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1.
The tangential velocity profile for pseudoplastic power-law fluids in a hydrocyclone is determined with an analytical solution to a simplified momentum balance equation by the method of perturbation. A numerical solution of the non-linear two-point boundary-value problem by the finite-difference method provides a verification of the perturbation solution. The tangential velocity is found to be controlled by a modified Reynolds number involving the radial velocity at the outer radius of the hydrocyclone and the consistency and flow-behavior indices of the fluid. The radial position of the maximum tangential velocity decreases with an increase in the modified Reynolds number and/or the degree of pseudoplasticity of the fluid. This analysis suggests that improved performance of hydrocyclones may be possible for pseudoplastic fluid systems as the tangential velocity profiles are steeper and the free-vortex zone is extended inwards. 相似文献
2.
Hydrocyclones are widely used in the mining and chemical industries. An attempt has been made in this study, to develop a CFD (computational fluid dynamics) model, which is capable of predicting the flow patterns inside the hydrocyclone, including accurate prediction of flow split as well as the size of the air-core. The flow velocities and air-core diameters are predicted by DRSM (differential Reynolds stress model) and LES (large eddy simulations) models were compared to experimental results. The predicted water splits and air-core diameter with LES and RSM turbulence models along with VOF (volume of fluid) model for the air phase, through the outlets for various inlet pressures were also analyzed. The LES turbulence model led to an improved turbulence field prediction and thereby to more accurate prediction of pressure and velocity fields. This improvement was distinctive for the axial profile of pressure, indicating that air-core development is principally a transport effect rather than a pressure effect. 相似文献
3.
《International Journal of Mineral Processing》2005,75(1-2):53-68
The flow behavior in hydrocyclone is quite complex. This complexity of flow processes has led designers to rely on empirical equations for predicting the equipment performance. The publications on empirical models of the hydrocyclone far out-number few fluid-flow-modeling attempts. Empirical models correlate a classification parameter, such as the cut-size, with device dimensions and slurry properties. However, these can only be used within the extremes of the experimental data from which the model parameters were determined. On the other hand, models based on Computational Fluid Dynamics (CFD) techniques have proven to be useful in simulating fluid flow in hydrocyclones, and in predicting the separation efficiency of solid particles in the separator for a wide range of operating and design conditions. The shape and size of a hydrocyclone separator has a direct influence on the internal flow structure of the continuous phase and, thereby, the separation of the particulate phase. Hydrocylcones usually have a single inlet that distributes the feed stream near the end wall between the vortex finder and the sidewall. Effect of spigot diameter, i.e., 10 and 20 mm and inlet water velocities (5.91–12.35 m/s) on the water splits and particle classification in the hydrocyclone have been studied. The cut size of the hydrocyclone, operated at very low pulp density, has been predicted using discrete phase modeling technique. The studies revealed that with an increase in feed flow rate and decrease in spigot diameter the cyclone sharpness of separation improves. These predictions were found similar in line with the experimental observations. 相似文献
4.
About 30 samples representing major lithologies of Sulu ultrahigh-pressure (UHP) metamorphic rocks were collected from surface exposures and exploration wells, and compressional (Vp) and shear wave (Vs) velocities and their directional dependence (anisotropy) were determined over a range of constant confining pressures up to 600 MPa and temperatures ranging from 20 to 600 °C. Samples range in composition from acidic to ultramafic. P- and S-wave velocities measured at 600 MPa vary from 5.08 to 8.64 km/s and 2.34 to 4.93 km/s, respectively. Densities are in the range from 2.60 to 3.68 g/cm3. To make a direct tie between seismic measurements (refraction and reflection) and subsurface lithologies, the experimental velocity data (corresponding to shallow depths) were used to calculate velocity profiles for the different lithologies and profiles of reflection coefficients at possible lithologic interfaces across the projected 5000-m Chinese Continental Scientific Drilling Program (CCSD) crustal segment. Comparison of calculated in situ velocities with respective intrinsic velocities suggests that the in situ velocities at shallow depths are lowered by an increased abundance of open microcracks. The strongly reflective zone beneath the Donghai drill site can be explained by the impedance contrasts between the different lithologies. Contacts between eclogite/peridotite and felsic rocks (gt-gneiss, granitic gneiss), in particular, may give rise to strong seismic reflections. In addition, shear-induced (lattice preferred orientation (LPO)-related) seismic anisotropy can increase reflectivity. For the explanation of the high velocity bodies (>6.4 km/s) around 1000 m and below 3200-m depth, large proportions of eclogite/peridotite (about 40 and 30 vol.%, respectively) are needed. 相似文献
5.
