Linear Stability Analysis and Application of a New Solution Method of the Elastodynamic Equations Suitable for a Unified Fluid-Structure-Interaction Approach

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Solution Method ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Fluid Structure ◽  
Structure Interaction

In the conventional approach for fluid-structure-interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: partitioned methods and monolithic methods. Both methods use separate sets of equations for fluid and solid that have different unknown variables. A unified solution method has been presented in the previous work of Giannopapa and Papadakis (2004, “A New Formulation for Solids Suitable for a Unified Solution Method for Fluid-Structure Interaction Problems,” ASME PVP 2004, San Diego, CA, July, PVP Vol. 491–1, pp. 111–117), which is different from these methods. The new approach treats both fluid and solid as a single continuum; thus, the whole computational domain is treated as one entity discretized on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, the elastodynamic equations are reformulated so that they contain the same unknowns as the Navier–Stokes equations, namely, velocities and pressure. Two time marching and one spatial discretization scheme, widely used for fluid equations, are applied for the solution of the reformulated equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps, and beam dimensions is also presented. For all cases examined, the numerical solution was stable and robust and therefore is suitable for the next stage of application to full fluid-structure-interaction problems.

scholarly journals Linear Stability Analysis and Validation of a Unified Solution Method for Fluid-Structure-Interaction on Structural Dynamic Problems

2005 ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Solution Method ◽  
Fluid Structure Interaction ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Structural Dynamic ◽  
Fluid Structure ◽  
Structure Interaction

In the conventional approach for fluid-structure interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: Partitioned methods and monolithic methods. Both methods use two separate sets of equations for fluid and solid. A unified solution method has been presented [1], which is different from these methods. The new method treats both fluid and solid as a single continuum, thus the whole computational domain is treated as one entity discretised on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, 2 time marching and one spatial discretisation scheme, widely used for fluids’ equations, are applied for the solution of the equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps and beam sizes is also presented. For all cases examined the numerical solution was stable and robust and proved to be suitable for the next stage of application to full fluid-structure interaction problems.

scholarly journals Indicative Results and Progress on the Development of the Unified Single Solution Method for Fluid-Structure Interaction Problems

2007 ◽  
Author(s):  
C. G. Giannopapa
Keyword(s):  
Solution Method ◽  
Numerical Models ◽  
Fluid Structure Interaction ◽  
Test Case ◽  
Computational Domain ◽  
Fluid Structure ◽  
Strongly Coupled ◽  
Structure Interaction ◽  
Fully Implicit ◽  
The Difference

This paper presents the progress on the development of a novel unified solution method for solving strongly coupled fluid-structure interaction problems. The method has been developed and fully tested for solids in [1]. The new approach is based on continuum mechanics formulation for fluids and structures where both continua can be solved using the momentum and continuity equation. The difference between the two continua lies in the constitutive equations. In this framework a single set of equations is used for the simultaneous solution of both fluid and solid. The common equations are written such that velocity and pressure are unknown variables for both continua. The discretisation method used for the solution of the problems is finite volumes. The physical interface between the two continua is treated as an internal part of the computational domain and no explicit exchange of information is needed. The test case used to demonstrate the idea is wave propagation in liquid filled flexible vessels. The solution is fully implicit and transient. Results regarding pressure, velocity and wall distention at different times and various locations along the tube are presented. The method is stable and robust and can be used for the next step of development and validation against classical analytical and numerical models.

Fluid–Structure Interaction of High Aspect-Ratio Hair-Like Micro-Structures Through Dimensional Transformation Using Lattice Boltzmann Method

2016 ◽  
Vol 08 (08) ◽  
pp. 1650095 ◽  
Author(s):  
H. Devaraj ◽  
Kean C. Aw ◽  
E. Haemmerle ◽  
R. Sharma
Keyword(s):  
Fluid Flow ◽  
Drag Force ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Structural Response ◽  
Momentum Exchange ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Micro Structures

