Immersed Boundary Technique Research Articles

Immersed Boundary Method for Numerical Simulation of Inviscid Compressible Flows

A technique for the numerical simulation of the interaction between an inviscid compressible medium and solid bodies is described. The boundary condition on the solid surface is set using the immersed boundary approach. An immersed boundary technique is proposed for the considered class of problems. The performance of the technique is demonstrated by solving test problems in acoustic scattering.

DNS of Turbulent Flows in Ducts with Complex Shape

We carry out Direct Numerical Simulation (DNS) of flows in closed straight ducts with complex peripheral shape. To perform the simulations the Navier-Stokes equations in cylindrical coordinates are discretized by a second-order finite difference scheme, and the immersed-boundary technique is used to resolve the flow close to walls of complex shape. The basic geometry is a circular pipe of radius R, with imposed sinusoidal perturbations of the type $\eta R \sin (N_{w}\theta )$ . Simulations by varying N w at fixed η were performed to investigate the effect of the perturbation wavenumber. Additional simulations by fixing N w and varying η also allow to investigate the influence of the amplitude of the wall corrugations. The modifications of the near-wall structures due to change in the shape of the walls are well depicted through contour plots of the radial component of the vorticity. The presence of geometrical disturbances anchors the structures at the locations where curvature changes, and the shape of the structures is strongly linked to the amplitude of the wall corrugation. Our interest is also in understanding the influence of the shape of the surface on wall friction. We were expecting some changes in the profile of the total stress with respect to that of the circular pipe, which instead were not found. This is a first indication that changes in the near-wall region do not affect the outer region, and that Townsend’s similarity hypothesis holds.

Simulation of moving boundaries interacting with compressible reacting flows using a second-order adaptive Cartesian cut-cell method

A high-order adaptive Cartesian cut-cell method, developed in the past by the authors [1] for simulation of compressible viscous flow over static embedded boundaries, is now extended for reacting flow simulations over moving interfaces. The main difficulty related to simulation of moving boundary problems using immersed boundary techniques is the loss of conservation of mass, momentum and energy during the transition of numerical grid cells from solid to fluid and vice versa. Gas phase reactions near solid boundaries can produce huge source terms to the governing equations, which if not properly treated for moving boundaries, can result in inaccuracies in numerical predictions. The small cell clustering algorithm proposed in our previous work is now extended to handle moving boundaries enforcing strict conservation. In addition, the cell clustering algorithm also preserves the smoothness of solution near moving surfaces. A second order Runge–Kutta scheme where the boundaries are allowed to change during the sub-time steps is employed. This scheme improves the time accuracy of the calculations when the body motion is driven by hydrodynamic forces. Simple one dimensional reacting and non-reacting studies of moving piston are first performed in order to demonstrate the accuracy of the proposed method. Results are then reported for flow past moving cylinders at subsonic and supersonic velocities in a viscous compressible flow and are compared with theoretical and previously available experimental data. The ability of the scheme to handle deforming boundaries and interaction of hydrodynamic forces with rigid body motion is demonstrated using different test cases. Finally, the method is applied to investigate the detonation initiation and stabilization mechanisms on a cylinder and a sphere, when they are launched into a detonable mixture. The effect of the filling pressure on the detonation stabilization mechanisms over a hyper-velocity sphere launched into a hydrogen–oxygen–argon mixture is studied and a qualitative comparison of the results with the experimental data are made. Results indicate that the current method is able to correctly reproduce the different regimes of combustion observed in the experiments. Through the various examples it is demonstrated that our method is robust and accurate for simulation of compressible viscous reacting flow problems with moving/deforming boundaries.

Hydrodynamic studies on two wiggling hydrofoils in an oblique arrangement

The propulsive performance of an oblique school of fish is numerically studied using an immersed boundary technique. The effect of the spacing and wiggling phase on the hydrodynamics of the system is investigated. The hydrodynamics of the system is deeply affected by the spacing between each fish in the school. When the horizontal separation is smaller than the length of the fish body, the downstream fish exhibits a larger thrust coefficient and greater propulsive efficiency than the isolated fish. However, the corresponding values for the upstream fish are smaller. The opposite behavior occurs when the horizontal separation increases beyond the length of fish body. The propulsive performance of the entire oblique school of fish can be substantially enhanced when the separations are optimized.

Combined immersed boundary method and multiple-relaxation-time lattice Boltzmann flux solver for numerical simulations of incompressible flows

method combining the immersed boundary technique and a multi-relaxation-time (MRT) lattice Boltzmann flux solver (LBFS) is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations (LBEs). The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution. The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.

