A new immersed boundary method for compressible Navier–Stokes equations

This paper presents an immersed boundary method for compressible Navier–Stokes equations in irregular domains, based on a local radial basis function approximation. This approach allows one to define a reconstruction of the radial basis functions on each irregular interface cell to treat both the Dirichlet and Neumann boundary conditions accurately on the immersed interfaces. Several numerical examples, including problems with available analytical solutions and the well-documented flow past an airfoil, are presented to test the proposed method. The numerical results demonstrate that the proposed method provides accurate solutions for viscous compressible flows.     

Gust response: Simulation of an aeroelastic experiment by a fluid–structure interaction method

In this paper fluid–structure interaction simulations regarding a gust generator experiment are presented, which has been conducted in 2010 in the Transonic Wind Tunnel in Göttingen (DNW-TWG), Germany. The main objective of the experiment was the investigation of the dynamic response problem of an elastic wing model concerning an encountering generic gust induced by a gust generator. Fluid–structure simulations, using a finite element structural model and a computational fluid dynamics model based on time-accurate, Reynolds-averaged Navier–Stokes equations, are compared to the experiment to validate the numerical methodology. Comparisons include steady and unsteady deflections of the elastic wing and pressure distributions. Finally, the results of simulated transfer functions of the gust generator to the elastic wing are presented in comparison to the test data.     

Active feedback control of sound radiation in elastic wave metamaterials immersed in water with fluid–solid coupling

Acta Mechanica Sinica - Due to their potential properties unlike traditional materials and structures, elastic wave metamaterials have received significant interests in recent years. With the...     

A fictitious domain finite element method for simulations of fluid–structure interactions: The Navier–Stokes equations coupled with a moving solid

The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier–Stokes equations coupled with a moving solid. This method presents the advantage to predict an optimal approximation of the normal stress tensor at the interface. The dynamics of the solid is governed by Newton׳s laws and the interface between the fluid and the structure is materialized by a level-set which cuts the elements of the mesh. An algorithm is proposed in order to treat the time evolution of the geometry and numerical results are presented on a classical benchmark of the motion of a disk falling in a channel.     

SPH modeling of fluid–solid interaction for dynamic failure analysis of fluid-filled thin shells

This work concerns the prediction of failure of a fluid-filled tank under impact loading, including the resulting fluid leakage. A water-filled steel cylinder associated with a piston is impacted by a mass falling at a prescribed velocity. The cylinder is closed at its base by an aluminum plate whose characteristics are allowed to vary. The impact on the piston creates a pressure wave in the fluid which is responsible for the deformation of the plate and, possibly, the propagation of cracks. The structural part of the problem is modeled using Mindlin–Reissner finite elements (FE) and Smoothed Particle Hydrodynamics (SPH) shells. The modeling of the fluid is also based on an SPH formulation. The problem involves significant fluid–structure interactions (FSI) which are handled through a master–slave-based method and the pinballs method. Numerical results are compared to experimental data.     

An unsteady point vortex method for coupled fluid–solid problems

A method is proposed for the study of the two-dimensional coupled motion of a general sharp-edged solid body and a surrounding inviscid flow. The formation of vorticity at the body’s edges is accounted for by the shedding at each corner of point vortices whose intensity is adjusted at each time step to satisfy the regularity condition on the flow at the generating corner. The irreversible nature of vortex shedding is included in the model by requiring the vortices’ intensity to vary monotonically in time. A conservation of linear momentum argument is provided for the equation of motion of these point vortices (Brown–Michael equation). The forces and torques applied on the solid body are computed as explicit functions of the solid body velocity and the vortices’ position and intensity, thereby providing an explicit formulation of the vortex–solid coupled problem as a set of non-linear ordinary differential equations. The example of a falling card in a fluid initially at rest is then studied using this method. The stability of broadside-on fall is analysed and the shedding of vorticity from both plate edges is shown to destabilize this position, consistent with experimental studies and numerical simulations of this problem. The reduced-order representation of the fluid motion in terms of point vortices is used to understand the physical origin of this destabilization.      

Numerical investigation of separation efficiency of the cyclone with supercritical fluid–solid flow

The utilization of hydrogen is gaining increasing attention due to its high heating value and environmentally friendly combustion product. The supercritical water circulating fluidized bed reactor is a promising and potentially clean technology that can generate hydrogen from coal gasification. Cyclone is a vital part of the reactor which can separate incomplete decomposition of pulverized coal particles from mixed working fluid. This paper aims to gain in-depth understanding of the cyclone separation mechanisms under supercritical fluid by computational fluid dynamics (CFD). Although the amount of supercritical carbon dioxide in mixed working fluid is minor, it obviously influences the flow fields and separation efficiency of a cyclone. The simulation results suggest that both the decreasing content of supercritical carbon dioxide and adding the extra dipleg cause the promoting performance of cyclones. Research findings could refine the design of supercritical fluid–solid cyclones.     