3D printed hair-like micro-structures have been previously demonstrated in a novel micro-fluidic flow sensor aimed at sensing air flows down to rates of a few milliliters per second. However, there is a lack of in-depth understanding of the structural response of these ‘micro-hairs' under a fluid flow field. This paper demonstrates the use of lattice Boltzmann methods (LBM) to understand this structural response towards a better optimization of the micro-hair flow sensors designed to suit the end applications' needs. The LBM approach was chosen as an efficient alternative to simulate Navier–Stokes equations for modeling fluid flow around complex geometries primarily for improved accuracy and simplicity with lesser computational costs. As the spatial dimensions of the sensor's flow channel are much larger in comparison to the actual micro-hairs (the sensing element), a multidimensional approach of combining two-dimensional (D2Q9) and three-dimensional (D3Q19) lattice configurations were implemented for improved computational speeds and efficiency. The drag force on the micro-hairs was estimated using the momentum-exchange method in the D3Q19 configuration and this drag force is transferred to the structural analysis model which determines the micro-hair deformation using Euler–Bernoulli beam theory. The entirety of the LBM Fluid–Structure Interaction (FSI) model was implemented within MATLAB and the obtained results are compared against the numerical model implemented on a commercially available software package.

Fluid-Structure Interaction Approach for Numerical Investigation of a Flexible Hydrofoil Deformations in Turbulent Fluid Flow

2018 ◽  
Author(s):  
M. Benaouicha ◽  
S. Guillou ◽  
A. Santa Cruz ◽  
H. Trigui
Keyword(s):  
Fluid Flow ◽  
Numerical Model ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Time Step ◽  
Fluid Structure ◽  
Turbulent Fluid Flow ◽  
Turbulent Fluid ◽  
Structure Interaction ◽  
Ale Formulation

The study deals with a 3D Fluid-Structure Interaction (FSI) numerical model of a rectangular cantilevered flexible hydrofoil subjected to a turbulent fluid flow regime. The structural response and dynamic deformations are studied by analyzing the oscillations frequencies and amplitudes, under a hydrodynamics loads. The obtained numerical results are confronted with experimental ones, for validation. The numerical model is performed in the same geometric, physical and material conditions as the experimental set-up carried out in a hydrodynamic tunnel. A polyacetal (POM) flexible hydrofoil NACA0015 with an angle of attack of 8° is considered to be immersed in a fluid flow at a Reynold number of 3 × 105. The structure is initially at rest and then moved by the action of the fluid flow. The numerical model is based on a strong coupling procedure for solving the Fluid-Structure Interaction problem. The Arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations is used and an anisotropic diffusion equation is solved to compute the fluid mesh velocity and position at each time step. The finite volume method is used for the numerical resolution of the fluid dynamics equations. The structure deformations are described by the linear elasticity equation which is solved by the finite elements method. The Fluid-Structure coupled problem is solved by using the partitioned FSI implicit algorithm. A good agreement between numerical and experimental results for the hydrodynamics coefficients and hydrofoil deformations, maximum deflection and frequencies is obtained. The added mass and damping are analyzed and then the FSI effect on the dynamic deformations of the structure is highlighted.

Scalability study of an implicit solver for coupled fluid-structure interaction problems on unstructured meshes in 3D

2016 ◽  
Vol 32 (2) ◽  
pp. 207-219 ◽  
Author(s):  
Fande Kong ◽  
Xiao-Chuan Cai
Keyword(s):  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Coupled System ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Krylov Method ◽  
Fine Mesh ◽  
Processor Cores ◽  
Fully Coupled

Fluid-structure interaction (FSI) problems are computationally very challenging. In this paper we consider the monolithic approach for solving the fully coupled FSI problem. Most existing techniques, such as multigrid methods, do not work well for the coupled system since the system consists of elliptic, parabolic and hyperbolic components all together. Other approaches based on direct solvers do not scale to large numbers of processors. In this paper, we introduce a multilevel unstructured mesh Schwarz preconditioned Newton–Krylov method for the implicitly discretized, fully coupled system of partial differential equations consisting of incompressible Navier–Stokes equations for the fluid flows and the linear elasticity equation for the structure. Several meshes are required to make the solution algorithm scalable. This includes a fine mesh to guarantee the solution accuracy, and a few isogeometric coarse meshes to speed up the convergence. Special attention is paid when constructing and partitioning the preconditioning meshes so that the communication cost is minimized when the number of processor cores is large. We show numerically that the proposed algorithm is highly scalable in terms of the number of iterations and the total compute time on a supercomputer with more than 10,000 processor cores for monolithically coupled three-dimensional FSI problems with hundreds of millions of unknowns.

