Three-dimensional Two-phase Flow Research Articles

Multivariate efficiency assessment and optimization of unitized regeneration proton exchange membrane fuel cell based CCHP system

Targeting the shortcomings of low round-trip efficiency (RTE) in unitized regeneration proton exchange membrane fuel cell (UR-PEMFC), a model incorporated combined cooling, heating, and power (CCHP) technology for UR-PEMFC was proposed, which integrated a three-dimensional two-phase flow field model with a zero-dimensional system model. Additionally, a multi-criterion evaluation system was introduced for the URFC-CCHP system, which encompasses three decision-making methods. To illustrate the applicability of the model, the assessments of four typical flow field configurations were utilized as case studies and presented their rankings. The results reveal that, compared to a system focused on electrical power output, the system exhibited a remarkable enhancement in RTE, increasing from 35.96 % to 76.67 %. Notably, during the cold season, the RTE surpassed that of the warm season by 8.74 %–10.62 %. Operating under a cyclic condition of fast charging and slow discharging proved to be conducive to maintaining the optimal RTE of the system. Furthermore, the computational outcomes of the three decision-making methods in the multi-criterion evaluation system exhibited consistency, unanimously identifying the optimal flow field as the three-serpentine flow field, while designating the single-serpentine flow field as the least favorable. It aims to present a novel technology for enhancing the RTE of UR-PEMFC.

Enhancing Oil–Water Flow Prediction in Heterogeneous Porous Media Using Machine Learning

The rapid and accurate forecasting of two-phase flow in porous media is a critical challenge in oil field development, exerting a substantial impact on optimization and decision-making processes. Although the Convolutional Long Short-Term Memory (ConvLSTM) network effectively captures spatiotemporal dynamics, its generalization in predicting complex engineering problems remains limited. Similarly, although the Fourier Neural Operator (FNO) demonstrates adeptness at learning operators for solving partial differential equations (PDEs), it struggles with three-dimensional, long-term prediction. In response to these limitations, we introduce an innovative hybrid model, the Convolutional Long Short-Term Memory-Fourier Neural Operator (CL-FNO), specifically designed for the long-term prediction of three-dimensional two-phase flows. This model integrates a 3D convolutional encoder–decoder structure to extract and generate hierarchical spatial features of the flow fields. It incorporates physical constraints to enhance the model’s forecasts with robustness through the infusion of prior knowledge. Additionally, a temporal function, constructed using gated memory-forgetting mechanisms, augments the model’s capacity to analyze time series data. The efficacy and practicality of the CL-FNO model are validated using a synthetic three-dimensional case study and application to an actual reservoir model.

Multiphase flow dynamics in metal foam proton exchange membrane fuel cell

Porous metal foam holds substantial promise as a material for bipolar plates in high-performance proton exchange membrane fuel cells (PEMFC) due to its exceptional properties in reactant redistribution. However, the intricate structure of metal foam flow field (MFF) presents challenges for mass transfer and water management. In this study, a three-dimensional two-phase flow model for metal foam is developed to analyze and capture flow patterns. MFFs are reconstructed based on detailed structural analysis and various pore sizes are discussed. Employing the Volume of Fluid (VOF) method, we delve into multiphase flow dynamics, specifically focusing on the removal of liquid droplets within the MFF. It reveals the MFF with moderate pore sizes exhibit a trade-off performance, striking a balance between optimal mass transfer and minimal parasitic loss. The porous structure's pivotal role is highlighted, contributing significantly to both through-plane and in-plane mass transfer and convection. Furthermore, we classify three flow patterns of liquid droplet, with the “split-up” pattern emerging as the most effective for water management and mass transfer. This study illuminates water behavior in porous metal foam bipolar plates, introduces a systematic methodology for assessing mass transfer and water management capabilities in MFFs for PEMFC.

