Direct-forcing Immersed Boundary Method Research Articles

Three-dimensional numerical simulation of violent free surface deformation based on a coupled level set and volume of fluid method

The purpose of this study is to evaluate the ability of the coupled level set and volume of fluid (CLSVOF) method to reproduce violent three-dimensional (3D) free surface deformation induced by different types of dambreak problems. A 3D CLSVOF-based numerical solver is developed, and the finite difference method is adopted to discretize the fluid domain. By applying these methods, the VOF advection equation is solved under the tangent of hyperbola framework to capture the interactions with the weighted linear interface calculation scheme (THINC/WLIC). The OCRWENO scheme is employed to accurately handle the LS advection equation, and the Navier–Stokes equations are discretized by a projection method. For dealing with fluid–structure interactions, the direct forcing immersed boundary method is employed. The developed numerical solver is applied to model free surface evolution in a variety of dambreak experiments. Good agreement is obtained between the numerical simulation and experimental results for each case, thus proving the suitability of the proposed numerical approach for the simulation of violent free surface deformation. The numerical solver developed in this paper has potential for reproducing strongly nonlinear free surface phenomena in other ocean engineering applications.

Simulation of dielectric barrier discharge actuator at low Reynolds number

PurposeThe purpose of this study is to the modeling of the dielectric barrier discharge (DBD) actuator on the Eppler 387 (E387) airfoil in low Reynolds number conditions.Design/methodology/approachA validated direct-forcing immersed boundary method is used to solve the governing equations. A linear electric field model is used to simulate the DBD actuator. A ray-casting technique is used to define the geometry.FindingsThe purposed model is validated against the former studies. Next, the drag and lift coefficients in the static stall of the E387 airfoil are investigated. Results show that when the DBD actuator is on, both of the coefficients are increased. The effects of the location, applied voltage and applied frequency are also studied and find that the leading-edge actuator with higher voltage and frequency has better improvement in the forces. Finally, the dynamic stall of the E387 with the DBD actuator is considered. The simulation shows that generally when the DBD is on, the lift coefficient in the pitch-up section has lower values and in the pitch-down has higher values than the DBD off mode.Practical implicationsIt is demonstrated that using the DBD actuator on E387 in the low Reynolds number condition can increase the lift and drag forces. Therefore, the application of the airfoil must be considered.Originality/valueThe results show that sometimes the DBD actuator has different effects on E387 airfoil in low Reynolds number mode than the general understanding of this tool.

Effects of an inserted circular cylinder on a steady lid-driven rectangular cavity flow

This paper provides numerical investigations of flow in a steady lid-driven cavity of depth to width ratio 1/3 containing a circular cylinder. The inner cylinder is treated using a direct-forcing immersed boundary method, and a project method is applied to solve the incompressible Navier-Stokes equations. Three different Reynolds numbers and positions of the cylinder are considered; for a lower Reynolds number, flow structures are weakly affected by the cylinder near the left wall while two clockwise vortices attached to the cylinder are formed as the cylinder moves rightwards; for a moderate Reynolds number, an anticlockwise bottom vortex is formed for the cylinder near the left wall, and it disappears as the cylinder is shifted rightwards; for the largest Reynolds number, two anti-clockwise vortices attached the cylinder are formed for the cylinder close to the left wall, and as the cylinder moves gradually closer to the left wall a bottom vortex is formed and disappears together with the clockwise vortex to the right side of the cylinder.

Is Lagrangian weight crucial in the direct forcing immersed boundary method?

