Application of Lumley’s Drag Reduction Model to Two-Phase Gas-Particle Flow in a Pipe

1991 ◽  
Vol 113 (1) ◽  
pp. 130-136 ◽  
Author(s):  
Kee Soo Han ◽  
Myung Kyoon Chung ◽  
Hyung Jin Sung
Keyword(s):  
Drag Reduction ◽  
Fluid Model ◽  
Average Particle Size ◽  
Viscous Sublayer ◽  
Particle Flow ◽  
Average Particle ◽  
Two Phase ◽  
Reduction Model ◽  
Sublayer Thickness ◽  
Two Fluid Model

A “two-fluid model” has been incorporated with Lumley’s drag reduction model to analyze the mechanism of momentum transfer in the turbulent dilute gas-particle flow in a vertical pipe. The change of the effective viscous sublayer thickness by the presence of particles is modeled by Lumley’s theoretical model. The numerical computations of the friction factor and the pressure drop in a fully developed pipe flow are in good agreement with the corresponding experimental data for an average particle size of 15 μm. It is proved that Lumley’s model is successful in predicting the correct reduction behavior of the drag in the gas-particle flows. It has been confirmed that the effective viscous sublayer thickness for two-phase gas-particle flow is dependent on the particle relaxation time, Kolmogoroff time scale and the solids-gas loading ratio.

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.

The magnetic properties of some superconducting mercury colloids

1956 ◽  
Vol 238 (1213) ◽  
pp. 175-193 ◽  
Keyword(s):  
Surface Energy ◽  
Temperature Dependence ◽  
Fluid Model ◽  
Average Particle Size ◽  
Energy Parameter ◽  
Mean Value ◽  
Average Particle ◽  
Magnetization Curves ◽  
Two Fluid Model ◽  
London Theory

Magnetization curves have been measured for fourteen colloidal mercury specimens whose average radius varied from 3 x 10 -6 to 15 x 10 -6 cm. For small applied fields the magnetic moment is proportional to the field and the observed temperature dependence of the slope is as predicted by the London theory. However, the dependence of these initial slopes on the average particle size cannot be explained by the London theory; the values found experi­mentally, extrapolated to 0°K, are numerically in better agreement with Pippard’s modification of the London equation, but this does not correctly describe the temperature dependence. Measurements of the area of the magnetization curves give a mean value of ─5 ± 12 Å for the surface-energy parameter β , which means that the influence of this surface energy is negligible for most specimens. It was found that them magnetization curves of drops small compared with the penetration depth can be scaled to have the same shape at all temperatures. This property has been explained quantitatively by a suitable modification of the two-fluid model of the superconducting state, but the theory does not seem adequate to explain some of the hysteresis features in the magnetization curves of larger drops.

scholarly journals Natural modes of the two-fluid model of two-phase flow

2021 ◽  
Vol 33 (3) ◽  
pp. 033324
Author(s):  
Alejandro Clausse ◽  
Martín López de Bertodano
Keyword(s):  
Two Phase Flow ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Phase ◽  
Natural Modes ◽  
Two Fluid Model ◽  
Two Fluid

Two-Phase Flows in Mini-/Micro-Gas Flow Channels of PEM Fuel Cells

2013 ◽  
Author(s):  
Sung Chan Cho ◽  
Yun Wang
Keyword(s):  
Pressure Drop ◽  
Gas Flow ◽  
Fluid Model ◽  
Pem Fuel Cells ◽  
Two Phase ◽  
Micro Gas Flow ◽  
Two Fluid Model ◽  
The Impact ◽  
Two Fluid ◽  
Phase Pressure

In this paper, two-phase flow dynamics in a micro channel with various wall conditions are both experimentally and theoretically investigated. Annulus, wavy and slug flow patterns are observed and location of liquid phase on different wall condition is visualized. The impact of flow structure on two-phase pressure drop is explained. Two-phase pressure drop is compared to a two-fluid model with relative permeability correlation. Optimization of correlation is conducted for each experimental case and theoretical solution for the flows in a circular channel is developed for annulus flow pattern showing a good match with experimental data in homogeneous channel case.

