Flow Patterns – Two-phase Flow

One of the most challenging aspects of dealing with the two-phase flow or multi-phase flow is that it can take many different forms. Spatial distributions and velocities of the liquid and vapor phases in the flow channel is a very important aspect in many engineering branches. Pressure drops and heat transfer coefficients strongly depend on the local flow structure, and thus it is important in the engineering of nuclear reactors. The observed flow structures are defined as two-phase flow patterns, and these have particular identifying characteristics. These different flow patterns have been categorized according to the direction of flow relative to gravitational acceleration.

  • Flow patterns in vertical tubes
  • Flow patterns in horizontal tubes
flow patterns
Table of basic flow patterns in vertical tubes.

The main flow regimes in vertical tubes are shown in the table. It must be noted that flow quality values and flow rate depend on the fluid and pressure. In horizontal tubes, there can also be stratified flow (especially at low flow rates), at which the two phases separate under the effect of gravity.

The vapor/gas phase tends to be distributed as small bubbles at low vapor flow rates for a constant liquid flow rate. Increasing void fraction causes the agglomeration of bubbles into larger plugs and slugs. Further agglomeration of slugs, caused by further increasing void fraction, causes separation of the phases into annular patterns wherein liquid concentrates at the channel wall, and vapor flows in the central core of the vertical channel.

For horizontal channels, gravitational force tends to drain the liquid annulus toward the bottom of the channel, resulting in stratified flow. The gravitational force acting on the liquid phase can be overcome by kinetic forces at high flow rates, causing stratified flows to revert to annular flows. At very high flow rates, the annular film is thinned by the shear of the vapor core, and all the liquid is entrained as droplets in the vapor phase. This flow regime is usually known as the mist flow.

See also: Engineering Data Book III, Thome, J.R., Wolverine Tube Inc, 2004.

Flow Patterns – Vertical Tubes

“Bubbly
In the bubbly flow, the liquid flow rate is high enough to break up the gas into bubbles, but it is not high enough to cause the bubbles to become mixed well within the liquid phase. The bubbles vary widely in size and shape, but most commonly, they are nearly spherical and are much smaller than the diameter of the tube.
Slug flow
Increasing void fraction causes agglomeration of bubbles into larger plugs and slugs. These slugs are similar in dimension to the tube diameter. These slugs travel at a speed that is a substantial fraction of the gas velocity and occur intermittently. Since these large gas slugs are separated from one another by slugs of liquid, they cause enormous pressure and liquid flow rate fluctuations. In some cases, a downward flow can be observed near the tube wall, even though the net flow of fluid is upward. This is caused by the gravitational force.
Churn flow
Churn flow, also referred to as froth flow is a highly disturbed flow of two-phase fluid flow. The increasing velocity of a slug flow causes the structure of the flow to become unstable. The churn flow is characterized by the presence of a very thick and unstable liquid film, with the liquid often oscillating up and down. Due to its nearly chaotic properties, it is one of the least understood gas-liquid flow regimes.

A typical example of churn flow is boiling flow in nuclear reactors during accidents. Especially for many accident scenarios, boiling may lead to a high void fraction, including churn-turbulent flow. Its flow structure and induced pressure changes may have a strong impact on safety.

Annular flow
Annular flow is a flow regime of two-phase gas-liquid flow. It is characterized by the presence of a liquid film flowing on the channel wall (forming an annular ring of liquid) while the gas flows as a continuous phase up in the center of the tube. The flow core can contain entrained liquid droplets. The velocity of the gas core is very large, and it is large enough to cause high-frequency waves and ripples at the interface. This flow regime is particularly stable, and it is desired flow regime for high-velocity, high-quality two-phase fluid flow.

Both adiabatic annular flows (without heat exchange) and diabatic annular flows (with heat exchange) occur in industrial applications:

In the case of BWR, in which a phase transition (evaporation) occurs, detailed knowledge of this flow regime is highly important. At given combinations of flow rate through a channel, pressure, flow quality, and linear heat rate, the liquid wall film may exhaust, and the wall may be dried out. This phenomenon is usually known as “dry out”. Dryout is accompanied by a rapid rise in wall temperature and is important in the safety of BWRs.

