scholarly journals Validation of friction factor predictions in vertical slurry flows with coarse particles

2020 ◽  
Vol 68 (2) ◽  
pp. 119-127 ◽  
Author(s):  
Artur Bartosik
Keyword(s):  
Mathematical Model ◽  
Reynolds Number ◽  
Friction Factor ◽  
Particle Diameter ◽  
Solid Particles ◽  
Coarse Particles ◽  
Carrier Liquid ◽  
Different Types ◽  
Slurry Flows ◽  
The Mathematical Model

AbstractThe paper presents validation of a mathematical model describing the friction factor by comparing the predicted and measured results in a broad range of solid concentrations and mean particle diameters. Three different types of solids, surrounded by water as a carrier liquid, namely Canasphere, PVC, and Sand were used with solids density from 1045 to 2650 kg/m3, and in the range of solid concentrations by volume from 0.10 to 0.45. All solid particles were narrowly sized with mean particle diameters between 1.5 and 3.4 mm. It is presented that the model predicts the friction factor fairly well. The paper demonstrates that solid particle diameter plays a crucial role for the friction factor in a vertical slurry flow with coarse solid particles. The mathematical model is discussed in reference to damping of turbulence in such flows. As the friction factor is below the friction for water it is concluded that it is possible that the effect of damping of turbulence is included in the KB function, which depends on the Reynolds number.

An enhanced composting process with bioaugmentation: Mathematical modelling and process optimization

2021 ◽  
pp. 0734242X2110337
Author(s):  
Tea Sokač ◽  
Anita Šalić ◽  
Dajana Kučić Grgić ◽  
Monika Šabić Runjavec ◽  
Marijana Vidaković ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Simulation ◽  
Process Conditions ◽  
Air Flow Rate ◽  
Optimal Process ◽  
Composting Process ◽  
Different Types ◽  
Adiabatic Reactor ◽  
The Mathematical Model ◽  
Good Agreement

In this paper, two different types of biowaste composting processes were carried out – composting without and with bioaugmentation. All experiments were performed in an adiabatic reactor for 14 days. Composting enhanced with bioaugmentation was the better choice because the thermophilic phase was achieved earlier, making the composting time shorter. Additionally, a higher conversion of substrate (amount of substrate consumed) was also noticed in the process enhanced by bioaugmentation. A mathematical model was developed and process parameters were estimated in order to optimize the composting process. Based on good agreement between experimental data and the mathematical model simulation results, a three-level-four-factor Box-Behnken experimental design was employed to define the optimal process conditions for further studies. It was found that the air flow rate and the mass fraction of the substrate have the most significant effect on the composting process. An improvement of the composting process was achieved after altering the mentioned variables, resulting in shorter composting time and higher conversion of the substrate.

scholarly journals Numerical investigation on the solid particle erosion in elbow with water–hydrate–solid flow

2019 ◽  
Vol 103 (1) ◽  
pp. 003685041989724 ◽  
Author(s):  
Liang Zhang ◽  
JiaWei Zhou ◽  
Bo Zhang ◽  
Wei Gong
Keyword(s):  
Reynolds Number ◽  
Flow Velocity ◽  
Erosion Rate ◽  
Particle Diameter ◽  
Stokes Number ◽  
Solid Particles ◽  
Curvature Radius ◽  
Premature Failure ◽  
Solid Flow ◽  
Erosion Zone

