Development of a Discrete-time Aerodynamic Model for Cfd- Based Aeroelastic Analysis

System identification is used to develop an accurate and computationally efficient discrete-time aerodynamic model of a three-dimensional, unsteady CFD solution. This aerodynamic model is then used in place of the unsteady CFD solution in a coupled aeroelastic analysis resulting in a substantial savings in computational time. The methodology has the advantage of producing an explicit mathematical relationship for the aerodynamic forces acting on a structure while still retaining the accuracy of the complete unsteady CFD solution. The explicit aerodynamic model can then be coupled with the known structural model and recast in state-space form. Using the combined state-space form, stability and control analysis for the aeroelastic system can be completed based on an eigenvalue solution for the state matrices. Results address the extent to which this methodology is applicable to aerospace applications. Nomenclature ρ = free stream density a = free stream speed of sound CFD = Computational Fluid Dynamics [C] = generalized damping matrix f = frequency fa = generalized aerodynamic force vector [I] = identity matrix [K] = generalized stiffness matrix [M] = generalized mass matrix M = Mach number nr = number of roots or mode shapes q = free stream dynamic pressure q = generalized displacement vector Introduction Predicting instabilities in the aeroelastic behavior of aerospace structures is important in the design of modern aircraft which operate over a wide envelope. However, a complete aeroelastic analysis is often difficult to complete due to the complex structural, aerodynamic, and control interactions associated with even the simplest flight vehicles. In order to obtain the most accurate predictions for aircraft flight characteristics, contemporary research has turned toward the development of an integrated computational model capable of capturing these complex interactions. One of the most powerful computational tools available for aerodynamic analysis is the CFD model. Such a model is often desirable for advanced aerospace applications since it makes the fewest assumptions about the characteristics of the flow field and is capable of accurately predicting complex shock interactions for transonic and supersonic flows around a complicated three-dimensional geometry. For aeroelastic analysis, one can take advantage of these benefits by coupling an unsteady Euler or Navier-Stokes CFD algorithm to an accurate structural dynamics solver and predict the complete aeroelastic response of a structure. However, the computational time required for a CFD-based aeroelastic simulation has typically limited the use of such models in an operational environment even with recent advances in CPU speeds. Furthermore, this type of formulation is not amenable to a controls analysis since a transfer function or state-space representation for the CFD model is not explicitly defined. When running a coupled aeroelastic simulation, it is the unsteady CFD solution at each time step which requires the overwhelming proportion of CPU time. Hence, recent research has targeted the acceleration of this solution through various modeling techniques. In particular, system identification has been shown to yield a significant savings in computational time for CFD-based aeroelastic analysis. * Graduate Research Assistant, Student Member AIAA. † Assistant Professor, Senior Member AIAA. ‡ Aerospace Engineer, Member AIAA. Copyright © 1999 by Timothy J. Cowan and Andrew S. Arena, Jr.. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.