Mach Wave and Acoustical Wave Structure in Nonequilibrium Gas-Particle Flows

2021 ◽  
Author(s):  
Joseph T. C. Liu
Keyword(s):  
Pressure Coefficient ◽  
Relaxation Times ◽  
Simple Wave ◽  
Wave Structure ◽  
Particle Flow ◽  
Mach Wave ◽  
Flow Parameters ◽  
Particle Flows ◽  
Wall Boundary Conditions ◽  
Wave Problems

In this Element, the gas-particle flow problem is formulated with momentum and thermal slip that introduces two relaxation times. Starting from acoustical propagation in a medium in equilibrium, the relaxation-wave equation in airfoil coordinates is derived though a Galilean transformation for uniform flow. Steady planar small perturbation supersonic flow is studied in detail according to Whitham's higher-order waves. The signals owing to wall boundary conditions are damped along the frozen-Mach wave, and are both damped and diffusive along an effective-intermediate Mach wave and diffusive along the equilibrium Mach wave where the bulk of the disturbance propagates. The surface pressure coefficient is obtained exactly for small-disturbance theory, but it is considerably simplified for the small particle-to-gas mass loading approximation, equivalent to a simple-wave approximation. Other relaxation-wave problems are discussed. Martian dust-storm properties in terms of gas-particle flow parameters are estimated.

Research on Particle Flow Erosion Precision Electroforming Technology

2013 ◽  
Vol 771 ◽  
pp. 75-81
Author(s):  
Nai Chang Dai ◽  
Sheng Dong Yu
Keyword(s):  
Mechanical Property ◽  
Glass Bead ◽  
Cathode Surface ◽  
Special Functions ◽  
Particle Flow ◽  
Metallic Nickel ◽  
Microscopic Structure ◽  
Huge Amount ◽  
Deposit Surface ◽  
Particle Flows

t is possible to get electroforming deposit with numerous special functions by adoption of traditional electroforming technique, but in which there are defects such as uneven electroforming deposit and unstable performance, etc. In order to enhance the quality and speed of electroforming deposit, this article has proposed the particle flow erosion precision electroforming technology, particle flows such as huge amount of micro glass bead is used in the process of electro-deposit for erosion of electroforming deposit surface, so that micro glass beads continuously abrade and impact cathode surface. As indicated in electroforming test of metallic nickel, in comparison with traditional electroforming technology, particle flow erosion precision electroforming technology can effectively change the microscopic structure of electroforming deposit, refine grain and realize evener distribution of grains, so as to reduce the diffracted intensity of all crystal faces and enhance mechanical property of electroforming deposit.

scholarly journals Numerical Analysis of the Mud Inflow Model of Fractured Rock Mass Based on Particle Flow

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Yongjian Pan ◽  
Huajun Wang ◽  
Yanlin Zhao ◽  
Qiang Liu ◽  
Shilin Luo
Keyword(s):  
Rock Mass ◽  
Pressure Gradient ◽  
Flow Direction ◽  
Fractured Rock ◽  
Water Pressure ◽  
Water Inrush ◽  
Quadratic Function ◽  
Particle Flow ◽  
Fractured Rock Mass ◽  
Particle Flows

Water inrush and mud outburst are one of the crucial engineering disasters commonly encountered during the construction of many railways and tunnels in karst areas. In this paper, based on fluid dynamics theory and discrete element method, we established a fractured rock mass mud inflow model using particle flow PFC3D numerical software, simulated the whole process of fractured rock mass mud inflow, and discussed the effect of particle size and flow velocity on the change of pressure gradient. The numerical simulation results show that the movement of particles at the corner of the wall when the water pressure is first applied occurs similar to the vortex phenomenon, with the running time increases, the flow direction of particles changes, the vortex phenomenon disappears, and the flow direction of particles at the corner points to the fracture; in the initial stage, the slope of the particle flows rate curves increases in time, and the quadratic function is used for fitting. After the percolation velocity of particles reaches stability, the slope of the curve remains constant, and the primary function is used for fitting; the particle flow rate and pressure gradient are influenced by a variety of factors, and they approximately satisfy the exponential function of an “S” curve.

