Satish Lele
lelepiping@gmail.com

Two Phase Flow
In fluid mechanics, two-phase flow occurs in a system containing gas and liquid with a meniscus separating the two phases. Two-phase flow is a particular example of multiphase flow.
The most commonly studied cases of two-phase flow are in large-scale power systems. Coal and gas-fired power stations used very large boilers to produce steam for use in turbines. In such cases, pressurized water is passed through heated pipes and it changes to steam as it moves through the pipe. The design of boilers requires a detailed understanding of two-phase flow heat-transfer and pressure drop behavior, which is significantly different from the single-phase case. Even more critically, nuclear reactors use water to remove heat from the reactor core using two-phase flow.
Another case where two-phase flow can occur is in pump cavitation. Here a pump is operating close to the vapor pressure of the fluid being pumped. If pressure drops further, which can happen locally near the vanes for the pump, for example, then a phase change can occur and gas will be present in the pump. Similar effects can also occur on marine propellers; wherever it occurs, it is a serious problem for designers. When the vapor bubble collapses, it can produce very large pressure spikes, which over time will cause damage on the propeller or turbine.

The above two-phase flow cases are for a single fluid occurring by itself as two different phases, such as steam and water. The term 'two-phase flow' is also applied to mixtures of different fluids having different phases, such as air and water, or oil and natural gas. Sometimes even three-phase flow is considered, such as in oil and gas pipelines where there might be a significant fraction of solids.
Characteristics of two-phase flow: Several features make two-phase flow an interesting and challenging branch of fluid mechanics.

  • Surface tension makes all dynamical problems nonlinear (see Weber number).
  • In the case of air and water at standard temperature and pressure, the density of the two phases differs by a factor of about 1000. Similar differences are typical of water liquid/water vapor densities.
  • The sound speed changes dramatically for materials undergoing phase change, and can be orders of magnitude different. This introduces compressible effects into the problem.
  • The phase changes are not instantaneous, and the liquid vapor system will not necessarily be in phase equilibrium.

The most common class of Multiphase Flows are two-phase flows, and these include the following:
Gas-liquid flows: This is probably the most important form of multiphase flow, and is found widely in a whole range of industrial applications. These include pipeline systems for the transport of oil-gas mixtures, evaporators, boilers, condensers, submerged combustion systems, sewerage treatment plants, air-conditioning and refrigeration plants, and cryogenic plants. Gas-liquid systems are also important in the meteorology and in other natural phenomena.
Gas-solid flows: Flows of solids suspended in gases are important in pneumatic conveying and in pulverized fuel combustion. Fluidized beds may also be regarded as a form of gas-solid flow. In such beds, the solid remains within the fixed container while the gas passes through. However, within the bed itself, both the gas and the solid are undergoing complex motions.
Liquid-liquid flows: Examples of the application of this kind of flow are the flow of oil-water mixtures in pipelines and in liquid-liquid solvent extraction mass transfer systems. Solvent extraction equipment includes packed columns, pulsed columns, stirred contactors and pipeline contactors.
Liquid-solid flows: The most important application of this type of flow is in the hydraulic conveying of solid materials. Liquid-solid suspensions also occur in crystallization systems, in china clay extraction and in hydro-cyclones.
Design Parameters in Two-phase Flow:
The more important design parameters for two-phase flow systems include the following:
Pressure drop: Pressure losses occur in two-phase flow systems due to friction, acceleration and gravitational effects. If a fixed flow is required, then the pressure drop determines the power input of the pumping system. Here, examples are the design of pumps for the pipeline transport of slurries, or for pumping of oil-water mixtures. If the available pressure drop is fixed, the relationship between velocity and pressure drop needs to be invoked in order to predict the flow rate. An example of this latter application is in the prediction of the circulation rate in natural circulation boiler systems.
Heat transfer coefficient: Heat transfer coefficients in two-phase systems are obviously important in determining the size of heat exchangers in such systems. Examples here are thermo-syphon reboilers in distillation plant and condensers in power plant.
Mass transfer coefficient: This is important in the design of separation equipment and also in predicting the situation of combined heat and mass transfer such as in the condensation of vapor mixtures.
Mean phase content (e): This quantity represents the fraction by volume or by cross-sectional area of a particular phase. In gas-liquid flows, the gas mean phase content eG is often referred to as the Void Fraction and the liquid phase fraction eL the liquid holdup. In systems containing a solid phase, the mean solid phase content is referred to as the solid hold-up. Mean phase content can be important in governing the inventory of a particular phase within a system, particularly when that phase is toxic or valuable. Mean phase content also governs the gravitational pressure gradient.
Flux limitations: Limitations in mass and heat fluxes are important in the design of two-phase flow systems. Examples of mass flux limitations include Critical Flow (which tends to occur at lower velocities in multiphase system than those found in single-phase systems), Flooding and Flow Reversal in counter-current flow systems (for example in a reflux condenser), and minimum fluidization velocities in Fluidized Beds. Heat flux limitations are important in boiling, where exceeding the burnout or critical heat flux can lead to poor system performance or physical damage due to excessive increases in the channel wall temperature.
Modeling Approaches for Two-phase Flows: A wide range of models have been developed for two-phase flow systems. These include:
Homogeneous model: In the homogeneous model, the two phases are assumed to be traveling at the same velocity in the channel and the flow is treated as being analogous to a single phase flow.
Separated flow models: Here, the two fluids are considered to be traveling at different velocities and overall conservation equations are written taking this into account.
Multi-fluid model: Here, separate conservation equations are written for each phase, these equations containing terms describing the interaction between the phases.
Drift flux model: Here, the flow is described in terms of a distribution parameter and an averaged local velocity difference between the phases.
Computational fluid dynamic (CFD) models: In contrast to the above models, the Computational fluid dynamic, CFD, models usually involve two or three dimensions, and attempt to describe the full flow field.

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