Immersed Boundary Method Research Articles

Thermal rarefied gas flow simulations with moving boundaries based on discrete unified gas kinetic scheme and immersed boundary method

Rarefied gas flows in complex geometries with heat transfer and moving boundaries have received remarkable attention due to the prevailing of micro/nano science and engineering applications. This study presents an immersed boundary (IB)-based discrete unified gas kinetic scheme (DUGKS) for the simulation of complex moving boundary thermal rarefied flows. The fluid and temperature fields are solved according to the DUGKS with Shakhov collision model (SDUGKS), which is capable of modeling non-unit Prandtl number problems in all Knudsen regimes. The IB approach, featured by its superior performance to incorporate complicated boundary constraints on Cartesian grids, is applied here to handling the interaction between the micro gas and curved boundaries. Specifically, for the IB adopted in this study, we use the least square method for the reconstruction of the distribution functions near the boundary. The accuracy of the IB-SDUGKS is explored comprehensively in six benchmark problems, including the micro lid-driven cavity flow, thermal equilibrium gas in a circular domain, thermal transpiration in an enclosure, moving shuttle in a rarefied gas, movement of a piston with pressure differences and particle free motion in a lid-driven cavity. The present results agree well with the corresponding analytical and direct simulation Monte Carlo (DSMC) solutions, illustrating the versatility of the present IB-SDUGKS complex thermal rarefied flows.

An improved immersed boundary method with local flow pattern reconstruction and its validation

This study introduces an immersed boundary (IB) method based on coefficient array transformations of discrete equations for local cells and local flow pattern reconstruction, for the simulation of turbulent flow and combustion chemistry inside combustors with complex structure. This IB method is combined with a geometric scanning algorithm that traverses each fluid grid point in the vicinity of the wall, and based on the exact wall positions and normal vectors obtained from the scanning, the coefficient matrices of the individual grid points and their discrete forms of the governing equations are transformed, and the boundary conditions are added implicitly and exactly. The effectiveness of the method is validated through simulations of a cylinder, a gas turbine model combustor [Meier et al., “Spray and flame structure of a generic injector at aeroengine conditions,” in Proceedings of the ASME 2011 Turbo Expo: Power for Land, Sea, and Air (American Society of Mechanical Engineers, 2011), pp. 61–72 and Freitag et al., “Measurement of initial conditions of a kerosene spray from a generic aeroengine injector at elevated pressure,” Atomization Sprays 21, 521 (2011)], and a specific aero-engine combustor, demonstrating precision comparable to traditional body-fitted mesh approaches, especially for complex combustor structures. The simulation demonstrates that the IB method achieves accuracy comparable to a fitted grid when it provides boundary information of similar quality and detail for control equations. The locally reconstructed IB method introduced in this paper successfully delivers high-precision boundary conditions, making it valuable for practical engineering applications.

Hyper-local source strength retrieval and apportionment of black carbon in an urban area

Neighborhood-scale air pollution hotspots have recently been identified through detailed field campaigns, including the 100x100 Black Carbon Experiment which took place in West Oakland, CA, in 2017. Here, high-resolution nested atmospheric simulations are used together with a Bayesian inversion framework to estimate source apportionment at the hyper-local scale for a neighborhood in West Oakland. Forward simulations are performed with the Weather Research and Forecasting (WRF) model using 6 grid nests from 11.25 km to 2 m horizontal resolution. On the finest grid, building geometries are resolved using the immersed boundary method. Seven point sources and four line sources at known locations are included in the forward simulation for two 1-h periods during the 2017 field campaign. Data from 12 black carbon sensors are used to perform source inversion using a Markov Chain Monte Carlo approach, which provides a probability distribution for each of the 11 source strengths. From this, a most-likely plume can be created using the peaks of the distributions, and source apportionment can be estimated for each sensor. In addition, a composite plume can be constructed to indicate 90% confidence that concentrations are above or below a specified value. With this probabilistic analysis, it is possible to determine that more than half of the neighborhood has black carbon concentrations of higher than 0.4 μg/m3, with some areas higher than 3 μg/m3 during the time periods studied.

