Environmental Fluid Mechanics

, Volume 13, Issue 4, pp 371–388 | Cite as

Inter-phase slip velocity and turbulence characteristics of micro particles in an obstructed two-phase flow

  • Manabendra Pathak
  • Mohd. Kaleem Khan
Original Article


A computational investigation has been made to study the effects of particle size on inter-phase slip velocity and flow turbulence in a solid–liquid two-phase flow through a rectangular duct. Finite volume method with an algebraic slip mixture model and renormalization k-\(\varepsilon \) model has been used in the simulation. Simulations have been made for three different sizes of particles to show their effects on mean and turbulent flow properties. The presence of obstruction changes the typical stratified distribution of micro particles in the stagnation and recirculation regions where stagnation region is characterized with high value of solid particles concentration and recirculation region is characterized with low value. The slip velocity between the particles and liquid phases has been observed more in the upstream compared to the downstream of the obstruction. The change in particles distributions and slip velocities caused by the presence of obstruction disappears at certain downstream distance of the obstruction and the flow properties regain their un-disturbed states. This settling distance depends upon the particle size. Particles enhance the flow turbulence and the effect in complex flow region has been observed more for large size particles. Even though Stokes number associated with the flow is small, the turbulence and slip velocity have been increased due to flow disturbance created by the obstruction.


Two-phase flows Algebraic slip mixture model Volume fraction  Slip velocity Turbulence modulations 

List of symbols


Acceleration of the secondary phase

\(C_{1\varepsilon }\)

Model constant

\(C_{2\varepsilon }\)

Model constant

\(C_{\mu }\)

Model constant


Size of the obstruction


Hydraulic diameter of the duct


Solid particle diameter


Fanning friction factor


Drag function


Production of turbulence kinetic energy


Mean pressure gradient


Acceleration due to gravity


Turbulence kinetic energy


Mean pressure


Mass-averaged mean velocity of the mixture


Mass-averaged mean velocity of individual phase


Drift velocity


Slip velocity


Coordinate in tensor notation


Normalised distance of first grid point from the wall

Greek letters

\(\alpha \)

Void fraction

\(\rho _{m}\)

Mass averaged mean density

\(\mu _{t}\)

Eddy viscosity

\(\varepsilon \)

Turbulence dissipation rate

\(\sigma _{k}\)

Model constant

\(\sigma _{\varepsilon }\)

Model constant


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of Technology PatnaPatnaIndia

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