0
Research Papers: Multiphase Flows

# Computations of Particle-Laden Turbulent Jet Flows Based on Eulerian Model

[+] Author and Article Information
Pandaba Patro

e-mail: ppatro@mech.iitkgp.ernet.in

Sukanta K. Dash

e-mail: sdash@mech.iitkgp.ernet.inDepartment of Mechanical Engineering,
IIT,
Kharagpur 721302, India

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 6, 2013; final manuscript received August 17, 2013; published online October 3, 2013. Assoc. Editor: Francine Battaglia.

J. Fluids Eng 136(1), 011301 (Oct 03, 2013) (16 pages) Paper No: FE-13-1007; doi: 10.1115/1.4025364 History: Received January 06, 2013; Revised August 17, 2013

## Abstract

Numerical simulations using an Eulerian two-fluid model were performed for spatially developing, two-dimensional, axisymmetric jets issued from a 30-mm-diameter circular nozzle. The nozzle was simulated separately for various flow conditions to get fully developed velocity profiles at its exit. The effect of interparticle collisions in the nozzle gives rise to solids pressure and viscosity, which are modeled using kinetic theory of granular flows (KTGF). The particle sizes are in the range of 30 $μm$ to 2 mm, and the particle loading is varied from 1 to 5. The fully developed velocity profiles are expressed by power law, $U=Uc(1-(r/R))N$. The exponent, N, is found to be 0.14 for gas phase, irrespective of particle sizes and particulate loadings. However, the solid-phase velocity varies significantly with the particle diameter. For particle sizes up to 200 $μm$, the exponent is 0.12. The center line velocity ($Uc$) of the solid phase decreases and, hence, the slip velocity increases as the particle size increases. For 1 mm and 2 mm size particles, the exponent is found to be 0.08 and 0.05, respectively. The developed velocity profiles of both the phases are used as the inlet velocities for the jet simulation. The modulations on the flow structures and turbulent characteristics of gas flow due to the solid particles with different particle sizes and loadings are investigated. The jet spreading and the decay of the centerline mean velocity are computed for all particle sizes and loadings considered under the present study. Additions of solid particles to the gas flow significantly modulate the gas turbulence in the nozzle as well as the jet flows. Fine particles suppress the turbulence, whereas coarse particles enhance it.