On wave-current interaction with a horizontal cylinder near free surface by a fourth-order-accurate finite volume compact solver

We present a numerical solver for dealing with the problem of wave-current interaction with a horizontal cylinder near free surface. The solver solves the filtered Navier-Stokes equations which are discretized using a fourth-order-accurate compact finite volume scheme on a collocated grid. The turbulence effect is modelled by a subgrid-scale model using a large eddy simulation, and the free surface and the cylinder are modelled by a volume of fluid method and a ghost cell immersed boundary method. The pressure-velocity coupling is ensured via a momentum interpolation method. We obtain the hydrodynamic force and its spectra characteristics, dynamic pressure distribution, streamline topology and vorticity patterns with different immersed depths under uniform currents, regular waves and wave-current flows. Validation is performed by comparing the calculated hydrodynamic force with the measured data within one wave period. The results show that the position of vortex shedding and dissipation is different for the cases under different immersed depth in regular waves and wave-current flows. The dynamic pressure around the cylinder as the force reaches its peak value changes with immersed depth. The value and phase of the force are sensitive to immersed depth.

Simulation-based insights into cell encapsulation dynamics in droplet microfluidics

In the context of microfluidic technology, investigating the encapsulation of single cells is of great importance, providing valuable insight into cellular behavior and contributing to advancements in single-cell analysis. This paper presents a computational investigation into the dynamics of single-cell encapsulation within a flow-focusing microfluidic system, with a specific emphasis on addressing the challenges associated with high-efficiency encapsulation. This study utilizes a combined lattice Boltzmann and immersed boundary method to provide an accurate simulation of a three-phase system. This allowed for an in-depth exploration of various critical parameters, including cell injection frequency, cell size, and inlet position. This study identifies optimal conditions for maximizing single-cell encapsulation efficiency, emphasizing the impact of the ratio between cell injection and droplet generation frequencies on encapsulation outcomes. This study investigates the effects of cell-induced changes on droplet formation characteristics. It explains the generation of larger droplets and the occurrence of additional satellite droplets. These findings provide insight into the microfluidic platforms designed for single-cell assays, which have potential applications in various fields such as drug development and personalized therapies.

Hydrodynamics and propulsion of a hydrofoil undergoing leading-edge pitching and traveling wave-based surface undulation

We numerically study the fluid–structure interaction of a free-stream flow across a hydrofoil pitching at its leading edge with superimposed traveling wave-based surface undulations. We utilize an in-house code that employs the sharp interface immersed boundary method and consider a constant pitching amplitude θ0 = 5°, a constant local amplitude-to-thickness ratio AL=0.15, and wave number K = 20 of surface undulation. We compare the effect of surface undulation on a pitching hydrofoil with that of a hydrofoil undergoing pure pitching or experiencing pure surface undulation. The findings reveal that surface undulation on the pitching hydrofoil increases thrust on the hydrofoil. The onset of asymmetry in the vortex street occurs at a lower pitching Strouhal number (St) due to the early formation of a vortex dipole. In addition to the presence of an asymmetric inverse von Kármán vortex street, higher pitching frequencies reveal re-deflection of the asymmetric inverse von Kármán vortices. We quantified dynamics of vortex dipole to explain the occurrence of asymmetric and re-deflected reverse von Kármán vortex street. Furthermore, the analysis reveals an optimum combination of St and phase speed that yields higher propulsive efficiency, as both motions compete in generating thrust. A linearly superimposed scaling analysis for the time-averaged thrust of the combined motion is also presented. The computations and scaling are found to be in good agreement.

Numerical Simulation of Flows Using the Fourier Pseudospectral Method and the Immersed Boundary Method

The present work proposes the application of a computational methodology based on the coupling of the Fourier Pseudospectral Method (FPSM) and the Immersed Boundary Method (IBM) for conducting flow simulations over slender airfoils. This methodology, termed IMERSPEC, leverages the benefits of both high accuracy and low computational cost inherent in pseudospectral methods, thanks to the utilization of the Fast Fourier Transform algorithm. IBM is employed to impose non-periodic boundary conditions in the Navier–Stokes equations, addressing the requirement of periodicity at boundaries for FPSM convergence and to accurately represent the immersed slender airfoil in the flow. The aerodynamic behavior of the analyzed profiles was assessed by calculating lift and drag coefficients, which were then compared with existing literature results. Consistently favorable outcomes were observed, particularly in flows at lower Reynolds numbers, demonstrating the effectiveness of the IMERSPEC methodology for simulating complex flows computationally. Additionally, weight functions, fundamental to IBM, are employed flexibly for aerodynamic force calculations. Specifically, within the same simulation, a Cubic function is utilized for drag calculation while a Hat function is employed for lift calculation, yielding results more closely aligned with the literature’s findings. This approach offers an alternative to previously proposed methods for IBM implementation.

