Time-wise Evolution Research Articles

Hyperbolic high-fidelity simulations of cratering on a particle bed induced by a turbulent supersonic plume

A recently proposed hyperbolic granular model (Balakrishnan and Bellan, 2024) has been used to investigate the problem of supersonic-jet induced cratering on a solid-particle bed. This model relies upon the concept of added mass and a fluid-mediated particle pressure to render the system of equations hyperbolic. The jet is modeled using Large Eddy Simulation (LES) and the solid phase is modeled in an Eulerian framework using a Kinetic-Theory-based model modified for dense particle collections. The formulation also incorporates pseudo-turbulent kinetic energy (PTKE) which has been shown to modify a flow field laden with particles. The results explore the influence of the jet-to-ambient fluid density ratio, of the ambient fluid density, and of PTKE. A detailed analysis of the local and time-wise evolution of the added mass is presented through quantification of convection, added mass source and velocity-difference contributions. A quantitative assessment of the PTKE equation shows that while production is mostly effective at the crater base and walls, the dissipation and source term, both of which are also effective in the ejecta, nearly balance each other. The influence of the PTKE is mostly observed in the dilute particle regions (soil/gas interface and ejecta), with no effect on the macroscopic length scales of the flow. Both the jet-to-ambient fluid density ratio and the ambient fluid density affect the macroscopic crater features through entertainment into the jet that is determined by the former, and through the density of the fluid entrained, determined by the latter. This complex interaction governs the evolution of the crater diameter, visible top-view depth, and lower depth of the compacted region.

An Enthalpy-Balance Model for Timewise Evolution of Temperature during Wet Stirred Media Milling of Drug Suspensions.

Nanosuspensions have been used for enhancing the bioavailability of poorly soluble drugs. This study explores the temperature evolution during their preparation in a wet stirred media mill using a coupled experimental-enthalpy balance approach. Milling was performed at three levels of stirrer speed, bead loading, and bead sizes. Temperatures were recorded over time, then simulated using an enthalpy balance model by fitting the fraction of power converted to heat ξ. Moreover, initial and final power, ξ, and temperature profiles at 5 different test runs were predicted by power-law (PL) and machine learning (ML) approaches. Heat generation was higher at the higher stirrer speed and bead loading/size, which was explained by the higher power consumption. Despite its simplicity with a single fitting parameter ξ, the enthalpy balance model fitted the temperature evolution well with root mean squared error (RMSE) of 0.40-2.34°C. PL and ML approaches provided decent predictions of the temperature profiles in the test runs, with RMSE of 0.93-4.17 and 1.00-2.17°C, respectively. We established the impact of milling parameters on heat generation-power and demonstrated the simulation-prediction capability of an enthalpy balance model when coupled to the PL-ML approaches.

Ejecta from Granular-Medium Cratering by a Supersonic Jet Entering a Continuum Atmosphere

High-fidelity three-dimensional numerical simulations are analyzed to investigate cratering on a granular bed of particles due to a supersonic multi-species fluid jet. In the simulations, the volume-averaged two-phase equations are solved with a multi-species large-eddy simulation formulation for the fluid and a kinetic-theory-based model for the particle bed. The simulations vary according to the ratio of the jet-to-ambient-fluid density (and pressure) and the ambient density. The characteristics of the jets and crater are different according to the cross-sectional shape, which is determined by the jet/ambient density ratio: a conical shape is observed when the ratio is near unity, and a parabolic shape occurs when this ratio is large. Craters are characterized by their diameter, an upper depth, and a lower depth, with the difference between the two depths accounting for the granular medium compaction zone. The variation of the crater diameter timewise evolution is evaluated, and the evolution of the ratio between the upper or lower crater depths and the crater diameter is examined. Joint probability density functions of the Mach number based either on the fluid velocity or the relative velocity between the fluid and particles show that a large portion of the granular medium is dominated by subsonic conditions. The azimuthally averaged ejecta’s radial variation is inspected, and joint probability density functions elucidate the regions where gravity effects are important.

On the starting vortex generated by a translating and rotating flat plate

Abstract

A semi-theoretical model for simulating the temporal evolution of moisture-temperature during industrial fluidized bed granulation

Moisture plays a major role in determining the attributes of granules prepared by fluidized bed granulation (FBG). Here, a semi-theoretical droplet-based evaporation rate model was developed and incorporated into moisture mass-enthalpy balances to simulate the temporal evolution of bed moisture-temperature. Experimental data from a GPCG30 unit were used to fit the model parameters. With only two fitting parameters, the model demonstrated excellent capability to describe the moisture-temperature evolution for a wide range of operating conditions. Then, in a global process model (GPM) approach, the evaporation parameters were fitted to multi-linear functions of inlet air temperature, binder concentration, and spray rate. The GPM was validated successfully by simulating a different data set which was not used in its calibration. As the GPM demonstrated a good predictive capability, it was further used to investigate the impacts of process parameters. Numerical simulations suggest that the proposed GPM predicts the experimentally well-established trends of moisture-temperature profiles in previously published data, proving the applicability of the GPM approach. This study has demonstrated the capabilities of simple process models as a practical approach to predict time-wise evolution of bed moisture-temperature profiles in industrial FBG modeling, while also pointing out their limitations.

