Mathematical model of burden distribution for the bell-less top of a blast furnace

Due to the difficulty in measuring the burden trajectory directly in an actual blast furnace （BF）, a mathematical model with Coriolis force and gas drag force considered was developed to predict it. The falling point and width of the burden flow were obtained and analyzed by the model, the velocities of particles at the chute end were compared with and without the existence of Coriolis force, and the effects of chute length and chute torque on the falling point were also discussed. The simulation results are in good agreement with practical measurements with laser beams in a 2500 m3 BF.

ESTABLISHMENT AND APPLICATIONS OF MATHEMATICAL MODELS FOR CONCENTRATION DISTRIBUTIONS IN Mo－Fe－Ni－Co DIFFUSION QUARTERNARY （Ⅰ） Establishment of Mathematical Models

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Improving mathematical model of burden distribution and correcting chute angle to cope with fluctuation of stock line

Accurate evaluations of the burden distribution are of critical importance to stabilize the operation of blast furnace.The mathematical model and discrete element method(DEM)are two attractive methods for predicting burden distribution.Based on DEM,the initial velocities of the pellet,sinter,and coke were calculated,and the velocity attenuations of the above three particles between the burden and the chute were analyzed.The initial velocity and velocity attenuation were applied to a mathematical model for improving the accuracy.Additionally,based on the improved model,a scheme for rectifying the chute angles was proposed to address the fluctuation of the stock line and maintain a stable burden distribution.The validity of the scheme was confirmed via a stable burden distribution under different stock lines.The mathematical model has been successfully applied to evaluate the online burden distribution and cope with the fluctuation of the stock line.

A Mathematical Model of Renal Blood Distribution Coupling TGF,MR and Tubular System

Objective:To investigate the relationship between renal blood distribution and the physiological activities of the kidney. Methods:A mathematical model is developed based on Hagan-Poiseuille law and mass transport, coupling mechanics of myogenic response (MR), tubuloglomerular feedback (TGF) and the tubular system in the renal medulla. The model parameters, including the permeability coefficients, the vascular lumen radius and the solute concentration at the inlet of the tubes, are derived from the experimental results. Simulations of the blood and water flow in the loop of Henel, the collecting duct and vas rectum, are carried out by the model of the tubular system in the renal medulla, based on conservations of water and solutes for transmural transport. Then the tubular model is coupled with MR and TGF mechanics. Results:The results predict the dynamics of renal autoregulation on its blood pressure and flow,and the distributions are 88.5% in the cortex, 10.3% in the medulla, and 1.2% at papilla,respectively. The fluid flow and solute concentrations along the tubules and vasa recta are obtained. Conclusion:The present model could assess renal functions qualitatively and quantitatively and provide a methodological approach for clinical research.

Mathematical model of burden distribution in bell-less top blast furnace

The burden distribution in the shaft of blast furnace is known to affect the gas distribution,heat transfer,and chemical reactions inside the furnace.However,the internal layer structure of burden in the shaft cannot be directly measured.Hence,a mathematical model for evaluating burden profile and layer structure was established.A sensitivity analysis based on the model was implemented to elucidate the effect of some factors on the burden distribution,including the stockline height and the mass of central coke.The results show that the width of funnel zone widens with the increase in stockline height,and the mass percentage of ore to coke in this zone slightly increases.Besides,the mass of central coke shows a significant influence on the width of coke channel,and 2%of batch mass of coke is recommended to implement central coke charging operation.The model has been indirectly verified by the gas temperature in operating blast furnace and successfully applied to online evaluate burden distribution.

An improved model of partition curve based on accumulation normal distribution function

Extensive studies based on partition curve of gravity separation have been investigated. All created models are merely used to simulate density distribution at the same size fraction. However, they cannot be used to predictive distribution of materials depending on compound feature of density and size. According to this situation, an improved model of partition curve based on accumulation normal distribution, which was distinguished from conventional model of accumulation normal distribution for partition curve, was proposed in this paper. It could simulate density distribution at different size fractions by using the density-size compound index and conflating the partition curves at different size fractions as one partition curve. The feasibility of three compound indexes, including mass index, settlement index and transformation index, were investigated. Specific forms of the improved model were also proposed. It is found that transformation index leads to the best fitting results, while the fitting error is only 1.75 according to the fitting partition curve.

Mathematical models and expert system for grate-kiln process of iron ore oxide pellet production(Part Ⅰ):Mathematical models of grate process

Grate process is an important step in grate-kiln pellet production.However,as a relatively closed system,the process on grate is inaccessible to direct detection,therefore,it is hard to control.As a result,mathematical models of temperature distribution,moisture distribution and oxidation degree distribution in pellet bed,with good universality,computation speed and calculation accuracy,are presented based on analysis of heat transfer and physical-chemical reactions during grate process.And real-time visualization of temperature,moisture and oxidation degree distribution in pellet bed during grate process is realized.Model validation is displayed,and the similarity of 91% is proved.The results can reveal real time status on grate,and provide a solid foundation for the subsequent study of artificial intelligence control system of pellet production.

