Numerical Simulation of Airfoil Vibrations Induced by Turbulent Flow

2014 ◽  
Vol 17 (1) ◽  
pp. 146-188 ◽  
Author(s):  
Miloslav Feistauer ◽  
Jaromír Horáček ◽  
Petr Sváček
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Vertical Direction ◽  
Turbulence Models ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Element Discretization ◽  
Flow Equations

AbstractThe subject of the paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil with large amplitudes. The airfoil with three degrees of freedom performs rotation around an elastic axis, oscillations in the vertical direction and rotation of a flap. The numerical simulation consists of the finite element solution of the Reynolds averaged Navier-Stokes equations combined with Spalart-Allmaras or κ–ω turbulence models, coupled with a system of nonlinear ordinary differential equations describing the airfoil motion with consideration of large amplitudes. The time-dependent computational domain and approximation on a moving grid are treated by the Arbitrary Lagrangian-Eulerian formulation of the flow equations. Due to large values of the involved Reynolds numbers an application of a suitable stabilization of the finite element discretization is employed. The developed method is used for the computation of flow-induced oscillations of the airfoil near the flutter instability, when the displacements of the airfoil are large, up to ±40 degrees in rotation. The paper contains the comparison of the numerical results obtained by both turbulence models.

Numerical Simulation of Glottal Flow in Interaction with Self Oscillating Vocal Folds: Comparison of Finite Element Approximation with a Simplified Model

2012 ◽  
Vol 12 (3) ◽  
pp. 789-806 ◽  
Author(s):  
P. Sváček ◽  
J. Horáček
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Finite Element Approximation ◽  
Vocal Folds ◽  
Multistep Method ◽  
Element Approximation ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Stabilized Finite Element Method

AbstractIn this paper the numerical method for solution of an aeroelastic model describing the interactions of air flow with vocal folds is described. The flow is modelled by the incompressible Navier-Stokes equations spatially discretized with the aid of the stabilized finite element method. The motion of the computational domain is treated with the aid of the Arbitrary Lagrangian Eulerian method. The structure dynamics is replaced by a mechanically equivalent system with the two degrees of freedom governed by a system of ordinary differential equations and discretized in time with the aid of an implicit multistep method and strongly coupled with the flow model. The influence of inlet/outlet boundary conditions is studied and the numerical analysis is performed and compared to the related results from literature.

Numerical Simulations of Nonlinear Post-Critical Vibrations of an Airfoil After Flutter Instability

2011 ◽  
Author(s):  
Jaromi´r Hora´cˇek ◽  
Miloslav Feistauer ◽  
Petr Sva´cˇek
Keyword(s):  
Numerical Simulations ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Mass Matrix ◽  
Vertical Direction ◽  
Navier Stokes ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Classical Flutter

The contribution deals with the numerical simulation of the flutter of an airfoil with three degrees of freedom (3-DOF) for rotation around an elastic axis, oscillation in the vertical direction and rotation of a flap. The finite element (FE) solution of two-dimensional (2-D) incompressible Navier-Stokes equations is coupled with a system of nonlinear ordinary differential equations describing the airfoil vibrations with large amplitudes taking into account the nonlinear mass matrix. The time-dependent computational domain and a moving grid are treated by the Arbitrary Lagrangian-Eulerian (ALE) method and a suitable stabilization of the FE discretization is applied. The developed method was successfully tested by the classical flutter computation of the critical flutter velocity using NASTRAN program considering the linear model of vibrations and the double-lattice aerodynamic theory. The method was applied to the numerical simulations of the post flutter regime in time domain showing Limit Cycle Oscillations (LCO) due to nonlinearities of the flow model and vibrations with large amplitudes. Numerical experiments were performed for the airfoil NACA 0012 respecting the effect of the air space between the flap and the main airfoil.