Comprehensive REE + Y and sensitive redox trace elements of Algerian phosphorites (Tébessa, eastern Algeria): A geochemical study and depositional environments tracking

The Algerian sedimentary phosphorites of marine origin are located mainly in the Tébessa region, which is part of the Eastern Saharan Atlas. These phosphorites are hosted by Paleocene-Eocene series and crop out in two main sedimentary areas: the northern sites (Djebel El Kouif, Djebel Dyr and Djebel Tazbant) and the southern sites, which include the Djebel Onk commercial world-class ore deposits that are represented in this study by the Kef Essenoun sector. This study reports a detailed investigation of these phosphorites at a regional scale and is aimed to characterizing the evolution of their depositional environments. Field and laboratory works consist of a systematic sampling of outcrops, petrographical (OM and SEM-EDS), mineralogical (XRPD) and chemical (major, trace and rare earth elements by ICP-MS) analyses associated with a PCA statistical treatment. The time-wise evolution of the depositional environments was constrained based on rare earth elements (REE) and selected redox sensitive element proxies, such as Ce, Eu, Y, Mn, U and V.The results show that the phosphorites have a granular fabric with variable grain sizes. The grains can contain micro-remains and impurities related to their origin, which was most often fecal pellets. Carbonate fluor-apatite is the main mineral phase in these phosphorites, where P2O5 contents show large variations between different outcrops (average from 18.39 to 30.16 wt%). A marked evolution of depositional environments is observed in their vertical trends from sub-reduced and sub-oxic in the lower beds to rather oxic conditions in the upper layers. This evolution shows a significant shift along the sedimentary profiles reflecting more open connection to Tethyan seawater towards younging trend. These results contrast remarkable changes of depositional conditions during Paleocene–Eocene transition.

Insight into first-order breakage kinetics using a particle-scale breakage rate constant

This study formulates a particle-scale breakage rate constant of the linear time-variant population balance model (PBM) for batch dry-milling. The breakage rate constant separates material properties from the milling environment which is defined by the impact energy distribution obtained by the discrete element method (DEM). The breakage rate constant determined by experiments and DEM simulations of the ball milling of polydispersed silica glass were in close agreement confirming the validity of the proposed methods. The breakage rate constant formulated in this study also allowed a detailed and rigorous energy-based analysis of the milling environment which provided insight into the origin of first-order breakage kinetics and the time-invariance of the breakage rate constant. Feeds of varying polydispersity and the time-wise evolution of the particle size distribution (PSD) were simulated in DEM to show that the PSD does not affect the specific breakage rate constant as assumed in first-order breakage. The adherence to first-order breakage kinetics was attributed to the low feed loading in the mill and the absence of particle beds where mechanical multi-particle interactions can cause non-first-order breakage. It was found that a threshold impact energy must be accounted for in the analysis of DEM results because the majority of low energy impacts do not contribute to particle breakage. Without rigorous assessment of the impact energy distribution, DEM simulations may lead to an erroneous evaluation of milling performance. The findings of this study contribute to a unified DEM−PBM framework to model and analyze milling process and demonstrate that milling performance can be quantified from particle-scale interactions using DEM.

THE PROCESS OF THE DEVELOPMENT OF HYPOXIA IN AN ABNORMAL BLOOD FLOW

Interrupted blood flow diminishes the concentration of oxygen in tissues. Hypoxia first appears in the region distal to the capillaries and grows throughout the entire t issue. However, the time-wise evolution of hypoxic area is diverse when some of capillaries are blocked in a multi-capillary domain with different oxygen squirt. The process of the development of hypoxia through time course is analyzed mathematically in the domain. Each source in steady state is controlled by a time sensitive function to simulate the occlusion.

