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

- 268 Downloads

## 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

## References

- 1.Squires KD, Eaton JK (1990) Particle response and turbulence modification in isotropic turbulence. Phys Fluids A 2:1191–1203CrossRefGoogle Scholar
- 2.Gore RA, Crowe CT (1989) Effect of particle size on modulating turbulent intensity. Int J Multiphase Flow 15:279–285CrossRefGoogle Scholar
- 3.Elghobashi S, Truesdell GC (1993) On the two-way interaction between homogeneous turbulence and dispersed solid particles. 1. Turbulence modification. Phys Fluids A 5:1790–1801CrossRefGoogle Scholar
- 4.Best J, Bennett S, Bridge J, Leeder M (1997) Turbulence modulation and particle velocities over flat sand beds at low transport rate. J Hydraulic Eng 123(12):1118–1129CrossRefGoogle Scholar
- 5.Righetti M, Romano GP (2004) Particle–fluid interactions in a plane near wall turbulent flow. J Fluid Mech 505:93–121CrossRefGoogle Scholar
- 6.Kulick JD, Fessler JR, Eaton JK (1994) Particle response and turbulence modification in fully developed channel flow. J Fluid Mech 177:133–166Google Scholar
- 7.Kaftori G, Hetsroni G, Banerjee S (1995) Particle behavior in the turbulent boundary layer. II. Velocity and distribution profiles. Phys Fluids 7:1107–1127CrossRefGoogle Scholar
- 8.Nezu I, Azuma R (2004) Turbulence characteristics and interaction between particles and fluid in particle-laden open-channel flows. J Hydraulic Eng 130:988–1001CrossRefGoogle Scholar
- 9.Muste M, Patel VC (1997) Velocity profiles for particles and liquid in open-channel flow with suspended sediment. J Hydraulic Eng 123:742–751CrossRefGoogle Scholar
- 10.Yuan Z, Michaelides EE (1992) Turbulence modulation in particulate flows—a theoretical approach. Int J Multiphase Flow 18(5):779–785CrossRefGoogle Scholar
- 11.Barton IE (1995) Computation of particle tracks over a backward-facing step. J Aerosol Sci 26(6):883–901CrossRefGoogle Scholar
- 12.Yong JS, Sang SK (1996) Effect of obstructions on the particle collection efficiency in a two stage electrostatic precipitator. J Aerosol Sci 27(1):61–74CrossRefGoogle Scholar
- 13.Brandon DJ, Aggarwal SK (2001) A numerical investigation of particle deposition on a square cylinder placed in a channel flow. Aerosol Sci Technol 34(4):340–352Google Scholar
- 14.Manninen M, Taivassalo V, Kallio S (1996) On the mixture model for multiphase flow. Report 288, VIT Publications, Technical Research Center of Finland, Vuorimiehentie 5, FinlandGoogle Scholar
- 15.Ling J, Skudarnov PV, Lin CX, Ebadian MA (2003) Numerical investigations of liquid–solid slurry flows in a fully developed turbulent flow region. Int J Heat Fluid Flow 24(3):389–398CrossRefGoogle Scholar
- 16.Lin CX, Ebadian MA (2008) A numerical study of developing slurry flow in the entrance region of a horizontal pipe. Comput Fluids 37(8):965–974CrossRefGoogle Scholar
- 17.Pathak M (2011) Computational investigations of solid–liquid particle interaction in a two-phase flow around a ducted obstruction. J Hydraulic Res 49(1):96–104CrossRefGoogle Scholar
- 18.Noguchi K, Nezu I (2009) Particle-turbulence interaction and local particle concentration in sediment-laden open-channel flows. J Hydroenviron Res 3:54–68CrossRefGoogle Scholar
- 19.Yang CY, Lei U (1998) The role of the turbulent scales in the settling velocity of heavy particles in homogeneous isotropic turbulence. J Fluid Mech 371:179–205CrossRefGoogle Scholar
- 20.Yang TS, Shy SS (2005) Two-way interaction between solid particles and homogeneous air turbulence: particle settling rate and turbulence modification measurements. J Fluid Mech 526:171–216CrossRefGoogle Scholar
- 21.Wang G, Ni J (1990) Kinetic theory for particle concentration distribution in two-phase flow. J Eng Mech 116(12):2738–2748CrossRefGoogle Scholar
- 22.Wang GQ, Ni JR (1991) The kinetic theory for dilute solid/liquid two-phase flow. Int J Multiphase Flow 17(2):273–281CrossRefGoogle Scholar
- 23.Song XQ, Lin JZ, Zhao JF (1996) Research on reducing erosion by adding ribs on the wall in particulate two-phase flows. Wear 193(1):1–7CrossRefGoogle Scholar
- 24.Forder A, Thew M, Harrison D (1998) A numerical investigation of solid particle erosion experienced within oilfield control valves. Wear 216(2):184–193CrossRefGoogle Scholar
- 25.Fan JR, Luo K, Zhang XY (2004) Large eddy simulation of the anti-erosion characteristics of the ribbed-bend in gas–solid flows. J Eng Gas Turbines Power 126(3):672–679CrossRefGoogle Scholar
- 26.Habib MA, Badr HM (2004) Numerical calculations of erosion in an abrupt pipe contraction of different contraction ratios. Int J Numer Method Fluids 46(1):19–35CrossRefGoogle Scholar
- 27.Schiller l, Naumann AZ (1933) A drag coefficient correlation. Zeitschrift Verein Deutscher Ingenieure 77(12):318–320Google Scholar
- 28.Badr HM, Habib MA, Ben-Mansour R, Said SAM (2005) Numerical investigation of erosion threshold velocity in a pipe with sudden contraction. Comput Fluids 34(6):721–742CrossRefGoogle Scholar
- 29.Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere, New YorkGoogle Scholar
- 30.Kaushal DR, Sato K, Toyota T, Funatsu K, Tomita Y (2005) Effect of particle size distribution on pressure drop and concentration profile in pipeline flow of highly concentrated slurry. Int J Multiphase Flow 31(7):809–823CrossRefGoogle Scholar