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

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## Abstract

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.

## Keywords

Two-phase flows Algebraic slip mixture model Volume fraction Slip velocity Turbulence modulations## List of symbols

*a*Acceleration of the secondary phase

- \(C_{1\varepsilon }\)
Model constant

- \(C_{2\varepsilon }\)
Model constant

- \(C_{\mu }\)
Model constant

*D*Size of the obstruction

- \(D_{h}\)
Hydraulic diameter of the duct

- \(d_{p}\)
Solid particle diameter

- \(f_{h}\)
Fanning friction factor

- \(f_{drag}\)
Drag function

- \(G_{k}\)
Production of turbulence kinetic energy

*i*Mean pressure gradient

*g*Acceleration due to gravity

*k*Turbulence kinetic energy

*p*Mean pressure

- \(u_{m}\)
Mass-averaged mean velocity of the mixture

- \(u_{k}\)
Mass-averaged mean velocity of individual phase

- \(u_{DK}\)
Drift velocity

- \(u_{pq}\)
Slip velocity

- \(x_{i}\)
Coordinate in tensor notation

- \(y_{p}^{+}\)
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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