Analysis of Flow Past Oscillatory Cylinders Using a Finite Element Fixed Mesh Formulation

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Felipe A. González ◽  
Marcela A. Cruchaga ◽  
Diego J. Celentano
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Numerical Data ◽  
The Body ◽  
Body Motion ◽  
Immersed Boundary ◽  
Element Formulation ◽  
Flow Past ◽  
Body Velocity

In this work, we propose a fixed mesh finite element formulation to solve the fluid dynamic on an Eulerian mesh dealing with immersed bodies in motion. The study is focused on the computation of the fluid dynamic forces acting on immersed bodies which strongly depend on the evolution of the vortex shedding. The frequency of vortex detachment for flow past cylinder problems can be modified when the cylinder moves, promoting the modification of the wake of vortices. Synchronization phenomena appear when the frequencies of the resulting flow pattern coincide with the frequency of the imposed body motion. To study this problem, we propose to describe the immersed body surface by a collection of markers that moves according to the imposed body motion. The markers are updated using a Lagrangian scheme. In this framework, a distinct aspect of the present work is the imposition of the body velocity as an internal immersed boundary condition for the fluid dynamic analysis. To transfer the body velocity to the fluid along the fluid–solid interface, a restriction on the flow velocity is added into the weak form of the Navier–Stokes equations by means of a penalty technique. This work encompasses the study of flows past a crossflow, streamwise, and rotational oscillating cylinders. The results are satisfactorily compared with numerical data reported in the literature, showing a proper behavior for the analysis of long-term vibrating systems at low Reynolds numbers.

FINITE ELEMENT APPROACH TO IMMERSED BOUNDARY METHOD WITH DIFFERENT FLUID AND SOLID DENSITIES

2011 ◽  
Vol 21 (12) ◽  
pp. 2523-2550 ◽  
Author(s):  
DANIELE BOFFI ◽  
NICOLA CAVALLINI ◽  
LUCIA GASTALDI
Keyword(s):  
Finite Element ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Biological Tissues ◽  
Immersed Boundary ◽  
Fluid Structure ◽  
Finite Element Approach ◽  
Boundary Method ◽  
Element Approach

The Immersed Boundary Method (IBM) has been designed by Peskin for the modeling and the numerical approximation of fluid-structure interaction problems, where flexible structures are immersed in a fluid. In this approach, the Navier–Stokes equations are considered everywhere and the presence of the structure is taken into account by means of a source term which depends on the unknown position of the structure. These equations are coupled with the condition that the structure moves at the same velocity of the underlying fluid. Recently, a finite element version of the IBM has been developed, which offers interesting features for both the analysis of the problem under consideration and the robustness and flexibility of the numerical scheme. Initially, we considered structure and fluid with the same density, as it often happens when dealing with biological tissues. Here we study the case of a structure which can have a density higher than that of the fluid. The higher density of the structure is taken into account as an excess of Lagrangian mass located along the structure, and can be dealt with in a variational way in the finite element approach. The numerical procedure to compute the solution is based on a semi-implicit scheme. In fluid-structure simulations, nonimplicit schemes often produce instabilities when the density of the structure is close to that of the fluid. This is not the case for the IBM approach. In fact, we show that the scheme enjoys the same stability properties as in the case of equal densities.

scholarly journals A Stress Mapping Immersed Boundary Method for Viscous Flows

2021 ◽  
Vol 87 (3) ◽  
pp. 1-20
Author(s):  
Karim M. Ali ◽  
Mohamed Madbouli ◽  
Hany M. Hamouda ◽  
Amr Guaily
Keyword(s):  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Cross Flow ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Element Formulation ◽  
Navier Stokes Equations ◽  
Boundary Method ◽  
Background Grid ◽  
Dimensional Simulation

This work introduces an immersed boundary method for two-dimensional simulation of incompressible Navier-Stokes equations. The method uses flow field mapping on the immersed boundary and performs a contour integration to calculate immersed boundary forces. This takes into account the relative location of the immersed boundary inside the background grid elements by using inverse distance weights, and also considers the curvature of the immersed boundary edges. The governing equations of the fluid mechanics are solved using a Galerkin-Least squares finite element formulation. The model is validated against a stationary and a vertically oscillating circular cylinder in a cross flow. The results of the model show acceptable accuracy when compared to experimental and numerical results.

