Solid Phase Contribution in the Two-Phase Turbulence Kinetic Energy Equation

1990 ◽  
Vol 112 (3) ◽  
pp. 351-361 ◽  
Author(s):  
T. W. Abou-Arab ◽  
M. C. Roco
Keyword(s):  
Kinetic Energy ◽  
Energy Equation ◽  
Solid Phase ◽  
Density Ratio ◽  
Turbulence Kinetic Energy ◽  
Time Averaging ◽  
Two Phase ◽  
Carrier Fluid ◽  
Double Time ◽  
Energy Equations

This paper presents a multiphase turbulence closure employing one transport equation, namely, the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A double-time averaging approach for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less restrictive assumptions comparative to the previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

scholarly journals Effect of a Symmetric Contraction on the Concentration Profiles of a Particle-Laden Slurry

2011 ◽  
Author(s):  
A. Deshpande ◽  
K. Ramisetty ◽  
F. W. Chambers ◽  
M. E. McNally ◽  
R. M. Hoffman
Keyword(s):  
Single Phase ◽  
Solid Phase ◽  
Fluid Dynamic ◽  
Density Ratio ◽  
Primary Phase ◽  
Solid Particles ◽  
Concentration Profiles ◽  
Two Phase ◽  
Horizontal Pipe ◽  
Slurry Concentration

In-line measurements and sample stream withdrawals for on-line and/or at-line measurements of slurries flowing in horizontal pipes can be complicated by nonuniform slurry profiles. More uniform profiles would improve measurements. Area contractions are a common means used to produce more uniform velocity fields for single phase flows. For example, contractions are used to condition the flow entering wind tunnel test sections and make velocity profiles more uniform at venturi throats. It was desired to determine whether area contractions could be used to make slurry concentration profiles more uniform in horizontal pipe flows. An ASME flow nozzle with a contraction diameter ratio of 0.5 was chosen as a well defined geometry to consider in a Computational Fluid Dynamic (CFD) study of the effects of a contraction on slurry concentration profiles. The pipe was 2.8 m long with a 50.8 mm diameter. The entrance of the contraction was placed at 35 pipe diameters from the inlet in fully developed flow. A length of 20 diameters followed the contraction. The slurry had a xylene liquid phase and an ADP solid phase with a density ratio of 1.7. The simulations were performed at primary phase velocities of 2 m/s and 4 m/s, corresponding to Reynolds numbers of 1.4E05 and 2.8E05. Spherical particle diameters of 38, 75, and 150 μm were used at concentrations of 0.05, 0.2, and 0.3. ANSYS FLUENT 12 software was used with the standard k-ε turbulence model and standard wall function. The mixture multi-phase model was used for the two-phase flow. An unstructured tetrahedral meshing scheme was used with 1.4 million elements. The grid was adjusted until the condition 30 < y+ <60 for the mesh point nearest the wall was satisfied. A grid refinement study was performed to insure grid independence. The computational scheme first was validated by comparing pipe flow velocity and concentration profiles to results in the literature. The computations performed with the contraction showed that in all cases the concentration profiles of the solid particles displayed greater uniformity than the profiles in the pipe upstream of the contraction. The effect of the contraction was more pronounced for the larger particles. As in the case of single phase flows, the contraction caused the axial turbulence intensity to decrease. The greater uniformity of the concentration profiles at the exit plane of the nozzle, suggest that the contraction can provide better conditions for performing measurements of a particle-laden slurry.

