基于DEM的无钟高炉布料料流轨迹研究

摘要：离散单元仿真技术被广泛用于研究高炉布料过程中炉料运动的规律,其计算散料运动的方法得到了国内外专家的认可。利用SOLIDWORKS和EDEM的Geometry建立无钟炉顶高炉几何模型,基于DEM结合炉料物理参数进行数学模拟,研究了溜槽倾角、料线深度和溜槽结构对料流轨迹的影响。结果表明：焦炭落点半径随溜槽倾角的增大而增大,倾角为13.3°时,炉料在下落过程中不与溜槽接触;随着料线深度的增大,焦炭的落点半径随之增大,但增量减小;在相同倾角下,矩形溜槽布焦炭时的落点半径比半圆形溜槽的小0.3m,且料流更集中,布料效果略优;有衬板溜槽比光面溜槽布焦炭时的落点半径小0.13m,料流宽度也较小,且能通过料与料之间的摩擦降低炉料对溜槽表面的磨损。     

Velocity Profile and Flow Resistance Models for Developing Chute Flow

A developing boundary layer starts at the spillway crest until it reaches the free surface at the so-called inception point, where the natural air entrainment is initiated. A detailed reanalysis of the turbulent velocity profiles on steep chutes is made herein, including mean values for the parameters of the complete turbulent velocity profile in the turbulent rough flow regime, given by the log-wake law. Accounting both for the laws of the wall and the wake, a new rational approach is proposed for a power-law velocity profile within the boundary layer of turbulent rough chute flow. This novel approach directly includes the power-law parameters and does not require for a profile matching, as is currently required. The results obtained for the turbulent velocity profiles were applied to analytically determine the resistance characteristics for chute flows. The results apply to the developing flow zone upstream of air inception in chute spillways.     

无料钟料流运动轨迹数学模拟

结合无料钟设备结构,分段建立了炉料运动轨迹方程,计算值与实测值吻合较好.分析了影响料流质心落点半径的诸因素,结论如下:溜槽倾角是决定料流质心落点半径的根本因素;料线、溜槽悬挂点至零料线距离、溜槽结构参数对料流质心落点半径影响较大;溜槽耐磨衬板的种类及溜槽角速度对料流质心落点半径具有一定的影响;而节流阀至溜槽悬挂点距离对其影响很小.     

Effect of Chute Rotation on Particles Movement for Bell-less Top Blast Furnace

For the bell-less top blast furnace, when particles move along the chute, the particles motion direction and the frictional force acting on them will change due to the chute rotation, which consequently influences the velocity at the tip of chute, changes the burden flow width and impact point, and finally affects the stock profile and gas flow distribution. So the influence of chute rotation needs to be considered when calculating the burden trajectory with a mathematical model. The mathematical model was established to analyze the influence of Coriolis force on particle velocity at chute tip as well as height and width of burden flow in chute, and to summarize the effect of Coriolis force on burden distribution, thereby making the calculation result more accurate.     

Development of Air Concentration on Chute Spillways

To protect hydraulic structures such as spillways, chutes, and bottom outlets against cavitation damage, air is normally added by means of aerators in regions where the cavitation number falls below a critical value. Although aerators have been investigated for more than 30 years, the current design methods for aerator spacing are not reliable. The detrainment process was not previously investigated in detail because of limited laboratory instrumentation. The research presented in this paper provides new model data for hydraulic chutes of variable bottom slope. An advanced remote-controlled, fiber-optical instrumentation was employed to investigate the streamwise development of air concentration contours, velocity contours, and air bubble size along a 14-m model chute. The main hydraulic parameters such as bottom slope, inflow Froude number, inflow depth, and two distinctly different air supply devices for air-water flow generation were employed. Results enable prediction of the reduction of bottom and average air concentration, depending on the inflow air concentration and the chute slope. The minimum air concentration is proven to be a function of the streamwise Froude number. The point of minimum air concentration is constrained by the point of air inception. Downstream of this point the air concentration increases from the surface aeration, depending on the chute slope.     

Self-Aeration and Friction over Rock Chutes in Uniform Flow Conditions

Interaction between the free surface and the bed material in flow over rock chutes under macroroughness conditions leads to a high air entrainment into the flow. The note reports on an experimental study about air diffusion features in the flow over a long rock chute. Air concentration profiles and water depths over a uniform bed material were measured. An empirical equation for the average air concentration in macroroughness condition for steep slopes is proposed. A new Darcy-Weisbach equivalent friction factor for long chutes as a function of the slope and the relative equivalent depth has also been found.     

