scholarly journals The effect of the filling degree of the tumbling mill chamber on the bifurcation value of the froude number

2021 ◽  
pp. 21-24
Author(s):  
Kateryna Deineka ◽  
Yurii Naumenko ◽  
Tamara Myronenko
Keyword(s):  
Froude Number ◽  
Visual Analysis ◽  
Relative Size ◽  
Experimental Studies ◽  
Fine Fraction ◽  
Coarse Fraction ◽  
Spherical Particles ◽  
Charge Movement ◽  
Filling Degree ◽  
Tumbling Mill

The influence of the filling degree of the drum chamber on the bifurcation value of the Froude number in the case of self-excitation of self-oscillations of a two-fraction granular charge with a minimum swing is considered. Such a pulsating mode of the charge movement is used in the self-oscillating grinding process in a tumbling mill. The coarse fraction that simulated the milling bodies consisted of spherical particles of an incoherent granular material with a relative size in the chamber ψb=0.00733. The fine fraction, simulating the material to be ground, was cement with a relative particle size ψm≈0.092∙10-3. The value of the adopted analogue of the kinematic viscosity of the two-fraction granular loading approached the value of 10-3 m2/s. The main variable factor in experimental studies was the filling degree of the drum chamber with loading at rest κb=0.25, 0.35, and 0.45. An additional factor was the degree of filling the gaps between the spherical particles of the coarse fraction with particles of the fine fraction κb=0, 0.25, 0.5, and 1. The method of visual analysis through the transparent end wall of the chamber of transient processes of the loading behavior with a smooth change and fixation of the velocity was applied. The bifurcation minimum value of the rotation speed was recorded, at which the steady-state circulation mode of the load movement turns into a transient pulsation one with a minimum swing. A decrease in the bifurcation values of the Froude number Frb on the cylindrical surface of the chamber with an increase in κb has been established. An increase in the intensity of the decrease in Frb with an increase in κm was revealed. The recorded effect is due to an increase in the connected properties of a two-fraction loading during self-excitation of self-excited oscillations with an increase in κb and κm. The numerical values of the boundaries of the range of bifurcation values of the Froude number for a tumbling mill Frb=0.0484–1.17 have been determined. The obtained Frb range corresponds to the Reynolds value in the range Re=40–197. The maximum Frb value is obtained with coarse grinding. An increase in the likelihood of self-excitation of self-oscillations of the intra-chamber loading with a decrease in the fineness of grinding was revealed

scholarly journals ESTABLISHING THE ROTATION SPEED VARIATION RANGE LIMITS FOR AUTO-EXCITATION OF SELF-OSCILLATING GRINDING IN A TUMBLING MILL

2020 ◽  
Vol 4 ◽  
pp. 32-35
Author(s):  
Kateryna Deineka ◽  
Yurii Naumenko
Keyword(s):  
Visual Analysis ◽  
Rotation Speed ◽  
Relative Size ◽  
Fine Fraction ◽  
Coarse Fraction ◽  
The Self ◽  
Cement Clinker ◽  
Crushed Material ◽  
Degree Of Filling ◽  
Tumbling Mill

The influence of the structure of a two-fraction polygranular feed of the chamber on the value of the drum rotation speed at auto-excitation of self-excited oscillations with a maximum swing is considered. Such a pulsating mode of movement of the charge is used in the self-oscillating process of grinding in a tumbling mill. The coarse fraction simulated the grinding bodies was steel bullets with a relative size ψdb=0.026. The fine fraction, simulated the particles of the crushed material, was a cement clinker with a relative particle size ψdm=0.00013. Variable factors of experimental studies were: the degree of filling the chamber in the state of rest κbr=0.25; 0.29; 0.33 and the degree of filling the gaps between the particles of the coarse fraction with particles of the fine fraction κmbgr=0.0625; 0.375; 0.6875; 1. The method of visual analysis of transient processes of self-oscillating modes of feed behavior in the cross section of the rotating drum chamber is applied. Measurements of the speed limits of the drum rotation were carried out with auto-excitation of self-oscillations of the filling. The magnitude of the self-oscillation swing was estimated by the increase in the difference between the maximum and minimum values of the filling dilatancy for one period of pulsations. An increase in the upper limit of the speed range ψω2 with a decrease in κbr and κmbgr was established. The growth rate of ψω2 increases at low values of κbr and κmbgr. Some increase in the lower limit of the ψω1 range with a decrease in κbr and κmbgr was revealed. An increase in the range of speeds of rotation was recorded at the maximum range of self-oscillations ψω1–ψω2 with a decrease in the connected interaction of the intra-mill filling. This coherent interaction is due to an increase in κbr and κmbgr. The value of the ψω1–ψω2 range varies from 1.01–1.03 at κbr=0.33 and κmbg=1 to 1.22–1.66 at κbr=0.25 and κmbgr=0.0625. The range gets its maximum value with fine and superfine grinding

scholarly journals THE DRUM ROTATION VELOCITY VALUE WHEN AUTO-OSCILLATION SELF-EXCITATION WITH MAXIMUM SWING OF A POLYGRANULAR INTRACHAMBER FILL

