Boundary Method Research Articles

Phase-field electrochemical simulations of reconstructed graphite electrodes

Graphite currently serves as the most predominant anode material in lithium-ion batteries due to its favorable balance of energy density, material cost, and relative safety in operations. While graphite anodes are manufactured mainly by randomly packing graphite particles, there is an avenue to improve the anode performance through optimized electrode microstructure. This is especially crucial for fast charging/discharging operations, where lithium plating is exaggerated and poses a critical safety concern. Therefore, the capability to investigate detailed electrochemical processes in electrode microstructures is essential for graphite anode designs. In this work, we incorporate the Cahn–Hilliard phase-field equation into a smoothed boundary method electrochemical simulation framework to account for phase transformations in graphite electrode complex microstructures upon lithiation/delithiation. These simulations quantitatively demonstrate that (i) modeling phase-separating graphite as a Li solid-solution material will overestimate graphite electrodes’ performance, (ii) particle size determines the electrode performance, (iii) pore tortuosity is important to enhance electrodes’ performance noticeably for thick electrodes, and (iv) introducing tunnels can spread insertion reaction more uniformly throughout the electrodes. Moreover, a substantial portion of this work focuses on simulating the behavior of thick electrodes. Thick electrode design holds a promising opportunity to increase overall energy density and our model enables computational predictions for such electrodes in an easy manner without conducting physical experiments. Thus, the presented simulation framework offers a fast and robust tool for designing electrode microstructures and operation protocols on digitally represented complex electrode microstructures. This approach has the potential to advance the electrode design of lithium-ion batteries.

Particle resolved direct numerical simulations for heat transfer analysis of a spouted bed

In this paper, fully coupled particle resolved direct numerical simulations are used for heat transfer calculations. For modelling fluid velocity and temperature, the immersed boundary method (IBM) is used. Particle-particle heat transfer is modelled using well-established relations from the literature. Two-way coupling between particles and fluid is obtained using a body force that is a function of the solid volume fraction present in the fluid grid cell. Results are compared with those of spouted bed experiments to validate the simulations, and good agreement is observed. At the end of the paper, several interesting characteristics of spouted bed are obtained using simulations. The speedup of the method used for simulations was tested on multi-core CPU clusters. It is observed that the simulations scales almost linearly with the number of CPUs (tests were done up to 500 CPUs), showing the capability of the particle resolved DNS to be used on multi-CPU architectures.

Numerical investigation and optimization on dynamic power generation performance of enhanced geothermal system

The Enhanced geothermal system (EGS) is a crucial technology for the development and utilization of hot dry rock (HDR). However, current research typically overlooks the strong coupling characteristics of fracture seepage, wellbore transport, and thermoelectric conversion, leading to a lack of precision in describing the dynamic operational performance of EGS throughout its entire lifecycle. A dynamic numerical model of evaporator and condenser is established by the moving boundary (MB) method. Subsequently, the dynamic power generation process is integrated with a coupled thermal-hydraulic-mechanical (THM) model of the fractured reservoir, proposing a methodology for calculating the dynamic performance of EGS throughout its lifecycle.Traditional EGS models exhibit significant deviations between calculated results and actual performance due to the neglect of instantaneous changes in injection temperature and the failure to consider the nonlinear characteristics of heat exchangers. The production pressure difference is a primary factor influencing the net output power of EGS. Therefore, selecting an appropriate injection pressure is crucial to ensuring continuous power generation throughout the EGS lifecycle. By optimizing the operating parameters of the actual EGS project, the optimal injection flow rate, fracture aperture, initial fracture permeability and well spacing are 50 kg/s, 0.03 m, 1.5 × 10−10 m2 and 350 m respectively.

