Numerical calculation of bluff body flutter derivatives via computational fluid dynamics.

摘要

With the immense leap in computational speeds in the recent past, numerical experiments are fast maturing as a viable complement, if not an alternative, to wind tunnel investigations to study the various aerodynamic and aeroelastic phenomena. The central focus of the present study is the numerical calculation of flutter derivatives--fluid force coefficients associated with body oscillatory motions. These aeroelastic coefficients play an important role in determining the stability or instability of long, flexible structures under ambient wind loading.; Flutter derivatives are obtained most directly by simulating cross flow across an oscillating bluff body and comparing the unsteady lift and moment forces thus determined with theoretical expressions for the same written in terms of flutter coefficients. For a numerical simulation, such an approach would entail internal boundary motion in the flow, which requires considerable computational effort in case of most Eulerian non-adaptive grid-based schemes. An alternate approach to calculation of flutter derivatives using indicial functions has been proposed in the present study. In this approach, flutter derivatives are obtained analytically from step-start flow definitions that elicit indicial or impulse response functions for the unsteady lift and moment forces. These transient responses are obtained via numerical simulation. In recent years, the finite element method (FEM) has gained considerable acceptance in the solution of problems governed by the viscous, incompressible flow equations. FIDAP, one such general fluid dynamics analysis package that employs the finite element methodology, has been used to simulate flow circumstance that produce the above-mentioned indicial responses for a variety of bluff sections.; FEM is based on an Eulerian formulation of the governing equations. For moderate-to-high Reynolds number flows, convection often dominates and the grid points required to simulate the flow can be computationally prohibitive. Vortex methods, on the other hand, offer an efficient way to track vorticity in convection dominated regions of an external flow, while grid-based finite difference schemes provide the flexibility and accuracy to capture the viscosity dominated regions of the flow. Therefore, a hybrid finite difference--vortex method flow solver has been devised in this study for two-dimensional flow across bluff sections. For calibration purposes, the bluff body of primary focus is chosen as a square cylinder. Development along these lines, internationally, is still in a nascent state. The coupled solver developed in the present study employs an Eulerian finite difference grid in the viscous region next to the bluff section boundaries and a Lagrangian vortex particle domain in flow regions away from the boundaries. Results of this portion of the study match selected results from the recent literature.