2020 ◽  
pp. 61-69
Author(s):  
Kateryna Deineka ◽  
Yurii Naumenko ◽  
Anatolii Zmiievskyi
Keyword(s):  
Visual Analysis ◽  
Large Fraction ◽  
Relative Size ◽  
Experimental Studies ◽  
Rotation Velocity ◽  
The Self ◽  
Spherical Particles ◽  
Crushed Material ◽  
Fill Fraction ◽  
Degree Of Filling

The influences of the structure of two-fractional polygranular intrachamber fill on the drum rotation velocity value when auto-oscillation self-excitation with maximum swing is considered. The pulsating mode of flow of such intrachamber fill is used in the self-oscillating grinding process in a tumbling mill. Spherical particles of non-coherent granular material of 2.2 mm size were used as a large fraction modeling the grinding bodies. Cement was used as the small fraction modeling the particles of the crushed material. The factors of experimental studies were accepted: the gaps between particles of large fraction degree of filling at rest dispersed particles of small fraction 0, 25, 50 and 100%, the relative size of particles of large fraction in the drum chamber 0.519, 0.733, 1.04, 1.47, 2.08, 2.93, 4.15 and 5.87% (drum chamber radius 212, 150, 106, 75, 53, 37.5, 26.5 and 18.75 mm), the chamber degree of filling at rest 25, 35 and 45%. The method of visual analysis of transient processes of self-oscillating fill flow modes in the cross section of a rotating chamber was applied. Measurements of the drum rotation velocity during fill self-excited self-oscillations were performed. The magnitude of the self-oscillation swing was estimated by the increase in the difference of the maximum and minimum values of the fill dilatation over one period of pulsating. The magnitude of the relative drum rotation velocity at the maximum range of fill self-oscillation swing varied within 0.777-1.4. The effect of a decrease in the relative drum rotation velocity value, when the maximum polygranular intrachamber fill self-oscillations swing, with enhanced fill coherent properties has been registered. A decrease in the relative rotational velocity was established with a decrease in the relative particle size of large fill fraction and an increase in the content of small fill fraction and an increase in the chamber degree of filling. A sharp intensification of the decrease in the relative rotation velocity at a value of the relative size of large particles of less than 0.015 is revealed.

scholarly journals INFLUENCE OF SMALL FRACTION OF POLYGRANULAR FILL OF ROTATING DRUM ON SELF-OSCILLATION SWING

2019 ◽  
pp. 31-37
Author(s):  
Deineka Kateryna
Keyword(s):  
Visual Analysis ◽  
Large Fraction ◽  
Relative Size ◽  
The Self ◽  
Spherical Particles ◽  
Rotating Drum ◽  
Crushed Material ◽  
Maximum Range ◽  
Size Of Particles ◽  
Degree Of Filling

The influence of the structure of two-fractional polygranular fill of a rotating drum on the self-oscillation swing is considered. The pulsating mode of flow of such intrachamber fill is used in the self-oscillating grinding process in a tumbling mill. Spherical particles of non-coherent granular material of 2.2 mm size were used as a large fraction modeling the grinding bodies. Cement was used as the small fraction modeling the particles of the crushed material. The factors of experimental studies were accepted: the gaps between particles of large fraction degree of filling at rest dispersed particles of small fraction 0, 25, 50 and 100%, the relative size of particles of large fraction in the drum chamber 0.519, 0.733, 1.04, 1.47, 2.08, 2.93, 4.15 and 5.87% (drum chamber radius 212, 150, 106, 75, 53, 37.5, 26.5 and 18.75 mm), the chamber degree of filling at rest 25, 35 and 45%. The method of visual analysis of fill motion patterns in the cross section of a rotating chamber and measurement of dilatation was applied.Video of the fill pulsating flow was taken. The magnitude of the self-oscillation swing was estimated by the increase in the difference of the maximum and minimum values of the fill dilatation over one period of pulsating. The maximum range of self-oscillation swing reached the value of 1.36. The change of the self-oscillation swing from zero at the beginning of self-excitation of pulsations to the maximum value with the greatest increase of dilatation was revealed. The effect of a decrease in the maximum range of self-oscillation swing with enhanced fill coherent properties has been registered. The attenuation of the spray of particles of large fraction in the chamber due to the coherent effect of the small fraction was established. An increase in the self-oscillation swing of single-grain fill was found with a decrease in the relative particle size and the chamber degree of filling. A decrease in the self-oscillation swing of two-fractional fill was found with an increase in the content of small fraction, a decrease in the relative size of particles of a large fraction, and an increase in the chamber degree of filling.

