This study presents a numerical framework for modeling two-phase flow in confined environments, focusing on the interplay between capillary and viscous forces. The model integrates the Cahn-Hilliard and Navier-Stokes (CH-NS) equations, utilizing a diffuse-interface approach to capture interfacial dynamics without the limitations of sharp-interface models. Implemented in the finite element platform FEniCS, the framework incorporates Dirichlet boundary conditions to model a fully non-wetting phase. The validation of the proposed model is achieved through two applications: The retraction of an oil droplet from a capillary tube and the drainage of water-wet microfluidic chips. Numerical results align with experimental data, demonstrating the framework's ability to replicate interfacial behaviors, including capillary-driven dynamics and fingering phenomena. This work provides a versatile computational tool for studying immiscible fluid flow, offering potential for advancements in fundamental research on microfluidics, enhanced oil recovery, and remediation of contaminated soil.
This study examines buoyancy-driven magneto-convection within an anisotropic porous cavity incorporating internal heat generation/absorption. The top and bottom boundaries are subjected to sinusoidal heat fluxes, whereas the vertical walls are thermally insulated. The flow and heat transfer behavior are numerically analyzed using the Darcy-Brinkman extended model, implemented via FVM and the semi-implicit method for pressure-linked equations (SIMPLE) algorithm. The influence of key parameters, including the periodicity parameter, permeability ratio, thermal conductivity ratio, Hartmann number, internal heat generation/absorption, and orientation angle on the flow structure and heat transfer efficiency within the system is analyzed. The findings show that the cavity exhibits a multicellular convective pattern, where the anisotropic permeability tilt induces sinusoidal flow features near the thermally active walls. In contrast, a strong magnetic field () suppresses the flow circulation, and higher levels of internal heat generation/absorption lead to reduced heat transfer efficiency. The study is conducted for a steady, two-dimensional, Darcy-Brinkman model. This study could be beneficial for the solar collector designs, thermal management systems, setups for room ventilation, and electronic cooling applications.
An extension of the direct flux reconstruction scheme for simulating compressible multi-component flows using the Euler equations is presented via adaptive filtering and positivity preservation. It is not an unknown fact that high-order schemes are not robust in the vicinity of shocks and other flow discontinuities. Thus, in the presented work, an adaptive filtering procedure for shock capturing, which dissipates Gibbs oscillations around shocks, has been used. While shock capturing dissipates spurious oscillations associated with shocks, it doesn't guarantee that the physical quantities will not attain unphysical states. These unphysical states are not just due to high-order interpolations, but also when these physical values are already near zero. Thus, in the present work, we also use a simple positivity-preserving scheme that can be applied when solving the multi-component Euler equations. The developed flow solver is then validated using problems for both 1-dimensional and 2-dimensional flows.
This paper examines the application of PINN models to solving a two-dimensional cylinder flow problem with limited data. Using data obtained by direct numerical simulation, a surrogate PINN model was developed and trained. The model utilizes the governing equations of fluid dynamics and heat transfer, enabling it to accurately predict flow parameters such as velocity components, pressure, and temperature. The direct computational flow model was numerically solved using the SIMPLE algorithm, which couples pressures and velocities. The results showed that the PINN model, which does not contain initial and boundary conditions from direct numerical simulation, is capable of reproducing complex dynamic processes such as the formation of a Kármán vortex street behind a cylinder. However, limitations were identified due to the lack of initial and boundary conditions, which led to increased errors at the boundaries of the computational domain. For example, from the data obtained using the PINN model, a very small absolute difference in error for the velocity and temperature components between the reference data and the predicted values can be noted. Thus, for the horizontal velocity component, the maximum relative error was no more than 2.5%. For the temperature component, the relative error was no more than 0.02%. However, the relative error for pressure was 60%–75%. The main reason for this large error is the lack of a reference pressure value or initial pressure conditions in the loss function. The results show that the PINN surrogate model with eight hidden layers of 200 neurons successfully copes with the task of modeling complex unsteady flow. The integration of physical laws made it possible to achieve relatively satisfactory accuracy using only 10,000 data points.
To address the challenges of multiphase flow inside the mining riser of deep-sea natural gas hydrates, a three-dimensional simulation model of gas–liquid–solid three-phase flow in the mining riser of a horizontal well is established for deep-sea hydrate. A test system is developed for gas–liquid–solid three-phase flow in the hydrate mining riser using a similar principle. The experimental results are compared with numerical simulations, and the comparison accuracy is over 90.8%. The accuracy and effectiveness of the theoretical model are verified. Based on this, the effect of particle size, gas–liquid–solid ratio, and injection flow velocity on the multiphase flow transport characteristics and flow field-riser wall collision force are investigated. The results indicate that as the particle size increases, the overall gas and liquid phase velocities do not change significantly. In the radial direction, the velocities increase from near the wall to the center of the riser. However, the solid-phase velocity decreases with increasing particle size, while the gas-phase volume fraction decreases. In contrast, the liquid-phase volume fraction increases, the solid-phase concentration decreases, and the collision force on the riser wall becomes stronger. As the gas phase proportion increases, the velocity of the gas and liquid phases also increases, with the radial direction increasing from near the wall toward the center of the riser. The velocity of the solid phase decreases as the proportion of the gas phase increases. There is no clear trend in the volume fractions of the gas and liquid phases, but the concentration of the solid phase increases with the gas phase volume fraction, also increasing the collision force. In the actual mining project, a higher flow velocity should be selected, which can not only improve the transportation efficiency, but also effectively prevent the wear of the mining riser caused by the collision of particles on the riser wall. The research results can effectively guide the safe extraction of deep-sea natural gas hydrates.
