Two-dimensional Numerical Model Research Articles

Two-phase flow characteristic and gas removal strategy of the paper-based microfluidic fuel cell

Paper-based microfluidic fuel cell powered by capillary force has the advantages of compactness, low cost, and high sensitivity, presenting broad application prospects in portable electronic devices. However, the gas-liquid mass transfer mechanism within the porous medium remains unclear, with a lack of two-phase flow theories adapted to the unique paper-based system. In this study, a two-dimensional two-phase numerical model of a Y-shaped paper-based microfluidic fuel cell is developed to reveal the two-phase flow characteristics under capillary action and explore gas removal strategies. The reliability of the model is validated by real experimental data. By coupling multiple physical fields, the study elucidates the working principle and gas-liquid flow phenomena within the cell. Then, the effects of contact angle, inlet fuel concentration, and paper type on output performance, gas distribution, parasitic effect, and fuel utilization are discussed. The results indicate that increasing the contact angle and using paper with a larger average pore size and porosity as the channel substrate are ideal for promoting gas discharge. The optimal gas removal rate reached 42.30 %, with a favorable power density of 33.92 mW/cm2. This study provides a theoretical basis for a deeper understanding of the two-phase mass transfer process in paper-based microfluidic fuel cell.

Exploring time-series transformers for spatio-temporal prediction of microstructural evolution of polycrystalline grain

This study introduces a novel microstructure prediction model (polycrystalline grain transformers: PGTs) for metal solidification processes, leveraging the capabilities of transformer networks. The model’s primary purpose is to predict the dynamic evolution of polycrystalline microstructures within additive manufacturing conditions. To facilitate the training of the PGTs model, we generated a comprehensive dataset through a two-dimensional multi-phase field numerical simulation model. The inherent strength of transformer networks lie in its multi-head attention mechanism, which enables the PGTs model to autonomously identify crucial feature information within the input sequence, particularly related to structural evolution. Our research outcomes underscore the robustness of the PGTs model, as it closely aligns with predictions obtained from conventional phase-field calculations. Importantly, this model exhibits a remarkable improvement in computational efficiency, surpassing traditional phase-field methods by several orders of magnitude. This breakthrough opens up new avenues for research, offering an efficient and cost-effective strategy for delving deep into the intricate relationship between solidification processes and material mechanical properties. Notably, we mark this study as the pioneering application of transformer networks in numerical simulations of the metal solidification process, showcasing its immense potential across various domains, including material design.

Research on Macroscopic Mechanical Behavior of Recycled Aggregate Concrete Based on Mesoscale.

Recycled concrete is a heterogeneous composite material, and the composition and volume fraction of each phase affect its macroscopic properties. In this paper, ANSYS APDL was used to construct a two-dimensional numerical model of recycled aggregate concrete with different replacement rates of recycled aggregate (0%, 25%, 50%, 75% and 100%), and a uniaxial compression test was carried out to explore the relationship between recycled aggregate content and its macroscopic mechanical behavior. On this basis, the numerical simulation of different strain rates (0.1 s-1, 0.05 s-1, 0.01 s-1, 0.005 s-1 and 0.001 s-1) was carried out. It was found that with the increase in the recycled aggregate replacement rate, the peak stress decreases first and then increases, and the peak strain increases continuously. When the replacement rate of recycled aggregate exceeds 50%, the overall damage area of the material increases rapidly. The strain rate will change the path of the micro-crack initiation and expansion of recycled concrete, as well as the process of damage accumulation and evolution. As a result, the unit area and shape of recycled concrete are different at different strain rates, and the damage degree of each phase material is also different.

Simulating sea level extremes from synthetic low-pressure systems

Abstract. In this article we present a method for numerical simulations of extreme sea levels using synthetic low-pressure systems as atmospheric forcing. Our simulations can be considered to be estimates of the high sea levels that may be reached when a low-pressure system of high intensity and optimal track passes the studied region. We test the method using sites located along the Baltic Sea coast and simulate synthetic cyclones with various tracks. To model the effects of the cyclone properties on sea level, we simulate internal Baltic Sea water level variations with a numerical two-dimensional hydrodynamic model, forced by an ensemble of time-dependent wind and air-pressure fields from synthetic cyclones. The storm surges caused by the synthetic cyclones come on top of the mean water level of the Baltic Sea, for which we used a fixed upper estimate of 100 cm. We find high extremes in the northern Bothnian Bay and in the eastern Gulf of Finland, where the sea level extreme due to the synthetic cyclone reaches up to 3.5 m. In the event that the mean water level of the Baltic Sea has a maximal value (1 m) during the cyclone, the highest sea levels of 4.5 m could thus be reached. We find our method to be suitable for use in further studies of sea level extremes.