Verification of a novel innovative blade root design for wind turbines using a hybrid numerical method

Abstract To enhance the performance of horizontal axis wind turbines, it is proposed to place a cylindrical disc in front of the rotor in order to lead the incoming flow from the inner part to the outer part of the rotor blades. This is expected to increase the power output, as the kinetic energy is mainly captured at the outer part of the blades, where the relative wind speed is high. To assess the impact of this novel design idea, a hybrid numerical technique, based on solving the Reynolds-averaged Navier-Stokes equations, is utilized to determine the aerodynamic performance. The in-house developed EllipSys3D code, which is employed as basic numerical solver, is combined with an actuator disc representation of the wind turbine rotor and an immersed boundary technique for representing the upstream cylindrical disc. The impact of the disc on the rotor performance is assessed by systematically changing the size of the circular disc and its axial distance to the rotor. Based on a numerical study of a Megawatt size commercial wind turbine, it is found that up to 1.5% additional energy can be captured by placing a circular disc with a suitable diameter upstream of the rotor plane.

Automatic generation of locally refined Cartesian meshes: Data management and algorithms

SummaryThe paper describes the main features of an automatic and three‐dimensional Cartesian mesher specifically designed for compressible inviscid/viscous flow solvers based on an immersed boundary technique. The development of a meshing tool able of conducting non‐isotropic cell refinements is a very tiresome task. The major difficulty is to imagine, at the pre‐design phase, a light but flexible data management, which minimizes the memory and CPUs' resources. In particular, the embedded geometry has to be detected by means of a fast and robust tagging procedure. Cells in proximity of the wall have to be refined in a proper way to adequately solve large flow gradients. Smooth variation of mesh density between differently refined zones has to be guaranteed to increase the flow solver robustness. A procedure to obtain accurate data on the geometry surfaces should be foresee. Here, a robust algorithm is developed to reconstruct a surface triangulation starting from the intersection points among volume cells and the geometry surfaces. The paper attempts to address all the above issues to help the readers in designing their own tools and suggesting them a way forward.

CutFEM topology optimization of 3D laminar incompressible flow problems

This paper studies the characteristics and applicability of the CutFEM approach of Burman et al. (2014) as the core of a robust topology optimization framework for 3D laminar incompressible flow and species transport problems at low Reynolds numbers (Re<200). CutFEM is a methodology for discretizing partial differential equations on complex geometries by immersed boundary techniques. In this study, the geometry of the fluid domain is described by an explicit level set method, where the parameters of a discretized level set function are defined as functions of the optimization variables. The fluid behavior is modeled by the incompressible Navier–Stokes equations. Species transport is modeled by an advection–diffusion equation. The governing equations are discretized in space by a generalized extended finite element method. Face-oriented ghost-penalty terms are added for stability reasons and to improve the conditioning of the system. The boundary conditions are enforced weakly via Nitsche’s method. The emergence of isolated volumes of fluid surrounded by solid during the optimization process leads to a singular analysis problem. An auxiliary indicator field is modeled to identify these volumes and to impose a constraint on the average pressure. Numerical results for 3D, steady-state and transient problems demonstrate that the CutFEM analyses are sufficiently accurate, and the optimized designs agree well with results from prior studies solved in 2D or by density approaches.

CFD simulations of transient load change on a high head Francis turbine

Motivated by the importance of better understanding the structural integrity of high-head hydraulic turbines operating at intermittent conditions, complete 360º steady-state and transient simulations of a Francis turbine are presented in this paper. The main target of the work has been to investigate different numerical approaches such as mesh deformation for different operating conditions. Steady-state simulations were performed at the best efficiency point (BEP) and used as initial conditions for the transient simulations considering load rejection from BEP to part load (BEP2PL) and during load acceptance from BEP to high load (BEP2HL). Simulation results were compared with experimental data available for the Francis-99 project where close agreement was found for the mesh independent solution. The transient load analyses showed general trends in accordance with the measurement reports, especially for the pressure in vaneless space that is of high importance regarding RSI effects. Some deviations were identified for the net head at load rejection for which further investigations will be conducted. All CFD simulations were performed at model scale with ANSYS CFX v. 17 at either 96 or 120 cores (2.60 GHz). The immersed boundary technique was tested during the initial stages of the project, but had to be abandoned due to severe memory requirements. Pressure amplitudes and other instantaneous results were not considered.

