# Operational Optimisation of a Non-Recuperative 1-kWe Organic Rankine Cycle (ORC) Engine Prototype
## 4 Steady-State ORC Performance
### Part-Load Performance Maps
The operating optimum locus, which designates the set of operating parameters that minimise (or maximise) an objective function, is found to vary with the heat-source temperature, as observed in Figure 4. Regardless of the chosen performance indicator, the higher \(T_{\rm hs}\), the higher the working fluid mass flowrate that favours the ORC performance. In other words, the higher the heat-source temperature, the higher the optimum power scale. It is also worth noting that the maximum thermal efficiency does not vary significantly with the heat-source temperature, as shown in the second part of Table 2, while the exergy efficiency increases with decreasing heat-source temperature. At \(T_{\rm hs}\ =\)100 \({}^{\circ}\)C, the thermal efficiency remains low (\(\eta_{\rm th}\ =\)4.1 \(\pm\) 0.1%) compared either: (i) to the theoretical limit of the Carnot efficiency that is 22% with a heat-sink temperature at 18 \({}^{\circ}\)C or (ii) to the Chambadal-Novikov efficiency that is a theoretical limit derived from endoreversible thermodynamics, equal to 11.7% in the current conditions. This unexploited potential is accurately measured by the second-law indicator, that is, the exergy efficiency, equal to 18.7 \(\pm\) 0.3% for the optimal configuration with \(T_{\rm hs}\ =\)100 \({}^{\circ}\)C.  
The relatively low values of \(\eta_{\rm exg}\) are explained by the large superheat levels at the inlet of the expander unit which denote a lost potential. Indeed, the high superheat at the exhaust of the evaporator reflects that a higher evaporating pressure could have been reached, in turn leading to higher power output for a similar heat input. The limited built-in volume ratio of the scroll expander is the main reason why the overall thermal efficiency stagnates with increasing heat-source temperatures. As further explained in Section 4.2.2, the under-expansion phenomena occurring in the orbiting machine not only decrease the expander isentropic efficiency but also adversely affect the overall ORC efficiency. With increasing the sink-to-source temperature difference, the detrimental effects of the under-expansion losses grow due to an increase of the pressure ratio across the expander. The thermal efficiency value of 4.2% reported here for a 500-W ORC engine converting heat from a 100-K sink-to-source temperature difference, even though low, is comparable to the most up-to-date experimental data found in the literature, as reported in the review paper by [PERSON] et al. (2016), which reports thermal efficiency values comprised between 1% and 9% for 0.5- to 1-kW engines. The authors also note that the achieved efficiency increases with the power scale, due to relatively decreasing auxiliary losses. Care must then be taken to compare the efficiency achieved with micro-scale engines to that obtained with large-scale ORCs at a similar sink-to-source temperature difference. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline \(T_{\rm hs}\) & \(\dot{W}_{\rm heat}\) & \(\eta_{\rm th}\) & \(\eta_{\rm exg}\) & \(\eta_{\rm exg,k}\) & \(\dot{H}_{\rm ref}\) & \(\omega_{\rm exp}\) & \(P_{\rm exp}\) & \(P_{\rm cond}\) & \(\Delta T_{\rm sup}\) & \(\Delta T_{\rm sub}\) \\ (\({}^{\circ}\)C) &