Turbulence Measurements of Dye Concentration and Effects of Secondary Flow on Distribution in Open Channel Flows

This paper presents simultaneous turbulence measurements of velocity and tracer concentration using a combination of laser Doppler anemometer (LDA) and laser induced fluorescence (LIF) in rectangular and compound channels. Secondary flow, Reynolds stresses, Reynolds fluxes, and dye concentration distributions were measured near the water surface in both channels. An investigation of the effect of secondary flow on passive contaminant diffusion processes was carried out with relatively weak secondary flow in the rectangular channel and relatively strong secondary flow in the compound channel. The results show that the secondary flow clearly influences the spreading of the tracer concentration and the location of concentration peak, being different from the injection location. The transport rate of solute due to the secondary flow is not significant in the rectangular channel case but significant in the compound channel case. The transverse eddy viscosity is demonstrated to be equal to the transverse eddy diffusivity. The transverse eddy diffusivity near the water surface is larger than the vertical one. The Fickian law is valid in most regions investigated, but there are some regions where the Reynolds flux and concentration gradients are locally of the same sign due to the influence of secondary flow on the concentration distribution.     

Two-Phase Flow Characteristics of Stepped Spillways

An experimental study on a large model flume with fiber-optical instrumentation indicated that minimum Reynolds and Weber numbers of about 105 and 100, respectively, are required for viscosity and surface tension effects to become negligible compared to gravitational and inertial forces expressed by Froude similitude. Both the location of and the flow depth at the inception point of air entrainment can be expressed as functions of a so-called roughness Froude number containing the unit discharge, step height and chute angle. The depth-averaged air concentration is found to depend only on a normalized vertical distance from the spillway crest and the chute angle for chute slopes ranging from embankment to gravity dam spillways. Air concentration profiles can be expressed by an air bubble diffusion model. The pseudobottom air concentration allows the assessment of the cavitation risk of stepped chutes and is approximated by a regression function. Finally, a new velocity distribution function is presented consisting of a power law up to 80% of the characteristic nondimensional mixture depth, and a constant value above.     

不同溜槽形状下的料流偏析现象

 无钟炉顶设备主要通过改变溜槽倾角以调整布料矩阵,最终改变炉料在高炉内的分布。此外,炉料分布还受溜槽形状的影响,不同形状的溜槽,其料面偏析情况不同。为探究不同溜槽下的布料偏析现象,针对常见圆方比例不同的3种类型溜槽、带储料槽型溜槽以及破损溜槽,运用离散单元法对溜槽表面和布料特征进行研究,探究在不同溜槽下炉料的偏析现象和溜槽受力情况。模拟结果表明,相对于圆形出口溜槽,方形出口溜槽料流宽度小,分布均匀,更有利于精准布料;带储料槽溜槽可以减小炉料对溜槽的冲刷,延长溜槽寿命;破损溜槽料流宽度较大,炉料分布不均匀,会加大炉料在料面上的偏析。     

Hydraulic Design of Stepped Spillways

An experimental study on a large model flume using fiber-optical instrumentation indicated that the onset of skimming flow is a function of critical depth, chute angle, and step height. Uniform mixture depths that determine the height of chute sidewalls and uniform equivalent clear water depths are described in terms of a roughness Froude number containing unit discharge, chute angle and step height. The spillway length needed to attain uniform flow is expressed as a function of critical depth and chute angle. The flow resistance of stepped spillways is significantly larger than for smooth chutes due to the macro roughness of the steps. The friction factor for uniform aerated flow is of the order of 0.1 for typical gravity dam and embankment dam slopes, whereas the effect of relative roughness is rather small. The energy dissipation characteristics of stepped spillways and the design of training walls are also discussed. The paper aims to focus on significant findings of a research program and develops design guidance to lessen the need for individual physical model studies. A design example is further presented.     

Upwind Conservative Scheme for the Saint Venant Equations

An upwind conservative scheme with a weighted average water-surface-gradient approach is proposed to compute one-dimensional open channel flows. The numerical scheme is based on the control volume method. The intercell flux is computed by the one-sided upwind method. The water surface gradient is evaluated by the weighted average of both upwind and downwind gradients. The scheme is tested with various examples, including dam-break problems in channels with rectangular and triangular cross-sections, hydraulic jump, partial dam-break problem, overtopping flow, a steady flow over bump with hydraulic jump, and a dam-break flood case in a natural river valley. Comparisons between numerical and exact solutions or experimental data demonstrated that the proposed scheme is capable of accurately reproducing various open channel flows, including subcritical, supercritical, and transcritical flows. The scheme is inherently robust, stable, and monotone. The scheme does not require any special treatment, such as artificial viscosity or front tracking technique, to capture steep gradients or discontinuities in the solution.     