Direct Numerical Simulation of Transitional and Turbulent Flows Over Multi-Scale Surface Roughness—Part II: The Effect of Roughness on the Performance of a High-Pressure Turbine Blade

Abstract Turbine blades generally present surface roughness introduced in the manufacturing process or caused by in-service degradation, which can have a significant impact on aero-thermal performance. A better understanding of the fundamental physical mechanisms arising from the interaction between the roughness and the turbine flow at engine-relevant conditions can provide insights for the design of blades with improved efficiency and longer operational life. To this end, a high-fidelity numerical framework combining a well-validated solver for direct numerical simulation and a second-order accurate immersed boundary method is employed to predict roughness-induced aero-thermal effects on an LS89 high-pressure turbine (HPT) blade at engine-relevant conditions. Different amplitudes and distributions of surface roughness are investigated and a reference smooth-blade simulation under the same flow conditions is conducted for comparison. Roughness of increasing amplitude progressively shifts the blade suction side boundary layer transition upstream, producing larger values of the turbulent kinetic energy and higher total wake losses. The on-surface data-capturing capabilities of the numerical framework provide direct measurements of the heat flux and the skin friction coefficient, hence offering quantitative information between the surface topology and engineering-relevant performance parameters. This work may provide a benchmark for future numerical studies of turbomachinery flows with roughness.

Direct Numerical Simulation of Transitional and Turbulent Flows Over Multi-Scale Surface Roughness—Part I: Methodology and Challenges

Abstract High-fidelity simulation of transitional and turbulent flows over multi-scale surface roughness presents several challenges. For instance, the complex and irregular geometrical nature of surface roughness makes it impractical to employ conforming structured grids, commonly adopted in large-scale numerical simulations due to their high computational efficiency. One possible solution to overcome this problem is offered by immersed boundary methods, which allow wall boundary conditions to be enforced on grids that do not conform to the geometry of the solid boundary. To this end, a three-dimensional, second-order accurate boundary data immersion method (BDIM) is adopted. A novel mapping algorithm that can be applied to general three-dimensional surfaces is presented, together with a newly developed data-capturing methodology to extract and analyze on-surface flow quantities of interest. A rigorous procedure to compute gradient quantities such as the wall shear stress and the heat flux on complex non-conforming geometries is also introduced. The new framework is validated by performing a direct numerical simulation (DNS) of fully developed turbulent channel flow over sinusoidal egg-carton roughness in a minimal-span domain. For this canonical case, the averaged streamwise velocity profiles are compared against results from the literature obtained with a body-fitted grid. General guidelines on the BDIM resolution requirements for multi-scale roughness simulation are given. Momentum and energy balance methods are used to validate the calculation of the overall skin friction and heat transfer at the wall. The BDIM is then employed to investigate the effect of irregular homogeneous surface roughness on the performance of an LS-89 high-pressure turbine blade at engine-relevant conditions using DNS. This is the first application of the BDIM to realize multi-scale roughness for transitional flow in transonic conditions in the context of high-pressure turbines. The methodology adopted to generate the desired roughness distribution and to apply it to the reference blade geometry is introduced. The results are compared to the case of an equivalent smooth blade.

A time-varying boundary method for multimodal vibration suppression of beam

A time-varying boundary method for multimodal vibration suppression of beam

Flow-induced vibrations of ten tandem cylinders at low Reynolds number

Flow-induced vibrations of ten cylinders in tandem arrangement are numerically investigated by using the immersed boundary method with a low Reynolds number (Re = 100). Seven spacing ratios L/D (where L = center–center spacing between tandem cylinders and D = diameter of the cylinder) are selected from 1.1 to 4.0, and the reduced velocity Ur ranges from 2.0 to 13.5 with an increment of 0.5. Small (L/D < 2.0) and large (L/D > 2.0) spacing ranges are identified, both including two types of responses: wake-induced vibration (WIV; Ur = 2.0–9.0∼10.5 for a small L/D and Ur = 2.0–6.0∼6.5 for a large L/D) and wake-induced galloping (WIG; Ur > 9.0∼10.5 for a small L/D and Ur > 6.0∼6.5 for a large L/D). The largest vibration amplitude of each cylinder is obtained in the WIG region for the small L/D condition. The presence of downstream cylinders suppresses the vortex shedding of upstream cylinders and thus postpones the vibration of upstream cylinders at a small Ur, whereas the downstream cylinder enhances the vibration at a larger Ur due to the wake interference. For a small L/D, three flow regimes with the extended-body, reattachment, and co-shedding patterns are successively presented as Ur increases. For a large L/D, four types of flow regimes, namely, EB-2S (the extended-body with “2S” pattern), RT-2S (the reattachment with “2S” pattern), TR-2S (two-row vortex street with “2S” pattern), and CS-VS (co-shedding with variation shedding), are classified. Two new vortex shedding patterns, “2G (two counter-rotating vortices shed from each side per vibration cycle)” and “2C (two co-rotating vortices shed from each side per vibration cycle),” have been identified. In the WIV region, there is only one dominant vibration frequency for upstream cylinders (C1–C7), while a sub-harmonic frequency emerges and dominates C8–C10 when L/D is large. The fluctuating lift force spectra show a broad-band frequency distribution due to the irregular positions of the vortex generation and merging, and the dominant frequency in the WIG region decreases consecutively from C1 to C10.

