Waste Heat Recovery Systems with Isobaric Expansion Technology Using Pure and Mixed Working Fluids

: Economic expedience of waste heat recovery systems (WHRS), especially for low temperature difference applications, is often questionable due to high capital investments and long pay-back periods. With a simple design, isobaric expansion (IE) machines could provide a viable pathway to utilizing otherwise unproﬁtable waste heat streams for power generation and particularly for pumping liquids and compression of gases. Different engine conﬁgurations are presented and discussed. A new method of modeling and calculation of the IE process and efﬁciency is used on IE cycles with various pure and mixed working ﬂuids. Some interesting cases are presented. It is shown in this paper that the simplest non-regenerative IE engines are efﬁcient at low temperature differences between a heat source and heat sink. The efﬁciency of the non-regenerative IE process with pure working ﬂuid can be very high, approaching Carnot efﬁciency at low pressure and heat source/heat sink temperature differences. Regeneration can increase efﬁciency of the IE cycle to some extent. Application of mixed working ﬂuids in combination with regeneration can signiﬁcantly increase the range of high efﬁciencies to much larger temperature and pressure differences.


Introduction
Today, the lion's share of electricity generated globally is consumed by pumps and compressors. For instance, pumping systems consume around 20% of world's electricity demand [1]. Compressed air systems alone account for 10% of electricity consumed in the U.S. and European Union industries and 9.4% in China [2].
Most of the electricity production is based on large power stations using heat from the combustion of fossil fuels (such as coal and natural gas) accompanied by CO 2 , NOx and particulate emissions. Other methods (solar photovoltaics, wind, tidal, geothermal, etc.) constitute a lesser part of the electricity market. According to a recent evaluation, 72% of primary high-grade energy is lost after conversion, and 63% of this lost energy is waste heat with a temperature below 100 • C [3]. The only way to convert low-grade heat to power is based on the organic Rankine cycle (ORC). However, the real contribution of ORC produced power to the world's electricity generating capacity is insignificant. For instance, global installed power capacity in 2016 reached 6473 GW, of which 61.1% (3954 GW) was based on thermal energy sources [4], whereas the ORC represented only around 2.7 GW [5].
In other words, the contribution of the ORC accounts for 0.04% of the global electricity generating capacity and 0.07% of the generating capacity based on thermal (heat) energy sources. Therefore, it can be said with confidence that low grade and waste heat resources in power generation remain almost untapped. Such an inconsequential contribution of the ORC has mostly economic causes. ORC-based power generation is too expensive in the case of ultra-low-grade heat sources (below 100 • C) and low power ranges [6,7]. For instance, the share of units with power below 500 kW does not exceed 2% of the total installed ORC capacity [5], i.e., millions of small low-grade and waste heat sources remain unused.
Utilization of waste heat thus provides a possibility to increase efficiency of industrial processes and monetize an otherwise lost energy stream. Waste heat sources are plentiful, with the EU potential estimated at 300 TWh/y, of which one third is in the low temperature range of 100 to 200 • C [8].
Isobaric expansion engines defined in [9] are the oldest type of heat-to-mechanical power converters known. James Watt, Thomas Savery, Denis Papin and Thomas Newcomen, standing at the cradle of this invention [10,11], set forth the fundamental principles of conversion of heat into work bringing about the industrial revolution. Later on, these machines were displaced by more efficient well-known water steam expansion machines such as piston steam engines as well as steam turbines. Due to simple design by utilization of readily available components, IE machines provide a viable pathway to utilize waste heat steams in the low temperature (difference) range.
However, as shown in [9], IE engines can be efficient using some working fluids in a combination with heat regeneration. Afterwards, many aspects of IE-technology were investigated. Among them are problems of regeneration efficiency [12], as well as operation of IE engines as pumps [13] and compressors [14].
It is demonstrated that for the various types of IE engines configurations, attractive results can be obtained for low and ultra-low temperature waste heat recovery. With a thermodynamic model and the use of the REFPROP 10 database [15] for the retrieval of the physical properties of the working fluids, results on some single-component and binary mixtures are presented. We show the benefits of mixed working fluids in IE machines on a theoretical basis and that a wide temperature operating range can be achieved with binary mixed working fluids.
