EQUILIBRIUM VELOCITY DISTRIBUTION FUNCTIONS FOR A KINETIC MODEL OF TWO-PHASE FLOWS

1995 ◽  
Vol 05 (02) ◽  
pp. 191-211 ◽  
Author(s):  
LIONEL SAINSAULIEU
Keyword(s):  
Velocity Distribution ◽  
Gas Flow ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Velocity Distribution Function ◽  
Distribution Functions ◽  
Solid Particles ◽  
Navier Stokes ◽  
Two Phase ◽  
Entropy Balance

We consider a cloud of solid particles in a gas flow. The cloud is described by a probability density function which satisfies a kinetic equation. The gas flow is modeled by Navier-Stokes equations. The two phases exchange momentum and energy. We obtain the entropy balance of the gas flow and deduce some bounds for the volume fraction of the gas phase. Writing the entropy balance for the dispersed phase enables one to determine the particles equilibrium velocity distribution function when the gas flow is known.

Interaction of Shock and Expansion Wave With Solid Particles in Supersonic Flows

2002 ◽  
Author(s):  
Ali Dolatabadi ◽  
Javad Mostaghimi ◽  
Valerian Pershin
Keyword(s):  
Mach Number ◽  
Flow Regime ◽  
Drag Force ◽  
Gas Flow ◽  
Volume Fraction ◽  
Supersonic Flows ◽  
Operating Conditions ◽  
Solid Particles ◽  
Process Efficiency ◽  
Two Phase

Interaction of solid particles with shock and expansions in supersonic flows is analyzed. In this analysis, a dense cloud of solid particulates is modeled by using a fully Eulerian approach. The dispersed flow and the gas flow were considered in the Eulerian frame whereby most of the physical aspects of the gas-particle flow can be incorporated. In addition to the momentum and energy exchanges in the form of source terms appearing in the governing equations, the two phases were strongly coupled by considering the volume fraction of the particulate phase in the equations. The simulation performed for a High Velocity Oxy-Fuel (HVOF) process under typical operating conditions in which the powder loading is high and the two-phase flow is not dilute near the injection port. The simulations showed large variations in the flow regime in the region that most of the particles exist. Unlike the results corresponding to the Lagrangian approach, the flow becomes subsonic near the centerline and the drag force decreases significantly since the relative Mach number is small. The validation experiments showed that the variation of flow regime by changing the relative Mach number could significantly change the particle drag force, and consequently process efficiency.

Experimental Investigation on Air-Solid Two-Phase Mixture Discharge under AC Voltage

2011 ◽  
Vol 383-390 ◽  
pp. 4955-4961
Author(s):  
Wen Jun Yao ◽  
Zheng Hao He ◽  
He Ming Deng
Keyword(s):  
Gas Flow ◽  
Volume Fraction ◽  
Fundamental Problem ◽  
Solid Particles ◽  
Two Phase ◽  
The Common ◽  
Phase Mixture ◽  
Multi Phase ◽  
Inception Voltage ◽  
Statistical Rule

Multi-phase mixture (MPM) discharge has the common characteristics of randomness with air but more complex. How about the statistical rule of MPM discharge ? This is not only a fundamental problem for discharge research, but it has its own strong applied and practical characteristics. The air-solid two-phase mixtures(ASTPM) are employed to study and carry out some experiments for investigating the development and breakdown of MPM discharge under AC voltage. The results from experimental data show that the AC breakdown voltage and corona-inception voltage will drop when the solid particles are added to the discharge chamber with different permittivity and volume fraction. And there is no influence in gas flow and the corona current.

Numerical Simulation of Low-Speed Two Phase Flows Based on Preconditioning

2011 ◽  
Author(s):  
Yang-Yao Niu
Keyword(s):  
Stokes Equations ◽  
Volume Fraction ◽  
Splitting Method ◽  
Flow Simulation ◽  
Current Approach ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Vector Type ◽  
Dam Breaking

