Direct-forcing Immersed Boundary Method Research Articles

Parametric study of passive flow enhancement on a magnus VAWT blade using response surface methodology and direct-forcing immersed boundary method

The Magnus vertical axis wind turbine harnesses the principle of the Magnus effect in conjunction with a vertical axis orientation. This mechanism is based on the lift and drag produced by rotating cylinders to propel the rotor and generate power. The proposed method involved installing a flat plate near each rotating cylinder to generate a higher unidirectional torque. As the configuration of the plate affects both the flow pattern and the forces exerted on the blade, the current study aims to identify an optimal blade configuration consisting of a rotating cylinder and a flat plate. A numerical model of the direct-forcing immersed boundary method was used to simulate the flow past a single blade using the static rotor simulation approach, and the Box–Behnken design for the response surface methodology (RSM) was applied to find an optimized flat plate arrangement that would produce the highest mean torque coefficient (CT¯). Three design parameters were examined, specifically the length of the plate (L/D), the gap between the plate and the cylinder (g/D), and the plate's shift angle with respect to the cylinder axis (β). The Reynolds number was 5000, and the cylinder spin ratio (α) was 3. The optimum configuration to achieve a maximum CT¯ was identified at L/D=0.53, g/D=0.1, and β=0°. Validating this optimal CT¯ yielded a value of 0.290, indicating an increase in torque of almost 70% compared to the central design. Furthermore, this value corresponds closely to the predicted result obtained through the RSM optimization method. Considering the flow analysis at various positions, it is crucial to emphasize a critical scenario where the potential for countertorque emerges due to excessive drag at ψ=0° and ψ=315°.

Drag, lift and torque correlations for axi-symmetric rod-like non-spherical particles in locally linear shear flows

This paper derives new correlations to predict the drag, lift and torque coefficients of axi-symmetric non-spherical rod-like particles for several fluid flow regimes and velocity profiles. The fluid velocity profiles considered are locally uniform flow and locally linear shear flow. The novel correlations for the drag, lift and torque coefficients depend on the particle Reynolds number Rep, the orientation of the particle with respect to the main fluid direction θ, the aspect ratio of the rod-like particle α, and the dimensionless local shear rate G̃. The effect of the linear shear flow on the hydrodynamic forces is modeled as an additional component for the resultant of forces acting on a particle in a locally uniform flow, hence the independent expressions for the drag, lift and torque coefficients of axi-symmetric particles in a locally uniform flow are also provided in this work. The data provided to fit the coefficient in the new correlation are generated using available analytical expressions in the viscous regime, and performing direct numerical simulations (DNS) of the flow past the axi-symmetric particles at finite particle Reynolds number. The DNS are performed using the direct-forcing immersed boundary method. The coefficients in the proposed drag, lift and torque correlations are determined with a high degree of accuracy, where the mean error in the prediction lies below 2% for the locally uniform flow correlations, and bwlow 1.67%, 5.35%, 6.78% for the correlation accounting for the change in the drag, lift, and torque coefficients in case of a linear shear flow, respectively. The proposed correlations for the drag, lift and torque coefficients can be used in large-scale simulations performed in the Eulerian-Lagrangian framework with locally uniform and non-uniform flows.

Numerical Investigation of a Pitching NACA 0012 Wing with Plasma-Based Flow Control Using Prediction–Correction Direct-Forcing Immersed Boundary Method

Numerical Investigation of a Pitching NACA 0012 Wing with Plasma-Based Flow Control Using Prediction–Correction Direct-Forcing Immersed Boundary Method

An efficient isogeometric/finite-difference immersed boundary method for the fluid–structure interactions of slender flexible structures