Numerical simulations of conjugate convection combined with surface thermal radiation using an Immersed-Boundary Method

Dynamic and thermal interaction problems involving fluids and solids were studied through a finite volume-based Navier-Stokes solver, combined with immersed-boundary techniques and the net radiation method. Source terms were included in the momentum and energy equations to enforce the non-slip condition and the conjugate boundary condition including the radiative heat exchange. Code validation was performed through the simulation of two cases from the literature: conjugate natural convection in a square cavity with a conducting side wall; and a cubical cavity with conducting walls and a heat source. The accuracy of the methodology and the validation of the inclusion of moving bodies into the simulation was performed via a theoretical case

Numerical simulation of stirred tanks using a hybrid immersed-boundary method

Conventionally, multiple reference frame (MRF) method and sliding mesh (SM) method are used in the simulation of stirred tanks, however, both methods have limitations. In this study, a hybrid immersed-boundary (IB) technique is developed in a finite difference context for the numerical simulation of stirred tanks. IBs based on Lagrangian markers and solid volume fractions are used for moving and stationary boundaries, respectively, to achieve optimal efficiency and accuracy. To cope with the high computational cost in the simulation of stirred tanks, the technique is implemented on computers with hybrid architecture where central processing units (CPUs) and graphics processing units (GPUs) are used together. The accuracy and efficiency of the present technique are first demonstrated in a relatively simple case, and then the technique is applied to the simulation of turbulent flow in a Rushton stirred tank with large eddy simulation (LES). Finally the proposed methodology is coupled with discrete element method (DEM) to accomplish particle-resolved simulation of solid suspensions in small stirred tanks. It demonstrates that the proposed methodology is a promising tool in simulating turbulent flow in stirred tanks with complex geometries.

Curved boundaries in multi-layer Shallow Water Lattice Boltzmann Methods: bounce back versus immersed boundary

The Lattice Boltzmann Method has been successfully applied to solve Multilayer Shallow Water models for the simulation of gravity currents generated by laboratory lock exchange experiments in regular geometries. When complex boundaries are to be modelled, several approaches are feasible. In this work two types of boundary conditions are analyzed and compared in the simulation of lock exchange gravity currents impacting on vertical obstacles. The first one belongs to the common group of bounce back approaches; the second one is an adaptation of the immersed boundary technique to the Shallow Water dynamics. The analysis is carried out comparing accuracy against experimental data. Efficiency is also taken into account. Results show that the computational overhead introduced by the Immersed Boundary technique is not counterbalanced by a gain in accuracy for the considered kind of obstacles.

Immersed-boundary simulations of turbulent flow past a sinusoidally undulated river bottom

Turbulent flow past a sinusoidally undulated river bottom is a classical problem that arises in the stability analysis of a dune-forming erodible sand bed. Past studies by the present author and others of this problem in a long-wave perturbation expansion have provided seemingly contradictory results. Direct numerical simulations performed through an immersed-boundary technique now uncover an unexpectedly rich scenario, of which the previous findings were just a facet.

Front tracking method in modeling transport phenomena accompanying liquid–solid phase transition in binary alloys and semitransparent media

The paper presents the potential of an efficient front tracking method on a fixed control-volume grid in micro–macroscopic numerical modeling of both binary alloy solidification and a solid–liquid phase transition of single-component or doped optically functioning materials. In the former case, the method, basing on the assumption that an envelope of columnar dendrite tips moves locally according to a single crystal growth law, allows more precise identification of zones of different dendritic structures developing within the two-phase region, and thus more detailed analysis of some closing models. It is shown, by exploiting the commonly used benchmark problem that a porous medium model of the columnar mush must be carefully chosen since it strongly affects the predicted macro-segregation pattern. In the case of solidification of a single-component or doped semi-transparent material the combination of the front tracking method with the immersed boundary technique provides a new simulation method, which can handle different thermo-physical and optical properties of liquid and solid phases, processes of emission, absorption, reflection and refraction or transmission of thermal radiation at a diffusive or specular distinct solid–liquid interface detected by the front tracking technique. The method has been used in a detailed parametric analysis where the impact of different optical configurations of both phases and their various optical properties as well as variable transmissivity of solid–liquid interface on the phase change process development has been addressed.

On the interaction between shear dusty currents and buildings in vertical collapse: Theoretical aspects, experimental observations, and 3D numerical simulation

We investigate the behavior of vertical building collapses that, at impact on the ground, can generate shear dusty currents. These currents macroscopically resemble natural currents like dust storms and pyroclastic density currents, which may heavily interact with the surroundings while propagating. In particular, shear dusty currents are generated because of building collapse after pulverization, whereas pyroclastic density currents can be generated because of eruptive column or volcano collapse after fragmentation. Pyroclastic density currents can move for kilometers, and then load the surroundings by flow dynamic pressure; a similar dynamical behavior occurs in shear dusty currents that load buildings. We employed 3D engineering fluid dynamics to simulate the generation (by vertical collapse), and the propagation and building interaction of shear dusty currents. We used an Eulerian–Lagrangian multiphase approach to model the gas-particle flow, and an immersed boundary technique to mesh the domain, in order to account for sedimentary processes and complex 3D urban geometry in the computation. Results show that the local dynamic pressure of the shear current is amplified up to a factor ~10 because of flow-building interaction. Also, the surroundings consisting of multiple buildings and empty spaces make walls and streets as surfaces of particle accumulation, which from the collapse zone on can get thinner by exponential law. These results can help better assessing the intricate interaction between pyroclastic density currents and urban surroundings, as well as better link fragmentation, collapse and density current to each other.

