# Operational Optimisation of a Non-Recuperative 1-kWe Organic Rankine Cycle (ORC) Engine Prototype
## 4 Steady-State ORC Performance
### Part-Load Performance Maps
#### 4.2.2 Expander Performance  
The performance of scroll expanders is adversely affected by four main loss mechanisms that are: (i) radial and flank internal leakage, (ii) heat-transfer losses, (iii) friction losses and (iv) under- or over-expansion losses that occur due to a mismatch between the built-in and actual pressure ratios across the expander [51]. Two performance indicators are presented in Figure 7, using all 124 steady-state measurements gathered through the parametric optimisation study. A part-load performance map of the scroll expander is shown in Figure 7a, where the contours of the (electrical) isentropic efficiency are presented as functions of the pressure ratio imposed across the device, \(r_{P}\) and the scroll spindle speed, \(\omega_{\rm exp}\). First, it is worth noting that neither the pressure ratio nor the expander rotation speed have independent impact on the efficiency. The overall drop of the expander performance observed when increasing the pressure ratio is due to increased pressure losses and under-expansion phenomena, while the drop of efficiency at high RPMs is mainly due to increased pressure losses through the intake and exhaust ports and increased friction. Under-expansion phenomena are due to a mismatch between: (i) the pressure within the expansion chamber comprised between the involutes of the orbiting machine at the end of the expansion process and (ii) the condensing pressure. In other words, the vapour contained within the crescent-shaped chambers when opening up to the expander exhaust is at a higher pressure than that within the tube leading to the condenser. This mismatch is caused by the limited built-in volume ratio of the expander (equal to 3.5), which does not allow to fully expand the vapour stream. The Joule-Thompson expansion undergone  
Figure 6: Exergy destruction contributions of the various components of the ORC engine.  
by the under-expanded vapour during the pressure equalisation does not generate any power and thus destroys exergy. This irreversibility adversely affects the expander and overall ORC efficiencies.  
At low RPMs, the decrease in efficiency is due to increased thermal and mass-leakage losses. The latter are due to the pressure difference between two adjacent crescent-shaped expansion chambers in the scroll machine, which causes vapour to flow from an upstream high-pressure chamber to a downstream lower-pressure chamber without producing any expansion work. A measure of this mass-leakage phenomenon within the orbiting machine is provided by the filling factor, \(\phi_{\text{exp}}\), plotted in Figure 7b. This indicator can reach values greater than 1 when the mass leakage is important.  
As observed in previous studies [52; 53], the filling factor is found to decrease monotonically with the expander rotation speed, with values close to those measured in the cited references. The effect of the inlet temperature is also shown, as the filling factors reported for higher temperatures are greater than those at lower temperatures for a fixed RPM. For clarity reasons, errorbars are not shown in Figure 7b; the computed filling factors exhibit relative uncertainties below 2%.