In this contribution, we present a robust and efficient computational framework capable of accurately capturing the dynamic motion and large deformation/deflection responses of highly-flexible rods interacting with an incompressible viscous flow. Within the partitioned approach, we adopt separate field solvers to compute the dynamics of the immersed structures and the evolution of the flow field over time, considering finite Reynolds numbers. We employ a geometrically exact, nonlinear Cosserat rod formulation in the context of the isogeometric analysis (IGA) technique to model the elastic responses of each rod in three dimensions (3D). The Navier–Stokes equations are resolved using a pressure projection method on a standard staggered Cartesian grid. The direct-forcing immersed boundary method is utilized for coupling the IGA-based structural solver with the finite-difference fluid solver. In order to fully exploit the accuracy of the IGA technique for FSI simulations, the proposed framework introduces a new procedure that decouples the resolution of the structural domain from the fluid grid. Uniformly distributed Lagrangian markers with density relative to the Eulerian grid are generated to communicate between Lagrangian and Eulerian grids consistently with IGA. We successfully validate the proposed computational framework against two- and three-dimensional FSI benchmarks involving flexible filaments undergoing large deflections/motions in an incompressible flow. We show that six times coarser structural mesh than the flow Eulerian grid delivers accurate results for classic benchmarks, leading to a major gain in computational efficiency. The simultaneous spatial and temporal convergence studies demonstrate the consistent performance of the proposed framework, showing that it conserves the order of the convergence, which is the same as that of the fluid solver.

Influence of upstream staggered cylinder on vortex-induced vibration responses of side-by-side cylinders in turbulent flow

A direct-forcing immersed boundary method with large-eddy simulation was used to simulate the phenomenon of the vortex-induced vibration (VIV) of multiple cylinders in a flow field. The present study analyzed the influence of an upstream stationary cylinder on the vibration behavior of two side-by-side cylinders downstream in a staggered position. The latter two side-by-side cylinders were allowed to vibrate in the cross-flow direction. By using different center-to-center distances between cylinders, damping ratios, mass ratios, Reynolds numbers, and diameters of the upstream stationary cylinder, the VIV response and energy conversion efficiency of the vibrating cylinders were studied. The results showed that the amplitude and efficiency of the vibrating cylinders are significantly enhanced at reduced velocity UR*≥6.0 when compared with a single vibrating cylinder. The maximum values of amplitude and efficiency can be shifted and enhanced, respectively, by adjusting the mass ratio and damping ratio. Reducing the diameter of the stationary upstream cylinder can effectively improve efficiency, especially in the lock-in region.

An efficient method for particle-resolved simulations of neutrally buoyant spheres

We present a simple modification of the direct-forcing immersed boundary method (IBM) proposed by Uhlmann (2005) in order to enable it to be applied to particulate flows with solid-to-fluid density ratios around unity. The main difference with respect to the original formulation lies in the particle velocity update which is performed directly after the preliminary velocity field has been computed in the absence of any IBM volume forcing term. In addition, we apply the forcing term to the entire space occupied by the immersed solid object (instead of to the vicinity of its interface only). The present approach requires the evaluation of integrals of the velocity field over the volume occupied by the solid particle, which are evaluated efficiently as sums over the respective quantities available at particle-attached force points. The resulting method can be used seamlessly for density ratios down to ρp/ρf>0.5. The new formulation has been validated using three configurations: (i) lateral migration of a neutrally buoyant circular particle in two-dimensional Couette flow; (ii) the release from rest of a neutrally buoyant sphere in a free stream; (iii) the release of a particle in a free stream after an initial phase in which it is translationally fixed with an imposed angular velocity. In all three test cases the present IBM formulation yields a very good agreement with the available reference data. Thus, the proposed approach is a cost-efficient and accurate modification of the original method which allows for the simulation of fluid systems involving density-matched solid particles.

CDFIB: A convolutional direct forcing immersed boundary method for solving incompressible flows with time-varying geometries

When incorporating the immersed boundary method to model solid obstacles in incompressible flows, the conventional direct forcing immersed boundary (DFIB) method may face the issue of spurious force oscillations (SFO) due to the mass imbalance when integrating drag/lift forces around the solid obstacle. Although the SFO can be controlled with large time step size when employing conventional DFIB method, the method remains prone to large SFO when the time step size is small. When we deal with flow-structure interaction (FSI) scenarios, the solid bodies are driven by hydrodynamic forces that are produced by flow fluids. Unphysical acceleration/deceleration may happen during the simulations due to SFO, thus making the simulations unstable or even diverge. To alleviate the SFO, we thus propose a novel method for modeling the solid bodies in incompressible fluid flows by performing the convolution kernel, dubbed as cDFIB method. cDFIB method inherits the merits of DFIB method, while effectively suppressing SFO for both small and large time step size. From the numerical results of the SFO oscillating cylinder problem, the SFO is proportional to O(Δx) and O(Δt) for present cDFIB method. This property allows cDFIB method to solve challenging problems where employing large time step size becomes infeasible.

