Moving Boundary Conditions Research Articles

Examining a Conservative Phase-Field Lattice Boltzmann Model for Two-Phase Flows

In this study, a conservative phase-field lattice Boltzmann model is examined for simulating immiscible two-phase flows with large density and viscosity ratios. This model is built upon the Allen–Cahn equation, incorporating a filtered collision operator and high-order corrections in the equilibrium distribution functions. The numerical model is also integrated with the volumetric boundary scheme and the immersed boundary method to achieve various stationary and moving boundary conditions on arbitrary geometries for different application scenarios. A comprehensive evaluation of this phase-field solver is conducted through a range of academic and industrial cases. First, droplet splashing cases at different Reynolds numbers are studied. The phase-field LB model effectively captures the surface wave motion and splashing of the droplet, although some smearing of small structures is observed due to the diffused interface property of the numerical model. Second, a tuned liquid damper is simulated, accurately capturing sloshing forces on solid walls. In the simulation of a dam-breaking case, predicted gauge pressure and free-surface elevation time histories compare well with experimental data. Lastly, a gearbox case under dip lubrication is simulated, with both the gearbox churning loss and oil distribution being well predicted across a range of rotating speeds. The validation studies demonstrate the effectiveness of the present phase-field lattice Boltzmann model in simulating immiscible two-phase flows with large and realistic density and viscosity ratios. The strengths, limitations, and weaknesses of the conservative phase-field LB model are discussed, and suggestions for the development and application of this numerical model are provided.

Implementation of nozzle motion for material extrusion additive manufacturing in Ansys Fluent

ABSTRACT Most computational fluid dynamics (CFD) modelling of material extrusion additive manufacturing (MEX-AM) mainly relies on a moving boundary condition applied to the print bed and not the direct modelling of the motion of the nozzle. This paper presents step-by-step and detailed implementation of the nozzle motion as well as non-isothermal non-Newtonian flow during MEX-AM in Ansys Fluent. For nozzle motion the overset approach is used for the meshing which allows for the nozzle and the rest of the domain to be meshes separately, streamlining meshing and motion. The method is initially used to simulate a single strand, which was validated against experimental and numerical data. It was then applied to demonstrate out-of-plane nozzle motion in two case studies: three-layer printing and printing on a ramp. The model is further developed to simulate a single strand deposition with the well-known Cross–William–Landel–Ferry (Cross-WLF) behaviour for a thermal and shear-dependent material flow.

Analytical solution to the two-dimensional inverse heat conduction problem in an axisymmetric cylindrical coordinate system

The inverse heat conduction problem involves estimating an unknown cooling or heating action based on internal temperature histories in a body. Such a problem is ill-posed because the estimated results are highly sensitive to input data noise. An analytical solution is developed for the two-dimensional inverse heat conduction problem in an axisymmetric cylindrical coordinate system using the Laplace transform technique. On the basis of the known temperatures at multiple measuring points distributed on two cylindrical measuring surfaces along the axial direction inside the solid, the expressions for the surface temperature and heat flux are explicitly obtained in the form of a power series of time and eigenfunctions of the space variable. A comprehensive estimation error assessment is conducted using the internal temperature distribution that is obtained using a direct heat conduction analysis under the prescribed stationary and moving boundary conditions. The constant thermal condition is well reproduced using the present inverse solution, except in the vicinity of the discontinuity point. In addition, the effective heat flux and effective heat transfer coefficient are introduced to obtain the best estimation of the transient heat transfer in the major cooling area of the rotating cylinder.

Exploring enhanced heat transfer in wavy porous enclosures: Optimization and analysis of ternary nanofluid integration under varied boundary conditions with MHD mixed convection

This study explores the application of Al2O3-ZnO-Fe3O4/Water ternary nanofluids for enhanced thermal management in engineering applications, addressing the MHD Darcy–Forchheimer problem with an emphasis on optimizing cooling processes in a 2D-wavy cavity under various moving boundary conditions. Aimed at surpassing the limitations of conventional cooling fluids, the research employs the finite volume method within the OpenFOAM® framework to investigate the impact of nanofluid integration on heat transfer efficiency and entropy generation, utilizing partial heating and eight distinct boundary scenarios. By comparing the performance of ternary nanofluids against that of hybrid and mono nanofluids, we identify optimal conditions that significantly enhance cooling effectiveness, as evidenced by a 37% improvement in heat exchange efficiency over water. The findings demonstrate the superior performance of Al2O3-ZnO-Fe3O4/Water nanofluids in achieving higher average Nusselt numbers at low Darcy numbers, despite an increase in entropy. Optimal conditions were identified for the most favorable scenario involving the movement of cavity lids, based on the Nusselt number, specifically in Case 7 (ul1+ and ul2−). Decreasing the number of waves in the cavity enhances heat transfer and reduces irreversibility. Finally, the study shows that the influence of lid motion on skin friction significantly varies with Richardson numbers, and the use of nanofluids over pure water notably reduces skin friction.