Long-term variations in individual particle types in the aerosol of Phoenix, Arizona, as determined using automated electron microprobe analysis and multivariate statistical techniques

1993 ◽  
Vol 51 ◽  
pp. 742-743
Author(s):  
Karen A. Katrinak ◽  
James R. Anderson ◽  
Peter R. Buseck
Keyword(s):  
Electron Microprobe ◽  
Fine Fraction ◽  
Coarse Fraction ◽  
Motor Vehicles ◽  
Multivariate Statistical Methods ◽  
Multivariate Statistical ◽  
X Ray ◽  
Mineral Particles ◽  
Anthropogenic Air Pollutants

Aerosol samples were collected in Phoenix, Arizona on eleven dates between July 1989 and April 1990. Elemental compositions were determined for approximately 1000 particles per sample using an electron microprobe with an energy-dispersive x-ray spectrometer. Fine-fraction samples (particle cut size of 1 to 2 μm) were analyzed for each date; coarse-fraction samples were also analyzed for four of the dates.The data were reduced using multivariate statistical methods. Cluster analysis was first used to define 35 particle types. 81% of all fine-fraction particles and 84% of the coarse-fraction particles were assigned to these types, which include mineral, metal-rich, sulfur-rich, and salt categories. "Zero-count" particles, consisting entirely of elements lighter than Na, constitute an additional category and dominate the fine fraction, reflecting the importance of anthropogenic air pollutants such as those emitted by motor vehicles. Si- and Ca-rich mineral particles dominate the coarse fraction and are also numerous in the fine fraction.

Experimental Studies of Sedimentation Basin Dynamics

1977 ◽  
Vol 12 (1) ◽  
pp. 77-90
Author(s):  
J.F. Cordoba-Molina ◽  
P.L. Silveston ◽  
R. R. Hudgins
Keyword(s):  
Dynamic Response ◽  
Froude Number ◽  
Flow Model ◽  
Experimental Studies ◽  
Densimetric Froude Number ◽  
Number Range ◽  
The Real ◽  
Highly Correlated ◽  
Sedimentation Basins ◽  
Simple Flow

Abstract A simple Flow Model is proposed to describe the dynamic response of sedimentation basins. The response predicted by this model is linear as opposed to the real response of the basin which is nonlinear. However, the real response of the basin is highly correlated with its densimetric Froude number, and as a consequence our linear model effectively predicts the response of the basin in a restricted densimetric Froude Number range. Our experiments show that the response of the basin becomes more sluggish and erratic as the densimetric Froude number decreases.

scholarly journals Experimental and Theoretical Study of the Axial Distribution of Solid Phase Particles in a Fluidized Bed

2021 ◽  
Vol 64 (4) ◽  
pp. 349-362
Author(s):  
A. V. Mitrofanov ◽  
V. E. Mizonov ◽  
N. S. Shpeynova ◽  
S. V. Vasilevich ◽  
N. K. Kasatkina
Keyword(s):  
Fluidized Bed ◽  
Field Experiments ◽  
Solid Phase ◽  
Cell Model ◽  
Experimental Studies ◽  
Parametric Identification ◽  
Resistance Coefficient ◽  
Model Material ◽  
Spherical Particles ◽  
Axial Distribution