Experimental and Modeling Analyses of the Correlation between Local 3D Heterogeneities and the Macroscopic Observers of a Proton Exchange Membrane Fuel Cell Stack

In this study, we offer a complete investigation of a high-performing Proton Exchange Membrane Fuel Cell stack customized for automotive use. Our approach goes beyond traditional global electrochemical performance metrics such as polarization curves, ohmic resistance. Instead, we utilize specialized segmented high-surface sensors to measure current density and temperature in the active area plane, along with neutron imaging to determine liquid water distributions. Employing a pseudo three-dimensional two-phase flow model that integrates electrochemical and transport phenomena, we gain insight into the intricate relationships among these observables. The model proves particularly valuable in elucidating the operation of the anode and cathode sides, aspects challenging to capture solely through experimental mean. Our findings emphasize the substantial impact of fluid flow directions and current density on the distribution of liquid water. It is noteworthy that despite fluid flow direction, there is a consistent decrease in overall liquid water content with an increase in current density. This results in voltage instability within the cell, attributed to flooding phenomena, especially at low current densities. However, this is not observed in conditions representative of those encountered in on-field systems. We conduct a thorough analysis of this failure scenario to improve the fuel cell system’s control mechanisms.

Simulation and Experiment on Elimination for the Bottom-Sitting Adsorption Effect of a Submersible Based on a Submerged Jet

When a submersible is sitting on a seabed, it could lose buoyancy because of the bottom-sitting adsorption effect. In this article, a numerical calculation model and experimental scheme for eliminating the bottom-sitting adsorption effect of under-sea equipment were established. An analysis of the hydrostatic pressure variation on a submersible’s bottom was carried out, and a submerged water jet which was based on the method of soil liquefaction was proposed to solve the problem of reducing hydrostatic pressure. It was shown that a water jet could liquefy soil to restore hydrostatic pressure on the submersible’s bottom, and there was an optimal jet velocity to form the largest liquefied soil thickness. A rectangular pulsed jet was the best way to liquefy soil in terms of efficiency and the liquefaction degree, which can be seen from the calculation of the two-dimensional two-phase flow. Through the calculation of the three-dimensional two-phase flow, it was found that the soil liquefaction developed from the periphery to the center, and a variation in jet liquefaction with the top wall constraint was obtained. Finally, an experiment was carried out to prove that a submerged water jet could eliminate the bottom-sitting adsorption effect of a submersible. The results showed that the submerged jet was an efficient way to liquefy soil, and a submersible could quickly recover hydrostatic pressure on the bottom and refloat up independently.

Three-dimensional simulation of two-phase flow distribution in spherical concave-convex shaped flow field for alkaline water electrolyzer

Alkaline water electrolyzer (AWE) with KOH aqueous solution as electrolyte is one of the most mature routes for green hydrogen production, in which spherical concave-convex (SCC) shaped flow fields are widely applied. However, while the addition of SCC is known to have significant effects on complex two-phase flow, in particular on the generated hydrogen, detailed understandings of the flow distributions are still lacking. In this paper, we propose to demonstrate the three-dimensional (3D) two-phase flow distributions in SCC shaped flow field for AWE by COMSOL simulation method. First, the typical geometric model is extracted from the practical AWE, based on which the mesh model is constructed; Moreover, the basic 3D simulation results of channel without SCC are evaluated by comparing with the previous experimental studies to demonstrate the model validation; Finally, the 3D flow velocity and hydrogen fraction distributions are carefully illustrated that the SCC shaped structure averages the distribution in the channel effectively and the hydrogen concentration on the electrode surface are reduced, beneficial to the improvement of the electrolysis efficiency, at the outlet of the channel, half of the geometric height (z = 4 mm), the hydrogen fraction in the straight channel is less than 3%, while the hydrogen fraction at the outlet of the SCC channel is about 4%, or even 5% locally. We believe this work can not only provide a guideline for the 3D model establishment for two-phase flow in AWE, but give detailed hydrogen distribution understandings in varied conditions with different current densities.