As a result, IE technology can be an ideal fit for pumping liquids and compression of gases because it can utilize heat for compression and pumping directly, i.e., without the intermediate step of electricity generation, transmission and further conversion back to mechanical energy typical of today's industry. IE machines can also be attractive for electricity generation in low and medium power ranges.

Worthington-Type Isobaric Expansion Engines
Worthington-type heat engines relate to one of two known classes of IE machines. Bush-type engines [16], forming the second class, perform a different working cycle. Theoretically, Bush-type engines are more efficient than Worthington ones; however, the high efficiency can only be realized if dead volume of the heat exchangers does not severely influence the engine power and efficiency [17]. On the contrary, Worthington-type engines are less sensitive in this respect and can use any off-the-shelf heat exchanger. In this study, only Worthington-type engines were considered as they are more market-ready.
The Worthington-type IE machines can use any type of heat exchanger, including the most economical ones (gasketed and brazed plate, pillow plate etc.). Moreover, the large internal volume can even be useful for dampening pressure pulsations. In addition, this enables Worthington engines to use multiple heat sources and heat sinks with different temperatures. To demonstrate the wide variety of possible Worthington engine configurations, some of them are outlined below.

System Configurations
The basic principle of one of many possible modifications of Worthington-type engines is shown in Figure 1. The engine consists of a power or driving cylinder (1) with a pair of admission valves (2) and a pair of exhaust valves (3), as well as pumping cylinder (4) with a pair of suction valves (5) and a pair of discharge valves (6). The driving and pumping cylinders are equipped with driving and pumping pistons 7a and 7b, respectively, rigidly connected by rod 7c. As a result, both pistons and the rod form a so-called differential piston moving together as one unit. The engine scheme also includes a feed pump (P), heater/evaporator (H) and cooler/condenser (C). If the engine is used as a shaft power or electric generator, it can be equipped with a hydraulic motor (8) and electric generator (G). In operation, the feed pump (P) delivers a liquid driving fluid to the heater (H) where it is heated and turned into vapor. The hot pressurized vapor of the driving fluid is supplied to the upper and lower parts of the driving cylinder alternately, providing a reciprocating motion of the differential piston (7a-7b-7c). The spent working fluid is exhausted through the exhaust valves (3). The driving fluid does not expand in the cylinder, providing a constant force for the pumping in the pumping cylinder; therefore, each admission and each exhaust valve in the opposite chamber of the driving cylinder is open during every half of the cycle. The spent working fluid exhausted from the driving cylinder goes to the cooler/condenser (C) and then returns to the feed pump (P).
The pumping cylinder operates as a typical double-acting pump with self-acting valves. Under certain conditions, the efficiency of the engine can be increased several times by means of heat regeneration. The regenerative Worthington-type engine is shown in Figure 1b. In this case, the heat of the hot fluid exhausted from the driving cylinder is used for preheating of the cold driving fluid in the recuperator (R) installed upstream of the heater (H). This increases efficiency by decreasing the consumption of the heat used for the working fluid heating in the heater (H). The recuperator also decreases the heat The engine consists of a power or driving cylinder (1) with a pair of admission valves (2) and a pair of exhaust valves (3), as well as pumping cylinder (4) with a pair of suction valves (5) and a pair of discharge valves (6). The driving and pumping cylinders are equipped with driving and pumping pistons 7a and 7b, respectively, rigidly connected by rod 7c. As a result, both pistons and the rod form a so-called differential piston moving together as one unit. The engine scheme also includes a feed pump (P), heater/evaporator (H) and cooler/condenser (C). If the engine is used as a shaft power or electric generator, it can be equipped with a hydraulic motor (8) and electric generator (G). In operation, the feed pump (P) delivers a liquid driving fluid to the heater (H) where it is heated and turned into vapor. The hot pressurized vapor of the driving fluid is supplied to the upper and lower parts of the driving cylinder alternately, providing a reciprocating motion of the differential piston (7a-7b-7c). The spent working fluid is exhausted through the exhaust valves (3). The driving fluid does not expand in the cylinder, providing a constant force for the pumping in the pumping cylinder; therefore, each admission and each exhaust valve in the opposite chamber of the driving cylinder is open during every half of the cycle. The spent working fluid exhausted from the driving cylinder goes to the cooler/condenser (C) and then returns to the feed pump (P).