A phase field-immersed boundary-lattice Boltzmann coupling method for fluid-structure interaction analysis

Fluid-structure interaction (FSI) is critical in numerous engineering and scientific applications. This paper presents a numerical model for FSI simulations that integrates the lattice Boltzmann method (LBM) for fluid dynamics, the phase field method (PFM) for structural deformation and fracture, and the immersed boundary method (IBM) for fluid-solid coupling. The fluid employs an explicit time integration scheme with a smaller time step than the solid, which uses an implicit time integration scheme, satisfying the CFL condition. During the synchronization of fluid-solid interaction information, a multi-substep strategy is applied. The IBM is implemented using the iterative velocity method for boundary treatment. This approach facilitates the information transfer between domains with different time steps, enhancing the coupling accuracy through iterative computation. The effectiveness of the improved immersed boundary-lattice Boltzmann (IB-LBM) has been verified by the classical cylindrical flow case, which effectively prevents the particle penetration phenomenon and improves the calculation accuracy. The phase field-immersed boundary-lattice Boltzmann method (PF-IB-LBM) is subsequently deployed to simulate the deformation of an aluminum plate under hydrostatic pressure and the aftermath of a dam-break impact on an elastic plate. Verification of the coupling method substantiates its feasibility and efficacy. In addition, the proposed PF-IB-LBM is implemented to simulate the entire process of structural deformation and failure in response to fluid dynamics, which further confirms its capability to predict discontinuous mechanical behaviors such as damage and crack propagation under intricate fluid flows. The results emphasize the flexibility and efficiency of the proposed approach, providing a robust framework for solving more complex scenarios in engineering FSI problems.

Scramjet Intake Aerodynamic Studies Using Sharp Interface Immersed Boundary Method

In this present article, the use of a throttling device in the form of movable flap to study scramjet inlet unstart has been investigated numerically. The flap has been employed as an effort to simulate the rise in combustor pressure of the scramjet. Computational analysis for freestream Mach number and freestream pressure of and respectively, have been performed by a two-dimensional compressible CFD in-house Finite volume solver for perfect gas. Convective fluxes have been evaluated using AUSM scheme.Inviscidflow has been assumed for all the simulations. Particular point of interest in these simulations is the application of Immersed Boundary Method along the wall boundaries,enabling the use of structured grid for complex geometries. The results demarcate the starting condition of the inlet based on the flap throttling values. Comparative results in the form of Mach number and pressure contours are presented for different flap positions. The use of Immersed Boundary Method has been successfully displayed bysimulating a movable flap.

A GPU-accelerated computational fluid dynamics solver for assessing shear-driven indoor airflow and virus transmission by scale-resolved simulations

We explore the applicability of MATLAB for 3D computational fluid dynamics (CFD) of shear-driven indoor airflows. A new scale-resolving, large-eddy simulation (LES) solver titled DNSLABIB is proposed for MATLAB utilizing graphics processing units (GPUs). In DNSLABIB, the finite difference method is applied for the convection and diffusion terms while a Poisson equation solver based on the fast Fourier transform (FFT) is employed for the pressure. The immersed boundary method (IBM) for Cartesian grids is proposed to model solid walls and objects, doorways, and air ducts by binary masking of the solid/fluid domains. The solver is validated in two canonical reference cases and against experimental data. Then, we demonstrate the validity of DNSLABIB in a room geometry by comparing the results against another CFD software (OpenFOAM). Next, we demonstrate the solver performance in several isothermal indoor ventilation configurations and the implications of the results are discussed in the context of airborne transmission of COVID-19. The novel numerical findings using the new CFD solver are as follows. First, a linear scaling of DNSLABIB is demonstrated and a speed-up by a factor of 3-4 is also noted in comparison to similar OpenFOAM simulations. Second, ventilation in three different indoor geometries are studied at both low (0.1 m/s) and high (1 m/s) airflow rates corresponding to Re=5000 and Re=50000. An analysis of the indoor CO2 concentration is carried out as the room is emptied from stale, high CO2 content air. We estimate the air changes per hour (ACH) values for three different room geometries and show that the numerical estimates from 3D CFD simulations differ by 80%–150% (Re=50000) and 75%–140% (Re=5000) from the theoretical ACH value based on the perfect mixing assumption. Third, the analysis of the CO2 probability distributions (PDFs) indicates a relatively non-uniform distribution of fresh air indoors. Fourth, utilizing a time-dependent Wells-Riley analysis, an example is provided on the growth of the cumulative infection risk which is shown to reduce rapidly after the ventilation is started. The average infection risk is shown to reduce by a factor of 2 for lower ventilation rates (ACH=3.4-6.3) and 10 for the higher ventilation rates (ACH=37-64). Finally, we utilize the new solver to comment on respiratory particle transport indoors. A key contribution of the paper is to provide an efficient, GPU compatible CFD solver environment enabling scale-resolved simulations (LES/DNS) of airflow in large indoor geometries on a single GPU designed for high-performance computing. The demonstrated efficacy of MATLAB for GPU computing indicates a high potential of DNSLABIB for various future developments on airflow prediction.

