Finite Volume Research Articles

Enhancing building energy efficiency: Innovations in glazing systems utilizing solid-solid phase change materials

This study investigates the energy efficiency of a double-glazing window (DGW) integrating a solid–solid phase change material (SSPCM) with limited thickness, applied to the inner glass pane within the air gap. Numerical model, validated against experimental data, is developed using a finite volume method in ANSYS Fluent. In this model, the Discrete Ordinates (DO) model is applied to simulate radiation, while the enthalpy-porosity approach is used to capture the solidification and melting processes in the phase change material. With this model, the energy performance of the system is analyzed under various transient temperature values (10 to 30 °C) and ranges (1 to 5 °C) during the coldest and hottest days of the year, as well as during cloudy and sunny days in Montreal (Dfb), Vancouver (Cfb), and Miami (Aw). According to the obtained results in Montreal, the DGW-SSPCM system consistently saves energy under summer sunny conditions, with optimal performance when the SSPCM remains transparent. However, it incurs energy losses in cloudy days, where the energy lost is 2.3 times greater than the energy saved in sunny days. In Vancouver, the system shows consistent energy savings, particularly at Tc = 30 °C, with average savings of 20.5 kJ (23 %) under summer sunny conditions. The system is most beneficial in Vancouver, where winter energy savings in cloudy days (50.6 kJ) are 7.1 times greater than the losses in sunny days (7.1 kJ). In Miami, the system results in energy losses by 60 % and 5 % (at Tc = 30 °C) under both summer sunny and cloudy conditions, respectively, indicating unsuitability for its climate. During winter sunny conditions, all three cities experience energy losses, with Vancouver showing the lowest of 7.1 kJ (3 %) and Montreal the highest of 64.4 kJ (19 %) at Tc = 30 °C. In winter cloudy conditions, the system saves energy in all cities, with the highest savings in Miami of 54.5 kJ (26 %) at Tc = 30 °C. Overall, the SSPCM-DGW system has proven to be beneficial in Vancouver across various conditions in terms of energy and visual performance. These findings highlight the necessity of considering localized climate factors when designing and implementing energy-efficient glazing systems. Finally, the SSPCM-DGW system has provided complete visual clarity during office hours, making it more suitable for commercial buildings.

Exploring the drag reduction caused by a combined spike and jet setup for a hypersonic blunt object at low elevations

Abstract When hypersonic vehicles fly at low altitudes during the end of the trajectory, they often face extremely high dynamic pressure and greater resistance. Studying the drag reduction features of the hypersonic vehicle at low altitudes is highly important. The Reynolds-averaged N-S equations are solved using the finite-volume method with the SST k-ω turbulence model. Numerical simulations are conducted on three-dimensional hypersonic flow fields involving spike and combined spike and jet configurations at low altitudes with hypersonic speeds to investigate drag reduction effects and analyze flow field characteristics. The data indicates that the presence of a spike can effectively reduce drag during low-altitude hypersonic flight. Enhancing the spike length, its drag reduction efficiency first increases and then slightly decreases. Enhancing the Mach number, the length of the spike that achieves the best drag reduction efficiency becomes longer. A spike and jet combination can enhance drag reduction efficiency when flying at an angle of attack. Enhancing the spike length or the pressure ratio in this configuration can enhance its effectiveness in reducing drag. The findings of this study provide practical guidance for developing drag-reduction strategies for hypersonic aircraft flying at low altitudes.

Approach to stationarity for the KPZ fixed point with boundaries

Current fluctuations for the one-dimensional totally asymmetric exclusion process (TASEP) connected to reservoirs of particles, and their large scale limit to the KPZ fixed point in finite volume, are studied using exact methods. Focusing on the maximal current phase for TASEP, corresponding to infinite boundary slopes for the KPZ height field, we obtain for general initial condition an exact expression for the late time correction to stationarity, involving extreme value statistics of Brownian paths. In the special cases of stationary and narrow wedge initial conditions, a combination of Bethe ansatz and numerical conjectures alternatively provide fully explicit exact expressions.

