Immersed Boundary Technique Research Articles

Towards simulation of flapping wings using immersed boundary method

SUMMARYIn this work the immersed boundary method is applied to simulate incompressible turbulent flows around stationary and moving objects. The goal is to demonstrate that the immersed boundary technique along with a large eddy simulation approach is capable of simulating the effect of the so‐called leading edge vortex (LEV), which can be found in flapping wing aerodynamics. A Lagrangian method is used to approximate the solutions in the freshly cleared cells that lay within solid objects at one time step and emerge into fluid domain at the next time step. Flow around a stationary cylinder at ReD = 20, 40, and 3900 (based on cylinder diameter D) is first studied to validate the immersed boundary solver based on the finite volume scheme using a staggered grid. Then, a harmonically oscillating cylinder at ReD = 10 000 is considered to test the solver after the Lagrangian method is implemented to interpolate the solution in the freshly cleared cells. Finally, this approach is used to study flows around a stationary flat‐plate at several angles of attack and fast pitching flat‐plate. The rapidly pitching plate creates a dynamic LEV that can be used to improve the efficiency of flapping wings of micro air vehicle and to determine the optimum flapping frequency. Copyright © 2012 John Wiley & Sons, Ltd.

A penalty formulation for the throughflow modeling of turbomachinery

Despite the widespread use of fully three-dimensional Computational Fluid Dynamics (CFD) techniques, axisymmetric flow models still represent a key tool in turbomachinery design. In this paper, a novel method for the numerical solution of axisymmetric flow models for turbomachinery is presented and demonstrated for two cases, both relevant for the industrial perspective. The key feature of the proposed method is that the flow tangency condition to the blade mean line is enforced with a penalty term, which can also be interpreted as an immersed boundary technique. Differently from the techniques commonly applied for the solution of this kind of flows, the proposed method does not require additional constraint equations to be solved in bladed regions and is therefore very simple to be implemented into existing axisymmetric CFD codes. The techniques employed to deal with flows of high incidence angle (misalignments between the actual flow and the direction imposed by the blade) and to account for the aerodynamic losses and the blade blockage are also thoroughly discussed.The method has been implemented as an extension of the zFlow code for the numerical solution of the Euler equations in cylindrical coordinates, which is based on an hybrid finite element/finite volume space approximation, an implicit time integration scheme, and can deal with fluids of arbitrarily complex equations of state. The details of the numerical method are fully described in the paper.The performance of the developed code is demonstrated by the results obtained in the simulation of a single-stage axial fan, compared against a fully three-dimensional CFD simulation. The potentialities for more complex transonic flow conditions are finally demonstrated by the calculation of a double-stage low pressure steam turbine.

Fluid–structure interaction analysis on a flexible plate normal to a free stream at low Reynolds numbers

This paper presents a computational analysis of the fluid–structure interaction, especially for flexible structures. A flexible plate is placed normal to a free stream and the flow around it is simulated to investigate the effects of flexibility on the flow. The lattice Boltzmann method with an immersed boundary technique using a direct forcing scheme is used to simulate the fluid, and a finite element method with Euler beam elements is used to model the flexible plate. The direct forcing scheme of the lattice Boltzmann method is improved for the immersed boundary scheme by introducing the participation ratio of fluid lattices among the interpolated lattices. We compare the results of our proposed scheme with the known results of conventional schemes. Our results show that the flexibility of the plate significantly influences the reduction of the force coefficients induced by the flow. From the unsteady flow around the flexible plate, we find that the St of the flexible plate up to Re<80 increase regardless of the plate flexibility, but the St in the range of Re>120 is dependent on the plate flexibility. In the range of Re>120, the St of a very flexible plate increases with increasing Re, while the St of a rigid plate decrease with increasing Re.

Fluid–structure interaction of a flapping flexible plate in quiescent fluid

This paper presents the computational analysis of a fluid–structure interaction for a flapping flexible plate in quiescent fluid to investigate the effect of flexibility on the generation of propulsion that is critical for birds, insects, and micro-air vehicles with flapping wings. It is known that rotation of the flapping rigid plate or wing near the end of a translational stroke enhances propulsion. This study found that flexibility improves the efficiency of propulsion during the rotation process and creates an optimal point in the propulsion. The lattice Boltzmann method with an immersed boundary technique using a direct forcing scheme is used to simulate the fluid, while the finite element method with Euler beam elements is used to model structural deformation of the flexible plate. The direct forcing scheme of the lattice Boltzmann method was improved by introducing a participation ratio, which represents the ratio of fluid lattice points to effective interpolated points and modifies the force term for the zero-thickness plate.

