Linde cycle

Figure 5.9 The Joule-Thompson cycle (Linde cycle). The gas is first compressed and then cooled in a heat exchanger, before it passes through a throttle valve where it undergoes an isenthalpic Joule-Thomson expansion, producing some liquid. The cooled gas is separated from the liquid and returned to the compressor via the heat exchanger.

FIGURE 2 (a) Schematic for simple Linde-cycle refrigerator (b) temperature-entropy diagram for cycle. 

The Linde cycle is a simple cryogenic process based on Joule-Thompson effect. It is composed of different steps the gas is first compressed, then preliminarily cooled in a heat exchanger using liquid nitrogen, finally it passes through a lamination throttle valve to exploit the benefits of Joule-Thomson expansion. Some liquid is produced, and the vapour is separated from the liquid phase and returns back to the compressor through the heat exchanger. A simplified scheme of the overall process is reported in Fig. 2.9. 

In a temperature vs. entropy diagram (Rankine diagram), we are able to see the four steps to liquefy a gas in the case of the Linde cycle. Figure 23.7 shows the starting gas g at experiments under isobaric conditions, a heating in a counterflow heat exchanger in (1). Secondly, it is compressed isothermically to (2) and then from (2) to (3) it is isobarically cooled in a counterflow... 

FIGURE 23.7 Temperature vs. entropy diagram for the Linde cycle of liquefaction. Details are given in the text. 

The Linde cycle works for gases, such as nitrogen, that cool upon expansion at room temperature. In the case of hydrogen, it warms upon expansion at room temperature. For hydrogen gas, the cooling upon expansion requires a temperature below its pressure-dependent inversion temperature Tj x, where internal interactions allow the gas to do work when it is expanded. 

The Claude cycle has the advantage of being more efficient than the simple Linde cycle on the basis of work per unit mass of gas liquefied. As a result, it is possible to operate at a lower compressor discharge pressure than in the Linde cycle. 

Fig. 4.4. Simple Linde cycle used as (a) a refrigerator or (b) as a liquefier with (c) the temperature-entropy diagram for both processes.

The simple Linde cycle may also be used as a liquefier for fluids that have an inversion temperature that is above ambient temperature. Under such circumstances, the refrigeration duty, Q, is replaced by a draw-off stream of mass rhf representing the liquefied mass of fluid that is continuously withdrawn from the reservoir. Note that under these conditions, only the unliquefied mass of fluid is warmed in the counter-current heat exchanger and returned to the compressor. An energy balance around the heat exchanger, expansion valve, and liquid reservoir now results in... 

Fig. 4.5. Precooled Linde cycle with corresponding temperature-entropy diagram. The auxiliary refrigerant may be any fluid which condenses at ambient temperature under pressure except when the working fluid is neon, hydrogen, or helium.

Note that the first term on the right-hand side of the equation is the liquid yield expected from a simple Linde cycle operating between pi and the lower and upper... 

Example 4.9. Find the theoretical liquid yield, work per unit mass liquefied, and the figure of merit for a simple Linde dual-pressure liquefaction system using air as the working fluid. The liquefier operates between 0.101 and 20.2 MPa. Inlet and exit temperatures for both compressors are maintained at 293 K. The intermediate pressure is 3.03 MPa and the flow-rate ratio, w,/aw, of this stream is 0.80. What is the work per unit mass liquefied and the figure of merit if the simple Linde cycle had been used to accomplish the liquefaction ... 

Application of this method to an actual process can best be demonstrated by a numerical example. Consider a simple nitrogen liquefaction process using the simple Linde cycle shown previously in Fig. 4.4b. Conditions for this process are indicated in Table 4.2. Assuming, for simplicity, that there is no heat... 

Determine the fraction of air liquefied in a simple Linde cycle if the inlet conditions on the warm side of the two-channel heat exchanger are 310 K and 20.2 MPa while the exit conditions are 303 K and 0.101 MPa. Repeat the calculations for inlet conditions of 208 K and 20.2 MPa with exit conditions of 200 K and 0.101 MPa. 

Find the fraction of normal hydrogen that is liquefied in a precooled Linde cycle when hquid nitrogen is used as the precoolant bath under the following two conditions ... 

The liquefaction of helium can be accomplished by using a precooled simple Linde cycle with normal hydrogen as the precoolant. The operating conditions for this system involve the compression of 12 kg/h of helium. Inlet conditions to the compressor are 0.101 MPa and 295 K while outlet conditions are 6.06 MPa and 295 K. The temperature of the liquid hydrogen bath is held at 23 K, corresponding to a saturation pressure of 0.202 MPa. The heat exchanger is assumed to be ideal. Determine the liquefaction rate of helium, the mass... 

System performance is directly related to the effectiveness of the heat exchangers used in the system. Consider the simple Linde cycle (Fig, 4.4) with a heat exchanger that is less than 100 % effective, as depicted in the T S diagram of Fig. 5.19. Since the heat exchanger is not ideal, the returning cold... 

Example 5.9. A simple Linde cycle is utilized to liquefy nitrogen and operates between 0.101 and 10.1 MPa. If the temperature of the high-pressure gas leaving the compressor is 300 K and the compressor operates isothermally and reversibly, what is... 

Solution. Figure 4.4b shows the simple Linde cycle utilizing a heat exchanger with an effectiveness of 1.0. The property values obtained from the temperature-entropy diagram and verified by the tabulations of Strobridge for this cycle are ... 

For what value of a does y = 0 On a temperature-entropy diagram, sketch the simple Linde cycle and show the path of the cycle when the effectiveness of the heat exchanger just reduces the liquid yield to zero. 

If the compressor utilized in the simple Linde cycle of Example 5.9 operates with a thermodynamic efficiency of 70 % and the heat exchanger has an effectiveness of 0.95, what is the effect on the liquid yield, work per unit mass liquefied, and the figure of merit for the liquefier in this example What heat leak per unit mass compressed will reduce the liquid yield to zero for this operating cycle ... 

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