G. I. Fuks.

Regenerative Process of a Refrigeration Machine

The cycle of a refrigeration machine of the vapor-compression system comes close to the ideal cycle of a heat engine, to the Carnot cycle. In particular, this resemblance is close when the machine operates with a wet stroke or with slight superheating at the end of compression. In any case, the absorption of heat by the refrigerating agent takes place completely, and the rejection of heat for the most part, at temperatures very close to constant. A substantial deviation that most strongly affects the lowering of the coefficient of refrigeration of the refrigeration-machine cycle is the process of expansion of the refrigerating agent in the regulating valve and, in part, the process of cooling the superheated vapor in the condenser when the machine operates with a dry stroke. Expansion in the regulating valve, moreover, indirectly affects the coefficient of refrigeration, since the consequence of this process is an increase in the weight and, consequently, in the volume of the working agent passing through the machine per unit time.

It is not possible to eliminate these losses by a constructive addition to the ordinary scheme of a refrigerating installation. Even in a carbon-dioxide machine, where the influence of the losses is greatest, replacing the regulating valve by an expansion cylinder has not yielded practical results.

The application of the regenerative principle in the scheme of a refrigeration machine makes it theoretically possible to eliminate completely these losses of the cycle and to indicate a more perfect, and in some cases practically more advantageous, scheme of operation.

Suppose (Fig. 1) that it is required to construct a refrigeration machine producing a specified number \(Q_1\) Cal of cold at an absolute temperature \(T_1\), lower than the ambient temperature \(T_2\). Let us assume that the apparatus giving up and absorbing heat operate at \(t=\mathrm{Const.}\), at least within certain limits, marked on the diagram by the lines \(ab\) and \(cd\).

Let us divide the entire interval \(T_2 - T_1\) into a certain number \(n\) of intermediate parts. Let us call the intermediate temperatures respectively \(T_1'\), \(T_1''\), \(T_1'''\), etc., up to \(T_1^{(n-1)}\). Draw the intermediate isotherms, and imagine a series of elementary refrigeration machines, \(n\) in number, operating between the temperature limits \(T_1\) and \(T_1'\), \(T_1'\) and \(T_1''\), …, \(T_1^{(n-1)}\) and \(T_2\), respectively, and the indicated side boundaries \(ab\) and \(cd\); on the other hand, the condenser of the indicated elementary refrigeration machines may, under certain additional conditions, which will be discussed below, be simultaneously imagined as the evaporator of the following elementary machine in the chain. We shall imagine the processes of expansion and compression in each of the elementary machines as proceeding without absorption or rejection of heat. The coefficient of refrigeration of each of the elementary refrigeration machines operating according to the Carnot cycle will be, respectively:

For the first machine:

\[ K_1=\frac{Q_1}{AL'}=\frac{T_1}{T_1'-T_1} \]

For the second machine:

\[ K_2=\frac{Q_1''}{AL''}=\frac{T_1'}{T_1''-T_1'} \ldots \ldots \ldots \ldots \ldots (1) \]

For the \(n\)-th machine:

\[ K_n=\frac{Q^{(n-1)}}{AL^n}=\frac{T_1^{(n-1)}}{T_2-T_1^{(n-1)}} . \]

Here \(AL'\), \(AL''\), \(\ldots\), \(AL^n\), \(Q_1\), \(Q_1'\), \(Q_1''\), \(\ldots\), \(Q_1^{(n-1)}\), respectively, are the works and heats imparted to the working agent in the first, second, \(\ldots\), up to the \(n\)-th machine.

Introducing the notations:

\[ \begin{aligned} T_1'&=T_1+\Delta T'\\ T_1''&=T_1'+\Delta T''\\ T_1'''&=T_1''+\Delta T'''\\ &\cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot \tag{2}\\ T_2&=T_1^{(n-1)}+\Delta T^{(n)} \end{aligned} \]

we compute the work of each elementary machine. We have:

\[ \begin{aligned} AL_1&=Q_1\frac{\Delta T'}{T_1}\\ AL'&=Q_1'\frac{\Delta T''}{T_1'}\\ &\cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot \tag{3}\\ AL^{(n)}&=Q_1^{(n-1)}\frac{\Delta T^{(n)}}{T_1^{(n-1)}} \end{aligned} \]

