1. Asst. Prof. Dr. Hayder Mohammad Jaffal
Ministry of Higher Education &scientific Research
Mustansiriyah University
College of Engineering
Mechanical Engineering Department
Two Phase Flow – Introduction
(Section 1)
Asst. Prof. Dr. Hayder Mohammad Jaffal

2. Gas-liquid flow also occurs in boiling and condensation operations
Two phase flows are commonly found in ordinary life and in industrial processes
Gas-liquid flow also occurs in boiling and condensation operations
Inside pipelines which carry oil or gas alone, but which actually carry a mixture of oil and gas.
Single phase flow
Laminar, transition, and turbulent When the flow regime changes from laminar to turbulent the personality of the fluid completely changes the phenomena governing the transport processes change
Two phase flow
Similar situation However, there is a multitude of flow regimes The behavior of a gas–liquid mixture depends strongly on the flow regimes. Methods for predicting the major flow regimes are required, for the modeling and analysis of two-phase flow systems

3. Some definitions:
1-Void Fraction
In two-phase flow, void fraction is one of the most important parameters to be defined. It defines the cross-sectional area occupied by each phase. As it determines mean velocities of the liquid and the vapor, it represents a fundamental parameter in the calculation of pressure drop, flow pattern transitions and heat transfer coefficients.
Figure (1): Cross-sectional void fraction (α).

4. The void fraction of the vapor is defined as:
where AG is the sum of areas occupied by voids and AL is the sum of areas occupied by the liquid.The total cross-sectional area of the channel is called A.

5. 2-Mass velocity (mass flux )
The mass velocity (G) is defined to be the ratio of the mass flow rate ( m°) divided by the cross-sectional area of the flow channel:
Considering the continuity law, the mass velocity is the expression of the mean flow velocity multiplied by the mean density. The mass velocity has units of [kg/m²s].
3-Vapor quality (mass quality)
The vapor quality (x) is defined to be the ratio of the vapor mass flow rate ( m°G [kg /s]) divided by the total mass flow rate ( m°G + m°L):

6. Mass dryness fraction
Wetness fraction
4-Volume dryness fraction
The volume dryness fraction (β) is defined to be the ratio of the vapor volume flow rate ( QG [m³/s]) divided by the total volume flow rate ( QG + QL):

7. 5-True average velocities
The true average velocities (also called actual velocities) of the phases uG and uL are the velocities by which the phases actually travel. The cross sectional average true velocities are determined by the volumetric flow rates QG and QL [m³/s] of the vapor and liquid divided by the cross-sectional areas occupied by the respective phases:
From the equation of continuity it is possible to define liquid and vapor true mean velocities referred to their own cross sectional areas and their own mass flow rates as follows:

8. 6-Superficial velocities
The superficial velocities (also called volumetric fluxes) of the phases jG and jL are defined as the volumetric flow rate of the phase through the total cross-sectional area of the two-phase flow. It might also be expressed as the phase velocity if it would flow alone in the entire cross section. Thus:

9. The total superficial velocity is defined as:

10. 7-Drift velocities
The drift velocities of the phases VGj and VLj are defined as the true average velocity of the phase in relation to the total superficial velocity, namely:
8-Slip ratio
Occurs because the gas expands and speeds up relative to the liquid. It depend upon fluid properties and flow conditions.

11. Example (1):
Derive an expression for the slip ratio in terms of (α) and (β) only.
Solution:

12. Therefore
Substitute Eq.(2) in Eq.(1) to get :

13. Example (2):
A bubbly regime mixture flows in a (25 mm) inside diameter carbon steel pipe. The gas flow rate is (51m3/hr) and the bubble velocity is approximated to be (30 m/s) with a liquid flow rate of (8.5 m3/hr). Determine the void fraction and liquid velocity.
Solution:

14. Example (3):

15. Sub in Eq.(3)

17. Sub in Eq.(7)

18. Rearrange Eq.(8)