scholarly journals FSI in Wind Turbines: A Review

2020 ◽  
Vol 8 (3) ◽  
pp. 37
Author(s):  
Yogesh Ramesh Patel
Keyword(s):  
Wind Turbine ◽  
Wind Turbines ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Fluid Structure Interaction ◽  
Arbitrary Lagrangian Eulerian ◽  
Wind Turbine Blades ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Deformable Structure

This paper provides a brief overview of the research in the field of Fluid-structure interaction in Wind Turbines. Fluid-Structure Interaction (FSI) is the interplay of some movable or deformable structure with an internal or surrounding fluid flow. Flow brought about vibrations of two airfoils used in wind turbine blades are investigated by using a strong coupled fluid shape interplay approach. The approach is based totally on a regularly occurring Computational Fluid Dynamics (CFD) code that solves the Navier-Stokes equations defined in Arbitrary Lagrangian-Eulerian (ALE) coordinates by way of a finite extent method. The need for the FSI in the wind Turbine system is studied and comprehensively presented.

Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 1. Linear stability analysis

2013 ◽  
Vol 721 ◽  
pp. 268-294 ◽  
Author(s):  
L. Talon ◽  
N. Goyal ◽  
E. Meiburg
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stokes Equations ◽  
Variable Density ◽  
Local Concentration ◽  
Miscible Displacements ◽  
Instability Modes ◽  
Finger Tip

AbstractA computational investigation of variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells is presented. As a first step, two-dimensional base states are obtained by means of simulations of the Stokes equations, which are nonlinear due to the dependence of the viscosity on the local concentration. Here, the vertical position of the displacement front is seen to reach a quasisteady equilibrium value, reflecting a balance between viscous and gravitational forces. These base states allow for two instability modes: first, there is the familiar tip instability driven by the unfavourable viscosity contrast of the displacement, which is modulated by the presence of density variations in the gravitational field; second, a gravitational instability occurs at the unstably stratified horizontal interface along the side of the finger. Both of these instability modes are investigated by means of a linear stability analysis. The gravitational mode along the side of the finger is characterized by a wavelength of about one half to one full gap width. It becomes more unstable as the gravity parameter increases, even though the interface is shifted closer to the wall. The growth rate is largest far behind the finger tip, where the interface is both thicker, and located closer to the wall, than near the finger tip. The competing influences of interface thickness and wall proximity are clarified by means of a parametric stability analysis. The tip instability mode represents a gravity-modulated version of the neutrally buoyant mode. The analysis shows that in the presence of density stratification its growth rate increases, while the dominant wavelength decreases. This overall destabilizing effect of gravity is due to the additional terms appearing in the stability equations, which outweigh the stabilizing effects of gravity onto the base state.

scholarly journals Three-Dimensional Simulation of Fluid–Structure Interaction Problems Using Monolithic Semi-Implicit Algorithm

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 94 ◽  
Author(s):  
Cornel Marius Murea
Keyword(s):  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Time Step ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Dimensional Simulation ◽  
Updated Lagrangian

A monolithic semi-implicit method is presented for three-dimensional simulation of fluid–structure interaction problems. The updated Lagrangian framework is used for the structure modeled by linear elasticity equation and, for the fluid governed by the Navier–Stokes equations, we employ the Arbitrary Lagrangian Eulerian method. We use a global mesh for the fluid–structure domain where the fluid–structure interface is an interior boundary. The continuity of velocity at the interface is automatically satisfied by using globally continuous finite element for the velocity in the fluid–structure mesh. The method is fast because we solve only a linear system at each time step. Three-dimensional numerical tests are presented.

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