ПРОМИСЛОВИЙ ЦИКЛОННО-РОТАЦІЙНИЙ ПИЛОВЛОВЛЮВАЧ

Cyclone equipment is easy to manufacture and operate, versatile and economical, but its main drawback is the inability to capture finely dispersed dust. The article discusses the most important characteristics of the highly efficient industrial cyclonic rotary dust collector developed by us. The apparatus implements the principle of two-stage separation of heterogeneous dust-gas systems in a centrifugal field. In the first stage, working on the principle of a cyclone, and in the second - working on the principle of a rotary dust collector. During operation of the apparatus, a higher pressure on the periphery of the rotating part returns a concentrated dusty flow with a low gas flow to the cyclone part. Formed by a gap, between the cyclone body and the dividing cone, a closed circuit connects the output and input of the cyclone-rotational dust collector to each other. There is a negative feedback - an effective control mechanism for such complex probabilistic systems as gas heterogeneous curvilinear flows. Negative feedback stabilizes the processes occurring in such flows. The energy of the electric motor is used in the cyclone-rotational dust collector for the movement of dusty gas, concentration, coagulation of fine dust, its return from the rotary to the cyclone zone, dispersion and capture, with the aim of saving energy and material resources. The main task of the theory of centrifugal separation of dusty flows is to find the minimum diameter of a particle that has a practically perceptible relative radial velocity. Known deterministic models of centrifugal separation are either too simple and ignore many factors that determine the process, or in attempts to account for them are too cumbersome and difficult to solve, although they are also not free from various assumptions and limitations. The stochastic model takes into account the integral set of various influences on the radial drift of the Stokes particle from the center to the periphery of the swirling flow. The paper presents the results of the study of the structure of the three-dimensional two-phase gas flow with highly dispersed inclusions in cyclonic-rotary dust collectors using 3D geometric models with the aim of visualizing these flows using computer graphics methods. Numerical studies were carried out using the k-e model of turbulence with scaled wall functions.

Porous Media Model of Reservoir considering Seepage Stress Coupling and Seepage Field Analysis

In the process of reservoir exploitation, the range of rock stress field changes is much larger than the reservoir area where the seepage occurs; so the amount of calculation of the existing seepage stress full coupling method is often very huge. Based on the theory of seepage mechanics and rock mechanics, a coupling analysis model of reservoir multiphase seepage and stress is established, and a numerical solution is established by using finite element and finite difference methods. The evolution law of the seepage field and stress field and the change of rock mechanics parameters can be studied, with emphasis on the readjustment of rock stress distribution and its deformation characteristics under the influence of the seepage field. At the same time, to improve the calculation efficiency of numerical simulation, considering the difference between the seepage calculation area and stress calculation area, the finite element method is improved. The percolation area of the reservoir is calculated with a fine grid to obtain a more accurate distribution of underground fluid. The coarse grid is used to calculate the stress calculation area and to reduce the calculation time. The mechanical equilibrium equation in the fully coupled theory is discretized on the coarse grid by the finite element method. The mass conservation equation is discretized on the fine grid by the finite volume method. The numerical simulation of Terzaghi’s one-dimensional consolidation problem and Mandel’s two-dimensional consolidation problem shows that the calculation results of this method are in good agreement with the analytical solution. Through the numerical calculation of a two-dimensional single-phase flow single well production problem and a three-dimensional two-phase flow five-point well pattern production problem, the influence of the seepage stress coupling effect in reservoir numerical simulation is analyzed.

CFD analysis and prediction of centrifugal pump cavitation performance based on three-dimensional two-phase flow between impeller and worm gear

Cavitation performance is an important performance indicator of centrifugal pumps. The occurrence of cavitation will trigger a complex gas-liquid two-phase flow, which will reduce the efficiency of a low ratio centrifugal pump and cause machine vibration, as well as damage to the impeller, seriously affecting the working performance and preventing its normal operation. In this paper, CFD numerical simulation is used to analyze the cavitation characteristics of a centrifugal pump, obtain its internal flow law, calculate the cavitation margin of the device and the head generated by the pump under each inlet condition, and thus predict the critical cavitation margin of the pump at this flow point.

