A multivariate interpolation scheme, using radial basis functions, is presented, which results in a completely unified formulation for the fluid–structure interpolation and mesh motion problems. The method has several significant advantages. Primarily, all volume mesh, structural mesh, and flow-solver type dependence is removed, and all operations are performed on totally arbitrary point clouds of any form. Hence, all connectivity and user-input requirements are removed from the computational fluid dynamics–computational structural dynamics (CFD–CSD) coupling problem, as only point clouds are required to determine the coupling. Also, it may equally well be applied to structured and unstructured grids, or structural and aerodynamic grids that intersect, again because no connectivity information is required. Furthermore, no expensive computations are required during an unsteady simulation, just matrix–vector multiplications, since the required dependence relations are computed only once prior to any simulation and then remain constant. This property means that the method is both perfectly parallel, since only the data relevant to each structured block or unstructured partition are required to move those points, and totally independent from the flow solver. Hence, a completely generic ‘black box’ tool can be developed, which is ideal for use in an optimization approach. Aeroelastic behaviour of the Brite–Euram MDO wing is analysed in terms of both static deflection and dynamic responses, and it is demonstrated that responses are strongly dependent on the exact CFD–CSD interpolation used. Mesh quality is also examined during the motion resulting from a large surface deformation. Global grid quality is shown to be preserved well, with local grid orthogonality also being maintained well, particularly at and near the moving surface, where the original orthogonality is retained. Copyright © 2007 John Wiley & Sons, Ltd.

Unified fluid-structure interpolation and mesh motion using radial basis functions

Non-linear aeroelastic prediction for aircraft applications

The exploitation of computational fluid dynamics for aeroelastic simulations is mainly based on time-domain simulations. There is an intense research effort to overcome the computational cost of this approach. Significant aeroelasticeffectsdrivenbynonlinearaerodynamicsincludethetransonic flutterdipandlimit-cycleoscillations.The paper describes the use of Hopf bifurcation and center manifold theory to compute flutter speeds and limit-cycle responses of wings in transonic flow when the aerodynamics are modeled by the Euler equations. The cost of the calculations is comparable to steady-state calculations based on computational fluid dynamics. The paper describes twomethodsfor findingstabilityboundariesandthenanapproachtoreducingthefull-ordersystemtotwodegreesof freedom in the critical mode. Details of the three methods are given, including the calculation of first, second, and thirdJacobiansandthesolutionofsparselinearsystems.ResultsfortheAGARDwing,asupercriticaltransporttype of wing, and the limit-cycle response of the Goland wing are given. Nomenclature A = Jacobian matrix of R with respect to w B, C = second and third Jacobian operators h = (scalar) increment for finite differences F = quadratic and higher terms in R G = Taylor coefficients of the residual restricted to the critical eigenspace H = Taylor coefficients of the residual restricted to the noncritical eigenspace f = convective flux discretization kij = coefficients in center manifold expansion of y P = right eigenvector of A, P1 � iP2 Q = left eigenvector of A, Q1 � iQ2 qs = constant scaling vector for the augmented system R = residual vector v = vector for the matrix-free product w = vector of unknowns y = part of w in the noncritical eigenspace z = part of w in the critical eigenspace � t = time step � i = sequence of eigenvalues in the inverse power method � = bifurcation parameter (dynamic pressure) ! = frequency of critical eigenvalue or shift for the inverse power method Subscripts

/pdf/fast-prediction-of-transonic-aeroelastic-stability-and-limit-3pjz106i0a.pdf

Fast prediction of transonic aeroelastic stability and limit cycles

Unified Approach to CFD-CSD Interpolation and Mesh Motion using Radial Basis Functions

DOI: 10.2514/1.46971 Flutter prediction as currently practiced is almost always deterministic in nature, based on a single structural model that is assumed to represent a fleet of aircraft. However, it is also recognized that there can be significant structural variability, even for different flights of the same aircraft. The safety factor used for flutter clearance is in part meant to account for this variability. Simulation tools can, however, represent the consequences of structural variability in the flutter predictions, providing extra information that could be useful in planning physical tests and assessing risk. The main problem arising for this type of calculation when using high-fidelity tools based on computational fluid dynamics is the computational cost. The current paper uses an eigenvalue-based stability method together with Euler-level aerodynamics and different methods for propagating structural variability to stability predictions.The propagation methodsare Monte Carlo,perturbation, andinterval analysis. Thefeasibility of this type of analysis is demonstrated. Results are presented for the Goland wing and a generic fighter configuration.

Transonic Aeroelastic Stability Predictions Under the Influence of Structural Variability

This paper demonstrates coupled time-domain computational-fluid-dynamics (CFD) and computationalstructural-dynamics simulations for flutter analysis of a real aircraft in the transonic regime. It is shown that a major consideration for a certain class of structural models is the transformation method, which is used to pass information between the fluid and structural grids. The aircraft used for the calculations is the BAE Systems Hawk. A structural model, which has been developed by BAE Systems for simplified linear flutter calculations, only has a requirement for O(10) degrees of freedom. There is a significant mismatch between this and the surface grid on which loads and deflections are defined in the CFD calculation. This paper extends the constant volume tetrahedron tranformation, previously demonstrated for wing-only aeroelastic calculations, to multicomponent, or full aircraft, cases and demonstrates this for the Hawk. A comparison is made with the predictions of a linear flutter code.

D. Nardini

Papers

Aeroelastic calculations for the hawk aircraft using the euler equations