Dear Firouzi,

1)       I will explain you the basics. In two phase flows, the void fraction is the ratio of gas volume to the total volume of the gas-liquid mixture in the pipe regardless of their flow directions.

2)       So, when you set a two phase flow in a pipe (let say QL= 1 m3/s and QG= 0.2 m3/s) as co-current or counter current, the total volume in the pipe is the same.

3)       So, when you calculate superficial void fraction (or global void fraction), you can calculate as QG/(QG+QL) whatever they are in co-current or counter-current flow. Thus, you don’t need to consider plus or minus according to their directions.

4)        The equation that you mentioned is semi-empirical equation because C0 is obtained from experimental database. It is used to calculate actual or local void fraction in a two-phase flow. In the pipe, the actual (local) void fraction is different from superficial (global) void fraction. The local (actual) void fraction is somewhat lower than superficial (global) void fraction due to the drift (or slip) velocity. Thus, even in your equation, you don’t need to think about plus or minus according to direction of flow.    

5)       Please note that the equation that you mentioned may not be universal (general) for both co-current and counter-current two-phase flow. Please make it sure. The results can be affected.

6)       Also, please wait for suggestions from other researchers.

In this expression mixture velocity (um=uG-uL), you should include correction for the velocity direction for counter-current flow. In essence velocity of on eof your phases is negative w.r.t to the other phase due to counter current.

 Thanks for your replies.

In a paper by Ghiaasian et al. it is specifically mentioned that uL=jL (the liquid superficial velocity) is positive in the downward direction. So, the direction is already applied  in the formula.