Transonic flutter analysis using a fully coupled density based solver for inviscid flow

This paper focuses on the coupling between the high fidelity aerodynamic model for the flow field and the modal analysis of a typical wing section to carry out flutter analysis. This coupled aeroelastic model is implemented in one of the most widely used open source CFD codes called OpenFOAM. The model is designed to calculate the structural displacement in the time domain based on the free vibration modes of the structure by constructing the numerical model directly from the modal analysis. Essentially a second order ordinary differential equation is solved for each mode as a function of the generalised coordinates. A density based solver using central difference scheme of Kurganov and Tadmor is used to model the flow field. Two main cases of transonic flow over NACA 64A010 are modelled for a forced pitching oscillation airfoil and a self-sustained aerofoil respectively. The self-sustained two degrees of freedom case is modelled for three different possibilities covering damped, neutral and divergent oscillations. Predicted results show very good agreement with the numerical and experimental data available in the literature.

[1]  Koji Isogai,et al.  On the Transonic-Dip Mechanism of Flutter of a Sweptback Wing , 1979 .

[2]  John W. Edwards,et al.  AIAA 98-2421 An Overview of Recent Developments in Computational Aeroelasticity , 1998 .

[3]  E. Tadmor,et al.  New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection—Diffusion Equations , 2000 .

[4]  Sophie Papst,et al.  Computational Methods For Fluid Dynamics , 2016 .

[5]  Hrvoje Jasak,et al.  Dynamic Mesh Handling in OpenFOAM , 2009 .

[6]  Aleksandar Jemcov,et al.  OpenFOAM: A C++ Library for Complex Physics Simulations , 2007 .

[7]  Robert H. Scanlan,et al.  A Modern Course in Aeroelasticity , 1981, Solid Mechanics and Its Applications.

[8]  David M. Schuster,et al.  Computational Aeroelasticity: Success, Progress, Challenge , 2003 .

[9]  Juan J. Alonso,et al.  Application of a Non-Linear Frequency Domain Solver to the Euler and Navier-Stokes Equations , 2002 .

[10]  Her Mann Tsai,et al.  Calculation of Wing Flutter by a Coupled Fluid-Structure Method , 2001 .

[11]  O. Bendiksen.  Review of unsteady transonic aerodynamics: Theory and applications , 2011 .

[12]  H. Jasak,et al.  Automatic mesh motion for the unstructured finite volume method , 2007 .

[13]  Juan J. Alonso,et al.  Fully-implicit time-marching aeroelastic solutions , 1994 .

[14]  Oddvar O. Bendiksen,et al.  Fluid–structure interactions with both structural and fluid nonlinearities , 2008 .

[15]  Guru P. Guruswamy,et al.  A review of numerical fluids/structures interface methods for computations using high-fidelity equations , 2002 .

[16]  Weeratunge Malalasekera,et al.  An introduction to computational fluid dynamics - the finite volume method , 2007 .

[17]  C. J. Greenshields,et al.  Implementation of semi‐discrete, non‐staggered central schemes in a colocated, polyhedral, finite volume framework, for high‐speed viscous flows , 2009 .

[18]  Sergio A. Elaskar,et al.  High Speed Flow Simulation Using OPENFOAM , 2012 .

[19]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[20]  Yuan-Cheng Fung,et al.  An introduction to the theory of aeroelasticity , 1955 .

[21]  K. Isogai,et al.  Transonic dip mechanism of flutter of a sweptback wing. II , 1981 .

[22]  Alan H. Karp,et al.  A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides , 1990, TOMS.

[23]  Gecheng Zha,et al.  Flutter Prediction Based on Fully Coupled Fluid-Structural Interactions , 2004 .