Summing these equalities term by term, we obtain:

\[ \sum AL=AL=Q_1\frac{\Delta T'}{T_1}+Q_1'\frac{\Delta T''}{T_1'}+\cdots+Q_1^{(n-1)}\frac{\Delta T^{(n)}}{T_1^{(n-1)}}\ldots \tag{4} \]

Adding and subtracting from each term of the right-hand side, with the exception of the first, a term of the form

\[ Q_1\frac{\Delta T^{(n)}}{T_1} \]

we obtain:

\[ \begin{aligned} AL=&\frac{Q_1}{T_1}\left(\Delta T'+\Delta T''+\Delta T'''+\cdots+\Delta T^{(n)}\right) +\Delta T''\left(\frac{Q_1'}{T_1'}-\frac{Q_1}{T_1}\right)\\ &+\Delta T'''\left(\frac{Q_1''}{T_1''}-\frac{Q_1}{T_1}\right) +\Delta T^{(n)}\left(\frac{Q_1^{(n-1)}}{T_1^{(n-1)}}-\frac{Q_1}{T_1}\right)\ldots \tag{5} \end{aligned} \]

But \(\Delta T'+\Delta T''+\cdots=\sum \Delta T=T_2-T_1\), by condition. The quantities \(\Delta T'\), \(\Delta T''\), \(\Delta T'''\), \(\ldots\), are, in essence, positive. The expressions standing in parentheses cannot be negative, for, as is easy to prove, this would lead to a contradiction with the second law of thermodynamics. In the present case, all these quantities are equal to zero. Indeed, the elementary refrigeration cycles, according to what was said above, are connected by the relation that the condenser of each stage is the evaporator for the subsequent stage. With only two heat sources of different temperature, this is possible only under the condition of equality of the corresponding heats. Considering the first elementary cycle, one may write:

\[ Q_1'=Q_1+AL'\ldots \tag{6} \]

Putting \(AL'\) from (3), and making use of (2):

\[ Q_1' = Q_1 + Q_1 \frac{\Delta T'}{T_1} = \frac{Q_1}{T_1} T_1' \quad \text{or:} \]

\[ \frac{Q_1'}{T_1'} - \frac{Q_1}{T_1} = 0 \tag{7} \]

For the second cycle:

\[ Q_1'' = Q_1' \frac{T_1''}{T_1'} \quad \text{or:} \]

\[ \frac{Q_1''}{T_1''} - \frac{Q_1'}{T_1'} = 0 \quad \text{etc.} \]

Then, finally, from (5) we have

\[ AL = \frac{Q_1}{T_1}(T_2 - T_1) \tag{8} \]

\[ K = \frac{Q_1}{AL} = \frac{T_1}{T_2 - T_1} \tag{8'} \]

Increasing the number of compression stages, in the limit as \(n=\infty\), we have a series of elementary cycles, the compression and expansion lines of which will differ from the corresponding segments of the boundary curves \(ab\) and \(cd\) only by infinitely small quantities of higher orders. Thus, considering the entire installation as a whole, we arrive at a refrigerating machine operating according to the cycle \(1234\), where \(12\) and \(34\) are the arbitrarily chosen compression and expansion lines of the working agent. The overall coefficient of refrigeration of the installation, according to (8) or (8′), is equal to the coefficient of refrigeration of the ideal Carnot cycle.

Carrying out the regenerative process.

The regenerative process considered is, in the final analysis, just as difficult to carry out practically as the Carnot cycle, since for its realization it requires an infinitely large number of intermediate (elementary) cycles. Nevertheless, it is of great interest, since it indicates a path toward increasing the coefficient of refrigeration of an ordinary refrigerating machine. Up to certain limits, at least, this increase in the coefficient of refrigeration of an ordinary refrigerating installation may prove, as shown below, to be practically advantageous. The determination of these limits is the task of what follows.

To solve this problem, let us consider the cycle of a vapor-compression refrigerating machine operating between given temperature limits \(T_1\) and \(T_2\). To replace this machine by a regenerative installation with \(n\) stages of compression, it is first of all necessary to determine what the operating limits of each stage should be, i.e. to find the positions of the intermediate isotherms.

In doing so it is assumed, in accordance with reality, that the process of obtaining cold in the evaporator of each stage takes place entirely at \(t=\mathrm{Const.}\), i.e. lies on the diagram (Fig. 2) between the boundary curves \(ab\) and \(cd\). The process in the condenser can only partly take place inside the boundary curves (dry stroke). In the rest, we leave the processes arbitrary.

