computational and windtunnel results for two NASA laminar e ow airfoils. Finally, an aircraft performance simulation approach is used to analyze the potential aircraft performance benee ts while addressing trim drag considerations.

Multipoint inverse method for multielement airfoil design

A multipoint inverse method has been developed for the design of multielement airfoils with desired velocity distributions in incompressible potential flow. The method uses an isolated-airfoil, multipoint, inverse code to generate each element of the multielement airfoil and a two-dimensional panel method to analyze the multielement airfoil. Through Newton iteration, the variables associated with the design of the elements in isolation are adjusted to achieve desired multielement velocity distributions. As the paper demonstrates, changes in the velocity distributions over the elements in isolation result in remarkably similar changes in the velocity distributions over the corresponding elements of the multielement airfoil. This similarity results in two key features of the design method: 1) the use of the isolated airfoil velocity distributions as design variables to achieve desired distributions over the multielement airfoil, and 2) the calculation of the gradient information for the Newton iteration during the design of the isolated airfoils rather than by several panel-method analyses, resulting in substantial savings in computation time

Drag Reduction Methodology for Adaptive Tailless Aircraft

An approach is presented for determining optimum lift distributions for adaptive tailless aircraft. In this study, wing adaptation is achieved using multiple trailing-edge flaps that are used to optimally distribute the lift of the wing such that drag is minimized. For tailless aircraft that are stable in pitch, the lack of a secondary lifting surface makes it necessary that the lift distribution on the wing also satisfies a pitching-moment constraint to ensure trim. The current work implements a numerical approach that solves for the optimal scheduling of multiple trailing-edge flaps on the wing of a tailless aircraft for various flight conditions with a pitching-moment constraint to reduce both induced and profile drag. The approach uses superposition to construct the spanwise lift distribution from basic and additional loadings, and decomposes the flap-angle distribution into mean and variation distributions. Together, these elements enable the solution of the problem using semi-analytical methods that also provide insight. The results are presented for a planar, swept, tapered wing with two airfoil-section choices to verify the theory and provide insight for trade studies.