Finite Element Simulation of a Gust Response of an Ultralight 2-DOF Airfoil

2014 ◽  
Author(s):  
Jaromír Horáček ◽  
Petr Sváček
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Turbulent Viscosity ◽  
Equations Of Motion ◽  
Sudden Change ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian

Flexibly supported two-degrees of freedom (2-DOF) airfoil in two-dimensional (2D) incompressible viscous turbulent flow subjected to a gust (sudden change of flow conditions) is considered. The structure vibration is described by two nonlinear ordinary differential equations of motion for large vibration amplitudes. The flow is modeled by Reynolds averaged Navier-Stokes equations (RANS) and by k–ω turbulence model. The numerical simulation consists of the finite element (FE) solution of the RANS equations and the equations for the turbulent viscosity. This is coupled with the equations of motion for the airfoil by a strong coupling procedure. The time dependent computational domain and a moving grid are taken into account with the aid of the arbitrary Lagrangian-Eulerian formulation. In order to avoid spurious numerical oscillations, the SUPG and div-div stabilizations are applied. The solution of the ordinary differential equations is carried out by the Runge-Kutta method. The resulting nonlinear discrete algebraic systems are solved by the Oseen iterative process. The aeroelastic response to a sudden gust is numerically analyzed with the aid of the developed FE code. The gust responses exhibit similar oscillations as those found in literature.

scholarly journals Simulation of Free Airfoil Vibrations in Incompressible Viscous Flow — Comparison of FEM and FVM

10.14311/1690 ◽  
2012 ◽  
Vol 52 (6) ◽  
Author(s):  
Petr Sváček ◽  
Jaromír Horáček ◽  
Radek Honzátko ◽  
Karel Kozel
Keyword(s):  
Viscous Flow ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Vertical Direction ◽  
Navier Stokes ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Incompressible Viscous Flow ◽  
Naca 0012

This paper deals with a numerical solution of the interaction of two-dimensional (2-D) incompressible viscous flow and a vibrating profile NACA 0012 with large amplitudes. The laminar flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form. The profile with two degrees of freedom (2-DOF) can rotate around its elastic axis and oscillate in the vertical direction. Its motion is described by a nonlinear system of two ordinary differential equations. Deformations of the computational domain due to the profile motion are treated by the arbitrary Lagrangian-Eulerianmethod. The finite volume method and the finite element method are applied, and the numerical results are compared.

Simulation of Tethered Underwater Kites Moving in Three Dimensions for Power Generation

2017 ◽  
Author(s):  
Amirmahdi Ghasemi ◽  
David J. Olinger ◽  
Gretar Tryggvason
Keyword(s):  
Numerical Simulation ◽  
Power Generation ◽  
Stokes Equations ◽  
Simulation Models ◽  
Three Dimensions ◽  
Ocean Current ◽  
Design Parameters ◽  
Immersed Boundary ◽  
Computational Domain ◽  
Flow Equations

In this paper, a numerical simulation of tether undersea kites (TUSK) used for power generation is undertaken. The effect of varying key design parameters in these systems is studied. TUSK systems consist of a rigid-winged kite, or glider, moving in an ocean current. One proposed TUSK concept uses a tethered kite which is connected by a flexible tether to a support structure with a generator on a surface buoy. The numerical simulation models the flow field in a three-dimensional domain near the rigid undersea kite wing by solving the full Navier-Stokes equations. A moving computational domain method is used to reduce the computational run times. A second-order corrector-predictor method, along with Open Multi-Processing (OpenMP), is employed to solve the flow equations. In order to track the rigid kite, which is a rectangular planform wing with a NACA 0021 airfoil, an immersed boundary method is used. The tension force in the elastic tether is modeled by a simple Hooke’s law, and the effect of tether damping is added. PID control methods are used to adjust the kite pitch, roll and yaw angles during power (tether reel-out) and retraction (reel-in) phases to obtain the desired kite trajectories. During the reel-out phase the kite moves in successive cross-current motions in a figure-8 pattern, the tether length increases and power is generated. During reel-in the kite motion is along the tether, and kite hydrodynamic forces are reduced so that net positive power is produced. The effects of different key design parameters in TUSK systems, such as the ratio of tether to current velocity, and tether retraction velocity, are then further studied. System power output, kite trajectories, and vorticity flow fields for the kite are also determined.

