Unsteady and Post-Stall Aerodynamic Modeling for Flight Dynamics Simulation

Abstract

This paper presents a methodology for flight dynamics simulation inclu ding three-dimensional unsteady and post-stall aerodynamics. This is accomplished by integrating a decambering viscous correction into a linearized unsteady vortex lattice method. Coupling the aerodynamic model with the nonlinear rigid-aircraft equations of motion results in a low-order, medium-fidelity framework for flight dynamics simulation. The numerical studies first evaluate the im portance of unsteady aerodynamic effects on the dominant aircraft modes, illustrating the errors incurred on the prediction of the short period when quasi-steady approximations are employed. Next, the combined impact of unsteady and post-stall aerodynamics is assessed on a maneuvering aircraft. Furthermore, the framework is expected to be a suitable design-oriented tool for flight con trol synthesis and to incorporate aeroelastic modeling. I. Introduction High fidelity aerodynamic models implemented in the form of l ook-up tables [1‐3] are commonplace in certified flight simulators and training devices. Force and moment inf ormation for these look-up tables is commonly developed using some combination of the following techniques: Computational Fluid Dynamics (CFD), experimental testing of models in wind tunnels (static and dynamic), and/or experimental flight testing. Both CFD methods and data from experiments are capable of representing forces and moments in the nominal flight regime, where aerodynamics are expected to be linear, and beyond this range where significan t amounts of flow separation exist (aerodynamic stall). The primary disadvantage of using these high-fidelity repre sentations of forces and moments is the significant effort required to develop the look-up table. Each expected operating condition, defined not only by the aerodynamic inflow angles but also three components of angular rates, derivatives of these rates, and other explanatory variables as desir ed, must be run as a CFD or experimental test case to develop the look up table. It is often not feasible to perform such an extensive study due to limited resources, or because the required level of detail is simply not available at early conceptual design stages. The methodology presented in this research represents a departure from the high-fidelity approach discussed above. A medium fidelity aerodynamics model is considered, based on an unsteady vortex lattice method (UVLM) [4, 5] with a post-stall model based on iterative decambering [6, 7]. The UVLM is a fully unsteady, three-dimensional aerodynamic method, which is very accurate as long as potentialflow conditions are satisfied [ 8] ‐ in practice this requires low speed, attached flow. Howeve r, with increasing angles of attack, the boundary layer on the upper surface of a wing thickens and finally separates. If separation occurs, then potential-flow predictions deviate from the real viscous flo w. The underlying idea of the decambering methodology is that this mismatch due to the boundary-layer displacement thickness and separation can be related to an effective change in the chordwise camber. In other words, the goal is to match the potential-flow solution to the viscous one by introducing a decambering variable, which is effectively a camber correction ‐ it can also be seen as a rotation of the airfoil, modifying the effective angle of incidence to fit vi scous data. This idea has been around for several decades, but most recent progress can be found in Refs. [6, 9‐12]. While the scheme relies on a 2D airfoil data, 3D effects can be incorporated by accounting for the aerodynamic interference among all lifting-surface airfoils. This can be easily done on the UVLM, for instance, when enforcing the boundary conditions. A strip-theory philosophy for engineeringlevel predictions of wing aerodynamics at high angles of attack has been extensively adopted before [13‐17], leading