The pumping cylinder operates as a typical double-acting pump with self-acting valves. Under certain conditions, the efficiency of the engine can be increased several times by means of heat regeneration. The regenerative Worthington-type engine is shown in Figure 1b. In this case, the heat of the hot fluid exhausted from the driving cylinder is used for preheating of the cold driving fluid in the recuperator (R) installed upstream of the heater (H). This increases efficiency by decreasing the consumption of the heat used for the working fluid heating in the heater (H). The recuperator also decreases the heat load on the cooler/condenser resulting in a smaller heat exchange area and size of the condenser. In the case of high temperature operation, excluding conventional positive seals, a seal-less design can be used. Such a single-acting machine, as shown in Figure 2a, consists of a cylinder (1) with admission and exhaust valves (2) and (3), a free piston (4) and a diaphragm unit. The diaphragm unit includes two semispherical covers (5) and (6) with a diaphragm (7) clamped in between. The upper cover (6) is equipped with suction and discharge valves (8) and (9). The piston (4) here plays only a role of a heat barrier dividing the hot vapors of working fluid (shown in orange) in the lower part of the cylinder (1) and cold liquid working fluid (shown in blue) in the upper part. In this design the cold liquid working fluid acts as a driving piston. It transmits the pressure of hot working fluid through the diaphragm (7) to the liquid to be pumped (shown in yellow-green).
the hot vapors of working fluid (shown in orange) in the lower part of the cylinder (1) and cold liquid working fluid (shown in blue) in the upper part. In this design the cold liquid working fluid acts as a driving piston. It transmits the pressure of hot working fluid through the diaphragm (7) to the liquid to be pumped (shown in yellow-green).
Apparently, if the liquid to be pumped can be used also as the driving working fluid, the diaphragm unit can be eliminated. In this case the suction and discharge valves (8) and (9) can be installed directly in the upper part of the cylinder (1), as shown in Figure  2b. Such a pump can be used, for instance, for pumping of liquefied gases, light hydrocarbons on refineries and in the chemical industry.
In the case of pumping warm or hot liquid, the cylinder with the thermal barrier piston can be eliminated entirely, and the diaphragm unit plays the role of the driving and pumping cylinders at the same time. Here the admission and exhaust valves related to the driving part are also installed directly in the lower cover (5), the diaphragm unit. The diaphragm IE-pump is similar to that of the piston IE-pump; however, the initial and final pressures both in the driving and pumping cylinders are equal. The main advantage of the diaphragm-based design is an almost frictionless and leak-free operation, as shown in Figure 2c.  (4), lower diaphragm cover (5), upper diaphragm cover (6), diaphragm (7), suction valve (8) and discharge valve (9).
If the IE machine is used only as a shaft power/electricity generator, the useful work can also be extracted directly from the driving piston by means of some kinematic (crank, swash plate, etc.) mechanism rather than by the hydraulic output. The example with a Apparently, if the liquid to be pumped can be used also as the driving working fluid, the diaphragm unit can be eliminated. In this case the suction and discharge valves (8) and (9) can be installed directly in the upper part of the cylinder (1), as shown in Figure 2b. Such a pump can be used, for instance, for pumping of liquefied gases, light hydrocarbons on refineries and in the chemical industry.
In the case of pumping warm or hot liquid, the cylinder with the thermal barrier piston can be eliminated entirely, and the diaphragm unit plays the role of the driving and pumping cylinders at the same time. Here the admission and exhaust valves related to the driving part are also installed directly in the lower cover (5), the diaphragm unit. The diaphragm IE-pump is similar to that of the piston IE-pump; however, the initial and final pressures both in the driving and pumping cylinders are equal. The main advantage of the diaphragm-based design is an almost frictionless and leak-free operation, as shown in Figure 2c.