Modeling Density Waves and Circulations in Vertical Cross-Section in Adhesive Contacts

This work continues the study of the process of friction between a steel spherical indenter and a soft elastic elastomer previously published in our paper. It is done in the context of our previous experimental results obtained on systems with strongly pronounced adhesive interaction between the surfaces of contacting bodies during the process of friction between a steel spherical indenter and a soft elastic elastomer. In the present paper, we concentrate on the theoretical study of the processes developing in a vertical cross-section of the system. For continuity, here the case of indenter motion at a low speed at different indentation depths is considered as before. The analysis of the evolution of normal and tangential contact forces, mean normal pressure, tangential stresses, as well as the size of the contact area is performed. Despite its relative simplicity, a numerical two-dimensional (2D = 1 + 1) model, which is used here, satisfactorily reproduces experimentally observed effects. Furthermore, it allows direct visualization of the motion in the vertical cross-section of the system, which is currently invisible experimentally. Partially, it recalls two-dimensional (2D = 1 + 1) models recently proposed to describe the “turbulent” shear flow of solids under torsion and in cellular materials. The observations extracted from the model help us to understand better the adhesive processes that underlie the experimental results.

Towards the understanding of convective dissolution in confined porous media: thin bead pack experiments, two-dimensional direct numerical simulations and physical models

We consider the process of convective dissolution in a homogeneous and isotropic porous medium. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is thus driven by a Rayleigh–Taylor instability at the pore scale. We investigate the flow at the scale of the pores using Hele-Shaw type experiment with bead packs, two-dimensional direct numerical simulations and physical models. Experiments and simulations have been specifically designed to mimic the same flow conditions, namely matching porosities, high Schmidt numbers and linear dependency of fluid density with solute concentration. In addition, the solid obstacles of the medium are impermeable to fluid and solute. We characterise the evolution of the flow via the mixing length, which quantifies the extension of the mixing region and grows linearly in time. The flow structure, analysed via the centreline mean wavelength, is observed to grow in agreement with theoretical predictions. Finally, we analyse the dissolution dynamics of the system, quantified through the mean scalar dissipation, and three mixing regimes are observed. Initially, the evolution is controlled by diffusion, which produces solute mixing across the initial horizontal interface. Then, when the interfacial diffusive layer is sufficiently thick, it becomes unstable, forming finger-like structures and driving the system into a convection-dominated phase. Finally, when the fingers have grown sufficiently to touch the horizontal boundaries of the domain, the mixing reduces dramatically due to the absence of fresh unmixed fluid. With the aid of simple physical models, we explain the physics of the results obtained numerically and experimentally. The solute evolution presents a self-similar behaviour, and it is controlled by different length scales in each stage of the mixing process, namely the length scale of diffusion, the pore size and the domain height.

The impact of aerosols as ice nucleating particle on microphysics and electrification in the cumulus model

Here, a heterogeneous ice nucleation parameterization associated with aerosol acting as ice nucleating particle (INP) was implanted into a two-dimensional numerical cumulus model. To explore the impact of INP on microphysical and electrical processes, a comparison was conducted with the original approach, which employs an empirical formula. Simulation results indicate that INP greatly impacted microphysical evolution in the heterogeneous ice nucleation process, reducing total liquid precipitation amounts and causing a slight precipitation delay, as well as increasing the diameter and mixing ratio of ice crystals and the expansion of the vertical distribution of ice crystals. This led to a notable change in electrification in thunderstorms. The increase of ice crystal diameter was the dominant contributor to the enhancement of electrification using the new parameterization. Additionally, unlike the structure of thunderclouds in a mature stage, which always retains a normal dipole structure adopting the empirical formula, a tripole structure developed a lower positive charge, and the polarity inversion with upper negative and lower positive charges occurred when the new parameterization was adopted. This predominately was the result of abundant ice crystals present below the reversal temperature. The electrification characteristics of thunderstorms may have a close connection with lightning activity. It has been found that charge structure changed significantly in the two cases, with the tripolar charge structure facilitating the production of inverted intra-cloud (IC) flashes and negative Cloud-to-ground (CG) flashes simulated by the new parameterization; additionally, clouds simulated using the empirical formula may be able to develop normal IC lightning and positive CG flashes. Therefore, it will be very meaningful to obtain greater insight into the characteristics of thunderstorms electrification in cumulus model with aerosols.

