Boundary Method Research Articles

An averaged mass correction scheme for the simulation of high subsonic turbulent internal flows using a lattice Boltzmann method

This paper addresses the simulation of internal high-speed turbulent compressible flows using lattice Boltzmann method (LBM) when it is coupled with the immersed boundary method for non-body-fitted meshes. The focus is made here on the mass leakage issue. The recent LBM pressure-based algorithm [Farag et al. Phys. Fluids 32, 066106 (2020)] has shown its superiority on classical density-based algorithm to simulate high-speed compressible flows. Following our previous theoretical work on incompressible flows [Xu et al. Phys. Fluids 34, 065113 (2022)], we propose an averaged mass correction technique to mitigate mass leakage when simulating high-Mach-number compressible flows. It is adapted to deal here with a density, which is decoupled from the zero-moment definition. The simulations focus on two generic but canonical configurations of more complex industrial devices, the straight channel at different angles of inclination at Mach numbers (Ma) ranging from 0.2 to 0.8, and the National Aeronautics and Space Administration Glenn S-duct at Ma = 0.6. The present results show that mass leakage can be a critical issue for the accuracy of the solution and that the proposed correction technique effectively mitigates it and leads to significant improvements in the prediction of the solution.

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°.

Fluid–structure interaction for mechanical filament valve mimicking a biological leaflet valve

The biological leaflet valve is a structure found in blood vessels and the cardiac system, designed to maintain a unidirectional flow within the vessels. Two filaments inspired by the biological leaflet are installed inside the channel, and behavior of two filaments is explored by using immersed boundary method. It is observed that the filaments serve as a valve, maintaining the unidirectional flow inside the channel depending on the length (L) and the initial inclined angle (θ) of the filaments. The behavior of the filaments is classified into three modes based on the flow characteristics around the filaments. The pressure and vorticity fields in the vicinity of the filaments are examined to investigate the influence of the surrounding flow on the behavior of filaments. The present study reveals the time sensitivity of valve response, the power consumption, and hydrodynamic efficiency (ηV,steady) of the filament valve, noting that the response speed of the filament valve can vary up to 2.5 times depending on L and θ. The dynamic behavior of the filament valve is analyzed with respect to changes in the properties of the filaments, observing a monotonic decrease in hydrodynamic efficiency with an increase in the bending rigidity (γ) of the filaments. As a result, the present study will be employed as a cornerstone in the development of a mechanical system that emulate biological structures through biomimetics.

Wall-modeled large eddy simulation in the immersed boundary-lattice Boltzmann method

This work presents the wall-modeled large eddy simulation (WMLES) in the immersed boundary-lattice Boltzmann method (IB-LBM). Here, the wall model with both diffusive- and sharp-interface immersed boundary methods (IBMs) is incorporated into the IB-LBM to handle the turbulent boundary layer in high Reynolds number turbulent flows. To maintain the numerical stability, two collision models, i.e., multiple-relaxation-time (MRT) and recursive regularized (RR), are implemented. The performance of these models in the WMLES is examined and compared in the simulation of internal and external flows by considering four benchmarks, i.e., turbulent flow in a channel, flow around a hull of submarine, flow around an Ahmed car model, and flow around a circular cylinder. It is found that a diffusive-interface IBM with wall model is capable to achieve excellent results for the simulation of external flows around bluff objects but fails in the simulation of internal flows of underestimating the wall shear stress due to its extra dissipation. The sharp-interface IBM with the wall model predicts the internal flow very well but fails in some simulations of external flow around bluff bodies due to the failure in the separation flow modeling. It is also found that the MRT-LBM is less dissipative than the RR-LBM, but it generates spurious nonphysical noise in the turbulent flows and tends to be unstable at high Reynolds numbers. Therefore, the diffusive-interface IBM with the wall model is more suitable for the external turbulent flow modeling, while its sharp-interface counterpart is more suitable for the internal turbulent flow modeling. The RR-LBM outperforms the MRT-LBM for the better stability and less nonphysical noise.

