Iterative method for solving fully-coupled fluid solid systems

2010 ◽  
pp. 653-670
Author(s):  
Elisabeth Longatte
Keyword(s):  
Stokes Equations ◽  
Cross Flow ◽  
Elastic Cylinder ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Ale Formulation ◽  
Volume Method ◽  
Fully Coupled ◽  
Solid System

This work is concerned with the modelling of the interaction of a fluid with a rigid or a flexible elastic cylinder in the presence of axial or cross-flow. A partitioned procedure is involved to perform the computation of the fully-coupled fluid solid system. The fluid flow is governed by the incompressible Navier-Stokes equations and modeled by using a fractional step scheme combined with a co-located finite volume method for space discretisation. The motion of the fluid domain is accounted for by a moving mesh strategy through an Arbitrary Lagrangian-Eulerian (ALE) formulation. Solid dyncamics is modeled by a finite element method in the linear elasticity framework and a fixed point method is used for the fluid solid system computation. In the present work two examples are presented to show the method robustness and efficiency.

Fully-Coupled Fluid Solid Computation for Simulation of Flutter in Tubes and Tube Arrays

2010 ◽  
Author(s):  
E. Longatte
Keyword(s):  
Stokes Equations ◽  
Dynamic Instability ◽  
Mechanical Energy ◽  
Linear Equations ◽  
Cross Flow ◽  
Arbitrary Lagrangian Eulerian ◽  
Flexible Cylinder ◽  
Physical Point ◽  
Ale Formulation ◽  
Fully Coupled

This work is concerned with the modelling of the interaction of a fluid with a rigid or a flexible elastic cylinder in presence of axial or cross-flow. A partitioned procedure is involved to performe the computation of the fully-coupled fluid solid system. The fluid flow is governed by the incompressible Navier-Stokes equations and modeled by using a fractional step scheme combined with a co-located finite volume method for space discretisation. The motion of the fluid domain is accounted for by a moving mesh strategy through an Arbitrary Lagrangian-Eulerian (ALE) formulation. Solid dyncamics is modeled by descrete or beam elements in the linear elasticity framework and systems are solved through a finite element method. The resulting strongly coupled fluid solid set of non linear equations is solved by means of a partitioned solution procedure. A fixed point method combined with under-relaxation is involved to ensure the optimal convergence of the iterative procedure. In the present work two examples are presented to show the methodology robustness and efficiency. The purpose is to attempt to simulate a fluid structure interaction resulting in the development of a dynamic instability induced by a positive damping generation of the system. Both flutter of a flexible cylinder conveying an internal fluid and fluid-elastic instability of a tube array submitted to an external cross flow are investigated numerically. According to first results the partitioned procedure relies on consistant numerical methods ensuring energy conservation at the interface and describing with a sufficient accuracy the mechanical energy transfer between fluid and solid systems through the interface with a limited numerical diffusion. Therefore it seems to be qualitatively convenient for simulation of flutter. For a quantitative evaluation of the methodology further complementary simulations validating these developments from a physical point of view will be required in order to confirm these first trends.

scholarly journals A Comparative Numerical Study on the Performances and Vortical Patterns of Two Bioinspired Oscillatory Mechanisms: Undulating and Pure Heaving

2015 ◽  
Vol 2015 ◽  
pp. 1-25 ◽  
Author(s):  
Mohsen Ebrahimi ◽  
Madjid Abbaspour
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Leading Edge ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
And Performance ◽  
Volume Method ◽  
Thrust Production ◽  
High Thrust

The hydrodynamics and energetics of bioinspired oscillating mechanisms have received significant attentions by engineers and biologists to develop the underwater and air vehicles. Undulating and pure heaving (or plunging) motions are two significant mechanisms which are utilized in nature to provide propulsive, maneuvering, and stabilization forces. This study aims to elucidate and compare the propulsive vortical signature and performance of these two important natural mechanisms through a systematic numerical study. Navier-Stokes equations are solved, by a pressure-based finite volume method solver, in an arbitrary Lagrangian-Eulerian (ALE) framework domain containing a2D NACA0012foil moving with prescribed kinematics. Some of the important findings are (1) the thrust production of the heaving foil begins at lower St and has a greater growing slope with respect to the St; (2) the undulating mechanism has some limitations to produce high thrust forces; (3) the undulating foil shows a lower power consumption and higher efficiency; (4) changing the Reynolds number (Re) in a constant St affects the performance of the oscillations; and (5) there is a distinguishable appearance of leading edge vortices in the wake of the heaving foil without observable ones in the wake of the undulating foil, especially at higher St.

scholarly journals Numerical Simulation of Cross-Flow Vortex-Induced Vibration of Hexagonal Cylinders with Face and Corner Orientations at Low Reynolds Number

2020 ◽  
Vol 8 (6) ◽  
pp. 387
Author(s):  
Farid Piran ◽  
Hassan Karampour ◽  
Peter Woodfield
Keyword(s):  
Reynolds Number ◽  
Numerical Model ◽  
Stokes Equations ◽  
Cross Flow ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Square Cylinders ◽  
The Face ◽  
Flow Vortex