Mathematical model of flow characteristic in multi-strand continuous casting tundishes

In this paper, the subject of mathematical model is a series of math expressions, which is used to calculate different regions＇ volume fraction and analyze flow characterization in multi-strand tundish. But research about mathematical model for multi-strand tundish is few, and so far, there has been no acknowledged math model for multi- strand tundish to describe its flow characteristic. If Sahai＇s model, which is originally proposed for the case of single-strand tundish （proposed in reference, and this model is widely used in the world）, is applied to describe flow feature in multi-strand tundish, the calculation results would be unreasonable. Based on the data of watermodel experiment results, the sum of each strand＇s dead region＇s volume fraction is bigger than 100%, and this obviously doesn＇T agree with reality; and the value of dead region＇s volume fraction is calculated to be minus according to mathematical simulation results data in another case. What＇s more, Sahai＇s model does not propose the standard of plotting the RTD-curve, and this makes scholars around the world can＇t achieve consensus of views about plotting RTD-curve. And the model doesn＇t consider the bypass flow and can＇t calculate its volume fraction, but bypass flow is critical to tundish metallurgy. And through Sahai＇s model, the calculation result of plug flow region＇s volume fraction is also not reasonable, because the model doesn＇t well describe the essence of plug flow. So these suggest that it is not reliable to apply Sahai＇s single-strand tundish model to multi-strand tundish case. Then a new model is attempted to propose in this paper for your discussion. In the new model, the standard of plotting RTD curve is definitely proposed, and relative calculation method is also proposed; and the feature of dead region is carefully studied and the model proposes a new method to calculate its volume fraction, and the calculation formula about its volume fraction can be adjustable according the actual demand; what＇s more, the new model considers the bypass flow and proposes a method to calculate its volume fraction for the first time, and then volume fraction of plug flow region, backmix flow region, dead region and bypass flow can be calculated and obtained at the same time; and this new model can better capture the deviation of reality flow pattern from ideal plug flow pattern, and reflects the feature of plug flow.

Droplets diameter distribution using maximum entropy formulation combined with a new energy-based sub-model

The maximum entropy principle(MEP) is one of the first methods which have been used to predict droplet size and velocity distributions of liquid sprays. This method needs a mean droplets diameter as an input to predict the droplet size distribution. This paper presents a new sub-model based on the deterministic aspects of liquid atomization process independent of the experimental data to provide the mean droplets diameter for using in the maximum entropy formulation(MEF). For this purpose, a theoretical model based on the approach of energy conservation law entitled energy-based model(EBM) is presented. Based on this approach, atomization occurs due to the kinetic energy loss. Prediction of the combined model(MEF/EBM) is in good agreement with the available experimental data. The energy-based model can be used as a fast and reliable enough model to obtain a good estimation of the mean droplets diameter of a spray and the combined model(MEF/EBM) can be used to well predict the droplet size distribution at the primary breakup.

DPM-CFD simulation of powder motion in the burden distribution process of COREX shaft furnace

Single off-gas outlet devised by one-step COREX shaft furnace will ultimately lead gas distribution to segregate,furthermore the distribution of powder on charge level is non-uniformity.DPM-CFD model was employed to simulate the pellet minus sieve powder motion in the burden distribution process,in order to quantitative description the non-uniformity distribution.The results showed that,the non-uniformity distribution is increasing with the melting rate increased.The powder segregates to the fourth quadrant where off-gas outlet lies is 2.4 or 2.5 fold of any other quadrant,while the melting rate is 130 t/h or 180 t/h.The best method to resolved the problem adds an symmetry off-gas outlet.

The monitoring of burden distribution uniformity and even sintering technology

After expanding the capacity by widening the trolley of the No. 3 sintering machine, severe uneven sintering occurred in the trolley＇ s lateral distribution, which affected the output and quality of sinter. In this study, the quantitative evaluation indices of the burden uniform distribution in the width direction of the sintering machine is introduced for the first time. By measuring the temperature of discharged gas, a plane temperature field is constructed. Through analyzing the temperature field and the burden layer＇ s differential thermal equilibrium, a mathematical model for evaluating the indices, which is an online reflection of the degree of uniform distribution, is built. Following the improvements in burden distribution equipment ,the optimization of the ignition system and the dynamic adjustment of the process ,the problem of uneven sintering in lateral distribution has been solved, and the quality and the yield of sinter have been improved.