Thermal management of GaN HEMT devices using subcooled flow boiling in an embedded manifold microchannel heat sink

Ultra-high heat flux thermal management has been an urgent demand for high electrical performance and reliability of GaN HEMT electronic devices, and direct fabrication of embedded heat sinks have proven to be an effective approach for its thermal management. In this work, a self-developed solver based on OpenFOAM has been employed and verified for numerical investigations of three-dimensional two-phase flow coupled with conjugate heat transfer. An extremely uneven heat source distribution in GaN HEMT is accounted for in the numerical modeling with localized refined mesh. The thermal performance and pressure drop during subcooled flow boiling are investigated and presented considering parametric effects of heat flux, mass velocity, inlet/outlet width ratio, manifold thickness and channel aspect ratio as well as substrate materials. The results indicate that GaN-on-Diamond structure provides a lower thermal resistance and better temperature uniformity, and the superior performance of GaN-on-SiC and GaN-on-Diamond are augmented with increasing heat flux during subcooled flow boiling. Additionally, it can be concluded that maximum temperature and pressure drop decrease with increasing channel height firstly, and then flatten out as the height/width ratio reaches 8 and 6, respectively. The flatten-out relationship between increasing height/width ratio and thermal/hydraulic performance is partly attributed to the balance of decreasing convective heat transfer coefficient and increasing effective area. Besides, flow pattern analysis for high-aspect ratio microchannels shows that hotspots at the bottom of inlet manifold promote the bubble nucleation and bubbles tend to accumulate at the bottom of channels because of nonuniform velocity distribution along the microchannel height.

Performance Comparison of Proton Exchange Membrane Water Electrolysis Cell Using Channel and PTL Flow Fields through Three-Dimensional Two-Phase Flow Simulation.

Water electrolysis technology is required to overcome the intermittency of renewable energy sources. Among various water electrolysis methods, the proton exchange membrane water electrolysis (PEMWE) cell has the advantages of a fast response and high current density. However, high capital costs have hindered the commercialization of PEMWE; therefore, it is important to lower the price of bipolar plates, which make PEMWE expensive. In addition, since the flow field inscribed in the bipolar plate significantly influences the performance, it is necessary to design the enhanced pattern. A three-dimensional two-phase flow model was used to analyze the two-phase flow and electrochemical reactions of the PEMWE anode. In order to compare the experimental results with the simulation, experiments were conducted according to the flow rate, and the results were in good agreement. First, as a result of comparing the performance of the channel and PTL (porous transport layer) flow fields, the channel flow field showed better performance than the PTL flow field. For the channel flow field, the higher the ratio of the channel width-to-rib width and the permeability of PTL, the performance got better. In the case of the PTL flow field, with the increased capillary pressure, the performance improved even if the PTL permeability decreased. Next, the direction of gravity affected the performance only when the channel flow field was used, and the X+ and Z+ directions were optimal for the performance. Finally, increasing the inlet flow rate could reduce the difference in performance between the channel and PTL flow fields, but the pressure drop gradually increased.

Optimization of the Aircraft Air/Oil Separator by the Response Surface Determined from Modeling of Three-Dimensional Two-Phase Flow

This paper presents optimisation of the geometry of the aircraft air–oil separator (AAOS) performed to improve the device performance. For this separator type, the most important operating parameters are the oil quality, efficiency and pressure drop. In order to understand the relationships between geometric parameters and their impact on the parameters of the separator operation, an analysis was conducted using the Response Surface Method (RSM). The analysis was made based on the results of numerical simulations and using the volume-of-fluid (VOF) method. Pareto analysis was also carried out, which determined the impact of the inlet width and height and the separator diameter on the device performance. By solving the optimisation task using a genetic algorithm, it was possible to propose a new geometry for the AAOS. The favourable geometric relations for the AAOS are indicated and they are compared with those preferred for other geometries of cyclone separators.