Use of Stereoscopy for Dam Break Flow Measurement

This investigation explored the applicability of video stereoscopy for the measurement of unsteady open channel flows. Specifically, the three-dimensional water surface profile and flow velocities associated with scale model dam break events were considered. Stereo images of the unsteady flow event were obtained using three, time-synchronized, video cameras situated above the tank such that, at all times, the area of interest was captured by at least two of the three cameras. To establish a point of reference from image to image, floating plastic tracking particles were placed on the water surface. The three-dimensional coordinates of the particles were then calculated using the camera positions and the locations of the individual plastic particles in the stereo images. Particle velocities were also deduced from the analysis of consecutive images. Based on this preliminary investigation we conclude that video stereoscopy is a promising method for measuring highly dynamic flows.     

无钟炉顶溜槽内颗粒的三维运动

 颗粒在高炉内的运动包括溜槽内运动及空区运动。炉料在空区的运动过程由溜槽末端的速度决定。因此,正确描述颗粒在溜槽内的运动对高炉精准布料十分重要。描述溜槽内颗粒运动的数学模型已有不少,但已有的数学模型是描述颗粒在溜槽内沿直线运动的一维模型。通过对实际高炉布料过程料流轨迹的监测发现,颗粒在溜槽内的运动并非一维运动,而是三维运动。笔者通过对颗粒在溜槽内的受力分析,建立颗粒运动的三维数学模型,准确计算炉料颗粒的落点,分析空区的料流宽度,分析溜槽长度,溜槽转速以及溜槽倾动距对颗粒三维运动的影响。计算结果与实测数据相吻合。     

溜槽形状及倾角对料流运动的影响

 在高炉生产中,装料制度直接决定了炉料在炉内分布状况,精确掌握高炉内装料情况是调节高炉煤气分布,确保高炉达到理想热平衡状态的必要条件。为了准确了解溜槽形状及倾角对料流运动的影响,引入离散单元模型分别对物料经过方溜槽和圆溜槽后的运动情况进行了数值模拟,并根据80%的界定对料流宽度和厚度的选取进行了定义,计算得到了溜槽在不同倾角时料流的宽度和厚度变化,分析变化规律后得到,对长度为2 800 mm的溜槽来说,溜槽倾角不宜小于30°;在相同溜槽倾角条件下,料流经过圆溜槽后的厚度要大于方溜槽;在径向方向上,圆溜槽的物料落点位置稍大于方溜槽。     

Side Outflow from Supercritical Channel Flow

Side flow on a flood plain from a side outlet of the main channel is investigated both theoretically and experimentally for supercritical main flow. The side outlet as a model simulates a failure of a river bank in a prototype. The discharge ratios of the side outflow to that of the main channel flow, the water depth, and the velocity at the side outlet are obtained. The theoretical discharge ratio is a function of the Froude number of the main channel flow. The theoretical spreading angle of the side flow and the theoretical relationship between the velocities and the distance from an upstream point of the side outlet are also compared and predicted. All the theoretical results are found to be in good agreement with the experimental data.     

Shallow Water Wave Propagation in Convectively Accelerating Open-Channel Flow Induced by the Tailwater Effect

Propagation of shallow water waves in viscous open-channel flows that are convectively accelerating or decelerating under gradually varying water surface profiles is theoretically investigated. Issues related to the hydrodynamics of wave propagation in a rectangular open channel are studied: the effect of viscosity in terms of the Manning coefficient; the effect of gravity in terms of the Froude number; wave translation and attenuation characteristics; nonlinearity and wave shock; the role of tailwater in wave propagation; and free surface instability. A uniformly valid nonlinear solution to describe the unsteady gradually varying flow throughout the complete wave propagation domain at and away from the kinematic wave shock as well as near the downstream boundary that exhibits the tailwater effect is derived by employing the matched asymptotic method. Different scenarios of hydraulically spatially varying surface profiles such as M1, M2, and S1 type profiles are discussed. Results from the nonlinear wave analysis are further interpreted and the influence of the tailwater effect is identified. In addition to the nonlinear wave analysis, a linear stability analysis is introduced to quantify the impact from such water surface profiles on the free surface instability. It is shown that the asymptotic flow structure is composed of three distinct regions: an outer region that is driven by gravity and channel resistance; a near wave shock region dominated by the convective inertia, pressure gradient, gravity and channel resistance; and a downstream boundary impact region where the convective inertia, pressure gradient, gravity and channel resistance terms are of importance. The tailwater effect is demonstrated influential to the flow structure, free surface stability, wave transmission mechanism, and hydrostatic pressure gradient in flow.     