The article presents the results of computational and experimental studies of the distribution of a model material (plastic spherical particles with a size of 6 mm) along the height of a laboratory two-dimensional apparatus of the fluidized bed of the periodic principle of action. To experimentally determine the distribution of the solid phase over the height of the apparatus, digital photographs of the fluidized bed were taken, which were then analyzed using an algorithm that had been specially developed for this purpose. The algorithm involved splitting the image by height into separate rectangular areas, identifying the particles and counting their number in each of these areas. Numerical experiments were performed using the previously proposed one-dimensional cell model of the fluidization process, constructed on the basis of the mathematical apparatus of the theory of Markov chains with discrete space and time. The design scheme of the model assumes the spatial decomposition of the layer in height into individual elements of small finite sizes. Thus, the numerically obtained results qualitatively corresponded to the full-scale field experiment that had been set up. To ensure the quantitative reliability of the calculated forecasts, a parametric identification of the model was performed using known empirical dependencies to calculate the particle resistance coefficient and estimate the coefficient of their macrodiffusion. A comparison of the results of numerical and field experiments made us possible to identify the most productive empirical dependencies that correspond to the cellular scheme of modeling the process. The resulting physical and mathematical model has a high predictive efficiency and can be used for engineering calculations of devices with a fluidized bed, as well as for setting and solving problems of optimal control of technological processes in these devices for various target functions.

scholarly journals Aerosol characterisation including oxidative potential as a proxy of health impact

2019 ◽  
Vol 29 (2) ◽  
Author(s):  
Miroslav Josipovic ◽  
Catherine Leal-Liousse ◽  
Belinda Crobeddu ◽  
Armelle Baeza-Squiban ◽  
C. Keitumetse Segakweng ◽  
...  
Keyword(s):  
Organic Carbon ◽  
Black Carbon ◽  
Fine Fraction ◽  
Health Impact ◽  
Coarse Fraction ◽  
Dry Season ◽  
Wet Season ◽  
Oxidative Potential ◽  
Ionic Content ◽  
Vaal Triangle

This study aimed to characterise aerosols sampled in the vicinity of a major industrialised area, i.e. the Vaal Triangle. It included thedetermination of oxidative potential as a predictive indicator of particle toxicity. Aerosol samples were collated through the cascadefiltering during an eight-month period (12 h over three days in one week). Three size fractions were analysed for organic carbon(OC), black carbon (BC) and oxidative potential (OP), while ionic content was presented as monthly and seasonal concentrations. Thecontinuous measurement of black carbon by an optical attenuation instrument was collated concurrently with cascade filtering. Thecarbonaceous content was low compared to the ionic one. Within the carbonaceous concentrations, the organic carbon was higherthan concentrations of black carbon in both seasons in the ultra-fine fraction; the opposite was the case for the fine fraction, whilethe coarse fraction concentrations of organic carbon in the dry season had higher concentrations than black carbon in the wet seasonand organic carbon in the wet season. The OP tended to increase as the size was decreasing for wet season aerosols, whereas, forthe dry season, the highest OP was exerted by the fine fraction. The ultrafine fraction was the one showing the most contrasting OPbetween the two seasons. Continuous monitoring indicated that the higher BC concentrations were recorded in the dry/winter partof the year, with the daily pattern of concentrations being typically bimodal, having both the morning and evening peaks in bothseasons. Within the ionic content, the dominance of sulphate, nitrate and ammonium was evident. Multiple linear correlations wereperformed between all determined compounds. Strong correlations of carboxylic acids with other organic compounds were revealed.These acids point to emissions of VOC, both anthropogenic and biogenic. Since they were equally present in both seasons, a mixtureof sources was responsible, both present in the wider area and throughout the year.

scholarly journals Investigating Subantarctic 14C Ages of Different Peat Components: Site and Sample Selection for Developing Robust Age Models in Dynamic Landscapes

Radiocarbon ◽  
2019 ◽  
Vol 61 (4) ◽  
pp. 1009-1027 ◽  
Author(s):  
Zoë A Thomas ◽  
Chris S M Turney ◽  
Alan Hogg ◽  
Alan N Williams ◽  
Chris J Fogwill
Keyword(s):  
Bulk Material ◽  
Sample Selection ◽  
Fine Fraction ◽  
Systematic Difference ◽  
Coarse Fraction ◽  
Sedimentary Sequences ◽  
Subantarctic Islands ◽  
Dynamic Landscapes ◽  
Age Model ◽  
Selection For