Oscillation of shallow flow past a cavity: Resonant coupling with a gravity wave

Self-excited oscillations of flow past a cavity are generated in a shallow free-surface system. The shear layer past the cavity opening has two basic forms: a separated free-shear flow; and a shear flow along a slotted plate. Instabilities of these classes of shear flows can couple with the fundamental gravity-wave mode of the adjacent cavity. The dimensionless frequencies of both types of oscillations scale on the length of the cavity opening, rather than the gap distance between the slats, i.e., a large-scale instability is always prevalent. A technique of high-image-density particle image velocimetry allows acquisition and interpretation of global, instantaneous images of the flow pattern, including patterns of vorticity and Reynolds stress correlation. Use of a cinema approach provides representations of the timewise evolution of the global, instantaneous flow structure, and thereby definition of the amplitude peaks and phase angles of the coupled fluctuations via auto- and cross-spectral techniques. These methods, along with global, averaged representations of the fluctuating flow field, provide insight into the onset of fully coupled (phase-locked) oscillations of the shear flow past the resonator cavity. The common, as well as the distinctive, features of the resonant-coupled instability of the shear flow past the slotted plate are characterized, relative to the corresponding coupled instability of the free-shear layer. Varying degrees of resonant coupling between the unstable shear layer and the adjacent resonator are attained by variations of the inflow velocity, which yield changes of the predominant oscillation frequency, relative to the resonant frequency of the adjacent cavity. Well-defined, coherent oscillations are indeed attainable for the case of the shear flow along the slotted plate, though their amplitude is significantly mitigated relative to the case of a free-shear layer. The degree of organization of the self-excited, resonant-coupled oscillation and the manner in which it varies with open area ratio and geometry of the plate are interpreted in terms of the flow structure on either side of, and within, the slotted plate; these features are compared with the corresponding structure of the free-shear layer oscillations.

Oxygen delivery through capillaries

During physical exertion the consumption rate increases and some cells suffer from the lack of oxygen. The time-wise evolution of hypoxia is analyzed mathematically under the condition the perfusion of each capillary is constant. The domain used contains multiple non-homogeneous capillaries of different solute out. Cells surrounding capillaries may consume or preserve more oxygen than are necessary at the beginning of new environment.

Experiments on Unsteady Turbulent Pipe Flow

The paper explores the time-wise evolution of selected turbulence parameters during gravity-driven flow establishment of incompressible fluids in rigid circular pipes. Two initial conditions are considered: flow starting from rest, passing through laminar-to-turbulent transition, and terminating in a turbulent steady state; and transient flow between two turbulent steady states. It is found that, in the second case, the properties considered, i.e., local temporal mean velocity and its transverse distribution, axial turbulence intensity, and wall shear stress, are monotonically increasing with time. However, for flow starting from rest, all properties are strongly affected by the development of turbulence. In particular, at the critical moment when laminar-to-turbulent transition is complete, the wall shear stress changes abruptly from one to the other, identifying wall shear stress as a very sensitive indicator of criticality.

Experiments on melting of a vertical ice layer immersed in immiscible liquid

Experiments on the melting of a vertical ice layer immersed in immiscible liquid yielded quantitative results both for the timewise evolution of the melting front and the heat transfer. Vegetable oil, which was contained in a rectangular vessel, was adopted as a testing liquid. A bubble-free ice block stuck on a cooled wall was installed vertically in the vessel. The experiments were carried out for the immiscible liquid temperatures from 7.6 to 30.0 °C, while for the cooled wall temperatures from 0 to −11.5 °C. The flow structure of the liquid and the melting front were extensively observed and recorded photographically. It was found that the heat transfer and the rate of melting are significantly affected by a couple of fluid motions of both the water melt induced by melting of ice and the immiscible liquid based on free convection.

Thermal performance characteristics of STC system with Phase Change Storage

Storing solar energy heat using Phase Change Materials (PCM) is an effective method. The combination of solar collector and PCM in one unit is being currently studied. The performance characteristics of the proposed Solar Tube Collector (STC) are being analysed analytically and experimentally. Fundamental experiments were performed to simulate a direct contact solar storage system, using two vertical cylindrical concentric tubes with the annular space between them filled Stearic acid ( C 18 H 38 O 2, melting temperature 70 °C). Experimental testing apparatus has been set up to simulated real system conditions, for an assumed initial and boundary conditions, to provide quantitative information concerning the heat transfer and the timewise evolution of the solid-liquid interface and to identify the role and pattern of natural convection and of the movement of the boundary layer in the liquid phase. For the heat charging mode, the experimental results for different types of fin structures have shown that the effect of melting process is strongly effected by the variation of the imposed conditions, in addition to the different trends of the melting profiles along the axial direction due to the effect of natural convection.

Time evolution of polarisation mode dispersion in 120 km installed optical submarine cable

The timewise evolution of polarisation mode dispersion (PMD) is measured. PMD varies very slowly in a 120 km installed optical submarine cable. The measured timewise evolution of PMD suggests that compensation with a response time shorter than a few minutes can greatly reduce the system performance degradation caused by PMD.

