Mass Conservation Research Articles

A numerical method for simulating variable density flows in membrane desalination systems

We present a novel method for simulating unsteady, variable density, fluid flows in membrane desalination systems. By assuming the density varies only with concentration and temperature, the scheme decouples the solution of the governing equations into two sequential blocks. The first solves the governing equations for the temperature and concentration fields, which are used to compute all thermophysical properties. The second block solves the conservation of mass and momentum equations for the velocity and pressure. We show that this is computationally more efficient than schemes that iterate over the full coupled equations in one block. We verify that the method achieves second-order spatial–temporal accuracy, and we use the method to investigate buoyancy-driven convection in a desalination process called vacuum membrane distillation. Specifically, we show that with gravity properly oriented, variations in temperature and concentration can trigger a double-diffusive instability that enhances mixing and improves water recovery. We also show that the instability can be strengthened by providing external heating.

Inundation Processes with Active Sediment Transportation in the Floodplain of West Rapti River, Nepal

The present study discusses flood hazard characteristics in the lower reaches of the West Rapti River based on the results obtained from field surveys and numerical computations using depth averaged 2-D numerical models for flood flow and associated sediment transportation. To evaluate the inundation process with sediment erosion and deposition in the floodplain, a new erosion term was introduced into the mass conservation equations for suspended sediment and bed sediment. The results obtained from numerical computations indicated that field data on the spatial distributions of depths for inundation, and sediment erosion and deposition can be evaluated by the numerical model. Thus, numerical predictions were performed for the inundated areas, and the accumulated volumes of sediment erosion/deposition for floods with return periods of 50, 100, and 200 years, as a step towards damage assessment and risk assessment due to floods with active sediment transportation in the floodplains.

3D-Numerical simulation of free convection inside a cubical cavity filled with non-Newtonian-Bingham fluid

This work focuses on a numerical study of the natural convection of a non-Newtonian viscoplastic fluid within a cubic enclosure. The viscoplastic behavior is described by the Bingham model. The considered three-dimensional convective flow is confined within a cavity, subjected to a horizontal temperature gradient, where the vertical walls have two imposed temperatures while the rest of the walls are adiabatic. The Navier-Stokes equations, along with the mass and energy conservation equations, are numerically solved. Fluid flow and heat transfer characteristics are systematically studied over a wide range of Rayleigh numbers Ra (103 - 106) and Bingham number Bn (0 - 20). Finally, comparisons were made with previous results obtained in two dimensions in order to analyze the existence of a three-dimensional effect on the flow of the Bingham fluid. The results show that the Nusselt number decreases with the increase of the Bingham number, and for the large values ​​of the latter the heat transfer is done by conduction. It is also noteworthy that the critical Bn of the 2D model is higher than that of the 3D model, which confirms the existence of the three-dimensional effect. This is attributed to the presence of a wall along the Z axis which hinders and limits the flow of fluid within the enclosure.

Leaching Thermodynamics of Low-Grade Copper Oxide Ore from [(NH4)2SO4]-NH3-H2O Solution.

This paper describes a highly alkaline low-grade copper oxide ore. Copper can be selectively leached out while other metals are retained. A thermodynamic model of the CuO-(NH4)2SO4-NH3-H2O system was established for the leaching of tenorite (CuO) under conditions of mass and charge conservation. MATLAB's fitting functions, along with the diff and solve functions, were used to calculate the optimal ammonia concentration and total copper ion concentration of tenorite under different ammonium sulfate concentrations. The effects of various ammonia-ammonium salt solutions (ammonium sulfate, ammonium carbonate, ammonium chloride) on the copper leaching rate were investigated. Results show that under the conditions of an ammonia concentration of 1.2 mol/L, an ammonia-ammonium ratio of 2:1, a liquid-solid ratio of 3:1, a temperature of 25 °C, and a leaching time of 4 h, the copper leaching rate from the ammonium sulfate and ammonium chloride solutions reaches 70%, which is slightly higher than that of ammonium carbonate. Therefore, an ammonia-ammonium sulfate system is selected for leaching low-grade copper oxide due to its lower corrosion to equipment compared to the chlorination system. The impact of this study on industrial applications includes the potential to find more sustainable and cost-effective methods for resource recovery. The industry can reduce its dependence on resources and mitigate its environmental impact. Readers engaged in low-grade oxidized copper research will benefit from this study.

