# Two-Phase Flow Patterns in Horizontal Tubes

Figure 1: Flow regimes in horizontal two-phase flow (Grey=liquid, White=vapor).

Horizontal two-phase flow exhibits flow patterns different from those in vertical two-phase flow, because gravity acts perpendicularly to the flow direction. Two-phase flow in horizontal tubes is more complex than vertical two-phase flow, because the flow is usually not axisymmetric, due to the effect of gravity. The flow patterns encountered in horizontal two-phase flow are defined as follows (Hewitt, 1998; Thome, 2004) and shown in Fig. 1:

Dispersed bubble flow. The vapor (gas) phase appears as distinct bubbles in a continuous liquid phase. The bubbles tend to rise to the top of the flow due to buoyancy effects. When the liquid velocity is high, the bubbles may be more uniformly distributed in the liquid, as in vertical flow.

Plug flow. An increase of quality results in larger vapor (gas) bubble size and the formation of bullet-shaped plugs, which tend to remain at the top of the flow channel due to buoyancy force.

Stratified flow. The liquid and vapor (gas) velocities in this regime are relatively slow, and the quality is relatively high. The liquid flows along the bottom of the tube due to gravity while the vapor (gas) phase flows at the top of the tube. It is also possible that a very thin layer of the liquid forms at the top of the flow channel.

Stratified wavy flow. As the vapor (gas) velocity increases in the stratified flows, the shear forces of the vapor (gas) flow over the liquid cause ripples on the top of the liquid phase and result in the formation of waves on the liquid-vapor (gas) interface. The waves climb up the sides of the tube and the liquid layer at the bottom of the channel starts to stretch thin.

Slug flow. The amplitude of the waves increases as the liquid flow rate increases. The crests can span the entire tube, and a bridge starts to develop, separating the slugs from one another. However, a substantial liquid phase remains and gravity pulls it to the bottom of the flow channel. The top of the flow channel is still wetted by a relatively thin film of liquid.

Annular-dispersed flow. Similar to the flow pattern in vertical two-phase flow, the liquid layer flows near the inner wall of the tube and the vapor (gas) flows in the central core. However, the liquid layer at the bottom is thicker than that on the top of the channel due to the effect of gravitational force.

Figure 2: Flow regime map for horizontal two-phase flow.

The most widely used flow pattern map for horizontal two-phase flow, proposed by Taitel and Dukler (1976), is shown in Fig. 2. This map is based on a semi-theoretical method, and it is computationally more difficult to use than other flow maps. The horizontal coordinate of the Taitel and Dukler (1976) map is the Martinelli parameter:

$X={{\left[ \frac{{{(d{{p}_{F}}/dz)}_{\ell }}}{{{(d{{p}_{F}}/dz)}_{v}}} \right]}^{1/2}}\qquad\qquad(1)$

where ${{(d{{p}_{F}}/dz)}_{\ell }}$ and ${{(d{{p}_{F}}/dz)}_{v}}$ are the pressure gradients for the liquid and vapor phases, flowing along the channel. The vertical coordinates of the Taitel and Dukler (1976) map are defined as

$F=\sqrt{\frac{{{\rho }_{v}}}{{{\rho }_{\ell }}-{{\rho }_{v}}}}\frac{{{j}_{v}}}{\sqrt{Dg\cos \theta }}\qquad\qquad(2)$
$K={{\left[ \frac{{{\rho }_{v}}{{j}_{v}}^{2}}{({{\rho }_{\ell }}-{{\rho }_{v}})Dg\cos \theta }\frac{D{{j}_{\ell }}}{{{v}_{\ell }}} \right]}^{1/2}}\qquad\qquad(3)$
$T={{\left[ \frac{{{(dp/dz)}_{\ell }}}{({{\rho }_{\ell }}-{{\rho }_{v}})g\cos \theta } \right]}^{1/2}}\qquad\qquad(4)$

where D is the tube diameter and θ is the angle of inclination of the channel to the horizontal. It can be seen that determination of the flow regime using Taitel and Dukler’s (1976) map requires the pressure gradient for the liquid and vapor phases flowing along the channel, which should be determined using appropriate flow models.

It should be pointed out that the flow maps presented in Two-Phase Flow Patterns in Vertical Tubes, and Fig. 2 were obtained for adiabatic two-phase flow; however, the transition boundaries between different flow regimes depend on the heat flux. Nevertheless, these flow maps are often used to determine the flow patterns for evaporation and condensation inside tubes, for which external heating or cooling is required. Application of these flow maps to forced convective boiling or condensation inside a tube may not yield reliable results.

## References

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA

Hewitt, G.F., 1998, “Multiphase Fluid Flow and Pressure Drop,” Heat Exchanger Design Handbook, Vol. 2, Begell House, New York, NY.

Taitel, Y., and Dukler, A.E., 1976, “A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas-Liquid Flow,” AIChE Journal, Vol. 22, pp. 47- 55.

Thome, J.R., 2004, Engineering Data Book III, Wolverine Tube, Inc., Huntsville, AL.