FEM simulation of turbulent flow in a turbine blade passage with dynamical fluid–structure interaction

Results are described from a combined mathematical modeling and numerical iteration schemes of flow and vibration. We consider the coupling numerical simulations of both turbulent flow and structure vibration induced by flow. The methodology used is based on the stabilized finite element formulations with time integration. A fully coupled model of flow and flow-induced structure vibration was established using a hydride generalized variational principle of fluid and solid dynamics. The spatial discretization of this coupling model is based on the finite element interpolating formulations for the fluid and solid structure, while the different time integration schemes are respectively used for fluid and solid structure to obtain a stabilized algorithm. For fluid and solid dynamics, Hughes' predictor multi-corrector algorithm and the Newmark method are monolithically used to realize a monolithic solution of the fully coupled model. The numerical convergence is ensured for small deformation vibrating problems of the structure by using different time steps for fluid and solid, respectively. The established model and the associated numerical methodology developed in the paper were then applied to simulate two different flows. The first one is the lid-driven square cavity flow with different Reynolds numbers of 1000, 400 and 100 and the second is the turbulent flows in a 3-D turbine blade passage with dynamical fluid-structure interaction. Good agreement between numerical simulations and measurements of pressure and vibration acceleration indicates that the finite element method formulations developed in this paper are appropriate to deal with the flow under investigation.

[1]  K. Namkoong,et al.  Computation of dynamic fluid-structure interaction in two-dimensional laminar flows using combined formulation , 2005 .

[2]  P. Durbin,et al.  Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage , 2001, Journal of Fluid Mechanics.

[3]  Jungwoo Kim,et al.  An immersed-boundary finite-volume method for simulations of flow in complex geometries , 2001 .

[4]  Klaus-Jürgen Bathe,et al.  Finite element analysis of incompressible and compressible fluid flows with free surfaces and structural interactions , 1995 .

[5]  Guru P. Guruswamy,et al.  Aeroelastic Analysis of Transonic Wings Using Navier-Stokes Equations and a Nonlinear Beam Finite Element Model , 1999 .

[6]  J. Ferziger,et al.  A ghost-cell immersed boundary method for flow in complex geometry , 2002 .

[7]  Tayfun E. Tezduyar,et al.  Modelling of fluid–structure interactions with the space–time finite elements: Solution techniques , 2007 .

[8]  Louis A. Povinelli,et al.  Large-scale computation of incompressible viscous flow by least-squares finite element method , 1994 .

[9]  K. M. Liew,et al.  A computational approach for predicting the hydroelasticity of flexible structures based on the pressure Poisson equation , 2007 .

[10]  Marcello Manna,et al.  Large eddy simulation of turbulent flows via domain decomposition techniques. Part 1: theory , 2005 .

[11]  P. Moin,et al.  Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow , 1998 .

[12]  In Chul Kim,et al.  Computations of flow over a flexible plate using the hybrid Cartesian/immersed boundary method , 2007 .

[13]  Guru P. Guruswamy,et al.  Fluid-structural interactions using Navier-Stokes flow equations coupled with shell finite element structures , 1993 .

[14]  Jørgen Juncher Jensen,et al.  Review of hydroelasticity theories for global response of marine structures , 2006 .

[15]  Tayfan E. Tezduyar,et al.  Stabilized Finite Element Formulations for Incompressible Flow Computations , 1991 .

[16]  Tayfun E. Tezduyar,et al.  Finite elements in fluids: Special methods and enhanced solution techniques , 2007 .

[17]  Jun Zhang,et al.  Enhanced multi-level block ILU preconditioning strategies for general sparse linear systems , 2001 .

[18]  C. Peskin.  Numerical analysis of blood flow in the heart , 1977 .

[19]  A. M. Awruch,et al.  Numerical simulation of fluid–structure interaction using the finite element method , 2005 .

[20]  Yakun Guo,et al.  NUMERICAL SIMULATION OF FLOW FEATURES AND ENERGY EXCHANGE PHYSICS IN NEAR-WALL REGION WITH FLUID-STRUCTURE INTERACTION , 2008 .

[21]  J. Wissink.  DNS OF SEPARATING, LOW REYNOLDS NUMBER FLOW IN A TURBINE CASCADE WITH INCOMING WAKES , 2003 .

[22]  K. Liew,et al.  Parallel-multigrid computation of unsteady incompressible viscous flows using a matrix-free implicit method and high-resolution characteristics-based scheme , 2005 .

[23]  Marcello Manna,et al.  Large eddy simulation of turbulent flows via domain decomposition techniques. Part 2: applications , 2005 .

[24]  K. M. Liew,et al.  An efficient parallel computation of unsteady incompressible viscous flow with elastic moving and compliant boundaries on unstructured grids , 2005 .

[25]  A. Huerta,et al.  Arbitrary Lagrangian–Eulerian formulation for fluid–rigid body interaction , 2001 .

[26]  Chang Shu,et al.  Numerical computation of three‐dimensional incompressible Navier–Stokes equations in primitive variable form by DQ method , 2003 .

[27]  W. Rodi.  DNS and LES of some engineering flows , 2006 .

[28]  M. Heil.  An efficient solver for the fully-coupled solution of large-displacement fluid-structure interaction problems , 2004 .

[29]  W. Rodi,et al.  Direct numerical simulation of flow and heat transfer in a turbine cascade with incoming wakes , 2006, Journal of Fluid Mechanics.

[30]  Parviz Moin,et al.  ADVANCES IN LARGE EDDY SIMULATION METHODOLOGY FOR COMPLEX FLOWS , 2002, Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena.

[31]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[32]  T. Tezduyar.  Computation of moving boundaries and interfaces and stabilization parameters , 2003 .

[33]  Guru P. Guruswamy,et al.  Direct coupling of Euler flow equations with plate finite element structures , 1995 .

[34]  Laszlo Fuchs,et al.  Large eddy simulation of the flow through the blades of a swirl generator , 2000 .

[35]  Shinobu Yoshimura,et al.  A monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure Poisson equation , 2005 .

[36]  S. Acharya,et al.  Large eddy simulation of turbulent flows in complex and moving rigid geometries using the immersed boundary method , 2005 .

[37]  G. Iaccarino,et al.  Immersed boundary technique for turbulent flow simulations , 2003 .

[38]  Lixiang Zhang,et al.  Large eddy simulation of turbulent flow in a true 3D Francis hydro turbine passage with dynamical fluid–structure interaction , 2007 .

[39]  M. S. Gadala,et al.  A complete finite element treatment for the fully coupled implicit ALE formulation , 2004 .

[40]  S. A. Jordan.  A Large-Eddy Simulation Methodology in Generalized Curvilinear Coordinates , 1999 .

[41]  Parviz Moin,et al.  Zonal Embedded Grids for Numerical Simulations of Wall-Bounded Turbulent Flows , 1996 .

[42]  M. Souli,et al.  ALE formulation for fluid–structure interaction problems , 2000 .

[43]  Tayfun E. Tezduyar,et al.  Finite elements in fluids: Stabilized formulations and moving boundaries and interfaces , 2007 .

[44]  P. Moin,et al.  DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research , 1998 .

[45]  Georgi Kalitzin,et al.  DNS of fully turbulent flow in a LPT passage , 2003 .

[46]  G. Hulbert,et al.  A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method , 2000 .

[47]  Charbel Farhat,et al.  Partitioned analysis of coupled mechanical systems , 2001 .

[48]  Samir Ziada,et al.  Flow-Induced Vibrations in Power and Process Plant Components—Progress and Prospects , 2000 .