This paper first applies flux vector type splitting method based on numerical speed of sound for computing incompressible single and multi-fluid flows. Here, a preconditioning matrix based on Chorin’s artificial compressibility concept is used to modify the incompressible multi-fluid Navier-Stokes Equations to be hyperbolic and density or volume fraction independent. The current approach can reduce eigenvalues disparity induced from density or volume fraction ratio and enhance numerical stability. Also, a simple convection-pressure flux-splitting method with high-order essentially non-oscillatory (ENO) type primitive variable extrapolations coupling with an ENO-MUSCL type volume fraction recompressed reconstruction within a mesh cell is used to maintain the preservation of sharp interface evolutions in multi-fluid flow simulation. Benchmark tests including a solid rotation test of a notched 2D cylinder, the evolution of spiral and rotational shapes of deformable circles, a dam breaking problem, the Rayleigh-Taylor instability and the cavitated flow problems are chosen to validate the current incompressible multi-fluid methodology.

scholarly journals Gas holdup in a reciprocating plate bioreactor: Non-Newtonian - liquid phase

2002 ◽  
Vol 56 (5) ◽  
pp. 198-203 ◽  
Author(s):  
Olivera Naseva ◽  
Ivica Stamenkovic ◽  
Ivana Bankovic-Ilic ◽  
Miodrag Lazic ◽  
Vlada Veljkovic ◽  
...  
Keyword(s):  
Gas Flow ◽  
Volume Fraction ◽  
Methyl Cellulose ◽  
Gas Holdup ◽  
Degree Of Polymerization ◽  
Operating Conditions ◽  
Solid Particles ◽  
Flow Index ◽  
Two Phase ◽  
Vibration Rate

The gas holdup was studied in non-newtonian liquids in a gas-liquid and gas-liquid-solid reciprocating plate bioreactor. Aqueous solutions of carboxy methyl cellulose (CMC; Lucel, Lucane, Yugoslavia) of different degrees of polymerization (PP 200 and PP 1000) and concentration (0,5 and 1%), polypropylene spheres (diameter 8.3 mm; fraction of spheres: 3.8 and 6.6% by volume) and air were used as the liquid, solid and gas phase. The gas holdup was found to be dependent on the vibration rate, the superficial gas velocity, volume fraction of solid particles and Theological properties of the liquid ohase. Both in the gas-liquid and gas-liquid-solid systems studied, the gas holdup increased with increasing vibration rate and gas flow rate. The gas holdup was higher in three-phase systems than in two-phase ones under otter operating conditions being the same. Generally the gas holdup increased with increasing the volume fraction of solid particles, due to the dispersion action of the solid particles, and decreased with increasing non-Newtonian behaviour (decreasing flow index) i.e. with increasing degree of polymerization and solution concentration of CMC applied, as a result of gas bubble coalescence.

Parallel Numerical Prediction of Pulverized Coal Particle Flow in Bifurcator-Type Flow Splitters

2003 ◽  
Vol 125 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Th. Frank ◽  
H. Schneider ◽  
K. Bernert ◽  
K. Pachler
Keyword(s):  
Numerical Simulation ◽  
Gas Flow ◽  
Stokes Equations ◽  
Decomposition Methods ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Numerical Effort ◽  
Tracking Model

This paper deals with the numerical simulation of two-phase flows based on the solution of the Navier-Stokes equations with a k−ε turbulence model for the gas phase and a particle tracking model of the disperse phase fulfilling the framework of the Eulerian-Lagrangian (PSI-cell) approach. The numerical procedures for the two phases are based on multigrid and domain decomposition methods applied to a block-structured grid. Due to the enormous numerical effort of such flow simulations the entire solving procedure has been parallelized for computers of MIMD architecture. The paper gives a short description of the applied and developed numerical methods. Furthermore the numerical simulation of a particle laden gas flow through a flow splitter from the area of power engineering is presented as an example for a real world application of the numerical approach.

MATHEMATICAL MODELING OF A TURBULENT FLOW IN A CENTRIFUGAL SEPARATOR

2021 ◽  
pp. 121-138
Author(s):  
Z.M. Malikov ◽  
◽  
M.E. Madaliev ◽  
Keyword(s):  
Mathematical Modeling ◽  
Turbulent Flow ◽  
Gas Flow ◽  
Stokes Equations ◽  
Solid Phase ◽  
Navier Stokes ◽  
Centrifugal Separator ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Carrier Gas Flow

The numerical results of mathematical modeling of a two-phase axisymmetric swirling turbulent flow in a separation zone of a centrifugal separator are presented. The motion of the carrier gas flow is described by the Reynolds-averaged Navier-Stokes equations. A system of equations is enclosed by the Spalart-Allmaras turbulence model. The study is based on the obtained fields of averaged velocities of the carrier medium, with account for turbulent diffusion. Numerical solution to the problem is implemented using the semi-implicit method for pressure linked equations (SIMPLE). The results obtained when the solid phase effect on the air flow dynamics is taken into account are compared with those obtained when the effect is left out of account. The numerical calculations are validated using the experimental data.