Erosion in pipeline caused by solid particles, which may lead to premature failure of the pipe system, is regarded as one of the most important concerns in the field of oil and gas. Therefore, the Euler–Lagrange, erosion model, and discrete phase model are applied for the purpose of simulating the erosion of water–hydrate–solid flow in submarine hydrate transportation pipeline. In this article, the flow and erosion characteristics are well verified on the basis of experiments. Moreover, analysis is conducted to have a good understanding of the effects of hydrate volume, mean curvature radius/pipe diameter ( R/ D) rate, flow velocity, and particle diameter on elbow erosion. It is finally obtained that the hydrate volume directly affects the Reynolds number through viscosity and the trend of the Reynolds number is consistent with the trend of erosion rate. Taking into account different R/ D rates, the same Stokes number reflects different dynamic transforms of the maximum erosion zone. However, the outmost wall (zone D) will be the final erosion zone when the value of the Stokes number increases to a certain degree. In addition, the erosion rate increases sharply along with the increase of flow velocity and particle diameter. The effect of flow velocity on the erosion zone can be ignored in comparison with the particle diameter. Moreover, it is observed that flow velocity is deemed as the most sensitive factor on erosion rate among these factors employed in the orthogonal experiment.

Rim Sealing of Rotor-Stator Wheelspaces in the Absence of External Flow

1991 ◽  
Author(s):  
J. W. Chew ◽  
S. Dadkhah ◽  
A. B. Turner
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Reynolds Numbers ◽  
External Flow ◽  
Rotating Disc ◽  
Different Types ◽  
The Mathematical Model

Sealing of the cavity formed between a rotating disc and a stator in the absence of a forced external flow is considered. In these circumstances the pumping action of the rotating disc may draw fluid into the cavity through the rim seal. Minimum cavity throughflow rates required to prevent such ingress are estimated experimentally and from a mathematical model. The results are compared with other workers’ measurements. Measurements for three different types of rim seal are reported for a range of seal clearances and for rotational Reynolds numbers up to 3 × 106. The mathematical model is found to correlate the experimental data reasonably well.

Chaotic Phenomena Induced by the Fast Plastic Deformation of Metals During Cutting

2005 ◽  
Vol 73 (2) ◽  
pp. 240-245 ◽  
Author(s):  
Zoltan Palmai
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Shear Stress ◽  
General Structure ◽  
Equation System ◽  
Qualitative Description ◽  
Balance Equations ◽  
Different Types ◽  
Energy Equations ◽  
The Mathematical Model

In the present study the examination of chip formation is focused on the primary shear zone, which is divided into two layers, and the variation of shear stress and temperature in time are given by two mechanical balance equations and three energy equations. All the five evolution differential equations are autonomous and nonlinear. The material characteristics are determined by an exponential constitutive equation. The mathematical model is suitable for the qualitative description of different types of chips, such as continuous chips and periodic or aperiodic shear localized chips, which is demonstrated by the general structure and typical solutions of the equation system.

Experimental Investigation of Convective Melting of Granular Packed Bed Under Microgravity

2002 ◽  
Vol 124 (3) ◽  
pp. 516-524 ◽  
Author(s):  
J. Jiang ◽  
Y. Hao ◽  
Y.-X. Tao
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Froude Number ◽  
Average Particle Size ◽  
Particle Diameter ◽  
Packed Bed ◽  
Melting Rate ◽  
Solid Particles ◽  
Average Particle ◽  
Stefan Number

To improve the understanding of convective melting of packed solid particles in a fluid, an experimental investigation is conducted to study the melting characteristics of a packed bed by unmasking the buoyancy forces due to the density difference between the melt and solid particles. A close-loop apparatus, named the particle-melting-in-flow (PMF) module, is designed to allow a steady-state liquid flow at a specified temperature. The module is installed onboard NASA’s KC-135 reduced gravity aircraft using ice particles of desired sizes and water as the test media. Experimentally determined melting rates are presented as a function of upstream flow velocity, temperature and initial average particle size of the packed bed. It is found that the melting rate is influenced mainly by the ratio of the Reynolds number (Re, based on the initial particle diameter) to the square of the Froude number (Fr), and the Stefan number (Ste). In general, the dimensionless melting rate decreases as Re/Fr2 increases and increases as Ste increases. With the absence of gravity, i.e., as the Froude number approaches infinity, a maximum melting rate can be achieved. The increase in the melting rate proportional to the Stefan number also becomes more pronounced under the zero gravity condition. The trend of average and local Nusselt number of the melting packed bed under microgravity, as a function of Reynolds number and Prandtl number, is discussed and compared with the case of nonmelting packed bed.