Numerical study of vortex-induced autorotation of an elliptic blade in lid-driven cavity flow

Large-scale eddies in a lid-driven cavity are potential sources of angular momentum which can induce rotational effect in a free-to-rotate inertial body due to fluid–structure interaction. The novel objective of the present study is to investigate vortex-induced autorotation of an elliptic blade hinged at the centre of a lid-driven cavity. The governing equations are numerically solved using iterative direct forcing immersed boundary method. The impact of Reynolds number and blade length on dynamics characteristics of the blade are analysed. Considering left to right motion of horizontal top lid, four different vortex-induced modes are identified as the steady blade response, including stationary position, small-amplitude fluttering, clockwise autorotation and counter-clockwise autorotation. Long blades are mostly potential for steady clockwise autorotation, particularly in higher Reynolds numbers, due to dominance of principal near-wall cavity vortex compared to other vortices. In contrast, effective role of central counter-clockwise vortex in a short blade and weak interaction of such blade with the near-wall cavity vortex leads to a steady counter-clockwise rotation, particularly in high Reynolds numbers. In the case of low Reynolds numbers or blade with moderate length, vortex-induced blade motions in clockwise and counter-clockwise directions are fairly balanced, leading to stationary position or small-amplitude fluttering modes.

Numerical modeling of flow past a volumeless and thin rigid body using direct forcing immersed boundary method

AbstractThe new capability has been added as the numerical method for modeling volumeless and thin rigid bodies to the direct forcing immersed boundary (DFIB) method. The DFIB approach is based on adding a virtual force to the Navier–Stokes equations of incompressible flow to account for the interaction between the fluid and structures. The volume of a solid function (VOS) identifies the stationary or moving solid structures in a given fluid domain. A new VOS‐based algorithm was developed to identify thin, rigid structure boundary points in fluid flow and ensure that the fluid cannot cross through the boundary of a thin rigid structure while moving or stationary. The DFIB method was first validated in a three‐dimensional (3D) turbulent flow over a circular cylinder. The large‐eddy simulation simulated the turbulent flow scales. The proposed algorithm was tested using a 3D turbulent flow past a stationary and rotating Savonius wind turbine that functions as a thin, rigid body. The validation results showed that the selected DFIB approach, combined with the novel algorithm, could simulate a thin, volumeless, rigid structure that is stationary and rotating in incompressible turbulent flows. The current method is also applicable for two‐way fluid‐structure interaction problems.

Numerical investigation of the flow inside a precession-driven cylindrical cavity with additional baffles using an immersed boundary method

In this paper, we present a numerical approach to solve the Navier–Stokes equations for arbitrary vessel geometries by combining a Fourier-spectral method with a direct-forcing immersed boundary method, which one allows to consider solid–fluid interactions. The approach is applied to a paradigmatic setup motivated by the precession dynamo experiment currently under construction at Helmholtz–Zentrum Dresden–Rossendorf. The experiment consists of a fluid-filled cylinder rotating about two axes, which induces a precession-driven flow inside the cavity. The cylinder is also equipped with baffles at the end caps with adjustable penetration depth to impact the flow. The numerical details and simulation results for the spin-up and precession-driven flow in a circular cylinder with additional baffles are presented. The results provide a first confirmation that the use of such baffles in the precession dynamo experiment is a useful way of influencing the flow, allowing more efficient driving without changing the known flow structure too much.

Direct Numerical Simulation of pulsating flow effect on the distribution of non-circular particles with increased levels of complexity: IB-LBM

Equilibrium position, as well as dynamic patterns of suspended particles, plays a dominant role in particle manipulation of segregation, transporting, or sorting. The current paper aims to investigate the falling manners of non-circular particles in an enclosure while the pulsatile flow is involved as a counter-flow. The direct-forcing immersed boundary method is coupled with the lattice Boltzmann method to simulate this widespread issue numerically. Corresponding boundary conditions are hired to take into account pulsatile flow. Findings were first successfully verified against the existing literature and the accuracy of the results is well-demonstrated. For the first time, a series of proof-of-principal simulations with an increased level of geometric complexity, particle aspect ratio, as well as the number and initial configuration (release positions), is carried out. The force resulting from the particle acceleration is also considered. It is shown that considering such factors, particle settling manners would markedly differ. The collective behavior of particles is also studied, and it is revealed that the presence of neighboring particles makes the influence of the particle shape less clear; however, pulsatile flow presents considerable differences in the settling manners of particles.

Drag enhancement by the addition of weak waves to a wave-current boundary layer over bumpy walls

We present direct numerical simulation results of a wave-current boundary layer in a current-dominated flow regime (wave driven to steady current ratio of 0.34) over bumpy walls for hydraulically smooth flow conditions (wave orbital excursion to roughness ratio of 10). The turbulent, wave-current channel flow has a friction Reynolds number of $350$ and a wave Reynolds number of $351$ . At the lower boundary, a bumpy wall is introduced with a direct forcing immersed boundary method, while the top wall has a free-slip boundary condition. Despite the hydraulically smooth nature of the wave-driven flow, the phase variations of the turbulent statistics for the bumpy wall case were found to vary substantially when compared with the flat wall case. Results show that the addition of weak waves to a steady current over flat walls has a negligible effect on the turbulence or bottom drag. However, the addition of weak waves to a steady current over bumpy walls has a significant effect through enhancement of the Reynolds stress (RS) accompanied by a drag coefficient increase of $11\,\%$ relative to the steady current case. This enhancement occurs just below the top of the roughness elements during the acceleration portion of the wave cycle: Turbulent kinetic energy (TKE) is subsequently transported above the roughness elements to a maximum height of roughly twice the turbulent Stokes length. We analyse the TKE and RS budgets to understand the mechanisms behind the alterations in the turbulence properties due to the bumpy wall. The results provide a mechanistic picture of the differences between bumpy and flat walls in wave-current turbulent boundary layers and illustrate the importance of bumpy features even in weakly energetic wave conditions.

An improved direct-forcing immersed boundary method for simulations of flow and heat transfer in particle-laden flows

In studies of particle-laden flow, the direct-forcing immersed boundary (IB) method is commonly utilized to fully resolve the flow around the particles. With the use of interpolation functions, the effective diameter of a particle is typically larger than the actual diameter, resulting in an erroneous flow field, an overestimated drag force, and an inaccurately estimated interphase heat transfer rate when the grid resolution is insufficient. Relatively high grid resolutions (typically dp/h > 20) are required to ensure accurate estimations of the momentum and heat transfer between fluid and particles, leading to high computational cost when simulating cases with numerous particles. To address these issues, we propose an improved direct-forcing IB method involving retraction of the Lagrangian points, which considers the interphase momentum and heat transfer simultaneously. The method establishes two sets of Lagrangian points for computing the drag force and heat transfer rate, respectively. Based on the optimal retraction distance of the two sets of Lagrangian points, two retraction functions of the Reynolds number and grid resolution are formulated. Using the developed retraction functions, we simulate the DKT process, non-isothermal flow past three in-line spheres, and gravitational settling of a sphere with variable temperature to validate the improved IB method. It is found that the drag force and Nusselt number can be accurately reproduced using the improved IB method with a relatively small grid resolution (dp/h = 10).

