## 2 Experimental Setup
### Performance Evaluation and Uncertainty Analysis  
The equipment mentioned in Table 2 is sufficient to measure parameters such as temperature, pressure, volumetric flow rate, etc. And performance parameters, including volumetric efficiency, adiabatic efficiency, and specific power, need to be calculated through formulas.  
The volumetric efficiency \(\eta_{V}\), which reflects the degree of perfection in utilizing the geometric dimensions of the compressor, is the ratio of the actual volumetric flow rate \(q_{V}\) to the theoretical volumetric flow rate \(q_{Vt}\) determined by the rotor geometry:  
\[\eta_{V}=\frac{q_{V}}{q_{Vt}} \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Measurement Instrument** & **Full Scale** & **Accuracy** \\ \hline Temperature & Pt100 (class B) & \(-\)5–80 \({}^{\circ}\)C & \(\sim\) \\  & Infrared thermal imager & \(-\)20–250 \({}^{\circ}\)C & \(\pm\)2 \({}^{\circ}\)C \\ \hline Pressure & MIDAS C08 & 0–6 bar & \(\pm\)0.25\% of full scale \\ \hline Volumetric flowrate & Vortex flowmeter & 0–200 m\({}^{3}\)/h & \(\pm\)1.5\% of full scale \\ \hline Water flowrate & Turbine flowmeter & 0–600 L/h & \(\pm\)1\% of full scale \\ \hline Power & Power analyzer & 0–15 kW & 1\% of measured valve \\ \hline \end{tabular}
\end{table}
Table 2: Measurement instruments used in the test rig.  
Figure 3: Photos of the test rig. (**a**) Exhaust pipeline. (**b**) Main body. (**c**) Power supply system and part of other systems.  
The isentropic efficiency \(\eta_{ad}\), which reflects the degree of perfection in the energy utilization of the compressor, is the ratio of the isentropic compression power consumption \(P_{ad}\) to the actual shaft power \(P_{s}\):  
\[\eta_{ad}=\frac{P_{ad}}{P_{s}} \tag{2}\]  
where adiabatic power \(P_{ad}\) can be calculated by  
\[P_{ad}=\frac{\kappa}{\kappa-1}p_{suc}q_{V}\Bigg{(}\left(\frac{p_{dis}}{p_{suc}} \right)^{\frac{\kappa-1}{\kappa}}-1\Bigg{)} \tag{3}\]  
Specific power \(P_{sp}\), indicating the energy efficiency comprehensively, is the ratio of the actual shaft power \(P_{s}\) to the actual volumetric flow rate \(q_{V}\):  
\[P_{sp}=\frac{P_{s}}{q_{V}} \tag{4}\]  
According to error propagation analysis, and using the standard deviation, the uncertainty of the volumetric efficiency, adiabatic efficiency, and specific power can be calculated by  
\[\begin{array}{l}E_{\eta_{V}}=\sqrt{\left(E_{q_{V}}\right)^{2}+\left(E_{q_{V }}\right)^{2}}\\ E_{\eta_{ad}}=\sqrt{\left(E_{P_{ad}}\right)^{2}+\left(E_{P_{s}}\right)^{2}}\\ E_{P_{sp}}=\sqrt{\left(E_{P_{s}}\right)^{2}+\left(E_{q_{V}}\right)^{2}}\\ \end{array} \tag{5}\]  
Taking the measured data at 9000 rpm and with a 10 L/min cooling water flow rate as an example, an error analysis was conducted as below. The relative error of the measured compressor volume flow rate \(E_{q_{V}}\) is \(\pm\)1.73%, and the relative error of the theoretical compressor volume flow rate \(E_{q_{V}}\) is \(\pm\)1%. Then, the relative error for the volumetric efficiency \(E_{\eta_{V}}\) can be calculated as \(\pm\)2.00%. The relative error of the isentropic compression power consumption \(E_{P_{ad}}\) is \(\pm\)2.02%, and the relative error of the actual shaft power \(E_{P_{s}}\) is \(\pm\)1%. Then, the relative error for the isentropic efficiency \(E_{\eta_{ad}}\) can be calculated as \(\pm\)2.25%. And the relative error of the specific power \(E_{P_{sp}}\) can be calculated as \(\pm\)2.00%.