# Two-phase flow

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Flow of gas and liquid in the same conduit

Different modes of two-phase flows.

In [fluid mechanics](/source/Fluid_mechanics), **two-phase flow** is a [flow](/source/Flow_(fluid)) of [gas](/source/Gas) and [liquid](/source/Liquid) — a particular example of [multiphase flow](/source/Multiphase_flow). Two-phase flow can occur in various forms, such as flows transitioning from pure liquid to vapor as a result of external [heating](/source/Heat), separated flows, and dispersed two-phase flows where one phase is present in the form of particles, [droplets](/source/Drop_(liquid)), or bubbles in a continuous carrier phase (i.e. gas or liquid).

## Categorization

The widely accepted method to categorize two-phase flows is to consider the velocity of each phase as if there is not other phases available. The parameter is a hypothetical concept called [Superficial velocity](/source/Superficial_velocity).

## Examples and applications

Historically, probably 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](/source/Boiler) to produce steam for use in [turbines](/source/Turbine). In such cases, pressurised 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 behaviour, which is significantly different from the single-phase case. Even more critically, [nuclear reactors](/source/Nuclear_reactor) use water to remove heat from the reactor core using two-phase flow. A great deal of study has been performed on the nature of two-phase flow in such cases, so that engineers can design against possible failures in pipework, loss of pressure, and so on (a [loss-of-coolant accident](/source/Loss-of-coolant_accident) (LOCA)).[1]

Another case where two-phase flow can occur is in pump [cavitation](/source/Cavitation). Here a pump is operating close to the [vapor pressure](/source/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](/source/Mixture) 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. Although oil and water are not strictly distinct phases (since they are both liquids) they are sometimes considered as a two-phase flow; and the combination of oil, gas and water (e.g. the flow from an offshore oil well) may also be considered a three-phase flow.

Other interesting areas where two-phase flow is studied includes water [electrolysis](/source/Electrolysis),[2] climate systems such as [clouds](/source/Cloud),[1] and in [groundwater](/source/Groundwater) flow, in which the movement of water and air through the soil is studied.

Other examples of two-phase flow include [bubbles](/source/Liquid_bubble), [rain](/source/Rain), [waves](/source/Wave) on the [sea](/source/Sea), [foam](/source/Foam), [fountains](/source/Fountain), [mousse](/source/Mousse), [cryogenics](/source/Cryogenics), and [oil slicks](/source/Oil_slick). One final example is in the electrical explosion of metal.

## Characteristics of two-phase flow

Several features make two-phase flow an interesting and challenging branch of fluid mechanics:

- [Surface tension](/source/Surface_tension) makes all dynamical problems [nonlinear](/source/Nonlinear) (see [Weber number](/source/Weber_number))

- [Coalescence](/source/Coalescence_(physics)) and [breakup](/source/Fluid_thread_breakup) of droplets can alter the bulk properties of the system, such as the drag when flowing through a channel[3]

- In the case of air and water at [standard temperature and pressure](/source/Standard_temperature_and_pressure), the [density](/source/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](/source/Compressible) effects into the problem

- The phase changes are not instantaneous, and the liquid vapor system will not necessarily be in phase equilibrium

- The change of phase means flow-induced pressure drops can cause further phase-change (e.g. water can evaporate through a valve) increasing the relative volume of the gaseous, compressible medium and increasing exit velocities, unlike single-phase incompressible flow where closing a valve would decrease exit velocities

- Can give rise to other counter-intuitive, negative resistance-type instabilities, like [Ledinegg instability](/source/Ledinegg_instability), [geysering](/source/Geyser), [chugging](/source/Rocket_engine#Combustion_instabilities), [relaxation instability](https://en.wikipedia.org/w/index.php?title=Relaxation_instability&action=edit&redlink=1), and flow maldistribution instabilities as examples of *static* instabilities, and other *dynamic* instabilities[4]

Additional exhaustive information, like applied mathematical models can be found in. [5][6][7][8][9]

## Acoustics

Gurgling is a characteristic [sound](/source/Sound) made by unstable two-phase fluid flow, for example, as liquid is poured from a bottle, or during [gargling](/source/Gargling).