Sound Insulation Characteristics of Sandwich Thin-Plate Acoustic Metamaterial: Analysis and Optimization

Addressing the demand for low-frequency noise control in ships and aiming to overcome the limitations imposed by the mass law of traditional materials, a sandwich thin-plate acoustic metamaterial (SPAM) was developed in this study. This structure is characterized by its simplicity and superior sound insulation performance. A sound insulation test was conducted to validate the exceptional low-frequency acoustic suppression capability of SPAM, and the effectiveness of the analytical model was also demonstrated. Subsequently, based on this model, a sensitivity analysis of the sound insulation characteristics of the SPAM relative to structural parameters was carried out. For the optimization process, the Logistic-Sine fusion chaotic mapping was employed to refine the dung beetle optimizer (DBO), enhancing the initial population distribution. The improved dung beetle optimizer (IDBO) was then used to further optimize and elevate the sound insulation performance of the SPAM. The outcomes indicate that the IDBO boasts superior optimization proficiency and accelerated convergence, while the optimized SPAM exhibits more remarkable sound insulation capabilities. Within the frequency range of 100–315[Formula: see text]Hz, the average sound transmission loss (STL) has increased by 11.94[Formula: see text]dB when compared to the pre-optimization values.

Effect of Different Basal Media and Organic Supplements on In Vitro Seedling Development of the Endangered Orchid Species Dendrobium moniliforme (L.) Swartz

The orchid Dendrobium moniliforme faces endangerment due to habitat loss and illegal harvesting, necessitating the development of an optimized artificial propagation system to aid conservation and reintroduction efforts. This study evaluated the effects of three plant growth media, namely Murashige and Skoog (MS), Hyponex, and Orchid Maintenance Medium (OMM) (P668), and various organic additives (apple homogenate, banana homogenate, and coconut water) on the in vitro seedling growth of D. moniliforme. The results reveal that, in early postgermination stages, seedlings achieve maximum growth in the Hyponex medium, with a fresh weight (92 mg) and root length (2.7 cm) approximately 20-fold greater than those in the MS medium and OMM. After 6 months, for seedlings grown in MS medium and OMM with banana (50 g·L−1), the mean fresh weights were 29 and 107 mg, respectively; however, the highest biomass was observed in seedlings grown in the Hyponex medium with coconut water (50 mL·L−1), exhibiting a mean fresh weight of 201 mg. This study highlights Hyponex medium with coconut water as the most effective combination for promoting D. moniliforme growth and identifies suitable organic supplements for the in vitro cultivation of seedlings from asymbiotic seed culture. This propagation system offers valuable technical support for the mass production and conservation of this epiphytic orchid.

Mass conservation in the validation of fluid-poroelastic structure interaction solvers

Benchmark problems commonly used to test numerical methods for fluid-poroelastic structure interaction often rely on simple examples constructed using the method of manufactured solutions. In this work, we show that such examples are not adequate to demonstrate the performance of the method, especially in cases when the poroelastic system is written in the primal or primal-mixed formulation, and when the dynamics of the poroelastic structure are driven only by dynamic loading from the fluid, which often occurs in biomedical applications. In those cases, the only forcing on the structure comes from the interaction with the fluid at the fluid-structure interface, where the coupling conditions are imposed. One of those conditions is a kinematic condition which enforces the conservation of mass. If this condition is not accurately satisfied, the resulting dynamics might lead to highly inaccurate results in the entire domain. We present three benchmark problems: Example 1 is based on the method of manufactured solutions; Example 2 is based on parameters used in geomechanics; and Example 3 is a benchmark problem with parameters from hemodynamics. Using these examples, we test the performance of the primal, primal-mixed and dual-mixed formulations. While all methods perform well in the first two examples, the primal and primal-mixed formulations exhibit large errors in Example 3, where the densities of the fluid and solid are comparable, and the structure dynamics is purely driven by the fluid loading. To recover the accuracy, we propose to use the primal and primal-mixed methods with a penalty term, which helps to enforce the conservation of mass.