A simple and efficient parallel immersed boundary-lattice Boltzmann method for fully resolved simulations of incompressible settling suspensions

This study presents an efficient and parallel fully resolved direct numerical simulation (FR-DNS) of settling suspensions on multiple CPU cores based on the boundary-thickening direct forcing immersed boundary method (BTDF-IBM) and incompressible lattice Boltzmann method (LBM). The simple BTDF-IBM is used to meet the no-slip and no-penetration conditions on particle boundaries, and the incompressible LBM is used to achieve the capability of large pressure fluctuations in suspensions. In addition, a theoretical force model is used to compensate for the unresolved lubrication force between the two approaching particles. A swap strategy for the streaming step is used to reduce the memory storage of the LBM particle density functions to half. A distribution and communication strategy is proposed to handle the IBM computing and complete the immersed boundary (IB) force of the particles residing in the interface region between adjacent subdomains. The developed BTDF-IBM-LBM solver “PFlows” can simulate large particle-laden flows with more than O(106) particles and with a particle volume fraction of up to 0.4. An almost linear parallel speedup and efficiency of higher than 0.8 are obtained by testing three-dimensional (3D) cases (up to 1.0 billion fluid grids and 0.45 million particles) and two-dimensional (2D) cases (up to 1.2 billion fluid grids and 2.39 million particles). Finally, the framework is applied to three large-scale real simulations involving 50,000 particles settling in 2D and 3D bounded and unbounded domains for qualitative and quantitative validations. The particle settling behaviors and disturbed complex fluid flows in the vertical channel are demonstrated. The Boycott effect in the inclined channel is uncovered by a new mechanism that combines particle sliding at the lower sidewall with fluid convection in the upper region. The hindered settling of particles in the 3D periodic domain, which is affected by the strong particle-fluid hydrodynamic interactions and particle-particle many-body interactions at a high solid volume fraction, are analyzed. The complex behaviors and statistical characteristics of the suspensions are preliminarily revealed and analyzed, which demonstrates the prospective capability of the present framework for FR-DNS of large-scale 2D and 3D suspension flows that are relevant to many industrial applications by IB-LBM.

Direct numerical simulation of a stationary spherical particle in fluctuating inflows

Fully resolved direct numerical simulations are conducted to study the effects of fluctuating freestream flow on the drag force and wake characteristics of a stationary spherical particle. Sinusoidal fluctuation around a mean value is adopted as the freestream velocity. The interaction between the particle and fluctuating flow is computed by the direct-forcing immersed boundary method. We principally consider the relative difference between the computed mean drag and the drag law of a uniform flow past the particle and the properties of drag fluctuation in different freestream fluctuation directions. For the influence of streamwise fluctuating inflow, the relative mean drag difference increases with the particle Reynolds number. At small or intermediate particle scale ratios, the relative mean drag difference is very close to zero, indicating that the classical drag law can be used in these cases, while a large particle scale ratio can induce a notable increase in the relative mean drag difference at a large particle Reynolds number and high fluctuation intensity. For the transverse fluctuating inflow, generally, there is an evident increase in the mean drag coefficient when the particle scale ratio is small. Compared with the streamwise fluctuation case, the drag fluctuation intensity is a little smaller with the transverse fluctuating inflow. An explicit empirical drag fluctuation law is obtained by fitting the data for streamwise fluctuating inflow. The wake characteristics are also analyzed, and they are found to be strongly dependent on the direction of inflow fluctuation.

A novel interpolation-free sharp-interface immersed boundary method

This paper describes a novel 2nd order direct forcing immersed boundary method designed for simulation of 2D and 3D incompressible flow problems with complex immersed boundaries. In this formulation, each cell cut by the immersed boundary (IB) is reshaped to conform to the shape of the IB. IBs are modeled as a series of 2D planes in 3D space that connect seamlessly at the edges of the cut cells, in a way that mimics conformal grid. IBs are represented in a continuous and consistent fashion from one cell to another, thus eliminating spatial pressure oscillations originating from inconsistent description of the IB as well as the traditional stair-step problem, leading to a more accurate resolution of the boundary layer. Boundary conditions are enforced at the exact location of the IB devoid of interpolation, which guarantees sound simulations even on grids with high aspect ratio, and enables simulations of flow packed with multiple IBs in close proximity. Boundary conditions for each phase across the IB are enforced independently, yielding a unique capability to solve flows with zero-thickness IBs. Simulations of a large number of 2D and 3D test cases confirm the prowess of the devised immersed boundary method in solving flows over multiple loosely/closely-packed IBs; stationary, moving and highly morphing IBs; as well as IBs with zero-thickness. Results show that predictions from the proposed scheme agree remarkably well with theoretical models and experimental data for both integral variables and local flow fields and they are often with less than 1% deviation from solutions obtained by conformal grid of similar resolution.