Particle resolved direct numerical simulation (PR-DNS) is one of the most powerful research tools for particle laden flows. Among a few most popular PR-DNS methods, the direct forcing immersed boundary method (DF-IBM) has obtained great success and has been adopted in various simulations of rigid particulate flows. Within DF-IBM, Eulerian and Lagrangian frameworks are used to depict the continuum and dispersed phases, respectively. Interpolation between the two frameworks is accomplished through a discrete delta function. It is generally believed that a Lagrangian weight attached to each Lagrangian marker, which is distributed on a particle’s surface, needs to be carefully chosen. To be more specific, the Lagrangian weight is supposed to match the local Eulerian cell. The matching requirement is not trivial for non-uniform Eulerian mesh or irregular shaped particles. There are various methods developed to calculate the Lagrangian weight. Here, the Lagrangian weights in a few testing cases have been calculated following two intuitively “straightforward” methods. It turns out there are substantial discrepancies in the Lagrangian weights obtained from different methods. However, further numerical examples demonstrate that such discrepancies have negligible effects on the flow dynamics. So a natural question is raised: Is Lagrangian weight crucial in the direct forcing immersed boundary method? A negative answer to this question is suggested. More detailed analysis is provided in a forthcoming paper.

On the coupling of a direct-forcing immersed boundary method and the regularized lattice Boltzmann method for fluid-structure interaction

The present paper provides an analysis of the force model effect on the regularization procedure based on the Hermite expansion in regularized lattice Boltzmann method (RLBM). It is shown that, when using the 2nd-order accurate in time semi-implicit force model of Guo et al. [15] in RLBM, the reconstruction of the non-equilibrium part of the distribution function has to start from the 1st-order Hermite polynomial, because the new distribution function (after a change of variables) contains the body force effect. Based on this Hermite regularization, an immersed boundary-regularized lattice Boltzmann (IB-RLB) coupling method is proposed for simulating transient fluid-structure interactions (FSI) with rigid and deformable solid objects. The fluid and solid solvers are coupled in a non-staggered way so that the stability and accuracy are well preserved. The proposed IB-RLB coupling method is then validated with several numerical test-cases, such as impulsively started plate, vortex-induced vibrations and 3D flapping flag, for which good agreements are found with the references.

Numerical Simulation of Flow behind Vortex Generators

In this study, flow behind rectangular vane type vortex generators mounted on a flat plate, is numerically simulated using the immersed boundary (IB) method. In the present work, the direct forcing IB method is employed because of its simplicity and high efficiency. Vortex generators of two different heights are numerically investigated. The height of vanes in the first case is close to the definition of submerged/low-profile vortex generators while the other case is closer to the definition of a conventional vortex generator. The resultant highly three-dimensional flow and its transition to turbulence have been studied. Counter-rotating vortices generated by these passive rectangular vortex generators are characterized. Streamwise evolution of non-dimensionalised maximum values of vorticity, vortex strength, streamwise velocity and wall-normal velocity are studied. The simulations show that the IB method in conjunction with DNS effectively simulates the time-dependent flow behind an array of passive vortex generators placed in an initially laminar boundary layer.

Turbulent flow of finite-size spherical particles in channels with viscous hyper-elastic walls

We study single-phase and particle-laden turbulent channel flows bounded by two incompressible hyper-elastic walls with different deformability at bulk Reynolds number $5600$. The solid volume fraction of finite-size neutrally buoyant rigid spherical particles considered is $10\,\%$. The elastic walls are assumed to be of a neo-Hookean material. A fully Eulerian formulation is employed to model the elastic walls together with a direct-forcing immersed boundary method for the coupling between the fluid and the particles. The data show a significant drag increase and the enhancement of the turbulence activity with growing wall elasticity for both the single-phase and particle-laden flows when compared with the single-phase flow over rigid walls. Drag reduction and turbulence attenuation is obtained, on the other hand, with highly elastic walls when comparing the particle-laden flow with the single-phase flow for the same wall properties; the opposite effect, drag increase, is observed upon adding particles to the flow over less elastic walls. This is explained by investigating the near-wall turbulence, where the strong asymmetry in the magnitude of the wall-normal velocity fluctuations (favouring positive $v^{\prime }$), is found to push the particles towards the channel centre. The particle layer close to the wall contributes to turbulence production by increasing the wall-normal velocity fluctuations, so that in the absence of this layer, smaller wall deformations and in turn turbulence attenuation is observed. For a moderate wall elasticity, we increase the particle volume fraction up to $20\,\%$ and find that particle migration away from the wall is the cause of turbulence attenuation with respect to the flow over rigid walls. However, for this higher volume fractions, the particle induced stress compensates for the decreasing Reynolds shear stress, resulting in a higher overall drag for the case with elastic walls. The effect of the wall elasticity on the overall drag reduces significantly with increasing particle volume fraction.