Genetic-algorithm-assisted design of chiral honeycomb membrane acoustic metamaterials for broadband noise suppression

Low-frequency sound wave reduction is hardly feasible for traditional sound absorbers such as porous media. In contrast, locally resonant acoustic metamaterials act as spatial frequency filters, effectively reducing low-frequency noise. However, these materials can have narrow bandgaps, add extra mass to the main system, and function only within a specifically adjusted frequency range. Therefore, this paper proposes a methodology for designing three-dimensional (3D) chiral honeycomb membrane-type acoustic metamaterials (MAM) based on acoustic circular dichroism (ACD), negative effective mass, and local resonance mechanisms (LRM). The paper also uses the genetic algorithm (GA) to maximize sound transmission attenuation and widen bandgaps. The accuracy of the simulations is validated with available experimental data. The key idea of the present study is to automatically design a MAM structure using modern optimization tools. A developed GA aims to maximize the average sound transmission loss (STL) across the desired low-frequency range of 0–850 Hz by optimizing the value of structural parameters associated with the configurations of masses, including rotation and linear offset, as well as their geometrical dimensions, including length and width. COMSOL Livelink with MATLAB is employed as a practical co-simulation tool to find an optimum value for structural parameters. Results indicate a 35% improvement in average STL along with an ultra-wide bandgap with a 507% bandgap coverage factor (BGCF) in the frequency range of interest, verifying the reliability of the developed algorithm. In addition, sound mitigation incidence is justified by exploring the negative effective parameters of the unit cell and displacement vector fields. The proposed designs demonstrate superior performance as both initial and optimized models broke the mass law within the investigated frequency range. Finally, the effect of the selected geometrical parameters on the objective function is observed through sensitivity analysis. This study presents the practical use of optimization algorithms to develop MAMs.

A high-order energy stable method for the MBE models with slope selection by using Lagrange multiplier approach

In this work, we develop high-order convex splitting implicit–explicit Runge–Kutta methods for Molecular Beam Epitaxy (MBE) model with slope selection, which plays key roles in materials science and physics for describing various phenomena, such as phase transitions, interactions and interfacial dynamics. Since the epitaxy surface height evolution equation is viewed as a dynamical form of a L2-gradient flow, MBE has the highly similar growing processes as the growing facets in phase-ordering process in magnetic systems. Within this context, we focus our attention on the systems with multiple components possess greater physical significance than their classical (single-component) counterparts. We rigorously prove that the proposed schemes both preserve the energy dissipation and mass conservation. Finally, the accuracy and efficiency of proposed schemes are demonstrated by some numerical experiments.

An interprocess communication-based two-way coupling approach for implicit–explicit multiphysics lattice discrete particle model simulations

In this study, the researchers have developed a Multiphysics-Lattice Discrete Particle Model (M-LDPM) framework that deals with coupled-fracture-poroflow problems. The M-LDPM framework uses two lattice systems, the LDPM tessellation and the Flow Lattice Element (FLE) network, to represent the heterogeneous internal structure of typical quasi-brittle materials like concrete and rocks, and to simulate the material’s mechanical and transport behavior at the aggregate scale. The researchers revisited the LDPM governing equations and added the influence of fluid pore pressure. They also derived the Flow Lattice Model (FLM) governing equations for pore pressure flow through mass conservation balances for uncracked and cracked volumes. The M-LDPM framework was implemented using Abaqus user element subroutine VUEL for the explicit dynamic procedure of LDPM and user subroutine UEL for the implicit transient procedure of FLM. The coupling of the two models was achieved using Interprocess Communication (IPC) between Abaqus solvers. The M-LDPM framework can simulate the variation of permeability induced by fracturing processes by relating the transport properties of flow elements with local cracking behaviors. The researchers validated the M-LDPM framework by comparing the numerical simulation outcomes with analytical solutions of classical benchmarks in poromechanics.