Development of an OpenFOAM solver for numerical simulations of shell-and-tube heat exchangers based on porous media model

• An innovative OpenFOAM solver of shell-and-tube heat exchangers was developed. • The coupling between porous media and drift flux two phase model was realized. • The feasibility of new solver was validated by two international benchmarks. • The key three dimensional thermal parameters of heat exchanger were achieved. As one of the most widely used types of heat exchangers, the shell-and-tube heat exchanger (STHX) offers the advantages of being low-cost, easy to clean, and highly reliable under high pressure and temperature conditions. Generally, a large number of tube bundles are used in the STHX to increase the heat transfer capacity. The three-dimensional (3D) two-phase flow simulation of the STHX is made exceedingly difficult if the tube bundle region is full-size modeled. Therefore, simplified models and approaches are required to meet the urgent demands of STHX engineering numerical simulation, especially for 3D analyses. Herein, we have developed an OpenFOAM solver “PorousDriftFoam” suitable for the two-phase flow and the boiling heat transfer numerical simulation of the STHX. The porous media model was applied to simplify the tube bundle region and the drift-flux model (DFM) was adopted in the two-phase flow computational fluid dynamics (CFD) simulation for the STHX. The heat transfer tubes are regarded as the solid region of porous media, while the shell side is considered the fluid region. We calculate the coupling heat transfer between the tube and the shell sides and consider the resistance introduced by the heat transfer tubes and support plates in the STHX. Two international benchmarks, the FRIGG test and the MB-2 experiments, were selected to fully validate the solver. For the FRIGG experiment, the predicted void fraction stands in good agreement with the experimental data, with an average absolute error of 0.07 and an average relative error of 13.3%. For the MB-2 experiment, the predicted values of pressure drop and temperature fit well with the experimental data. The developed solver could be applied in the 3D two-phase flow and heat transfer numerical simulation of a typical STHX in the industry.

Retracted: Water Transport in GDL Microstructures of Nonuniform Fiber Diameter Arrangement

In proton exchange membrane fuel cells (PEMFCs), the gas diffusion layer (GDL) plays an important role in the transport of reactants, water, heat, and electrons. Microstructure manipulation of porous media via a nonuniform fiber diameter arrangement could potentially be used to improve water transport behavior in GDLs. A numerical modeling approach is used to simulate GDL microstructures with uniform and nonuniform fiber diameters. The reconstructed porous microstructures’ water saturation and porosity are compared. The simulations of three-dimensional (3D) two-phase flow volume of fluid (VOF) models were completed on the OpenFOAM platform using the finite volume method (FVM). Simulations demonstrate that by adopting a nonuniform microstructural fiber diameter design, both porosity and water transport behaviors can be altered. As a result of the nonuniform fibrous arrangement, the ability to improve GDL performance by controlling water transport and porosity is possible. The results indicate that by manipulating the GDL microstructure, additional water pathways can be created, resulting in slightly increased water saturation. We propose that water transport can be improved by microstructural manipulation of the GDL, specifically by optimizing the arrangement and position of nonuniform fibers.

Fast evaluation of pressure and saturation predictions with a deep learning surrogate flow model

Numerical models for flow through porous media are essential for forecasting subsurface fluid flow response to support optimal decision-making to develop subsurface resources such as groundwater, geothermal, and oil and gas. For reservoir engineering, numerical flow simulation modeling is applied to support and maximize well ultimate recovery and recoverable reserves to maximize project economics and safety while minimizing environmental impacts. Subsurface models explore subsurface uncertainty based on integrating geological, geophysical, petrophysical, and reservoir engineering data and expert interpretations.To evaluate uncertainty, we rely on multiple geostatistical subsurface heterogeneity realizations paired with flow simulation forecasts to test the sensitivity of various reservoir development parameters and build an uncertainty model of reservoir performance. However, with large reservoir models, numerical flow simulation time increases, leading to a significant amount of professional time and computational effort that increases project costs, and increases cycle times resulting in delay or diminished decision quality. This issue motivates the utilization of surrogate, computationally efficient approximative flow models. Current methods focus on prediction accuracy and minimizing prediction error. When uncertainty is significant, prediction accuracy is insufficient, and we must consider the entire uncertainty distribution.We propose a new and general workflow to generate accurate and precise machine learning-based surrogate flow models to predict the relationship between the reservoir rock and fluids, development parameters, and the reservoir flow simulation responses. We train a deep convolutional neural network using the results from a three-dimensional two-phase flow simulator. Next, we use the trained model to generate ensemble predictions from the flow surrogate to evaluate the uncertainty based on the development parameters and geological information.The machine learning-based surrogate model uses exhaustive subsurface predictor features, porosity, permeability, well position, and an engineered feature representing non-dimensional time as input to predict exhaustive subsurface response features, pressure, and saturation distribution over discrete time steps as the output. The proposed workflow integrates the spatiotemporal aspect of subsurface flow modeling. It allows the practitioner engineer to explore subsurface uncertainty without the entire computational cost of numerical flow simulation to support optimum, timely development decision-making.