The Behavior of Long Thin Rectangular Plates under Normal Pressure-A Thorough Investigation.

Thin rectangular plates are considered basic structures in various sectors like aerospace, civil, and mechanical engineering. Moreover, isotropic and laminated composite plates subjected to transverse normal loading and undergoing small and large deflections have been extensively studied and published in the literature. Yet, it seems that the particular case of long thin plates having a high aspect ratio appears to be almost ignored by various scholars despite its engineering importance. The present study tries to fill this gap, yielding novel findings regarding the structural behavior of long thin plates in the small- and large-deflection regimes. In contrast to what is normally assumed in the literature, namely that a long plate with a high aspect ratio can be considered an infinitely long plate, the present results clearly show that the structural effects of the ends continue to exist near the remote ends of the long plate. An innovative finding is that long plates would (only on movable boundary conditions for the large-deflection regime) exhibit a larger mid-width displacement in comparison with deflections of infinitely long plates. This innovative higher deflection appears for both small and large-deflection regimes for both all-around simply supported and all-around clamped boundary conditions. This new finding was shown to be valid for both isotropic and orthotropic materials and presents a novel engineering approach for the old assumption well quoted in the literature that a relatively long plate on any boundary condition can be considered an infinite plate. Based on the present research, it is recommended that this assumption should be used carefully as the largest plate mid-deflection might occur at finite aspect ratios.

Mott waves and fragment size in viscoplastic metals

Previous ductile fragmentation analysis involves unloading wave (Mott wave) propagations in rate-independent rigid-plastic materials. This paper studies the dynamic fragmentations of a rigid-viscoplastic material in which there exists a rigid unloading zone and a viscoplastic unloading zone. A linear diffusion equation incorporating a moving boundary condition for the viscoplastic unloading zone is presented. The fracture process of an isolated crack in the infinite medium, and that of an array of equally spaced cracks, are investigated numerically. The crack array problem reveals an optimal crack spacing upon which the material fails and unloads most rapidly. Based on the 'principle of the rapidest unloading (PRU)', this crack spacing is regarded as the measure of fragment size. Systematic numerical calculations are conducted to obtain the fragment size data as functions of strain rate and viscosity coefficient. A modified Grady-Kipp fragment size formula is proposed to accommodate the viscous effect. In the case of non-viscous material, the formula returns to the classical Grady-Kipp fragment size model. Finite element simulations using rate-dependent constitutive model show similar trend of viscous effect on the fragment sizes, and the modified fragment size formula yields better agreement with the simulated data.

Enhanced Aerodynamic Performance of a Two-Dimensional Airfoil Using Moving Boundaries

The effects of moving boundary conditions on the aerodynamic performance of a two-dimensional NACA 0012 airfoil at different angles of attack (α) in a uniform freestream at a Reynolds number of 10,000 are numerically studied. The moving boundary conditions are motivated by inviscid potential flow around the airfoil, which also satisfies the viscous equations of motion. In this study, the wall is moved at the slip velocity of the inviscid flow, or a fraction of it. These prescribed moving boundary conditions are shown to suppress vortex shedding, thus allowing the drag to go toward zero and the lift coefficient toward 2πα over a wide range of angles of attack (α≤20°) even in the separated flow regime. It is shown that moving boundary conditions are effective over a wide range of their strengths with respect to the overall power required (required to overcome aerodynamic drag and move the airfoil boundary). This power is shown to attain a minimum near the inviscid flow moving boundary condition, which is around 10% or less of the power required for the stationary boundary condition. Finally, the effectiveness of the moving boundary conditions is demonstrated for fully turbulent flow regimes at Re=6 million as well.