If the IE machine is used only as a shaft power/electricity generator, the useful work can also be extracted directly from the driving piston by means of some kinematic (crank, swash plate, etc.) mechanism rather than by the hydraulic output. The example with a crank gear is shown in Figure 3a. Such a design is reminiscent of an old-fashioned steam engine with a very late cut-off. The admission valve remains open during the whole working stroke and closes at top dead center of the piston. Then, the discharge valve opens and remains open during the whole back stroke of the piston. When the piston reaches the bottom dead center, the discharge valve closes, and the admission valve opens, starting a new working cycle. The reciprocating piston with the crank gear mechanism can be replaced with different rotary piston machines, which is more convenient in some cases. displacement rotary lobe machine (RLM) is applied. Such an arrangement is similar to a conventional ORC installation. Roots machines were investigated as ORC expanders [18,19]. However, they do not perform expansion because a so-called built-in volume ratio is close to one, i.e., in the Roots converter vapor does not expand during the pressure-towork conversion. Roots machines operate as a typical hydraulic motor rather than a gas expansion machine. As a result, the functionality of the Roots machine does not differ from that of reciprocating Worthington-type ones outlined above. Moreover, the rotary lobes play the roles of pistons and valves at the same time. Such simplicity in a combination with high volumetric and mechanical efficiencies as well as low costs makes the Roots-based setups appealing. The installation does not produce inertial forces. In addition, power capacity of the largest Roots machines can reach the megawatt power range. However, the Roots machines cannot work at high temperatures and high pressure drops. For higher pressures and temperatures, other types of volumetric machines are necessary.

Cycle Calculations
Heat regeneration processes are rather difficult for modeling, above all in the case of cyclic processes. In IE engines using dense working fluids, the problem is complicated A straightforward example of such a machine is a so-called rotary lobe or Roots compressor/blower operating in a reverse mode, i.e., as pressure-to-shaft-power converter shown in Figure 3b. The setup also has a pump (P), heater (H), recuperator (R), and cooler (C). To convert the pressure of the hot working fluid to shaft power, a special positive displacement rotary lobe machine (RLM) is applied. Such an arrangement is similar to a conventional ORC installation. Roots machines were investigated as ORC expanders [18,19]. However, they do not perform expansion because a so-called built-in volume ratio is close to one, i.e., in the Roots converter vapor does not expand during the pressure-towork conversion. Roots machines operate as a typical hydraulic motor rather than a gas expansion machine. As a result, the functionality of the Roots machine does not differ from that of reciprocating Worthington-type ones outlined above. Moreover, the rotary lobes play the roles of pistons and valves at the same time. Such simplicity in a combination with high volumetric and mechanical efficiencies as well as low costs makes the Roots-based setups appealing. The installation does not produce inertial forces. In addition, power capacity of the largest Roots machines can reach the megawatt power range.
However, the Roots machines cannot work at high temperatures and high pressure drops. For higher pressures and temperatures, other types of volumetric machines are necessary.

Cycle Calculations
Heat regeneration processes are rather difficult for modeling, above all in the case of cyclic processes. In IE engines using dense working fluids, the problem is complicated due to phase changes or operation near the critical point. Under such conditions, heat capacity is not constant but a strong function of both temperature and pressure. As a result, the second law of thermodynamics poses limitations on the possible heat regeneration degree. This implies that changes of the enthalpy of the fluids/streams participating in Energies 2022, 15, 5265 6 of 14 the heat exchange process at each temperature level (within the temperature engine cycle temperature interval) matter.
The expansion-compression work performed by the engine per cycle is: where P H and P L are the high and low cycle pressures (pressures during the expansion and compression processes), and ∆V E is the change of vapor volume in the cylinder. If the cylinder volume at the beginning of the admission process (clearance volume) is negligible: where m is the total mass of the working fluid involved in the cycle, and ρ and v are density and specific volume of the working fluid. The pumping work, assuming an adiabatic process with negligible changes in kinetic and potential energies, can be determined as: where h(T, P) is the enthalpy of the working fluid per unit mass (specific enthalpy), and T P,out is the discharge temperature of the pump.
Assuming an isentropic pump operation, the discharge temperature can be found from the constant entropy equation: The net value of the work produced during the cycle is found as: The working fluid is heated up in a heater from the pump discharge temperature (usually slightly above the temperature of the cooler or the low cycle temperature) to the desired inlet temperature of the power cylinder (high cycle temperature T H ).
Without heat regeneration the amount of heat supplied to the working fluid in the heater is The thermal efficiency, defined as the useful work produced during a full cycle in relation to the supplied heat, is The supplied heat can be reduced by recovering a part of the heat of the working fluid exhausted from the power cylinder in a recuperative heat exchanger, as shown in Figure 4. In this case working fluid after the feed pump is heated in the recuperator from T P,out to some higher temperature T R,out at the outlet of the recuperator. Thus, the duty of the heater becomes  In the recuperator, the cold stream from the feed pump at pressure PH is heated by the hot stream discharged from the power cylinder. The temperature and pressure of the fluid discharging from the power cylinder (fluid delivering heat) depend on the way the discharge is arranged.  The T R,out value is determined by the regeneration process. Its scheme is shown in Figure 4.
