Fluid Flow Model Research Articles

Upscaling reactive transport models from pore-scale to continuum-scale using deep learning method

Reactive transport modeling of subsurface environments plays an important role in addressing critical problems of geochemical processes, such as dissolution and precipitation of minerals. Current transport models for porous media span various scales, ranging from pore-scale to continuum-scale. In this study, we established an upscaling method connecting pore-scale and continuum-scale models by employing a deep learning methodology of Convolutional Neural Networks (CNNs). We applied Darcy-Brinkmann-Stokes (DBS) method to simulate the fluid flow and reactive transport in pore-scale models, which would act as constituents of a continuum-scale model. The datasets of spatial pore distribution of subvolume samples were used as the input for the deep learning model, and the continuum (Darcy)-scale parameters such as permeability, effective surface area, and effective diffusion coefficient were figured out as outputs (i.e., labels). By applying the trained models of the subvolumes in the entire sample volume, we generated the initial field of porosity, permeability, effective diffusion coefficient, and effective surface area for continuum-scale simulation of a mineral dissolution problem. We took an acid dissolution case as an example to utilize the outcomes of trained deep learning models as input data in the continuum-scale simulation. This work presents a comprehensive upscaling workflow, as bridging the findings of microscale simulations to the continuum-scale simulations of a reactive transport problem.

Incompressible versus compressible fluid flow models: A case study on furnace tap-hole lancing

Pyrometallurgical furnaces, essential for metal extraction, operate at temperatures exceeding 1600°C and represent complex multiphase systems that challenge direct industrial research. Multiphysics models play a key role in shedding light on their intricate behaviours, supporting the refinement of design and operational strategies. Integral to the operation are the tap-holes, which facilitate the removal of molten products and are routinely opened by lancing, a process comparable to the use of a cutting torch, where high temperatures result from oxygen reacting with an iron lance. When the lance pierces the clay, oxygen gas enters the furnace, which could influence the behaviour of the molten material inside. In this work, a multiphase fluid flow model was used to investigate bulk flow dynamics, with a focus on the effects of the lancing process on the inside of the furnace, immediately behind the tap-hole. Incompressible and compressible multiphase fluid solvers were used and compared with respect their performance - the intention was to assess whether using a compressible solver would yield a different solution to the incompressible one. It was concluded that there are negligible disparities in bulk fluid flow behaviour between the solvers for the case studies examined, indicating that solver selection might be less consequential for certain aspects of oxygen lancing.

Darcy–Brinkman Model for Ternary Dusty Nanofluid Flow across Stretching/Shrinking Surface with Suction/Injection

Understanding of dusty fluids for different Brinkman numbers in porous media is limited. This study examines the Darcy–Brinkman model for two-dimensional magneto-hydrodynamic fluid flow across permeable stretching/shrinking surfaces with heat transfer. Water was considered as a conventional base fluid in which the copper (Cu), silver (Ag), and titanium dioxide (TiO2) nanoparticles were submerged in a preparation of a ternary dusty nanofluid. The governing nonlinear partial differential equations are converted to ordinary differential equations through suitable similarity conversions. Under radiation and mass transpiration, analytical solutions for stretching sheets/shrinking sheets are obtained. Several parameters are investigated, including the magnetic field, Darcy–Brinkman model, solution domain, and inverse Darcy number. The outcomes of the present article reveal that increasing the Brinkman number and inverse Darcy number decreases the velocity of the fluid and dusty phase. Increasing the magnetic field decreases the momentum of the boundary layer. Ternary dusty nanofluids have significantly improved the heat transmission process for manufacturing with applications in engineering, and biological and physical sciences. The findings of this study demonstrate that the ternary nanofluid phase’s heat and mass transpiration performance is better than the dusty phase’s performance.