OpenPFC: an open-source framework for high performance 3D phase field crystal simulations

We present OpenPFC (https://github.com/VTT-ProperTune/OpenPFC), a state-of-the-art phase field crystal (PFC) simulation platform designed to be scalable for massive high-performance computation environments. OpenPFC can efficiently handle large-scale simulations, as demonstrated by our strong and weak scaling analyses up to an 81923 grid on 65 536 cores. Our results indicate that meaningful PFC simulations can be conducted on grids of size 20483 or even 40963, provided there is a sufficient number of cores and ample disk storage available. In addition, we introduce an efficient implementation of moving boundary conditions that eliminates the need for copying field values between MPI processes or adding an advection term to the evolution equations. This scheme enhances the computational efficiency in simulating large scale processes such as long directional solidification. To showcase the robustness of OpenPFC, we apply it to simulations of rapid solidification in the regime of metal additive manufacturing using a recently developed quantitative solid-liquid-vapor PFC model, parametrized for pure tungsten (body-centered cubic) and aluminum (face-centered cubic).

A Conceptual Framework for Modeling Spatiotemporal Dynamics of Diesel Attenuation Capacity: A Case Study across Namyangju, South Korea

The vadose zone acts as a natural buffer against groundwater contamination, and thus, its attenuation capacity (AC) directly affects groundwater vulnerability to pollutants. A regression model from the previous study predicting the overall AC of soils against diesel was further expanded to the GIS-based overlay-index model. Among the six physicochemical parameters used in the regression model, saturation degree (SD) is notably susceptible to climatological and meteorological events. To accommodate the lack of soil SD historical data, a series of infiltration simulations were separately conducted using Phydrus code with moving boundary conditions (i.e., rainfall records). The temporal variation of SD and the resulting AC under transient conditions are captured by building a space–time cube using a temporal raster across the study area within the designated time frame (1997–2022). The emerging hot spot analysis (EHSA) tool, based on the Getis–Ord Gi* and Mann–Kendall statistics, is applied to further identify any existing pattern associated with both SD and AC in both space and time simultaneously. Under stationary conditions, AC decreases along depth and is relatively lower near water bodies. Similarly, AC cold spot trends also show up near water bodies under transient conditions. The result captures not only the trends across time but also shows the exact location where the changes happen. The proposed framework provides an efficient tool to look for locations that have a persistently low or a gradually decreasing ability to attenuate diesel over time, indicating the need for stricter management regulations from a long-term perspective.

Numerical simulation of flow behavior in basilar bifurcation computed tomography angiography.

In this study, a moving boundary deformation model based on four-dimensional computed tomography angiography (4D-CTA) with high temporal resolution is constructed, and blood flow dynamics of cerebral aneurysms are investigated by numerical simulation. A realistic moving boundary deformation model of a cerebral aneurysm was constructed based on 4D-CTA in each phase. Four hemodynamic factors (wall shear stress [WSS], wall shear stress divergence [WSSD], oscillatory shear index [OSI], and residual residence time [RRT]) were obtained from numerical simulations, and these factors were evaluated in basilar artery aneurysms. Comparison of the rigid body condition and the moving boundary condition investigating the relationship between wall displacement and hemodynamic factors clarified that the spatial-averaged WSS and maximum WSSD considering only the aneurysmal dome has a large difference between conditions during the peak systole, and there were also significant differences in OSI and RRT.

Experimental and computational investigation of heat transfer during quenching of semi-solid aluminum plates under hot cracking condition

The present work attempts to study the cooling characteristics of 7050 aluminium alloy under semi-solid conditions during the jet impingement quenching. An aluminium plate heated to 485℃ (10% liquid fraction) is prone to hot cracks, causing large fluctuations in the temperature data. The 2-D direct heat transfer problem is formulated with the finite element technique, and moving boundary conditions are applied to simulate the quenching process. The heat flux is estimated from the boiling curve parameters (Qmax, TDNB, TLeid) by matching the simulated and experimental temperature data. The cracks are incorporated as the interface elements in the finite element domain along with the phase change model to simulatethe heat transfer phenomena. The influence of phase change and hot cracks on heat transfer is studied in detail with static and dynamic cracking conditions. The parity plot reveals that experimental and simulation results are in good agreement for uncracked plates, with an error range of ± 3% and R2 = 0.9987. Phase change incorporation improves the simulation results for cracked plates, reducing the error range from ± 10% (without phase change) to ± 5% (with phase change) along with R2 values of 0.9929 and 0.9863, respectively. The Boiling curve parameters for the cracked plate are found to be Qmax: 7.2 MW/m2, TDNB: 190℃, and TLeid: 450℃. Further, the findings show that the crack originates in the impingement zone of the quenched side of the plate.