Wanwilai Kraipech Wu Chen Tom Dyakowski Andrzej Nowakowski 《International Journal of Mineral Processing》2006,80(2-4):100-115
Many empirical models have been used widely for designing hydrocyclones in industry. These empirical models consist of a set of design equations. Most of the design equations are based on the correlations obtained experimentally, using dimensionless similarity numbers. These equations have their limitations due to the specific systems used for model development. Therefore, in many cases, they cannot be used with confidence to predict the design of an individual separator, or the overall plant configuration that is required to meet different user requirements. A modified version of the existing design equations presented by previous researchers was developed. The design equations, describing four fundamental parameters: pressure drop, flow recovery to underflow, corrected cut size and classification function, were modified by fitting with set of experimental data to obtain the system-specific constant parameters. These modified design equations were then called, the fine-tuned design equations. Four sets of fine-tuned design equations describing all the fundamental parameters were constructed and used to predict the separation performance of many hydrocyclone operational systems at the Dow Chemical Company, Texas, USA. The performance of these equations is evaluated, and the limitations of their use are discussed, thus providing useful insights into hydrocyclone design. 相似文献
6.
From earlier work on 10.2-, 15.2-, 25.4-, and 38.1-cm hydrocyclones, it was concluded that the design variables which affect the hydrocyclone performance are the inlet and outlet dimensions and that the hydrocyclone body is merely a housing required to carry these parts. A single inlet only was used with each cyclone for that study. In the present investigation the effect of feed inlet diameter on the hydrocyclone behaviour was studied by changing inlets on the previously studied cyclones. The results confirm the above conclusions. 相似文献
7.
A discrete element method is applied to a three‐dimensional analysis related to sediment entrainment on a micro‐scale. Sediment entrainment is the process by which a fluid medium accelerates particles from rest and advects them upward until they are either transported as bedload or suspended by the flow. Modelling of the entrainment process is a critically important aspect for studies of erosion, pollutant resuspension and transport, and formation of bedforms in environmental flows. Previous discrete element method studies of sediment entrainment have assumed the flow within the particle bed to be negligible and have only allowed for the motion of the topmost particles. At the same time, micro‐scale experimental studies indicate that there is a small slip of the fluid flow at the top of the bed, indicating the presence of non‐vanishing fluid velocity within the topmost bed layers. The current study demonstrates that the onset of particle incipient motion, which immediately precedes particle entrainment, is highly sensitive to this small fluid flow within the topmost bed layers. Using an exponential decay profile for the inner‐bed fluid flow, the discrete element method calculations are repeated with different fluid penetration depths within the bed for several small particle Reynolds numbers. For cases with slip velocity corresponding to that observed in previous experiments with natural sediment, the predicted particle velocity is found to be a few percent of the fluid velocity at the top of the viscous wall layer, which is a reasonable range of velocities for observation of incipient particle motion. This method for prescribing the fluid flow within the particle bed allows for the current discrete element method to be extended in future studies to the analysis of sediment entrainment under the influence of events such as turbulent bursting. Additionally, predictions for the slip velocities and fluid flow profile within the bed suggest the need for further experimental studies to provide the data necessary for additional improvement of the discrete element method models. 相似文献
8.
