Collins liquefier

Helium gas in a Collins liquefier is compressed isothermally and reversibly from 0.101 MPa and 300 K to 1.41 MPa. After cooling this compressed gas to 60 K, 25% of the gas is expanded in the first expander to 0.101 MPa. The remaining gas is further cooled to 15 K where 50% of the original compressed gas is expanded in a second expander to 0.101 MPa. If both expanders operate adiabatically and reversibly, determine the liquid yield, work required per unit mass of helium compressed, work required per unit mass of helium liquefied, and the figure of merit, assuming that the expander work is dissipated externally. Determine these same quantities when the expanders have a thermodynamic efficiency of 70% and the compressor has an overall efficiency of 75%. 

We will then describe the Collins helium liquefier and coolers which use turboexpanders (Linde He liquefier). At the end of the chapter, we will describe cooling cycles which use regenerators and other cycles used in cryocoolers (Philips-Stirling, Gifford-McMahon (GM), Klimenko cycles and pulse tube refrigerators (PTRs)). 

For laboratory production of LHe, other so-called Collins-type liquefiers have been built with one or two stages of GM cooling before the Joule-Thomson expansion (e.g. ref. [50]). The thermodynamic analysis of Collins helium liquefaction cycle can be found in ref. [51]. 

In the past, liquid helium was supplied by a Collins cryostat and a small 4-liter/hr Joule-Thomson hydrogen-precooled helium liquefier. The total production of both was approximately 8 liters/hr. Present and short-term future requirements indicated a definite need for a liquefier of at least twice this capacity. 

The work of Kapitza [7] and the exceptionally notable developments of Collins [8] had in common the utilization of expansion engines in combination with counterflow heat exchangers, and both were successful in liquefying helium. The Collins system was the first to use multiple engines operating at intermediate temperatures and thereby eliminate the need for any auxiliary refrigeration. This feature, combined with certain constructional advantages [9], has led to a wide acceptance of the Collins system for helium liquefaction. 

The early concepts of Kirk and Stirling in which a reciprocating-flow thermal regenerator is used in place of a countercurrent heat exchanger have recently been refined and developed effectively into an air liquefier by the Philips Company [10]. The system is characterized by the use of two articulated pistons which provide a compression space and an expansion space, interconnected through a thermal regenerator. Unlike the Kapitza or Collins system, there are... 

Still another extension of the Claude cycle is the Collins helium liquefier, schematically represented in Fig. 4.18 with a typical set of operating conditions. Depending upon the helium inlet pressure, from two to five expansion engines are used in this system. The addition of a liquid nitrogen precoolant bath to this system results in a two- to threefold increase in liquefaction performance. 

Using mass and energy balances, derive suitable equations for the liquid yield and work per unit mass compressed for a Collins helium liquefier utilizing two expanders. Assume all of the components of the system except the expansion valve are ideal and that the work from the expanders is utilized in the compression process. Derive similar equations for a Collins helium liquefier that uses a nitrogen bath to precool the compressed helium gas before entering the first expander. 

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