Fractional differential equation with movable boundary conditions

In this research paper, we discuss the complex-valued solutions for the nonlinear fractional boundary value problem (FBVP) of complex order (δ = τ + ιa; 1 < τ ≤ 2, a ∈ R+) with movable boundary conditions. The fractional operators are taken in the sense of Riemann-Liouville (R-L) with complex order. By using the concept of Green’s function, the existence and uniqueness of solutions are established in this article. Also, we prove that the FBVP of complex order with movable boundary conditions is Ulam-Hyers Stable. Using illustrative examples, the results for this nonlinear FBVP have been shown.

Heat Transfer in the Solid Cathode of a Hollow Cathode Plasma Torch

After recalling the working principle of hollow cathode plasma torches, we evaluate the heat flux profile on the cathodic arc root. This evaluation takes into account the physics of the cathode sheath. Particular attention is devoted to electron emission from the cold copper cathode. This heat flux profile is then used as a moving boundary condition to obtain the temperature field in the solid cathode with a heat conduction study, with the aim of discussing the problem of its erosion.

Modeling of environmentally assisted intergranular crack propagation in polycrystals

AbstractPolycrystalline nickel‐based superalloys experience accelerated intergranular crack growth when exposed to dwell times in oxygen‐rich environments and a combination of high temperature and tensile mechanical loading. Increasing crack growth rates are observed for increasing amounts of environmental oxygen in a certain oxygen concentration range, while below and above that range crack growth rates remain approximately constant. A fully coupled chemo‐mechanical modeling framework accounting for the degradation of grain boundaries by oxygen has been presented by the authors. In this work, we expand the framework by a moving boundary condition to capture a realistic oxygen flux in grain boundary cracks for both edge cracks connected to the environment and interior cracks. In numerical simulation results, the behavior of the moving boundary condition is shown for intergranular crack propagation through a polycrystal subjected to cyclic loading. Finally, the capabilities of the modeling framework to qualitatively predict the dependence of the average crack growth rate on the environmental oxygen content, load level, and dwell time are evaluated and it is shown that predictions qualitatively agree with experimental observations for intergranular fracture.

Numerical simulation of the extrusion and layer deposition processes in 3D concrete printing with the Particle Finite Element Method

Abstract3D Concrete Printing (3DCP) is a rapidly evolving technology that allows for the efficient and accurate construction of complex concrete objects. In this paper, a numerical modelling approach is presented for the simulation of the printing process of cementitious materials, based on the homogeneous fluid assumption. To cope with the large deformations of the domain and the nonlinearity resulting from the use of a non-Newtonian rheological law, the Navier–Stokes equations are solved in the framework of the Particle Finite Element Method (PFEM). Furthermore, tailored solutions have been formulated and implemented for the time-dependent moving boundary conditions at the nozzle outlet and for the efficient handling of the inter-layer contact in the same PFEM framework. The overall computational cost is decreased by the implementation of an adaptive de-refinement technique, which drastically reduces the number of degrees of freedom in time. The proposed modelling approach is finally validated by simulating the printing process of six rectilinear layers and one multi-layer “wall”. The results show good agreement with the experimental data and provide valuable insights into the printing process, paving the way for the use of numerical modelling tools for the optimization of materials and processes in the field of 3D Concrete Printing.

Generalized FDTD scheme for the simulation of electromagnetic scattering in moving structures.

Electromagnetic scattering in moving structures is a fundamental topic in physics and engineering. Yet no general numerical solution to related problems has been reported to date. We introduce here a generalized FDTD scheme to remedy this deficiency. That scheme is an extension of the FDTD standard Yee cell and stencil that includes not only the usual, physical fields but also auxiliary, unphysical fields allowing a straightforward application of moving boundary conditions. The proposed scheme is illustrated by four examples - a moving interface, a moving slab, a moving crystal and a moving gradient - with systematic validation against exact solutions.

