Abstract
This paper presents the analytical treatment and the correlation procedure on “two-phase friction factor”in vertical upward mixed phase flow.
From previous results, shear distribution in annular liquid layer is given by Eq.(6) in terms of wall shear stress and liquid hold-up.
Velocity profile in the liquid layer may be assumed to have two regions of laminar sublayer and turbulent surface layer, as shown in Fig. 1.
Employing Eqs.(8) and (10) for the velocity distribution in these layers, the theoretical relation between“two-phase friction factor” fT. P. and its effective factors is as shown by Eq.(21), with the dimensionless groups of liquid Reynolds Number dL/μL, hold-up parameter φ, the factors of entrainment fraction L/Lf and φ/φf and the relative thickness of laminar sublaver c.
A number of data obtained by the author and other investigators were examined based on Eq.(21) for the ranges of dL/μL; 2 to 18000, pipe diameter d; 10 to 35mm i. d. and liquid viscosity μL; 1 to 44c. p.
The results were as follows;
For the range of pseudo-stream line flow (ReL<1, 000), the friction factor fT.P. may be substantially correlated by dL/μL and φ. The correlation diagram of fT. P.-ReL-φReL, is given in Fig. 2.
For the range of turbulent flow (ReL>1, 000), fT. P. may be practically correlated by dL/μL as shown in Fig. 5, and Eq.(39) may be applicable with ±30% deviation, furthermore the effects of entrainment fraction were discussed.
