Two-fluid model simulations of a bubbly vertical jet are presented. The purpose of these simulations is to assess the modeling of lift and turbulent dispersion forces in a free shear flow. The turbulent dispersion models used herein are based on the application of a kinetic transport equation, similar to Boltzmann’s equation, to obtain the turbulent diffusion force for the dispersed phase [1–4]. They have already been constituted and validated for the case of particles in homogeneous turbulence and jets [5] and for microscopic bubbles in grid generated turbulence and mixing layers [6,7]. It was found that it is possible to simulate the experimental data of Sun [8] (see Figs. 1–6) for a bubbly jet with 1 mm diameter bubbles. Good agreement is obtained using the model of Brucato et al. [9] for the modulation of the drag force by the liquid phase turbulence and a constant lift coefficient, $CL.$ However, little sensitivity is observed to the value of the lift coefficient in the range $0

1.
Drew
,
D. A.
,
2001
, “
A Turbulent Dispersion Model for Particles or Bubbles
,”
J. Eng. Math.
,
41
(
2–3
), NOV pp.
259
274
.
2.
Reeks
,
M. W.
,
1993
, “
On the Constitutive Relations for Dispersed Particles in Nonuniform Flows. I: Dispersion in a Simple Shear Flow
,”
Phys. Fluids A
,
5
(
3
), pp.
750
761
.
3.
Reeks
,
M. W.
,
1992
, “
On the Continuum Equations for Dispersed Bubbles in Non-Uniform Flows
,”
Phys. Fluids A
,
4
(
6
), pp.
1290
1302
.
4.
Reeks
,
M. W.
,
1991
, “
On a Kinetic Equation for the Transport of Bubbles in Turbulent Flows
,”
Phys. Fluids A
,
3
(
3
), pp.
446
456
.
5.
Lopez de Bertodano
,
M.
,
1998
, “
Two Fluid Model for Two-Phase Turbulent Jet
,”
Nucl. Eng. Des.
,
179
, pp.
65
74
.
6.
Moraga, F. J., Larreteguy, A. E., Drew, D. A., and Lahey, R. T., Jr., 2001, “Assessment of Turbulent Dispersion Models for Bubbly Flows,” Paper 379, 4th International Conference on Multiphase Flow. New Orleans LA, USA.
7.
Moraga
,
F. J.
,
Larreteguy
,
A. E.
,
Drew
,
D. A.
, and
Lahey
, Jr.,
R. T.
,
2003
, “
Assesment of Turbulent Dispersion Models for Bubbly Flow in the Low Stokes Number Limit
,”
Int. J. Multiphase Flow
,
29
(
4
), pp.
655
673
.
8.
Sun, T.-Y., 1985, “A Theoretical and Experimental Study on Noncondensible Turbulent Bubbly Jets,” Ph.D. Dissertation, The Pennsylvania State University, University Park, PA.
9.
Brucato
,
A.
,
Grisafi
,
F.
, and
Montante
,
G.
,
1998
, “
Particle Drag Coefficients in Turbulent Fluids
,”
Chem. Eng. Sci.
,
53
(
18
), pp.
3295
3314
.
10.
Kurose
,
R.
, and
Komori
,
S.
,
1999
, “
Drag and Lift Forces on a Rotating Sphere in Laminar Shear Flows
,”
J. Fluid Mech.
,
384
, pp.
183
206
.
11.
Sun
,
T.-Y.
, and
Faeth
,
G. M.
,
1986
, “
Structure of Turbulent Bubbly Jets -I. Methods and Centerline Properties, -II. Phase Property Profiles
,”
Int. J. Multiphase Flow
,
12
, pp.
99
126
.
12.
Drew, D. A., and Passman, S. L., 1998, Theory of multicomponent fluids, App. Math. Sci. 135, Springer.
13.
Tomiyama, A., 1998, “Struggle With Computational Bubble Dynamics,” Third Int. Conf. on Multiphase Flows, ICMF’98, Lyon, France.
14.
Ishii, M., 1987, Two-Fluid Model for Two-Phase Flow, 2nd Int. Workshop on Two-Phase Flow Fundamentals, Rensselaer Polytechnic Institute, Troy, NY.
15.
Auton
,
T. R.
,
1987
, “
The Lift Force on a Spherical Body in a Rotational Flow
,”
J. Fluid Mech.
,
183
, pp.
199
213
.
16.
Legendre
,
D.
, and
Magnaudet
,
J.
,
1998
, “
The Lift Force on a Spherical Bubble in Viscous Linear Flow
,”
J. Fluid Mech.
,
368
, pp.
81
126
.
17.
Bagchi
,
P.
, and
Balachandar
,
P.
,
2002
, “
Effect of Free Rotation on the Motion of a Solid Sphere in Linear Shear Flow at Moderate Re
,”
Phys. Fluids
,
14
, pp.
2719
2737
.
18.
Naciri, M. A., 1992, “Contribution a l’etude des forces exercees por un liquide sur une bulle de gaz, masse ajoutee et interactions hydrodynamiques,” Ph.D. Thesis, L’Ecole Central de Lyon, Lyon, France.
19.
Loth
,
E.
,
2001
, “
An Eulerian Turbulent Diffusion Model for Particles and Bubbles
,”
Int. J. Multiphase Flow
,
27
, pp.
1051
1063
.