A stabilized finite volume method based on the rotational pressure correction projection for the time-dependent incompressible MHD equations

This paper presents an efficient numerical scheme for solving the time-dependent incompressible Magnetohydrodynamics (MHD) equations based on the rotational pressure correction projection method within the finite volume framework. Utilizing the lowest equal-order mixed finite element pair (P1−P1−P1) to approximate the velocity, magnetic and pressure fields, our numerical scheme satisfies the discrete inf-sup condition by the pressure projection stabilization. To tackle the coupling inherent in the time-dependent incompressible MHD equations,the rotational pressure correction projection method is introduced to split the original problem into several linear subproblems. The unconditional stability of numerical schemes are provided,optimal error estimates in both L2 and H1-norms of numerical solutions are also presented.Finally, some numerical results are given to verify the established theoretical findings and show the performances of the considered numerical schemes.

A Priori Test of Scale-Similarity Parameterizations for Subgrid-Scale Fluxes in Convective Storms

Abstract This study evaluates a parameterization scheme for subgrid-scale (SGS) fluxes based on the scale-similarity assumption and employing a large-eddy simulation of an idealized back-building convective system. In this parameterization, the SGS fluxes are decomposed into the “Leonard term,” which depends only on the resolved scale components, the “Reynolds term,” which depends only on the SGS components, and the “cross term,” which corresponds to the interaction between the resolved scale and SGS components. Assuming a linear relationship between the Leonard term and the Reynolds and cross terms, SGS fluxes are expressed as the product of an empirical coefficient and the Leonard term. The Leonard term reasonably represents the SGS flux derived by a smooth filter operation, including the countergradient vertical SGS transport of potential temperature, which cannot be represented by a traditional eddy-diffusivity model. The dependence of the empirical coefficient on filter width is also evaluated. This dependence is related mainly to the Reynolds term, the magnitude of which varies widely with the filter width. The estimation based on the spectral decomposition of the Reynolds term explains the obtained dependence of the empirical coefficient for the vertical flux on filter width. In contrast, the variation of the empirical coefficient with filter width is not required to obtain the horizontal flux. For the parameterization of SGS fluxes in kilometer-scale models that use finite difference or volume methods, the Leonard term is expressed by the horizontal gradient of variables on a discrete grid. The Leonard term on a discrete grid also accurately represents the amplitude and spatial pattern of the SGS flux. Significance Statement Kilometer-scale numerical weather prediction models can reproduce deep convection explicitly. However, they cannot reproduce smaller inner structures within this deep convection. Therefore, a parameterization scheme that can express the nature of the transport associated with such structures is required. Using a large-eddy simulation with a horizontal resolution sufficient to express such inner structures, we evaluated a parameterization based on the scale similarity assumption, including an empirical coefficient. Based on spectral decomposition, we quantitatively estimated the relationship between the empirical coefficient and grid spacing. Our results provide guidance in selecting the value of the empirical coefficient in this parameterization.

Numerical simulation of two-phase oil–water flow in fractured-vuggy reservoirs based on the coefficient of porous medium proportion and coupled regions