Effects of suspension line on flow field around a supersonic parachute

Numerical simulations based on a simple “immersed boundary technique” are performed to investigate the effects of suspension lines on the flow field around a three-dimensional rigid supersonic parachute mode consisting of a capsule and a canopy. The computational results show that the flow field has an unsteady pulsating characteristic. Furthermore, it is shown that the suspension lines prompt the formation of shock waves around them, which subsequently interact with the wake from the capsule and the canopy shock system. A good qualitative agreement is observed between the numerical results and experimental data.

A Three-Dimensional Conservative Coupling Method Between an Inviscid Compressible Flow and a Moving Rigid Solid

We present a conservative method for the three-dimensional coupling between an inviscid compressible flow and a moving rigid solid. We consider an inviscid Euler fluid in conservative form discretized using a high-order monotonicity-preserving finite volume method with a directional operator splitting. An immersed boundary technique is employed through the modification of the finite volume fluxes in the vicinity of the solid. The method yields exact conservation of mass, momentum, and energy of the system, and also exhibits important consistency properties, such as conservation of uniform movement of both fluid and solid as well as the absence of numerical roughness on a straight boundary. The coupling scheme evaluates the fluxes on the fluid side and the forces and torques on the solid side only once every time step, ensuring the computational efficiency of the coupling. We present numerical results assessing the robustness of the method in the case of rigid solids with large displacements.

Effects of preferential concentration on collision and erosion between solid particles and tube bank in a duct flow

The impact and erosion on the stainless steel heat exchanger tubes located in the middle row of a 10×10 aligned tube bank caused by coal ash particles are investigated numerically by means of direct numerical simulations (DNS) to study the influence of preferential concentration on particle–tube interactions. The immersed boundary technique is applied to account for the coupling effect on the flow by the immersed tubes. A two-way coupled Lagrangian solver is developed for particle tracking. The experimentally validated particle–wall impact and erosion models are used to describe the collision between particles and tubes and the resulting erosion. The results demonstrate that the particles Stokes number has significant effects on particle dispersion patterns as well as collision and erosion characteristics. The global tube erosion of the first tube increases with the increment of the particle size, but the particles with an intermediate Stokes number of 1.6 cause the most erosion to the other downstream tubes with lower collision frequency, due to the preferential concentration. The maximum local tube erosion happens in the front side surface of each tube with certain angle region for all particles where more attention should be paid to prevent from erosion caused by coal ash particles.

High-resolution numerical modelling of flow—vegetation interactions

ABSTRACTIn this paper, we present and apply a new three-dimensional model for the prediction of canopy-flow and turbulence dynamics in open-channel flow. The approach uses a dynamic immersed boundary technique that is coupled in a sequentially staggered manner to a large eddy simulation. Two different biomechanical models are developed depending on whether the vegetation is dominated by bending or tensile forces. For bending plants, a model structured on the Euler–Bernoulli beam equation has been developed, whilst for tensile plants, an N-pendula model has been developed. Validation against flume data shows good agreement and demonstrates that for a given stem density, the models are able to simulate the extraction of energy from the mean flow at the stem-scale which leads to the drag discontinuity and associated mixing layer.

Interface-resolved direct numerical simulation of the erosion of a sediment bed sheared by laminar channel flow

A numerical method based upon the immersed boundary technique for the fluid–solid coupling and on a soft-sphere approach for solid–solid contact is used to perform direct numerical simulation of the flow-induced motion of a thick bed of spherical particles in a horizontal plane channel. The collision model features a normal force component with a spring and a damper, as well as a damping tangential component, limited by a Coulomb friction law. The standard test case of a single particle colliding perpendicularly with a horizontal wall in a viscous fluid is simulated over a broad range of Stokes numbers, yielding values of the effective restitution coefficient in close agreement with experimental data. The case of bedload particle transport by laminar channel flow is simulated for 24 different parameter values covering a broad range of the Shields number. Comparison of the present results with reference data from the experiment of Aussillous et al. (2013) yields excellent agreement. It is confirmed that the particle flow rate varies with the third power of the Shields number once the known threshold value is exceeded. The present data suggests that the thickness of the mobile particle layer (normalized with the height of the clear fluid region) increases with the square of the normalized fluid flow rate.