An immersed boundary-phase field fluid-surfactant model with moving contact lines on curved substrates

In this study, we propose an immersed boundary-phase field fluid-surfactant model that incorporates moving contact lines on complex geometries. To accurately capture the interface, we introduce an additional phase field variable to represent the solid phase, which remains fixed throughout the process. The modified Cahn–Hilliard equations are utilized to describe the interface. In order to address stiffness issues, a stabilization technique is incorporated into the calculations. To prevent streamlines from penetrating into solid obstacles, a boundary condition-enforced immersed boundary method is applied at the solid boundaries. The desired contact angle is ensured using the characteristic moving contact line method. All variables are treated independently in the computations, and the numerical results demonstrate the accuracy and excellent performance of our model on curved substrates with surfactants.

Implicit-explicit time integration for the immersed wave equation

Efficient solution strategies for wave propagation problems with complex geometries are essential in many engineering fields. Immersed boundary methods simplify mesh generation by embedding the domain of interest into an extended domain that is easy to mesh, introducing the challenge of dealing with cells that intersect the domain boundary. We consider the finite cell method that extends the weak form from the physical into the extended domain, multiplied by a small value, to stabilize badly cut cells. Combined with explicit time integration methods, the presence of finite cells with very little support in the physical domain results in tiny critical time step sizes. While the finite cell stabilization limits how small the critical time step size can become, this limit is still restrictive for many applications. Explicit transient analyses commonly use the spectral element method due to its natural way of obtaining diagonal mass matrices through nodal lumping. The resulting method is very efficient since nodal lumping renders the solution of the equation systems trivial while not reducing the accuracy or the critical time step size. The combination of the spectral element and finite cell methods is called the spectral cell method. Unfortunately, a direct application of nodal lumping in the spectral cell method is impossible due to the special quadrature necessary to treat the discontinuous integrand inside the cut cells. The existing approaches to lump the mass matrices of cut cells significantly reduce the accuracy of the approximation.We analyze an implicit-explicit (IMEX) time integration method to exploit the advantages of the nodal lumping scheme for uncut cells on one side and the unconditional stability of implicit time integration schemes for cut cells on the other. In this hybrid, immersed Newmark IMEX approach, we use explicit second-order central differences to integrate the uncut degrees of freedom that lead to a diagonal block in the mass matrix and an implicit trapezoidal Newmark method to integrate the remaining degrees of freedom (those supported by at least one cut cell). The immersed Newmark IMEX approach preserves the high-order convergence rates and the geometric flexibility of the finite cell method while retaining the efficiency of the nodal lumping scheme for uncut cells without compromising the critical time step size. We analyze a simple system of spring-coupled masses to highlight some of the essential characteristics of Newmark IMEX time integration. We then solve the scalar wave equation with immersed boundaries on two- and three-dimensional examples with significant geometric complexity to show that our approach is more efficient than state-of-the-art time integration schemes when comparing accuracy and runtime. While we focus on the finite and spectral cell methods, we expect other immersed methods to benefit equally from Newmark IMEX time integration.

Multivariate Peristalsis in a Straight Rectangular Duct for Carreau Fluids

Peristaltic flow in a straight rectangular duct is examined imposed by contraction pulses implemented by pairs of horizontal cylindrical segments with their axes perpendicular to the flow direction. The wave propagation speed is considered in such a range that triggers a laminar fluid motion. The setting is analyzed over a set of variables which includes the propagation speed, the relative occlusion, the modality of the squeezing pulse profile and the Carreau power index. The numerical solution of the equations of motion on Cartesian meshes is grounded in the immersed boundary method. An increase in the peristaltic pulse modality leads to the reduction in the shear rate levels on the central tube axis and to the movement of the peristaltic characteristics to higher pressure values. The effect of the no slip side walls (NSSWs) is elucidated by the collation with relevant results for the flow field produced under the same assumptions though with slip side walls (SSWs). Shear thinning behavior exhibits a significantly larger effect on transport efficiency for the NSSWs duct than on the SSWs duct.