A combined volume penalization/selective frequency damping approach for immersed boundary methods: Application to moving geometries

High-order numerical techniques and immersed boundary methods (IBMs) are gaining popularity to avoid constructing body-fitted meshes while accurately resolving complex flows on Cartesian grids. Recently, we have presented a new treatment for the immersed boundary method based on the combination of volume penalization and selective frequency damping (SFD) [J. Kou and E. Ferrer, “A combined volume penalization/selective frequency damping approach for immersed boundary methods applied to high-order schemes,” J. Comput. Phys. 472, 111678 (2023).], that offers improved accuracy for nonmoving geometries. The objective of SFD is to remove nonphysical, high-frequency oscillations inside the solid body and by doing so enhance the accuracy in the fluid region. The present paper extends the new immersed boundary treatment to moving geometries. The convergence of this approach is first validated by the method of manufactured solutions, where we design a one-dimensional advection–diffusion case, with a moving interface, to validate the numerical accuracy. Second, we simulate an unsteady flow past a plunging circular cylinder (Navier–Stokes solver). In this case, we show that the combination of volume penalization and SFD provides improved accuracy for moving geometries.

Cutoff wavenumber analysis of arbitrarily shaped waveguides using regularized method of fundamental solutions with excitation sources

AbstractThe method of fundamental solutions with excitation source (MFS‐ES) is a reliable method for determining the eigenvalues of a two‐dimensional hollow waveguide. However, the accuracy in MFS‐ES is extremely dependent on the choice of the auxiliary boundary. In this work, to avoid the problem, a regularized MFS‐ES (RMFS‐ES) is proposed. First, to overcome the shortcomings of MFS, a regularized method of fundamental Solutions (RMFS) is proposed by borrowing the ideas of singular boundary method (SBM) and single layer regularized meshless method (SRMM). Second, the expressions for the fundamental solutions at the singularities are given by utilizing the subtraction and adding‐back technique (SAB). Third, the excitation source method is introduced to overcome the problem that the RMFS may also have spurious frequencies. Finally, to improve the accuracy of RMFS‐ES in solving polygonal waveguide eigenvalue, a wedge scheme (WS) is given. Numerical results show that the meshless RMFS‐ES is a promising numerical method for waveguide eigenvalue problems.

Motion of a two-dimensional neutrally buoyant circular particle in two-sided lid-driven cavity flow with thermal convection

Understanding the interaction between a cold particle and confined fluid flow is of practical importance in many industrial applications. In this work, the motion of a two-dimensional circular neutrally buoyant particle in thermal flows in the two-sided lid-driven cavity has been numerically investigated by the lattice Boltzmann model with immersed boundary method. We examined the effects of Grashof number (Gr) and Reynolds number (Re) of cavity on the motion of particle in the range of 104 ≤ Gr ≤ 107 and 500 ≤ Re ≤ 3000. It is found that the motion of the cold particle in the cavity flow manifests four different modes, driven by the competition between buoyancy-driven natural convection and lid-driven forced convection. With the increase in Gr or the decrease in Re, the motion of the cold particle would evolve from modes I to IV. We further obtained the diagram of motion modes of the cold particle with regard to Gr and Re. And a power law correlation that relates the critical Gr to Re of the cavity is proposed and capable of well predicting the transition of particle motion modes.