## References

Kartushinsky, A., Michaelides, E. E., Rudi, Y., and Nathan, G., 2010, “RANS Modeling of a Particulate Turbulent Round Jet,” Chem. Eng. Sci., 65, pp. 3384–3393.
Elghobashi, S., 1994, “On Predicting Particle-Laden Turbulent Flows,” Appl. Sci. Res., 52(4), pp. 309–329.
Roul, M. K., and Dash, S. K., 2012, “Single-Phase and Two-Phase Flow Through Thin and Thick Orifices in Horizontal Pipes,” ASME J. Fluids Eng., 134, p. 091301.
Tanaka, T., and Tsuji, Y., 1991, “Numerical Simulation of Gas–Solid Two-Phase Flow in a Vertical Pipe: On the Effect of Inter-Particle Collision,” ASME/FED Gas–Solid Flows, 121, pp. 123–128.
Kartushinsky, A., and Michaelides, E. E., 2007, “Gas-Solid Particle Flow in Horizontal Channels: Decomposition of the Particle-Phase Flow and Inter-particle Collision Effects,” ASME J. Fluids Eng., 129, pp. 702–712.
Bolio, E. J., Yasuna, J. A., and Sinclair, J. L., 1995, “Dilute Turbulent Gas–Solid Flow in Risers With Particle–Particle Interactions,” AIChE J., 141(6), pp. 1375–1388.
Cao, J., and Ahmadi, G., 1995, “Gas-Particle Two-Phase Turbulent Flow in a Vertical Duct,” Int. J. Multiphase Flow, 21, pp. 1203–1228.
Mathiesen, V. T., Solberg, B. H., and Jertager, H., 2000, “Predictions of Gas/Particle Flow With an Eulerian Model Including a Realistic Particle Size Distribution,” Powder Technol., 112, pp. 34–45.
MilioliC. C., and Milioli, F. E., 2006, “Reaching the Statistical Steady State Regime in Two-Fluid Simulation of Risers,” Powder Technol., 167(1), pp. 26–32.
TsuoY. P., and Gidaspow, D., 1990, “Computation of Flow Patterns in Circulating Fluidized Beds,” AIChE J., 36(6), pp. 885–896.
Samareh, B., and Dolatabadi, A., 2008, “Dense Particulate Flow in a Cold Gas Dynamic Spray System,” ASME J. Fluids Eng., 130, p. 081702.
Abramovich, G. N., 1963, The Theory of Turbulent Jets, MIT, Boston.
Hedman, P. O., and Smoot, L. D., 1975, “Particle-Gas Dispersion Effects in Confined Coaxial Jets,” AIChE J., 21, pp. 372–379.
Modarress, D., Tan, H., and Elghobashi, S., 1984, “Two Component LDA Measurements in a Two Phase Turbulent Jet,” AIAA J., 22(5), pp. 624–630.
Fleckhaus, D., Hishida, K., and Maeda, M., 1987, “Effect of Laden Solid Particles on the Turbulent Flow Structure of a Round Free Jet,” Exp. Fluids, 5, pp. 323–333.
Melville, W. K., and Bray, K. N. C., 1979. “A Model of the Two-Phase Turbulent Jet,” Int. J. Heat Mass Transfer, 22, pp. 647–656.
Crowe, C. T., Gore, R. A., and Troutt, T. R., 1985, “Particle Dispersion by Coherent Structures in Free Shear Flows,” Part. Sci. Technol., 3, pp. 149–158.
Crowe, C. T., Chung, T. N., and Troutt, T. R., 1988, “Particle Mixing in Free Shear Flows,” Prog. Energy Combust. Sci., 14, pp. 171–194.
Hardalupas, Y., Taylor, A. M. P. K., and Whitelow, J. H., 1989, “Velocity and Particle-Flux Characteristics of Turbulent Particle-Laden Jets,” Proc. R. Soc. London, Ser. A, 426, pp. 31–78.
Yuu, S., Ikeda, K., and Umekage, T., 1996, “Flow-Field Prediction and Experimental Verification of Low Reynolds Number Gas-Particle Turbulent Jets,” Colloids Surf., A, 109, pp. 13–27.
Frishman, F., Hussainov, M., Kartushinsky, A., and Mulgi, A., 1997, “Numerical Simulation of A Two-Phase Turbulent Pipe-Jet Flow Loaded With Poly-Dispersed Solid Admixture,” Int. J. Multiphase Flow, 23(4), pp. 765–796.
Gidaspow, D., 1994, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions, Academic, Boston, MA.
Lun, C. K. K., Savage, S. B., Jeffrey, D. J., and Chepurniy, N., 1984, “Kinetic Theories for Granular Flow: Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General Flow Field,” J. Fluid Mech., 140, pp. 223–256.
Ding, J., and Gidaspow, D., 1990, “A Bubbling Fluidization Model Using Kinetic Theory of Granular Flow,” AIChE J., 36(4), pp. 523–538.
Elgobashi, S. E., and Abou-Arab, T. W., 1983, “A Two-Equation Turbulence Model for Two-Phase Flows,” Phys. Fluids, 26(4), pp. 931–938.
Gidaspow, D., Bezburuah, R., and Ding, J., 1992, “Hydrodynamics of Circulating Fluidized Beds, Kinetic Theory Approach,” Proceedings of the 7th Engineering Foundation Conference on Fluidization, pp. 75–82.
Hinze, J. O., 1975, Turbulence, McGraw-Hill, New York.
Launder, B. E., and Spalding, D. B., 1974, “The Numerical Computation of Turbulent Flows,” Comput. Methods Appl. Mech. Eng., 3, pp. 269–289.
Vasquez, S. A., and Ivanov, V. A., 2000, “A Phase Coupled Method for Solving Multiphase Problems on Unstructured Meshes,” Proceedings of ASME FEDSM, Boston.
Johnson, P. C., and Jackson, R., 1987, “Frictional-Collisional Constitutive Relations for Granular Materials, With Application to Plane Shearing,” J. Fluid Mech., 176, pp. 67–93.
Tsuji, Y., Morikawa, Y., and Shiomi, H., 1984, “LDV Measurements of an Air-Solid Two Phase Flow in a Vertical Pipe,” J. Fluid Mech., 139, pp. 417–434.
Jones, E., Yurteri, C., and Sinclair, J. L., 1999, “The Effect of Solids Loading on Particle Motion in Gas-Solid Flows,” Proceedings of Fluidization and Fluid-Particle Systems, Annual AIChE Meeting, Dallas, TX, pp. 65–71.
Park, C. J., and Chen, L. D., 1989, “Experimental Investigation of Confined Turbulent Jets: Part II. Particle-Laden Flow Data,” AIAA J., 27, pp. 1511–1516.
Gillandt, I., Fritsching, U., and Bauckhage, K., 2001, “Measurement of Phase Interaction in Dispersed Gas-Particle Two-Phase Flow,” Int. J. Multiphase Flow, 27, pp. 1313–1332.
Tsuji, Y., Morikawa, Y., Tanaka, T., and Karimine, K., 1988, “Measurement of an Axi-Symmetric Jet Laden With Coarse Particles,” Int. J. Multiphase Flow, 14, pp. 565–574.
Crowe, C. T., 2000, “On Models for Turbulence Modulation in Fluid–Particle Flows,” Int. J. Multiphase Flow, 26(5), pp. 719–727.
Hetsroni, G., 1989, “Particle–Turbulence Interaction,” Int. J. Multiphase Flow, 15(5), pp. 735–746.
Michaelides, E. E., 2006, Particles, Bubbles and Drops-Their Motion, Heat and Mass Transfer, World Scientific, New Jersey.
Gore, R. A., and Crowe, C. T., 1989, “Effect of Particle Size on Modulating Turbulent Intensity”, Int. J. Multiphase Flow, 15, pp. 279–285.
Yuan, Z., and Michaelides, E. E., 1992, “Turbulence Modulation in Particulate Flows–A Theoretical Approach,” Int. J. Multiphase Flow, 18, pp. 779–785.