Direct numerical simulation of channel flow with real surface roughness using a ghost cell immersed boundary method

This paper investigates the impact of real surface roughness on channel flow using direct numerical simulation assisted by a ghost cell immersed boundary method (DNS-GCIBM). The principles and implementations of DNS-GCIBM are first introduced. Two test cases, including the two-dimensional flow around a cylinder and the three-dimensional flow in a sinusoidal roughness channel are employed to demonstrate the practicability and accuracy of the proposed approach, especially in numerical studies on the rough wall-bounded flow. Using DNS-GCIBM, channel flows under conditions of Ma = 0.3 and Reτ≈300, with both the real-world and regular roughness surfaces are studied. The results are statistically analyzed using the triple decomposition technique. The outer layer similarity in the streamwise mean velocity and Reynolds stress profiles indicate that the impact of roughness on the boundary layer primarily localizes within roughness sub-layer. In the streamwise mean velocity profile, both regular and real-world roughness surfaces induce obvious increase to the roughness function ΔU+ as roughness height Ra increases, while discrepancy of ΔU+ between the two types of roughness can be found. Furthermore, turbulence statistics are sensitive to the variations of Ra. As Ra increases, it becomes challenging to organize coherent structures near the wall, resulting in the reduction of streamwise Reynolds stress intensity. In addition, although the skin friction coefficient and ΔU+ are almost the same, the real-world roughness and the corresponding equivalent regular roughness manifest different flow structures near the wall. The real-world roughness contributes greater spatial inhomogeneity but lower turbulence intensity.

Benchmarking the immersed boundary method for viscoelastic flows

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used to simulate biological fluid dynamics and other modeling scenarios in which a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems involving viscous incompressible fluids, it also can be applied to visoelastic fluids and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constitutive equation. In the viscoelastic context, however, relatively little work has explored the accuracy or convergence properties of this numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using either the idealized Oldroyd-B constitutive model or the more physically realistic, polymer-entanglement-based Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime.

Coupling of multicomponent transport models in particle-resolved fluid-solid simulations

An accurate and self-consistent methodology for mass transport of multi-component mixtures in multi phase media is a necessity for a proper description of complex physical and chemical processes in reactors such as catalytic packed beds. In this regard, a novel methodology has been developed to describe and couple underlying transport phenomena in fluid and porous media as well as at the solid-fluid interface. The methodology is symmetric as it treats all components in a mixture equally. The Maxwell-Stefan equations are symmetrically formulated, discretized conservatively and coupled with a compressible flow solver for the fluid part. The Dusty Gas Model is applied inside porous media by developing a self-consistent and robust numerical formulation. A ghost-cell Immersed Boundary Method is used to capture the physics at the solid-fluid interface with the implementation of a novel symmetric non-singular mass flux formulation. Several test cases are established to demonstrate the accuracy and robustness of the newly developed symmetric methodology in this paper. These test cases can be used as benchmark for the future development of symmetric methodologies for multicomponent systems in multi phase media.

A new re-redistribution scheme for weighted state redistribution with adaptive mesh refinement

State redistribution (SRD) is a recently developed technique for stabilizing cut cells that result from finite-volume embedded boundary methods. SRD has been successfully applied to a variety of compressible and incompressible flow problems. When used in conjunction with adaptive mesh refinement (AMR), additional steps are needed to preserve the accuracy and conservation properties of the solution if the embedded boundary is not restricted to a single level of the mesh hierarchy. In this work, we extend the weighted state redistribution algorithm to cases where cut cells live at or near a coarse-fine interface within the domain. We present numerical results that demonstrate that the algorithm is conservative when the coarse-fine interface intersects the embedded boundary. Additionally we compare the numerical solution of the Sod shock tube problem in an inclined cylinder with the analytic solution, and we compare the simulation of a shock hitting a cylindrical obstacle with experimental data. Finally we demonstrate the methodology for simulation of the multicomponent compressible Navier-Stokes equations in a piston-bowl geometry, and discuss the computational efficiency gained by not requiring the entire embedded boundary to be defined at the finest level.

Plaque heterogeneity and the spatial distributions of its components dictate drug-coated balloon therapy

Drug-coated balloon (DCB) angioplasty is one of the potential approaches to alleviating in-stent restenosis and treating peripheral artery disease. An in-silico model has been developed for sirolimus drug eluted from an inflated balloon in a patient-specific arterial cross-section consisting of fibrous tissue, fibrofatty tissue, dense calcium, necrotic core, and healthy tissue. The convection-diffusion-reaction equation represents the transport of drug, while drug binding, both specific and non-specific, can be modelled as a reaction process. The Brinkman equations describe the interstitial flow in porous tissue. An image processing technique is leveraged for reconstructing the computational domain. The Marker and Cell, and Immersed Boundary Methods are used to solve the set of governing equations. The no-flux interface condition and convection do amplify the tissue content, and the regions of dense calcium and necrotic core limited to or extremely close to the interface pose a clinical threat to DCB therapy. Simulations predict the effects of the positioning and clustering of plaque components in the domain. This study demands extensive intravascular ultrasound-derived virtual histology (VH-IVUS) imaging to understand the plaque morphology and determine the relative positions of different plaque compositions about the lumen-tissue interface, which have a significant impact on arterial pharmacokinetics.

Unsteady solute transport in Casson fluid flow and its retention in an atherosclerotic wall

In the current study, a mathematical model of convective solute transport and its retention in an atherosclerotic wall is examined. The artery wall is supposed to be permeable and has cosine-shaped stenosis caused by various sorts of abnormal growth or plaque formation. The flowing blood is modeled as the suspension of all red blood cells in plasma, thought to be Casson fluid. The Immersed Boundary Method (IBM) and the Marker and Cell (MAC) method are used to numerically solve the unsteady governing equations of motion along with the appropriate initial and boundary conditions. The final results of the quantitative studies contain the corresponding flow-field and solute distribution profiles for the full arterial length. The essential components are evaluated, including the wall shear stress, wall concentration, and concentration contours. According to simulation data, the permeability of the wall directly affects the solute transport within the therapeutic region. The yield stress does, however, increase flow resistance and decrease solute uptake within the tissue. The projected outcomes are remarkably in line with previously published findings, which supports the applicability of the model under investigation.

Discrete null field equation methods for solving Laplace's equation: Boundary layer computations

AbstractConsider Dirichlet problems of Laplace's equation in a bounded simply‐connected domain , and use the null field equation (NFE) of Green's representation formulation, where the source nodes are located on a pseudo‐boundary outside but not close to its boundary . Simple algorithms are proposed in this article by using the central rule for the NFE, and the normal derivatives of the solutions on the boundary can be easily obtained. These algorithms are called the discrete null field equation method (DNFEM) because the collocation equations are, indeed, the direct discrete form of the NFE. The bounds of the condition number are like those by the method of fundamental solutions (MFS) yielding the exponential growth as the number of unknowns increases. One trouble of the DNFEM is the near singularity of integrations for the solutions in boundary layers in Green's representation formulation. The traditional BEM also suffers from the same trouble. To deal with the near singularity, quadrature by expansions and the sinh transformation are often used. To handle this trouble, however, we develop two kinds of new techniques: (I) the interpolation techniques by Taylor's formulas with piecewise ‐degree polynomials and the Fourier series, and (II) the mini‐rules of integrals, such as the mini‐Simpson's and the mini‐Gaussian rules. Error analysis is made for technique I to achieve optimal convergence rates. Numerical experiments are carried out for disk domains to support the theoretical analysis made. The numerical performance of the DNFEM is excellent for disk domains to compete with the MFS. The errors with can be obtained by combination algorithms, which are satisfactory for most engineering problems. In summary, the new simple DNFEM is based on the NFE, which is different from the boundary element method (BEM). The theoretical basis in error and stability has been established in this article. One trouble in seeking the numerical solutions in boundary layers has been handled well; this is also an important contribution to the BEM. Besides, numerical experiments are encouraging. Hence the DNFEM is promising, and it may become a new boundary method for scientific/engineering computing.

Exascale Computational Fluid Dynamics in Heterogeneous Systems

Abstract Exascale computing has extended the reach of resolved flow simulations in complex, heterogeneous systems far beyond conventional computational fluid dynamics capabilities. As a result, unprecedented pore and microscale resolution have been achieved in domains that have been traditionally modeled by, and limited to, continuum, effective medium approaches. By making use of computational resources on the new exascale supercomputer, Frontier, at the Oak Ridge Leadership Computing Facility, we performed flow simulations that have pushed the limits of domain-to-resolution ratios by several orders of magnitude for heterogeneous media. Our approach is an incompressible, Navier–Stokes CFD solver based on adaptive, embedded boundary (EB) methods supported by the Chombo software framework for applied partial differential equations (PDEs). The computational workhorse in the CFD application code is an elliptic solver framework in Chombo for pressure-Poisson and viscous, Helmholtz terms that leverages a PETSc-hypre software interface tuned for accelerator-based platforms. We demonstrate scalability of the approach by replicating a unit cylinder packed with microspheres to achieve over 400 × 109 degrees-of-freedom simulated. These simulations model domain lengths of over 20 meters with channel volumes of over 400 cm3 and containing millions of packed spheres with 20 micron grid resolution, challenging current understanding of what it means to be a representative elementary volume (REV) of the continuum scale in heterogeneous media. We also simulate a range of Reynolds numbers to demonstrate wide applicability and robustness of the approach.

