## 3 Heat-to-Heat Applications
### Transcritical CO\({}_{2}\) Heat Pump Cycles
#### 3.1.1 Various Layouts  
For reaching a temperature lift of about 80-100 \({}^{\circ}\)C, a single-stage configuration is adequate, for keeping the system complexity low, which is one of the main advantages of CO\({}_{2}\) transcritical heat pumps. An internal heat exchanger can be also used, as shown in Figure 4, for exploiting the heat content of the pressurized gas, with smaller performance improvements as in subcritical heat pump cycles. Moreover, the large pressure difference reaching even 80-100 bar, makes the compression process very demanding in terms of compressor technology and performance. Relevant to this feature of this kind of heat pumps, different technologies are developed and tested at lab-scale units, mostly applicable for heat pumps in the domestic sector, with the aim to increase the flexibility and the COP [93]. However, these can be applied even in larger heat pumps for heat recovery, with heat supply from sources other than air. These two configurations leading to layout variants are briefly presented next, without restricting the use of additional (standard) variations, such as the use of internal heat exchanger, cascade cycles, or economizers [94; 95].  
Expansion Machine at the Gas Cooler Exit:  
The large pressure difference makes it appropriate to use expansion devices for recovering some power from the expansion process of CO\({}_{2}\) at the gas cooler exit. This power covers a fraction of the necessary power input for the compression process. Even if this device operates with low efficiency of 19% [96], due to the two-phase operation and other losses (e.g., mechanical), the work recovery potential is significant. [PERSON] et al. [97] reached an even lower isentropic efficiency of 11% using a reciprocating piston expander, probably due to the internal leakages, resulting however to a COP increase of 10%. [PERSON] et al. [98] used a rolling piston expander, reaching an isentropic efficiency of 58% and a COP increase by over 10%, without having any effect on the cooling capacity. Similar findings have been also reached by [PERSON] et al. [99]. Even higher improvement was experimentally observed with larger expansion machines based on scroll types by [PERSON] et al. [100], making it possible to increase the COP by 30%. The different expansion devices that have been proposed, as well as the coupling methods of the expander with the compressor, are reviewed with detail in a recent work by [PERSON] et al. [101], highlighting the benefits of this layout.  
Ejector for Assisting the Compression Process:  
The second layout for enhancing the cycle performance that is under development is to use an ejector for increasing the pressure of the superheated CO\({}_{2}\). This layout is often called the thermo-compression cycle and the performance improvement greatly depends on the features of the ejector [102]. The ejector efficiency is usually restricted to lower than 30-35% [103; 104], leading to a COP improvement of up to 10% [105], or even higher under varying operating conditions [106] and the use of multiple ejectors [107]. Detailed operational issues with this layout have been examined by [PERSON] et al. [108], highlighting the lubrication aspects as well.  
Comprehensive review works relevant to the use of ejectors in CO\({}_{2}\) transcritical vapor compression cycles have been recently prepared by [PERSON] [109], also focusing on other refrigerants, and by [PERSON] [110].