Double diffusive natural convection in a vertical rectangular enclosure—I. Experimental study

Double diffusive natural convection flows in a two-dimensional rectangular enclosure are investigated using an electrochemical technique with the vertical electrodes maintained at different temperatures. Schlieren flow visualization photographs show interesting timewise evolution of multicell flow structures in an enclosure for both aiding and opposing thermal and solutal buoyant forces. Details of the multicell flow characteristics including the temperature and concentration profiles as well as the overall heat and mass transfer characteristics in the cavity are presented.

Fluid-elastic vibration of flexible overflow weir.

The present paper describes the fundamental feature of the fluid-elastic vibration of flexible overflow weir, as observed in the French demonstration fast breeder reactor, Super Phenix-1. In the experimental study, the instability criterion of the fluid-elastic vibration was investigated using a simple experimental apparatus of a rectangular tank separated by a flexible weir. A spring-mass model for sloshing motion of liquid contained in the tank was developed to clarify the mechanism of the instability. The instability condition was analytically derived from the equations of the spring-mass model. The equations of the spring-mass model were also computationally integrated in time to simulate the timewise evolution of the fluid-elastic vibration. The comparison between the experimental and theoretical results indicate that the present theoretical model is capable of predicting the general characteristics of the vibration observed in the experiment. The present study revealed that the lag-time of the water fall at the weir is the most influential parameter on the fluid-elastic instability of a flexible overflow weir.

Outward phase change in a cylindrical annulus with axial fins on the inner tube

A theoretical analysis is presented for the phase change process occurring in a cylindrical annulus in which rectangular, uniformly spaced axial fins, spanning the annulus, are attached to the inner isothermal tube, while the outer tube is kept adiabatic. The model assumes conduction to be the only mode of heat transfer. The governing equations are solved by finite-difference methods. The time-wise evolution of the interface profile, phase-change fraction and energy stored/discharged and the effect of all the nine prescribable parameters are presented here. Based on the analysis a working formula VF = 1.1275 ( Fo Ste T f ) 0.624 ( N) 0.028 ( L) −1.385( W) −0.049 is suggested for engineering design purposes.

Gravity and Conduction Driven Melting in a Sphere

AbstractThe fundamental processes of melting, the well known Stefan and Neumann problems, have been of great interest from a theoretical point of view as well as for their wide applications. The yet unmolten part of the material undergoing phase change within spherical containments is generally presumed to remain stationary, an unlikely occurrence in practice. The differing densities of the liquid and the solid may readily cause a force imbalance on the solid in gravitational and perhaps microgravitational environments, thereby moving the solid away from the center. In the present work, an approach related to the theories of lubrication and film condensation was employed and an approximate closed-form solution of melting within spheres was obtained. It was shown that a group of dimensionless parameters containing, Prandtl, Archimedes and Stefan numbers describes the melting process. Fundamental heat transfer experiments were also performed on the melting of a phase-change medium in a spherical shell. Free expansion of the medium into a void space within the sphere was permitted. A step function temperature jump on the outer shell wall was imposed and the timewise evolution of the melting process and the position of the solid-liquid interface was photographically recorded. Numerical integration of the interface position data yielded information about the melted mass and the energy of melting that support the theory.

Inward Melting in a Vertical Tube Which Allows Free Expansion of the Phase-Change Medium

Experiments on the melting of a phase-change medium in a vertical tube yielded quantitative results both for the heat transfer and the timewise evolution of the melting front. The upper surface of the phase-change medium was bounded by an insulated air space, which accommodated the volume changes which accompany the melting process. Numerical solutions based on a pure conduction model were also performed for comparison purposes. It was found that the rate of melting and the heat transfer are significantly affected by fluid motions in the liquid melt induced by the volume change and by natural convection, with the former being significant only at early times. For melting initiated with the solid at the phase-change temperature, the experimentally determined values of the energy transfer associated with the melting process were about 50 percent higher than those predicted by the conduction model. Furthermore, the measured values of the energy stored in the liquid melt were about twice the conduction prediction. A compact dimensionless correlation of the experimental results was achieved using the Fourier, Stefan, and Grashof numbers. Initial subcooling of the solid substantially decreased the rate of melting, with corresponding decreases in the energy transfers for melting and sensible heat storage.

Stability of plane Couette flow with respect to finite two-dimensional disturbances

The stability of plane Couette flow is studied by applying a finite two‐dimensional disturbance to the basic laminar motion and following the timewise evolution of the quasi‐steady flow and the disturbance. This is accomplished by combining a Meksyn–Stuart type method with a quasi‐steady technique. Results show that plane Couette flow tends to slowly converge to a stable state for the Reynolds numbers and disturbance intensities studied. This is in disagreement with past investigations which were able to obtain nonlinear neutral stability curves.