Volume Conservation Equations Research Articles

Physics-informed data-driven model of dehydration reaction stage in the sintering process of ternary cathode materials

The sintering process is the main process that affects the performance of ternary cathode materials. Due to the closed, continuous, and long-term characteristics of the sintering process carried out in a roller kiln, the reaction state including reaction degree, particle size, and etc., of the raw materials cannot be directly obtained through sampling detection, resulting in ineffective temperature control. This article mainly focuses on modeling the dehydration reaction stage of the sintering process to obtain the reaction state of the raw materials. Firstly, a two-sphere model is established based on Newton’s second law and the particle volume conservation equation to describe the relationship between the particle radius and sintering temperature of lithium hydroxide and ternary precursor; Secondly, the chemical kinetic parameters of the dehydration reaction in the two-sphere model are obtained by combining the single heating rate scanning method with the multiple heating rate scanning method; Then, in order to improve the accuracy of the two-sphere model and reduce the impact of external environmental temperature changes, a physics-informed neural network model is constructed by combining the two-sphere model with the neural ordinary differential equation model. Finally, the effectiveness of the modeling method is verified through numerical simulation and empirical data.

Crucial 3-D viscous hydrodynamic contributions to the theoretical modeling of the cochlear response.

This study uses a 3-D representation of the cochlear fluid to extend the results of a recent paper [Sisto, Belardinelli, and Moleti (2021b). J. Acoust. Soc. Am. 150, 4283-4296] in which two hydrodynamic effects, pressure focusing and viscous damping of the BM motion, both associated with the sharp increase in the wavenumber in the peak region, were analyzed for a 2-D fluid, coupled to a standard 1-D transmission-line WKB approach to cochlear modeling. The propagation equation is obtained from a 3-D fluid volume conservation equation, yielding the focusing effect, and the effect of viscosity is represented as a correction to the local 1-D admittance. In particular, pressure focusing amplifies the BM response without modifying the peak admittance, and viscous damping determines the position of the response peak counteracting focusing, as sharp gradients of the velocity field develop. The full 3-D WKB formalism is necessary to represent satisfactorily the behavior of the fluid velocity field near the BM-fluid interface, strictly related to viscous losses. As in finite element models, a thin layer of fluid is effectively attached to the BM due to viscosity, and the viscous force associated with the vertical gradient of the fluid vertical velocity acts on the BM through this layer.

Considering "Trifecta" as a Single Outcome when Comparing Robotic With Open Partial Nephrectomy: A Mathematical Model of Volume Conservation and Systematic Review.

Trifecta represents a composite outcome reflecting the quality level of treatment in nephron sparing surgery. However, there is substantial heterogeneity concerning the criteria required for its fulfilment. The present study aimed to highlight the potential of a unified view for the different definitions of trifecta when comparing robotic and open approaches in partial nephrectomy. A systematic literature search was carried out for all relevant comparative studies published until April 2022. Trifecta definitions were clustered according to two criteria for postoperative renal function reduction. The first set as an upper limit the 10% decrease in the estimated glomerular filtration rate, while the second set as an upper limit 25 min of ischemia. To mathematically investigate the point of intersection between the above two groups, a suitable model of volume conservation equations was formulated. A total of 11 studies were investigated for their methodological features and grouped accordingly. The ischemic zone volume surrounding the tumor resection site emerged as the central parameter connecting the two main definitions. Specifically, for patients with solitary renal masses, a given change in the value of one parameter resulted in a fixed change in the value of the other. The two main definitions of the "trifecta outcome" extracted from the international literature represent the two sides of the same coin. Thus, trifecta achievement rates could be utilized by future studies as aggregate data to yield a quantitative estimate of the comparative effect between robotic and open approaches in partial nephrectomy procedures.

Under pressure: turbulent plumes in a uniform crossflow

Direct numerical simulation is used to investigate the integral behaviour of buoyant plumes subjected to a uniform crossflow that are infinitely lazy at the source. Neither a plume trajectory defined by the centre of mass of the plume $z_c$ nor a trajectory defined by the central streamline $z_{U}$ is aligned with the average streamlines inside the plume. Both $z_c$ and $z_{U}$ are shown to correlate with field lines of the total buoyancy flux, which implies that a model for the vertical turbulent buoyancy flux is required to faithfully predict the plume angle. A study of the volume conservation equation shows that entrainment due to incorporation of ambient fluid with non-zero velocity due to the increase in the surface area (the Leibniz term) is the dominant entrainment mechanism in strong crossflows. The data indicate that pressure differences between the top and bottom of the plume play a leading role in the evolution of the horizontal and vertical momentum balances and are crucial for appropriately modelling plume rise. By direct parameterisation of the vertical buoyancy flux, the entrainment and the pressure, an integral plume model is developed which is in good agreement with the simulations for sufficiently strong crossflow. A perturbation expansion shows that the current model is an intermediate-range model valid for downstream distances up to $100\ell _b$ – $1000 \ell _b$ , where $\ell _b$ is the buoyancy length scale based on the flow speed and plume buoyancy flux.

