^ Conventional gas compressors and expanders are often

^ classified in two groups corresponding to the principle of pressure change; static or dynamic action machines. They all have in common that the pressure change takes place more or less adiabatically, i.e. with relatively little exchange of heat with the surroundings, since the surface available for heat transfer during the process is much too small to allow any appreciable deviation from this regime. This causes a loss of power compared with a theoretical isothermal process.

One common design of a static or positive displacement machine is the reciprocating or rotating piston compressor. These types are normally used in a single stage up to a ratio of discharge to suction pressure of 6 - 8 and some times even higher, depending on the properties of the gas to be pumped and other working conditions. Consequently the adiabatic loss becomes quite important. Only at very high overall pressure ratios will a machine with two or more stages be used since this is an expensive solution. The power saving at moderate pressure ratio is not sufficient to pay for this more complicated design.

Another popular positive displacement type of compressor/expander is the screw machine. Its operational properties are similar to those of a piston machine, although there is a tendency to use it at even higher pressure ratios in a single stage.

Turbo machines operate on the dynamic principle, conver¬ ting high flow velocities into pressure, and are used exten¬ sively for large flow volumes. Although the pressure ratio per stage is limited, in particular for compressors, inter- cooling or heating between stages is rarely done. Due to the particular design conditions of such machines it would be too

< complicated and expensi.ve to provi.de for bringi.ng the gas out and back again for each stage. Only in the case of very high overall perssure ratio, when some intercooling or heating is

unavoidable, this is done by using two or more machines in series, each containing a fair number of stages, and executing the heat exchange in transferring the gas from one unit to the next. The adiabatic power loss becomes at least as large as for the common positive displacement machines.

Gear type machines are extensively applied as pumps and motors in hydraulic power systems. With a nearly incompres¬ sible liquid working fluid, normally oil, they can operate with very high efficiency at extreme pressure ratios. Some times similar machines are used as expanders in pneumatic systems for the operation of small power tools or starting of internal combustion engines. In such cases, with single stage operation and relatively large pressure ratio, the power efficiency becomes very poor.

A somewhat similar design, the "Roots blower", using meshing rotors with a profile to give continuous tightness, is some times used as a compressor for low pressure ratio. The common type uses two lobes, but three or up to four lobes are also found. Since the rotors are not fit to transmit power, they have to be synchronized by a separate set of gears. Two or three pair of rotors are some times used in series in order to increase the pressure.

It has been proposed to use multistage gear or Roots machines for the expansion or compression in open systems, i.e. sytems open to the atmosphere. Some patents pertaining to such applications can be referred to: - German patent application DE 3613734 Al (H. Bindert) describes a gear type machine to be used as an internal combustion motor with expansion of the exhaust gas through one or several stages of a gear expander with increasing flow volume.

DDR patent 123960 (A. Bauml) concerns a multistage gear or rather Roots type compressor, where all the stages are equal in design and volume capacity, sucking in air in parallel from the atmosphere at the same pressure. The discharge from one stage is delivered to the next one and injected into the void-space between the rotor lobes in

passage between the suction and discharge openings, thereby increasing the pressure approximately in arithmetic sequence (2x in the 2nd. stage, 3x in the 3rd. stage...). This leads to excessive pressure differences in the later stages.

French patent 660.528 covers a multistage Roots type compressor with up to four stages with diminishing volume capacity by reduction of the width of the rotors from one stage to the next. The machine is equipped with a water jacket, which can obviously provide only a very limited cooling of the gas during compression. For large pressure increase it is foreseen to use two or more machines in series in the usual way.

German patent 1243816 (Leybold) describes a Roots type vacuum pump with at least two stages, where the low pressure stage is placed in the middle between two parts of a later stage, which has been divided for this purpose. The object of this arrangement is to avoid the entry of lubricating oil into the low pressure stage. German patent 1903297 (A. Bader) concerns a gear pump primarily for lubricating oil with two parallel rotors, which can be driven with different speed of revolution. The purpose of this arrangement is to regulate the rate of flow.

None of the systems described have any provision for interstage heat exchange or other arrangements to adapt them •to the generation of a desirable thermodynamic cycle.