Level set function–based immersed interface method and benchmark solutions for fluid flexible-structure interaction

Using a hybrid Lagrangian-Eulerian approach, a level set function–based immersed interface method (LS-IIM) is proposed for the interaction of a flexible body immersed in a fluid flow. The LS-IIM involves finite volume method for the fluid solver, Galerkin finite element method for the structural solver, and a block-iterative partitioned method–based fully implicit coupling between the two solvers. The novelty of the proposed method is a level set function–based direct implementation of fluid-solid interface boundary conditions in both the solvers. Another novelty is the computation of the level set function from a geometric method instead of differential equations commonly used in level set methods—the novel geometric as compared to the traditional method is found to be more accurate and less time-consuming. The LS-IIM is demonstrated as second-order accurate. Verification study is presented first separately for both the solvers and then together for four fluid-structure interaction (FSI) problems, with different levels of complexity including lid-driven flow, channel flow, and free-stream flow. Benchmark solutions are presented for two class of FSI problems: first, easy to set up and less time-consuming and, second, a reasonably challenging and complex FSI problem involving sharp edges and forced-motion of the flexible structure. The benchmark solutions are proposed at steady state for the first problem, after a verification study with two open-source solvers and, at periodic state, after a validation with published experimental results for the second problem. Our benchmark solutions may be useful for verification study in future.     

Falling cards and flapping flags: understanding fluid–solid interactions using an unsteady point vortex model

A reduced-order model for the two-dimensional interaction of a sharp-edged solid body and a high-Reynolds number flow is presented, based on the inviscid representation of the solid’s wake as point vortices with unsteady intensity. This model is applied to the fall of a rigid card in a fluid and to the flapping instability of a flexible membrane forced by a parallel flow.     

Shear-wave resonances in a fluid–solid–solid layered structure

An inhomogeneous solid layer is bounded on one side by a fluid half-space and on the other by a homogeneous solid half-space. An acoustic wave in the fluid is incident on the layer. Experiments suggest that some kind of shear-wave resonance of the layer exists. Here, the layer is modeled with exponential variations of the material properties (Epstein model). Solutions in terms of hypergeometric functions are found. Genuine resonances are found but only when the layer is not bonded to the solid half-space; these are analogous to Jones frequencies in fluid–solid interaction problems. When the solid half-space is present, the resonances become complex: they are scattering frequencies. Simple but accurate asymptotic approximations are found using known estimates for hypergeometric functions with large parameters.     

A strongly coupled,embedded-boundary method for fluid–structure interactions of elastically mounted rigid bodies

In the present paper, an embedded-boundary formulation that is applicable to fluid–structure interaction problems is presented. The Navier–Stokes equations for incompressible flow are solved on a Cartesian grid which is not aligned with the boundaries of a body that undergoes large-angle/large-displacement rigid body motions through the fixed grid. A strong-coupling scheme is adopted, where the fluid and the structure are treated as elements of a single dynamical system, and all of the governing equations are integrated simultaneously and interactively in the time domain. A demonstration of the accuracy and efficiency of the method is given for a variety of fluid–structure interaction problems.     

Migration of a solid particle in the vicinity of a plane fluid–fluid interface

The slow migration of a small and solid particle in the vicinity of a gas–liquid, fluid–fluid or solid–fluid plane boundary when subject to a gravity or an external flow field is addressed. By contrast with previous works, the advocated approach holds for arbitrarily shaped particles and arbitrary external Stokes flow fields complying with the conditions on the boundary. It appeals to a few theoretically established and numerically solved boundary-integral equations on the particle’s surface. This integral formulation of the problem allows us to provide asymptotic approximations for a distant boundary and also, implementing a boundary element technique, accurate numerical results for arbitrary locations of the boundary. The results obtained for spheroids, both settling or immersed in external pure shear and straining flows, reveal that the rigid-body motion experienced by a particle deeply depends upon its shape and also upon the boundary location and properties.     

Blockage of constrictions by particles in fluid–solid transport

Blockage is an important phenomenon in particulate flow. Work was undertaken to provide a better understanding of key hydrodynamic multiphase flow factors which cause, or contribute to, stalling and blockage in particulate feeding systems such as those used for feeding biomass into reactors. Rubber and plastic particles were hydraulically conveyed along a horizontal rectangular duct leading to constrictions of different geometries. Experimental results showed that large size, irregular shape, high volumetric concentrations of particles, small constriction dimensions and particle compressibility all increased the likelihood of blockage. Reynolds number also had a significant effect on particle behaviour and blockage propensity. The pressure drop needed to break a blockage is also considered, based on a simple horizontal packed bed model.     