Influence and Mechanism of the Excavation Width on Excavation Deformations in Shanghai Soft Clay

This study investigated the influence and mechanism of the excavation width on excavation deformations in Shanghai soft clay. Based on three excavations that had different final excavation depths, dissimilar retaining structures and diverse geological conditions, 40 sets of two-dimensional numerical models with different excavation widths were employed to analyze the deformation rules affected by the excavation width. Moreover, a series of simplified models with different excavation widths were employed to analyze the effect of the excavation width on excavation deformations. The results show that under the same excavation depth, both the horizontal displacements of the retaining walls and ground surface settlements increase as the excavation width increases, but the increasing rate gradually decreases. Factors such as the unloading influence depth, the overlap degree of the passive zones, the stress state of the basal soils and the development of the relative shear stress have a significant influence on excavation deformations. With increasing excavation width, the unloading influence depth gradually deepens, the overlap area of the passive zones gradually decreases, the direction of the rotation of the major principal stress gradually reduces and the relative shear stress of the distant and deep soils gradually expands. Therefore, the constraint ability of the passive zones on excavation deformation gradually reduces and excavation deformations gradually increase.

Harbor Sedimentation Management Using Numerical Modeling and Exploratory Data Analysis

Sedimentation in the harbors’ basins is an environmental phenomenon that frequently disrupts safe shipping and necessitates costly dredging operations. The layout of harbors and the permeability of protective structures such as breakwaters influence sediment transport within harbor basins. Thus, through a multistep framework, this study investigates the sedimentation management issues for the Egyptian proposed Ezbet Elborg fishing harbor based on field measurements and a numerical morphodynamic coastal modeling system (CMS). First, field measurements were analyzed and evaluated for acquiring a full grasp of the research area’s bathymetry and hydrodynamics. Second, a two-dimensional (2D) numerical simulation CMS model was set up and calibrated against field measurements wherein the developed CMS model highly correlated with actual measurements by 97%. CMS results demonstrate that the predominant NNW wave with the formed longshore current on both the harbor’s sides affects sediment accumulation within the harbor’s basin. Third, 100 simulations for the proposed harbor including different structural modulation scenarios affecting the sedimentation issue were investigated via the calibrated CMS model. Finally, an exploratory data analysis (EDA) is performed via correlation matrix and ANOVA test for the CMS’s scenarios’ results to gain an in-depth view of the relation between the harbors’ layout and the structural characteristics with the sedimentation volumes. Results showed that breakwaters’ orientation affects sediment accumulation more than its length. Also, breakwater permeability and basin width are significantly affecting sediment accumulation. Ultimately, the current study makes a substantial contribution to integrated coastal structure management (ICSM) by helping coastal stakeholders to mitigate the negative impacts of the harbors’ sediment deposition aiming at sustaining both environmental and economic aspects.

Study on the Interaction Propagation Mechanism of Inter-Cluster Fractures under Different Fracturing Sequences

Horizontal-well multi-cluster fracturing is one of the most important techniques for increasing the recovery rate in unconventional oil and gas reservoir development. However, under the influence of complex induced stress fields, the mechanism of interaction and propagation of fractures within each segment remains unclear. In this study, based on rock fracture criteria, combined with the boundary element displacement discontinuity method, a two-dimensional numerical simulation model of hydraulic fracturing crack propagation in a planar plane was established. Using this model, the interaction and propagation process of inter-cluster fractures under different fracturing sequences within horizontal well segments and the mechanism of induced stress field effects were analyzed. The influence mechanism of cluster spacing, fracture design length, and fracture internal pressure on the propagation morphology of inter-cluster fractures was also investigated. The research results indicate that, when using the alternating fracturing method, it is advisable to appropriately increase the cluster spacing to weaken the inhibitory effect of induced stress around the fractures created by prior fracturing on subsequent fracturing. Compared to the alternating fracturing method, the propagation morphology of fractures under the symmetrical fracturing method is more complex. At smaller cluster spacing, fractures created by prior fracturing are more susceptible to being captured by fractures from subsequent fracturing. The findings of this study provide reliable theoretical support for the optimization design of fracturing sequences and fracturing processes in horizontal well segments.