Turbulent Wall Model for Immersed Boundary Methods

The paper describes the development of a wall model to extend the applicability of Immersed Boundary methods to high Reynolds number flows. A two-layer approach, based on a decomposition of the near-wall region, is adopted. An outer region is governed by the compressible RANS equations which are solved numerically by using a classical finite volume method. In the proximity of the wall, an inner zone is established and modelled by a simplified version of the thin-boundary-layer equations. The simulation platform is based on Cartesian meshes and an immersed boundary technique. It is able to solve the steady Euler/RANS equations in two- and three-dimensional coordinates. The robustness and the accuracy of the methodology are discussed. At present this work represents the last advance of a research activity whose final goal is a fast pre-design tool for aeronautical/industrial applications.

Numerical Simulation of 3D Free-Surface Flows by Using CIP-based and FV-based Methods

In this paper, three-dimensional free-surface flows are simulated by using two different numerical methods, the constrained interpolation profile (CIP)-based and finite volume (FV)-based methods. In the CIP-based method, the governing equations are solved on stationary staggered Cartesian grids by a finite difference method, and an immersed boundary technique is applied to deal with wave-body interactions. In the FV-based method, the governing equations are solved by applying collocated finite volume discretization, and body-fitted meshes are used. A free-surface boundary is considered as the interface of the multi-phase flow with air and water, and a volumeof-fluid (VOF) approach is applied to trace the free surface. Among many variations of the VOF-type method, the tangent of hyperbola for interface capturing (THINC) and the compressive interface capturing scheme for arbitrary meshes (CICSAM) techniques are used in the CIP-based method and FV-based method, respectively. Numerical simulations have been carried out for dam-breaking and wave-body interaction problems. The computational results of the two methods are compared with experimental data and their differences are observed.

Towards patient-specific cardiovascular modeling system using the immersed boundary technique

BackgroundPrevious research shows that the flow dynamics in the left ventricle (LV) reveal important information about cardiac health. This information can be used in early diagnosis of patients with potential heart problems. The current study introduces a patient-specific cardiovascular-modelling system (CMS) which simulates the flow dynamics in the LV to facilitate physicians in early diagnosis of patients before heart failure.MethodsThe proposed system will identify possible disease conditions and facilitates early diagnosis through hybrid computational fluid dynamics (CFD) simulation and time-resolved magnetic resonance imaging (4-D MRI). The simulation is based on the 3-D heart model, which can simultaneously compute fluid and elastic boundary motions using the immersed boundary method. At this preliminary stage, the 4-D MRI is used to provide an appropriate comparison. This allows flexible investigation of the flow features in the ventricles and their responses.ResultsThe results simulate various flow rates and kinetic energy in the diastole and systole phases, demonstrating the feasibility of capturing some of the important characteristics of the heart during different phases. However, some discrepancies exist in the pulmonary vein and aorta flow rate between the numerical and experimental data. Further studies are essential to investigate and solve the remaining problems before using the data in clinical diagnostics.ConclusionsThe results show that by using a simple reservoir pressure boundary condition (RPBC), we are able to capture some essential variations found in the clinical data. Our approach establishes a first-step framework of a practical patient-specific CMS, which comprises a 3-D CFD model (without involving actual hemodynamic data yet) to simulate the heart and the 4-D PC-MRI system. At this stage, the 4-D PC-MRI system is used for verification purpose rather than input. This brings us closer to our goal of developing a practical patient-specific CMS, which will be pursued next. We anticipate that in the future, this hybrid system can potentially identify possible disease conditions in LV through comprehensive analysis and facilitates physicians in early diagnosis of probable cardiac problems.

