A 2-D Immersed Boundary Method on Low Reynolds Moving Body

Boundary Elements and other Mesh Reduction Methods XLII

A simplified fluid-structure interaction model, consisting of a cylinder tethered by a spring system interacting dynamically with an incompressible two-dimensional lid-driven cavity flow, is solved using the immersed boundary method. Results show that when the spring forces are weaker than the fluid drag force, the springs stretch freely and the cylinder motion is the direct result of the fluid dynamics action. For higher values of spring forces, the cylinder motion reaches a maximum displacement, and the spring forces induce the cylinder to an oscillatory movement damped by the fluid drag forces. Subsequently the amplitude of the displacement decreases. The cylinder motion is restricted within the mainstream fluid flow, where the maximum displacement reduces as the Reynolds number increases.

Journal of Computational Physics, 2011

An immersed boundary method is proposed in the framework of discrete stream function formulation for incompressible flows. In order to impose the non-slip boundary condition, the forcing term is determined implicitly by solving a linear system. The number of unknowns of the linear system is the same as that of the Lagrangian points representing the body surface. Thus the extra cost in force calculation is negligible if compared with that in the basic flow solver. In order to handle three-dimensional flows at moderate Reynolds numbers, a parallelized flow solver based on the present method is developed using the domain decomposition strategy. To verify the accuracy of the immersed-boundary method proposed in this work, flow problems of different complexity (decaying vortices, flows over stationary and oscillating cylinders and a stationary sphere, and flow over low-aspect-ratio flat-plate) are simulated and the results are in good agreement with the experimental or computational data in previously published literatures.

2013

The accuracy and computational efficiency of various interpolation methods for the implementation of non grid-confirming boundaries is assessed. The aim of the research is to select an interpolation method that is both efficient and sufficiently accurate to be used in the simulation of vortex induced vibration of the flow around a deformable cylinder. Results are presented of an immersed boundary implementation in which the velocities near nonconfirming boundaries were interpolated in the normal direction to the walls. The flow field is solved on a Cartesian grid using a finite volume method with a staggered variable arrangement. The Strouhal number and Drag coefficient for various cases are reported. The results show a good agreement with the literature. Also, the drag coefficient and Strouhal number results for five different interpolation methods were compared it was shown that for a stationary cylinder at low Reynolds number, the interpolation method could affect the drag coeffi...

2003

Abstract: In the immersed boundary (IB) method, the surface of an object is reconstructed with forcing terms in the underlying flow field equations. The surface may split a computational cell removing the constraint of the near wall gridlines to be aligned with the surface. This feature greatly simplifies the grid generation process which is cumbersome and expensive in particular for structured grids and complex geometries.

2003

The application of the Immersed Boundary IB method to simulate incompressible, turbulent flows around complex configurations is illustrated; the IB is based on the use of non-body conformal grids, and the effect of the presence of a body in the flow is accounted for by modifying the governing equations. Turbulence is modeled using standard Reynolds-Averaged Navier-Stokes models or the more sophisticated Large Eddy Simulation approach.

Journal of Mechanics, 2014

An immersed boundary method is proposed for the simulation of the interaction of an incompressible flow with rigid bodies. The method is based on a new interpretation of velocity-vorticity formulation and no longer includes the force term which is an essential issue of common immersed boundary methods. The system is considered in an Eulerian frame and retrieving the vorticity in this formulation enforces continuity at the fluid-solid interface and rigid motion of the solid. The method focuses on the mutual kinematic relations between the velocity and vorticity fields and with retrieving the vorticity field and recalculating the velocities yields the solenoidal velocity field. The method is applied to the two dimensional problems and the results show that the solenoidality is satisfied acceptably. The comparisons with 2D test cases are provided to illustrate the capabilities of the proposed method.

Chinese Journal of Aeronautics, 2009

This article introduces a numerical scheme on the basis of semi-implicit method for pressure-linked equations (SIMPLE) algorithm to simulate incompressible unsteady flows with fluid-structure interaction. The Navier-Stokes equation is discretized spatially with collocated finite volume method and Eulerian implicit method in time domain. The hybrid method that combines immersed boundary method (IBM) and volume of fluid (VOF) method is used to deal with rigid body motion in fluid domain. The details of movement of immersed boundary (IB) and calculation of VOF are also described. This method can be easily applied to any existing finite-volume-based computational fluid dynamics (CFD) solver without complex operation, with which fluid flow interaction of arbitrarily complex geometry can be realized on a fixed mesh. The method is verified by low Reynolds number flows passing both stationary and oscillating cylinders. The drag and lift coefficients acquired by the study well accord with other published results, which indicate the reasonability of the proposed method.

Proceedings of 10th World Congress on Computational Mechanics, 2014

In this paper a simulation model is presented for the Direct Numerical simulation (DNS) of multiphase flow. This method combines the Volume of fluid model and Immersed Boundary method in order to investigate water-oil flow-pattern. The simulations were carried out on structured cartesian adaptive mesh refinement (SAMR), where the the Immersed Boundary represents the circular tube via Direct Forcing Method (DFM). The Volume of Fluid based on piecewise linear reconstruction interface, allow to define the fluid-fluid interface using a three dimensional version of the continuum surface force (CSF) model of Brackbill et al. (1992). The Navier-Stokes equations are discretized in the entire domain using a finite difference scheme, where a temporal discretization is based on SBDF scheme, with adaptive time stepping. The capabilities of the hybrid VOF-IB model are demonstrated with examples in wich complex topological changes in the interface are encountered. The overall methodology has been through a careful, series of verification tests whose results are reported. An oil-water flow-pattern application is presented.

JOURNAL OF CHEMICAL ENGINEERING OF JAPAN, 2012

The drag force acting on a system of densely packed particles is a common issue encountered during the uidization of particles. In this process, the bulk motion is induced by the drag action of uid ow. The discrete element method based on the Euler-Lagrange description can provide a realistic estimation of particle-uid and particle-particle interactions; however, it is not possible to simulate the ow phenomena in a space smaller than a particle size by using this method. However, the study of ow on such a scale is crucial for the drag force analysis. Therefore, in the present study, the immersed boundary method, which is a direct numerical simulation, is used to investigate the drag force by simulating the ow around each particle. In this simulation, particles were positioned according to di erent types of spatial arrangements in order to represent the di erent degrees of voidage, and the ow around these particles.