Construction of Kinetic Model of Vacuum Arc Magnetic Fluid Under External Magnetic Field

The external magnetic field is an important control method of vacuum arc at present. Because of its high efficiency and economy, it has become an important method to study the kinetic model of vacuum arc magnetic fluid. Therefore, the kinetic model of vacuum arc magnetic fluid under the external magnetic field is constructed. Firstly, the mass conservation equation, radial momentum conservation equation, axial momentum conservation equation, energy conservation equation, electromagnetic equations are analyzed. The boundary conditions of the dynamic model are cathode boundary, anode boundary and fluid wall boundary. The fluid dynamics calculation software FLUENT is used as the calculation platform, and its secondary development is carried out. Combining VC++self-programming and self-defined macro functions, according to the boundary conditions, the kinetic model of vacuum arc magnetic fluid under external magnetic field is solved, and the kinetic model analysis of vacuum arc magnetic fluid under external magnetic field is realized. Experimental analysis shows under the action of longitudinal magnetic field, the intensity of longitudinal magnetic field increases, the maximum point of ion rotation speed in the magnetic fluid of vacuum arc moves outward along the edge of vacuum arc, the number density of electrons gradually moves from the central axis to the radial direction, and the high density area increases first and then decreases; Under the action of transverse magnetic field, the intensity of transverse magnetic field increases, the ion pressure in vacuum arc magnetic fluid gradually shifts and increases, and the ion number density also increases.

Eulerian approach for erosion induced by particle-laden impinging jets

Particle dispersion and erosion play an important role in various engineering applications, particularly in impinging jet flows. This study presents a new Eulerian method for characterizing these phenomena in axisymmetric, laminar, and turbulent jets, impinging and transiently eroding a flat wall. The Eulerian mass and momentum conservation equations are solved assuming a one-way coupling between the flow and the particles. The carrier flow boundary layer velocity profiles in the laminar case are validated with analytical solutions. The particle calculation involves two stages, incident and reflected particles, connected via a restitution model. The reflected particles’ results offer insights into secondary erosion areas but are not used for the main erosion calculations. Subsequently, erosion at the eroded surface is computed using an empirical erosion model, followed by the displacement of computational nodes using the linear-elastic, small-strain deformation equations, all of which are solved transiently. The solutions reveal the spatial particle concentrations and momentum for different Stokes numbers: smaller Stokes particles follow the carrier flow streamlines, medium Stokes particles deviate, forming a W-shaped erosion profile, while the largest Stokes particles create a U-shaped profile. This numerical model offers a computationally efficient framework for CFD-based transient erosion calculation due to its Eulerian implementation.

Laws of conservation of mass and momentum for an ideal fluid in the inertial framework of special relativity

In the realm of Newtonian fluids, fundamental conservation laws such as those governing mass, momentum, and energy are rigorously upheld within absolute reference frames. However, within the framework of special relativity and the concept of space -time, the notions of separate conservation of mass and momentum no longer hold. Instead, the theory relies on Lorentz transformations and relative reference systems, typically denoted as S and S', moving uniformly relative to each other, each with its own temporal framework. Within the context of special relativity, particularly in the study of particles, significant findings pertain to the energy-momentum vector. These findings underscore the necessity, when studying fluids within inertial frames, to apply conservation principles to the energy-momentum tensor.

Basics of modern modeling and expansion of the relativity theory of time in the field of classical physics

Throughout history, many scientists considered time as the result of changing the world and believed that time is not true. Among those who say that time is not true, Einstein is the only one who was able to mathematically explain the relativity of time in the field of geometry (space time) and present his equations in relativistic physics. Although Einstein, like other scientists, did not provide a clear definition of time, he presented the relativity of time well. He showed that time is not independent of space and bends along with space. Also, Einstein used the speed of light to convert mass into energy to introduce the law of mass–energy equivalence. Currently, basic laws such as conservation of mass, conservation of energy and equivalence of mass and energy have been presented. Recently, due to the importance of time in the development of science, especially in the field of water and chemistry, “timemass equivalence law” has also been presented (by the author). In this research, with the aim of expanding the relativity of time in the flows of mass and energy (not the field of motion and geometry), while presenting new definitions of “phenomenon”, “time” and “specific speed of transformation”, in addition to the theory of “mass equivalence law” “Time” was completed, the general equations of equivalence of energy time—and timemass were introduced. Then, to check the results more accurately, the general masstime equation (in this study, absorption kinetics) by performing surface absorption experiments of heavy metals (Fe + 2, Pb + 2, Zn + 2, Ni + 2, Cd + 2, Cu + 2)) was investigated by the adsorbents of green walnut shell (GWH) and its biochar (GWHB), and the results are tested in different ways.