Fluid–structure interaction of deformable aortic prostheses with a bileaflet mechanical valve

Two different aortic prostheses can be used for performing the Bentall procedure: a standard straight graft and the Valsalva graft that better reproduces the aortic root anatomy. The aim of the present work is to study the effect of the graft geometry on the blood flow when a bileaflet mechanical heart valve is used, as well as to evaluate the stress concentration near the suture line where the coronary arteries are connected to graft. An accurate three-dimensional numerical method is proposed, based on the immersed boundary technique. The method accounts for the interactions between the flow and the motion of the rigid leaflets and of the deformable aortic root, under physiological pulsatile conditions. The results show that the graft geometry only slightly influences the leaflets dynamics, while using the Valsalva graft the stress level near the coronary-root anastomoses is about half that obtained using the standard straight graft.

직교 격자를 이용한 저 레이놀즈 수 유동장내 다중 배치된 실린더의 와유기 진동 해석

In this paper, the vortex-induced vibration of circular cylinders is studied using the immersed boundary method on the Cartesian mesh. The Reynolds numbers considered is from 100 to 200. Using the configuration of tendemly arranged multiple circular cylinders, the vortex shedding behind of the cylinders and their flow-induced motion are investigated. The staggered MAC grid arrangement, which is the typical grid system for the incompressible flow on the Cartesian meshes, is utilized. Pressure correction method is applied for solving the divergence-free incompressible velocity field. The body motion is described by immersed boundary technique that has advantages for moving object on the fixed computational domain. It is also discussed for the computational noise in hydrodynamic forces when body motion is represented by the immersed boundary method. The Predictor/Corrector method is used for simulating the nonlinear response of the elastically mounted cylinder excited by vortex-shedding.

Flow around a flexible plate in a free stream

This paper presents a numerical scheme for fluid-structure interaction, especially for flexible structures. The lattice Boltzmann method with an immersed boundary technique using a direct forcing scheme is used for the fluid, and a finite element method with Euler beam elements is used for the flexible plate. The direct forcing scheme of the lattice Boltzmann method was improved for the immersed boundary scheme by introducing the occupation ratio of fluid lattices among the interpolated lattices. We compared the results of our proposed scheme with the known results of conventional schemes. Using the proposed numerical scheme, the flow around the flexible plate in a free stream is simulated for the effect of flexibility. Our results show that the major role of the flexibility of the flexible plate is the reduction of the resistance from flow. From the unsteady flow around a flexible plate, we found that the St of the flexible plate up to Re 120 was dependent on plate flexibility. In the range of Re > 120, the St of very flexible plate increased with increasing Re, while the St of rigid plate decreased with increasing Re.

High-order finite-difference implementation of the immersed-boundary technique for incompressible flows

We present a novel numerical procedure for the solution of the incompressible Navier–Stokes equations around complex geometries by means of the immersed-boundary technique. Differently from most similar approaches available in the literature, the present numerical method achieves fourth-order accuracy with respect to both spatial and temporal discretization. The imposition of boundary conditions at immersed boundaries is sharp and not diffuse as in approaches using concentrated forces. The numerical procedure is based on a finite-difference discretization of a primitive-variable formulation of the Navier–Stokes equations on staggered grids. Biased adapted stencils are considered at boundary-near nodes and allow the accurate implementation of no-slip boundary conditions for the velocity. The decoupled computation of velocity and pressure is achieved by deriving a discrete Poisson problem with Neumann-like boundary conditions, indirectly implied by the velocity boundary conditions. The definition of the immersed-boundary geometry requires only the specification of intersection points between immersed boundaries and grid lines. Higher differential features of the boundary, such as tangential direction and curvature, are not needed. Obviously the high-order accuracy of the numerical procedure may be lost if the solution is not smooth, due to non-smoothness of the boundary.

Immersed-boundary methods for general finite-difference and finite-volume Navier–Stokes solvers

We present an immersed-boundary algorithm for incompressible flows with complex boundaries, suitable for Cartesian or curvilinear grid system. The key stages of any immersed-boundary technique are the interpolation of a velocity field given on a mesh onto a general boundary (a line in 2D, a surface in 3D), and the spreading of a force field from the immersed boundary to the neighboring mesh points, to enforce the desired boundary conditions on the immersed-boundary points. We propose a technique that uses the Reproducing Kernel Particle Method [W.K. Liu, S. Jun, Y.F. Zhang, Reproducing kernel particle methods, Int. J. Numer. Methods Fluids 20(8) (1995) 1081–1106] for the interpolation and spreading. Unlike other methods presented in the literature, the one proposed here has the property that the integrals of the force field and of its moment on the grid are conserved, independent of the grid topology (uniform or non-uniform, Cartesian or curvilinear). The technique is easy to implement, and is able to maintain the order of the original underlying spatial discretization. Applications to two- and three-dimensional flows in Cartesian and non-Cartesian grid system, with uniform and non-uniform meshes are presented.