Based on the flow characteristics of fluids in various reservoir media, fractured-vuggy oil reservoirs can be classified into seepage zones and conduit flow zones. An interface exists between these two regions, where the movement of formation fluid near this interface is characterized by a coupling or transitional phenomenon between seepage and conduit flow. However, the complexity of this coupling interface poses challenges for traditional numerical simulations in accurately representing the intricate fluid dynamics within fractured-vuggy oil reservoirs. This limitation impacts the development planning and production adjustment strategies for fractured-vuggy oil reservoirs. Consequently, achieving accurate characterization and numerical simulation of these systems remains a critical challenge that requires urgent attention. A new mathematical model for oil-water two-phase flow in fractured-vuggy oil reservoirs is presented, which developed based on a novel coupling method. The model introduces the concept of the proportion coefficient of porous media within unit grids and defines a coupling region. It employs an enhanced Stokes–Brinkman equation to address the coupling issue by incorporating the proportion coefficient of porous media, thereby facilitating a more accurate description of the coupling interface through the use of the coupling region. Additionally, this proportion coefficient characterizes the unfilled cave boundary, simplifying the representation of model boundary conditions. The secondary development on the open-source fluid dynamics software is conducted by using matrix & laboratory (MATLAB). The governing equations of the mathematical model are discretized utilizing finite volume methods and applying staggered grid techniques along with a semi-implicit calculation format for pressure coupling—the Semi-Implicit Method for Pressure Linked Equations algorithm—to solve for both pressure and velocity fields. Under identical mechanism models, comparisons between simulation results from this two-phase flow program and those obtained from Eclipse reveal that our program demonstrates superior performance in accurately depicting flow states within unfilled caves, thus validating its numerical simulation outcomes for two-phase flow in fractured cave reservoirs. Utilizing the S48 fault-dipole unit as a case study, this research conducted numerical simulations to investigate the water-in-place (WIP) behavior in fractured-vuggy oil reservoirs. The primary focus was on analyzing the upward trend of WIP and its influencing factors during production across various combinations of fractures and dipoles, thereby validating the feasibility of the numerical modeling approach in real-world reservoirs. The simulation results indicated that when multiple dissolution cavities at different locations communicated with the well bottom sequentially, the WIP in the production well exhibited a staircase-like increase. Furthermore, as the distance between bottom water and well bottom increased, its effect on water intrusion into the well diminished, leading to a slower variation in the WIP curve. These characteristics manifested as sudden influxes of water flooding, rapid increases in water levels, and gradual rises—all consistent with actual field production observations. The newly established numerical simulation method for fractured-vuggy oil reservoirs quantitatively describes two-phase flow dynamics within these systems, thus effectively predicting their production behaviors and providing guidance aimed at enhancing recovery rates typically observed in fractured-vuggy oil reservoirs.

Numerical Investigation of the transient process of direct collision between two droplets

Abstract The use of spray systems finds widespread applications in fields such as national defense and industry. These systems are employed for spray cooling, spray forming, spray coating, and inkjet painting. Within spray systems, atomized droplets play a crucial role, either impacting surfaces or colliding with each other. Understanding the impact process of these droplets is essential for optimizing spray system performance. In this study, computational simulations focus on direct collision of two droplets. Numerical methods are employed, including structured single-block and staggered grid systems for discretizing the spatial domain. The finite volume method iteratively solves the governing equations of mass and momentum. The coupling between velocities and pressure is handled using SIMPLER methods. During droplet collision, phenomena like deformation, breakup, and merging occur at the boundary. To accurately capture these movements, a level set function approach is utilized. Numerical simulations of a water droplet impinging on a flat surface are compared with experimental results for verification. When two droplets collide head-on with the same Reynolds number and Weber number, they merge into a single oscillating droplet at a fixed position. Increasing the Reynolds number of the two colliding droplets intensifies the oscillation phenomenon in the merged droplet. Even when two droplets collide at an angle or have different sizes, they still merge into a single oscillating droplet. The merged droplet moves in a direction where the original two droplets’ momentum cannot be fully offset.

Forecasting two-dimensional channel flow using machine learning

Over the past decade, the integration of artificial neural networks (ANNs) has garnered significant interest, capitalizing on their ability to discern intricate patterns within data. Focused on enhancing computational efficiency, this article explores the application of ANNs in forecasting fluid-dynamics simulations, particularly for the benchmark problem of fluid flow in a two-dimensional (2D) channel. Leveraging a multilayer perceptron trained on finite volume method numerical data, for both interpolation and extrapolation estimations and various grid resolutions, our findings demonstrate the ANN's prowess as a swift and accurate surrogate for traditional numerical methods. Overall, the results of this work mark a pioneering step toward leveraging machine learning for modeling complex relationships in fluids phenomena, promising transformative advancements in computational fluid dynamics.