Effects of heat transfer on MHD suction–injection model of viscous fluid flow through Differential transformation and Hermite wavelet techniques

Effects of heat transfer on MHD suction–injection model of viscous fluid flow through Differential transformation and Hermite wavelet techniques

Design and heat transfer numerical analysis of high-speed continuous casting mold water slot system

The water slot structure can reduce the temperature of the mold and increase the heat transfer between the mold and cooling water. It has significant impacts on high-speed continuous casting. Therefore, a three-dimensional model of heat transfer from mold to cooling water was used to analyze the influence of water slot size on the cooling capacity of a single water slot. Then, the fluid flow, heat transfer, and solidification three-dimensional models were used to analyze the temperature distribution and cooling effect of three kinds of water slot molds and non-water slot molds. Finally, the water slot mold was designed to achieve high-speed continuous casting. The results show that to make full use of the cooling water in the water slot, the width and height of a single water slot should be less than 8 mm. Compared with the conventional mold without the water slot structure, the temperature of the mold with the water slot structure significantly decreases. The final design of the mold water slot system is as follows: the water slot width and depth are 8 mm, and the number of water slots on one side of the mold is 9. The water slots have a symmetrical distribution, and the symmetrical plane is the middle plane of the mold. The high-speed continuous casting experiment was carried out, and the casting speed can reach 4–4.5 m/min. The water slot mold in this study can be applied in the high-speed continuous casting process.

Position‐based fluid simulation for robotic injection sealing of pavement cracks

AbstractAutomated crack sealing could significantly benefit the maintenance of road pavements, but there is difficulty in depositing the correct volume of sealant material into the hidden crack space. A simulated model of the material flow within a crack space would allow the development of a predictive control scheme, such that the repair robot can apply suitable trajectories and operational parameters to accomplish neatly sealed surfaces. For the first time, the position‐based fluid (PBF) method, a computationally cheap and fast but approximate model of fluid flows, is studied for its feasibility for sealant flow simulation in the robotic injection crack sealing scenario. A Real‐to‐Sim experiment is performed, in which a PBF simulation of sealant in a virtual robotic crack sealing environment is mirrored from the physical lab setup. The fluid simulation is tuned to match the real‐world dynamics through comparison with 132 simulation runs, varying the artificial viscosity parameters (fluid–fluid viscous interaction) and (fluid–wall viscous interaction). It was found that had a varied three‐stage influence on the simulation error while 's negative influence on the simulation error only effectively applied to fluids satisfying . Through comparing the physical and virtual crack sealing results, the simulation was validated with an average fluid level error of 1.26 mm along a 3.1 mm wide, 16 mm deep and 80 mm long artificial crack, which shows the usefulness of the PBF method for robotic injection sealing. The accuracy and computational requirements of the PBF method are also discussed.

Multi-objective optimization of parameters design based on genetic algorithm in annulus aerated dual gradient drilling

The optimization of drilling parameters is crucial for resolving the drilling problems in low-pressure and leaky formations using the annulus aerated dual gradient drilling technology. However, the previous studies have mostly focused on engineering applications and wellbore fluid flow models, with less emphasis on parameter optimization. This paper combines the wellbore multiphase flow model with genetic algorithms for the first time, proposing a key parameter optimization method for annulus aerated dual gradient drilling based on genetic algorithms. The study investigates the impact of selection operators on the performance of genetic algorithms and compares genetic algorithms with PSO algorithm and SAA. The results indicate that the convergence and stability of genetic algorithms can be improved by enhancing the selection operators. Compared to the gas–liquid ratio parameter optimization method, the IRSGA optimization method reduces the cost coefficient by 36.46%. Through comparative analysis of different optimization methods, the IRSGA demonstrates over 95% accuracy in large-scale computations. The research findings contribute to the optimization of parameters design under low-cost conditions and are of significant importance for promoting the use of this technology to address the serious issue of lost circulation in drilling technology.

A pressure-loss model for flow-through round-hole perforated plates of moderate porosity and thickness in laminar and turbulent flow regimes

In this paper, we proposed a novel fluid flow model for pressure loss through plates with circular perforations in both laminar and turbulent flows. The design of this model is based on the recent measurements conducted at ONERA in the framework of the ongoing European Union H2020 INVENTOR project, as well as an existing model for laminar flows. The new model is then validated against existing numerical simulations in the laminar regime and experiments in the turbulent regime. Overall, the predictions given by the new model agree well with the numerical simulations and experiments, and are superior to other models in the literature. This is significant, considering that the present model is much simpler than these previous models. To demonstrate the applicability of the new model in numerical simulations, two-dimensional channel flows are simulated using Reynolds-averaged Navier–Stokes (RANS) equations with the new model as a pressure-drop source term added to the momentum equations. Results show that the RANS predictions agree very well with the present model predictions.