Dual solutions of bioconvection hybrid nanofluid flow due to gyrotactic microorganisms towards a vertical plate

The impact of gyrotactic microorganisms in the mixed convection stagnation point flow of Cu-Al2O3/water hybrid nanofluid towards an immovable plate is numerically examined. The boundary layer equation coupled with the energy, nanoparticle volume fraction and conservation equations for microorganisms are simplified into a set of ordinary differential equations by adopting similarity transformation. The validation results are in a good agreement with previous studies approximately by 0% difference relative error. The results imply that the dual solutions only exist in the opposing flow up to a critical value/turning point. Beyond this turning point, the solutions are unavailable which reflects the separation of flow. The hybrid nanofluid is essential in delaying the separation process where the results show that λc,hnf=−3.5804>λc,Cu=−3.3903>λc,Al=−3.2016. Moreover, the advantage of this hybrid Cu-Al2O3/water nanofluid is in the augmentation of heat and mass transfer rates including the density of microorganisms which is higher than the Cu- and Al2O3-water nanofluids.

Numerical and experimental study on fluid compressibility in a two-stage reciprocating pump-compressor

• Liquid piston velocity decreases with increasing pressure due to liquid compressibility. • Liquid piston brings the compression process closer to thermodynamically efficient. • Liquid expansion leads to a decrease of the pump volumetric efficiency. • Pressure ratio has the greatest impact on a decrease of liquid layer height and velocity. Currently, multistage (two and three-stage) reciprocating compressors are used to compress the gas to medium and high pressures. One of the promising operating principles of such machines is a preliminary compression in a single-stage piston compressor and a final gas compression in a working cavity with a liquid piston. The main advantages of a compressor using a liquid piston are intensive cooling of the compressed gas and the absence of leaks and leakages in the cylinder-piston group. This makes it possible to increase the indicated isothermal efficiency and actual volumetric efficiency. The article considered the effect of liquid compressibility in the two-stage piston hybrid positive-displacement machine with a liquid piston. We developed a calculus methodology for the liquid compressibility during gas compression in the second stage of the compression section based on the volume conservation equation and Hooke's law. Numerical simulation showed that the degree of pressure ratio had the greatest impact on the relative decrease in the height and velocity of the liquid layer. We found that the relative decrease in the liquid layer height was within 1%. The relative decrease in the liquid piston velocity was within 5%. We carried out the experiment and validation of the results with a numerical simulation, which reflected the mathematical model validity. The model worked correctly based on an estimated experimental error. The parametric analysis of the test model showed the influence of the main working cavity parameters. The discrepancy in determining the dynamic pressure in the machine cavities conducting theoretical and experimental studies is within 10–15%. The paper analysed the liquid piston compressibility influence on the thermodynamic efficiency of the compression process and compressor performance.

Analysis of Liquid Piston Compressibility in the Two-Stage Hybrid Positive-Displacement Machine

The effect of liquid compressibility in the two-stage piston hybrid positive-displacement machine with a liquid piston was considered. Based on the volume conservation equation, we developed a calculus methodology for the liquid compressibility during gas compression in the second stage of the compressor section. A numerical experiment made it possible to establish that some parameters have the greatest effect on the relative decrease in the height and velocity of the liquid layer. These parameters are the degree of pressure ratio; pipeline length; the polytropic index of the compression; the number of crankshaft revolutions. We found that the relative decrease in the liquid layer height is within 1 %, and the relative decrease in the liquid piston velocity is within 5 %. The paper analyses the liquid piston compressibility influence on the thermodynamic efficiency of the compression process and compressor performance.