Vortex-induced vibrations (VIV) of hexagonal cylinders at Reynolds number of 1000 and mass ratio of 2 are studied numerically. In the numerical model, the Navier–Stokes equations are solved using finite volume method, and the fluid-structure interaction (FSI) is modelled using Arbitrary Lagrangian Eulerian (ALE) Scheme. The numerical model accounts for the cross-flow vibration of the cylinders, and is validated against published experimental and numerical results. In order to account for different angles of attack, the hexagonal cylinders are studied in the corner and face orientations. The results are compared with the published results of circular and square cylinders. Current results show that within the studied range of reduced velocities (up to 20), unlike circular and square cylinders, no lock-in response is observed in the hexagonal cylinders. The maximum normalized VIV amplitudes of the hexagonal cylinders are 0.45, and are significantly lower than those of circular and square cylinders. Vortex shedding regimes of the corner-oriented hexagons are mostly irregular. However, in the face-oriented hexagons, the shedding modes are more similar to the typical P + S and 2P modes.

scholarly journals Numerical Simulation of Unsteady Compressible Flow in Convergent Channel: Pressure Spectral Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Petra Pořízková ◽  
Karel Kozel ◽  
Jaromír Horáček
Keyword(s):  
Numerical Solution ◽  
Stokes Equations ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Airflow Velocity ◽  
Navier Stokes Equations ◽  
Convergent Channel ◽  
Volume Method ◽  
Predictor Corrector

This study deals with the numerical solution of a 2D unsteady flow of a compressible viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The flow is described by the system of Navier-Stokes equations for laminar flows. The numerical solution is implemented using the finite volume method (FVM) and the predictor-corrector Mac-Cormack scheme with Jameson artificial viscosity using a grid of quadrilateral cells. Due to the motion of the grid, the basic system of conservation laws is considered in the arbitrary Lagrangian-Eulerian (ALE) form. The numerical results of unsteady flows in the channel are presented for inlet Mach numberM∞=0.012, Reynolds numberRe∞=4481,and the wall motion frequency 100 Hz.

scholarly journals THREE-DIMENSIONAL BIOMECHANICAL AND VISUALISATION MODEL OF VERTIGO DISEASE IN THE SEMI-CIRCULAR CANAL

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Žarko Milošević ◽  
Dalibor Nikolić ◽  
Igor Saveljić ◽  
Velibor Isailović ◽  
Thanos Bibas ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Numerical Models ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Patient Specific ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Specific Patient ◽  
Continuity Equations ◽  
Ale Formulation

Benign paroxysmal positional vertigo (BPPV) is the most common type of vertigo. The symptoms of BPPV typically appear after angular movements of the head. BPPV leads to dizziness, nausea and imbalance. In this study, we examined a model of the semi-circular canal (SCC) with fully 3D three dimensional anatomical data from specific patient. A full Navier-Stokes equations and continuity equations are used for fluid domain with Arbitrary-Lagrangian Eulerian (ALE) formulation for mesh motion of finite element. Fluid-structure interaction for fluid coupling with cupula deformation is used. Particle tracking algorithm is implemented for particle motion. Motion of the otoconia particles which is main cause for BPPV is simulated. Velocity distribution, shear stress and force from endolymph side are presented for patient specific three SCC. We compared our numerical models with experiments with head moving and nystagmus eye tracking. Numerical simulation can give more details and understanding of the pathology of the specific patient in standard clinical diagnostic and therapy procedure for BPPV.

scholarly journals Vibrations of Nonlinear Elastic Structure Excited by Compressible Flow

2021 ◽  
Vol 11 (11) ◽  
pp. 4748
Author(s):  
Monika Balázsová ◽  
Miloslav Feistauer ◽  
Jaromír Horáček ◽  
Adam Kosík
Keyword(s):  
Compressible Flow ◽  
Nonlinear Elasticity ◽  
Vocal Tract ◽  
Stokes Equations ◽  
Vocal Folds ◽  
Nonlinear Material ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Reliable Solution

This study deals with the development of an accurate, efficient and robust method for the numerical solution of the interaction of compressible flow and nonlinear dynamic elasticity. This problem requires the reliable solution of flow in time-dependent domains and the solution of deformations of elastic bodies formed by several materials with complicated geometry depending on time. In this paper, the fluid–structure interaction (FSI) problem is solved numerically by the space-time discontinuous Galerkin method (STDGM). In the case of compressible flow, we use the compressible Navier–Stokes equations formulated by the arbitrary Lagrangian–Eulerian (ALE) method. The elasticity problem uses the non-stationary formulation of the dynamic system using the St. Venant–Kirchhoff and neo-Hookean models. The STDGM for the nonlinear elasticity is tested on the Hron–Turek benchmark. The main novelty of the study is the numerical simulation of the nonlinear vocal fold vibrations excited by the compressible airflow coming from the trachea to the simplified model of the vocal tract. The computations show that the nonlinear elasticity model of the vocal folds is needed in order to obtain substantially higher accuracy of the computed vocal folds deformation than for the linear elasticity model. Moreover, the numerical simulations showed that the differences between the two considered nonlinear material models are very small.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

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