DFIB-SPH study of submerged horizontal cylinder oscillated close to the free surface of a viscous liquid

The hydrodynamics is studied numerically of a horizontal cylinder undergoing forced in-line oscillation beneath the free surface of otherwise quiescent liquid at low Keulegan–Carpenter and Froude numbers. The direct forcing immersed boundary-smoothed particle hydrodynamics (DFIB-SPH) numerical model uniquely combines two well-established techniques: the direct forcing immersed boundary method and SPH. This facilitates accurate evaluation of the potentially violent free surface motions through SPH and the hydrodynamic force on the solid body using a volume integral. A parameter study is conducted covering a range of Keulegan–Carpenter numbers (KC = 3, 7, and 10) and submergence ratios () at fixed Reynolds number (Re = 100) and Froude number (Fr = 0.35). The flow pattern and transverse force coefficient are found to be affected by the proximity of the cylinder to the free surface. Spectral analysis suggests that free surface wave motions are linked to the transverse force acting on the submerged, oscillating cylinder.

Research on dam-break induced tsunami bore acting on the triangular breakwater based on high order 3D CLSVOF-THINC/WLIC-IBM approaching

In present study, high order three dimensional coupled level set and volume of fluid (CLSVOF) based simulations about dam-break induced tsunami bore interacting with the stationary triangular breakwater was numerically investigated. Under our CLSVOF approaching, VOF advection equation is solved by tangent of hyperbola for interface capturing (THINC) with weighed linear interface calculation (WLIC) scheme, and level set advection equation is solved directly by the high-resolution optimized compact reconstruction weighted essentially non-oscillatory (WENO) scheme. Navier-Stokes equations is solved by a projection method on a fixed staggered Cartesian finite difference mesh. The pressure Poisson equation is solved by the point successive over-relaxation (PSOR) method. The direct forcing immersed boundary method (IBM) was implemented for breakwater-tsunami bore interface treatment. Numerical experiments based on our high order 3D CLSVOF-THINC/WLIC-IBM method were carried out in a rectangular water channel with a stationary typical triangular breakwater. The numerical results were compared with corresponding laboratory experimental results and reasonable agreements were obtained with satisfied accuracy. Numerical cases with different shape of triangular breakwater are carried out then in order to investigate the free surface evolution and energy dissipation due to the breakwater and useful conclusion is obtained.

A boundary thickening-based direct forcing immersed boundary method for fully resolved simulation of particle-laden flows

A boundary thickening-based direct forcing (BTDF) immersed boundary (IB) method is proposed for fully resolved simulation of incompressible viscous flows laden with finite size particles. By slightly thickening the boundary thickness, the local communications between the Lagrangian points on the solid boundary and their neighboring fluid Eulerian grids are improved, based on an implicit direct forcing (IDF) approach and a partition-of-unity condition for the regularized delta function. This strategy yields a simple, yet much better imposition of the non-slip and non-penetration boundary conditions than the conventional direct forcing (DF) technique. In particular, the present BTDF method can achieve a numerical accuracy comparable with other representative improved methods, such as multi-direct forcing (MDF), implicit velocity correction (IVC) and the reproducing kernel particle method (RKPM), while its computing cost remains much lower than them and nearly equivalent to the conventional DF method. The dependence of the optimum thickness value of boundary thickening on the form of the different regularized delta functions is also revealed. By coupling the lattice Boltzmann method (LBM) with BTDF-IB, the robustness of the present BTDF IB method is demonstrated using numerical simulations of creeping flow (Re=0.1), steady vortex separating flow (Re=40) and unsteady vortex shedding flow (Re=200) around a circular cylinder. The accuracy and robustness of the present method for moving particle-laden flows are performed on three benchmark cases, such as free sedimentation of single circular cylinder, DKT sedimentation of two particles and Rayleigh-Taylor instability of 504 particles sedimentation in an enclosed cavity. The computational efficiency between the present BTDF method and the MDF method is also compared at last.

