Abstract

This paper deals with a numerical simulation of compressible viscous fluid flow around three flat plates with prescribed harmonic motion. This arrangement presents a simplified blade cascade with forward wave motion. The aim of this simulation is to determine the aerodynamic forces acting on the flat plates. The mathematical model describing this problem is formed by Favre-averaged system of Navier-Stokes equations in arbitrary Lagrangian-Eulerian (ALE) formulation completed by one-equation Spalart-Allmaras turbulence model. The simulation was performed using the developed in-house CFD software based on discontinuous Galerkin method, which offers high order of accuracy.

Highlights

  • In the forties of the 20th century, first papers focused on the aero-elasticity of blades in axial turbines appeared [1]

  • The developed in-house CFD software based on the discontinuous Galerkin method was applied to the numerical simulation of compressible viscous fluid flow through a simplified blade cascade with prescribed harmonic motion

  • The in-house CFD solver based on the discontinuous Galerkin method was developed for the numerical solution of compressible viscous flow problems in domains with moving boundaries

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Summary

Introduction

In the forties of the 20th century, first papers focused on the aero-elasticity of blades in axial turbines appeared [1]. Empirical criterion on arising of flutter is introduced in the paper [2] This criterion is based on a reduced blade frequency for bending blade vibration. The term flutter was established for flow attached to the vibration of blade when phase displacement between blade motion and induced aerodynamic forces occurs. For purpose of this study, we choose the travelling wave mode approach for the numerical modelling of the unsteady flow and flutter analysis in the simplified blade cascade formed by three flat plates. All flat plates in the cascade vibrate and their mutual movement prescribes the travelling waves in the cascade The aim of this numerical study is to determine aerodynamic forces acting on the flat plates in cascade, when the harmonic motion with phase delay is prescribed. For the numerical simulation one flow speed and forward travelling wave mode in the cascade were considered

Mathematical model
Discretization
Numerical results
Conclusion

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