* Churn flow* (*), also referred to as **froth flow* and *semiannular flow* is a highly disturbed flow of gas and liquid. It is characterized by the presence of a very thick and unstable liquid film, with the liquid often oscillating up and down. As an established flow regime, it appears only in vertical and near-vertical tubes and is usually bounded by the slug and the annular flow regimes. In contrast to these two regimes, both of which have a well-defined structure, churn flow appears chaotic and is one of the least understood of gas-liquid flow regimes. Due to its complexity, it is often thought merely as a transitional regime (Dukler & Taitel, 1986), but recent experimental evidence shows **Flooding** of the film (and the consequent entrainment of large chunks of liquid and their subsequent deposition) as one of its main features. Conditions in which churn flow occurs and some correlations for determining the pressure drop and the holdup in this flow regime are discussed below.

There are three bounds to the churn flow regime, these are: (1) the slug-churn transition; (2) the churn-annular transition; and (3) the maximum liquid flow rate limit above which churn flow does not occur. Of these, the slug-churn transition has received the most attention and is subject to some controversy. The major schools of thought on this have been reviewed recently by Jayanti & Hewitt (1992). Recent evidence suggests that Slug Flow is destabilized when the (downcoming) liquid film surrounding the Taylor bubble is flooded by the gas flowing upwards. Jayanti & Hewitt (1992) have proposed a model based on this mechanism, which may be used to determine the condition for the slug-churn transition. The conditions for the flooding of the film in the Taylor bubble in slug flow and the subsequent transition to churn flow are described by Eq. (1):

where and are the nondimensionalized velocities of the Taylor bubble and the film surrounding it, respectively, and m is a constant which depends on the length and the diameter of the test section. Further details of the model can be found in Jayanti & Hewitt (1992).

The churn-annular transition is often taken as the point at which the film ceases to flow downwards even intermittently, and is therefore associated with the *flow reversal* point in counter-current flow (Wallis, 1969). This criterion is expressed in the form of an upper limit of gas velocity above which churn flow does not occur:

where U_{gs} is the gas superficial velocity; ρ, the density; g, the acceleration due to gravity; and D, the pipe diameter.

There appears to be an upper limit on the liquid velocity also above which churn flow does not occur (Govier & Aziz, 1972). This can be expressed roughly as:

Understandably, the frictional *pressure gradient* is very high in churn flow, reflecting the violent interaction between the gas and the liquid phases. The nature of this interaction is not well understood and can only be represented in the form of empirical correlations. There are, however, few data for pressure drop and holdup in churn flow. The correlations and methods suggested here are based on a small number of data, notably, of Bharathan (1978) and Govan et al. (1991). The interfacial friction factor, f_{i}, can be correlated as a function of the void fraction, ε_{g}, as follows:

and

The pressure gradient, dp/dz, and the liquid holdup, ε = (1 − ε_{g}), can then be calculated by solving the following force balance equations on the inner core and on the pipe:

where the wall shear stress, τ_{w}, is given by:

and

where Re_{1s}, the liquid Reynolds number is based on the pipe diameter and the superficial liquid velocity.

#### REFERENCES

Bharathan, D. (1978) *Air-Water Counter-Current Annular Flow in Vertical Tubes*, EPR1 Report No. EPRI NP-786.

Dukler, A. E. and Taitel, Y. (1986) *Flow Pattern Transition in Gas-Liquid Systems: Measurement and Modelling*, in Multiphase Science and Technology, 2,1-94,1986, ed. G. F. Hewitt, J. M. Delhaye & N. Zuber, Hemisphere Publishing Corp.

Govan, A. H., Hewitt, G. F., Richter, H. J. and Scott, A. (1991) *Flooding and Churn Flow in Vertical Pipes*, Int. J. Multiphase Flow, 17, 27-44. DOI: 10.1016/0301-9322(91)90068-E

Govier G. W. & Aziz K. (1972) *The Flow of Complex Mixtures in Pipes*, Van Nostrand Reinhold.

Jayanti, S. and Hewitt, G. F. (1992) *Prediction of the Slug-to-Churn Flow Transition in Vertical Two-Pnase Flow*, Int. J. Multiphase Flow, 18, 847-860. DOI: 10.1016/0301-9322(92)90063-M

Wallis, G. B. (1969) One-Dimensional Two-Phase How, McGraw-Hill.