A non-iterative direct-forcing immersed boundary method for thermal discrete unified gas kinetic scheme with Dirichlet boundary conditions

A non-iterative immersed boundary-thermal discrete unified gas kinetic scheme (IB-TDUGKS) is developed for the simulation of thermal flows. Two sets of distribution functions are applied for the velocity and temperature fields respectively, where the influence of the heat on the fluid is considered by the Boussinesq approximation. The immersed boundary method with the direct-forcing model is used to handle the complex solid boundary, in which it is replaced by the generator of local body force and heat source/sink. However, the explicit force and heat source/sink in the conventional IB methods usually result in the unphysical fluid and heat penetrations. The iterative forcing approach can remove such deficiency, but it increases both the complexity of solutions and the computational load. Therefore, a non-iterative IB method is presented in this study. With the introduction of an adjustment parameter, the present approach evaluates the force and heat source/sink explicitly, and at the same time enforces the boundary conditions for both the velocity and temperature at the fluid-solid interface. Furthermore, the force and heat source/sink are conveniently incorporated into the DUGKS with the Strang-splitting scheme. The accuracy and feasibility of the present IB-TDUGKS is verified in several well-established thermal flow problems. The results agree well the data available in the literature.

Cavitation induction by projectile impacting on a water jet

The present paper focuses on the simulation of the high-velocity impact of a projectile impacting on a water-jet, causing the onset, development and collapse of cavitation. The simulation of the fluid motion is carried out using an explicit, compressible, density-based solver developed by the authors using the OpenFOAM library. It employs a barotropic two-phase flow model that simulates the phase-change due to cavitation and considers the co-existence of non-condensable and immiscible air. The projectile is considered to be rigid while its motion through the computational domain is modelled through a direct-forcing Immersed Boundary Method. Model validation is performed against the experiments of Field et al. (2012), who visualised cavity formation and shock propagation in liquid impacts at high velocities. Simulations unveil the shock structures and capture the high-speed jetting forming at the impact location, in addition to the subsequent cavitation induction and vapour formation due to refraction waves. Moreover, model predictions provide quantitative information and a better insight on the flow physics that has not been identified from the reported experimental data, such as shock-wave propagation, vapour formation quantity and induced pressures. Furthermore, evidence of the Richtmyer–Meshkov instability developing on the liquid–air interface are predicted when sufficient dense grid resolution is utilised.

Turbulence modulation in channel flow of finite-size spheroidal particles

Finite-size particles modulate wall-bounded turbulence, leading, for the case of spherical particles, to increased drag also owing to the formation of a particle wall layer. Here, we study the effect of particle shape on the turbulence in suspensions of spheroidal particles at volume fraction $\unicode[STIX]{x1D719}=10\,\%$ and show how the near-wall particle dynamics deeply changes with the particle aspect ratio and how this affects the global suspension behaviour. Direct numerical simulations are performed using a direct-forcing immersed boundary method to account for the dispersed phase, combined with a soft-sphere collision model and lubrication corrections for short-range particle–particle and particle–wall interactions. The turbulence reduces with the aspect ratio of oblate particles, leading to drag reduction with respect to the single-phase flow for particles with aspect ratio ${\mathcal{A}}{\mathcal{R}}\leqslant 1/3$, when the significant reduction in Reynolds shear stress is more than the compensation by the additional stresses, induced by the solid phase. Oblate particles are found to avoid the region close to the wall, travelling parallel to it with small angular velocities, while preferentially sampling high-speed fluid in the wall region. Prolate particles also tend to orient parallel to the wall and avoid its vicinity. Their reluctance to rotate around the spanwise axis reduces the wall-normal velocity fluctuation of the flow and therefore the turbulence Reynolds stress, similar to oblates; however, they undergo rotations in wall-parallel planes which increase the additional solid stresses due to their relatively larger angular velocities compared to the oblates. These larger additional stresses compensate for the reduction in turbulence activity and lead to a wall drag similar to that of single-phase flows. Spheres on the other hand, form a layer close to the wall with large angular velocities in the spanwise direction, which increases the turbulence activity in addition to exerting the largest solid stresses on the suspension, in comparison to the other studied shapes. Spherical particles therefore increase the wall drag with respect to the single-phase flow.