Validation of three-dimensional simulation method for two-phase flow in triangular-pitch tube bundle in secondary side of steam generators on porous two-fluid model

ABSTRACT In the design process of a steam generator, a porous-media-approach computational code is utilized for simulating three-dimensional two-phase flow behavior in the secondary side of steam generators. For the design of next-generation steam generators, the advanced thermal-hydraulic analysis code based on the two-fluid model has been developed by implementing constitutive equations into the ANSYS fluent. For code validation, experiments using two-phase simulant fluids were performed to collect data in a simulated steam generator with a triangular tube array. The simulant two-phase flow system selected in the experiment was an adiabatic sulfur hexafluoride gas and liquid ethanol system, which allowed us to achieve the density ratio of prototypic steam-water flow with low pressure (=0.68 MPa). In the experiment, void fraction and gas–liquid interfacial velocity distributions along U-tubes were measured. The code validation was conducted by analyzing code predictions for measured distributions of void fraction and interfacial velocity under prototypic full load and partial load conditions, i.e., 50–80% flow rate conditions. Their bias and random errors were evaluated. The reasonable random errors demonstrated the validity of the newly developed code based on the two-fluid model in terms of predictions of void fraction and interfacial velocity in the secondary side of steam generators.

On the dynamics of jet wiping: Numerical simulations and modal analysis

We analyze the flow of a planar gas jet impinging on a thin film dragged by a vertical moving wall. In the coating industry, this configuration is known as jet wiping, a process in which impinging jets control the thickness of liquid coatings on flat plates withdrawn vertically from a coating bath. We present three-dimensional (3D) two-phase flow simulations combining large eddy simulation (LES) and volume of fluid techniques. Three wiping configurations are simulated and the results are validated with experimental data from previous works. Multiscale modal analysis is used to analyze the dynamic interaction between the gas flow and the liquid film. In particular, we present a combination of multiscale Proper Orthogonal Decomposition (mPOD) and correlation analysis. The mPOD is used to identify the dominant traveling wave pattern in the liquid film flow, and the temporal structures are used to determine the most correlated flow features in the gas jet. This allows for revealing a two-dimensional mechanism for wave formation in the liquid coat. Finally, we use the numerical results to analyze the validity of some of the critical assumptions underpinning the derivation of integral film models of jet wiping.

A high-efficiency smoothed particle hydrodynamics model with multi-cell linked list and adaptive particle refinement for two-phase flows

The smoothed particle hydrodynamics method has been applied in modeling violent flows with the free surface. Much effort has been made in reducing the computational costs in simulating the three-dimensional two-phase flows with the violently deformed free surface and breaking waves. Although the adaptive particle refinement approach has been developed to concentrate fine resolution only in the region of interest, its efficiency still hardly meets the demand of large-scale numerical simulation. In order to improve its efficiency further, a multi-cell linked list algorithm coupling with the adaptive particle refinement for the smoothed particle hydrodynamics model is implemented in the graphic processing unit-based code. Particles are identified not only by its position but also by its resolution and trait. The accuracy of the numerical model for solving two-phase flows with the free surface is validated through computing a two-dimensional dam-break flow and the hydrodynamic flows of spheres vertically entering the water from the air. The numerical results agree well with the experimental data available. For the cases of water entry of a sphere of different densities, the development of open cavity and cavity sealing is discussed in terms of the pinch-off depth and the corresponding sphere depth. Simulations show that the smoothed particle hydrodynamics method with the adaptive particle refinement possesses the characteristics of good accuracy, time-saving, and high efficiency in simulating three-dimensional two-phase flows.