## See also

- [Multiphase flow](/source/Multiphase_flow)

- [Buckley–Leverett equation](/source/Buckley%E2%80%93Leverett_equation)

- [Darcy's law for multiphase flow](/source/Darcy's_law#Multiphase_flow) (for flow through porous media such as soil)

- [Slip ratio (gas–liquid flow)](/source/Slip_ratio_(gas%E2%80%93liquid_flow))

- [Mass flow meter](/source/Mass_flow_meter)

## Modelling

Simulation of bubble swarm using volume of fluid method

Modelling of two phase flow is still under development. Known methods are

- [Volume of fluid method](/source/Volume_of_fluid_method)

- [Level-set method](/source/Level-set_method)

- [Front tracking](https://en.wikipedia.org/w/index.php?title=Front_tracking&action=edit&redlink=1) by [Gretar Tryggvason](/source/Gretar_Tryggvason)

- [Lattice Boltzmann methods](/source/Lattice_Boltzmann_methods)

- [Smoothed-particle hydrodynamics](/source/Smoothed-particle_hydrodynamics) (SPH)

## References

1. ^ [***a***](#cite_ref-levy_1-0) [***b***](#cite_ref-levy_1-1) Salomon Levy, Two-Phase Flow in Complex Systems, Wiley, 1999

1. **[^](#cite_ref-2)** Bisang J.M., Colli A.N. (2022). "Current and Potential Distribution in Two-Phase (Gas Evolving) Electrochemical Reactors by the Finite Volume Method". *Journal of the Electrochemical Society*. **169** (3): 034524. [Bibcode](/source/Bibcode_(identifier)):[2022JElS..169c4524C](https://ui.adsabs.harvard.edu/abs/2022JElS..169c4524C). [doi](/source/Doi_(identifier)):[10.1149/1945-7111/ac5d90](https://doi.org/10.1149%2F1945-7111%2Fac5d90). [S2CID](/source/S2CID_(identifier)) [247463029](https://api.semanticscholar.org/CorpusID:247463029).

1. **[^](#cite_ref-3)** Cannon, I.; Izbassarov, D.; Tammisola, O.; Brandt, L.; Rosti, M. E. (2021). "The Effect of Droplet Coalescence on Drag in Turbulent Channel Flows". *Physics of Fluids*. **33** (8): 085112. [arXiv](/source/ArXiv_(identifier)):[2106.01647](https://arxiv.org/abs/2106.01647). [doi](/source/Doi_(identifier)):[10.1063/5.0058632](https://doi.org/10.1063%2F5.0058632).

1. **[^](#cite_ref-4)** Ghiaasiaan, S. M.Two-Phase Flow, Boiling, and Condensation: In Conventional and Miniature Systems, Cambridge University Press, 2008. pg 362.

1. **[^](#cite_ref-5)** Ishi, M.; Hibiki, T. (2006). *Thermo-Fluid Dynamics of Two-Phase Flow*. Springer. [ISBN](/source/ISBN_(identifier)) [9780387283210](https://en.wikipedia.org/wiki/Special:BookSources/9780387283210).

1. **[^](#cite_ref-6)** Peker, S. M.; Helvaci, S.S. (2008). *Solid–Liquid Two Phase Flow*. Elsevier. [ISBN](/source/ISBN_(identifier)) [978-0-444-52237-5](https://en.wikipedia.org/wiki/Special:BookSources/978-0-444-52237-5).

1. **[^](#cite_ref-7)** Gross, S.; Reusken, A. (2011). *Numerical Methods for Two-phase Incompressible Flows*. Springer. [ISBN](/source/ISBN_(identifier)) [978-3-642-19685-0](https://en.wikipedia.org/wiki/Special:BookSources/978-3-642-19685-0).

1. **[^](#cite_ref-8)** Stewart, H.B.; Wendroff, H. (1984). ["Two-phase flow: models and methods"](https://www.sciencedirect.com/science/article/abs/pii/0021999184901037). *Journal of Computational Physics*. **56** (3): 363–409. [Bibcode](/source/Bibcode_(identifier)):[1984JCoPh..56..363S](https://ui.adsabs.harvard.edu/abs/1984JCoPh..56..363S). [doi](/source/Doi_(identifier)):[10.1016/0021-9991(84)90103-7](https://doi.org/10.1016%2F0021-9991%2884%2990103-7).

1. **[^](#cite_ref-9)** Tiselj, I.; Petelin, S. (1997). ["Modeling of two-phase flow with second-order accurate scheme"](https://www.sciencedirect.com/science/article/abs/pii/S0021999197957788). *Journal of Computational Physics*. **136** (2): 503–521. [Bibcode](/source/Bibcode_(identifier)):[1997JCoPh.136..503T](https://ui.adsabs.harvard.edu/abs/1997JCoPh.136..503T). [doi](/source/Doi_(identifier)):[10.1006/jcph.1997.5778](https://doi.org/10.1006%2Fjcph.1997.5778).

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