scholarly journals DEVELOPMENT OF A MATHEMATICAL MODEL FOR THE RESEARCH OF THE DYNAMICS OF VIBRATION MILL WITH TWO DRIVES FOR BULK MATERIALS FINE GRINDING

2021 ◽  
pp. 89-99
Author(s):  
Volodymyr Topilnytskyy ◽  
Dariya Rebot
Keyword(s):  
Mathematical Model ◽  
Optimal Designs ◽  
High Tech ◽  
Bulk Materials ◽  
Fine Grinding ◽  
Different Types ◽  
Parameterized Model ◽  
The Mathematical Model ◽  
Universal Equipment ◽  
Vibration Mill

Reducing by grinding the size of various materials as raw materials for its further use is an urgent applied task. The requirements for the final product obtained by fine grinding are its homogeneity in shape and size of individual parts. It is necessary to reduce the time of the grinding operation, reduce energy consumption to obtain a unit of product of the required quality. One way to solve the problem is to use high-tech universal equipment, namely mills for fine grinding of materials. One way to solve the given problem is to use high-tech universal equipment, namely mills for fine grinding of materials. Their optimal design, construction, manufacture and operation are ensured by studying their dynamics at the stage of their development. In particular, such a study of the dynamics can be carried out on the basis of previously created mathematical models of these mills. The use of computer technology and appropriate mathematical CAD systems will speed up and optimize the process of studying the dynamics of the corresponding mill of fine grinding of materials. The purpose of the research is to build a mathematical nonlinear parameterized model of vibrating mill with two drives for bulk materials fine grinding for further study on its basis the dynamics of the mill with the development of optimal designs for mills with similar structure and the principle of operation and selection of optimal modes of operation. The mathematical model is presented as a system of expressions describing the of the mill points motion, which will include in the form of symbolic symbols all its parameters (kinematic, geometric, dynamic, force). This model is constructed using the Lagrange equation of the second kind and asymptotic methods of nonlinear mechanics. The mathematical model for studying of the dynamics of vibration mill with two drives for bulk materials fine grinding is nonlinear and universal. The non linearity of the model makes it possible to adequately determine of the above parameters influence on the amplitude of oscillations of the mill working chamber as the main factor in the intensity in the technological process of the fine grinding bulk materials fine grinding. The possibility of a wide range of changes in the parameters of the mill in the obtained models makes it universal based on the possibility of application for the study of dynamic processes in vibrating mills of different types with two or one drive which are different by shape, size, location of the suspension and more. This model can also be used to develop optimal designs for vibrating mills for different industries, which will be used to grind different types of materials in different volumes and productivity.

NUMERICAL SIMULATION OF THE PROPAGATION OF A GAS SHOCK WAVE IN ELECTRICALLY CHARGED AND NEUTRAL GAS SUSPENSION IN A FLAT CHANNEL

2020 ◽  
Vol 2 ◽  
pp. 9-18
Author(s):  
D.A. TUKMAKOV
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Shock Wave ◽  
Solid Particles ◽  
Grid Function ◽  
Heat Conducting ◽  
Gas Suspension ◽  
Carrier Medium ◽  
The Mathematical Model ◽  
Electrically Charged

In this paper, we consider the propagation of a shock wave from a pure gas into a heterogeneous mixture consisting of solid particles suspended in a gas and having an electric charge. The applied mathematical model takes into account the speed and thermal interaction of the carrier and dispersed components of the mixture. The force interaction of particles and gas was described by the Stokes force. The carrier medium was described as a viscous compressible heat–conducting gas. The equations of the mathematical model were solved by the explicit finite–difference method of the second order of accuracy, using the non–linear correction of the grid function. The system of equations of the mathematical model was supplemented by boundary and initial conditions for the desired functions. As a result of numerical simulation, it was found that in an electrically charged gas suspension there is a difference in gas pressure and velocity, “average density” and velocity of the dispersed component, compared with similar values in a gas suspension with an electrically neutral dispersed component. The revealed differences in the dynamics of neutral and electrically charged dusty media can be explained by the fact that the dispersed component of an electrically charged gas suspension is affected by both aerodynamic drag forces and Coulomb forces. Due to interfacial interaction, the dynamics of the carrier medium changes.