The main purpose of the present invention is to permit designing thermodynamic systems to approach any desired theoretical cycle of pressure and temperature variation. Currently available equipment is suffering from considerable restrictions and lack of flexibility in this respect:

Compression and expansion has to be nearly adiabatic over quite large increments of pressure. - Although gliding temperature heat exchange can be realized either by using gases which are non-condensible in the actual range (Joule or Brayton cycle) or zeotropic

mixtures of condensible fluids, both of these solutions present strong restrictions in the choice of temperature curves. There are bindings leading to mismatch in the heat exchangers.

Similarly, when a trans-critical process is used to generate near constant temperature in the low side heat transfer with phase change and a continuous temperature glide at the high side, a satisfactory match is difficult to achieve.

According to the present invention these difficulties inherent of the prior art are eliminated or at least substan¬ tially reduced and the above purpose achieved by applying multistage gear compressors and expanders in combination with interstage heat exchangers and appropriate other equipment like liquid separators, evaporators, condensors, mass exchan¬ gers, throttling devices etc, as specified in the appending patent claims.

A gear machine which lends itself to a design with many stages and smaller pressure increments, without much penalty in extra costs, can serve to relieve many of the normal restrictions.

By a multistage "gear machine" is meant a machine in which pairs of meshing gears, e.g. like those of a gear pump, are utilized to compress or expand a working fluid flowing through the machine. Also machines of the above discussed Roots type, having not more than two teeth per gear are con¬ templated for the systems of the present invention. However, gears of the ordinary hydraulic pump type, having at least seven teeth, are much preferred.

Another advantage of many compression or expansion stages and correspondingly small pressure increments is that internal leakage in the machine is reduced to a minimum without extreme demands on the design. The entire aggregate has the character of a labyrinth seal. Also since the machine is completely balanced and can be built with large inlet and outlet gates, it lends itself to operation at high speed. This favours compact design and moderate cost.

A special benefit of a gear machine is its complete insensitivity to liquid slugging. It is therefore problem- free to apply it for compression and expansion of gas/liquid mixtures or even pure liquids.

Further objects and advantages of the inventon will appear from the following description of various embodiments thereof, with reference to the drawings in which:

Fig. 1 is a schematic longitudinal section through a preferred embodiment of a multistage gear machine according to the invention,

Fig. 2 is a cross-section taken on lines A-A in fig. 1,

Fig. 3 is a flow diagram illustrating the gas flow through the machine shown in fig. 1,

Fig. 4 is a PV diagram indicating the theoretical com¬ pression curve when using the multistage gear compression machine as shown in fig. l and when using a conventional adiabatic single stage compressor for the same pressure ratio,

Fig. 5 is a diagram illustrating the influence of the number of stages on the theoretical energy consumption,

Fig. 6a is a flow diagram like fig. 3 showing a detail of an advantageous embodiment of the invention,

Fig. 6b is a PV diagram showing the compression curve using the embodiment of fig. 6a,

Figs. 7a and 7b are a system and T-s diagram respectively illustrating a typical prior art heat pump, while

Figs. 8a and 8b are similar diagrams showing a heat pump system according to the invention.

Figs. 9a, 9b and 9c are system, T-s and PV diagrams respectively illustrating another eaxmple of a heat pump or refrigeration system based on the principles of the present invention.

Fig. 10 is a part sectional view of a gear machine.

Figs, lla and lib are system and T-s diagrams respec¬ tively of another typical prior art trans-critical heat pump or refrigeration plant, while

Fig. 12a and 12b are similar diagrams of a corresponding system according to the invention, and

Fig. 13a, 13b and 14a, 14b are diagrams illustrating yet another comparative example of a prior system versus a system according to the present invention.

The multistage gear machine 1 shown in figs, l and 2 is described as a compressor below, but it may also be used as an expander as appearing from one of the examples to follow. It is generally comprised of a casing 2 in which a series of pairs of mating, cylindrical spur gears are supported. In the example shown there are four pairs, designated I, II, III and IV respectively, each of which constitutes a stage of the compressor 1, "I" representing the lowest pressure stage and "IV" the highest one. One of the gears of each pair I - IV is mounted on a common drive shaft 3 while the other gear of each pair is mounted on a common, idle shaft 4 driven via the gear transmission. Shaf s 3 and 4 are supported in bearings 3' , 4' respectively. Stages I - IV are separated by partition walls 5 forming, together with circumferential walls 6 encircling the gears, a chamber having inlet and outlet ports or gates 7 and 8 respectively for each pair of gears, and having the least possible clearing thereto without preventing rotation of the gears. The partition walls 6 may be provided with circum¬ ferential seals (not shown) engaging the gear lateral surfaces for sealing between the individual stages, and a shaft seal 9 prevents gas leaking from stage I to the exterior.