Vortex dynamics and new lift enhancement mechanism of wing–body interaction in insect forward flight

2016 ◽  
Vol 795 ◽  
pp. 634-651 ◽  
Author(s):  
Geng Liu ◽  
Haibo Dong ◽  
Chengyu Li
Keyword(s):  
Vortex Dynamics ◽  
High Speed ◽  
Stokes Equations ◽  
The Body ◽  
Immersed Boundary ◽  
Dramatic Improvement ◽  
Forward Flight ◽  
Body Interaction ◽  
Enhancement Mechanism ◽  
Lift Enhancement

The effects of wing–body interaction (WBI) on aerodynamic performance and vortex dynamics have been numerically investigated in the forward flight of cicadas. Flapping wing kinematics was reconstructed based on the output of a high-speed camera system. Following the reconstruction of cicada flight, three models, wing–body (WB), body-only (BD) and wings-only (WN), were then developed and evaluated using an immersed-boundary-method-based incompressible Navier–Stokes equations solver. Results have shown that due to WBIs, the WB model had a 18.7 % increase in total lift production compared with the lift generated in both the BD and WN models, and about 65 % of this enhancement was attributed to the body. This resulted from a dramatic improvement of body lift production from 2 % to 11.6 % of the total lift produced by the wing–body system. Further analysis of the associated near-field and far-field vortex structures has shown that this lift enhancement was attributed to the formation of two distinct vortices shed from the thorax and the posterior of the insect, respectively, and their interactions with the flapping wings. Simulations are also used to examine the new lift enhancement mechanism over a range of minimum wing–body distances, reduced frequencies and body inclination angles. This work provides a new physical insight into the understanding of the body-involved lift-enhancement mechanism in insect forward flight.

Phonon Prediction in Toroidal Carbon Nanotubes Using a Continuum Finite Element Approach

2007 ◽  
Author(s):  
Michael J. Leamy ◽  
Anthony A. DiCarlo
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Tangent Space ◽  
Interatomic Potential ◽  
Virtual Work ◽  
Body Motion ◽  
Element Formulation ◽  
Metric Tensor ◽  
Energy Behavior ◽  
Basis Vectors

This work develops a tensor-based, reduced-order shell finite element formulation used to predict the phonon behavior of toroidal carbon nanotubes (CNTs). Displacements referencing two covariant basis vectors lying in the toroid’s tangent space, and one basis vector orthogonal to the tangent space, capture the kinematics of the toroidal CNT. These basis vectors compose a curvilinear coordinate system. Although specific attention is on toroidal CNTs, the formulation can be quickly adapted to cylindrical or other curvilinear CNTs by appropriate replacement of the metric tensor components and Christoffel symbols. The finite element procedure originates from a variational statement (Hamilton’s Principle) governing virtual work from internal, external (not considered), and inertial forces. Internal virtual work is related to changes in atomistic potential energy accounted for by an interatomic potential computed at reference area elements. Small virtual changes in the displacements allow a global mass and stiffness matrix to be computed, and these matrices then allow phonons to be predicted via the general eigenvalue problem. Results are generated for example toroidal CNTs documenting zero-energy behavior (rigid body motion) and the lowest phonons, which include the expected breathing-like and bending-like phonons.