Influence of pin fins and channel geometry on the hydrothermal performance of hexagonal mini-channel heat sink for cooling cylindrical batteries

This study numerically and experimentally examined the effects of pin fin configuration and channel geometry on the performance of a hexagonal mini-channel heat sink (HMCHS) to cool cylindrical lithium-ion battery cells. Various configurations of HMCHS with circular pin fins are studied, including circular fins centrally positioned within flat channels, circular fins positioned within grooved channels, circular fins situated within hybrid channels transitioning between wavy and straight channels and circular fins placed within hybrid channels that incorporate secondary flow channels between the primary flow channels. This numerical study utilized the finite volume method to investigate the laminar water flow at Reynolds numbers below 800. Findings showed that the HMCHS exhibited superior thermal performance compared with the conventional cylindrical mini-channel heat sink design. Moreover, the incorporation of pin fins into the HMCHS design was more effective in enhancing the Nusselt number than simply increasing the Reynolds number across various configurations. Meanwhile, the hybrid channel design with secondary channels, combined with the addition of pin fins, achieved the optimal overall performance of the HMCHS, resulting in the highest performance index of 1.88.

Reduction in wave shoaling over a linear transition bottom using a porous medium

Wave shoaling, which involves an increase in wave amplitude due to changes in water depth, can damage shorelines. To mitigate this damage, we propose using porous structures such as mangrove forests. In this study, we use a mathematical model to examine how mangroves, acting as a porous breakwater, can reduce wave shoaling amplitude. Shallow water equations are used as the governing equations and are modified to account for the presence of porous media. To measure the wave reduction generated by the porous media, the wave transmission coefficient is estimated using analytical and numerical approaches. The separation of variables method and the staggered finite volume method are utilized for each approach, respectively. The numerical results are then validated against the previously obtained analytical solutions. We then vary the friction and porosity parameters, influenced by the presence and extent of porous media, to evaluate their effectiveness in reducing wave shoaling.

Investigation of Aerodynamic Performance of Multi-element Airfoil in Free Surface Effect

Abstract This study examines the aerodynamic performance of the 30P30N multi-element airfoil flying on a free surface, a numerical computational model is established, the governing equations are addressed through the application of the finite volume method, while the volume of fluid method is utilized for the simulation of two-phase flow. Different mesh strategies and turbulence models are compared, with the numerical methods validated against experimental data. The aerodynamic properties of the 30P30N multi-element airfoil on the free surface at different wavelengths and wave heights are given by numerical computations, which show that the ground effect of the 30P30N multi-element airfoil differ from those on a clean airfoil, the aerodynamic coefficients of the 30P30N multi-element airfoil decrease as flight altitude lowers, with the pitching and drag moment of the slat is opposite to that of the main airfoil and the flap. Additionally, when the 30P30N multi-element airfoil flies over a regular wave surface, the aerodynamic coefficients of each component exhibit periodic behavior.

Numerical studies of hydrodynamic relativistic astrophysical jet: The modification of vorticity transport equation

In this Letter, we have carried out the two-dimensional numerical simulation of axisymmetric relativistic jet in cylindrical coordinates by employing higher order finite volume method in PLUTO [Mignone et al., “PLUTO: A numerical code for computational astrophysics,” Astrophys. J. Suppl. Ser. 170, 228 (2007)] solver. The modified vorticity transport equation has been proposed for relativistic flow by taking the curl of the momentum equation, which shows significant change in the baroclinic vorticity production term due to relativistic effect. Both mathematical analysis and numerical results show that the vorticity production term due to baroclinic torque is heavily influenced due to the presence of specific enthalpy gradient and square of Lorentz factor gradient in a relativistic fluid flow.

Study on Agglomeration and Plugging Behavior of Fine Particles in Reservoir Based on DEM-CFD Coupling

Abstract Given the particularity, significance, and complexity of particle migration behavior in fine silt sand hydrate reservoirs, the agglomeration and plugging behavior of free fine particles are mainly studied. Based on the discrete element method (DEM) and computational fluid dynamics (CFD), the DEM-CFD coupled 3D wellbore sand production numerical model is established and verified. The DEM module divides the reservoir particles into coarse and fine components according to the actual particle size distribution, and assigns adhesive and non-adhesive rolling resistance linear models, respectively. The CFD module uses the finite volume method to solve the incompressible Darcy flow in coarse grids. The results show that the DEM-CFD coupled numerical model established can effectively simulate the phenomenon of fine particle agglomeration during particle migration; Compared with the condition without particle agglomeration, fine particle agglomeration can lead to lower wellbore sand production and more severe pore blockage and permeability loss in the surrounding reservoir; The influences of different production and reservoir parameters such as flow rate, porosity and mud content on the variation of wellbore sand production and reservoir permeability under the condition of fine particle agglomeration is further determined, and relevant production measures and suggestions are put forward. The research results help to clarify the sand production mechanism and characteristics of fine silt sand reservoirs and are expected to provide theoretical and technical support for the efficient and safe development of natural gas hydrate resources in fine silt sand reservoirs.