As appearing from fig. 1 and 2 the gear pairs are arran¬ ged in a relationship of successively reduced transport volu¬ me, or with other words in a manner such that the volume rate of flow of the gas to be compressed is successively reduced from stage to stage during the compression process.

In the embodiment of the multistage gear compressor 1 according to the invention this is achieved by using gears having same diameter in all stages and gradually reduced width from the first to the last stage, such as shown in fig. 1. This results in a simple and economic structure. However, the same effect could be achieved in another way, such as by equal gear width and gradually reduced diameter.

The gear pairs I - IV may be formed in any practical

manner and from any convenient material known to persons skilled in the art, e.σ. such as those used in conventional hydraulic gear pumps. Like for the latter various modifica¬ tions to provide deviations from ordinary tooth profiles may be made, in order to obtain a higher efficiency and reduced pressure pulses and noise. The gears may also be formed from self-lubricating plastics or sintered materials. The number of teeth on each gear would be selected from considerations of the required flow rate capacity of the machine and should preferably be as few as convenient while ensuring a problem- free pøower transmission. Normally from seven to twenty teeth would be used.

As schematically indicated in the flow diagram shown in fig. 3 the gas to be compressed, e.g. air at atmospheric pressure P _Q and temperature T , upon being compressed to pres¬ sure P. and temperature T. in the first stage I, is directed in series through passages or conduits 11, 12, 13 including gas conditioning means 11', 12', 13', such as heat exchangers, to cause intercooling between the subsequent stages II - IV. Preferably, according to the invention such intercooling would take place in a manner so as to bring the gas which, owing to the compression process, has a temperature at the exit of each stage higher than the initial temperature T ₀ , back to the latter temperature T during the cooling process before enter¬ ing the subsequent stage. This is indicated in the PV chart, fig. 4, in which the curve T _Q represents the isothermal for this temperature.

As is wellknown an "ideal" compression process involving the least possible loss of energy will follow an isotherm, which is a theoretical process not easily realized in prac¬ tice. Through the above described process using the multi¬ stage gear machine according to the invention there will be no volume displacement between the two profiles within the indi¬ vidual stages while passing from the lower to the higher pressure, and the compression takes place by back flow from the pressure side when the tooth space opens to the latter.

No gas displacement occurs until the tooth profiles engage upon leaving the pressure space, which results in an energy loss. In the fig. 4 diagram this loss is represented by the area of the shaded triangles above the isotherm T _fi . It is evident from that diagram that by using a sufficient number of stages and intercooling this loss could be made as small as desirable. In practice the pressure ratio across each stage should not be higher than 2, for example, which normally would imply a corresponding ratio between the transport volume of the individual stages, i.e. between the width of any adjacent pair of gears in the example described above and shown in figs. 1 - 2.

For comparison, the diagram on fig. 4 also indicates the theoretical compression curve S (constant entropy) for a typical adiabatic single stage compressor working with the same pressure ratio. As seen the curve S _Q deviates more from the isotherm _n the higher the pressure ratio. By using a multistage gear compressor and cooling the gas between the stages, the isothermal curve T_ can be approached and the power consumption reduced, in spite of the fact that the gear machine has a generic loss due to the lack of volume displace¬ ment between suction and discharge openings. Thus, the energy gained by using a multistage gear compressor according to the invention is represented by the unshaded area between the adiabatic curve S and the "step-wise" curve I - IV above the isothermal curve T _Q with the deduction of the shaded area above the adiabat.

Naturally the same theoretical energy gain would be obtained by using a conventional compressor having several stages as well. However, a such multistage type of conven¬ tional compressor would have to be large and expensive and rather unpractical.

The crux of the invention lies in the recognition of the fact that actual thermodynamical processes, such as in heat pump, refrigeration systems etc, can be made to approach the corresponding theoretical or "ideal" processes, in an eco¬ nomical and practical manner, by incorporating a multistage

gear machine of the above described type in the thermodynamic system. Owing to its simple construction, based on conventio¬ nal, cylindrical spur gears, such a machine can be made very compact and at low costs, even with a considerable number of stages.