Mist flow
Mist flow is a flow regime of two-phase gas-liquid flow. It occurs at very high flow rates and very high flow quality. This condition causes the liquid film flowing on the channel wall to be thinned by the shear of the gas core on the interface until it becomes unstable and is destroyed. The flow core in the mist flow entrains all the liquid as droplets in the gas phase. Droplets may wet the tube wall, but this occurs intermittently and only locally. In the heated channel, the presence of a mist flow regime is accompanied by significantly higher wall temperatures and high fluctuation of wall temperatures.
Bubbly - Slug - Churn - Annular - Mist - Flow
Sketches of flow regimes for two-phase flow in a vertical pipe. Source: Weisman, J. Two-phase flow patterns. Chapter 15 in Handbook of Fluids in Motion, Cheremisinoff N.P., Gupta R. 1983, Ann Arbor Science Publishers.
flow patterns - vertical flow - Hewitt
The vertical flow regime map of Hewitt and Roberts (1969) for flow in a 3.2cm diameter tube, validated for both air/water flow at atmospheric pressure and steam/water flow at high pressure. Source: Brennen, C.E., Fundamentals of Multiphase Flows, Cambridge University Press, 2005, ISBN 0521 848040

Flow Patterns – Horizontal Tubes

“Bubbly
In contrast to the bubbly flow in the vertical channel, the bubbly flow in the horizontal channel is strongly influenced by gravitational force. Due to the buoyancy, bubbles are dispersed in the liquid with a higher concentration in the upper half of the channel. This regime typically occurs at higher flow rates because, at lower flow rates, the gravitational force tends to drain the liquid annulus toward the bottom of the channel, resulting in stratified flow.
“Stratified
In two-phase fluid flow, the gravitational force plays a very important role because the fluid with lower density (e.g.,, gas) is always above the fluid with higher density. Stratified flows are very common in nature, for example, in the ocean and the atmosphere. In the internal flows, the stratified flow occurs at low liquid and gas velocities. As the velocity of the gas increases, the horizontal interface becomes more disturbed, and waves may be formed. This flow regime is usually known as the stratified-wavy flow.
“Plug
Further increase in the gas velocity causes that waves reach the top of the tube. Whether the flow will be plug or slug flow depends especially on the void fraction that causes agglomeration of bubbles into larger plugs and slugs. In the plug flow, the diameters of the bubbles are smaller than the tube. Slugs are similar in dimension to the tube diameter. The slugs travel at a speed that is a substantial fraction of the gas velocity and occur intermittently. Since these large gas slugs are separated from one another by slugs of liquid, they cause large pressure and liquid flow rate fluctuations.
“Annular
Similar to vertical flow, at larger gas flow velocities, the liquid forms a continuous annular film on the channel wall. The horizontal annular flow is characterized by the presence of a thicker liquid film flowing on the bottom of the channel wall. The gas flows as a continuous phase in the center of the tube. The flow core can contain entrained liquid droplets. The velocity of the gas core is very large, and it is large enough to cause high-frequency waves and ripples at the interface. This flow regime is particularly stable, and it is desired flow regime for high-velocity, high-quality two-phase fluid flow.
Mist flow
Mist flow is a flow regime of two-phase gas-liquid flow. It occurs at very high flow rates and very high flow quality. This condition causes liquid film flowing on the channel wall to be thinned by the shear of the gas core on the interface until it becomes unstable and is destroyed. The flow core in the mist flow entrains all the liquid as droplets in the gas phase. Droplets may wet the tube wall, but this occurs intermittently and only locally. In the heated channel, the presence of a mist flow regime is accompanied by significantly higher wall temperatures and high fluctuation of wall temperatures.
bubble, plug, slug, annular, mist, stratified or wavy flow
Sketches of flow regimes for two-phase flow in a horizontal pipe. Source: Weisman, J. Two-phase flow patterns. Chapter 15 in Handbook of Fluids in Motion, Cheremisinoff N.P., Gupta R. 1983, Ann Arbor Science Publishers.
flow patterns - horizontal flow
A flow regime map for an air/water mixture flow in a horizontal, 2.5cm diameter pipe at 25◦C and 1bar. Solid lines and points are experimental observations of the transition conditions, while the hatched zones represent theoretical predictions. Source: Mandhane, J.M., Gregory, G.A. and Aziz, K.A. (1974). A flow pattern map for gas-liquid flow in horizontal pipes. Int. J. Multiphase Flow

Flow patterns during evaporation

The previous section describes various flow patterns and shortly describes their behavior. These flow patterns were considered to be at constant void fraction and constant superficial velocities. But many industrial applications have to consider a variable void fraction and variable superficial velocities. In the nuclear industry, we have to deal with flow patterns during evaporation (i.e., during changes in the void fraction).