In the recuperator, the cold stream from the feed pump at pressure P H is heated by the hot stream discharged from the power cylinder. The temperature and pressure of the fluid discharging from the power cylinder (fluid delivering heat) depend on the way the discharge is arranged.
We assume that the pressure of the fluid exhausted from the power cylinder decreases from the high cycle pressure P H to the low cycle pressure P L in a throttle located before the recuperator. The exhaust valve of the power cylinder may play the role of the throttle. This pressure reduction process is considered as a Joule-Thompson expansion.
Neglecting the changes in kinetic and potential energy, the temperatures in the power cylinder and at the inlet of the recuperator, T E and T D , are related by an equation ensuring no enthalpy change in this process: in which P E is the pressure of the working fluid in the power cylinder (before the exhaust valve) which change during the discharge process consisting of the pressure reduction stage and displacement of the working fluid from the power cylinder at the low cycle pressure.
Change of P E and T E during the discharge process can be obtained from the energy balance assuming the adiabatic process in the power cylinder: Although the amount of working fluid in the cylinder reduces the energy, the balance equation, Equation (10), is the same as that for adiabatic expansion of a fluid of constant mass.
From Equations (9) and (10) the variable inlet temperature of the fluid delivering heat T D can be calculated. Then, applying the method presented in [12], the enthalpy of the working fluid entering the heater can be obtained.
To simplify the calculations of the recuperator process, we assumed that the working fluid coming from the power cylinder to the recuperator is well mixed. In other words, instead of variable inlet temperature T D , its average value found from the enthalpy balance was used. This assumption is justified if amount of the working fluid in the recuperator is much larger than m. Otherwise, the assumption results in a conservative value of heat exchanged in the recuperator.
The specific enthalpy of the fluid after discharging and mixing is h(T H , P H ) − (P H − P L )v. Therefore T D can be obtained from equation If temperatures of the streams entering the recuperator are known, the maximum thermodynamically allowed heat transfer between two fluids, or the maximum amount of regenerated heat Q R , is: where Dh is the maximum enthalpy difference within the temperature interval T P,out ≤ T ≤ T D : Accordingly, the maximum enthalpy of the working fluid entering the heater is: Energies 2022, 15, 5265 8 of 14 The efficiency of a regenerative IE cycle can now be written as: To evaluate how an IE machine performs compared to other machines, the calculated efficiency was compared with the Carnot efficiency η C showing the theoretical maximum, the Novikov η N [20] efficiency, which is a realistic measure for practically achievable efficiencies. This is shown in Reference [21] for a variety of power plants, e.g., nuclear, geothermal, steam. The relation is also known as the Curzon-Ahlborn efficiency and is a result of the assumption that all engine parts are ideal, yet the heat transfer from the reservoirs is irreversible. The Novikov efficiency relates only to the theoretical maximum power point of the (heat) engine or cycle but is widely used for comparing power generating processes. A newly established empirical correlation by Gangar et. al. [22] based on a survey of 34 commercial ORC installations η ORC was also used for comparison. This relation is derived from operational ORC systems and the efficiencies that were reported. Definitions are as follows: Carnot Novikov Gangar

Results
All presented results are from running the calculation model against the physical properties of the working fluids referenced from REFPROP version 10 [15]. For singlecomponent working fluids, we show that with low temperature and pressure difference the efficiency of the IE cycle approaches the Carnot efficiency. With mixtures, the calculation becomes more involved. While multiple mixtures are supported by REFPROP, we chose to present the mixtures that have a firm backdrop in practice and the literature: ammonia/water (NH 3 /H 2 O) [23,24] mixtures and carbon dioxide/acetone (CO 2 /C 3 H 6 O) [25,26]. These mixtures show a significant increase in efficiency when regeneration is applied to the IE cycle.