It is customary in multistage compressors (and expanders) to use a more or less constant pressure ratio in the different stages, i.e. Pl../Po = P2„/P.1....etc. This is close to the energy optimum. The same rule can be applied for gear machines, but frequently it may be expedient to distri¬ bute the pressure lift differently with a view to adapt to a particular process pattern. The choice of the number of stages must depend primarily on a reasonable balance of in¬ vestment and energy efficiency. The larger the number of stages, the better the efficiency and the more expensive the system. A sample calculation of a simple compression process can serve to illustrate the situation:

Let us assume that we are compressing air (adiabatic exponent K = 1.4) from 1 to 5 bar (Pl/Po=5) . By a reversible adiabatic process in a single stage (normal compressor) the theoretical power consumption per kg gas at 20"C entry temperature (V = 0.8409 m 3/kg) will be

Wad, = —K p*o vO ^~ (-£- ¹ - ll ^{= 171} * ⁸ ^/^

If on the other hand it had been possible to realize an ideal isothermal process, the corresponding power requirement would have been

Wi.s = p*o . voIn —p = 135.3 kJ/'kg^ with a step-wise compression in 5 stages, which seems reasonable for a gear machine for the given conditions, the

₅ pressure ratio per stage could be π = - = = 1.38 and the corresponding theoretical power

W _κ = 5 (77 - 1) P*o ^v o 159.7 kJ/kg

This is considerably less than for the conventional single stage adiabatic machine, but of course higher than for the ideal isothermal process.

If the cheapest possible machine is wanted, a lower number of stages n should be chosen. A larger number will improve the efficiency within a reasonable limit at some extra expense. The following table can give an indication of how the power requirement per kg gas varies with n for the same conditions. It is clear that an increase beyond n = 5 gives only a very limited improvement in the present case. At increasing n the effect of friction losses will also have to be considered.

n

_N kJ/kg 179.1 159.7 152.2

The same relationship is shown in greater detail in Fig. 5, indicating how the number of stages n influences the theo¬ retical power requirement W at varying overall pressure ratio P/Po. A comparison of the different processes was also shown in the PV diagram Fig. 4 (for 4 stages) where the theoretical power is represented by the area enclosed by the trace of the process in question.

At a given volume ratio of the various stages their pressure ratio is also decided, independent of the overall pressure lift. The last stage will automatically adjust its pressure to fit the delivery, however, while the other stages remain unaffected. In order to avoid overcompression in cases when the discharge pressure can fluctuate more than the last stage can absorb, the last but one (or possibly the two or three last but one stages) can be fitted with a special relief check valve 16 and bypass to the outlet 17 as indicated schematically on Fig. 6a for a compressor of 5 stages raising the pressure fron P to P.. By this devise the part of the compressor which would otherwise work with an excess pressure,

will be unloaded. The corresponding PV diagram under these conditions appears in Fig. 6b. This represents a further advantage over the normal rotary compressors with continuous displacement and a built-in constant volume ratio. The number of stages must always be sufficient for the compressor to manage the maximum overall pressure lift to which it will be exposed.

A multistage gear machine can, as already mentioned, be used equally well as an expander with or without interheating. The high pressure gas is supplied to the set of gears with the smallest transport volume and made to pass successively through stages of increasing flow capacity. The last stage will automatically adjust to a change of the back-pressure within its range capability. When large variations have to be coped with, it will be expedient to equip the last but one and possible more stages with check-valve(s) opening in the direc¬ tions into the machine and connection(s) to the outlet. These will function in a similar way as described for the compressor and prevent over-expansion at reduced pressure ratio.

A multistage gear machine can be applied equally well to compression and expansion. By interstage heating between stages an isothermal expansion process can be approached, or for that matter adapted to another desired gliding temperature variation. This may be useful for instance in designing thermal power processes.

As an example of using the principles according to the invention in designing a suitable thermodynamic process we can take a heat pump for raising the temperature in a finite flow of liquid or gas from temperature t to t_. The heat pump takes low temperature heat from the ambience (at T ) .