The experimental study of the hydrodynamics of the sediments and the physical analysis of the process of exchange at the water-sediment interface in a zone of swash are essential for the understanding of the sedimentary transport processes in coastal environments, in particular to control and forecast the evolution of the coastline. The objective of this study was to exploit the technique of Ultrasonic Doppler Velocimetry (UDV) to examine the evolution of the velocity field at the water-sediment interface in a zone of swash in various conditions of incidental regular waves in a wave flume. The velocities were measured in different conditions of the swash within the sediment bed, and in the fluid vein at the swash edge. These measurements show: an exponential distribution of velocities inside the sediment bed; a difference in the velocity gradient at the water-sediment interface, between the velocity in the water vein at the swash edge and the interstitial flow in the swash. The measurements obtained in the wave flume made it possible to observe an evolution of the velocity profiles according to the phases of the swash, which are characterized by a phase shift between the free flow at the swash edge and the interstitial flow during the two phases of the swash: uprush and backwash. 相似文献
9.
在环形水槽内模拟了太湖底泥的起动规律,分析了太湖底泥运动的不同状态,以及上覆水中总磷(TP)浓度随流速的变化关系,实验得出的太湖底泥在3种起动标准下对应的起动流速分别为35、45和60cm/s,并观察到上覆水中TP浓度在3种不同起动流速处出现了较大的跳跃;然后利用泥沙起动的理论模型计算了太湖底泥在3种不同起动标准(个别动、少量动、普遍动)下的起动流速和起动切应力,其值分别为37.9、46.7、59.8cm/s和0.428、0.636、1.042N/m2。两种方法得到的起动流速值比较接近,基本上反映了太湖底泥起动的实际状况。 相似文献
10.
ZHENHUA JIANG 《Sedimentology》1995,42(6):935-945
A new model, which couples fluid and particle dynamics, has been developed to study the motion of the sediment-water mixture during intense bedload transport, including the velocity profiles of both sediment and water, the roughness length of an upper plane bed and the thickness of moving sediment layers. Standard mixing length theory is used to model the motion of water above the boundary between the overlying water and the sediment-water mixture. The turbulent flow within the moving sediment layers is described by a shear stress model, in which the effective viscosity of the flowing water is proportional to the velocity difference between the fluid and the sediment. The particle dynamics method, in which the equations of motion of each of many particles are solved directly, is applied to model the movement of sediment particles. The particle-fluid interaction is expressed by a velocity-squared fluid drag force exerted on each sediment particle. Both computer simulation results and theoretical analysis have shown that the velocities of both sediment and fluid during intense sediment transport decrease exponentially with depth in the top layers of a fast-moving sediment—water mixture. The thickness of the moving sediment layers, obtained from the computer simulation results, is proportional to the shear stress, which agrees with previous experimental observations. 相似文献
11.
Modified Christoffel equations are derived for three-dimensional wave propagation in a general anisotropic medium under initial
stress. The three roots of a cubic equation define the phase velocities of three quasi-waves in the medium. Analytical expressions
are used to calculate the directional derivatives of phase velocities. These derivatives are, further, used to calculate the
group velocities and ray directions of the three quasi-waves in a pre-stressed anisotropic medium. Effect of initial stress
on wave propagation is observed through the deviations in phase velocity, group velocity and ray direction for each of the
quasi-waves. The variations of these deviations with the phase direction are plotted for a numerical model of general anisotropic
medium with triclinic/ monoclinic/orthorhombic symmetry 相似文献
12.
YE Jiaren HAO Fang CHEN JianyuFaculty of Earth Resources China University of Geosciences Wuhan Hubei E-mail: jrye@cug.edu.cn Ren Xifei Zhu Xiling 《《地质学报》英文版》2003,77(3):402-412
The Damintun depression is one of the four depressions in the Liaohe basin in northern China, and is a rift basin developed in the Paleogene. This paper discusses in detail the characteristics of pressure and fluid potential of the Damintun depression based on a synthesis of the data from boreholes, well tests and seismic surveys. Data from sonic logs, well tests and seismic velocity measurements are used to study the pressure characteristics of the areas. From the sonic log data, shales can be characterized as normally pressured, slightly overpressured or highly overpressured; from the well test data, the pressure-depth gradient in oil-producing intervals implies hydrostatic pressure in general. Most seismic profiles in the Damintun depression are of sufficiently high quality for seismic velocities to be measured. The fluid pressures, excess pressures and pressure coefficients in 47 representative seismic profiles are predicted using formula calculation methods, and further transformed to fluid potenti 相似文献
13.
