Two-phase flows are those flows in which there is a mixture of two physical states (solid, liquid or vapor). In cryogenic applications, such flows are almost always a mixture of a cryogenic liquid along with its corresponding vapor. A mixture of liquid helium
and helium vapor would be a typical example.

While the complexity and potential issues of two-phase flows are such that they are frequently avoided in cryogenic designs (see Defining Cryogenics in Cold Facts, Vol 32 No 3), there are cases where two-phase flows are either desirable or unavoidable. Two-phase flows are found in many areas of cryogenics including LNG, large-scale helium systems and space cryogenics.

A principal advantage of two-phase flows is that they can provide isothermal heat sinks. Due to the latent heat of boiling, heat added to the liquid part of a two-phase flow will convert liquid to vapor in the two-phase flow but will not increase the mixture’s temperature. This feature is used in the cooling schemes of the Tevatron, HERA and Large Hadron Collider (LHC) magnets and in most superconducting radio frequency cavity systems such as the X-ray Free Electron LASER (XFEL).

Two-phase flows are also important in thermosyphon systems (see Defining Cryogenics in Cold Facts, Spring 2012) where the density difference between the liquid and gas phases drives the natural convection heat transfer that provides cooling.

There are a number of disadvantages to two-phase flows. These flows typically have a higher pressure drop when flowing though pipes and other components, flow instabilities may develop that result in pressure surges and vibrations, incorrectly designed systems may trap the vapor phase against surfaces resulting in inadequate cooling and many flow components such as pumps, flow meters and turboexpanders may not function properly in two-phase flows.

In addition, in cases where the flow is on an incline (a common occurrence in particle accelerator tunnels), all the liquid may flow to the downhill side. This may necessitate the use of weirs or shorter flow paths to maintain the desired liquid-vapor ratio.

Due to these issues and complexities, detailed modelling and sometimes experimentation is required whenever two-phase flows are used in cryogenic systems, to ensure proper performance. Care must also be taken that a nominally single-phase (say pure liquid) flow in a system does not suddenly become twophase due to heat inputs or pressure drops resulting in unexpected problems.

One way to characterize two-phase flows is by their flow regimes, which describe the arrangement and relative fractions of the liquid and vapor in the flow.

In non-cryogenic fluids, the Baker diagram provides a map of the various flow regimes as a function of flow properties. Experiments by Theilacker and Rode at Fermilab National Accelerator Laboratory (CSA CSM) showed, however, that the Baker diagram isn’t valid for two-phase helium and provided an alternative diagram. Their research on helium flow regimes can be found in “An Investigation into Flow Regimes for Two-Phase Helium Flow,” J.C. Theilacker and C. Rode, Adv.Cryo.Engr. Vol. 33 (1988).

Extensive modelling and experimentation was carried out for the particular case of He II two-phase flow in support of the LHC and International Linear Collider projects. One outcome of this research was the determination of an upper limit for the velocity of the vapor phase that should not be exceeded if one wanted to remain in the desirable stratified flow regime.

An introduction to two-phase flow may be found in Cryogenic Two-Phase Flow, N.N. Filina and J.G. Weisend II, Cambridge University Press (1996).

An example of the use of two-phase flows to cool large magnets via a thermosyphon is given in “The Cryogenic System for the Superconducting Solenoid Magnet of the CMS Experiment,” D. Delikaris et al., Proceedings of Fifteenth International Conference on Magnetic Technology (1997).

Other examples of two-phase cooling are “Forced Two-phase Helium Cooling Scheme for the Mu2e Transport Solenoid,” G. Tatkowski et al., Adv.Cryo.Engr.-IOP Conf. Series: Materials Science and Engineering 101 (2015) and “Superfluid Helium Cryogenics for the Large Hadron Collider Project at CERN,” P. Lebrun, Cryogenics 34 (1994).

Examples of modelling and experiments on He II two-phase flow include: “He II Two Phase Flow in an Inclinable 22 m Long Line,” B. Rousset et al., Adv.Cryo.Engr. Vol. 45a (2000) and “An experimental and numerical study of He II two-phase flow in the TESLA test facility,” Yu Xiang, et al. Cryogenics 42 (2002).

Examples of work on cryogenic twophase flows are given in “Two-phase heat transfer and pressure drop of LNG during saturated flow boiling in a horizontal tube,” D. Chen and Y. Shi, Cryogenics 58 (2013) and “Hierarchy of Two-Phase Flow Models for Autonomous Control of Cryogenic Loading Operation,” D. G. Luchinsky et al., Adv.Cryo.Engr.-IOP Conf. Series: Materials Science and Engineering 101 (2015).