Simulation of wave scattering over a floating platform in the ocean with a coupled CFD-IBM model

A numerical study of linear wave scattering over a floating platform has been simulated by an efficient numerical model in this letter. The non-hydrostatic model is used to simulate the free surface and the uneven bottom. For the solid body modelling, the immersed boundary method (IBM) is implemented by introducing a virtual boundary force into the momentum equations to emulate the boundary conditions. This implementation enhances the ability of the model to simulate interactions between waves and floating structures. A numerical case involving wave interactions with a floating platform is studied to validate the numerical model. By simulating the wave propagation, the numerical model captures the variation of the wave scattering very well, which verifies the performance of the numerical model and the robust strategy of the IBM.

Mass transport at gas-evolving electrodes

Direct numerical simulations are utilised to investigate mass-transfer processes at gas-evolving electrodes that experience successive formation and detachment of bubbles. The gas–liquid interface is modelled employing an immersed boundary method. We simulate the growth phase of the bubbles followed by their departure from the electrode surface in order to study the mixing induced by these processes. We find that the growth of the bubbles switches from a diffusion-limited mode at low to moderate fractional bubble coverages of the electrode to a reaction-limited growth dynamics at high coverages. Furthermore, our results indicate that the net transport within the system is governed by the effective buoyancy driving induced by the rising bubbles and that mechanisms commonly subsumed under the term ‘microconvection’ do not significantly affect the mass transport. Consequently, the resulting gas transport for different bubble sizes, current densities and electrode coverages can be collapsed onto one single curve and only depends on an effective Grashof number. The same holds for the mixing of the electrolyte when additionally taking the effect of surface blockage by attached bubbles into account. For the gas transport to the bubble, we find that the relevant Sherwood numbers also collapse onto a single curve when accounting for the driving force of bubble growth, incorporated in an effective Jakob number. Finally, linking the hydrogen transfer rates at the electrode and the bubble interface, an approximate correlation for the gas-evolution efficiency has been established. Taken together, these findings enable us to deduce parametrisations for all response parameters of the systems.

An immersed boundary method coupled non-hydrostatic model for free surface flow

An efficient numerical model has been developed for the study of three-dimensional free surface flow, which combines a non-hydrostatic model with the immersed boundary method (IBM). The model utilizes the transformed σ coordinate in the vertical direction, which has been found to be highly effective in accurately capturing the free surface and uneven bottom. In addition, IBM is implemented by introducing a virtual boundary force into the momentum equations to emulate the natural boundary conditions. This implementation enhances the ability of the model in simulating the interactions of wave and solid structures. A robust boundary recognition method is used to identify the location of IB cells neighboring the virtual boundary. Furthermore, a water elevation correction method has been proposed to handle the integral discontinuity in the vertical direction caused by the submerged solid bodies. By adding the virtual boundary forces to the IB cells, the no-slip velocity condition at the solid boundary is effectively enforced. To validate the performance of the model, the numerical results have been compared with experimental data. The benchmark tests focused on the free surface evolution, velocity distributions and the dynamic pressures verified the performance of the numerical model and the robust strategy of the IBM.

Coupling of the immersed boundary and Fourier pseudo-spectral methods applied to solve fluid–structure interaction problems

The current manuscript addresses fluid–structure interaction (FSI) problems to the analysis of vortex-induced vibration (VIV), employing the methodology designated as IMERSPEC2D. The approach seamlessly integrates the Fourier pseudo-spectral method (FPSM) and the immersed boundary method (IBM) to solve the Navier–Stokes (NS) and continuity equations. Simultaneously, the effects of cylindrical structure, involving 1 and 2 degrees of freedom (d.o.f.) are simulated, by incorporating structural motion equations into NS via the IBM source term and implementing a two-way FSI algorithm. In the paper are presented the comparison of low and high-order temporal integration methods applied to solve the dynamic behavior of the structure and the dimensionless of the cylinder’s structural motion equations, resulting in an increase in computational time step from 1E(-9\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-9$$\\end{document}) to 1E(-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-3$$\\end{document}). Validation results to refined mesh simulations include the accurate representation of the lock-in phenomenon to simulations of 1 d.o.f. obtaining the range between reduced velocity 5.456 and 5.568 and the maximal amplitude is 0.352. Notably, the eight-shape pattern of the 2 d.o.f. cylinder displacement is obtained and the formation of C2S wake patterns is achieved, as presented by other authors. In conclusion, the dimensionless approach reduces computational time, while the high-order both of IMERSPEC methodology and time advancement integration to FSI improve the results of the cylinder’s motion and alters distinct vortex shedding patterns in fluid dynamics.