Having drawn \(n-1\) intermediate isobars, let us call the isotherms corresponding to them within the region \(abcd\) \(T_{12}, T_{13}, \ldots, T_{1(n-1)}\). The beginning or end of the compression line of each stage lies on the boundary curve \(cd\).

For the first stage:

\[ Q_{21}=Q_{11}+AL_1 \qquad \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (9) \]

where \(Q_{21}\) is the heat given off in the condenser,

\(Q_{11}\) is the heat received in the evaporator of the first stage per \(1\ kg\).

The output of the first stage:

\[ K_1=\frac{Q_{11}}{AL_1} \qquad \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (10) \]

Correspondingly, for the 2nd, 3rd . . . \(n\)-th stage:

\[ \begin{aligned} Q_{22}&=Q_{12}+AL_2,\\ Q_{23}&=Q_{13}+AL_3,\\ &\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (9)\\ Q_{2(n-1)}&=Q_{1(n-1)}+AL_{(n-1)},\\ Q_{2n}&=Q_{1n}+AL_n, \end{aligned} \]

\[ \begin{aligned} K_2&=\frac{Q_{12}}{AL_2},\\[4pt] K_3&=\frac{Q_{13}}{AL_3},\\ &\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (10)\\ K_n&=\frac{Q_{1n}}{AL_n}. \end{aligned} \]

If the condenser of each stage serves simultaneously as the evaporator of the following one, then this can be carried out only in the case when no accumulation of heat occurs in this condenser-evaporator. It is clear that, under the condition of operation with only one agent, this is possible only when the weight quantity of working substance in the second, 3rd, etc. stage, per \(1\ kg\) of the agent of the preceding stage, is respectively \(g_2, g_3 \ldots g_n\).

Then the condition for the joint operation of the separate stages will be:

\[ \begin{aligned} Q_{21}&=g_2 Q_{12},\\ Q_{22}&=g_3 Q_{13},\\ Q_{23}&=g_4 Q_{14}, \qquad \ldots \ldots \ldots \ldots \ldots \ldots \ldots (11)\\ Q_{2(n-1)}&=g_n Q_{1n}. \end{aligned} \]

Substituting these relations into (10) and making use of (9), we have:

\[ \begin{aligned} K_1&=\frac{Q_{11}}{AL_1},\\[6pt] K_2&=\frac{Q_{21}}{g_2 AL_2} =\frac{Q_{11}+AL_1}{g_2 AL_2},\\[6pt] K_3&=\frac{Q_{22}}{g_3 AL_3} =\frac{Q_{12}+AL_2}{g_3 AL_3}, \qquad \ldots \ldots \ldots \ldots \ldots (12)\\[6pt] K_n&=\frac{Q_{2(n-1)}}{g_n AL_{(n)}} =\frac{Q_{1(n-1)}+AL_{(n-1)}}{g_n AL_{(n)}}. \end{aligned} \]

As a result of the operation of the whole installation, we shall obtain \(Q_{11}\) Cal. of refrigeration at temperature \(T_1\), having expended for this the work

\[ AL = AL_1 + g'' AL_2 + g''' AL_3 + \cdots + g^{(n)} AL_n \ldots \tag{13} \]

where \(g'', g''', g'''', \ldots g^n\) is the amount of agent operating in each stage per 1 kg of working agent of the first stage.

It is clear that:

\[ g'' = g_2 \]

Further:

\[ \begin{aligned} g''' &= g_2 g_3,\\ g'''' &= g_2 g_3 g_4,\\ &\cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\\ g^n &= g_2 g_3 g_4 \ldots g_n \end{aligned} \tag{14} \]

Then the work of the whole machine will be:

\[ AL = AL_1 + g_2 AL_2 + g_2 g_3 AL_3 + g_2 g_3 g_4 AL_4 + \cdots + g_2 g_3 \ldots g_n AL_n \ldots \tag{15} \]

and the overall coefficient of refrigeration capacity:

\[ K = \frac{Q_n}{AL} = \frac{Q_{11}}{AL_1 + g_2 AL_2 + \cdots + g_2 g_3 g_4 \ldots g_n AL_n} \ldots \tag{16} \]

For the final determination of \(k_1, k_2, \ldots k_n\) and \(k\), it is necessary to introduce one more condition. This is understandable, since condition (11) can freely be satisfied with any choice of the condensation (isotherm). Among the variety of possible conditions it is natural to choose the condition of equality of the works of the separate stages, i.e., to set:

\[ AL_1 = g'' AL_1 = g''' AL''' = \cdots = g^{(n)} AL_{(n)} \ldots \tag{17} \]