Numerical study of owls' leading-edge serrations

Owls' silent flight is commonly attributed to their special wing morphology combined with wingbeat kinematics. One of these special morphological features is known as the leading-edge serrations: rigid miniature hook-like patterns found at the primaries of the wings' leading-edge. It has been hypothesized that leading-edge serrations function as a passive flow control mechanism, impacting the aerodynamic performance. To elucidate the flow physics associated with owls' leading-edge serrations, we investigate the flow-field characteristic around a barn owl wing with serrated leading-edge geometry positioned at 20° angle of attack for a Reynolds number of 40 000. We use direct numerical simulations, where the incompressible Navier–Stokes equations are solved on a Cartesian grid with sufficient resolution to resolve all the relevant flow scales, while the wing is represented using an immersed boundary method. We have simulated two wing planforms: with serrations and without. Our findings suggest that the serrations improve suction surface flow by promoting sustained flow reattachment via streamwise vorticity generation at the shear layer, prompting weaker reverse flow, thus augmenting stall resistance. Aerodynamic performance is negatively impacted due to the shear layer passing through the serration array, which results in altered surface pressure distribution over the upper surface. In addition, we found that serrations increase turbulence level in the downstream flow. Turbulent momentum transfer near the trailing edge increased due to the presence of serrations upstream the flow, which also influences the mechanisms associated with separation vortex formation and its subsequent development over the upper surface of the wing.

1-D Finite Element Artificial Boundary Method for Saturated Layered Half-Space Site Response under Obliquely Incident P-SV Waves

A novel finite element scheme is derived to evaluate the transient dynamic response of a multi-layered saturated porous half-space due to obliquely incident P or SV wave. The system consists of N − 1 layers with different thickness and properties that overlay on a saturated half-space from which the wave is input. Biot theory is utilized to describe the mechanism of saturated poroelastic media. In this method finite computational area is truncated from the infinite domain by a horizontal artifitial boundary introduced in the underlying half-space. Wave inputting effects and absorbing boundary condition at the bounday are derived. The spatial problem is then transformed approximatedly into a one-dimensional problem based on the Snell's law. The transient 1-D problem is descritized spacially by means of FEM and solved by the standard time intergration algorithm. Numerical examples show that the proposed 1-D finite element artificial boundary method can provide accurate results for seismic performance of saturated layerd half-space under obliquely incident waves with low values of permeability or frequency content. The method is applied in site response analysis of Hong Kong-Zhuhai-Macao immersed tunnel project. By comparison with the analytical solutions, it is demonstrated for geotechnic earthquake engineering problems, site response solutions with satisfactory accuracy can be achieved by the proposed method.

Fluid–structure interaction with a Finite Element–Immersed Boundary approach for compressible flows

This paper presents the mathematical modeling and numerical simulations of fluid–structure interaction (FSI) problems. The fluid domain is discretized using a Cartesian block-structured mesh and solved using the Finite Volume Method (FVM), using the LES methodology with Smagorinsky turbulent closure model. The fluid flow in the system is considered compressible, with properties that vary. The Immersed Boundary Method (IBM) is used to model the solid–fluid interface, and the structure deformation was solved using the Finite Element Method (FEM). The Multi-direct Forcing Scheme is used to calculate the fluid-dynamics forces through the IBM. After calculating the fluid forces exerted on the solid, the forces are interpolated and transferred to the FEM model, providing the deformation of the structure at each time step. The structural domain was discretized with Hexahedral eight-noded element with extra shape functions. The simulations were carried out using MFSIm (in-house code), a multiphysics simulation framework developed by the Fluid Mechanics Laboratory of the Federal University of Uberlândia with financial support from Petrobras. This paper demonstrates the practical application of FSI analysis in an industrial context, specifically focusing on a pipeline system within a Fluid Catalytic Cracking Unit (FCCU) used in the oil and gas industry. The analysis involves the use of butterfly valves positioned at different angles of opening. The results are treated statistically, and a surface response is generated. Machine learning is employed to predict the surface response, showing the valve configurations that yield the maximum and minimum displacement magnitudes of the evaluated structural probes.

