Mesh Strategies for Accurate Computation of Unsteady Spoiler and Aeroelastic Problems

Abstract

A modi cation of the spring analogy scheme that uses axial linear spring stiffness with selective spring stiffening/relaxationis presented. An alternate approach to solvingthe geometric conservation law is taken that eliminates the need for storage of metric Jacobians at previous time steps. The method is applied to the computation of the turbulent ow about an airfoil with a two-dimensional moving spoiler surface. The aeroelastic response at low dynamic pressure of an airfoil to a single large-scale oscillation of a spoiler surface is simulated in a study of the effect of uid domain convergence and subiterative strategies. A critical issue in the computation of aeroelastic response with a strongly nonlinear ow eld is shown to be the convergence of the uid domain. It is con rmed that it is possible to achieve accurate solutions with a very large time step for aeroelastic problems using the uid solver and aeroelastic integrator as discussed. Furthermore, it is shown that a local pseudo-time-based subiterative method is essential for the computation of the present cases. Nomenclature= spring analogy boundary condition array h = nondimensional plunge, h ¤ / c ¤ i, j, k = grid point indices J = metric Jacobian K = spring stiffness matrix k m = element spring stiffness M = grid mass matrix m = subiteration index n = time-step index p = nondimensional pressure Q = conserved solution vector, q , q u, q v, q w , e q = solution vector, q , u, v, w , p q 1 = dynamic pressure r i jk = grid position vector, (x, y, z) etc. a = angle of attack (pitch) d = grid displacement d sp = spoiler de ection angle d g = central difference operator (g direction) f h = plunge damping ratio f a = pitch damping ratio n , g , f = coordinates in computational space q = density

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