In this study, we report the results of an investigation of lithological interpretation of the crust in the central Fennoscandian Shield (in Finland) using seismic wide-angle velocity models and laboratory measurements on P- and S-wave velocities of different rock types. The velocities adopted from wide-angle velocity models were compared with laboratory velocities of different rock types corrected for the crustal PT conditions in the study area. The wide-angle velocity models indicate that the P-wave velocity does not only increase step-wise at boundaries of major crustal layers, but there is also gradual increase of velocity within the layers. On the other hand, the laboratory measurements of velocities indicate that no single rock type is able to provide the gradual downward increasing trends. Thus, there must be gradual vertical changes in rock composition. The downward increase of velocities indicates that the composition of the crust becomes gradually more mafic with increasing depth. We have calculated vertical velocity profiles for a range of possible crustal lithological compositions. The Finnish crustal velocity profiles require a more mafic composition than an average global continental model would suggest. For instance, on the SVEKA'81 transect, the calculated models suggest that the crustal velocity profiles can be simulated with rock type mixtures where the upper crust consists of felsic gneisses and granitic–granodioritic rocks with a minor contribution of amphibolite and diabase. In the middle crust, the amphibolite proportion increases. The lower crust consists of tonalitic gneiss, mafic garnet granulite, hornblendite, pyroxenite and minor mafic eclogite. Assuming that these rock types are present in sufficiently extensive and thick layers, they would also have sufficiently high acoustic reflection coefficients for generating the generally well-developed reflectivity in the crust in the central part of the shield. Density profiles calculated from the lithological models suggest that there is practically no density contrast at Moho in areas of the high-velocity lower crust. Comparison of reflectors from FIRE-1 and FIRE-3 transects and the velocity model from SVEKA'81 wide-angle transect indicated that the reflectors correlate with velocity layering, but the three-dimensional structures of the crust complicate such comparisons. 相似文献
14.
A Fluid-Dynamical Study of Crystal Settling in Convecting Magmas 总被引：1，自引：3，他引：1
Thermal convection in magma chambers is believed to be almostalways highly time-dependent, or ‘turbulent’, andpredicted convective velocities are commonly orders of magnitudelarger than settling velocities for typical crystals calculatedfrom Stokes' Law. To understand crystal settling in magma chamberswe have therefore undertaken a theoretical and experimentalstudy of particle settling in a turbulently convecting fluid. The regime of interest is where the ratio, S, of the Stokes'Law settling velocity, vs, to the root mean square verticalcomponent of convective velocity, W, at mid-depth in the fluidis less than unity. Although vs < W, settling is still possiblebecause convective velocities are height-dependent and mustdecrease to zero at the boundaries of the fluid. Particles immediatelyadjacent to the bottom boundary settle out with their full Stokes'settling velocities. At the same time, convection is vigorousenough to ensure that the distribution of particles in the fluidis uniform. It follows that the number of particles in suspensiondecays with time according to an exponential law, and the decayconstant is simply the ratio of vs to h, the depth of the fluid.Experiments confirm this relationship, at least for low particleconcentrations, provided S < 0.5 and there is no re-entrainmentof particles from the floor of the tank. We apply this relationship to crystals in magma chambers andso calculate residence times for typical crystals. We find thatfor basaltic magmas the predicted residence times are smallcompared with the many thousands of years that a chamber takesto solidify if cooling is dominated by conduction through thecountry rock. We therefore conclude that crystal settling maybe an efficient differentiation mechanism. Significant magmaticevolution may, however, take place on time-scales that are competitivewith these residence times. If the settling of crystals is the rate-limiting step duringthe crystallization of a magma chamber it is expected that asteady state will be achieved at which the rate of supply ofcrystals into the convecting magma by crystallization balancesthe rate at which crystals settle out. We show how this ideacan explain both the lack of hydraulic equivalence in cumulaterocks and the commonly observed discrepancy between the relativeproportions of phenocrysts of various phases in fractionatedbasaltic lavas and the calculated relative proportions of thesemineral phases in the fractionating assemblage. Finally, anattempt is made to calculate the steady-state crystal contentof convecting magma chambers. Comparison of the predicted crystalcontents with the observed phenocryst contents of typical basalticlavas suggests that magma chambers may often cool more rapidlythan would be expected for conduction through the country rockalone. 相似文献
15.
