Interface Immersed Boundary Method Research Articles

High-order moving immersed boundary and its application to a resolved CFD-DEM model

The sharp interface immersed boundary method (IBM) is a powerful tool to simulate the flow around moving objects. This paper extends this method to simulate the motion of particles immersed in a fluid. We introduce a new implicit coupling scheme between the solid and fluid phases, verify the high–order of convergence of the scheme, and validate it using four cases. The fluid dynamics is simulated using a streamline upwind Petrov–Galerkin and pressure-stabilizing Petrov–Galerkin (SUPG/PSPG) stabilizations. The particles’ dynamics and contact are solved using Newton’s second law of motion and a soft sphere contact model derived from the discrete element method. The first validation case is the sedimentation of a lone particle with a Reynolds number smaller than 32. The second validation case is the rise of a positively buoyant particle at a high Reynolds number (2500). The third validation case demonstrates the stability of the scheme when particles are in contact and exhibit the classical drafting, kissing, and tumbling (DKT) behavior. Finally, we use the scheme to study the Boycott effect with a larger number of particles (64) to show the stability of the scheme in cases with numerous particle–particle and particle–wall contacts.

A sharp interface immersed boundary method for thin-walled geometries in viscous compressible flows

Compressible flows at low Mach numbers are prevalent in various engineering applications, such as combustion, aeroacoustics, heat transfer, and more. In this study, we present a sharp interface immersed boundary method (IBM) tailored for low Mach number viscous compressible flows. The IBM is developed using a robust interpolation scheme, ensuring stability for complex geometries with zero-thickness walls. To satisfy the boundary condition, the interpolation needs to use points from the same side, thus preventing interaction across the zero-thickness wall. Additionally, a simple modification is proposed to fully eliminate interaction between two opposite sides when performing stencil calculations for high order schemes. This is achieved by gradually reducing the order when the stencil is close to the wall. Furthermore, the IBM efficiently addresses the issue of moving objects in compressible flows, specifically the treatment of fresh cells, without necessitating any special treatment. Results showcase the method’s applicability to aerodynamic simulations at low Mach numbers, simulations of compression and expansion processes, and direct numerical simulations of aeroacoustics.

Kinetic modeling of immersed boundary layer for accurate evaluation of local surface stresses and hydrodynamic forces with diffuse interface immersed boundary method

The motivation of this paper is to examine the evaluation of local surface stresses and hydrodynamic forces acting on a stationary or moving body using a diffuse interface immersed boundary method (IBM). This task is not trivial for the diffuse IBM because it uses a smoothed regularized delta function in the transfer steps between Lagrangian and Eulerian locations. In our earlier work [D. Xu et al., Phys. Rev. E 105, 035306 (2022)], a particle distribution function (PDF) discontinuity-based kinetic immersed boundary method (KIBM) was proposed based on the Boltzmann equation. This paper is a continuation of our work on the improvement of the KIBM in the framework of the diffuse interface IBM. In the present study, the concept of the immersed boundary layer (IBL) is brought forward, and the dynamic effects of particle advection and collision in the IBL are coupled and evaluated within a numerical time step scale in a kinetic manner. Consequently, the PDFs on both sides of the IBL are reconstructed, and the general immersed boundary force density can be obtained accurately and efficiently. Meantime, the local surface stress distribution acting on the body wall from the actual fluid can be conveniently and accurately calculated by the moment of the PDFs. Finally, some commonly used problems involving incompressible fluid flows in the continuum flow regime with stationary and moving boundaries are simulated by the present KIBM, and the results show that the present KIBM can significantly accelerate the rate of convergence and has a good agreement with other numerical and experimental results.