The Estimation of the Thermal Properties of Refractory Materials According to the Temperatures Acceleration Curve at the Blast Furnace Blowing-In

2015 ◽  
Vol 1095 ◽  
pp. 476-482 ◽  
Author(s):  
A.N. Dmitriev ◽  
Maxim O. Zolotykh ◽  
Yury A. Chesnokov ◽  
Oleg Yu. Ivanov ◽  
Galina Yu. Vitkina
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Blast Furnace ◽  
Thermal Properties ◽  
Thermal Conductivity Coefficient ◽  
Refractory Materials ◽  
Different Types ◽  
Definition Of ◽  
The Mathematical Model

In a laying of a hearth it is usually used to ten different types of the flameproof materials. The characteristics of materials declared by the manufacturer can differ from the actual. For creation of the mathematical model [1, 2] temperatures distributions in a laying of the concrete furnace it is necessary to know thermal conductivity of materials of the specific parties used at construction of the furnace. Definition of the thermal conductivity coefficient allows adapt mathematical model for specific conditions of use. The technique of determination of thermal properties of refractory materials on the temperatures acceleration curve at blowing-in of the blast furnace is described.

scholarly journals Study on Rock-Breaking Depth and Damage Area under Particle Jet Impact

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Fushen Ren ◽  
Tiancheng Fang ◽  
Xiaoze Cheng
Keyword(s):  
Mathematical Model ◽  
Impact Velocity ◽  
Particle Diameter ◽  
Rock Breaking ◽  
Water Jet ◽  
Experimental Results ◽  
Damage Area ◽  
Jet Impact ◽  
Mathematical Calculation ◽  
The Mathematical Model

Particle jet impact drilling technology is an efficient method which mainly uses high-velocity particles to break rock. As the important criterion for evaluating rock-breaking effect, rock-breaking depth and damage area were studied in this paper. Firstly, a particle jet impact rock-breaking test device was developed, and laboratory experiments have been carried out. Then, based on the spherical cavity expansion theory, the mathematical model of rock-breaking depth and damage area under particle jet impact was established. Afterward, the effect of water-jet impact velocity, impact angle, and particle diameter on rock-breaking depth and damage area was analyzed by comparing experimental results and mathematical calculation. The results show that rock-breaking depth and damage area would increase with increase of water-jet impact velocity and decrease slightly with increase of particle diameter. And the combination of 8° and 20° is recommended for nozzle layout. The experimental results and mathematical calculation are basically consistent, which could verify the correctness of the mathematical model. The study has significance for development and application of particle jet impact rock-breaking technology and perfection of theoretical research.

Research on the Mathematical Model of the Plastic Profile Cooling Analysis

2012 ◽  
Vol 164 ◽  
pp. 214-217
Author(s):  
Xiang Shan Huang ◽  
Li Dan Chen
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Thermal Analysis ◽  
Reynolds Number ◽  
Theoretical Basis ◽  
Flow State ◽  
Function Blocks ◽  
Plastic Profile ◽  
The Mathematical Model ◽  
Fluid Parameters

According to the assumption of the plastic profile cooling analysis, Prandtl number Pr and Reynolds number Re can be derived from the fluid parameters. The paper judge and analyze the movement of flow state, further study the formula of heat transfer coefficient α, thermal analysis and boundary conditions in Reynolds number Re. The experimental results show mathematical model, which provides a theoretical basis for the cooling and forming of function blocks, it has certain guiding significance.

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