DNS Study of Collision and Coalescence Over a Wide Range of Volume Fraction

2010 ◽  
Author(s):  
G. Luret ◽  
T. Me´nard ◽  
J. Re´veillon ◽  
A. Berlemont ◽  
F. X. Demoulin
Keyword(s):  
Kinetic Energy ◽  
Weber Number ◽  
Volume Fraction ◽  
Density Ratio ◽  
Liquid Volume ◽  
Kinetic Energy Density ◽  
Two Phase ◽  
Liquid Volume Fraction ◽  
Gas Phases ◽  
Wide Range

Among the different processes that play a role during the atomization process, collisions are addressed in this work. Collisions can be very important in dense two-phase flows. Recently, the Eulerian Lagrangian Spray Atomization (ELSA) model has been developed. It represents the atomization by taking into account the dense zone of the spray. Thus in this context, collisions modeling are of the utmost importance. In this model results of collisions are controlled by the value of an equilibrium Weber number, We*. It is defined as the ratio between the kinetic energy to the surface energy. Such a value of We* has been studied in the past using Lagrangian collision models with various complexity. These models are based on analysis of collisions between droplets that have surface at rest. This ideal situation can be obtained only if droplet agitation created during a collision has enough time to vanish before the next collision. For a spray, this requirement is not always fulfill depending for instance on the mean liquid volume fraction. If there is not enough time, collisions will occur between agitated droplets changing the issue of the collision with respect to the ideal case. To study this effect, a DNS simulation with a stationary turbulence levels has been conducted for different liquid volume fractions in a cubic box with periodic condition in all directions. For liquid volume fraction close to zero the spray is diluted and collisions between spherical droplets can be identified. For a volume fraction close to one, collisions between bubbles are found. For a middle value of the volume fraction no discrete phase can be observed, instead a strong interaction between both liquid and gas phases is taking place. In all this case the equilibrium value of the Weber number We* can be determined. First propositions to determine We* as a function of the kinetic energy, density ratio, surface tension coefficient and the volume fraction will be proposed.

Numerical Investigation on Premixed Combustion Using a Fiber Mat Burner With a Boiler

2002 ◽  
Author(s):  
T. Golder ◽  
O. Kawaguchi
Keyword(s):  
Energy Equation ◽  
Solid Phase ◽  
Numerical Study ◽  
Radiant Energy ◽  
Radiative Properties ◽  
Local Thermal Equilibrium ◽  
Combustion Model ◽  
Non Local ◽  
Two Phases ◽  
Energy Equations

This paper presents a numerical study of combustion and multi mode heat transfer in inert porous media. In this case a sintered fiber mat is used. From this work it is understood that the premixed flame is stabilized on the downstream surface of the fiber mat burner. The influence of the flame location, the radiative properties of the porous material, the solid thermal conductivity, and stoichiometry on the flame speed and flame stability are determined using a one-dimensional conduction, convection, radiation, and combustion model. The fiber mat is allowed to emit, absorb, and scatter radiant energy. Non-local thermal equilibrium between the solid and gas was taken into account. Here, separate energy equations for the two phases are introduced, i.e. gas energy equation for the entire system and solid energy equation for the fiber mat. The results indicate that stable combustion can be maintained near the downstream surface of the fiber mat which is mostly controlled by solid-phase radiation.

The RANS, PDF and TBL Simulations of Turbulent Gas-Solid Particle Flow in Vertical Pipe

2006 ◽  
Author(s):  
Alexander I. Kartushinsky ◽  
Efstathios E. Michaelides ◽  
Leonid I. Zaichik
Keyword(s):  
Solid Particle ◽  
Solid Phase ◽  
Fluid Model ◽  
Coupling Model ◽  
Particle Flow ◽  
Particle Collision ◽  
Two Phase ◽  
Turbulence Modulation ◽  
Carrier Fluid ◽  
Two Fluid Model