Photocatalytic antibiotic degradation in coated open microchannels by applying 2D and 3D flow modeling with kinetics

The accumulation of active pharmaceutical ingredients in the aqueous environment is a serious problem that will become even more concerning in the future. In this work, the photocatalytic degradation of ciprofloxacin (CIP) in aqueous solution was assessed over P25-TiO2 coated open microchannels with gravity-driven flow under UV-A irradiation. The deposition of different amounts of TiO2 in the microchannels was carried out via a facile, self-developed procedure. The degradation kinetics of ciprofloxacin was described via the Langmuir-Hinshelwood mechanism. Since the flow characteristics in the microchannel had influence on the concentration distribution of CIP in the microchannel, the coupled momentum and mass conservation law was solved numerically in MATLAB 2023a (2D case) as well as in ANYS Fluent 2023 R1 (2D and 3D cases). Although the implemented 2D model in MATLAB 2023a allowed the preliminary estimation of the selected kinetic parameters, namely adsorption equilibrium constant and specific Langmuir-Hinshelwood rate constant, the sensitivity of the model was not satisfactory which was attributed to the empirical correlations used for the estimation of the external mass transfer coefficient. The 2D and 3D models in ANSYS Fluent 2023 R1 predicted efficiently the outlet concentration of ciprofloxacin for different inlet CIP concentrations and liquid phase flow rates. Therefore, the as developed 2D and 3D models in ANSYS Fluent 2023 R1 can be used for the design of reactors containing coated microchannels with gravity-driven flow for photocatalytic degradation of active pharmaceutical ingredients.

An efficient product design tool for aftertreatment system

A numerical simulation technique based on the conservation of mass and energy in the gas phase has been developed to optimize the aftertreatment system with the lowest costs. Both oxygen storage capacity model and catalyst deterioration model have been integrated into the three-way catalyst performance model. Applications have been discussed, including XY-L 1.5L I3 gasoline turbocharged direct injection (GTDI) production hybrid vehicle, BY-L 1.5L I4 GTDI hybrid vehicle, XY-L (overseas version) 1.5L I4 GTDI hybrid vehicle, and G-L7 1.5L I4 GTDI hybrid vehicle. Vehicle tests in support of the proposed model have been described. The developed model covers the complete range of the cold start, high temperature and volume flow conditions. To optimize a three-way catalyst performance, this work simulated the effect of air fuel ratio, space velocity, temperature, biasing adjustment on the catalyst efficiency. The simulations presented the technique’s capability of well predicting emissions on fresh and full useful life aged aftertreatment systems, respectively, and carried out under transient conditions. The investigation indicated that excess fueling was used upon engine start to heat the catalyst up to its full operating temperature of greater than 350°C. The model results prompted a redesign of the I3 and I4 1.5L GTDI China 6b, Euro VId and Tier 3/SULEV30 exhaust systems over the world light vehicle test procedure (WLTP) and federal test procedure (FTP) cycles, respectively, for example, the model suggested that the latest design for the SULEV30 aftertreatment system on XY-L (overseas version) 1.5L I4 GTDI hybrid vehicle with the revised calibrations in the areas of cold-start and closed-loop fuel treated emissions of NMOG, NOx, and CO to the 70% of the SULEV30 standards with a $64 cost reduction relative to the baseline.

Laser Cladding Path Planning for Curved Metal Parts

In depositing multiple layers on the surface of failed metal parts, the overlap rate is a critical factor in determining the surface smoothness and uniformity of the coating thickness. Therefore, special attention must be given to the spacing between adjacent melt tracks when planning laser paths on complex metal parts. A strategy for selecting the overlap rate for multi-track cladding is proposed, based on the key parameters of surface curvature, mass conservation, and the profile of single-track coatings. A multi-track overlap model is developed, expressing the relationship between coating morphology and the overlap rate. The optimal spacing value is determined to achieve the goal of high-quality coating remanufacturing. To verify the effectiveness of this method, nickel-based powder was used for laser forming on the surface of metal gears. The results showed that the surface of the cladding layer was smooth and flat, further demonstrating that this model helps improve the repair quality and overall performance of curved metal parts. Thus, it provides valuable guidance for the remanufacturing of failed metal parts.