The Calculation of Two-Phase Gas/Liquid Homogenous Flow in Bearing Chambers

2006 ◽  
Vol 532-533 ◽  
pp. 717-720 ◽  
Author(s):  
Hao Tian Wu ◽  
Guo Ding Chen
Keyword(s):  
Flow Model ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Structural Parameters ◽  
Differential Method ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Lubrication Oil ◽  
Oil Flow

The research of lubrication oil flow on gas/liquid two-phase flow is necessary in the designing process of engine bearing. It influences the consequent design and the whole engine’s reliability. This paper proposes the two-phase homogenous flow model considering lubrication oil and air. Based on the homogenous flow model, the Navier-Stokes equations is solved by the methods of the turbulent model and Finite Differential Method (FDM) to obtain the flow field and the influence of conditional and structural parameters on the flow. With the results, the results from single flow model and two-phase homogenous flow are compared. And the effects of air volume fraction, rotor speed and lubrication oil speed at entrance on exit pressure and speed are discussed.

Numerical Modeling of Evolution of Boundary Between Incompressible Gas and Liquid in Two-Dimensional Region

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov
Keyword(s):  
Numerical Modeling ◽  
Interphase Boundary ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Numerical Code ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Incompressible Media ◽  
Good Agreement

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.

scholarly journals Experimental and Numerical Study on Water Filling and Air Expelling Process in a Pipe with Multiple Air Valves under Water Slow Filling Condition

Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2511
Author(s):  
Jintao Liu ◽  
Di Xu ◽  
Shaohui Zhang ◽  
Meijian Bai
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Practical Method ◽  
Navier Stokes ◽  
Physical Processes ◽  
Two Phase ◽  
Saint Venant Equations ◽  
Water Filling ◽  
Air Valve

This paper investigates the physical processes involved in the water filling and air expelling process of a pipe with multiple air valves under water slow filling condition, and develops a fully coupledwater–air two-phase stratified numerical model for simulating the process. In this model, the Saint-Venant equations and the Vertical Average Navier–Stokes equations (VANS) are respectively applied to describe the water and air in pipe, and the air valve model is introduced into the VANS equations of air as the source term. The finite-volume method and implicit dual time-stepping method (IDTS) with two-order accuracy are simultaneously used to solve this numerical model to realize the full coupling between water and air movement. Then, the model is validated by using the experimental data of the pressure evolution in pipe and the air velocity evolution of air valves, which respectively characterize the water filling and air expelling process. The results show that the model performs well in capturing the physical processes, and a reasonable agreement is obtained between numerical and experimental results. This agreement demonstrates that the proposed model in this paper offers a practical method for simulating water filling and air expelling process in a pipe with multiple air valves under water slow filling condition.

TRIGGERING OF DETONATION PROCESSES IN PROPULSION CHAMBER

2021 ◽  
Vol 14 (2) ◽  
pp. 40-45
Author(s):  
D. V. VORONIN ◽  
Keyword(s):  
Thermal Conductivity ◽  
Numerical Modeling ◽  
Gas Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Chemically Reacting ◽  
Plane Disk ◽  
And Diffusion

The Navier-Stokes equations have been used for numerical modeling of chemically reacting gas flow in the propulsion chamber. The chamber represents an axially symmetrical plane disk. Fuel and oxidant were fed into the chamber separately at some angle to the inflow surface and not parallel one to another to ensure better mixing of species. The model is based on conservation laws of mass, momentum, and energy for nonsteady two-dimensional compressible gas flow in the case of axial symmetry. The processes of viscosity, thermal conductivity, turbulence, and diffusion of species have been taken into account. The possibility of detonation mode of combustion of the mixture in the chamber was numerically demonstrated. The detonation triggering depends on the values of angles between fuel and oxidizer jets. This type of the propulsion chamber is effective because of the absence of stagnation zones and good mixing of species before burning.

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