The initiation of particle movement by wind 总被引：4，自引：0，他引：4
W. G. NICKLING 《Sedimentology》1988,35(3):499-511
When air blows across the surface of dry, loose sand, a critical shear velocity (fluid threshold, ut), must be achieved to initiate motion. However, since most natural sediments consist of a range of grain sizes, fluid threshold for any sediment cannot be defined by a finite value but should be viewed as a threshold range which is a function of the size, shape, sorting and packing of the surface sediment. In order to investigate the initiation of particle movement by wind a series of wind-tunnel tests was carried out on a range of pre-screened fluvial sands and commercially available glass beads with differing mean sizes and sorting characteristics. A sensitive laser-monitoring system was used in conjunction with a high speed counter to detect initial grain motion and to count individual grain movements. Test results indicate that when velocity is slowly increased over the sediment surface the smaller or more exposed grains are first entrained by the fluid drag and lift forces either in surface creep (rolling) or in saltation (bouncing or hopping downwind). As velocity continues to rise, larger or less exposed grains may also be moved by fluid drag. On striking the surface saltating grains impart momentum to stationary grains. This impact may result in the rebound of the original grain as well as the ejection of one or more stationary grains into the air stream at shear velocities lower than that required to entrain a stationary particle by direct fluid pressure. As a result, there is a cascade effect with a few grains of varying size initially moving over a range of shear velocities (the fluid threshold range) and setting in motion a rapidly increasing number of grains. Results of the tests showed that the progression from fluid to dynamic threshold, based on grain movement, can be characterized by a power function, the coefficients of which are directly related to the mean size and sorting characteristics of the sediment. 相似文献
16.
In dressing plants, the rapid determination of the corrected cut point in hydrocyclone classification is desirable, useful, and important. In this work, classification tests have been carried out on white sand using a 10-cm diameter hydrocyclone to examine closely the relation between the recovery to underflow and the corrected separation size, . The study was carried out at wide ranges of: apex diameter, vortex-finder diameter, solid content of feed, and length of vortex finder.A simple, yet reliable, equation relating the solid recovery of underflow to , is developed using all the obtained results. The predicted data show good agreement with the experimental. 相似文献
17.
为估算松花江干流哈尔滨至同江段相距660 km的河冰厚度分布,用松花江干流短期实测水文和气象资料,在静态水域斯蒂芬冰厚计算公式基础上,引入水流流速的动能效应。假设河流内水流量相等,建立流速同河流宽度的简单关系,估算了一些调查断面的冰下平均流速;用地表温度资料,对干流域内缺少气象资料的调查断面,在证明结冰期间属于同一天气系统的前提下,用距离平方反比法进行空间插值。最后获得松花江干流河冰厚度统计关系式。用计算的哈尔滨至同江河冰厚度与有限的实测数据比较,发现该方法能够体现人为调节流速对冰生长速率的影响,对计算长距离河冰厚度具有一定精度。 相似文献
18.