Mathematical Modelling in Placing of Fresh Concrete

The main problem in working with fresh concrete is the aggregate segregation during filling of formwork. The segregation is strongly related to W/C (Water/Cement) ratio. The fresh concrete is usually considered as a Non-Newtonian fluid since it is a mixture of aggregate, cement and water. The flow behavior of the fresh concrete to W/C ratio plays a crucial role in the quality of the high performance concretes by affecting the flow behavior of the fresh concrete. The aggregates in the fresh concrete usually cause segregation in the final product depending on the flow condition. In this study, the mechanism of segregation in such systems was theoretically investigated. The mould filling of fresh concrete was numerically investigated and aggregates were considered as Lagrangian particles and segregation was identified from trajectories of such particles. It was found that the aggregates were trapped at the dead zones leading to segregation in the system. The particle size and geometry of the mould was found to have significantly affect the segregation in the system.

Variation of singularity of earthquake-size distribution with respect to tectonic regime

Frequency-size relation of earthquakes in a region can be approximated by the Gutenberg-Richter law(GR). This power-law model involves two parameters: a-value measuring seismic activity or earthquake productivity, and b-value describing the relation between frequencies of small and large earthquakes.The spatial and temporal variations of these two parameters, especially the b-value, have been substantially investigated. For example, it has been shown that b-value depends inversely on differential stress. The b-value has also been utilized as earthquake precursor in large earthquake prediction.However, the physical meaning and properties of b-value including its value range still remain as an open fundamental question. We explore the property of b-value from frequency-size GR model in a new form which relates average energy release and probability of large earthquakes. Based on this new form of GR relation the b-value can be related to the singularity index(1-2/3 b) of fractal energy-probability power-law model. This model as applied to the global database of earthquakes with size M ≥ 5 from 1964 to 2015 indicates a systematic increase of singularity from earthquakes occurring on mid-ocean ridges, to those in subduction zones and in collision zones.

Simulation of water temperature distribution in Fenhe Reservoir

In order to evaluate the need of controlling the temperature of water discharged from the Fenhe Reservoir, the reservoir water temperature distribution was examined. A three-dimensional mathematical model was used to simulate the in-plane and vertical distribution of water temperature. The parameters of the model were calibrated with field data of the temperature distribution in the Fenhe Reservoir. The simulated temperature of discharged water is consistent with the measured data. The difference in temperature between the discharged water and the natural river channel is less than 3 ℃ under the current operating conditions. This will not significantly impact the environment of downstream areas.

Simulation and experiment of six-bed PSA process for air separation with rotating distribution valve

In this work,a six-bed pressure swing adsorption(PSA)process was investigated to produce medical oxygen from air,which uses the combination of six-way rotating distribution valve and PSA and has the main advantage of effectively saving space compared to the traditional two-bed or four-bed PSA process and can obtain greater productivity.The mathematical model of adsorption beds was developed based on the separation mechanism and the interaction among different equipment.Moreover,a pilot-scale device has been constructed to verify the accuracy of mathematical model by experiment.The oxygen product conformed to the medical standard(>93%(vol))with a recovery of over 57%.Some related parameters were also discussed in detail,such as step time,ratio of length to the diameter,flow rate of product.

Research on Location-Routing Problem with Empirical Analysis for Regional Logistics Distribution

The location of the distribution facilities and the routing of the vehicles from these facilities are interdependent in many distribution systems. Such a concept recognizes the interdependence;attempts to integrate these two decisions have been limited. Multi-objective location-routing problem (MLRP) is combined with the facility location and the vehicle routing decision and satisfied the different objectives. Due to the problem complexity, simultaneous solution methods are limited, which are given in different objectives with conflicts in functions satisfied. Two kinds of optimal mathematical models are proposed for the solution of MLRP. Three methods have been emphatically developed for MLRP. MGA architecture makes it possible to search the solution space efficiently, which provides a path for searching the solution with two-objective LRP. At last the practical proof is given by random analysis for regional distribution with nine cities.

Study on the Transportation Problem of Petrol Secondary Distribution with Considering Shortage Cost

Petrol is a kind of strategic natural resources. Provide legitimate transportation plans for the petrol secondary distribution are the key links to guarantee the petrol provision. If the total supply is insufficient, some petrol stations can’t avoid shortage because their demands could not be met. So the shortage cost will appear. This paper studies the problem of how to arrange the transportation plan in order to minimize the total cost when the total volume of supply is insufficient. Given the storage volume, the sales rate and the unit shortage cost of every petrol station, considering the full loading constraints of the compartment vehicle, a mixed integer programming model for minimizing the total cost of petrol secondary distribution is established. A Lingo program is compiled for solving the model. Finally, simulation on an example has been done and a reasonable transportation plan is obtained. The model and algorithm in this paper can provide a theoretical basis for dispatching department to make transportation plan.

A fast commonly-used algorithm of P-III distribution curve and its application

Based on theoretical analysis and studying other methods, P-III curve is transformed into an incomplete G function by means of mathematical expression transformation, thus the mathematical model of the fast commonly-used algorithm is drawn out. Algorithm comparison and practices demonstrate that the mathematical model has an easy algorithm, agile resolution process, very good commonality, faster convergence rate and better calculation accuracy, and can be applied to other respects.