On the Immersed Boundary Method: Finite Element Versus Finite Volume Approach

2012 ◽  
Author(s):  
Angelo Frisani ◽  
Yassin A. Hassan
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Finite Volume ◽  
Stokes Equations ◽  
Numerical Results ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Order Accuracy ◽  
Navier Stokes Equations ◽  
Two Dimensional Flow

A projection approach is presented for the coupled system of time-dependent incompressible Navier-Stokes equations in conjunction with the Immersed Boundary Method (IBM) for solving fluid flow problems in the presence of rigid objects not represented by the underlying mesh. The IBM allows solving the flow for geometries with complex objects without the need of generating a body fitted mesh. The no-slip boundary constraint is satisfied applying a boundary force at the immersed body surface. Using projection and interpolation operators from the fluid volume mesh to the solid surface mesh (i.e., the “immersed” boundary) and vice versa, it is possible to impose the extra constraint to the incompressible Navier-Stokes equations as a Lagrange multiplier in a fashion very similar to the effect pressure has on the momentum equations to satisfy the divergence-free constraint. The projection operation removes the immersed boundary surface slip and non-divergence-free components of the velocity field. The boundary force is determined implicitly at the inner iterations of the fractional step method implemented. No constitutive relations for the immersed boundary objects fluid interaction are required, allowing the formulation introduced to use larger CFL numbers compared to previous methodologies. An overview of the immersed boundary approach is presented showing third order accuracy in space and second order accuracy in time when the simulation results for the Taylor-Green decaying vortex are compared to the analytical solution using the Immersed Finite Element Method (IFEM). For the Immersed Finite Volume Method (IFVM) a ghost-cell approach is used. Second order accuracy in space and first order accuracy in time are obtained when the Taylor-Green decaying vortex test case is compared to the analytical solution. The numerical results are compared with the analytical solution also for adaptive mesh refinement (for the IFEM) showing an excellent error reduction. Computations were performed using IFEM and IFVM approaches for the time-dependent incompressible Navier-Stokes equations in a two-dimensional flow past a stationary circular cylinder at Re = 20, and 40, where shedding effects are not present. The drag coefficient and the recirculation length error compared to the experimental data is less than 3–4%. Simulations for the two-dimensional flow past a stationary circular cylinder at Re = 100 were also performed. For Re numbers above 46, unsteadiness generates vortex shedding, and an unsteady flow regime is present. The results shown are in excellent quantitative and qualitative agreement with the flow pattern expected. The numerical results obtained with the discussed IFEM and IFVM were also compared against other immersed boundary methodologies available in literature and simulation performed with the commercial computational fluid dynamics code STAR-CCM+/V5.02.009 for which a body fitted finite volume numerical discretization was used. The benchmark showed that the numerical results obtained with the implemented immersed boundary methods are very close to those obtained from STAR-CCM+ with a very fine mesh and in a good agreement with the other IBM techniques. The IBM based of finite element approach is numerically more accurate than the IBM based on finite volume discretization. In contrast, the latter is computationally more efficient than the former.

A Benchmark Comparison of Coupled and Segregated Iterative SUPG Finite Element Formulation for Incompressible Flow

2006 ◽  
Author(s):  
Jianhui Xie ◽  
R. S. Amano
Keyword(s):  
Finite Element ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Cost Effective ◽  
Element Formulation ◽  
Application Problem ◽  
The Individual ◽  
Solution Efficiency ◽  
Fully Coupled

In fluid flow and heat transfer, the finite element based fully coupling solution for all conservation equations is cost effective for most of the two dimensional, isothermal problems, but suffers in the storage and solution efficiency for large three dimensional problems. The segregated solution algorithm has been designed to address large scale simulation with avoiding the direct formulation of a global matrix. There is trade-off between performing a large number of less expensive iterations by segregated solvers compared to less number of more expensive fully coupled solvers. In this paper, a Finite Element based scheme based on preconditioned GMRES coupled algorithm and SUPG (Streamline Upwind Petrov-Galerkin) pressure prediction/correction segregated formulations have been discussed to solve the steady Navier-Stokes equations. A systematic comparison and benchmark between the segregated and fully coupled formulation has been presented to evaluate the individual benefits and strengths of the coupling and segregated procedure by studying lid-driven cavity problem and large industry application problem with respect to the system storage and solution convergence.

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