NUMERICAL ANALYSIS AND DIFFUSER VANE SHAPE OPTIMIZATION OF A RADIAL COMPRESSOR WITH THE OPEN-SOURCE SOFTWARE SU2

In recent years, the usage of open-source computational fluid dynamics tools is on a rise both in industry and academia. SU2 is one of these open-source tools. Unlike other open-source alternatives, SU2 is equipped with boundary condition types, solvers and methods that are especially developed for the analysis and design of turbomachinery. The aim of this work is to explore and investigate the capabilities of SU2 in the prediction of performance parameters of radial compressors. Two different single stage shrouded compressor geometries, one with a vaneless diffuser and the other with a vaned diffuser have been investigated with steady state CFD. The compressors were designed by MAN Energy Solutions Schweiz AG. Computational results with SU2 showed a satisfactory agreement with both the experimental data and reference CFD solutions obtained with Fidelity Flow, which is formerly known as Numeca Fine TURBO. Only at the relatively higher mass flow rates the difference between references and SU2 were higher compared to other operating points. After performance parameters were successfully calculated with SU2, the optimization tools that come with SU2 were also used. A 2D adjoint optimization study on the vane of the vaned diffuser was carried out. The study was carried out at a single operating point that is close to choke conditions. The loss generated by the large separated flow region at the suction side of the diffuser vane was reduced by 0.55 % in the optimized geometry using minimal modifications on the existing vane geometry to keep the performance of the compressor intact at other operating points. However, the resulting modification increased the total pressure loss by 0.86 % at one of the design operating points. This performance penalty could be due to the discontinuity in the vane geometry generated by the optimizer. Overall, the study shows that SU2 has the basic numerical schemes and models that are required for the analysis of radial turbomachinery flows and geometry optimization.

Regularized singular boundary method for calculating wave forces on three-dimensional large offshore structure

How to quickly calculate the singularity of the special Green's function at origin has been a difficult problem that has plagued ocean dynamics for many years. This letter proposes a regularized singular boundary method (RSBM) based on the special Green's function and origin intensity factor (OIF) technique. The source points of the RSBM only need to be arranged on the boundary of the obstacle. By linearly combining the OIF of the modified Helmholtz equation and the OIF of the Helmholtz equation, an explicit OIF suitable for three-dimensional ocean dynamics is derived. The derived OIF does not contain singular integrals and is easy to use. The RSBM replaces the Green's function at origin with the OIF. Therefore, it is no longer necessary to reuse the integral form of Green's function as basis function at origin. The computational efficiency and accuracy have been significantly improved. Numerical experiments show that the RSBM can accurately calculate the wave forces on large three-dimensional offshore structure.

A Lithium Depletion Age for the Carina Association

The dispersed remnants of stellar nurseries, stellar associations, provide unparalleled samples of coeval stars critical for studies of stellar and planetary formation and evolution. The Carina Stellar Association is one of the closest stellar associations to Earth, and yet measurements of its age have varied from 13 to 45 Myr. We aim to update the age of Carina using the lithium depletion boundary (LDB) method. We obtain new measurements of the Li 6708 Å absorption feature in likely members using optical spectra from the Goodman High Throughput Spectrograph on SOAR and NRES on LCO. We detect the depletion boundary at M K ≃ 6.8 (M5). This age is consistent within uncertainties across six different models, including those that account for magnetic fields and spots. We also estimate the age through analysis of the group’s overall variability, and by comparing the association members’ color–magnitude diagram to stellar evolutionary models using a Gaussian Mixture Model, recovering ages consistent with the LDB. Combining these age measures we obtain an age for the Carina association of Myr. The resulting age agrees with the older end of previous age measurements and is consistent with the lithium depletion age for the neighboring Tucana-Horologium moving group.

Experimental and numerical investigation to elucidate the fluid flow through packed beds with structured particle packings