An improved direct-forcing immersed boundary method with inward retraction of Lagrangian points for simulation of particle-laden flows

The direct-forcing immersed boundary is widely adopted to study particle-laden flows. The effective hydrodynamic diameter of the particle is much or less overestimated by the original immersed boundary method, depending on the particle Reynolds number and grid resolution. In this paper, we propose an improved method to dynamically correct the effective hydrodynamic diameter by retracting inward the Lagrangian points to varying distances. The retraction distance is determined by querying a function fitted in this paper. The improved method is tested and validated by several cases, including falling of a spherical particle under gravity, the uniform flow past two stationary particles and the drafting-kissing-tumbling phenomenon of two settling particles. It turns out the improved method not only provides better results for the drag force but also predicts the flow field more accurately. What's more, due to the insensitivity to grid resolution, the improved method is suitable for simulating large-scale fluid–particle systems such as fluidized bed, which are computationally expensive.

Simulation of dynamic stall using direct-forcing immersed boundary method at low Reynolds number

PurposeThe purpose of this study is simulation of dynamic stall behavior around the Eppler 387 airfoil in the low Reynolds number flow with a direct-forcing immersed boundary (DFIB) numerical model.Design/methodology/approachA ray-casting method is used to define the airfoil geometry. The governing continuity and Navier–Stokes momentum equations and boundary conditions are solved using the DFIB method.FindingsThe purposed method is validated against numerical results from alternative schemes and experimental data on static and oscillating airfoil. A base flow regime and different vortices patterns are observed, in accordance with other previously published investigations. Also, the effects of the reduced frequency, the pitch oscillation amplitude and the Reynolds number are studied. The results show that the reduced frequency has a major effect on the flow field and the force coefficients of the airfoil. On the other hand, the Reynolds number of the flow has a little effect on the dynamic stall characteristics of the airfoil at least in the laminar range.Practical implicationsIt is demonstrated that the DFIB model provides an accurate representation of dynamic stall phenomenon.Originality/valueThe results show that the dynamic stall behavior around the Eppler 387 is different than the general dynamic stall behavior understanding in the shedding phase.

Semi-implicit direct forcing immersed boundary method for incompressible viscous thermal flow problems: A Schur complement approach

An extended immersed boundary method utilizing a semi-implicit direct forcing approach for the simulation of confined incompressible viscous thermal flow problems is presented. The method utilizes a Schur complement approach to enforce the kinematic constraints of no-slip and the corresponding thermal boundary conditions for immersed surfaces. The developed methodology can be straightforwardly adapted to any existing incompressible time marching solver based on a segregated pressure-velocity coupling. The method accurately meets the thermal and the no-slip boundary conditions on the surfaces of immersed bodies for the entire range of Rayleigh numbers 103⩽Ra⩽106. Strategies for further increasing the computational efficiency of the developed approach are discussed. The method has been extensively verified by applying it for the simulation of a number of representative fully 3D confined natural convection steady and periodic flows. Complex dynamic phenomena typical of this kind of flow including vortical structures and convection cells and instability characteristics, were simulated and visualized and the results were found to compare favorably with results known from literature.

