Nonlinear aeroelastic analysis is essential for high-altitude long-endurance (HALE) aircraft. In the current paper, we have presented a computational aeroelastic tool for nonlinear-aerodynamics/nonlinear-structure interaction. Specifically, a consistent nonlinear time-domain aeroelastic methodology has been integrated via tightly coupling a geometrically exact nonlinear intrinsic beam model and the generalized unsteady vortex-lattice aerodynamic model with vortex roll-up and free wake. The effects of discrete gust as well as flow separation at various angles of attack from attached flow to the stall and poststall ranges are also included in the nonlinear aerodynamic model. A HALE-wing model is analyzed as a numerical example. The trim angle of attack is first found for the wing, and the results show that aeroelastic instability could occur at higher angles of attack. The HALE-wing model under the trim condition is then analyzed for various gust profiles to which it is subject. It is found that for certain gust levels, the elastic deformations of the HALE wing tend to become unstable: notably, the in-plane deflections become very significant. It is noted for the unstable solution of the HALE wing that the flow may be well beyond the stall range. An engineering approach with the use of the nonlinear sectional lift is attempted to consider such stall effects.

Nonlinear-Aerodynamics/Nonlinear-Structure Interaction Methodology for a High-Altitude Long-Endurance Wing

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.

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Poststall prediction of multiple-lifting-surface configurations using a decambering approach

Numerical algorithms and solutions of generalized nonlinear lifting-line theory over an elliptical wing are examined, with emphasis on near/poststall flows. First, a thorough analysis on the circulation-based and angle-of-attack-based correction methods (Γ and α methods, respectively) highlights their respective numerical poststall characteristics. The stability of the method is demonstrated, producing single and multiple solutions in the pre- and poststall regions, respectively. Second, artificial dissipation added to the α method is shown to be an effective means of controlling the poststall flow region. Finally, a strongly coupled algorithm is presented, allowing to bypass the interpolation phase via the use of Legendre polynomials. The model sheds light on poststall flow behavior, in agreement with several papers studying formation of stall cell patterns.

Nonlinear Generalized Lifting-Line Coupling Algorithms for Pre/Poststall Flows

A modern nonlinear-lifting-line-theory algorithm allowing the prediction of aerodynamic coefficients and lifting-surface-pressure distribution for multiple aircraft configurations is presented. The algorithm is applied to isolated wing, high-lift systems (slat/main/flap), and multisurface configurations, with emphasis on the treatment of high-lift geometry representations. The fuselage is not geometrically modeled, but its influence is appropriately taken into account for the aerodynamic-coefficient evaluation. The results show good agreements with wind-tunnel and/or high-fidelity numerical data for the prediction of the maximum lift coefficient and the poststall behavior in subsonic and transonic conditions. The use of sectional airfoil data obtained via solutions of the Reynolds-averaged Navier–Stokes equations with infinite-swept-wing assumptions—so-called 2.5-dimensional model—is shown to greatly improve the results over traditional two-dimensional solutions.

Preliminary-Design Aerodynamic Model for Complex Configurations Using Lifting-Line Coupling Algorithm

The present work describes the design optimization of a variable-span morphing wing to be fitted to a small UAV which flies in the speed range 11m/s to 40m/s. An in-house aerodynamic shape optimization code, which uses a viscous two-dimensional panel method formulation coupled with a non-linear lifting-line algorithm or a non-linear vortex lattice algorithm and a sequential quadratic programming optimization routine, is used to solve a drag minimization problem to determine the optimal values of wing span for various speeds of the vehicle’s flight envelope while subject to geometric constraints. A simple weight representation model based on semi-empirical formulae and data obtained from a wing prototype was used to estimate the variable-span wing weight. Near its maximum speed it is possible to obtain a 20% wing drag reduction with the variable-span wing in comparison with the original fixed wing. An analysis is also developed and performed to compute the roll rate available with asymmetric span control of the variable-span wing showing that this matches the roll authority of a conventional wing with aileron control.

Design Optimization of a Variable-Span Morphing Wing for a Small UAV

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 .ow and can be extended to compressible subsonic .ow 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 C(sub l) and C(sub m) curves for an airfoil. The implementation of the approach for iterative decambering of wing sections is then discussed. A novel feature of the current e.ort is the use of a multidimensional Newton iteration for taking into consideration the coupling between the di.erent 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 a from 0 to 25 deg. The results are compared for both increasing and decreasing directions of a, and they show that a hysteresis loop can be predicted for post-stall angles of attack.

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Sung Wan Kim

Papers

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

An Iterative Decambering Approach for Post-Stall Prediction of Wing Characteristics from Known Section Data