Modelling grain growth with the generalized Kampmann-Wagner numerical model

The multi-phase Kampmann-Wagner Numerical (KWN) model, which had been successfully applied for modeling particle precipitation (i.e. Ostwald ripening), is extended toward grain growth modeling. The extensions consist of adopting grain topology- and size-dependent growth rate equation obtained from either the reported parameterization of phase field simulations results or theoretical analysis. Global volume conservation equation is imposed in the extended model to reflect the spacing filling constraints that grains do not overlap and no voids appear. The extended model has been applied to simulate ideal grain growth, grain growth with the initial states of lognormal/normal/Weibull distributions, bi-modal grain size distribution and arbitrary Voronoi tessellations, and the simulation results have been verified by Hillert's asymptotic solution and phase field simulation results. The extension has enabled the KWN approach applicable to model grain growth thus reducing the threshold for the establishment of an efficient Integrated Computational Materials Engineering modeling framework.

Oil transport in shale nanopores and micro-fractures: Modeling and analysis

The mathematical modeling and analysis for the apparent permeability of shale oil with complicated compositions in dual-wettability shales (superior to existing single-component or single-wettability analysis), which is the core of this work, will help understand the detailed contributions of the considered mechanisms. Based on a previously established flow enhancement model, the effects of the mixed wettability and those triggered by asphaltenes, namely, the wettability alteration, the pore radius reduction, and the viscosity increment, are taken into account by respective corrections of the variables in the model. The effect of the mixed wettability is quantified by the water-wet area ratio, while the surface coverage, the adsorption thickness, and the volume fraction in the free phase are utilized to quantify the effects of asphaltenes. The volume fraction of asphaltenes in the free phase is related to that in both phases by the volume conservation equation. The full mathematical model and its several simplifications are achieved. Comprehensive sensitivity analysis and comparisons are carried out to demonstrate the effects of each variable (i.e., the pore radius, the initial water-wet surface ratio, the relative adsorption thickness, and the surface coverage) on: (1) the flow enhancement; (2) the relative importance of all mechanisms; (3) the differences among organic pores/inorganic pores/micro-fractures; and (4) the overall contribution of asphaltenes. The effect of different adsorption patterns (characterized by the relative adsorption thickness and the surface coverage) is also discussed.

An improved 2D MoF method by using high order derivatives

The MoF (Moment of Fluid) method is one of the most accurate approaches among various interface reconstruction algorithms. Alike other second order methods, the MoF method needs to solve an implicit optimization problem to obtain the optimal approximate interface, so an iteration process is inevitable under most circumstances. In order to solve the optimization efficiently, the properties of the objective function are worthy of studying. In 2D problems, the first order derivative has been deduced and applied in the previous researches. In this paper, the high order derivatives of the objective function are deduced on the convex polygon. We show that the nth (n≥2) order derivatives are discontinuous, and the number of the discontinuous points is two times the number of the polygon edge. A rotation algorithm is proposed to successively calculate these discontinuous points, thus the target interval where the optimal solution is located can be determined. Since the high order derivatives of the objective function are continuous in the target interval, the iteration schemes based on high order derivatives can be used to improve the convergence rate. Moreover, when iterating in the target interval, the value of objective function and its derivatives can be directly updated without explicitly solving the volume conservation equation. The direct update makes a further improvement of the efficiency especially when the number of edges of the polygon is increasing. The Halley's method, which is based on the first three order derivatives, is applied as the iteration scheme in this paper and the numerical results indicate that the CPU time is about half of the previous method on the quadrilateral cell and is about one sixth on the decagon cell.

Simulating cross-shore material exchange at decadal scale. Theory and model component validation

A model is developed to simulate the cross-shore (CS) exchange of sand and the resulting profile response at decadal scale to be used in regional coastal evolution models. The CS model consists of modules for calculating dune erosion and overwash, wind-blown sand transport, and bar-berm material exchange. The sand transport equations included in these modules are formulated based on relevant physics in combination with empirical observations and then validated towards laboratory and field data. In order to couple the transport equations to the evolution of key morphological features describing the profile a set of sand volume conservation equations are employed and solved together with the transport equations. The features that are modeled include dune height (from dune foot to crest), the locations of the landward dune foot, seaward dune foot, berm crest, and shoreline as well as the longshore bar volume. The CS model is employed and tested at three different field sites in a companion paper (Palalane et al., 2016), whereas in the present paper the properties of the model are demonstrated by simulating the evolution of the dune, berm, and shoreline in connection with accretion and erosion of sand in a groin compartment. This case derives from a study at Westhampton Beach that focused on shortening the length of a number of groins in order to release accumulated sand in the groin field to eroding downdrift beaches.