The numerical simulation of turbulent gas-solid particle flow in vertical round pipe is performed & analyzed by three different approaches: RANS 2D modeling, PDF approach (Zaichik’s model 2001) & by two-phase TBL (turbulent boundary layer approach). The given performances include all relevant force factors imposed on the motion of solid phase (two-fluid model is considered): particle-turbulence, particle-particle, particle-wall interactions, two-lift the Magnus & Saffman forces and buoyancy (gravitational) force. The dispersed phase is considered as a polydispersed phase composed of finite number of particle fractions and the mass & momentum equations are closed with the help of implementation of original “collision” model (Kartushinsky & Michaelides, 2004). The two/four-way coupling model of Gillandt & Crowe (1998) is accounted for turbulence modulation. The numerical results show that retaining of second diffusion terms in both directions (in streamwise & transverse directions) aligns the average x-velocity components of gas and dispersed phases as well as the particle mass concentration and k-profiles across the flow in case of both PDF and RANS 2D approaches that versus the distributions of parameters obtained by two-phase TBL approach. This is reasonable due to additional effect of fluxes diffusion of the carrier fluid & solid phase in the main direction derived from turbulence fluctuation and inter-particle collision which smoothes the profile shapes.

Numerical Simulation of Flow on Stepped Spillway Combined with Wide Tailing Piers and Stilling Basin

2012 ◽  
Vol 170-173 ◽  
pp. 2047-2050
Author(s):  
W.L. Wei ◽  
B. Lv ◽  
Y.L. Liu ◽  
X.F. Yang
Keyword(s):  
Velocity Field ◽  
Kinetic Energy ◽  
Dissipation Rate ◽  
Pressure Field ◽  
Free Water ◽  
Energy Dissipation Rate ◽  
Turbulence Kinetic Energy ◽  
Physical Parameters ◽  
Stepped Spillway ◽  
Two Phase

In this paper, a two-phase flow model combined with the Realizable k–ε turbulence model was used to simulate hydraulic characteristics of two-type dissipaters: the stepped spillway combined with stilling pool and the stepped spillway combined with wide tailing pier and stilling pool. The distributions of physical parameters, such as velocity field, pressure field, turbulence kinetic energy and turbulence dissipation rate were obtained. The grid was generated by using the regional division method, the unstructured grids used for the irregular and complex parts and the structured grids for the regular and simple parts, and the grid density is arranged according to the flow gradient size. The finite volume method was adopted to discretized the control equations; and the VOF method was adopted to deal with the free water surface; and the PISO algorithm was used to solve the velocity and pressure coupling equations. A comparative analysis of the two energy-dissipators in the velocity field, pressure field, turbulence kinetic energy and turbulence kinetic energy dissipation rate shows that the dissipation of overflow for a stepped spillway together with wide tailing piers and a stilling pool jointing energy dissipator is better than that with pier situation.

Scale-up Technique of Slurry Pipelines—Part 1: Turbulence Modeling

1986 ◽  
Vol 108 (4) ◽  
pp. 269-277 ◽  
Author(s):  
M. C. Roco ◽  
S. Mahadevan
Keyword(s):  
Kinetic Energy ◽  
Finite Volume ◽  
Solid Wall ◽  
Mathematical Formulation ◽  
Specific Interaction ◽  
Scale Up ◽  
Three Dimensions ◽  
Semiempirical Methods ◽  
Time Averaging ◽  
Two Phase

A kinetic energy turbulence model is proposed for the flow simulation and scale-up of slurry pipelines (in Part 1). The numerical integration is performed by using a modified finite volume technique with application to high convective, two-phase flows, in two and three dimensions (in Part 2 [1]). The mixture kinetic energy and eddy viscosity one-equation turbulence models are compared. The constitutive equations and model constants are tested using laboratory experiments and then employed for large-scale applications. The governing equations are derived from the space/time averaging of the momentum equations and integrated in the pipe cross section using the finite volume approach. The specific interaction stresses (liquid-liquid, liquid-solid, solid-solid and solid-wall) are expressed in the mathematical formulation. The predictions for the velocity and concentration distributions, as well as on the mean velocity-headloss correlations, have been compared to available experimental data (water-sand, water-glass, water-coal mixtures; of concentrations αS = 5 – 40 vol percent, in pipes of various diameters D = 40 – 500 mm). The suggested model can simulate multi-species particulate pipe flow for which the semiempirical methods cannot be satisfactorily applied. The numerical tests and comparison to experiments show the model capabilities to scale-up data from laboratory to real flow situations via infinitesimal two-phase flow analysis.

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