By following the calculation method as described in Equations (1)-(15), the cumulative enthalpy curves are determined for pure ammonia as a working fluid compared with a mixture of ammonia water 65/35 wt.%. By employing a mixture, the theoretical maximum heat transfer with regeneration between the heat delivering and heat receiving fluid is increased drastically. Figure 5 illustrates the case when the fluid delivering heat is at low pressure and the fluid receiving heat is at high pressure. While the temperature and pressure at the coldand hot inlets are the same for both processes shown in Figure 5, it can be seen that the heat transfer process of the mixture is more efficient, which is expressed in a higher change in the temperature of the fluids. For the pure working fluid, as shown in Figure 5a, the phase change takes place at a single temperature, and most of the latent heat is not used in the heat transfer process due to thermodynamic limitations. On the contrary, the mixture, as shown in Figure 5b, shows a boiling trajectory where most of the heat transfer takes place in the vapor-liquid region of the mixture. Thus, the use of mixtures in the regenerative process can significantly increase the degree of heat exchange between the fluids and thus cycle efficiency. A more detailed report on the thermodynamic aspects and physical limits of heat regeneration is given in [12].

Efficiency of Single-Component Working Fluids
Efficiencies of several single-component working fluids in Worthington cycle with and without regeneration have previously been investigated [9]. However, in order to understand some critical features of the Worthington cycle, we investigated several types of such fluids calculating relative (to Carnot) efficiencies at different temperature and pressure differences. An overview of the working fluids including the characteristic properties, chosen temperature and pressure levels used in this study is provided in Table 1.  [25,26] All these working fluids demonstrated a similar behavior shown in Figure 6 for ammonia, water, CO2 and acetone as typical examples. It can be seen that the highest relative efficiency is reached at the point of phase transition at high cycle pressure . At low temperature and pressure differences (below 5-10 °C and 0.5-2 bar), these efficiencies approach the Carnot efficiency.
Any further increase in temperature and pressure difference leads to a decrease in the specific efficiency. This decline is notably pronounced for the highest efficiencies: the higher the efficiency, the sharper the drop. High efficiencies (above 0.7 of the Carnot efficiency) are possible within the temperature range of about 20 °C. The efficiencies which are of practical and industrial interest (mostly above 0.5 of the Carnot efficiency) can be reached at the temperature difference below 50 °C.

Efficiency of Single-Component Working Fluids
Efficiencies of several single-component working fluids in Worthington cycle with and without regeneration have previously been investigated [9]. However, in order to understand some critical features of the Worthington cycle, we investigated several types of such fluids calculating relative (to Carnot) efficiencies at different temperature and pressure differences. An overview of the working fluids including the characteristic properties, chosen temperature and pressure levels used in this study is provided in Table 1.  [25,26] All these working fluids demonstrated a similar behavior shown in Figure 6 for ammonia, water, CO 2 and acetone as typical examples. It can be seen that the highest relative efficiency is reached at the point of phase transition at high cycle pressure P H . At low temperature and pressure differences (below 5-10 • C and 0.5-2 bar), these efficiencies approach the Carnot efficiency.
Any further increase in temperature and pressure difference leads to a decrease in the specific efficiency. This decline is notably pronounced for the highest efficiencies: the higher the efficiency, the sharper the drop. High efficiencies (above 0.7 of the Carnot efficiency) are possible within the temperature range of about 20 • C. The efficiencies which are of practical and industrial interest (mostly above 0.5 of the Carnot efficiency) can be reached at the temperature difference below 50 • C. participating in the heat exchange process leads to further deviation from reversibility, i.e., the Carnot limit.
It can be also seen that regeneration can slightly extend the temperature and pressure differences. However, the benefit of a regenerative cycle is small, and it increases towards higher temperature differences. When a pure working fluid becomes supercritical, a gradual increase in efficiency is seen, so regeneration becomes more important under supercritical conditions.  The decrease in specific efficiency with increasing temperature difference is explained by the difference in temperatures of the heat source and working fluid and similarly for the cold sink and working fluid. A larger temperature difference between fluids participating in the heat exchange process leads to further deviation from reversibility, i.e., the Carnot limit.
It can be also seen that regeneration can slightly extend the temperature and pressure differences. However, the benefit of a regenerative cycle is small, and it increases towards higher temperature differences. When a pure working fluid becomes supercritical, a gradual increase in efficiency is seen, so regeneration becomes more important under supercritical conditions.