An immersed boundary-discrete unified gas kinetic scheme for simulating natural convection involving curved surfaces

In this work, an immersed boundary-discrete unified gas kinetic scheme (IB-DUGKS) is proposed and presented for the simulation of natural convection with a curved body surface. In this method, two distribution functions are employed for velocity and temperature field, respectively, and they are coupled under the Boussinesq approximation. The IB-DUGKS provides an effective way for the DUGKS to treat a curved boundary. The Strang-splitting method is used to handle the IB force, and its accuracy is first validated by comparing with another implementation method for the base case of natural convection in a square cavity. The widely used direct-forcing immersed boundary method is adopted due to its simplicity, with an iteration procedure to ensure the accuracy of no-slip condition on the immersed boundary. Natural convection between an outer square and an inner circular cylinder is then simulated under different geometric configurations, including different aspect ratios and locations of the cylinder relative to the cavity. The numerical results are in excellent agreement with the results from the literature, confirming the accuracy and robustness of the proposed method.

A computational study of the three-dimensional fluid–structure interaction of aortic valve

In this paper, we describe a three-dimensional simulation of the fluid–structure interaction (FSI) of the aortic valve using a direct-forcing immersed-boundary method. The geometry of the valve is taken from a bioprosthetic valve, and the computational framework is based on a previous partitioned approach that is versatile for handling a range of biological FSI problems involving large deformations. When applying the approach in the heart valve simulation, we implemented an efficient parallel algorithm based on domain decomposition to handle the costly flow simulation. As compared with previous simulations of the aortic valve, our simulation was able to capture both realistic deformation of the leaflets and vortex structures in the flow, thus providing a balanced modeling approach for the flow and the valve. The results show that the pressure distribution on the leaflet surface is highly nonuniform and the jet flow contains a sequence of vortices during the opening process. After the valve is fully opened, both the three leaflets and the jet still experience significant oscillations. The drag resistance of the valve is also characterized, and it is found that the resistance is approximately equivalent to the inertial force of accelerating the fluid column of three diameter length. These details could be potentially used to characterize FSI of the aortic valve.

Reduction of the discretization stencil of direct forcing immersed boundary methods on rectangular cells: The ghost node shifting method

We present an analytical study of discretization stencils for the Poisson problem and the incompressible Navier–Stokes problem when used with some direct forcing immersed boundary methods. This study uses, but is not limited to, second-order discretization and Ghost-Cell Finite-Difference methods. We show that the stencil size increases with the aspect ratio of rectangular cells, which is undesirable as it breaks assumptions of some linear system solvers. To circumvent this drawback, a modification of the Ghost-Cell Finite-Difference methods is proposed to reduce the size of the discretization stencil to the one observed for square cells, i.e. with an aspect ratio equal to one. Numerical results validate this proposed method in terms of accuracy and convergence, for the Poisson problem and both Dirichlet and Neumann boundary conditions. An improvement on error levels is also observed. In addition, we show that the application of the chosen Ghost-Cell Finite-Difference methods to the Navier–Stokes problem, discretized by a pressure-correction method, requires an additional interpolation step. This extra step is implemented and validated through well known test cases of the Navier–Stokes equations.

Three-dimensional simulation of a self-propelled fish-like body swimming in a channel

ABSTRACTIn this study, a three-dimensional simulation of a fish-like body swimming in a channel with non-slip walls was carried out to investigate the effects of kinematics on swimming performance. Self-propelled swimming in an inertial coordinate system was examined by using the direct forcing immersed boundary method. The fish body consisted of several rigid bodies and behaved analogously to a multi-segment robotic fish. The computational program was first validated by simulating fluid flow around a circular cylinder at Reynolds number (Re) =100 and Re = 1000, as well as around a settling particle. The results were compared with experimental and numerical results from past research in the area. A virtual parametric study of the tail-beat frequency, phase difference between neighboring body segments, and body amplitude was then conducted. The effect of the lateral and vertical distance between the model body and walls on swimming performance is also discussed. The results for the velocity and vorticity fields around the model body provided evidence for the mechanism of thrust generation and highlighted the effects of kinematics on swimming performance.