In the article on Void fraction, a description was given of the one-dimensional flow method and the *drift flux* j_{GL} was defined as the flux of the gas phase relative to a plane moving at the total superficial velocity U.

A prime assumption of the one-dimensional method was that the local velocity and void fraction were constant across the channel; in fact, they can vary considerably. Thus, the flow parameters have to be averaged over the cross-section and models incorporating these averages are often referred to as *drift flux models*. Following Zuber and Findlay (1975), we may define average and weighted mean values of the local parameters. Let F be any one of the local parameters (for example, u_{G}, U, U_{L}). An average value for F over a channel cross-section A can be defined as follows:

and a weighted mean value for P may be also defined:

Expressions for average gas velocity and the weighted mean gas velocity are obtained as follows:

where u_{GU} is the *drift velocity* of the gas phase relative to the total flow velocity U at a given point in the channel (note for the one-dimensional model, j_{GL} = ε_{G}u_{GU}). Equation (4) can be written as:

where

Similarly, the weighted mean liquid velocity is given by:

and the slip ratio is given by:

For the case of no local velocity difference between the phases (u_{GU} = 0):

thus for C_{0} ≠ 1, the slip ratio is not unity, even though the phases are travelling at the same velocity at each point in the channel. This arises because of differences between the distribution of velocity and void fraction. If uGU is constant across the channel, then Eq. (8) can be converted into a void-quality relationship of the form:

where x is the quality (fraction of the total mass flow which is vapor); ρ_{L} and ρ_{G}, the liquid and gas phase densities; and m, the mass flux.

In fully-developed bubble and/or slug flow, C_{0} is usually of the order of 1.1–1.2. It is often convenient to correlate data for void fraction in terms of the parameters C_{0} and u_{GU}. An extensive empirical correlation in this form is that of Chexal and Lellouche (1991).

#### REFERENCES

Chexal, B. and Lellouche, G. (1991) *Void Fraction Correlation for Generalised Applications.* Nuclear Safety Analysis Centre of the Electric Power Research Institute, Report NSAC/139.

Zuber, N. and Findlay, J. A. (1965) Average Volumetric Concentration in Two-Phase Flow Systems. *J. Heat Transfer* 87, 453-468.