Construction of the absorbing boundary condition for the flow of Oldroyd-B fluid over a semi-infinite plate with magnetic effect

As a kind of non-Newtonian fluid, the Oldroyd-B fluid has widespread applications. To study the flow characteristics deeply is of great significance. In this paper, we consider a simple model of the Oldroyd-B fluid flow over a semi-infinite plate in a magnetic field. The governing equation is formulated, and the numerical solutions are obtained using the finite difference method. To deal with the semi-infinite region, the artificial boundary method is applied to construct the absorbing boundary condition (ABC) with the (inverse) z-transform, which converts the semi-infinite region to a finite one. To test the accuracy of the numerical scheme, a numerical example by introducing the source term is presented. Graphs show the rationality of the ABC by comparing the fluid flow velocity between the direct truncated boundary condition and the ABC. The effects of the amplitude, the frequency, the relaxation time parameter, the retardation time parameter, and the magnetic field on the magnitude and the cycle of flow velocity are investigated and discussed. The main findings are that the retardation time parameter promotes the velocity of the fluid flow, while the relaxation time and magnetic field hinder the fluid flow. When the relaxation time is equal to the retardation time, the Oldroyd-B fluid can approximate the Newtonian fluid. In addition, the oscillating cycle becomes shorter for a smaller relaxation time parameter or a larger magnetic field and frequency.

Simulating chemical mixing and molten pool shape in dissimilar welds using thermal fluid dynamics

Estimating the properties of dissimilar metal welded joints made using modern high-energy beam techniques presents significant challenges due to the complex nature of the process. These complexities arise from the different thermal and mechanical properties of the materials involved. The properties of a welded joint are primarily determined by the element mixing and final chemical composition when two dissimilar metals are fused together, or when a dissimilar filler material is used. Hence, a representative model capable of tracking elemental distribution and temperature is essential for accurately estimating the micro-scale and macro-scale mechanical properties of the joint, thus optimising the joining process. In this work, a high-fidelity thermal fluid flow model in the multiComponentlaserbeamFoam computational fluid dynamics (CFD) solver is used to simulate the process of laser beam welding. For this purpose, the joining process of AISI 304 stainless steel with a low alloy steel filler material (G3Si1) is simulated. This framework is rigorously validated with experimental results showing the capabilities of such modelling approach. Different strategies to model the filler and material properties are explored: a stationary filler model, applied through the parent material's thickness, was found to accurately mirror experimental results. This model is then used to study the flow properties, thermocapillary effect, and diffusion on the intermixing of composition, aspects that have not been previously examined in depth. The thermocapillary forces were concluded to be the most significant, dictating the peak composition value, the shape and topology of the molten pool. Diffusion fluxes were found to be negligible and not responsible for the majority of the mixing.

Permeability Data Treatment from Analogous Outcrop for Use in Three-Dimensional Reservoir Model

Over the past forty years, the study of analogous outcrops has become a common practice in the petroleum industry to access more comprehensive geological datasets and better parameterize various geological features. As most reservoirs do not outcrop and all the data obtained are restricted to those collected from wells located in areas of major interest or from indirect measurements, the study of analogous outcrops has brought important contributions to improve the production routines and still represents a helpful information resource. The use of data from analogous outcrops permits, for example, to estimate the sedimentary facies distribution in true reservoirs, and thus to improve on the reliability of fluid flow modeling during the oil field exploration. However, such data must be processed to become equivalent to the data collected under the reservoir conditions and the results obtained to be more realistic. This work presents the statistical method used to make permeability data obtained from an outcrop compatible with the subsurface conditions of poorly consolidated and tectonically deformed sandstone reservoirs. The studied outcrop is predominantly composed of Eocene fluvial sandstones (Resende Formation) of the Volta Redonda Basin, located in the Central Segment of the Continental Rift of Southeastern Brazil. These deposits are affected by deformation bands and faults. From statistical analysis, it was intended that the permeability data become more suitable to be used, in the next phase of the studies, to build a 3D flow model, in which it will be possible to test the potential of different tectonic structures acting as hydraulic barriers in poorly consolidated and deformed reservoirs. The methodological approach applied in this study made it possible to turn compatible the permeability data obtained in conditions of no confining pressures from the outcrop with reservoir conditions under confinement pressures of 2,000 psi. Such pressure conditions are frequently observed in important Maastrichtian reservoirs found in the Brazilian Southeastern Margin.