Day ahead demand response model with algorithm-based consumption classification and tariff planning

Demand Response (DR) programs effectively support the supply-demand balance in power systems. This study proposes a new Time-of-Use (ToU) tariff model, a type of price-based demand response (DR). The proposed model aims to shape the daily consumption profile of the distribution region by encouraging consumers through tariffs. Generally, in ToU demand response, various presumptions are being adopted to define consumption periods and consumer classes. It is unlikely that these presumptions are suitable for every day of the year and every consumer in the system. Achieving these definitions and classifications based on algorithms, free from human error, will increase the success and comprehensiveness of the DR program. To maximize success in this context, a deep learning model has been leveraged for day-ahead consumption forecasting. The forecasted daily consumption profile is partitioned into ToUs by using the Moving Boundary method. In addition, consumers within the region have been segmented based on the similarities in consumption behavior. Tariffs have been priced for each cluster through an optimization model that considers their participation rates in total consumption and contributions to consumption in ToU regions. The proposed model has been tested over a dataset belonging to a distribution system where different types of consumers coexist. Two sample days have been chosen as one is a weekday and the other is a weekend. The results prove that shifting consumption as encouraged by the proposed TOU method reduces consumers' costs. While, the profitability of the system operator is also preserved.

Extension of a sharp-interface immersed-boundary method for simulating parachute inflation

In this work, the sharp-interface immersed boundary (IB) method proposed by Mittal et al. (J Comput Phys 227(10):4825–4852, 2008) is extended to fluid-structure-interaction (FSI) simulation of parachute inflation by utilizing several open-source tools. The method employs a Cartesian-grid ghost-cell methodology to accurately represent the immersed boundary, and it is suitable for solving moving-boundary flows with arbitrarily complex geometries. The finite-element code CalculiX is employed to solve the structural dynamics of the parachute system. The IB flow solver is coupled with CalculiX in a minimally-invasive manner using the multi-physics coupling library preCICE. The implicit fluid-structure coupling together with the Aitken adaptive under-relaxation scheme is considered to improve the numerical accuracy and stability. The developed approach is validated by a benchmark FSI case. Numerical experiments on the inflation process of several typical parachutes are further conducted. The breathing process, flow structure, canopy displacement and drag coefficient are analyzed to demonstrate the applicability of the present approach for simulating parachute inflation.

Study of gravitational sedimentation of two flexible circular shaped particles using Immersed Boundary Method

This work numerically illustrates the Drafting, Kissing, and Tumbling (DKT) phenomena between two flexible, interacting, and circular particles in a bounded medium. The original Immersed Boundary (IB) Method was employed to conduct the study in a two-dimensional setup for different fluid viscosities. Two scenarios were considered: in one, the interacting particles were assumed to have the same flexibility, whereas in the other, the particles had different flexibility. The study attempted to explore the impact of flexibility on the dynamics of particles. For the same flexibility case, we observed multiple DKTs for higher flexibility cases and wobbling motion for the less flexible case in a less viscous fluid medium. For a higher viscous fluid medium, we observed drafting phase only. In the case when the leading particle was made more flexible than the trailing particle, irrespective of any flexibility and fluid viscosity of the particle, their configuration status was retained, i.e., the leading particle remained leading, and the trailing particle remained trailing. In the case when the leading particle was less flexible than the trailing particle, for a higher viscous fluid medium, the particles experienced drafting and kissing only, but for a lower viscous fluid medium, the particles had one cycle of DKT. The results obtained are physically justified.

An improved porous media model for simulating the flow–nets interaction

This study presents an improved porous media model for simulating the interaction between the fixed aquaculture nets and flow. The fluid motion is computed based on the Reynolds time-averaged Navier–Stokes equations on the regular Eulerian mesh. The porous media model simulates the nets, where the interface between the complex shapes of the nets and the fluid is determined by the continuous forced immersed boundary (IB) method. The fluid volume fraction is defined and embedded in the porous media coefficients and porosity equations to set the porous media parameters at IB. Several cases validate the model, including the flow interactions with the single net panel, gravity net cage, and offshore aquaculture platform. Meanwhile, the effects of incoming velocity, attack angle, solidity, and the shape of the net on the simulation are investigated. The numerical model can reasonably predict the hydrodynamic of the nets with a relative error of less than 8%. Moreover, the computational efficiency of the hydrodynamic of complex shaped nets is significantly improved, with a maximum of about 11.54 times.

