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682 CHAPTER 65 1962 Guide And Data Bool fig. 7 .... Performance of Hydrogen Liquefaction Cycles The simple Linde cycle is the most widely used cycle for hydrogen liquefaction. The modem Linde cycle (Fig. 6) uses Eubatmospheric liquid nitrogen as a precoolant and JouleThomson expansion for liquefaction. Particular notice should be taken of the provisions for gas and .liquid phase ortho para conversion. Overall, the advantages of the Linde cycle include its simplicity, proven design and relatively high yield. Disadvantages am its high operating pressure, liquid nitrogen requirement and high work value. (A typical Linde cycle work curve (Fig. 7) reveals minimum values 59 percent higher than the most efficient cycle shown.) The two critical design areas are the temperature approach at the warm end of the Joule-Tbomson beat exchanger and maintenance of the liquid nitrogen bath as close to the nitrogen triple point as practicable. The dual-pressure Unde cycle (Fig. 6) owes its existence to the fact that Joule-Thomson cooling is approximately pro portional to the expansion pressure ratio and compression work is .proportional to the logarithm of the compression ratio. Thus, the intermediate pressure stream produces most of its potentially available cooling but requires much less recompression work than the liquefaction stream which expands to one atmosphere pressure. Addition of a heat ex changer below the intermediate pressure expansion is a recent innovation which improves the performance of the cycle by reducing heat exchanger irreversibility. The advantages of the dual-pressure Linde cycle are that it retains much of the simplicity and proven design features of the simple Linde cycle and offers lower work values. Possible disadvantages of the cycle are its use of liquid nitrogen, high operating pressure, special compressor requirement, and Lower yield per pound of gas circulated than the Linde cycle. The precooled expansion engine cycle (see Fig. 6) repre sents a logical extension of hydrogen Iiquefier technology.' This cycle retains much of the simplicity of the simple Unde cycle butoffers the advantage of high efficiency at low operat ing pressures. The principal disadvantages of the cycle are its liquid nitrogen requirement and use of a low-temperature ex pansion engine. Critical design areas include design of the ex pansion engine and the heat exchanger which it brackets. From a performance and operating cost standpoint this cycle may represent the optimum since it has been shown that a combination of vapor cycle and expansion refrigeration is most efficient for supporting hydrogen liquefaction. The three-expander cycle (see Fig. 6) is an example of a class ofcycles which obtain all necessary auxiliary refrigeration from expansion engines.Since these are primarily low-pressurecycles they are particularly suited for large plants using turbo-ex* panders. Features of the three-expander cycle include its low liquefaction work requirement, low-pressure operation and absence of precooling liquid. Disadvantages of the cycle ioclude a relatively low yield and heavy reliance on efficient turbo-expanders. The most critical design problem is that of achieving high efficiency from the turbo-expaDders. Expander efficiences of from 75 to 85 percent of isentropic are required to make this cycle competitive with other modern cycles. In summarizing liquefaction cycles it can be said that in the past hydrogen liquefiera were based on the ample Unde cycle because of its simplicity and proven design. As indicated by the curves of Fig. 7 for larger liquefaction plants the dif- Cryogemes 683 faitccw in cycle performance become important enough to -jpport more complex systems. Low or intermediate pressure possibly with turbo-expanders, are indicated for future -Lnts deducing more than 20,000 liters of liquid per day. Table 1 .... Emfs of Some Thermocouple Materials at Low Temperatures (fnft Arc far Thwaoeotplii Mad* of Capper Witt the Indicated Alloy as (b* Ofbar Oaiuaulf liquefaction Equipment Pespite the low temperatures involved and hazardous na~ tjue of the material, hydrogen liquefiera are constructed with commercially available components to a great extent. With omvisions for explosion-proofing, purging or isolation, comjoercisl equipment is used exclusively for compressors, ?ftCTpifn pumps, instruments, controls and gas handling