A Physically Based, One-Dimensional Two-Fluid Model for Direct Contact Condensation of Steam Jets Submerged in Subcooled Water

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
David Heinze ◽  
Thomas Schulenberg ◽  
Lars Behnke
Keyword(s):  
Direct Contact ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Interfacial Area ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Two Fluid Model ◽  
Contact Condensation ◽  
Two Fluid

A simulation model for the direct contact condensation of steam in subcooled water is presented that allows determination of major parameters of the process, such as the jet penetration length. Entrainment of water by the steam jet is modeled based on the Kelvin–Helmholtz and Rayleigh–Taylor instability theories. Primary atomization due to acceleration of interfacial waves and secondary atomization due to aerodynamic forces account for the initial size of entrained droplets. The resulting steam-water two-phase flow is simulated based on a one-dimensional two-fluid model. An interfacial area transport equation is used to track changes of the interfacial area density due to droplet entrainment and steam condensation. Interfacial heat and mass transfer rates during condensation are calculated using the two-resistance model. The resulting two-phase flow equations constitute a system of ordinary differential equations, which is solved by means of the explicit Runge–Kutta–Fehlberg algorithm. The simulation results are in good qualitative agreement with published experimental data over a wide range of pool temperatures and mass flow rates.

Numerical Simulation of Boiling Two-Phase Flow in Tight-Lattice Rod Bundle by 3-Dimensional Two-Fluid Model Code ACE-3D

2008 ◽  
Author(s):  
Hiroyuki Yoshida ◽  
Takeharu Misawa ◽  
Kazuyuki Takase
Keyword(s):  
Void Fraction ◽  
Lift Force ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Phase ◽  
Rod Bundle ◽  
Fraction Distribution ◽  
Two Fluid Model ◽  
Tight Lattice ◽  
Two Fluid

Two-fluid model can simulate two phase flow less computational cost than inter-face tracking method and particle interaction method. Therefore, two-fluid model is useful for thermal hydraulic analysis in large-scale domain such as a rod bundle. Japan Atomic Energy Agency (JAEA) develops three dimensional two-fluid model analysis code ACE-3D, which adopts boundary fitted coordinate system in order to simulate complex shape channel flow. In this paper, boiling two-phase flow analysis in a tight lattice rod bundle is performed by ACE-3D code. The parallel computation using 126CPUs is applied to this analysis. In the results, the void fraction, which distributes in outermost region of rod bundle, is lower than that in center region of rod bundle. At height z = 0.5 m, void fraction in the gap region is higher in comparison with that in center region of the subchannel. However, at height of z = 1.1m, higher void fraction distribution exists in center region of the subchannel in comparison with the gap region. The tendency of void fraction to concentrate in the gap region at vicinity of boiling starting point, and to move into subchannel as water goes through rod bundle, is qualitatively agreement with the measurement results by neutron radiography. To evaluate effects of two-phase flow model used in ACE-3D code, numerical simulation of boiling two-phase in tight lattice rod bundle with no lift force model (neglecting lift force acting on bubbles) is also performed. From the comparison of numerical results, it is concluded that the effects of lift force model are not so large on overall void fraction distribution in tight lattice rod bundle. However, higher void fraction distribution in center region of the subchannel was not observed in this simulation. It is concluded that the lift force model is important for local void fraction distribution in rod bundles.

Prediction of Parameters Distribution of Upward Boiling Two-Phase Flow With Two-Fluid Models

2002 ◽  
Author(s):  
Wei Yao ◽  
Christophe Morel
Keyword(s):  
Void Fraction ◽  
Fluid Model ◽  
Constitutive Relations ◽  
Turbulent Dispersion ◽  
Dispersion Force ◽  
Liquid Temperature ◽  
Two Phase ◽  
Radial Profiles ◽  
Two Fluid Model ◽  
Two Fluid

In this paper, a multidimensional two-fluid model with additional turbulence k–ε equations is used to predict the two-phase parameters distribution in freon R12 boiling flow. The 3D module of the CATHARE code is used for numerical calculation. The DEBORA experiment has been chosen to evaluate our models. The radial profiles of the outlet parameters were measured by means of an optical probe. The comparison of the radial profiles of void fraction, liquid temperature, gas velocity and volumetric interfacial area at the end of the heated section shows that the multidimensional two-fluid model with proper constitutive relations can yield reasonably predicted results in boiling conditions. Sensitivity tests show that the turbulent dispersion force, which involves the void fraction gradient, plays an important role in determining the void fraction distribution; and the turbulence eddy viscosity is a significant factor to influence the liquid temperature distribution.

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