Preserving Steady-State in One-Dimensional Finite-Volume Computations of River Flow

When using finite-volume methods and the conservative form of the Saint Venant equations in one-dimensional flow computations, it is important to establish the correct balance between the discretized flux vector and the geometric source terms. Over the last few years various improvements to numerical schemes have been presented to achieve this correct balance, focusing on the capability to simulate water at rest on irregular geometries (C-property). In this paper it is shown that common schemes can lead to energy-violating solutions in the case of steady flow. We present developments based on the Roe TVD finite-volume scheme for one-dimensional Saint Venant equations, which results in a method that not only satisfies the C-property, but also preserves the correct steady flow when stationary boundary conditions are used. We also present a totally irregular channel test case for the verification of the method.     

Conservative Formulation for Natural Open Channels and Finite-Element Implementation

This investigation considers an approximate formulation of the St. Venant equations for natural channels, in which the fully conservative form is developed by revising the boundary pressure term accounting for the topographic variation in the momentum equation. As such a formulation has the potential to enhance the performance of existing models used in practice, the accuracy implications for this approximate formulation are examined using an error analysis for a simplified case. Further, an energy calculation is performed which illustrates that an earlier formulation actually results in energy gain for some cases. A more general formula for the constant water surface elevation that corrects this is introduced and tested. It is found that the refined formulation presented here is accurate for hydraulic jumps, steep surge waves, and flood wave propagation in natural channels. The shock capturing capability of the approximate formulation is illustrated for both steady- and unsteady-flow situations using the finite-element method, for which this approximate equation formulation adapts naturally. Using the characteristic-dissipative-Galerkin finite-element scheme, good results are obtained for the case of a hydraulic jump in a diverging rectangular channel, with the maximum percent error associated with the approximate formulation determined to be only 0.34%. For the case of dam break wave propagation in a converging and diverging rectangular channel, the model performs similarly well, with the maximum error only 0.0064%. Further, the approximate formulation is used to simulate the flood routing in a natural channel, the Oldman River in southern Alberta. The computational results are in good agreement with the observed data. The arrival time of peak flow is 5?h earlier and the magnitude of peak discharge is only 3.8% lower than the observed value.     

Junction and Drop-Shaft Boundary Conditions for Modeling Free-Surface, Pressurized, and Mixed Free-Surface Pressurized Transient Flows

A junction and drop-shaft boundary conditions (BCs) for one-dimensional modeling of transient flows in single-phase conditions (pure liquid) are formulated, implemented and their accuracy are evaluated using two computational fluid dynamics (CFD) models. The BCs are formulated in the case when mixed flows are simulated using two sets of governing equations, the Saint-Venant equations for the free-surface regions and the compressible water hammer equations for the pressurized regions. The proposed BCs handle all possible flow regimes and their combinations. The flow in each pipe can range from free surface to pressurized flow and the water depth at the junction or drop shaft can take on all possible levels. The BCs are applied to the following three cases: (1) a three-way merging flow; (2) a three-way dividing flow; and (3) a drop shaft connected to a single-horizontal pipe subjected to a rapid variation of the water surface level in the drop shaft. The flow regime for the first two cases range from free surface to pressurized flows, while for the third case, the flow regime is pure pressurized flow. For the third case, laboratory results as well as CFD results were used for evaluating its accuracy. The results suggest that the junction and drop-shaft BCs can be used for modeling transient free-surface, pressurized, and mixed flow conditions with good accuracy.     

Direct Integration of the Equation of Gradually Varied Flow

The steady flow in open channels, when the depth of the flow varies gradually with distance, is governed by the classic gradually-varied-flow equation. The solution of this ordinary differential equation allows the tracing of the longitudinal profiles of the water surface of the flow. In this note, a relation obtained by direct integration is proposed for a wide rectangular channel, when Manning’s formula is used for the computation of the energy slope. Then the profiles for subcritical and supercritical flow in a mild and steep channel are presented and a comparison with the Bresse solution, relative to the same channels, is carried out.