ABSTRACTPrecise radiocarbon (14C) dating of sedimentary sequences is important for developing robust chronologies of environmental change, but sampling of suitable components can be challenging in highly dynamic landscapes. Here we investigate radiocarbon determinations of different peat size fractions from six peat sites, representing a range of geomorphological contexts on the South Atlantic subantarctic islands of the Falklands and South Georgia. To investigate the most suitable fraction for dating, 112 measurements were obtained from three components within selected horizons: a fine fraction <0.2 mm, a coarse fraction >0.2 mm, and bulk material. We find site selection is critical, with locations surrounded by high-ground and/or relatively slowly accumulating sites more susceptible to the translocation of older carbon. Importantly, in locations with reduced potential for redeposition of material, our results show that there is no significant or systematic difference between ages derived from bulk material, fine or coarse (plant macrofossil) material, providing confidence in the resulting age model. Crucially, in areas comprising complex terrain with extreme relief, we recommend dating macrofossils or bulk carbon rather than a fine fraction, or employing comprehensive dating of multiple sedimentary fractions to determine the most reliable fraction(s) for developing a robust chronological framework.

Investigation of Supercritical Flow and Shape of Flip Bucket Spillways on Coefficients of Dynamic Pressure

2020 ◽  
Vol 143 (6) ◽  
Author(s):  
Hessam Vatandoust ◽  
Hamidreza Yarmohammadi ◽  
Mohammadreza Kavianpour
Keyword(s):  
Froude Number ◽  
Pressure Fluctuation ◽  
Dynamic Pressure ◽  
Pressure Coefficient ◽  
Pressure Fluctuations ◽  
Experimental Studies ◽  
Flow Speed ◽  
Middle Part ◽  
Statistical Characteristics ◽  
Pressure Coefficients

Abstract Pressure fluctuation is one of the major turbulent flow characteristics. It may cause crucial problems for hydraulic structures. This research is based on experimental studies, and it focuses on the measurements of pressure fluctuations along flip bucket spillways with different geometrical characteristics. The function of the flip bucket spillway is discharging floods from reservoir dams which are energy storage source measurements of dynamic pressures on three different models of flip buckets that were performed for this investigation. Pressure fluctuation of the flip buckets have been measured within a range of Froude numbers from 5 to 13 (Fr = u/gy, where u is the flow speed, y is the depth, and g is 9.81 m/s2). Statistical characteristics of pressure fluctuations, the location, and the values of maximum and minimum fluctuations have also supplemented the study. The results show that the coefficients of pressure fluctuations (Cp = RMS/(0.5(u2/g)) where RMS is the root-mean-square of pressure fluctuation, u is the flow speed, and g is 9.81 m/s2) reduce as the Froude number (Fr) of flow increases, except a maximum Froude number. Pressure coefficients increase along the flip bucket with incremental mutations in the transformation area of the flip bucket. In the middle part of the flip bucket spillway, pressure coefficient values decrease. Additionally, as B/r (B is the width of the flip bucket and r is the radius of the flip bucket) ratio increases, pressure coefficients become larger and this process continues along the flip bucket.

scholarly journals Analytical and numerical assessment of the effect of highly conductive inclusions distribution on the thermal conductivity of particulate composites

2019 ◽  
Vol 53 (25) ◽  
pp. 3499-3514 ◽  
Author(s):  
Kamran A Khan ◽  
Falah Al Hajeri ◽  
Muhammad A Khan
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Numerical Models ◽  
Random Network ◽  
Experimental Studies ◽  
Percolation Model ◽  
Spherical Particles ◽  
Particulate Composites ◽  
Advanced Composites ◽  
Micromechanical Models

Highly conductive composites have found applications in thermal management, and the effective thermal conductivity plays a vital role in understanding the thermo-mechanical behavior of advanced composites. Experimental studies show that when highly conductive inclusions embedded in a polymeric matrix the particle forms conductive chain that drastically increase the effective thermal conductivity of two-phase particulate composites. In this study, we introduce a random network three dimensional (3D) percolation model which closely represent the experimentally observed scenario of the formation of the conductive chain by spherical particles. The prediction of the effective thermal conductivity obtained from percolation models is compared with the conventional micromechanical models of particulate composites having the cubical arrangement, the hexagonal arrangement and the random distribution of the spheres. In addition to that, the capabilities of predicting the effective thermal conductivity of a composite by different analytical models, micromechanical models, and, numerical models are also discussed and compared with the experimental data available in the literature. The results showed that random network percolation models give reasonable estimates of the effective thermal conductivity of the highly conductive particulate composites only in some cases. It is found that the developed percolation models perfectly represent the case of conduction through a composite containing randomly suspended interacting spheres and yield effective thermal conductivity results close to Jeffery's model. It is concluded that a more refined random network percolation model with the directional conductive chain of spheres should be developed to predict the effective thermal conductivity of advanced composites containing highly conductive inclusions.

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