The present study is focused on several numerical experiments on high-speed compressible fluid flows inside a long horizontal multi-cylinder positioned channel using a double distribution function based extended lattice Boltzmann (LB) approach. Initially, an algorithm of the lattice Boltzmann approach to simulate the compressible flows is developed and stabilized by introducing the Lagrange multipliers approach to calculate the equilibrium distribution function, Knudsen-number-dependent relaxation time, and large adaptive stencils in the velocity discretization scheme. Subsequently, the algorithm/code is validated by comparison of the present results against the existing benchmark results. The LB simulations are carried out at the supersonic state for two different Mach numbers, 1.5 and 1.7. The channel is enclosed from the top and bottom sides, with surfaces having symmetric boundary conditions. At the inlet and outlet, Dirichlet and Neumann boundary conditions are employed, respectively, for density, velocity, temperature, and pressure. Three different studies based on the configuration of the multi-cylinders are carried out. Inside the channel, the multi-cylinders are either positioned in a tandem manner, vertical (side-by-side) manner, or staggered manner with varying angles of incidences. Various physical parameters like the coefficient of pressure, drag and lift coefficient, temperature flow field, and so forth, are computed and reported throughout the study.
In this study, the heat and mass transfer rates in electrically conducting Casson ternary hybrid nanofluid flows () were investigated, considering various factors such as variable thermal conductivity, Joule heating, viscous dissipation, chemical reactions, Darcy–Forchheimer flow, and nonlinear thermal radiation. The use of ternary hybrid nanofluids, combining aluminum oxide, copper nanoparticles, and titanium oxide in blood, can significantly improve thermal conductivity and heat transfer efficiency, making them useful in engineering fields such as heat exchangers, aerospace, renewable energy, and electronic cooling. The study focuses on the effects of nonlinear thermal radiation, viscous dissipation, Joule heating, Soret number, chemical reactions, Darcy–Forchheimer effect, and curvature on the flow of Casson fluid over a stretching cylinder. The partial differential equations governing the system are transformed into ordinary differential equations using a similarity variable and solved using the Sixth-Order Runge–Kutta (RK6) method in MATLAB, validated against previous studies for accuracy. The analysis includes the impact of physical parameters on velocity, temperature, and concentration profiles, as well as skin friction coefficient, local Nusselt number, and Sherwood number. A higher Casson parameter leads to an increased yield stress, resulting in greater resistance and a reduction in the velocity distribution. Variable thermal conductivity, nonlinear thermal radiation, Eckert number, and nanoparticle volume fraction improve heat transfer. Higher nanoparticle concentrations increase thermal conductivity, leading to improved heat transfer and higher Nusselt numbers.
We propose a locally adaptive non-hydrostatic model and apply it to wave propagation generated by a moving bottom. This model is based on the non-hydrostatic extension of the shallow water equations (SWE) with a quadratic pressure relation, which is suitable for weakly dispersive waves. The approximation is mathematically equivalent to the Green-Naghdi equations. Applied globally, the extension requires solving an elliptic system of equations in the whole domain at each time step. Therefore, we develop an adaptive model that reduces the application area of the extension, thereby reducing the computational time. The elliptic problem is only solved in the area where the dispersive effect might play a crucial role. To define the non-hydrostatic area, we investigate several potential criteria based on the hydrostatic SWE solution. We validate and illustrate how our adaptive model works by first applying it to simulate a simple propagating solitary wave, where exact solutions are known. Following that, we demonstrate the accuracy and efficiency of our approach in more complicated cases involving moving bottom-generated waves, where measured laboratory data serve as reference solutions. The adaptive model yields similar accuracy as the global application of the non-hydrostatic extension while reducing the computational time by more than .
A new Galerkin-type meshfree method is developed for solving incompressible Navier-Stokes equations by integrating the key strengths of the semi-Lagrangian (SL) method and the element-free Galerkin (EFG) method. This integration not only effectively resolves the convection-dominance problem but also fully preserves the meshfree property of the EFG method. In the absence of grid constraints, the operations of backward tracing and interpolation in the SL method can be executed more conveniently. To achieve both good stability and accuracy, the SL method is employed to handle the convection terms, while the EFG method is utilized for the diffusion terms. To decouple the velocity and pressure, a novel fractional step algorithm is derived within the SL framework. This algorithm circumvents the Ladyzhenskaya-Babuška-Brezzi (LBB) constraint and permits the utilization of equal-order velocity-pressure interpolation. Given that the SL method exhibits unconditionally stable characteristics for convection terms, the Galerkin method offers an optimal approximation for diffusion terms, the fractional step algorithm decouples velocity and pressure variables, and the meshfree feature streamlines the implementation of the SL method, the proposed method is anticipated to be an efficient approach for solving the incompressible Navier-Stokes equations. Numerical examples with available analytical solutions are solved to show the accuracy, stability, and convergence behavior of the proposed method. The results demonstrate that the new method exhibits superior stability compared to the EFG method, and it reaches a first-order convergence rate in temporal direction and second-order convergence rate in spatial direction under first-order discretization. After that, numerical tests on the square-cavity-driven flow and the doubly periodic shear layer flow further validate the accuracy and stability of the proposed method.
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