## Figures

Fig. 1

Flow field around a jet, a schematic diagram

Fig. 2

Effect of boundary conditions on the axial and radial velocity profiles of both the phases: the velocities are normalized by the centerline velocity

Fig. 3

Effect of grid on the predictions of (a) gas-phase velocity, (b) solid-phase velocity, and (c) gas turbulent kinetic energy

Fig. 4

Computational domain used for the two-phase jet

Fig. 5

Axial development of the normalized centerline velocity for different mesh sizes

Fig. 6

Normalized mean velocity profiles at X/D = 10 for different mesh sizes

Fig. 7

Computed (a) gas-phase velocity, (b) solid-phase velocity, and (c) gas turbulent intensity: a comparison with the experiments of Modarress et al. [14] for glass beads at D = 20 mm, β = 0.85, and Reg = 1.33×104 in a vertical downward two-phase flow. Model 1 is algebraic granular temperature model, and model 2 is full granular temperature equation.

Fig. 8

Computed (a) velocity profiles of both phases and (b) gas turbulent intensity: a comparison with the experiments of Tsuji et al. [31] for polystyrene pellets at D = 30 mm, β = 1.3, and Reg = 2.3×104 in a vertical upward flow. Velocities are nondimensionalized with the centerline velocity of the gas phase.

Fig. 9

Nozzle exit gas-phase velocity profiles for different cases. Symbols are the power function fitting profiles with N = 0.14.

Fig. 10

Nozzle exit solid-phase velocity profiles for different cases. Symbols are the power function fitting profiles with N = 0.12.

Fig. 11

Centerline velocity as a function of mean velocity for both phases

Fig. 12

Nozzle exit solid-phase velocity profiles for (a) dp = 1 mm, N = 0.08 and (b) dp = 2 mm, N = 0.05. Solid-phase density = 2990 kg/m3.

Fig. 13

Variation of the centerline velocity with mean velocity for the solid phase at (a) dp = 1 mm and (b) dp = 2 mm

Fig. 14

Radial variation of the gas-phase turbulence intensity. Symbols: turbulence intensity from single-phase flow simulations. Squares ◻ are for case 2, diamonds ◇ are for case 4, and triangles ▽ are for cases 1 and 3.

Fig. 15

Radial variation of the turbulence intensity with particle diameter

Fig. 16

Normalized axial velocity as a function of radial distance: a comparison with the experiments of Abramovich [12] for Reg = 2.2×104

Fig. 17

(a) Normalized solid-phase axial velocity as a function of radial distance: a comparison with the experimental data of Frishman et al. [21] for Reg = 5×104,dp = 23μm, and β = 0.62 and (b) effect of interparticle collisions with full granular temperature equation on centerline velocity profiles for dp = 200μm, β = 5, and Reg = 2.06×104

Fig. 18

Decay of the centerline velocity (normalized by the velocity at the inlet) for different particle sizes: (a) gas phase and (b) solid phase ρs = 2500 kg/m3, β = 1

Fig. 19

Decay of the centerline velocity (normalized by the velocity at the inlet) for different particulate loadings: (a) gas phase and (b) solid phase ρs = 2500 kg/m3, dp = 200μm

Fig. 20

Slip velocity profiles along the centerline: (a) different particle diameters, β = 1, and (b) different particle loadings, dp = 200μm

Fig. 21

Variations of the jet velocity half-width: (a) different particulate loadings, dp = 200 μm, (b) different particle sizes, β = 1

Fig. 22

Effect of particulate loading (β) on the mean velocity profiles at X/D = 20, dp = 200μm, and Um = 10 m/s

Fig. 23

Mean velocity profiles (normalized by the centerline velocity) as a function of the radial distance at different axial positions, dp = 200μm

Fig. 24

Mean velocity profiles as a function of the radial distance at different axial positions for different Stokes numbers (St)

Fig. 25

Decay of mean velocity along the centerline for different Stokes numbers (St)

Fig. 26

Normalized velocities at X/D = 20 for different Stokes number (St)

Fig. 27

Variations of (a) turbulent kinetic energy (normalized with respect to the nozzle exit) and (b) turbulent modulations along the centerline for different particle sizes, ρs = 2500 kg/m3, β = 1

Fig. 28

Variations of (a) turbulent kinetic energy (normalized with respect to the nozzle exit) and (b) turbulent modulations on the center line as a function of the axial distance for different particulate loadings, ρs = 2500 kg/m3, dp = 200μm

Fig. 29

Variations of the turbulent kinetic energy as a function of the radial distance, β = 1, (a) St = 2, (b) St = 100

Fig. 30

Turbulent modulation as a function of the radial distance, β = 1, (a) St = 2, (b) St = 100

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections