The science of thermodynamics plays a major role in cryogenics. It underlies the various refrigeration cycles, from Carnot to Brayton (Cold Facts Vol. 32 No. 2) and Joule-Thomson, is a fundamental part of the definition of terms such as coefficient of performance (Cold Facts Vol. 31 No. 1) and even explains why it is more efficient to absorb heat at higher temperatures within cryostats (Cold Facts Winter 2009).

A driving motivation of engineers everywhere is to design systems that accomplish more using less energy while still working within the physical limits imposed by the laws of thermodynamics. One way to analyze this problem is to use the concept of exergy.

Engineers also define exergy as “availability” or “available work” and often think of it as the work available in the system to carry out certain activities, such as providing cryogenic cooling. When exergy is reduced, the loss of exergy is called irreversibilities. These irreversibilities exist in all real cryogenic systems and examples include pressure drop through heat exchangers, backflow through pumps, non-ideal expansions through valves and heat transfer through displacers in cryocoolers (Cold Facts Winter 2009).

There are many formulas for exergy, each dependent on specific situations, but a simple example based on a steady flow system is:
e = h – T0s

where for a given point in the thermodynamic process: e is the exergy per unit mass, h is the enthalpy per unit mass and s is the entropy per unit mass with T0 being the reference temperature, typically taken as the ambient temperature. By defining the exergy as a thermodynamic state function we can then calculate it based on the temperature and pressure of the flow at any point in the system.

In an exergy analysis (also sometimes called a “second law analysis”) engineers calculate the exergy and irreversibilities throughout the system or component under study and the system is optimized by trying to minimize the irreversibilities, thus maximizing the utilization of exergy.

While an exergy analysis can be complicated, it is a very powerful tool. Researchers can apply exergy analysis at all levels, from individual components such as heat exchangers to complete cryogenic plants and to integrated systems that include both the cryogenic plants and the components they are cooling.

Exergy analyses are valid for everything from small cryocoolers to large air separation plants (Cold Facts Vol. 31 No. 2). The results of such an analysis allow the designer to identify where the irreversibilities are, which in turn shows where engineering resources should be applied to optimize the system or component for better thermodynamic performance.

Figure 1 shows a typical result of an exergy analysis, this one for the entire cryogenic helium cooling system of the Large Hadron Collider. Note that the exergy is decreased by various irreversibilities as the analysis moves from the cryogenic refrigerators on the left hand side to the items being cooled on the right hand side. The relative sizes of the irreversibilities (i.e. the loss of exergy) indicate where additional engineering research and development efforts may provide the most benefit.

Engineers may also use exergy analysis to compare different plant cycles or cooling options for the same cryogenic load to find the optimal solution. A very thorough introduction to exergy and second law analysis, including some applications to refrigeration cycles, is given in “Advanced Engineering Thermodynamics” by A. Bejan, Wiley (2016). Examples of using exergy analysis to examine integrated cryogenic systems are given in “Exergy Analysis of the Cryogenic Helium Distribution System for the Large Hadron Collider (LHC),” S. Claudet, Ph. Lebrun, L. Tavian and U. Wagner, Adv. Cryo. Engr. Vol. 55 (2010) and “Integrated Design of Cryogenic Refrigerator and Liquid Nitrogen Circulation Loop for HTS Cable,” H.M. Chang, K.N. Ryu and H.S. Yang, Cryogenics, Vol. 80 (2016).

An example of using exergy analysis to compare different cryoplants is given in “Exergy Analysis of Large-Scale Helium Liquefiers: Evaluating Design Trade-Offs”, R.J. Thomas, P. Ghosh and K. Chowdhury, Adv. Cryo. Engr. Vol 59B (2014). And an application of exergy analysis to cryocoolers is provided in “Exergy-Based Figure of Merit for Regenerative and Recuperative Heat Exchangers with Applications Multistage Cryocoolers,” A. Ravex, C. Dodson and T. Fraser, Adv. Cryo. Engr. Vol 57B (2012).