Simulation of liquid–vapour phase transitions and multiphase flows by an improved lattice Boltzmann model

An improved lattice Boltzmann (LB) model with a new scheme for the interparticle interaction force term is proposed in this paper. Based on the improved LB model, the equation-free method is implemented for simulating liquid–vapour phase change and multiphase flows. The details of phase separation are presented by numerical simulation results in terms of coexistence curves and spurious currents. Compared with existing models, the proposed model can give more accurate results in a wider temperature range with the spurious currents reduced and less time consumed. Characteristics of phase separation can be quickly and accurately reflected by the proposed method. Then, the contact angle of the solid surface is numerically investigated based on the proposed model. The proposed model is valid for steady flow with near zero velocity; unsteady cases will be investigated in further studies. This work will be helpful for our long-term aim of multi-scale modelling of convective boiling.     

Direct simulation of liquid–gas–solid flow with a free surface lattice Boltzmann method

Direct numerical simulation of liquid–gas–solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary – in particular, if the bubble–particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble–particle interaction at a size ratio of 1–2 orders of magnitude that makes simulations feasible on currently available super-computing resources. With the presented approach, simulations of bubbles in suspension columns consisting of more than 100,000 fully resolved particles become possible. Furthermore, we demonstrate the significance of particle-resolved simulations by comparison to previous unresolved solutions. The results indicate that fully resolved direct numerical simulation is indeed necessary to predict the flow structure of bubble–particle interaction problems correctly.     

Numerical simulation of gas–solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas–solid phases was predicted using the Eulerian–Eulerian two-fluid model (TFM) approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas–solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Simulation of wave–body interaction: A desingularized method coupled with acceleration potential

A two-dimensional, potential-theory based, fully nonlinear numerical wave tank (NWT) is developed for the simulation of wave–body interaction. In this NWT, the concept of acceleration potential is adopted in addition to the velocity potential. Both potentials are solved using the desingularized boundary integral equation method (DBIEM). By tapping the strength of the DBIEM, a new acceleration-potential solving method is proposed, which turns the originally implicit kinematic boundary condition on the surface of a passively moving body into an explicit one. Unlike the other existing methods such as the mode decomposition method, the indirect method and the iterative method, the present method requires solving of only one boundary value problem to determine the acceleration potential, and hence significantly enhances the computational efficiency. Using this NWT, the nonlinear interaction between a freely floating barge and various incident waves is investigated. It is confirmed that the new acceleration potential solving method outperforms other existing methods, saving at least 45% of the computational time.     

Numerical investigation of fluid–particle interactions for embolic stroke

Roughly one-third of all strokes are caused by an embolus traveling to a cerebral artery and blocking blood flow in the brain. The objective of this study is to gain a detailed understanding of the dynamics of embolic particles within arteries. Patient computed tomography image is used to construct a three-dimensional model of the carotid bifurcation. An idealized carotid bifurcation model of same vessel diameters was also constructed for comparison. Blood flow velocities and embolic particle trajectories are resolved using a coupled Euler–Lagrange approach. Blood is modeled as a Newtonian fluid, discretized using the finite volume method, with physiologically appropriate inflow and outflow boundary conditions. The embolus trajectory is modeled using Lagrangian particle equations accounting for embolus interaction with blood as well as vessel wall. Both one- and two-way fluid–particle coupling are considered, the latter being implemented using momentum sources augmented to the discretized flow equations. It was observed that for small-to-moderate particle sizes (relative to vessel diameters), the estimated particle distribution ratio—with and without the inclusion of two-way fluid–particle momentum exchange—were found to be similar. The maximum observed differences in distribution ratio with and without the coupling were found to be higher for the idealized bifurcation model. Additionally, the distribution was found to be reasonably matching the volumetric flow distribution for the idealized model, while a notable deviation from volumetric flow was observed in the anatomical model. It was also observed from an analysis of particle path lines that particle interaction with helical flow, characteristic of anatomical vasculature models, could play a prominent role in transport of embolic particle. The results indicate therefore that flow helicity could be an important hemodynamic indicator for analysis of embolus particle transport. Additionally, in the presence of helical flow, and vessel curvature, inclusion of two-way momentum exchange was found to have a secondary effect for transporting small to moderate embolus particles—and one-way coupling could be used as a reasonable approximation, thereby causing substantial savings in computational resources.     

An immersed boundary vector potential-vorticity meshless solver of the incompressible Navier–Stokes equation

We present a strong form meshless solver for numerical solution of the nonstationary, incompressible, viscous Navier–Stokes equations in two (2D) and three dimensions (3D). We solve the flow equations in their stream function-vorticity (in 2D) and vector potential-vorticity (in 3D) formulation, by extending to 3D flows the boundary condition-enforced immersed boundary method, originally introduced in the literature for 2D problems. We use a Cartesian grid, uniform or locally refined, to discretize the spatial domain. We apply an explicit time integration scheme to update the transient vorticity equations, and we solve the Poisson type equation for the stream function or vector potential field using the meshless point collocation method. Spatial derivatives of the unknown field functions are computed using the discretization-corrected particle strength exchange method. We verify the accuracy of the proposed numerical scheme through commonly used benchmark and example problems. Excellent agreement with the data from the literature was achieved. The proposed method was shown to be very efficient, having relatively large critical time steps.