Immersed Boundary Double Layer method: An introduction of methodology on the Helmholtz equation

The Immersed Boundary (IB) method of Peskin (1977) [1] is useful for problems that involve fluid-structure interactions or complex geometries. By making use of a regular Cartesian grid that is independent of the geometry, the IB framework yields a robust numerical scheme that can efficiently handle immersed deformable structures. Additionally, the IB method has been adapted to problems with prescribed motion and other PDEs with given boundary data. IB methods for these problems traditionally involve penalty forces which only approximately satisfy boundary conditions, or they are formulated as constraint problems. In the latter approach, one must find the unknown forces by solving an equation that corresponds to a poorly conditioned first-kind integral equation. This operation can therefore require a large number of iterations of a Krylov method, and since a time-dependent problem requires this solve at each step in time, this method can be prohibitively inefficient without preconditioning. This work introduces a new, well-conditioned IB formulation for boundary value problems, called the Immersed Boundary Double Layer (IBDL) method. In order to lay the groundwork for similar formulations of Stokes and Navier-Stokes equations, this paper focuses on the Poisson and Helmholtz equations to introduce the methodology and to demonstrate its efficiency over the original constraint method. In this double layer formulation, the equation for the unknown boundary distribution corresponds to a well-conditioned second-kind integral equation that can be solved efficiently with a small number of iterations of a Krylov method without preconditioning. Furthermore, the iteration count is independent of both the mesh size and spacing of the immersed boundary points. The method converges away from the boundary, and when combined with a local interpolation, it converges in the entire PDE domain. Additionally, while the original constraint method applies only to Dirichlet problems, the IBDL formulation can also be used for Neumann boundary conditions.

Direct reduction of iron-ore with hydrogen in fluidized beds: A coarse-grained CFD-DEM-IBM study

Hydrogen metallurgy technology uses hydrogen as the reducing agent instead of carbon reduction, which is one of the important ways to reduce carbon dioxide emissions and ensure the green and sustainable development of iron and steel industry. Due to the advantages of high gas-solid contact efficiency and outstanding mass and heat transfer, direct reduction of iron ore in fluidized beds has attracted much attention. Based on the three-layer unreacted shrinking core model and considering the diversity of particle structure during the reaction process, a multi-reaction path (multi-resistance network) model was established. In this study, a coarse-grained CFD-DEM-IBM solver based on hybrid CPU–GPU computing is developed to simulate the direct reduction process of two kinds of iron ore with hydrogen in fluidized beds, where the developed unreacted shrinking core model is used to model the reduction reactions, a coarse-grained model and multiple GPUs enable the significant acceleration of particle computation, and the immersed boundary method (IBM) enables the use of simple mesh even in complex geometries of reactors. The predicted results of particle reduction degree are in good agreement with the experimental values, which proves the correctness of the CFD-DEM-IBM solver. In addition, the effects of reaction kinetic parameters and operating temperature on particle reduction degree are also investigated. Present study provides a method for digital design, optimization and scale-up of ironmaking reactors.

Novel drag and Nusselt number models based on direct numerical simulations of a bidisperse gas–solid system

AbstractFlow and heat transfer in a bidisperse gas–solid system with freely moving spheres are simulated by particle‐resolved direct numerical simulation (PR‐DNS). Gas–solid coupling is enforced by the direct‐forcing immersed boundary method. Compard with the DNS database, it is found that the existing polydisperse drag correction model developed from static systems combined with various monodisperse drag models underestimates the drag force on dynamic arrays of particles. The existing Nusselt number correction model developed from static systems combined with various monodisperse models overestimates the Nusselt number of dynamic arrays of particles. Sensitivity analysis indicates that the effects of the granular temperature on the drag force and Nusselt number are negligible. Novel polydisperse drag and Nusselt number models are derived based on the database. The advantages of the derived polydisperse drag and Nusselt number models are demonstrated and confirmed by comparing the results of the computational fluid dynamics–discrete element method using various drag and Nusselt number models with experimental or additional PR‐DNS data.