Generation of diurnal internal solitary waves (ISW-D) in the Sulu Sea: From geostationary orbit satellites and numerical simulations

Our recent study reported the existence of internal solitary waves with the diurnal tidal cycle (ISW-D) in the Sulu Sea, however, the three-dimensional characteristics and generation mechanism of ISW-D are still unclear (Huang et al., 2023). In this work, the spatial–temporal characteristics, generation mechanism and propagating process of ISW-D in the Sulu Sea are first preliminary investigated based on high-temporal-resolution Geostationary Orbiting Satellite (GOS) images and high-spatial-resolution two-dimensional numerical model (MITgcm). GOS images from 2018-2022 are retrieved and a total of 13 pairs of ISW-D packets are found. ISW-D occur at spring tide during May–August, with an average interpacket distance of 198 km and a phase speed of 2.30 m/s. To further knowledge of the generation mechanism and propagation process of ISW-D, the non-linear and non-hydrostatic numerical simulations are conducted. The comparison of ISW-D parameters with GOS images proves the validity of numerical simulations. The results of numerical simulations and theoretical parameters indicate that ISW-D are generated at the sill near Pearl Bank by internal tide release mechanism. Moreover, three sensitivity experiments are designed to investigate the effects of tidal force and seawater stratification on the generation and propagation of ISW-D. The results reveal that the ISW-D is generated by diurnal tides with stronger intensity than semidiurnal tides. Seawater stratification does not influence the generation of ISW-D but modulates the propagation process. Phase speeds from GOS images and theoretical model show a positive correlation between the phase speeds of ISW-D and the intensity of seawater stratification.

Numerical study on dynamic flow of flexible extension nozzle in rocket motors

The use of extension nozzles in rocket propulsion systems is one of the effective methods to increase the geometric expansion ratio and thrust of the nozzle. As a new type of extension nozzle, the flexible extension nozzle can achieve continuous changes in nozzle expansion ratio. To explore the characteristics of the flow field structure at the “bulge” structure and the step structure in the actual configuration of the flexible extension nozzle, and the impact on the performance of the nozzle, a three-dimensional numerical simulation model of the flexible extension nozzle was first established to study the flow field at the “bulge” structure, and then a two-dimensional unsteady numerical simulation model was established by using the coupling technology of dynamic grid and overlapping grid to study the flow field at the step structure. The results show that during the unfolding of the nozzle surface, a complex flow structure of “expansion fan-mixing layer-shock-vortex” were formed in the step area at the junction of the fixed section and the moving extension section. The specific impulse loss of the 3D model is larger than that of the 2D model due to the consideration of the “bulge” structure. The flow loss of the “bulge” structure and the step structure to the nozzle is 0.73% and 0.65% respectively.

Effect of sintering on stress distribution of thermal barrier coatings for high temperature blade

In the process of long-term high temperature service, thermal barrier coatings (TBCs) will inevitably be sintered, leading to pores healing and porosity decline, which will affect the microstructure and the stability of mechanical properties of TBCs. To understand the relationship between the microstructural changes of sintered TBCs and the mechanical properties, in this work, the cross-sectional microstructure of TBCs at different sintering times were investigated by scanning electron microscopy (SEM). After calculating the porosity and pore size distribution, two-dimensional (2D) numerical models were developed for five different porosities (16 %–12 %) by an improved reconstruction method with layer-by-layer labeling. Based on the results of finite element (FE) analysis after thermal cycling, it was found that the coating's irregular pore structures lead to stress concentration, which affects the mechanical properties of the coating to a great extent. For the whole TC layer, the level of stresses increases and the absolute value of maximum stress augments significantly by 46 % associated with the doubled increase of stress concentration areas with the densification of coating. For the local areas of TC layer, the changes in pore morphology led to a more complex variation in local stress fields. At the TC/BC interface, the Mises stress level tends to increase with decreasing porosity during sintering. At the TC surface, coatings with lower porosities cause higher stresses near this region. The insights gained from the numerical results contribute to a better understanding of the failure behavior of real TBCs systems and help to further remedy the deficiencies and difficulties of the experimental work.