Then, from equalities (12) and (10), we have

\[ \begin{aligned} K_1 &= \frac{Q_{11}}{AL_1},\\ K_2 &= K_1 + 1,\\ K_3 &= K_2 + 1,\\ &\cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\\ K_{(n)} &= K_{(n-1)} + 1 \end{aligned} \tag{18} \]

which may also be written as:

\[ \begin{aligned} K_1 &= \frac{Q_{11}}{AL_1},\\ K_2 &= K_1 + 1,\\ K_3 &= K_1 + 2,\\ K_4 &= K_1 + 3,\\ &\cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\ \cdot\\ K_{(n)} &= K_1 + (n-1) \end{aligned} \tag{19} \]

The work of the whole refrigerating installation will be:

\[ AL = n \cdot AL_1 \ldots \tag{20} \]

and the coefficient of refrigeration:

\[ K=\frac{K_1}{n} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (31) \]

In the case where each stage operates according to the Carnot cycle, these equalities lead to an identical temperature difference. Indeed, in this case:

\[ K=\frac{T_1}{T_2-T_1}\quad \text{and} \]

\[ K_1=\frac{T_1}{\Delta T_1} \]

According to (21),

\[ \frac{T_1}{n\Delta T_1}=\frac{T_1}{T_2-T_1}, \text{ i.e.} \]

\[ \Delta T_1=\frac{T_2-T_1}{n} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots (22) \]

\[ K_2=K_1+1=\frac{nT_1}{T_2-T_1}+1 \quad \text{or} \]

\[ \Delta T_2=\Delta T_1 \]

Continuing further, we obtain:

\[ \Delta T_1=\Delta T_2=\Delta T_3=\ldots=\Delta T_n=\frac{T_2-T_1}{n} \ldots \ldots \ldots (22') \]

The coefficient of refrigeration will in this case be the same as that of a Carnot machine between the limits \(T_2-T_1\).

If, however, the separate elementary machines do not operate according to the Carnot cycle, but at least according to the usual cycle of a refrigerating machine, then, with equality of the separate works, there will be no equality of temperature differences, and the overall coefficient of refrigeration will, of course, be lower than that for the Carnot cycle. Nevertheless, it is clear that, with an increase in the number of stages, the coefficient of refrigeration of the entire installation approaches the ideal one more and more; i.e., the relative difference between an arbitrary cycle with two isotherms and the Carnot cycle between the same isotherms becomes ever smaller as the isotherms are shifted toward one another.

Taking into account the unreliability and complexity of the known equations of state of wet and superheated vapor, a number of graphical calculations were carried out on the \(JS\) diagram for multistage regenerative cycles of an ammonia refrigerating installation under various conditions. Table I gives the intermediate temperatures of some cycles.

TABLE I

This table shows that the separation temperatures lie very close to the theoretical ones, calculated according to the Carnot cycle. The deviations, at most about \(1^\circ\) C., are possibly caused by a certain inaccuracy of the table, whose scale is not sufficiently large for these calculations.

Having established this circumstance, one may construct, on the \(jS\) diagram, for the given temperature limits of operation of the refrigerating machine, a series of multistage cycles and calculate the coefficient of performance of each of them. In practice this is most simply accomplished by trial. Having estimated by eye the temperature \(T_{(n-1)}\), we construct on the diagram the cycle of the upper stage. Having determined its coefficient of performance, we calculate the coefficient of performance of the next stage by reducing the number obtained by unity.

For the wet cycle of a refrigerating machine (Fig. 3), moreover, one may regard as known the heat of the condenser of the \(n-1\) stages, per 1 kg of working agent, equal to the latent heat of vaporization at temperature \(t_{(n-1)}\). But, since

\[ \frac{Q_{2(n-1)}}{A l_{(n-1)}} = K_{(n-1)} + 1 = K_{(n)} \ldots \ldots \ldots \ldots \ldots \ldots (23) \]

one can calculate the work of the \(n-1\) stage and, plotting it on the diagram, determine graphically \(t_{(n-2)}\).

Continuing this construction, we arrive at the temperature \(t'_1 \gtrless t_1\)—the specified evaporator temperature. Depending on the result obtained, we repeat the construction, shifting the temperature \(t_{(n-1)}\) upward or downward. The practically possible variation of temperatures is so small that a satisfactory agreement is obtained with a small number of trials, even with a large number of stages.