Efficiency of Binary Mixture Working Fluids
It was suggested in [9] that application of mixed working fluids could lead to some efficiency improvements due to better regeneration. In [31] some hydrocarbon mixtures were investigated for Bush-type engines, and a slight increase in efficiency was found.
In contrast to pure working fluids, mixtures of working fluids can also provide significant benefits because the temperature of the reservoirs, i.e., heat source and sink temperatures, is often not constant [32]. In this case a mixture with a suitable temperature glide can be used to match evaporator and condenser profiles more precisely.
We numerically investigated several types of binary mixtures with different composition in the temperature range up to 200 • C. Among them are binary mixtures of different hydrocarbons, oxygenates (alcohols, ethers, etc.), fluorinated refrigerants, hydrofluoroethers (Novec™) and inorganic substances. The main goal of this investigation was to evaluate whether mixed working fluids are able to considerably improve efficiency of Worthingtontype IE engines due to improved heat regeneration. Many mixtures demonstrated a serious increase in efficiency as compared to single-component working fluids.
Compared to pure working fluids, at high temperature differences binary mixtures in combination with regeneration can increase efficiency several times. In Figure 7 results are presented for a range of pressures of a 65/35 wt.% mixture of ammonia/water and a 60/40 wt.% CO 2 /acetone system. For lower pressure differences the relative efficiencies are the highest at >50%. Benefits of regeneration are even more pronounced with the CO 2 /acetone mixture, showing efficiencies above the Novikov efficiency for a large heat source and a temperature difference, viz., of up to 100 • C ∆T for ammonia/water and up to 200 • C ∆T for CO 2 /acetone.

Efficiency of Binary Mixture Working Fluids
It was suggested in [9] that application of mixed working fluids could lead to some efficiency improvements due to better regeneration. In [31] some hydrocarbon mixtures were investigated for Bush-type engines, and a slight increase in efficiency was found.
In contrast to pure working fluids, mixtures of working fluids can also provide significant benefits because the temperature of the reservoirs, i.e., heat source and sink temperatures, is often not constant [32]. In this case a mixture with a suitable temperature glide can be used to match evaporator and condenser profiles more precisely.
We numerically investigated several types of binary mixtures with different composition in the temperature range up to 200 °C. Among them are binary mixtures of different hydrocarbons, oxygenates (alcohols, ethers, etc.), fluorinated refrigerants, hydrofluoroethers (Novec™) and inorganic substances. The main goal of this investigation was to evaluate whether mixed working fluids are able to considerably improve efficiency of Worthington-type IE engines due to improved heat regeneration. Many mixtures demonstrated a serious increase in efficiency as compared to single-component working fluids.
Compared to pure working fluids, at high temperature differences binary mixtures in combination with regeneration can increase efficiency several times. In Figure 7 results are presented for a range of pressures of a 65/35 wt.% mixture of ammonia/water and a 60/40 wt.% CO2/acetone system. For lower pressure differences the relative efficiencies are the highest at >50%. Benefits of regeneration are even more pronounced with the CO2/acetone mixture, showing efficiencies above the Novikov efficiency for a large heat source and a temperature difference, viz., of up to 100 °C ∆T for ammonia/water and up to 200 °C ∆T for CO2/acetone.

Discussion
It can be seen that the simple non-regenerative cycle can provide a high thermal efficiency (close to the maximum possible Carnot efficiency), using a low temperature and pressure difference. However, the Worthington-type machines can provide such high efficiencies only within a narrow temperature-pressure range. At the higher temperature and pressure differences, the relative efficiency inevitably drops down. Regeneration is able to extend this high-efficiency temperature difference to some extent. Nevertheless, such a simple cycle can be of interest for a number of applications. For instance, in utilization of low temperature geothermal energy which can be economical if heat rejected by the IE engine is used for district heating or in industry (drying, etc.). Other examples are heat utilization of low temperature proton exchange membrane fuel cells (LTPEMFCs), generally operating between 55 and 80 • C, and waste heat recovery of marine diesel engines circulating water. The impressive efficiency at low temperature/pressure difference can use relatively inexpensive off-the-shelf Roots machines in an IE cycle.
Another way to extend the temperature difference covered by the simple non-regenerative cycles is a cascade. Such a two-stage cascade is shown in Figure 8 as an example. The cascade is a combination of two IE-installations shown previously in Figure 1; each IE engine utilizes a certain temperature difference. The condenser/cooler (CH) of the first stage in this case plays the role of heater/evaporator for the second stage of the cascade.