A sharp interface immersed boundary method for flow-induced noise prediction using acoustic perturbation equations

In this paper, a hybrid computational aero/hydro-acoustic approach is proposed to deal with acoustic scattering and flow-induced noise problems based on the sharp interface immersed boundary method (IBM). For the flow field, the incompressible Navier–Stokes equations are solved by an in-house direct numerical simulation solver. The acoustic field is predicted by solving acoustic perturbation equations (APEs). Both flow and acoustic solid boundaries with complexity and mobility are dealt with by the sharp interface IBM. Benchmark acoustic problems with varied scatterers in two and three dimensions are presented to validate the accuracy of the acoustic codes and boundary treatments. Then, the feasibility and accuracy of the present hybrid approach are validated by considering the problem of flow past a circular cylinder at a Reynolds number of 200. Subsequently, the present method is used to predict the noise generated by flow around a four-cylinder array in two-dimensions with two arrangements (i.e., square array and diamond array), and the flow and acoustic physics are investigated in detail. The results show that the square array retains a monopole-like sound-radiation shape, while the directivity pattern of the diamond array produces a dipole-like shape. In both the square and diamond arrays, the propagation of acoustic waves is affected by the Doppler effect, and the latter array results in a larger alternation of the propagation angle compared with the single cylinder due to the influence of the geometric configuration. The intensity of the radiated acoustic pressure is much greater for the diamond array compared to the square one in most circumferential directions, and the acoustic intensity of both arrays is greater than that of the single cylinder. The spectrums of the far-field acoustic pressure indicate that the two arrays and the single cylinder have similar peak frequencies and profiles, with vortex shedding playing the predominant role in noise generation in all three configurations.

Role of solution reconstruction in hypersonic viscous computations using a sharp interface immersed boundary method.

This work discusses the development of a sharp interface immersed boundary (IB) method for viscous compressible flows and its assessment for accurate computations of wall shear and heat fluxes in hypersonic flows. The IB method is implemented in an unstructured Cartesian finite-volume (FV) framework and resolves the geometric interface sharply on the nonconformal mesh through direct imposition of boundary conditions employing a local reconstruction approach. The efficacy of the IB-FV solver is investigated for canonical high-speed viscous flows over a range of Mach numbers. The numerical results indicate that the surface pressure and shear stress distributions are computed with reasonable accuracy, whereas surface heat fluxes for aerodynamically blunt configurations are underpredicted. Employing a set of carefully designed experiments and simple diagnostic tools, we probe the possible causes for the underprediction in heat flux. We show that there exist two sources of error-one due to grid resolution and the other due to solution reconstruction, with the latter being more prominent and responsible for the observed underprediction in heat fluxes. Studies reveal that the heat flux estimates are sensitive to the choice of temperature reconstruction and linear interpolations could lead to poor estimates of heat flux. Our investigations conclusively point out the fact that existing polynomial-based reconstruction approaches for sharp interface IB techniques are not necessarily adequate for heat transfer predictions in high Reynolds number hypersonic flows.

DNS of droplet impact on a solid particle: Effect of wettability on solid conjugate heat transfer

Heat transfer between solid particles and liquid droplets is a key phenomenon encountered in many industrial applications. We investigate the fluid dynamics and heat transfer between a liquid droplet and a static solid particle by means of direct numerical simulations. The presence of the solid particle is represented through a sharp interface immersed boundary method (IBM) on a Cartesian computational grid, whereas the motion of the gas-liquid interface is tracked by a mass conservative volume of fluid method (VOF). To account for the thermal coupling between the gas and the liquid, and more specifically the conjugate heat transfer between the fluid and the solid, a second order accurate diffused interface formulation is proposed for the conduction term in the energy equation. A detailed validation of the method is also presented. We have studied the effect of wettability and solid conductivity both of which have been found to have significant effect on the total heat transfer rate.