In the southern part of the Slovensky Kras Mountains, located on the Hungarian–Slovakian border, a transboundary karstic aquifer
Dolny vrch/Alsóhegy underlies the structure and discharges groundwater flow to 15 major karst springs around its margin. Hydrograph
recession curves from nine-gauged springs on the Slovak part of the aquifer were analysed, and for each individual spring,
depletion hydrograph equations were classified into different categories based on recessional parameters quantitatively describing
individual groundwater flow sub–regimes. Discharge depletion was used to create recessional equations, and these were linked
to karstification degree, a qualitative scale ranging from 1 to 10. A new application of hydrograph separation was based on
examining and combining pairs of springs that likely fit into the category of overflow/underflow springs for a single groundwater
reservoir. Recession-curve analysis performed on coupled discharges of two pairs of neighbouring springs was conducted to
examine their possible linkage as a single groundwater reservoir, with an overflow outlet and underflow outlet. In the process
of discharge coupling, discharges of the springs, hypothesized to be branches of the same source and observed at the same
time were simply added together. By analyzing the resulting new time series, a new classification of sub-regimes could be
generated. Surprisingly, new facts were revealed about the overflow/underflow springs, which primarily were not recognized
previously as being connected components of a single groundwater reservoir. Summations of combined overflow/underflow discharge
volumes of a single spring reservoir led to discovery of apparent presence of turbulent flow sub-regimes on the coupled recession
curve. Presence of possible overflow/underflow springs of a single groundwater basin should be considered during hydrograph
analyses if the springs have attributes that suggest they may be part of a combined flow system. Treating these springs as
separate entities as a result can produce significant misinterpretation of drainage parameters. Furthermore, identification
of overflow branches facilitates the generation of new research ideas for further speleological investigations nearby, and
for assessing the system in a more effective manner. 相似文献
19.
Mohamed K. Salah 《地学前缘(英文版)》2014,5(6):845-854
The 3-D P- and S-wave velocity models of the upper crust beneath Southwest Iberia are determined by inverting arrival time data from local earthquakes using a seismic tomo~raphy method. We used a total of 3085 P- and 2780 S-wave high quality arrival times from 886 local earthquakes recorded by a per- manent seismic network, which is operated by the Institute of Meteorology （IM）, Lisbon, Portugal. The computed P- and S-wave velocities are used to determine the 3-D distributions of Vp/Vs ratio. The 3-D velocity and Vp/Vs ratio images display clear lateral heterogeneities in the study area. Significant veloc- ity variations up to ~6% are revealed in the upper crust beneath Southwest lberia, At 4 km depth, both P- and S-wave velocity take average to high values relative to the initial velocity model, while at 12 km, low P-wave velocities are clearly visible along the coast and in the southern parts. High S-wave velocities at 12 km depth are imaged in the central parts, and average values along the coast; although some scattered patches of low and high S-wave velocities are also revealed. The Vp/Vs rztio is generally high at depths of 4 and 12 km along the coastal parts with some regions of high Vp/Vs ratio in the north at 4 km depth, and low Vp/Vs ratio in the central southern parts at a depth of 12 km, The imaged low velocity and high Vp/Vs ratios are related to the thick saturated and unconsolidated sediments covering the region; whereas the high velocity regions are generally associated with the Mesozoic basement rocks. 相似文献
20.
Aleksander Grm Tomaž Šuštar Tomaž Rodič Franci Gabrovšek 《Mathematical Geosciences》2017,49(5):657-675
Scallops and flutes are common dissolution rock forms encountered in karst caves and surface streams. Their evolution is only partially understood and no numerical model that simulates their formation has been presented. This work at least partially fills the gap by introducing a numerical approach to simulate the evolution of different initial forms of soluble surfaces embedded in a turbulent fluid. The aim is to analyze wall dissolution phenomena from basic principles and to identify stable profiles. The analysis is based on a finite volume moving boundary method. The underlying mathematical model is a \(k-\epsilon \) turbulent model for fluid flow coupled with turbulent scalar transport. The rock wall is treated as a moving boundary, where the normal wall retreat velocity is proportional to the under-saturation of the boundary fluid cells with respect to the mineral comprising the wall. As the flow time scale is several orders of magnitude smaller than the dissolution time scale, stationary flow field, concentration field and wall propagation velocity are calculated for each iteration. The boundary at all points is then moved by distracting minimal velocity along the entire boundary from the actual velocity at a certain location, and then normalized to the maximum allowed shift, which is equal to half the height of the boundary cell. In this way only deformation of the initial wall is calculated. The method was applied to several different initial profiles. During the evolution, the profiles progressively converged towards stable forms. In this work, a framework is proposed for a computation of the moving boundary problem related to slow dissolution of a soluble surface. 相似文献