Peridynamic modeling of seepage in multiscale fractured rigid porous media

AbstractThe numerical simulation of seepage in fractured porous media holds significant relevance for subsurface energy development. The presence of fractures at various scales profoundly influences the hydraulic properties of porous media during seepage. A peridynamic (PD)‐based frame is proposed for the seepage problem analysis of multiscale fractured porous media, in which micro‐fractures are implicitly represented like the porous media, macro‐fractures are explicitly represented. For fluid flow modeling, the peridynamic bonds are divided into three types: pore seepage bond, fracture seepage bond, and fluid exchange bond. The micro‐permeabilities of different bonds are derived by Darcy's law, Poiseuille's law, and fluid exchange model, respectively. The proposed peridynamic model can naturally simulate the seepage problem of porous rock with multiscale fractures in a unified framework. Then, four cases of pore seepage and fracture seepage are analyzed using the proposed model, fractured porous media seepage with micro‐fractures and macro‐fractures are respectively considered. The predicted results are compared with the available theoretical solutions, the close agreement shows that the wide validity and applicability of the proposed model in multiscale seepage problems.

Simulation of two-phase flow in 3D fractured reservoirs using a projection-based Embedded Discrete Fracture Model on Unstructured tetrahedral grids (pEDFM-U)

The modeling of fluid flow in heterogeneous, anisotropic and fractured porous media is relevant in many applications, including hydrocarbon and groundwater extraction, dispersion of contaminants, hydrogen or carbon dioxide (CO2) storage. Thus, accurate and scalable simulation of fluid flow through these formations continues to be a great challenge. The presence of fractures that are explicitly modeled, ranging from flow barriers to highly conductive channels, significantly increases the complexity of the numerical simulation. The Embedded Discrete Fracture Model (EDFM) produces results that can be as accurate as those obtained using equidimensional Discrete Fracture Models (DFM) at a much lower computational cost for highly conductive fractures, but it is not adequate for impermeable barriers. In contrast, the pEDFM (projection-based Embedded Discrete Fracture Model) produces accurate results for both, channels and barriers by using additional matrix-fracture connectivities. In its current versions, it is restricted to cartesian and corner-point grid geometries and to the classical Two Point Flux Approximation (TPFA) scheme. In this work, for the first time, the pEDFM is extended to handle unstructured tetrahedral meshes (pEDFM-U). In addition, interface fluxes are approximated by using the Multipoint Flux Approximation method with a Diamond stencil (MPFA-D). This allows for simulation of highly heterogeneous and anisotropic geo-models. The developed method is robust and can deal with full permeability tensors on arbitrary tetrahedral meshes. The advective terms are discretized considering an implicit First Order Upwind (FOU) method. Our method is implemented within the DARSim (Delft Advanced Reservoir Simulation) open-source simulator framework. Through several test cases, the proposed method showed to be robust and capable to accurately capture the effects of both high and low permeability fractures for general tetrahedral meshes, under arbitrary heterogeneous and anisotropic permeability tensors for the rock matrix.