A schematic system diagram and temperature/entropy (T-s) chart for the normal, prior art process of a compression heat pump, using an evaporating and condensing working fluid, is shown in fig. 7a and 7b respectively. A single stage conven¬ tional compressor 20a, e.g. of the reciprocating or rotary type and driven by a motor 22, sucks in gas in a saturated or slightly superheated state A and compresses it in a single

stage to the considerably superheated state B. The gas is then cooled and condensed at a near constant temperature and pressure in the condensor 24 to a state C of slightly sub- cooled liquid. It is then irreversibly throttled in the expansion valve 26 and supplied to the evaporator 28 in state D. After evaporation in evaporator 28 by absorption of ambi¬ ent heat the gas is again supplied to the compressor 20 in state A. As appearing from the T-s chart 7b the heat transfer to the fluid to be heated from t to t takes place with a considerable temperature difference, causing an important loss of power, which means a low efficiency process.

An alternative system according to the invention is illu¬ strated in fig. 8a and 8b, again giving a schematic system diagram and T-s chart respectively. Gas from the evaporator 28' at state A' is sucked into the first stage of the 4 stage gear compressor 20' driven by motor 22'. After a first com¬ pression in two stages I and II it is cooled from state B' and partly condensed in the first section "a" of the condensor 24'. After separation of the liquid in liquid/gas separator 30 the remaining gas is further compressed in the next com¬ pressor stage III and partly condensed in the second section "b" and third section "c" of condensor 24' until the fluid is completely liquified in state C . It is then throttled in 4 stages through expansion valves 26', and the flashgas from each stage is supplied to the appropriate compressor stage in state D' . It is seen from the T-s chart fig. 8b how the •temperature loss to the fluid being heated from t- to t_ is reduced by this procedure, resulting in a reduction of the theoretical power consumption. The efficiency is also further improved by the multistage throttling and recompression.

Another samle application of the principles according to the invention, involving a special expansion aggregate to reduce the throttling loss and thereby improve the efficiency of a normal refrigeration or heat pump plant, is illustrated in fig. 9a - d. In a normal prior art system the gas coming from the evaporator 7 is compressed in the convential compres¬ sor 41 driven by motor 42, condensed in the condensor 43 and,

(through a line not indicated in the drawing) throttled back to the evaporator 47 through a single expansion valve 48. This gives a throttling line as indicated by 0 in the T-s chart fig. 9b, leading to a loss of power as shown by hatching and a loss of refrigeration capacity of the same magnitude.

Now, according to the present invention, for the purpose of reducing these losses an expansion aggregate consisting of a series of throttling valves 45 and liquid/gas separators 46 in combination with a gear compressor 44 can be applied. The gas formed in each throttling is conveyed to this machine and recompressed to the condensation pressure. By this device the throttling curve in the T-s chart fig. 9b takes the shape as indicated by 0' and the power and capacity losses are dramati¬ cally reduced. Two alternative forms of the liquid gas sepa¬ rators are shown in the system diagram. In the principal case the liquid is cooled successively by direct flashing into the separators 46. In the alternative system the liquid cooling is done by special heat exchanges 46'. The thermodynamic effect is practically the same. By increasing the number of throttling and recompression stages, the theoretical loss can be reduced as much as desired.

In stead of using a normal multistage compressor with a corresponding number of cooperating gears (e.g. of the type shown in fig. 1) , it may be expedient in this particular case to use a machine with only one or a limited number of sets of gears and increase the number of pressure stages by providing inlet openings or gates 50 between the regular suction and discharge, as indicated schematically in figure 10. Gas from the lowest pressure is sucked in through the regular suction gate (not shown) in the normal way while that from succes¬ sively higher pressure is injected to the intertooth spaces 49 when they are closed off in passage from suction to discharge. These extra suction openings 50 must obviously be spaced at a peripheral center distance "d" not less than the width of the tooth space 49 plus the width of the gate 50 itself. This limits the number of extra gates 50 which can be accomodated for each set of gears. A similar arrangement may be used in

connection with gear compressors which are primarily applied for other purposes.

The described procedure leads to a rigid relation between the interstage pressure as defined by the requirement of a constant product of mass and specific volume in the constant volume intertooth space. Normally this leads to very reason¬ able pressure increments. The corresponding PV diagram fig. 9c shows how the loss by lack of progressive displacement of the gear machine is reduced by this system (shown by hatching in the diagram) . This opens the possibility to use gear machines efficiently at higher pressure ratios.

An expansion aggregate in accordance with the described principles is a very rational design for inclusion in conven¬ tional refrigeration and heat pump systems, also as retrofit, and should be considered part of the present invention.

Yet another example refers to a transcritical process for a refrigeration or heat pump plant. The choice of suitable working media for such applications is limited and the use of transcritical systems will widen the selection and give some other advantages in special cases.