Evaporation-driven gravitational instability in the liquid layer of a polymer solution: Theoretical and numerical studies

The drying of the thin liquid film of polymer solution is a complex process accompanying instabilities induced by concentration gradients that develop during the evaporation. This study investigates evaporation-driven gravitational instabilities (Rayleigh–Taylor instability) in the thin liquid film of a polymer solution based on theoretical and numerical analyses, specifically focusing on the onset of instability at the early stage of the drying process. Evaporation-driven convection is taken into account by employing a dynamic moving boundary condition and concentration-dependent material functions (dynamic viscosity and diffusivity). A theoretical analysis predicts the onset of gravitational instability (τc), showing good agreement with the results of a numerical simulation analysis (τd), suggesting scaling relationships between the onset of instability and the initial concentration (Ci), τc∼Ci−1/2, for a slow evaporation rate and dilute concentration range, which rapidly increases with an increase in the concentration due to an instability-retardation effect. A nonlinear two-dimensional numerical simulation visualizes the development of a polymer-dense layer, pluming, and a convection–diffusion flow throughout the liquid film under transient evaporation. The concentration-gradient-driven convection–diffusion flow enhances the gravitational instability and pluming further at higher frequencies. Meanwhile, for a polymer solution with high viscosity, viscosity thickening delays the onset of instability, retarding the development of instability. This study provides a fundamental understanding of the mechanism behind how convective instability develops in a drying polymer solution during evaporation and information on how to develop pluming of a polymer-dense skin layer at early stages of drying of a polymer solution film. The findings suggest that the proper control of hydrodynamic instability induced by a concentration gradient in a thin polymer solution film is important to prevent or enhance the formation of a convection pattern in the thin polymer film.

A Study of the Non-Linear Seepage Problem in Porous Media via the Homotopy Analysis Method

A non-Darcy flow with moving boundary conditions in a low-permeability reservoir was solved using the homotopy analysis method (HAM), which was converted into a fixed-boundary mathematical model via similarity transformation. Approximate analytical solutions based on the HAM are guaranteed to be more accurate than exact analytical solutions, with relative errors between 0.0089% and 2.64%. When λ = 0, the pressure drop of the Darcy seepage model could be instantaneously transmitted to infinity. When λ > 0, the pressure drop curve of the non-Darcy seepage model exhibited the characteristics of tight support, which was clearly different from the Darcy seepage model’s formation pressure distribution curve. According to the results of the HAM, a moving boundary is more influenced by threshold pressure gradients with a longer time. When the threshold pressure gradients were smaller, the moving boundaries move more quickly and are more sensitive to external influences. One-dimensional, low-permeability porous media with a non-Darcy flow with moving boundary conditions can be reduced to a Darcy seepage model if the threshold pressure gradient values tend to zero.

Modelling of Hydraulic Dynamics in Sludge Treatment Reed Beds with Moving Boundary Condition

The conventional method of simulation using fixed mesh method (FMM) of discretization is a well-known and trusted procedure in modelling hydraulic dynamics. However, new ideas of innovation in modelling should be advanced. The moving mesh method (MMM) has been considered as a novel approach in modelling hydraulic dynamics after depending on the existing simulation model for decades. The MMM is capable of describing the moving boundary condition of an actual wetland system due to water ponding. An idealized model should be able to simulate the actual hydraulic flows through the system with the corresponding porosity. Hence, a combination of MMM and FMM (MM-FMM) of discretization for hydraulic dynamics is studied in this project to model the flux with respect to water ponding scenario in a sludge treatment reed bed and unsaturated transient flow within the bed. Such method has evidently proved to simulate the actual hydraulic flows in contrast to conventional method. The application of MMM limits the maximum flux to keep within its saturated conductivity, thus reduces the effect of flow overprediction. Subsequently, the simulated results for hydraulic head and moisture content can be predicted for actual condition of different cases according to their respective fluxes.

Fluid circulation driven by collectively organized metachronal waves in swimming T. aceti nematodes.

Recent experiments have shown that the nematode T. aceti can assemble into collectively undulating groups at the edge of fluid drops. This coordinated state consists of metachronal waves and drives fluid circulation inside the drop. We find that the circulation velocity is about 2 mm/s and nearly half the speed of the metachronal wave. We develop a quasi-two-dimensional hydrodynamics model using the Stokes flow approximation. The periodic motion of the nematodes constitute our moving boundary condition that drives the flow. Our model suggests that large-amplitude excursions of the nematode tails produce the fluid circulation. We discuss the constraints on containers that would enhance fluid motion, which could be used in the future design of on demand flow generating systems.