Simulation of Shock/Boundary-Layer Interactions with Bleed Using Immersed-Boundary Methods

This work utilizes an immersed boundary (IB) method to simulate the effects of arrays of discrete bleed ports in controlling shock wave / turbulent boundary layer inter actions . Both Reynolds averaged Navier -Stokes (RANS) and hybrid large -eddy / Reynolds -averaged Navier -Stokes (LES/RANS) turbulence closures are used with the IB technique. The approach is validated by conducting simulations of Mach 2.5 flow over a perfo rated plate containing 18 individual bleed holes. Predictions of discharge coefficient as a function of bleed plenum pressure are compared with experimental data. Simulations of an impinging oblique shock / boundary layer interaction at Mach 2.45 with an d without active bleed control are also performed. The 68 -hole bleed plate is rendered as an immersed object in the computational domain. Wall pressure predictions show that, in general, the LES/RANS technique under -estimate s the upstream extent of axi al separation that occurs in the absence of bleed. Good agreement with P itot -pressure surveys throughout the interaction region is obtained, however. Active suction completely removes the separation region and induces local disturbances in the wall pres sure distributions that are associated with the expansion of the boundary layer fluid into the bleed port and its subsequ ent re -compression. Predicted Pitot -pressure distributions are in good agreement with experiment for the case with bleed. Swirl stre ngth probability -density distributions are used to estimate the evolution of turbulence length -sca les throughout the interaction, and the effects of bleed on the amplification of Reynolds stresses are highlighted. Finally, simple improvements to engineerin g-level bleed models are proposed based on the computational results.

Numerical Simulations of Effects of Micro Vortex Generators Using Immersed-Boundary Methods

This work presents an immersed-boundary technique for compressible, turbulent flows and applies the technique to simulate the effects of micro vortex generators in controlling oblique-shock/turbulent boundary-layer interactions. The Reynolds-averaged Navier-Stokes equations, closed using the Menter k-ω turbulence model, are solved in conjunction with the immersed-boundary technique. The approach is validated by comparing solutions obtained using the immersed-boundary technique with solutions obtained on a body-fitted mesh and with experimental laser Doppler anemometry data collected at Cambridge University for Mach 2.5 flow over single micro vortex generators. Simulations of an impinging oblique-shock boundary-layer interaction at Mach 2.5 with and without micro vortex-generator flow control are also performed, considering the development of the flow in the entire wind tunnel. Comparisons are made with experimental laser Doppler anemometry data and surface-pressure measurements from Cambridge University and an analysis of the flow structure is performed. The results show that three dimensional effects initiated by the interaction of the oblique shock with the sidewall boundary layers significantly influence the flow patterns in the actual experiment. The general features of the interactions with and without the micro vortex-generator array are predicted to good accord by the Reynolds-averaged Navier-Stokes/ immersed-boundary model.

Simulation of vortex dynamics in a cylinder wake by the Immersed Boundary technique

The dynamics of flow past a circular cylinder is investigated at Reynolds number (Re) between 20 and 3900 using the rectangular mesh. The Re is defined based on the cylinder diameter D and the free-stream velocity U∞. This is achieved by using the Immersed Boundary (IB) method that helps to impose boundary conditions on a given surface not coinciding with the computational grid. Two interpolation techniques, namely bi-linear proposed by the authors and unidirectional quadratic by Muldoon and Acharya (2005), are compared for both the laminar and the turbulent flow regime. The unsteady Navier?Stokes (N?S) equations are solved using a symmetry-preserving finite-difference scheme of second-order spatial and temporal accuracy. Large-Eddy Simulations (LES) with the dynamic subgrid model are used to resolve the turbulent flow at Re = 1000 and 3900. When compared with experiments, it reveals that the IB method is worth pursuing and both the interpolations generate almost identical results for a wide range of Reynolds numbers. The bi-linear interpolation is easy to implement and take less computational time because of its simplicity.