Discussion
It can be seen that the simple non-regenerative cycle can provide a high thermal efficiency (close to the maximum possible Carnot efficiency), using a low temperature and pressure difference. However, the Worthington-type machines can provide such high efficiencies only within a narrow temperature-pressure range. At the higher temperature and pressure differences, the relative efficiency inevitably drops down. Regeneration is able to extend this high-efficiency temperature difference to some extent. Nevertheless, such a simple cycle can be of interest for a number of applications. For instance, in utilization of low temperature geothermal energy which can be economical if heat rejected by the IE engine is used for district heating or in industry (drying, etc.). Other examples are heat utilization of low temperature proton exchange membrane fuel cells (LTPEMFCs), generally operating between 55 and 80 °C, and waste heat recovery of marine diesel engines circulating water. The impressive efficiency at low temperature/pressure difference can use relatively inexpensive off-the-shelf Roots machines in an IE cycle.
Another way to extend the temperature difference covered by the simple non-regenerative cycles is a cascade. Such a two-stage cascade is shown in Figure 8 as an example. The cascade is a combination of two IE-installations shown previously in Figure 1; each IE engine utilizes a certain temperature difference. The condenser/cooler (CH) of the first stage in this case plays the role of heater/evaporator for the second stage of the cascade. Therefore, every engine can convert heat with a small reservoir temperature difference with a relatively high efficiency. Every engine in the cascade, shown in Figure 8, serves its own pump/motor. However, the cascade setups can be designed differently, when all engines drive only one pump and/or hydraulic motor, etc. Generally, the cascade can utilize more broad temperature differences as compared to single stage IE engines. Cascade setups are thus suitable for use of heat from different temperature waste streams. In this case every stage can use not only the heat from the upstream stage but heat from any other suitable source. This is of interest for the recovery of heat from for example diesel engines by coupling exhaust and cooling water waste heat, i.e., multiple heat Therefore, every engine can convert heat with a small reservoir temperature difference with a relatively high efficiency. Every engine in the cascade, shown in Figure 8, serves its own pump/motor. However, the cascade setups can be designed differently, when all engines drive only one pump and/or hydraulic motor, etc. Generally, the cascade can utilize more broad temperature differences as compared to single stage IE engines. Cascade setups are thus suitable for use of heat from different temperature waste streams. In this case every stage can use not only the heat from the upstream stage but heat from any other suitable source. This is of interest for the recovery of heat from for example diesel engines by coupling exhaust and cooling water waste heat, i.e., multiple heat streams with two different temperatures. Refineries as well as the chemical and food industries are other typical examples of multiple temperature level heat sources for IE cascade application.
Mixed working fluids make it possible to operate in much broader temperature and pressure difference ranges typical of medium and high-pressure reciprocating piston IE engines. IE engines with mixed working fluid can be used for power generation and as heatdriven pumps and compressors. The examples are pumps for irrigation and for the transfer of liquefied gases and refrigerants for district heating and water supply, air compressors, Energies 2022, 15, 5265 13 of 14 refrigeration and air conditioning compressors and compressors of heat pumps. Air compressors are of interest in view of the recent efforts towards the development of compressed air energy storage systems. The second particular case is a high-pressure compression of hydrogen for storage and hydrogen refueling stations, etc.

Conclusions
A high quantity of recoverable energy is still lost in most industrial processes. Possible methods of (ultra) low-grade heat utilization using different types of isobaric expansion (IE) machines are presented and discussed. It is shown that the efficiency of non-regenerative machines with single-component working fluids can be high, approaching the Carnot efficiency at a low heat source/heat sink temperature difference. Regeneration can increase this efficiency only to some extent. For an efficient utilization of higher temperature differences, there are two approaches. The first is a so-called cascade, i.e., a combination two or more IE machines; each of them utilizes only some part of the available temperature difference. The second is an application of binary mixtures as working fluid in a combination with regeneration. At high temperature differences, such a combination can increase efficiency several times when compared to single-component working fluids.
The IE engine can become a suitable means for recovery of heat energy due to its simple design and economical application. Ongoing research and experiments will further develop IE technology and improve system configurations for the plethora of applications.