The present paper presents an experimental and numerical investigation of the dispersion of the gaseous jet flow and co-flow for the simple unit cell (SUC) and body-centred cubic (BCC) configuration of particles in packed beds. The experimental setup is built in such a way that suitable and simplified boundary conditions are imposed for the corresponding numerical framework, so the simulations can be done under very similar conditions as the experiments. Accordingly, a porous plate is used for the co-flow to achieve the uniform velocity and the fully developed flow is ensured for the jet flow. The SUC and BCC particle beds consist of 3D-printed spheres, and the non-isotropy near the walls is mostly eliminated by placing half-spheres at the channel walls. The flow velocities are analysed directly at the exit of the particle bed for both beds over 36 pores for the SUC configuration and 60 pores for the BCC configuration, for particle Reynolds numbers of 200, 300, and 400. Stereo particle image velocimetry is experimentally arranged in such a way that the velocities over the entire region at the exit of the packed bed are obtained instantaneously. The numerical method consists of a state-of-the-art immersed boundary method with adaptive mesh refinement. The paper presents the pore jet structure and velocity field exiting from each pore for the SUC and BCC packed particle beds. The numerical and experimental studies show a good agreement for the SUC configuration for all flow velocities. For the BCC configuration, some differences can be observed in the pore jet flow structure between the simulations and the experiments, but the general flow velocity distribution shows a good overall agreement. The axial velocity is generally higher for the pores located near the centre of the packed bed than for the pores near the wall. In addition, the axial velocities are observed to increase near the peripheral pores of the packed bed. This behaviour is predominant for the BCC configuration as compared to the SUC configuration. The velocities near the peripheral pores can become even higher than those at the central pores for the BCC configuration. It is shown that both the experiments as well as the simulations can be used to study the complex fluid structures inside a packed bed reactor.

An immersed boundary method‐discrete unified gas kinetic scheme simulation of particle‐laden turbulent channel flow on a nonuniform orthogonal mesh

AbstractParticle‐resolved simulations of turbulent particle‐laden flows provide a powerful research tool to explore detailed flow physics at all scales. However, efficient particle‐resolved simulations for wall‐bounded turbulent particle‐laden flows remain a challenging task. In this article, we develop a simulation approach for a turbulent channel flow laden with finite‐size particles on a nonuniform mesh by combining the discrete unified gas kinetic scheme (DUGKS) and the immersed boundary method (IBM). The standard discrete delta function was modified according to reproducible kernel particle method to take into account mesh non‐uniformity and correctly conserve force moments. Simulation results based on uniform and nonuniform meshes are compared to validate and examine the accuracy of the nonuniform mesh DUGKS‐IBM. Finally, the computational performance of the nonuniform mesh DUGKS‐IBM is discussed.

BiGlobal stability analysis for flow in complex geometry based on immersed boundary method

A numerical framework of global stability analysis based on the immersed boundary (IB) method is established for predicting the unsteadiness onset of flow system including complex geometry. The solid wall is considered as the boundary force term and the stability analysis is applied on the orthogonal Cartesian grid, which facilitate the application of spectral collocation method in the stability analysis. To convert the linearized N-S equation with source term to homogeneous, the boundary force can be viewed as an unknown quantity, and then the no-slip boundary condition is introduced into the governing equation to close the system. The method is first tested on two canonical cases, the flow past a stationary cylinder and an isolated airfoil. The relevant results are consistent with phenomena observed in the numerical calculations and experiments, verifying the effectiveness of the method. Applying the spectral collocation method contributes to the accuracy of stability analysis and reduces the grid nodes, making it more feasible to consider complex geometry. Then, to highlight the superiority of treating the flow system with complex geometry, such as including multi-objects, the method is applied to the stability analysis of the flow past a four-square-arranged cylinder cascade. The abundant instability perturbation modes induced by the interaction of multi-objects and the corresponding relationship with the whole system are captured, which is also verified by the unsteady calculation.

An improved slip‐wall model for large eddy simulation and its implementation in the local domain‐free discretization method

AbstractIn this paper, a slip‐wall model for large eddy simulation (LES) is improved and implemented in an immersed boundary method named the local domain‐free discretization (DFD) method. Considering that the matching location may be in the viscous sublayer, the physics‐based interpretation of a Robin‐type wall closure is complemented. Then, the slip‐wall wall model is improved, in which the slip length is redefined and the Robin boundary condition is imposed at the solid wall. The improved slip‐wall model is implemented in the local DFD method to evaluated the tangential velocity at an exterior dependent node, and then the requirement on high resolution of boundary layers can be alleviated. The non‐equilibrium effects are accounted for by adding an explicit correction to the wall shear stress. In order to validate the present wall‐modeled LES/DFD method, a series of turbulent channel flows at various Reynolds numbers, the flow over periodic hills and the flows over a NACA 4412 airfoil at a high Reynolds number are simulated. The predicted results agree well with the referenced experimental data and numerical results. Especially, the results of the separated flow over the airfoil at a near‐stall condition demonstrate the performance of the present wall‐modeled LES/DFD method for complex flows.