A Hermite-type collocation mesh-free approach for simulating incompressible viscous fluid flows

In this work, a novel Hermite-type mesh-free model for incompressible viscous fluid flows is proposed, as a way, to overcome the numerical difficulties experienced by solving under weak or strong formulation the pure stream-function Navier–Stokes equation. In this model a dimensionless virtual domain is utilized, in order to make an accurate dimensionless shape-functions of the recently developed Hermite-type collocation Weighted Least Square approximation, by using dimensionless scale parameters. Then, a Jacobian transformation matrix is built to express the shape-functions spatial derivatives from the virtual to the considered domain. The resolution of the obtained nonlinear algebraic system is performed by the High Order Continuation Method. Numerical tests were investigated on incompressible viscous isothermal fluid flows in lid-driven cavity, backward-facing step, sudden expansions and around various obstacle shapes. They show the advantages of the proposed model compared to the reference Hermite-type collocation models used for pure stream-function equation and the weak Galerkin procedures as Finite Element Method and Element Free Galerkin method, in term of computation accuracy, number of degree of freedom, implementation simplicity and computation time. The numerical and experimental results of literature confirm the validity and capability of the proposed dimensionless model to simulate fluid flows in a expended-lengths inflow–outflow geometry and around obstacles of circular, inclined elliptical and Joukowski airfoil shapes.

X-ray Insights into Fluid Flow During Rock Failures: Nonlinear Modeling of Fluid Flow Through Fractures with Varied Roughness

Fluid flow and evolution mechanisms in fractured rocks are fundamental tasks in engineering fields such as geohazards prediction, geothermal resource exploitation, oil and gas exploitation, and geological sequestration of carbon dioxide. This study employed an enhanced X-ray imaging digital radiography to investigate nonlinear flow model of fluid through different roughness fractures. The X-ray images of fluid flow during rock failure were analyzed using a multi-threshold segmentation method applied to the X-ray absorption dose. The result show that a proposed nonlinear flow equation considers the joint roughness coefficient and the uniaxial compressive strength of the jointed rock, enabling a better understanding of the nonlinear flow behavior in fractured rock masses. This modeling approach has important theoretical and practical implications. By accounting for key factors influencing fluid flow behavior, it can help guide monitoring efforts to support early warning of fractured rock mass instability. Additionally, a more mechanistic understanding of flow processes may inform strategies to prevent engineering geological hazards.

Lie group and stability analysis of tangent hyperbolic fluid flow driven by a shrinking sheet

This study elaborates on the mathematical modeling of tangent hyperbolic fluid flow driven by a shrinking sheet in a porous medium. The roles of Soret-Dufour and thermal radiation are considered to model the energy and concentration equations. The primary objective is to find an appropriate similarity transformation through Lie group analysis, which helps to produce the self-similar equations from the governing nonlinear partial systems. The similarity solutions are calculated numerically using the “bvp4c” solver in Matlab. Additionally, adequate suction is required to obtain the similarity solutions. As expected, dual solutions are found within a certain range of the suction parameter. The skin friction coefficient, heat, and mass transfer rates at the sheet are observed for pertinent flow constraints of physical interest. It reveals that the dual solutions bifurcate from a critical point, and beyond this point, no solution exists. Furthermore, the branches of dual solutions on the nondimensional velocity, temperature, and concentration profiles depict different characteristics. Thus, a linear temporal stability analysis has been employed to test the flow stability, revealing that the upper branch is physically reliable. The heat transfer rate increases by 7.69% and 9.55% in the upper and lower branches, respectively, for Soret parameter changes from 0.6 to 0.9. Meanwhile, the mass transfer rate decreases by 85.30% and 324.60% in the upper and lower branches, respectively. The consequences of Weissenberg and suction parameters show an opposite character on the velocity, temperature, and concentration profiles in the upper branch.