Phase Equilibrium with External Fields: Application to Confined Fluids

This work addresses the problem of finding the equilibrium spatial segregation of components in systems that have multiple regions, each of them subject to the effect of external fields. The specifications are the temperature, region volumes, component amounts, and additional variables that characterize the effect of such fields. The formulation leads to the mathematical problem of minimizing the Helmholtz energy of the system, subject to constraints that represent component mass balances and volume conservation equations applied to each region. Among other uses, the approach is suitable for determining the equilibrium conditions in batch adsorption. The formulation is general but the focus of this work is on the compositional segregation in isothermal reservoirs due to gravity and the spatial segregation of components close to pore walls. Calculations using the Steele and DRA potentials to model fluid–wall interactions demonstrate the formulation, and its solution procedure provides results that are gene...

Implementation and clinical application of a deformation method for fast simulation of biological tissue formed by fibers and fluid.

BackgroundThe aim of this paper is to provide a general discussion, algorithm, and actual working programs of the deformation method for fast simulation of biological tissue formed by fibers and fluid. In order to demonstrate the benefit of the clinical applications software, we successfully used our computational program to deform a 3D breast image acquired from patients, using a 3D scanner, in a real hospital environment.ResultsThe method implements a quasi-static solution for elastic global deformations of objects. Each pair of vertices of the surface is connected and defines an elastic fiber. The set of all the elastic fibers defines a mesh of smaller size than the volumetric meshes, allowing for simulation of complex objects with less computational effort. The behavior similar to the stress tensor is obtained by the volume conservation equation that mixes the 3D coordinates. Step by step, we show the computational implementation of this approach.ConclusionsAs an example, a 2D rectangle formed by only 4 vertices is solved and, for this simple geometry, all intermediate results are shown. On the other hand, actual implementations of these ideas in the form of working computer routines are provided for general 3D objects, including a clinical application.

Noninvasive Methods for Hydraulic Characterization of Density Currents with Application to Submarine Fan Experiments

AbstractLaboratory experiments are a convenient way to study morphodynamic processes associated with subaqueous fans. However, the flows driving such systems can be difficult to hydraulically characterize due to the shallowness of the flows, the spatial and temporal dynamics of the autogenic channels, and the mixing at the interface of the ambient fluid and density current. The objective of this study is to develop a set of methods to quantify hydraulic variables in laterally unconstrained and morphologically active density currents. Herein, a methodology is presented capable of characterizing a density current flow field with direct application to submarine fan experiments. This is done with a combination of: (1) particle tracking velocimetry (PTV) analysis of tracers within the density current, (2) flow width measurements from overhead images, and (3) solution of the mass and volume conservation equations in one-dimension to obtain layer-averaged velocity, depth, and fractional excess density.

Mixed convection flow of a nanofluid over a stretching surface with uniform free stream in the presence of both nanoparticles and gyrotactic microorganisms

In this paper, a detailed analysis is given for the mixed convection flow of a nanofluid over a stretching surface with uniform free stream in the presence of both nanoparticles and gyrotactic microorganisms. By means of a novel nanofluid model proposed by Kuznetsov and Nield (2013) [24], we reduce the original governing equations embodying the conservation of mass, momentum, thermal energy, nanoparticle volume fraction and conservation equation for microorganisms to a set of five ordinary differential equations with coupled linear boundary conditions. The recursively analytical solutions with high precision are then obtained by the improved homotopy analysis method (HAM). Besides, the influences of important physical parameters such as the Brownian motion parameter Nb, the thermophoresis parameter Nt, the bioconvection Rayleigh number Rb, the bioconvection Péclet number Pe on the local wall friction, the local Nusselt number, the local wall mass flux, the local wall motile microorganisms flux, as well as the profiles of velocity, temperature, nanoparticles concentration and density of motile microorganisms are examined and discussed in detail.

Wave Breaking in Dense Plumes

AbstractSinking dense plumes are important in many oceanographic settings, notably the polar formation of deep and bottom waters. The dense water sources feeding such plumes are commonly affected by tidal modulation, leading to plume variability on short time scales. In a simple unsteady theory of one-dimensional plumes (based on conservation equations for volume, momentum, and buoyancy), this plume variability is manifested as waves that travel down the resulting current. Using numerical techniques applied to the hyperbolic conservation equations, this study investigates the novel concept that these waves may break as they travel down the plumes, triggering intense local mixing between the dense fluid and surrounding ocean. The results demonstrate that the waves break at geophysically relevant distances from the plume source. The location of wave breaking is very sensitive to plume drag from the seabed, the properties of the dense source, and the amplitude and period of the source modulation. To the extent that the simple model represents the real world, these results suggest that wave breaking originating from the tidal modulation of dense plumes could lead to a strong and previously unexplored source of local deep-ocean mixing.