A Semianalytical Model for Simulating Fluid Flow in Tight Sandstone Reservoirs with a Bottom Aquifer

Water breaks through along fractures is a major concern in tight sandstone reservoirs with a bottom aquifer. Analytical models fail to handle the three-dimensional two-phase flow problem for partially penetrating inclined fractures, so time-consuming numerical simulation are often used for this problem. This paper presents an efficient semianalytical model for this problem considering three-dimensional fractures and two-phase flow. In the model, the hydraulic fracture is handled discretely with a numerical discrete method. The three-dimensional volumetric source function in real space and superposition principle are employed to solve the model analytically for fluid flow in the reservoir. The transient flow equations for flow in three-dimensional inclined fractures are solved by the finite difference method numerically, in which two-phase flow and stress-dependent properties are considered. The eventual solution of the model and transient responses are obtained by coupling the model for flow in the reservoir and discrete fracture dynamically. The validation of the semianalytical model is demonstrated in comparison to the solution of the commercial reservoir simulator Eclipse. Based on the proposed model, the effects of some critical parameters on the characteristics of water and oil flow performances are analyzed. The results show that the fracture conductivity, fracture permeability modulus, inclination angle of fractures, aquifer size, perforation location, and wellbore pressure drop significantly affect production rate and water breakthrough time. Lower fracture conductivity and larger inclination angle can delay the water breakthrough time and enhance the production rate, but the increment tends to decline gradually. Furthermore, water breakthrough will occur earlier if the wellbore pressure drop and aquifer size are larger. Besides, the stress sensitivity and perforation location can delay the water breakthrough time.

Transverse flow-induced vibrations of a sphere in the proximity of a free surface: A numerical study

In this paper, we present a numerical study on the transverse flow-induced vibration (FIV) of an elastically mounted sphere in the vicinity of a free surface at subcritical Reynolds numbers. We assess the interaction dynamics and the vibration characteristics of fully submerged and piercing spheres that are free to vibrate in the transverse direction. We employ the recently developed three-dimensional two-phase flow–structure interaction solver to investigate fully and partially submerged configurations of an elastically mounted sphere. To begin, we examine the vortex-induced vibration (VIV) phenomenon and the vortex-shedding modes of a fully-submerged sphere vibrating freely in all three spatial directions. We systematically verify and analyze the mode transitions and the motion trajectories in the three degrees-of-freedom (3-DOF) for the Reynolds number up to 30000. We next simulate the transversely vibrating (1-DOF) full-submerged sphere over a wide range of reduced velocities 3≤U∗≤20, whereby the reduced velocity is adjusted by changing the freestream Reynolds number. The VIV response amplitude and the topology of the wake structure are compared with the measurements for the mode I and mode II response branches. We further look into the effect of the free surface on the FIV response of a transversely vibrating sphere in the proximity of a free surface. The response dynamics of the sphere is studied for three representative values of normalized immersion ratio (h∗=h∕D, where h is the distance from the top of the sphere to undisturbed free-surface level and D is the sphere diameter), at h∗=1 (fully submerged sphere with no free-surface effect), h∗=0 (where the top of the sphere touches the free surface) and h∗=−0.25 (where the sphere pierces the free surface). At the lock-in range, we observe that the amplitude response of the sphere at h∗=0 is decreased significantly compared to the case at h∗=1. It is found that the vorticity flux is diffused due to the free-surface boundary and the free surface acts as a sink of energy that leads to a reduction in the transverse force and amplitude response. When the sphere pierces the free surface at h∗=−0.25, the amplitude response at the lock-in state is found to be greater than all the submerged cases studied with the maximum peak-to-peak amplitude of ∼2D. We find that the interaction of the piercing sphere with the air–water interface causes a relatively large surface deformation and has a significant impact on the synchronization of the vortex shedding and the vibration frequency. The streamwise vorticity contours and pressure distribution are employed to understand the VIV characteristics and wake dynamics. Increased streamwise vorticity gives rise to a relatively larger transverse force to the piercing sphere at h∗=−0.25, resulting in greater positive energy transfer per cycle to sustain the large-amplitude vibration. Lastly, we study the sensitivity of large-amplitude vibration on the mass ratio, m∗, and, Froude number, Fr, at the lock-in state.