Fig. 11a illustrates a conventional transcritical process by a system diagram and temperature/entropy (T-s) chart fig. lib. Gas in a near saturated or slightly superheated state E is sucked into compressor 60 and discharged at super-critical pressure and relatively high temperature, state F. After cooling to near ambient temperature in the heat exchanger or cooler 64, state G, the gas is throttled in the expansion valve 66 and injected as a mixture of liquid and gas (state H) into the evaporator 68. After evaporation it is again fed to the compressor 60 in state E. When the heat is given off (process F - G) to a fluid of more or less constant tempera¬ ture, for instance the ambience, there is a very considerable loss by the irreversible heat exchange in cooler 64. Also the single stage throttling causes an important loss of power and refrigeration capacity.

A system to considerably reduce these drawbacks, using the principles according to the present invention, is illu-

strated in a system flow diagram fig. 12a and T-s chart fig. 12b, using a four stage gear compressor 60'. Again the gas from the evaporator 68 is sucked into the first stage of the compressor 60 at state E' and compressed in four steps with intercooling in the coolers 64. The high pressure gas at state G is then throttled in the expansion valve 66' to an intermediate pressure and injected into the gas/liquid sepa¬ rator 70. The gas fraction is supplied to the second stage of the compressor while the remaining liquid at state H is fur¬ ther throttled to the evaporator pressure through valve 66" to reach state H' . After evaporation it is again supplied to the compressor 60' in state E. It is also possible to use addi¬ tional throttling stages in accordance with the principles as described in connection with fig. 7a and b.

The advantage in reducing the theoretical power require¬ ment is apparent by comparing the T-s diagrams figs. 10 b and lib. A constant temperature of heat rejection t was assumed. It is, however, possible to adapt the process to any desired temperature glide.

Since most of the available working media have a critical point between 30 and 50 bar, transcritical operation may also be desirable with a view to reduce the pumping volume. It also has an interesting advantage in improved heat exchange.

The principle as explained above and illustrated by examples of application, will show how it is possible to approach any desired thermodynamic cycle with a closer match than obtainable with normal systems used today. Application of multistage gear machines in combination with interstage heat exchangers offer much increased flexibility towards this aim.

Multistage gear expanders can be used to achieve an approach to a theoretical gliding temperature process in a very similar way as described for the compressor in previous examples. Figs. 13a and b show the system diagram and T-s chart respectively for a refrigeration plant according to conventional technology, cooling a fluid flow from temperature t to t . The working fluid is compressed in the conventional

compressor 80 from state K to state L, cooled and condensed to state M in the condensor 84, throttled to the evaporator pressure in expansion valve 86 and injected into the evapora¬ tor 88 in state IV. After evaporation by absorption of the refrigeration load it is returned to the compressor in a near saturated or slightly superheated condition, state K. The process exibits two important thermodynamic losses, by the single stage throttling M-N and by irreversible heat exchange N-K.

The process can be modified to reduce these losses by using a multistage, e.g. 5 stage gear expander 81 according to the invention as indicated in the corresponding diagrams figs. 14a and b. The compressor 80 and condensor 84 is left un¬ changed from the conventional system, although a multistage gear compressor could have been used to advantage as previ¬ ously examplified. The multistage gear expander 81, which essentially could be similar to the gear machine 1 illustrated in figs. 1 and 2, is used to give a better approach to a more ideal theoretical process of step-wise expansion and evapora¬ tion as illustrated in the T-s chart fig. 14b. Liquid from the condensor 84 at state M is supplied to the first stage of the expander 81 and two succeeding stages to reach a partly expanded stage N' , while the two final expander stages coope¬ rate with a mul isection evaporator 88 working with a mixture of gas and liquid. Since the power produced by the first (liquid) stage is quite small, it may be more practical to replace this with a simple throttling valve. This would simplify the flow regulation in the system. The power gene¬ rated in the expander 81 may be used to reduce the external driving power for the compressor as indicated schematically in fig. 14a.

There are many ways in which the application of multi¬ stage gear machines can be combined to improve thermodynamic processes, and only some typical cases are shown in the exam¬ ples. Frequently it is a matter of choice whether to use a compressor or an expander to generate an approach to a gliding temperature for instance. In some cases it is possible to

combine expansion and compression in different gear pairs in the same machine, thus creating a self-contained aggregate without any need of external exchange of power.