For the dry cycle of a refrigerating machine (Fig. 4), only the beginning of compression of each stage is predetermined, namely, on the limiting curve. Nevertheless, having estimated, as before, the temperature \(t_{(n-1)}\), we determine \(K_{(n)}\) and \(K_{(n-1)}\). The selection of the end of compression of the \((n-1)\) stage presents no special difficulties in this case either, since to each point on the condensation isobar of the \((n-1)\) stage there corresponds a definite value of the heat content, from which one can calculate also the work of the \((n-1)\) stage and check them with (23). Here too the selection may be carried out within limits so small that in practice this is not difficult.

Having constructed the \((n-1)\) cycle, in the same way we construct \((n-2)\), and so on.

With a small number of stages it may prove more expedient to proceed by a somewhat different method. From the general relations (11) and (17) one may write:

\[ z_n Q_{1n} = Q_{1(n-1)} + A l_{(n-1)} \ldots \ldots \ldots \ldots \ldots \ldots (24) \]

\[ A l_{(n-1)} = z_n A l_n \ldots \ldots \ldots \ldots \ldots \ldots (25) \]

Eliminating \(z_n\), we have:

\[ \frac{A l_{(n-1)}}{A l_n} = \frac{Q_{2(n-1)}}{Q_{1n}} \ldots \ldots \ldots \ldots \ldots \ldots (26) \]

which, for the wet cycle of a refrigerating machine, gives the relation (Fig. 3).

\[ \frac{\Delta L_{(n-1)}}{\Delta L_{(n)}} = \frac{R_{(n-1)}}{J_3 - J'_n} \tag{27}^{1)} \]

from which, with the constructed cycle of the \(n\)-th stage, the work of the \((n-1)\)-th stage is determined.

For dry running, relation 26 is rewritten: (Fig. 4)

\[ \frac{\Delta L_{(n-1)}}{\Delta L_{(n)}} = \frac{J_4 - J'_{n-1}}{J''_{(n-1)} - J'_n} \tag{28}^{2)} \]

This relation makes it possible to check the correctness of the construction of point 4, since \(\Delta L_{(n-1)}\) and \(J_4\) are determined simultaneously.

By these methods, the coefficients of refrigeration were calculated for various operating conditions of the refrigerating machine and for various numbers of stages of compression. The results of some calculations are collected in Tables II and III.

TABLE II.

\(^{1)}\) \(R_{n-1}\) is the latent heat of vaporization at temperature \(T_{(n-1)}\), \(J_3\) is the heat content at point 3 (see Fig. 3), \(J'_n\) is the heat content of the liquid at temperature \(T_n\).

\(^{2)}\) \(J_4\) is the heat content of the vapor at point 4 (see Fig. 4), \(J''_{n-1}\) and \(J'_{(n-1)}\) are the heat contents of dry saturated vapor and liquid at temperature \(T_{(n-1)}\).

TABLE III.

From these calculations the following conclusions may be drawn:

1. The increase in the coefficient of refrigeration of the cycle of a refrigerating machine by introducing multistage compression with regeneration reaches rather considerable values. With a moderate number of stages (3–4), values of \(K\) are obtained that amount on average to 88–90% of the coefficient of refrigeration of the Carnot cycle.

2. The improvement in the performance of the refrigerating machine is especially considerable at large differences between the evaporation and condensation temperatures. The degree of perfection of the cycle, which can be evaluated by the ratio of the coefficient of refrigeration of the cycle to the coefficient of refrigeration of the Carnot cycle between the same temperature limits, already with 4 stages becomes almost independent of the temperature interval. This shows that in this way the loss of refrigerating capacity is in fact destroyed, the loss being a consequence of the irreversibility of the process of throttling the liquid in the regulating valve and of the nonconstancy of the cooling temperature of the superheated vapor.

3. The relative increase in the coefficient of refrigeration is considerably greater with dry operation of the refrigerating installation than with wet operation. In practice, refrigerating installations now usually operate with dry operation, and the reason for this may be considered clarified as a result of recent investigations in this field. Nevertheless, excessively high superheating is of no benefit. From the very principle of operation with regeneration it is clear that, in this case, the operation of the machine can take place in the region that is practically most advantageous in the sense of losses due to heat exchange between the working agent and the walls of the compressor cylinder.