Particle Flow Simulation for Large Diameter Squat Silos Eccentric Discharge

2011 ◽  
Vol 99-100 ◽  
pp. 1106-1112
Author(s):  
Fang Yuan ◽  
Cheng Ying Dong ◽  
Yao Hui Song ◽  
Song Song Zhang
Keyword(s):  
Lateral Pressure ◽  
Large Diameter ◽  
Pressure Coefficient ◽  
Side Wall ◽  
Operating Conditions ◽  
Particle Flow ◽  
Scale Model ◽  
Maximum Pressure ◽  
Centrifuge Model Test ◽  
Eccentric Distance

The scale model of squat silo in large diameter was established with Particle Flow Code (PFC3D) in this paper. This scale model uses the centrifuge model test principle for reference and provides the field of gravity in the calculation of archetypal squat silo. When the silo filled with granules reaches static equilibrium state, record the static lateral pressure measurement values of its each column measured wall, followed by eccentric discharge simulation in different operating conditions, while monitoring the changes of Measured walls in five different directions during discharging granules, in order to analyze the influence of eccentric discharge on the lateral pressure of large diameter squat silos wall. Thus the following conclusion can be obtained: （1）Overpressure coefficient is close extensive between eccentric distance and far extensive between physical reference of storing material.（2）Under the same condition, the overpressure coefficient of same side wall will be minished with the increasing of discharge port.（3）For the same silo model, maximum pressure coefficient is related with eccentric distance, discharge port size and the position with the wall measured, and its value is greater than the calculated value of standard, because the overpressure coefficient calculation formula is only related with silo diameter and eccentric distance, and this is worth further discussion.

An analytical and experimental investigation of the trajectories of particles entrained by the gas flow in nozzles

1969 ◽  
Vol 35 (3) ◽  
pp. 549-559 ◽  
Author(s):  
John H. Neilson ◽  
Alastair Gilchrist
Keyword(s):  
Gas Flow ◽  
Particle Trajectory ◽  
Approximate Analytical Solution ◽  
The Other ◽  
Particle Flow ◽  
Conical Nozzle ◽  
Small Particles ◽  
Erosion Damage ◽  
Particle Flows ◽  
The Moment

Among the parameters which determine the erosion damage sustained by the walls of a nozzle in which a mixture of gas and particles is flowing, is the angle between the direction of the particle flow and the wall surface at the moment of impact. In this work an approximate analytical solution is made for a number of gas particle flows to determine broadly the features on which particle trajectory depends and some experimental results are given which confirm the theoretical computations. It is shown that the divergent region of a conical nozzle is unlikely to suffer a severe particle attack but that for parallel flow convergent-divergent nozzles the convex region near the exit may be affected. The choke, on the other hand, is most susceptible to particle attack even by fairly small particles. It may be said, in general, that any particle which enters the choke section with a velocity which, in the absence of effects from the gas would allow the particle to strike the choke wall, will in fact hit the wall at some point along the length of the choke.

scholarly journals The Development and Application of a Kinetic Theory for Modelling Dispersed Particle Flows

2021 ◽  
Author(s):  
Mike Reeks
Keyword(s):  
Kinetic Theory ◽  
Boundary Layers ◽  
Kinetic Equations ◽  
Turbulent Boundary Layers ◽  
Collision Kernel ◽  
Gravitational Settling ◽  
Particle Pair ◽  
Particle Flows ◽  
Wall Boundary Conditions ◽  
Near Wall

Abstract This Freeman Scholar article reviews the formulation and application of a kinetic theory for modeling the transport and dispersion of small particles in turbulent gas-flows, highlighting the insights and understanding it has provided and some of the long standing problems in the modeling of dispersed flows it has resolved. The theory has been developed and refined by numerous authors and now forms a rational basis for modeling complex particle laden flows. The formalism and methodology of this approach are discussed and the choice of closure of the kinetic equations involved which ensures realizability and well posedness with exact closure for Gaussian carrier flow fields. The historical development is presented and how single particle kinetic equations resolve the problem of closure of the transport equations for particle mass, momentum and kinetic energy /stress (the so called continuum equations) and the treatment of the dispersed phase as a fluid. The mass fluxes associated with the turbulent aerodynamic driving forces and interfacial stresses are shown to be both dispersive and convective in inhomogeneous turbulence with implications for the build up of particles concentration in near wall turbulent boundary layers and particle pair concentration at small separation. It is shown how this approach deals with the natural wall boundary conditions for a flowing particle suspension and examples are given of partially absorbing surfaces with particle scattering, and gravitational settling; how this approach has revealed the existence of contra gradient diffusion in a developing shear flow and the influence of the turbulence on gravitational settling (the Maxey effect). Particular consideration is given to the general problem of particle transport and deposition in turbulent boundary layers and near wall behavior including particle resuspension. Finally the application of a particle pair formulation for both monodisperse and bidisperse particle flows is reviewed where the differences between the two are compared through the influence of collisions on the particle continuum equations and on the particle collision kernel for the clustering of particles and the degree of random uncorrelated motion (RUM) at the small scales of the turbulence. The inclusion of bidisperse particle suspensions implies the application to polydisperse flows and the evolution of particle size distribution.

scholarly journals Thermo-Fluid Mechanics of gas-Solid Particle Flows over horizontal Flat Plate