Force convective heat transfer simulation in a rectangular channel with multiple square obstacles via finite element method

This study investigated fluid flow and forced convective heat transfer in rectangular microchannels with square barriers, as illustrated in Fig. 1 . In the first situation, three obstacles were positioned along the microchannel’s top wall. In the second scenario, obstacles were positioned along the microchannel’s bottom wall. In the final example, three square obstacles are placed symmetrically on either side of the microchannel wall. With the help of the Finite Element Method (FEM), we investigate the physicochemical behavior of the microchannel. The development of computer code within COMSOL multiphysics made it possible to simulate heat transport and fluid flow. The results include the implications of the rarefaction effect on fluid flow and heat transmission and decisions regarding the location of barriers and the shape of obstacles in squares. In addition, with the lowest value in skin friction and a lower Nusselt number, the third example, which has barriers on both sides, provides a valuable method for reducing the fluid temperature at the exit of the microchannel. This is because it has barriers on both sides. In the section under “Results and Discussion,” we provide an in-depth analysis of the numerical data derived from the microchannel. • Objective: This study aims to numerically investigate forced convective heat transfer in a rectangular channel featuring multiple square obstacles. The simulation employs the FEM to model fluid flow and temperature distribution. • Geometry and complexity: The channel geometry incorporates square obstacles, introducing geometric complexity. The FEM is chosen for its capability to handle intricate geometries accurately.

Innovative stochastic finite difference approach for modelling unsteady non-Newtonian mixed convective fluid flow with variable thermal conductivity and mass diffusivity

A novel stochastic numerical scheme is introduced to solve stochastic differential equations. The development of the scheme is based on two different parts. One part finds the solution for the deterministic equation, and the second part is the numerical approximation for the integral part of the Wiener process term in the stochastic partial differential equation. The scheme’s stability and consistency in the mean square sense are also ensured. Additionally, a respective mathematical model of the boundary layer flow of Casson fluid on a flat and oscillatory plate is formulated. Wiener process terms perturb the model to be studied. This scheme will be solved in contexts including deterministic and stochastic. The influence of different parameters on velocity, temperature, and concentration profiles is demonstrated in various graphical representations. The main objective of this study is to present a reliable numerical approach that surpasses the limitations of traditional numerical methods to analyze non-Newtonian mixed convective fluid flows with varying transport parameters. Our objective is to demonstrate the capabilities of the new stochastic finite difference scheme in enhancing our comprehension of stochastic fluid flow phenomena. This will be achieved by comprehensively examining its mathematical foundations and computer execution. Our objective is to develop a revolutionary method that will serve as a valuable resource for scientists and engineers studying the modeling and understanding of stochastic unstable non-Newtonian mixed convective fluid flow. This method will address the challenges posed by the fluid’s changing thermal conductivity and mass diffusivity.

A positivity preserving and oscillation-free entropy stable discontinuous Galerkin scheme for the reactive Euler equations

The reactive Euler equations are a basic model for fluid flows with chemical reactions. In this work, we construct a high order positivity preserving and oscillation-free entropy stable discontinuous Galerkin (DG) scheme for the reactive Euler equations. The main ingredients of the scheme include (i) entropy preserving and entropy stable fluxes to achieve entropy stability, (ii) artificial damping terms to restrain spurious oscillations near the shocks, and (iii) positivity preserving limiters to guarantee the positivity of solutions. These ingredients are compatible with each other so that our scheme simultaneously enjoys the properties of entropy stable, oscillation-free and positivity preserving. Another distinctive feature of our scheme is that it is entropy stable for both the thermodynamic and mathematical entropies. Numerical experiments validate the designed high convergence orders of the scheme and demonstrate its good performances for discontinuous problems.

Radiation effect on convective boundary layer dusty flow over a stretching surface

The effect of radiation evolved from fluids and particles on a convective balanced boundary layer dusty fluid flow model has been analyzed over a vertical stretching surface. Models are available with the consideration of radiation and viscous dissipation in fluid phase only. However, an equal and opposite reaction/force is also developed in the particle/dust phase, which was not taken into account in the previous literature. So, this paper investigates a model where the radiation and viscous dissipation are coupled through both the fluid and particle phase equations. A linear stretching of surface generates the boundary layer flow. By the help of suitable similar transformation, the prevailing equations are transferred to ordinary non-linear differential equations of order three and are solved numerically by the bvp4c method of MATLAB. An analysis has been performed to show the effectiveness of different thermophysical parameters on different boundary layer characteristics. The numerical results are in good agreement with the past literature, validating the present method and result. Graphs are plotted for different flow characteristics to explore the physics of problem.