Detailed knowledge of phase changes and the behavior of the flow during the phase change is one of the most important considerations in the design of a nuclear reactor, especially in the following applications:

  • convective evaporation - vertical channelBWR – Boiling Water Reactors
    • A boiling water reactor is cooled and moderated by water like a PWR, but at a lower pressure (7MPa), which allows the water to boil inside the pressure vessel producing the steam that runs the turbines. Evaporation, therefore, occurs directly in fuel channels. Therefore BWRs are the best example for this area because coolant evaporation occurs at normal operation, and it is a very desired phenomenon.
    • In BWRs, there is a phenomenon that is of the highest importance in reactor safety. This phenomenon is known as the “dry out” and is directly associated with changes in flow pattern during evaporation. At normal, the fuel surface is effectively cooled by boiling coolant. However, when the heat flux exceeds a critical value (CHF – critical heat flux), the flow pattern may reach the dry-out conditions (a thin film of liquid disappears). The heat transfer from the fuel surface into the coolant is deteriorated due to a drastically increased fuel surface temperature.
  • PWR – Pressurized Water Reactors
    • In PWRs at normal operation, the flow is considered to be single-phase. But a great deal of study has been performed on the nature of two-phase flow in case of transients and accidents (such as the loss-of-coolant accident – LOCA or trip of RCPs), which are of importance in reactor safety and in must be proved and declared in the Safety Analysis Report (SAR). In the case of PWRs, the problematic phenomenon is not the dry out. In the case of PWRs, the critical flow is an inverted annular flow. This flow occurs when a fuel rod cladding surface is overheated, which causes the formation of a local vapor layer, causing a dramatic reduction in heat transfer capability. This phenomenon is known as a departure from nucleate boiling – DNB. The difference in flow regime between post-dry outflow and post-DNB flow is depicted in the figure.
    • In PWRs, evaporation also occurs in steam generators. Steam generators are heat exchangers that convert feedwater into steam from heat produced in a nuclear reactor core. The steam produced drives the turbine.
 
Difference in the flow regime: Dryout vs. DNB
Dryout vs. DNB
convective evaporation - horizontal channel
 
Convective Evaporation - Vertical Channel
convective evaporation - vertical channelConvective evaporation in a vertical channel is depicted in the figure. This figure shows the typical order of the flow regimes that are encountered from inlet to outlet of a heated channel. At the inlet, the liquid enters subcooled (at the lower temperature than saturation). In this region the flow is single-phase. As the liquid heats up, the wall temperature correspondingly rises. As the wall temperature exceeds the saturation temperature (e.g., 285°C at 6.8 MPa), subcooled boiling begins. Bubbles nucleate in the superheated thermal boundary layer on the heated wall but tend to condense in the subcooled bulk.

Further increase in liquid temperature causes that the liquid bulk reaches its saturation temperature, and the convective boiling process passes through the bubbly flow into the slug flow. Increasing void fraction causes that the structure of the flow becomes unstable. The boiling process passes through the slug and churns flow into the annular flow regime with its characteristic annular film of the liquid. At given combinations of flow rate through a channel, pressure, flow quality, and linear heat rate, the liquid wall film may exhaust, and the wall may be dried out. At the dry-out point, the wall temperature significantly rises to dissipate the applied heat flux. The post-dry outflow (mist or drop flow) in the heated channel is undesirable because the presence of such a flow regime is accompanied by significantly higher wall temperatures and high fluctuation of wall temperatures.

Convective Evaporation - Horizontal Channel
Convective evaporation in a horizontal channel is very similar to the evaporation in the vertical channel. But gravitational force tends to drain the liquid toward the bottom of the channel for the horizontal channel, and the vapor phase concentrates at the channel’s top. Typical flow regimes, including cross-sectional views of the flow structure, are depicted in the figure below.

At the inlet, the liquid enters subcooled (at a lower temperature than saturation). In this region, the flow is single-phase. As the liquid heats up, the wall temperature correspondingly rises. As the wall temperature exceeds the saturation temperature (e.g.,, 285°C at 6.8 MPa), subcooled boiling begins. The convective boiling process passes through bubbly, plug regimes, and flow can be either stratified or unstratified (depending on the flow velocity). As can be seen, the channel dries out occurs at the top of the tube, where the film thickness is thinner due to gravitational force. Dryout then progresses around the perimeter from top to bottom along the channel.

convective evaporation - horizontal channel

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.
  10. White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN: 978-0077422417

See above:

Two-phase Flow