Adaptive mesh refinement for simulating fluid‐structure interaction using a sharp interface immersed boundary method

SummaryIn this article, adaptive mesh refinement (AMR) is performed to simulate flow around both stationary and moving boundaries. The finite‐difference approach is applied along with a sharp interface immersed boundary (IB) method. The Lagrangian polynomial is employed to facilitate the interpolation from a coarse to a fine grid level, while a weighted‐average formula is used to transfer variables inversely. To save memory, the finest grid is only generated in the local areas close to the wall boundary, and the mesh is dynamically reconstructed based on the location of the wall boundary. The Navier‐Stokes equations are numerically solved through the second‐order central difference scheme in space and the third‐order Runge‐Kutta time integration. Flow around a circular cylinder rotating in a square domain is firstly simulated to examine the accuracy and convergence rate. Then three cases are investigated to test the validity of the present method: flow past a stationary circular cylinder at low Reynolds numbers, flow past a forced oscillating circular cylinder in the transverse direction at various frequencies, and a free circular cylinder subjected to vortex‐induced vibration in two degrees of freedom. Computational results agree well with these in the literature and the flow fields are smooth around the interface of different refinement levels. The effect of refinement level has also been evaluated. In addition, a study for the computational efficiency shows that the AMR approach is helpful to reduce the total node number and speed up the time integration, which could prompt the application of the IB method when a great near‐wall spatial resolution is required.

Effect of flow and fluid properties on the mobility of multiphase flows through porous media

In this paper we quantify the effect of capillary number (Ca), contact angle (θ) and viscosity ratio (M) on the mobility of multiphase flow through porous media. The focus is mainly on oil-water flows through porous rocks observed during the water flooding process. Simulations are performed using a finite volume method employing a staggered grid formulation. Interactions between fluids and complex solid boundaries are resolved by a direct forcing, implicit and sharp interface immersed boundary method (IBM). The fluid-fluid interface is tracked by a mass conservative sharp interface volume of fluid (VOF) method. IBM and VOF are coupled by imposing the contact angle as a boundary condition at the three phase contact line. Our methodology has been verified/validated for several test cases including multiphase Poiseuille flow in a channel, a viscous finger in a channel and mesh convergence of the contact force. Two types of porous structures are considered: (i) a repeated single pore and (ii) a random multi-pore arrangement. Temporal evolution of phase pressure difference and oil saturation have been studied as viscous fingers penetrate the pores. We observed that the residual oil saturation for different capillary numbers shows exactly the opposite trend for the single and multi pore arrangement. The residual oil saturation for multi-pore shows a well defined linear trend with logCa,θ and logM.

An improved ghost-cell sharp interface immersed boundary method with direct forcing for particle laden flows

In this paper, an accurate and stable sharp interface immersed boundary method(IBM) is presented for the direct numerical simulation of particle laden flows. The current IBM method is based on the direct-forcing method by incorporating the ghost-cell approach implicitly. An important feature of this IBM is the sharp representation of the solid surface, contrary to other variants of IBM for freely moving particles in which the solid surface is diffuse. Moreover, a correction of the diameter is not necessary for obtaining accurate results. The current ghost-cell IBM is stable because spurious oscillations incurred due to discontinuity in the pressure and velocity field in moving particle simulations is avoided. An algorithm for accurate torque computation is developed. The proposed algorithm is verified by comparison to an analytical expression and is shown to give a substantial improvement over the existing method. Finally, the present IBM is validated for various test cases of single and multi-particle systems and is shown to be accurate and robust for a wide range of flow conditions.

A Sharp-Interface Immersed Boundary Method for Simulating Incompressible Flows with Arbitrarily Deforming Smooth Boundaries

We develop a sharp interface immersed boundary (IB) method to simulate the interactions between fluid flows and deformable moving bodies. Fluid–solid interfaces are captured using a level-set (LS) function, which is updated at every time step by a reinitialization procedure. Motions of solid bodies are dynamically coupled with fluid flows by calculating the fluid forces exerted on solid bodies. The accuracy and robustness of the LS-based IB method are tested systematically in the context of several benchmark cases and self-propelled fish swimming. The effects of computational parameters on the accuracy of deformable body capturing are analyzed. It is found that the algorithm performs well in simulating the flow motions surrounding the deforming and moving bodies.