Utilization of direct forcing immersed boundary methods for the optimization of inertial focusing microfluidics

Inertial focusing microfluidics have gained significant momentum in the last decade for their ability to separate and filter mixtures of particles and cells based on size [1-3]. However, the most important feature is that the separation is passive, without the need for external forces. At the heart of inertial focusing is the balance between counteracting lift forces: shear and wallinduced lift. Shear-induced lift is a product of the curvature of the fluid flow and the rotation of the particle in the flow, while wall-induced lift is generated by the disturbance of the fluid by the particle near a wall. This phenomenon was first observed by Segre and Silberberg for the focusing of particles in a pipe, and was later extended to the focusing of cells and particle in rectangular channels [4]. Taking advantage of inertial focusing we explore particle capture utilizing an expanded channel microfluidics chip design. By expanding a small region of the straight channel microvortices form in the well, which allows for size selective trapping of particles.

Aeroacoustic simulation of a cross-flow fan using lattice Boltzmann method with a RANS model

The present study developed an unsteady RANS approach based on the lattice Boltzmann method (LBM), which can perform direct aeroacoustic simulations of low-speed fans at lower computational cost compared with the conventional LBM-LES approach. In this method, the k-ω turbulence model is incorporated into the LBM flow solver, where the transport equations of k and ω are also computed by the lattice Boltzmann method, similar to the Navier-Stokes equations. In addition, moving boundaries such as fan rotors are considered by a direct-forcing immersed boundary method. This numerical method was validated in a two-dimensional simulation of a cross-flow fan. As a result, the simulation was able to capture an eccentric vortex structure in the rotor, and the pressure rise by the work of the rotor can be reproduced. Also, the peak sound of the blade passing frequency can be successfully predicted by the present method. Furthermore, the simulation results showed that the peak sound is generated by the interaction between the rotor blade and the flow around the tongue part of the casing.

A direct forcing immersed boundary method for cavitating flows

AbstractIn the current study, an immersed boundary method for simulating cavitating flows with complex or moving boundaries is presented, which follows the discrete direct forcing approach. Although the immersed boundary methods are widely used in various applications of single phase, multiphase, and particulate flows, either incompressible or compressible, and numerous alternative formulations exist, to the best of the authors' knowledge, a handful of computational works employ such methodologies on cavitating flows. The herein proposed method, following previous works of the author's group, tries to fill this gap and to solidify the development of a computational tool of a simple formulation capable to tackle complex numerical problems of cavitation modeling. The method aims to be used in a wide range of applications of industrial interest and treat flows of engineering scales. Therefore, a validation of the method is performed by numerous benchmark test‐cases, of progressively increasing complexity, from incompressible low Reynolds number to compressible and highly turbulent cavitating flows.

Turbulent flow simulation of a single-blade Magnus rotor

This paper presents numerical studies of the Magnus effect for a kinetic turbine on a horizontal axis. To focus on the Magnus blade, a single self-spinning cylindrical blade is assumed. An iterative direct-forcing immersed boundary method is employed within the Eulerian-Lagrangian framework due to its capability to treat complex and moving geometries. The Eulerian fluid domain is discretized using the finite volume method while the Magnus rotor is represented by a set of discrete points/markers. The aim of the numerical studies is to provide insights for the design process and predict aerodynamic performances under various operating conditions. Results for stationary and self-spinning cylinders in turbulent flows are found to be in good agreement with published data. By increasing the aspect ratio of the cylinder (simulated segment length over its diameter) from 3 to 10, a 30% drop in lift coefficient and a 22% increase in drag coefficient were observed, which is believed to be attributed to an enhancement of the three-dimensionality of the near-wake. For the Magnus rotor, key parameters such as dynamic forcing and frequency, distribution of pressure coefficient and torque have been produced for two cases with different structural designs and working conditions. With increase of the aspect ratio from 3 to 10, stable forces are observed from the root side of the blade and the torque coefficient increases from 0.68 to 2.1, which indicates a superior performance in terms of power extraction.