Research of Flow-Induced Vibration of Flexible Plate Based on Fluid-Solid Interaction Method

2014 ◽  
Vol 945-949 ◽  
pp. 642-645
Author(s):  
Ren Qiang Xi ◽  
Xue Dong Jiang ◽  
Yun Song He
Keyword(s):  
Finite Element ◽  
Fluid Flow ◽  
Degrees Of Freedom ◽  
Data Transfer ◽  
Stokes Equations ◽  
Linear Equations ◽  
Solution Procedure ◽  
Element Formulation ◽  
Flexible Plate ◽  
Arbitrary Lagrangian Eulerian

This work is concerned with the modelling of the interaction of fluid flow with flexible solid structures. The fluid flow considered is governed by the incompressible Navier-Stokes equations and modelled with stabilised low order velocity-pressure finite elements. The governing equation of fluid movement is described by an arbitrary Lagrangian-Eulerian (ALE) strategy. The structure is represented by means of an appropriate standard finite element formulation. A simple data transfer strategy based on a finite element type interpolation of the interface degrees of freedom guarantees kinematic consistency and equilibrium of the stresses along the interface. The resulting strongly coupled set of non-linear equations is solved by means of a partitioned solution procedure, which is based on the Newton-Raphson methodology and incorporates the full linearization of the overall incremental problem.

Agglomeration-based physical frame dG discretizations: An attempt to be mesh free

2014 ◽  
Vol 24 (08) ◽  
pp. 1495-1539 ◽  
Author(s):  
Francesco Bassi ◽  
Lorenzo Botti ◽  
Alessandro Colombo
Keyword(s):  
Finite Element ◽  
Convergence Rates ◽  
Numerical Test ◽  
High Order ◽  
Test Cases ◽  
Computational Domain ◽  
Element Discretization ◽  
Mesh Free ◽  
Domain Boundaries ◽  
Coarse Grids

In this work we consider agglomeration-based physical frame discontinuous Galerkin (dG) discretization as an effective way to increase the flexibility of high-order finite element methods. The mesh free concept is pursued in the following (broad) sense: the computational domain is still discretized using a mesh but the computational grid should not be a constraint for the finite element discretization. In particular the discrete space choice, its convergence properties, and even the complexity of solving the global system of equations resulting from the dG discretization should not be influenced by the grid choice. Physical frame dG discretization allows to obtain mesh-independent h-convergence rates. Thanks to mesh agglomeration, high-order accurate discretizations can be performed on arbitrarily coarse grids, without resorting to very high-order approximations of domain boundaries. Agglomeration-based h-multigrid techniques are the obvious choice to obtain fast and grid-independent solvers. These features (attractive for any mesh free discretization) are demonstrated in practice with numerical test cases.

scholarly journals AUTOMATIC INSERTION OF A TURBULENCE MODEL IN THE FINITE ELEMENT DISCRETIZATION OF THE NAVIER–STOKES EQUATIONS

2009 ◽  
Vol 19 (07) ◽  
pp. 1139-1183 ◽  
Author(s):  
CHRISTINE BERNARDI ◽  
TOMÁS CHACÓN REBOLLO ◽  
FRÉDÉRIC HECHT ◽  
ROGER LEWANDOWSKI
Keyword(s):  
Finite Element ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Stokes Equations ◽  
A Posteriori Error Estimates ◽  
Navier Stokes ◽  
Mesh Adaptivity ◽  
Finite Element Discretization ◽  
Navier Stokes Equations ◽  
Element Discretization

We consider the finite element discretization of the Navier–Stokes equations locally coupled with the equation for the turbulent kinetic energy through an eddy viscosity. We prove a posteriori error estimates which allow to automatically determine the zone where the turbulent kinetic energy must be inserted in the Navier–Stokes equations and also to perform mesh adaptivity in order to optimize the discretization of these equations. Numerical results confirm the interest of such an approach.

An Assessment of Turbulence Models for Predicting the Fluid Flow in Spiral Casing of a Hydraulic Turbomachine Using SUPG-Finite Element Method

2013 ◽  
Author(s):  
N. Parameswara Rao ◽  
K. Arul Prakash
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Spatial Discretisation ◽  
High Reynolds ◽  
Spiral Casing ◽  
Element Method

Numerical simulation of complex three-dimensional flow through the spiral casing has been studied using a finite element method. An explicit Eulerian velocity correction scheme has been employed to solve the Reynolds averaged Navier-stokes equations. The simulation has been performed to describe the flow in high Reynolds number (106) regime and two k-ε turbulence models (standard k-ε and RNG k-ε) have been used for computing the turbulent flow. A streamline upwind Petrov Galerkin technique has been used for spatial discretisation. The velocity field and the pressure distribution inside the spiral casing has been studied. It has been observed that very strong secondary flow is evolved on the cross-stream planes.

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