Fixed Grid Simulation of Radiation-Conduction Dominated Solidification Process

In this paper conduction-radiation controlled solidification process of semitransparent materials was numerically analyzed. New approach in this kind of simulations, which is based on the fixed grid front tracking method combined with the immersed boundary technique, was adopted and examined. The presented method enables accurate dealing with solidification processes of semitransparent materials which have different optical and thermophysical properties of solid and liquid phases as well as with absorption, emission, and reflection of the thermal radiation at the solid-liquid interface without applying moving mesh methods. The proposed numerical approach was examined by solving several simplified thermal radiation problems with complex fixed and moving boundaries both in two-dimensional and axisymmetric spaces. For some of them the accuracy of obtained results was proved by comparing with reference works, other showed capabilities of the proposed method. For simplified solidification processes of semitransparent materials three configurations of optical properties, i.e., semitransparent solid phase and opaque liquid phase, opaque solid phase and semitransparent liquid phase, and semitransparent both phases were considered. The interface between solid and liquid phases was treated to be opaque, absorbing, emitting, and reflecting diffusely the thermal radiation. Results of the numerical simulations show that the presented numerical approach works well in this kind of problems and is promising for simulation of real solidification processes of semitransparent materials.

Effect of stair‐step and piecewise linear topography on internal wave propagation in a geophysical flow model

The paper describes the effect of a stair‐step representation of bottom topography, common in most numerical models, on the propagation of internal waves in a geophysical flow. An analytical solution was used to predict the effect of stair‐step and piecewise linear representations of topography on the reflection and transmission of internal waves. The Estuary Lake and Coastal Model (ELCOM) was used to simulate the transmission of a train of small‐amplitude internal gravity waves propagated along a variable depth rectangular channel containing a linearly stratified fluid. The effect of the different obstacle approximations was examined in terms of the interference of the resulting wave number content, and hence the associated reflection coefficients, which could be directly compared to the analytical theory. It was shown that for Gaussian obstacles of varying lengths and heights, the full bottom cells and partial bottom cells solutions from ELCOM agree with the stair‐step and piecewise linear solutions from the theory, respectively. It was shown that when Gaussian obstacles with weak slopes are represented by stair steps, an aliasing that is similar to that in discrete Fourier transform can occur, resulting in reflection coefficients that are much higher than the exact solution. On the other hand, piecewise linear approximations produce significantly attenuated aliasing. An immersed boundary technique that enforces a no‐flux condition at the actual sloping bottom, similar to that of the analytical solution, is found not to produce better numerical results.

A Lagrangian method for the treatment of freshly cleared cells in immersed boundary techniques

The present study describes a novel approach treating freshly cleared cells when simulating incompressible flows using the immersed boundary method. The method calculates material derivative in Lagrangian coordinate system to approximate the solution at the freshly cleared cells. In this study, we use a simple test case to compare our proposed method with the commonly used one-dimensional interpolation method in the Eulerian coordinate system.

Numerical study of solid particle erosion on the tubes near the side walls in a duct with flow past an aligned tube bank

AbstractComputational fluid dynamic (CFD) tool has been applied to investigate the erosion of duct walls and that of tubers (10 × 10 aligned tube bank in the duct) near side walls, which is caused by coal ash particle impaction. The flow field is obtained by using direct numerical simulation (DNS) method. The coupling between tubes and flows are made through the immersed boundary technique. Particles are tracked by using Lagrangian approach and further coupled with gas phase. Four coal ash particles are considered 6.2, 20, 80, and 200 μm. In the end, the erosion of the duct walls and that of the tubes near side walls has been well predicted and characterized. © 2009 American Institute of Chemical Engineers AIChE J, 2010

An immersed boundary method to solve fluid–solid interaction problems

We describe an immersed-boundary technique which is adopted from the direct-forcing method. A virtual force based on the rate of momentum changes of a solid body is added to the Navier–Stokes equations. The projection method is used to solve the Navier–Stokes equations. The second-order Adam–Bashford scheme is used for the temporal discretization while the diffusive and the convective terms are discretized using the second-order central difference and upwind schemes, respectively. Some benchmark problems for both stationary and moving solid object have been simulated to demonstrate the capability of the current method in handling fluid–solid interactions.