A consistent model of the initiation, early expansion, and possible extinction of a spark-ignited flame kernel

Modelling the establishment and growth of spark-ignited (SI) flame kernels has always been a topic of great interest, especially due to their key role in affecting the performance of SI engines. A major issue is that the unsteady conditions and the small kernel size hinder the application of the typical (both linear and non-linear) flame stretch correlations, valid only long after the ignition stage. Overcoming such limitations, this work presents a novel, mathematically consistent, and compact model that enables prediction of flame kernel initiation and early expansion, including its possible extinction. Firstly, spark-driven initiation models from literature are discussed, and an effective flame kernel initiation method is proposed. Then, the expansion model is defined complementing the mass, energy, and species conservation equations for the spherical kernel with the reactant and temperature profiles outside of it using the theory of transient thermodiffusive flames. After accounting for the convective flow caused by the combustion-induced density reduction and the variable thermodynamic properties of the reacting fuel/air mixture, the result is a two-equation model that predicts the kernel expansion even up to its possible extinction due to flame stretch. After calibration of the expansion model, successful validation is achieved against literature data on lean propane/air flames, and the influence of the model parameters is examined in detail. The proposed expansion model is formulated also aiming for inclusion into the simulation of combustion in SI engines, enabling more accurate predictions at part loads, as well as more effective estimation of the cycle-to-cycle variation thanks to the good model sensitivity to the parameters most affecting the ignition.

A model-based design approach for low-pressure axial fan blades considering the air flow system characteristics

The paper puts forward a computer methodology for designing low-pressure axial fan blades for small-capacity refrigeration applications. Based on the blade element theory (BET), the airfoil efficiency of the airfoil, the principles of mass and momentum conservation together with empirical correlations for the flow irreversibilities, a mathematical model was devised for screening the blade geometric parameters (e.g., radial chord and pitch variation, and hub radius) by varying the induction coefficient distribution for a given fan diameter, motor speed, and airflow system characteristic curve. The best blade configuration is selected by means of a tailor-made optimization algorithm and undergoes a series of linear transformations for translating the fan parametrization into a CAD drawing. Two new fan blades were designed, one for maximum blade efficiency (MBE) and another for maximum airflow rate (MAR). In comparison with the free-swirl design approach, a standard procedure adopted in the open literature, the proposed blades showed an efficiency and an airflow by 20 % (MBE) and 14 % (MAR) higher than the reference. The airflow characteristics of the new designs were also assessed by means of wind-tunnel testing, which confirmed an increase of 11 % in the case of MBE design, while an enhancement of 10 % was observed in the case of MAR design.

Non-homogeneous anisotropic bulk viscosity for acoustic wave attenuation in weakly compressible methods

A major limitation of the weakly compressible approaches to simulate incompressible flows is the appearance of artificial acoustic waves that introduce mass conservation errors and lead to spurious oscillations in the force coefficients. In this work, we propose a non-homogeneous anisotropic bulk viscosity term to effectively damp the acoustic waves. By implementing this term in a computational framework based on the recently proposed general pressure equation, we demonstrate that the non-homogeneous and anisotropic nature of the term makes it significantly more effective than the isotropic homogeneous version widely used in the literature. Moreover, it is computationally more efficient than the pressure (or mass) diffusion term, which is an alternative mechanism used to suppress acoustic waves. We simulate a range of benchmark problems to comprehensively investigate the performance of the bulk viscosity on the effective suppression of acoustic waves, mass conservation error, order of convergence of the solver, and computational efficiency. The proposed form of the bulk viscosity enables fairly accurate modelling of the initial transients of unsteady simulations, which is highly challenging for weakly compressible approaches, and to the best of our knowledge, existing approaches can't provide an accurate prediction of such transients.