4. For one and the same temperature difference, the improvement in the cycle is considerably greater in the case of a high condensation temperature than of a low tem-

temperature of evaporation. With expensive water for the condenser, or with its high temperature, the saving may prove so considerable that it fully justifies the introduction of five- and six-stage regenerative compression.

1. In practice, the most indicative are the last lines of each table. They show the gain in the degree of refrigerating capacity attained by multistage regenerative compression in comparison with an ordinary refrigerating machine, in %. Under average operating conditions of a refrigerating installation and with 3–4 stages of compression, this gain reaches 15–20%, a magnitude which can in no way be neglected in the balance of a refrigerating installation.

These figures have a quite real, and not merely theoretical, significance. According to the data of the German literature, it may be considered established that the degree of refrigerating capacity of a two-stage refrigerating installation is approximately 10% higher than that of a single-stage one (under average conditions). A glance at Tables 2 and 3 convinces us that this figure is higher than the theoretical gain. The reason for this must be sought in the loss of refrigerating capacity, not taken into account by us, due to the thermal influence of the walls of the compressor cylinder, which, naturally, will be smaller with smaller temperature limits for each stage.

The constructive realization of the regenerative multistage cycle is readily associated with a multistage turbocompressor. In this case the complication of the installation will be no greater than that which exists in the use of multistage turbocompressors in general. The intermediate coolers may be made in the gas passages from one stage to another.

The constructive scheme of a multistage regenerative refrigerating installation is shown in Fig. 5.

The compressor of the first stage draws the vapors of the refrigerating agent from the evaporator. The compressed vapor is sent to the first intermediate cooler, where it is condensed. An equal amount of liquid by weight passes through the first regulating valve into the evaporator.

The condensation of the vapor is effected at the expense of the heat of evaporation of the refrigerating agent operating in the second stage. This agent, in the form of liquid, is led through the second regulating valve from the second intermediate cooler into the first, and is drawn off from there in the form of vapor by the compressor of the second stage, and so on.

The compressor of the last, \(n\)-th stage sends all the vapor drawn from the \(n\)-th intermediate cooler into the condenser, where the vapor is cooled and condensed by water. Through the \(n\)-th regulating valve, the liquid from the condenser passes into the \(n\)-th intermediate cooler.

The intermediate coolers may operate by mixing or by surface heat transfer, depending on the structural features of the installation.

It must be expected that in the large refrigerating installations of the future, which by their very nature will be compelled to operate with a considerable difference between the evaporation and condensation temperatures, the multistage regenerative process will take the place appropriate to it. It should also be noted that, with a small constructive change, such an installation can yield a certain quantity of refrigeration at a temperature higher than the evaporator temperature, which in the practical balance of a refrigerating installation may also play its part.

To the article by Prof. G. M. Fuks, “Regenerative Process of a Refrigeration Machine.”

Diagram 1.

Labels visible in the diagram: \(T\), \(s\), \(a\), \(b\), \(c\), \(d\), \(1\), \(2\), \(3\), \(4\), \(T_2\), \(T_{n-1}\), \(T_{n-2}\), \(T'_2\), \(T'_1\), \(T_1\).

Diagram 2.

Labels visible in the diagram: \(T\), \(s\), \(T_2(T_{2n})\), \(T_{2(n-1)}(T_{1n})\), \(T_{2(n-2)}[T_{1(n-1)}]\), \(T_{2(n-3)}[T_{1(n-2)}]\), \(T'_{2,2}(T_{1,3})\), \(T'_{2,1}(T_{1,2})\), \(T_1(T_{1,1})\).

Diagram 3.

Labels visible in the diagram: \(J\), \(s\), \(t_2\), \(t_{n-1}\), \(t_{n-2}\), \(A l_n\), \(3A l_{(n-1)}\).

Diagram 4.

Labels visible in the diagram: \(J\), \(s\), \(t_2\), \(t_{n-1}\), \(t_{n-2}\), \(A l_n\), \(A l_{n-1}\), \(4_n\), \(4_{(n-1)}\).

Diagram 5.

Labels visible in the diagram:

• Compressor, \(n\)-th stage
• Condenser
• \(n\) R. х.
• Compressor, \(n-1\)-st stage
• \((n-1)\) intermediate cooler
• \((n-1)\) R. v
• \(k-2\) intermediate cooler
• Compressor, 1st stage
• 1 intermediate cooler
• 1 R. v
• Evaporator