equip ment. Pgh pressure cycle heat exchangers, expansion valves, Squid valves, and liquid lines have been constructed as cus tom items. Brazed, extended-surface heat exchangers are commercially available for low-pressure cycles. Of all Iiquefier components, hydrogen turbo-expanders gtand ss the main item requiring some degree of development. Ibis is due to the high sonic velocity of hydrogen and the small size of hydrogen liquefiera built in previous years. The frigh sonic velocity of hydrogen imposes higher tip speeds on the turbine wheel than is common with air expanders and results in high rotative speeds for small units. However, even vith turbine wheels of 4 to 6 in. diameter, the possible throughput of a hydrogen expander is large. Thus, there is a minimum size of plant for which a turbo-expander is prac ticable. MEASUREMENT OF LOW TEMPERATURES Thegas thermometer is the mostaccurate means of determ mining the true thermodynamic temperature according to the definition of Lord Kelvin. Precision gas thermometry is an arduous and exacting occupation and requires complex and bulky equipment that is not suitable for ordinary practical temperature measurement. However, a simple constantvolume gas thermometer is sometimes very well suited for measuring low temperatures. Such a thermometer can con sist of a bulb having a volume of one or two cubic inches connected by a capillary tube to a manometer or dial pressure gage of small volume and filled with pure helium. The pres sure will be almost proportional to the absolute temperature of the' bulb, so calibration at a few points is sufficient. A vapor-pressure thermometer consists of a bulb partly filled with a volatile liquid or solid and partly with vapor in equilibrium with the condensed phase, connected by a pres sure-transmitting tube to a pressure measuring instrument. This instrument is especially adapted to certain applications because it is simple arul quite sensitive in certain temperature regions. Also its reproducibility is limited only by the pressure measuring device. The principal disadvantages of the vaporpretEure thermometer are its limited temperature range and its non-linear response. A precaution that should be observed --1 --- urw,r.nr#cnni t.hprmomftter is tO mometer. Thermocouples are widely used to measure low tempera- hires. They can be used in relatively inaccessible locations, have low heat capacity, respond quickly to temperature changes, and can be read at a convenient location. Their dis advantages are that they require expensive accessory equip ment and they become rather insensitive at very low temperahires. The sensitivity of all thermocouples approaches zero at absolute zero. Many materials have been used to construct thermocouples of which the most popular for low-temperature ose at the present time are copper and oonstantan. It is com- T K 0 2 4 6 8 10 12 14 16 18 20 25 30 60 70 90 100 110 120 180 190 240 300 OtiJiuniurty* Farce Au + 2.11 Atomic % Co mfcrovoft* 0.00 2.04 8.04 17.76 37.01 47.57 67.23 89.78 115.0 142.9 173.1 259.5 360.1 472.6 595.8 728.3 869.0 1171.1 1495.4 1836.3 2190.3 2555.8 2930.5 3312.6 3700.6 4093.2 4489.6 4888.7 5290.1 5693.3 6098.1 6504.0 6910.6 7317.6 7724.8 8131.9 8538.8 8945.3 9351.1 9756.3 10160.0 10564.0 ofcrovoOs 0.00 0.70 2.76 6.14 10.79 16.64 23.66 31.78 40.97 51.22 62.48 95.18 134.1 178.6 228.5 283.3 342.8 474.7 622.4 784.4 960.5 1149.8 1351.9 1566.5 1793.1 2031.8 2282.4 2545.0 2819.8 3106.7 3405.2 3714.1 4033.3 4362.7 4702.2 5051.9 5411.7 5781.5 6161.5 6551.7 6952.1 7362.9 -- Ag + 0.37 Atomic % Ao miera*oih 0.00 0.65 2.05 4.25 7.40 11.15 15.25 24.10 33.20 41.70 49.5 57.1 77.9 84.3 90.7 96.9 109.4 115.9 128.9 135.3 142.2 148.8 155.5 162.3 169.7 177.1 184.8 192.9 mon practice to calibrate a few pieces of wire from spools of copper and constant&n and use the calibration for all thermo couples made from the same two spools. The Constantsa wire should be of thermocouple quality for good results because some constant&n wire has inhomogeneities that will behave like local thermocouples and cause errors when they are lo cated in a temperature gradient. Thermocouple junction^ may be made with soft or hard solder or by welding. The method of making the junction will have no effect on the calibration of the thermocouple. For low temperature work it U usually advisable to use rather small thermocouple wire, for example, No. 30 BdsS gage. Care should be exercised in