Influence mechanism of tip clearance on flutter stability with different aerodynamic coupling effects for transonic compressor

Flutter is a highly destructive aeroelastic problem in modern compressors, which hinders the improvements of aero-engine performance and reliability. Because the aerodynamic work is mainly concentrated in the blade tip region, the tip clearance which is associated to the complex tip clearance flow has a considerable effect on the flutter stability. In this paper, in order to investigate the influence mechanism of the tip clearance on the flutter stability at different nodal diameters (ND), a series of compressor models were established with different tip clearances based on a transonic compressor rotor. The aerodynamic damping at each ND is obtained by influence coefficient method (ICM), while phase-shifted boundary method (PSB) is adopted to analyze the influence of the tip clearance on the flutter stability at different NDs. The results indicate the worst flutter stability for each tip clearance always appears at ND=1, where the aerodynamic damping exhibits a nonmonotonic trend of increasing first and decreasing thereafter along with the rising tip clearance. Two kinds of action are exerted by the tip clearance flow on the flow structures to alter the flutter stability: one is the tip clearance vortices which is generated on the suction side and impinge on the pressure side; the other is the interference of tip clearance vortices to the shock wave and to the flow separation. Besides, the influence of the changing aerodynamic coupling effect makes the above action bring about more drastic fluctuations to the unsteady pressure. At larger NDs, the unsteady pressure amplitude and phase fluctuate more sharply for larger tip clearances. Therefore, diverse change trends of the aerodynamic damping with the increasing tip clearance appear at different NDs, while the impingement of tip clearance vortices on the adjacent pressure side has a constantly stabilizing effect at different NDs.

Hydrodynamics of pitching hydrofoil in a plane Poiseuille flow

Several advanced medical and engineering tasks, such as microsurgery, drug delivery through arteries, pipe inspection, and sewage cleaning, can be more efficiently handled using micro- and nano-robots. Pressure-driven flows are commonly encountered in these practical scenarios. In our current research, we delve into the hydrodynamics of pitching hydrofoils within narrow channels, which may find their potential applications in designing bio-inspired robots capable of navigating through pressure-driven flows in confined channels. In this paper, we have conducted a numerical investigation into the flow characteristics of a National Advisory Committee for Aeronautics (NACA) 0012 hydrofoil pitching around its leading edge within a plane Poiseuille flow using a graphical processing unit accelerated sharp interface immersed boundary method solver. Our study considers variations of the wall clearance from 20% to 50% of the channel width. We have explored the hydrodynamic features such as instantaneous and time-averaged values of lift, drag, input power, and torque for different wall clearance ratios and oscillation frequencies in the range of Reynolds number 100–200 based on the mean velocity and channel width. We have tried to explain the force, torque, and power variations by examining the flow features in the near wake. While the hydrodynamic coefficients showed significant variations with changes in wall clearance and the Strouhal number (St), we did not observe significant variations with alterations in the Reynolds number (Re).

Shape optimization of sound barriers using an isogeometric meshless method

The sound barrier is an important means to reduce noise caused by traveling vehicles on roads or railways. Structural design and optimization of the sound barrier can effectively reduce the use of materials and improve the noise reduction effect. In this paper, a new isogeometric singular boundary method is proposed and applied to the shape optimization of sound barriers. The geometric structure is accurately represented by using non-uniform rational B-splines. The acoustic shape sensitivity of the control points was calculated using the direct differentiation method and the adjoint variable method. After that, the method of moving asymptotes is adopted as an optimizer to search for the optimal layout of the design objective. In the numerical procedure, the shoelace formula is introduced to calculate the area of the closed structure, which only uses the discrete node information on the boundary. The proposed approach completely avoids the mesh division in the finite element method as well as the singular integral calculation in the boundary element method. More importantly, it can be seamlessly connected with the computer-aided design system for the subsequent treatment by engineers. Three numerical examples are provided to illustrate the accuracy and effectiveness of the proposed isogeometric method. This work provides a simple and effective way for the structural optimization design of sound barriers.

A general integration kernel formulation for immersed boundary method

This study proposes a new robust and accurate immersed boundary method for the immersion of solid bodies within a fluid with a Cartesian grid. The present method introduces the signed distance fields to recognize the immersed geometry contours, eliminating the need of Lagrangian points. To fully maximize the advantages offered by signed distance fields, a general integration kernel formulation is introduced into the direct forcing method to replace the conventional regularized delta function. With the combination of signed distance fields and kernel function, an interpolation along the radial direction instead of three-dimensional directions is feasible, which further reduces the extra calculation cost involved by immersed boundary method. The numerical results at low Reynolds numbers are compared to experimental and previous numerical results, which shows the efficiency and accuracy of this new method. Upon thorough validation, the proposed method in this paper demonstrates excellent performance across various scenarios, including static and moving cases as well as two- and three-dimensional configurations. And our method greatly reduces the cost of pretreatment of immersed geometry contours and apparently improves the convenience of the method.