Effect of nanoparticles size on thermal performance of nanofluid in a trapezoidal microchannel-heat-sink

This paper deals with spherical nanoparticles size effects on thermal performance and pressure drop of a nanofluid in a trapezoidal microchannel-heat-sink (MCHS). Eulerian–Eulerian two-phase numerical approach is utilized for forced convection laminar, incompressible and steady three dimensional flow of copper-oxide nanoparticles with water as base fluid at 100 to 200nm diameter and 1% to 4% volume concentration range. Continuity, momentum, energy and volume conservation equations are solved at whole of the computational domain via finite volume method. Obtained results signify that pressure drop increases 15% at Re=500 and 1% volume concentration while nanoparticles diameter increases from 100 to 200nm. By increasing volume concentration, nanoparticles size effect becomes more prominent and it is observed that increment rate of pressure drop is intensified for above 150nm particles diameter. Unlike the pressure drop, heat transfer decreases with an increase in nanoparticles diameter. Also, it is observed that with an increase in nanoparticles diameter, average Nusselt number of base fluid decreases more than that of the nanoparticles and this signifies that base fluid has more efficacy on thermal performance of copper-oxide nanofluid.

The Arctic Ocean in summer: A quasi‐synoptic inverse estimate of boundary fluxes and water mass transformation

The first quasi‐synoptic estimates of Arctic Ocean and sea ice net fluxes of volume, heat and freshwater are calculated by application of an inverse model to data around the ocean boundary. Hydrographic measurements from four gateways to the Arctic (Bering, Davis, and Fram Straits and the Barents Sea Opening) completely enclose the ocean, and were made within the same 32‐day period in summer 2005. The inverse model is formulated as a set of full‐depth and density‐layer‐specific volume and salinity transport conservation equations, with conservation constraints also applied to temperature, but only in non‐outcropping layers. The model includes representations of Fram Strait sea ice export and of interior Arctic Ocean diapycnal fluxes. The results show that in summer 2005 the transport‐weighted mean properties are, for water entering the Arctic: potential temperature 4.49°C, salinity 34.50 and potential density (σ0) 27.34 kg m−3; and for water leaving the Arctic, including sea ice: 0.25°C, 33.81, and 27.13 kg m−3, respectively. The net effect of the Arctic in summer is to freshen and cool the inflows by 0.69 in salinity and 4.23°C, respectively, and to decrease density by 0.21 kg m−3. The volume transport into the Arctic of waters above ∼1000 m depth is 9.2 Sv (1 Sv = 106 m3 s−1), and the export (similarly) is 9.3 Sv. The net oceanic and sea ice freshwater flux is 187 ± 48 mSv. The net heat flux (including sea ice) is 189 ± 37 TW, representing loss from the ocean to the atmosphere.

Thermodynamic speed of sound in multiphase systems

A procedure to evaluate the thermodynamic speed of sound in systems with any number of fluid phases is presented in this paper. Starting from the definition of speed of sound, the derivation of the procedure uses the conservation equations for volume, entropy, and number of moles of each component, the derivatives of several thermodynamic properties, and the solution of a system of linear equations. A computer algebra program was used to automatically derive and implement in computer the required expressions. The calculated thermodynamic speeds of sound reported in this paper are in very good agreement with results published recently, based on numerical derivatives, but show some discrepancies with earlier results available in the literature.

Analyzing the tidal‐related origin of subinertial flows through the Strait of Gibraltar

The effects of tidal dynamics on subinertial flows through the Strait of Gibraltar are analyzed. As found in previous studies, an empirical orthogonal function analysis of subinertial currents at the Camarinal Sill yields two dominant oscillation modes. The first mode presents a barotropic character and rather irregular fluctuations and it has been related to meteorological forcing. The second mode is baroclinic and presents a clear deterministic behavior with time that seems to be related to tidal forcing. Against the hypothesis proposed in previous studies stating that tidal mixing cycles explain the second mode, we show, by using a one‐dimensional numerical model of two‐layer immiscible shallow water, that the origin of this mode may basically be related to nonlinear interactions among the main semidiurnal tidal constituents through the advective terms in the momentum balance and other nonlinear terms in the volume conservation equations. That mode is also crucial to understanding the vertical shear time variations of the horizontal currents. In particular, it minimizes the differences in the maximum shear between neap and spring tides.