A DNS study of flow and heat transfer through slender fixed-bed reactors randomly packed with spherical particles

A fully resolved direct numerical simulation of flow and heat transfer is presented for slender randomly packed bed reactors. The flow and temperature field are solved over a non-body fitted, non-conformal Cartesian computational domain. The coupling between fluid and solid (both spherical particles and cylindrical wall) is enforced by a second order accurate, sharp interface immersed boundary method (IBM). The present numerical technique neither requires any challenging volumetric mesh generation process nor demands manipulation of the geometry near the particle-particle and particle-wall contact points. Conjugate heat transfer has been considered where the temperature field is calculated both inside the solid particles and in the fluid. A discrete element method (DEM) is used to generate the random packings of spherical particles in the cylindrical column, and a methodology is proposed to calculate the radial porosity profile of the bed.The column-to-particle diameter ratio (N) is varied from 4 to 8, and two separate cases have been considered where N→∞. The particle Reynolds number (Red) is varied from 1 to 500. The numerically obtained pressure drop and overall wall-to-bed heat transfer coefficient for different simulation cases are critically compared with empirical correlations and a good agreement is reported. Moreover, based on the current numerical results, correlations are proposed for the pressure drop and the wall-to-bed heat transfer coefficient. The effect of the column-to-particle diameter ratio (N) on both the flow and heat transfer, as-well-as the effect of the solid to fluid thermal conductivity ratio on the conjugate heat transfer are discussed. Furthermore, the fully resolved accurate numerical simulations have helped to elucidate the detailed pore-scale flow and heat transfer feature in the packed beds.

Immersed boundary method simulation of natural convection over fixed and oscillating cylinders in square enclosure

Numerical experiments are performed to study natural convection over moving and fixed heated cylindrical geometries using a simple and efficient sharp interface immersed boundary method (IBM). The current IBM implementation uses a coupled MAC-SOLA solver where SOLA based iterative pressure correction techniques are used to satisfy mass conservation at the intercepted cells while strongly maintaining the boundary conditions that are implemented using interpolation along the direction normal to the complex boundary surface. An overall second order accuracy is maintained in the discretization and interpolation schemes. The present numerical approach provides simplicity, computational efficiency and accuracy for solving moving boundary cases. Predictions are compared with available experimental and numerical data for several fixed and moving boundary cases. Throughout smooth flow and thermal profiles are obtained. Observations are made on the dynamic behavior of the flow features and temperature fields due to natural convection during oscillations of a hot cylinder in a cold square enclosure. The effects of different parameters, viz: Rayleigh number, cylinder diameter, enclosure, eccentricity, amplitude and frequency of oscillation and axis of oscillation on the heat transfer and flow structures are reported. Augmentation of heat transfer due to dynamic interaction of the moving buoyant plume with the boundary layer attached to the cold enclosure wall is also investigated in detail. The present study focuses on understanding the physics of natural convection over moving boundaries within fixed enclosures and can be useful in envisioning better design or optimization of the process.

Direct numerical simulation for flow and heat transfer through random open-cell solid foams: Development of an IBM based CFD model

In the present contribution a sharp interface Immersed Boundary Method (IBM) for flow and heat transfer has been developed to fully resolve highly complex random solid structure on a non-body fitted Cartesian computational grid. A 3D image data set from a Micro-CT (computed tomography) scan of an actual foam geometry is usually converted into a surface mesh of unstructured triangular elements and the current frame work can embed it as an immersed boundary in the CFD domain. A second-order implicit (semi-implicit) method is used to incorporate fluid-solid coupling for flow (heat transfer) at the non-conforming immersed boundary in a structured grid. Both temperature Dirichlet and Neumann boundary conditions, as well as a conjugate heat transfer condition are incorporated at the fluid–solid interface. The proposed method is validated rigorously with existing literature results. The use of a Cartesian grid for flow makes this method robust, computational friendly, and at the same time it avoids the tedious volumetric mesh generation process for very complex shapes. To demonstrate the capability of the current method, it is applied to study flow and heat transfer of a typical foam sample with different flow properties. A closure for pressure drop and heat transfer coefficient are derived for the typical foam sample.