Simulation of regular wave impact on beam-plate structure on a slope

In order to study the peculiarities of wave slamming on beam-plate structures on a slope, two-dimensional numerical models of regular waves have been developed on the basis of the FLUENT software. Firstly, the validity of the numerical wave flume was verified. Then, with plentiful simulations, the parametric studies were performed for different wave steepness, structure geometry, and the distance between the underside of the horizontal plate and the still water level. The effects of the three parameters on the impact pressure and vertical velocities were investigated. Lastly, the statistical relationship between the waves’ impact pressures and the corresponding flow velocities was investigated. The results had a certain significance to the further understanding of the mechanism of the impact of the waves.

Numerical Simulation on the Two-Degree-of-Freedom Flow-Induced Vibration of a Submerged Floating Tunnel under Current

The submerged floating tunnel (SFT) is a novel form of transportation infrastructure for crossing deeper and wider seas. One of the primary challenges in designing SFTs is understanding their hydrodynamic response to complex environmental loads. In order to investigate the two-degree-of-freedom (2-DOF) flow-induced vibration (FIV) response of SFTs under current, a two-dimensional (2D) numerical model was developed using the Reynolds-averaged Navier–Stokes (RANS) method combined with the fourth-order Runge–Kutta method. The numerical results were validated by comparing them with the existing literature. The study then addressed the effects of coupled vibration and structural parameters, i.e., the mass ratio and natural frequency ratio, on the response and wake pattern of SFTs, numerically. The results indicated that coupled vibration had a significant impact on the SFT response at reduced velocities of Urwx ≥ 4.4. A decrease in mass ratio (m* < 1) notably amplified the 2-DOF vibration amplitudes of SFTs at Urwx ≥ 4.4, particularly for in-line vibration. Similarly, a decrease in natural frequency ratio (Rf < 1) significantly suppressed the in-line vibration of SFTs at Urwx ≥ 2.5. Therefore, for the design of SFTs, careful consideration should be given to the effect of mass ratio and natural frequency ratio on in-line vibration.

Numerical simulation and experimental validation on the mechanism of crater evolution in electrical discharge micromachining

The plasma-material interaction and evolution mechanism of a solitary crater governs the nature of the surface, either plain or textured, created through the electrical discharge micromachining (EDMM) process. Therefore, it is indispensable to understand the fundamentals of a single crater evolution, which involves melt pool hydrodynamics and material vaporization under intense plasma pressure. The plasma pressure during the workpiece heating phase alters the vaporization phenomenon and melt ejection, warranting an in-depth understanding. In light of this, the current work proposes a two-dimensional (2-D) multiphysics numerical model of the melt pool hydrodynamics during EDMM. The model incorporates thermal evolution along with the effects of active plasma pressure during the heating phase of the substrate with the help of a coupled thermo-fluidic model. The simulation results reveal the predominant role of plasma pressure on the crater morphology evolution, plasma flushing efficiency (PFE) and recast layer thickness (RLT). The predicted single crater profile is validated using single-spark experiments with reasonable agreement. Thereafter, the formation mechanism of a single crater has been extended to multi-crater creation for textured surface generation.

Impact of Wellbore Cross-Sectional Elongation on the Hydraulic Fracturing Breakdown Pressure and Fracture Initiation Direction

Investigation of breakdown pressure in wellbores in complex conditions is of great importance, both in fracture design and in wellbore log interpretation for in situ stress estimation. In this research, using a two-dimensional numerical model, the breakdown pressure is determined in ellipsoidal and breakout wellbores. To find the breakdown pressure, the mixed criterion is used, in which the toughness and the tensile strength criteria must be satisfied concurrently. In breakout boreholes, the breakdown pressure is lower than the circular wellbores; indeed, the ratio of the breakdown pressure of the breakout wellbore to the breakdown pressure in the circular wellbore is between 1 and 0.04, depending on the deviatoric stress and the width and depth of the breakout zone. In breakout wellbores, the fracture initiation position depends on the deviatoric stress. In small deviatoric stresses, the fracture initiation position is aligned with the minimum in situ stress, unlike circular boreholes; and in large deviatoric stresses, the fracture initiates in the direction of the major principal stress. In large wellbores, the breakdown pressure is controlled by the tensile strength of the rock; and in small wellbores, the breakdown pressure is under the control of the energy spent to create new crack surfaces.

