Abstract
Lagrangian-Eulerian formulations based on a generalized variational principle
of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual (GMRES) method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GMRES-Hughes-Newmark algorithm presented in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.
of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual (GMRES) method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GMRES-Hughes-Newmark algorithm presented in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation.
Original language | English |
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Pages (from-to) | 87-96 |
Number of pages | 10 |
Journal | Applied Mathematics and Mechanics |
Volume | 31 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 2010 |
Keywords
- flow-induced vibration
- fluid-structure interaction
- generalized variational principle
- numerical methods
- generalized minumum residual (GMRES) method