MATHEMATICAL MODEL AND NUMERICAL METHODS OF FILTRATION PROCESSES OF LIQUID SOLUTIONS

Filtration processes of liquid solutions are fundamental in many natural and industrial applications, such as environmental protection, chemical engineering, water purification, and petroleum extraction. This article develops a mathematical model for describing filtration processes and explores various numerical methods for solving the governing equations. The model is based on Darcy’s law, continuity equation, and constitutive relations of liquid solutions in porous media. Numerical methods, including finite difference, finite element, and finite volume approaches, are discussed with applications to various filtration scenarios. We also provide analysis of the stability, convergence, and efficiency of these methods.

Simulation of the Full‐Process Dynamics of Floating Vehicles Driven by Flash Floods

AbstractFlash flooding has become more prominent under climate change, threatening people's life and property. Post‐event investigations of recent events emphasize the role of floating debris, such as vehicles, in exacerbating damage. Few modeling methods and tools have been developed to simulate the full‐process dynamics of floating debris driven by large‐scale flood waves in real world. In this work, a fully coupled model is developed for simulating the full‐process interactive movements of vehicles driven by flash flood hydrodynamics, from entrainment, transport to deposition. The proposed coupled modeling system consists of a finite volume shock‐capturing hydrodynamic model solving the 2D shallow water equations and a 3D discrete element method (DEM) model. The proposed two‐way coupling approach estimates the hydrostatic and hydrodynamic forces acting on solid objects using the water depth and velocity predicted by the hydrodynamic model; the resulting counter forces on the fluid flow are then considered by adding extra source terms in the hydrodynamic model. A multi‐sphere method is further embedded in the DEM model to better represent vehicle shapes. New calculation modules are further implemented to represent the vehicle entrainment, contact and stopping motions. The coupled model is applied to reproduce a flash flood event hit Boscastle in the UK in 2004. Over 100 vehicles were moved and carried downstream by the highly transient flood flow. The model well predicts the hydrodynamics, interactive transport process and the final locations of vehicles. The proposed coupled model provides a new tool for simulating large‐scale flash flooding processes, including debris dynamics.

Resolving subgrid-scale structures for multiphase flows using a filament moment-of-fluid method

Multiphase flows are present in many industrial and engineering applications as well as in some physical phenomena. Capturing the interface between the phases for complex flows is challenging and requires an accurate method, especially to resolve fine-scale structures. The moment-of-fluid (MOF) method improves drastically the accuracy of interface reconstruction compared to previous geometrical methods. Instead of refining the mesh to capture increased levels of detail, the MOF method, which uses zeroth and first moments as well as a conglomeration algorithm, enables subgrid structures such as filaments to be captured at a small extra cost. Coupled to a finite volume Navier–Stokes solver, the MOF method has been tested on a fixed grid and validated using well-known benchmark problems such as the dam break flows, the Rayleigh–Taylor and Kelvin–Helmholtz instability problems, and a rising bubble. The ability of the novel filament MOF method to capture the filamentary structures that eventually form for the Rayleigh–Taylor instability and rising bubble problems is assessed. Good agreement has been found with other numerical results and experimental measurements available in the literature.