2021 ◽  
Vol 33 (1) ◽  
pp. 1-8
Author(s):  
K. SREERAM REDDY ◽  
◽  
Ch. MAHESH ◽  
Keyword(s):  
Mathematical Model ◽  
Flat Plate ◽  
Solid Particle ◽  
Particle Concentration ◽  
Relaxation Times ◽  
Temperature Profiles ◽  
Clear Fluid ◽  
Similarity Transformations ◽  
Particle Flows ◽  
Mixture Velocity

Mathematical model has been developed to protect fluid and solid particle homogeneous mixture velocity concentration and temperature for a heated horizontal flat plate. Conversation equation based on Eulerian scale are approximated for small relaxation times through stream function and similarity transformations. Parametric database generated through computer program for arbitrary constants on comparison with clear fluid reveals the particle concentration has pronounced effect on velocity and temperature profiles.

scholarly journals METHOD FOR SOLVING THE PROBLEM OF FREE SPREADING OF A TURBULENT POTENTIAL FLOW BEHIND A PRESSURE-FREE PIPE

2020 ◽  
Vol 8 (3) ◽  
pp. 82-86
Author(s):  
Viktor Kochanenko ◽  
Maria Aleksandrova
Keyword(s):  
Turbulent Flow ◽  
Potential Flow ◽  
Radial Flow ◽  
Simple Wave ◽  
Radial Expansion ◽  
Two Dimensional ◽  
Engineering Construction ◽  
General Flow ◽  
Flow Parameters ◽  
First Time

The paper substantiates the design scheme and General formulation of the method for solving the problem of coupling various flows necessary in the practice of hydraulic engineering construction of GTS. In the scheme given in the article, when solving the problem of free spreading of a turbulent two-dimensional water flow with a uniform flow, a simple wave borders, and not a General flow, such as a radial flow. The analysis of the three characteristic zones of the flow. It is proved that a turbulent flow under free spreading transforms into a radial one, and the elements of the radial expansion of the flow are determined. The equations for determining the geometric shape and flow parameters for all three sections of the flow with its free spreading are obtained. The research results in this paper are obtained for the first time and complete the research started in the works of other authors.

A Numerical Method for Gas-Particle Flows With Accumulation

2006 ◽  
Author(s):  
Xiang Zhao ◽  
Sijun Zhang
Keyword(s):  
Mathematical Model ◽  
Numerical Modelling ◽  
Numerical Method ◽  
Fluid Model ◽  
Particle Flow ◽  
Flow Conditions ◽  
Accumulation Zone ◽  
Particle Flows ◽  
Two Fluid Model ◽  
Two Fluid

A mathematical model is proposed to describe the gas-particle flow in a bed packed with particles. The model is in essence the same as the two fluid model developed on the basis of the space-averaged theorem but extended to consider the interactions among the gas, powder and packed particles and the static and dynamic holdups of powder. In particular, a method is proposed to determine the boundary between powder mobile and non-mobile zones, i.e. the profile of powder accumulation zone. The validity of the numerical modelling is examined by comparing the predicted and measured distributions of powder accumulation under various flow conditions.

Experiment on the straw particle flow in a centrifugal pump

2020 ◽  
Vol 234 (3) ◽  
pp. 252-262
Author(s):  
Qihua Zhang ◽  
Weidong Zhang ◽  
Zhaoxu Yan ◽  
Shun Kang ◽  
Zhiang Xie
Keyword(s):  
Centrifugal Pump ◽  
High Efficiency ◽  
Pure Water ◽  
Erosive Wear ◽  
Particle Flow ◽  
Variable Frequency Drive ◽  
Stable Mode ◽  
Subtle Change ◽  
Flow Passage ◽  
Particle Flows

Centrifugal pump is extensively used in wastewater, pulp, and biomass industries for transporting of particle flows. The motion and distribution of flexible particles are critical for continuous and stable pumping. In this work, a test rig is set up for straw particle flow pumping. A stroboscopic flash is employed to capture the distribution of the straw particle. The pump performance is measured and compared to that of clear water. By increasing the particle concentration, the process from stable pumping to eventually clogging is observed. Firstly, in a wide operation range with 0.1% concentration, the particle is uniformly distributed in the flow passage and the pump is running in a hydrodynamic stable mode where the power increases gradually and is slightly over the pure water circumstance. However, the high efficiency region is shifted to lower flow rate and it becomes narrower as compared to the pure water case. Secondly, at 0.2% and 0.4% concentration, the performance resembles the 0.1% case. But with increasing concentration, the inception of small flocs is observed. In addition, small air bubble is formed near the rotating axis. This subtle change continues until clogging happens. By gradually increasing the concentration of particle, more and more particles are attached to the growing flocs. Finally, the pump runs into mechanical wear between particles and flow passage, and then it is fully clogged. In this condition, the power consumption increases rapidly and the variable frequency drive is used to bring down the shaft speed. The long-term running shows relatively light erosive wear on the surface of impeller and volute by the particles, but no damage is observed.

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