## 1 Introduction  
Utilizing low grade heat as an energy source and recovering waste heat from various processes provides avenues for sustainable energy in the future with fewer environmental problems. Low grade heat is defined by its low temperature often combined with low capacity and intermittent availability. Examples are waste heat (i.e., excess industrial heat, rejected heat of combustion engines), solar heat and geothermal heat. A recent study showed that for the EU alone, waste heat potential in industry amounts to 304.13 TWh/year [1]. The fundamental technology to convert low-grade heat to electricity or to upgrade it to a higher temperature is available [2]. One of the most mature technologies, which is offered commercially, is the organic Rankine cycle (ORC). The working principle is analogous to the classical water/steam cycle. However, instead of working with water/steam, alternative working fluids are used with beneficial thermophysical properties to cope with low temperature heat. It is important to recognize that these working fluids can also have an environmental impact. As such an important effort is put in the development of new generation working fluids with low global warming potential (GWP) and zero ozone depletion potential (ODP) [3; 4]. While the basic concept of an ORC is well accepted in industry, there is huge potential to increase performance by adapting the operating regime or the cycle layout. One of the most promising concepts is the supercritical ORC (SCORC) with performance improvements up to 10% [5]. Instead of evaporating the working fluid at a constant temperature the working fluid is heated at supercritical state while gradually increasing the temperature. One of the immediate benefits is a better match with the heat source profile resulting in a higher thermal efficiency and more heat being captured from the heat source [6; 7]. It is interesting to note that there was a similar evolution with the classical Rankine cycle shifting to supercritical operation to increase thermal efficiency. The benefit in supercritical fossil fuel power plants is mainly seen in a superior efficiency due to the higher work availability of the steam entering the turbine. The main challenge was the development of new materials that could withstand the high pressures and temperatures [8]. Currently both, supercritical and ultra-supercritical plants, are the standard. The first supercritical CO\({}_{2}\) power cycle was proposed in the late 1940s, but [PERSON] and [PERSON] [9; 10] initiated the interest by presenting theoretical fundamentals and possible configurations of the cycle. Interest in the topic dwindled mainly due to the limited amount of suitable heat sources. After the development of compact heat exchangers and materials in the 1990s, interest renewed in the topic. Nonetheless, most studies have focused on a cycle with a nuclear reactor as a heat source and hence the employment of such a cycle for low grade waste heat is relatively new. Recent times have seen more research in transcritical CO\({}_{2}\) cycles utilizing low grade heat. Another interesting application is heat upgrading with the use of heat pump technology. CO\({}_{2}\) is a natural refrigerant that is used in heating and cooling applications. It was one of the early refrigerants to be used in a commercially feasible vapor compression system for refrigeration. Examples of some other refrigerants that were used early on include ether, ammonia, sulphur dioxide and methyl chloride. Very high operating pressures caused difficulties in the wide use of CO\({}_{2}\) as the primary choice for a refrigerant. Ammonia systems were preferred over CO\({}_{2}\) systems as they had good efficiency, however, CO\({}_{2}\) systems are smaller in size and did not pose toxicity risks. In a subcritical heat pump, the refrigerant always remains under the critical point and heat rejections takes place via condensation. Whereas, in a transcritical cycle, the heat rejection occurs at a supercritical pressure by single-phase sensible cooling.