GPU parallel implementation of a finite volume lattice Boltzmann method for incompressible flows

This work presents a graphics processing units (GPU) parallel algorithm of a cell-centered finite volume lattice Boltzmann method (FVLBM) on unstructured meshes. In the present GPU parallel algorithm, the parallelization is performed in the physical space. To reduce the frequency of GPU memory accesses, this algorithm develops coalesced access to GPU memory. In addition, to avoid the race for resources leading to data anomalies, such as dirty read or phantom read etc., and the double counting for flux calculation, the efficient face-based data structure often used for flux calculation in cells in the central processing unit (CPU) version of FVLBM is modified into a face-based data structure used for the fluxes on all faces, followed by a cell-based loop for the final residuals in all cells. Therefore, the proposed GPU parallel algorithm does not need to use the resource lock and retains the high efficiency of the face-based data structure in the fluxes computation to enhance its’ parallel efficiency. Additionally, to demonstrate the computational efficiency of the proposed GPU parallel algorithm, various benchmark studies are performed in this work by the proposed parallel scheme on a double precision NVIDIA GeForce RTX 3090Ti GPU card, including (a) the lid-driven flow in a two-dimensional (2D) square cavity, (b) a 2D flow past a cylinder, and (c) the lid-driven flow in a three-dimensional (3D) cubic cavity. The numerical results show that the proposed GPU parallel algorithm can be as accurate as the original CPU serial scheme with 1 to 2 orders of speedup.

Modulation of Residual Current on Impacts of Shoreline Changes in the Yangshan Deepwater Harbor

Abstract Coastal land reclamation projects significantly alter tidal wave propagation and residual flow structures. This study focuses on the Yangshan Deepwater Harbor (YDH) in China, aiming to scrutinize the effects of construction activities on residual flow patterns employing the Finite Volume Community Ocean Model (FVCOM). By calculating Lagrangian residual currents across different tidal periods, we analyzed alterations in flow patterns and velocity distribution pre- and post-construction. The research findings reveal that, although the residual flow direction in the harbor and the southern sea area remains largely unchanged from the pre-construction phase, the northern sea area has experienced a shift in residual flow direction. It is noteworthy that after the implementation of the project, the residual flow at the East Entrance was greatly weakened. This study underscores that coastal constructions can lead to remarkable influence on residual currents and emphasizes the necessity for thorough hydrodynamic assessments in the planning and implementation stages of coastal constructions.

Analysis of the Effectiveness of Using a High-Accuracy Numerical Algorithm in the Simulation of Two-Phase Flow Problems

The continuous technical development of weapons and ammunition, as well as the growing requirements placed on new equipment, require the use of modern tools for their designing and testing. The analysis of the operation of powder propellant systems, which is the focus of interior ballistics, requires particularly specialised tools due to the complexity of the phenomena occurring during a shot. The development of numerical methods and the increase in the computing power of modern computers have enabled the modelling and simulation of highly complex physical problems and the development of numerical schemes with a theoretically arbitrary high order of accuracy. In this study, an attempt was made to develop a one-dimensional model of two-phase flows with a high order of solution accuracy in time, based on the finite volume method. The use of a two-phase flow model in the context of interior ballistics allows, among other things, the analysis of wave phenomena occurring during firing, which is crucial for safety reasons, especially in tank guns. The developed algorithm for solving two-phase systems was checked using recognised test problems for this type of model. The results of the work will be used to develop a numerical model to solve the main problem of interior ballistics.

Application of operating scenarios and analysis of unstable flow characteristics at various angles of inlet guide vane.

In this study, we analyzed the performance characteristics of an axial flow pump with different angles of internally installed inlet guide vanes (IGVs). We predicted the pump's performance based on changes in the IGV angle and analyzed the impact of these angle variations on pump operation in the low-flow region. Additionally, we used real operational data from two sewage treatment plants to propose efficient operational scenarios. For turbulence flow analysis, the Reynolds-averaged Navier-Stokes equations were discretized based on the finite volume method. The grid formation was evaluated using the grid convergence index to select the optimal grid. Then, the internal flow was analyzed in detail through transient-state analysis. Through fast Fourier transform analysis, we confirmed that adjusting the IGV angle during pump operation in the low-flow region in response to load changes results in more stable operation compared with the existing method (valve control). Overall, our findings verified that energy reduction and efficient operation can be achieved through IGV angle adjustment compared with valve control.