Data-driven hydraulic property analysis and prediction of two-dimensional random fracture networks

The large parameter space and uncertainty of the discrete fracture networks (DFNs) make the hydraulic characteristics have multiple possibilities. Statistical analysis of hydraulic characteristics based on a large amount of data is a standard practice and central to DFN methodology. The present study developed a two-dimensional (2D) DFN numerical seepage model based on Matlab and Comsol from modeling and parameter calculation to simulation to investigate the influence of parameters involved fracture network on seepage characteristics of DFNs. In total, 1728 2D DFN models were generated with increasing fracture density, fracture length, power-law exponent, fracture orientations, and fracture included angles, and 1728 × 3 = 5184 numerical simulations of fluid flow along the x-axis, y-axis, and center through the DFN models are conducted using a self-developed numerical code. The influence of fracture geometric features on connectivity and permeability are estimated, respectively. And to realize the prediction of permeability tensor by known geological data, a theoretical model based on the Snow model and a data mining model based on the back-propagation model are discussed. The analysis helps researchers and engineers can make informed decisions and develop effective strategies for addressing the challenges posed by uncertainty hydraulic property of the fractured rock masses.

Comprehensive numerical modeling of intermittent flow cooling with enhanced photovoltaic efficiency in PVT/NPCM systems

The photoelectric conversion efficiency of photovoltaic thermal (PVT) systems is a key concern in solar energy research. The widespread use of continuous nanofluid cooling in PVT/NPCM (Nano-Enhanced Phase Change Material) systems leads to heightened energy consumption. In order to improve efficiency of the PVT/NPCM systems, a two-dimensional transient heat transfer numerical model is established to analyze the PVT/NPCM system with intermittent flow cooling. Corresponding govern equations with boundary conditions are proposed, and numerically solved by using the finite element method. Simulation results are compared with experimental data, showing a deviation of less than 7 %. The findings indicate that the intermittent cooling reduces the flow energy consumption required to drive 2220 L of nanofluid compared to continuous cooling over a 7-h period. Furthermore, under intermittent cooling conditions, the average electrical efficiency stands at approximately 19.7 %. Notably, the electrical efficiency of PVT/NPCM systems employing intermittent flow cooling closely aligns with those employing continuous flow cooling, exhibiting a maximum deviation of merely 0.0348 %. Additionally, intermittent flow cooling emerges as a favorable choice under solar radiation intensities surpasses 1000W/m2, enabling a significant reduction in overall energy consumption while maintaining commendable cooling performance.

Research on the blockage effect in a shock tube

The shock tube is a crucial experimental apparatus in the field of explosive impact. Limited research has been conducted on the visualization of the internal flow field in shock tubes under blockage conditions, and there is a lack of comprehensive understanding of the mechanisms behind blockage effects. This paper presents experimental and numerical investigations into the propagation of shock waves inside a shock tube and their interaction with obstructive elements. Blockage effect experiments were conducted on a shock tube test platform, where pressure data were obtained through a pressure monitoring system. Additionally, schlieren imaging technology was employed to visualize the evolution of shock wave fronts. A two-dimensional numerical model of the shock tube was established using Fluent software, and the computed results exhibited excellent agreement with the experimental data, confirming the accuracy of the numerical model. The mechanism of the blockage effect was revealed through analysis of pressure-time curves and images depicting the evolution of shock wave fronts. Furthermore, adjustments to parameters on the validated numerical model allowed for analysis and comparison of different blockage ratios. The results indicate that the disturbance to the flow field caused by the blockage effect is primarily due to the reflection of shock waves between the front surface of the obstructive element and the shock tube wall. This reflection leads to differences in pressure curves compared to free-field conditions, and such differences increase with higher blockage ratios.