*4.3. Flight Conditions*

During a real flight, pressure and temperature changes occur simultaneously. In order to assess the behavior for this combined change, tests were performed in the climate chamber emulating realistic flight conditions, as given in Table 1.

Figure 5 shows the compressor map using corrected mass flow and pressure ratio for different altitudes according to the standard atmosphere [6], as given in Table 1.

**Figure 5.** Pressure ratio over corrected air mass flow for measurements with simulated altitudes of 600, 1000, 2000, 3000 and 4000 m corrected to 0 m (15 ◦C, 1000 mbar(a)).

The correction terms, Equations (5) and (7), describe the behavior of the speed limit with varying altitudes well in the range of error, and it can be concluded that the correction terms are also valid for combined temperature and pressure changes with increasing altitude. Therefore, these equations can be used to calculate all relevant limits for the examined compressor. Of course, this is only valid if the speed, and not the power, limits the compressor map such as for the investigated Rotrex EK10AA.

### *4.4. Influence of Power Limit on the Compressor Map at Varying Inlet Pressures*

For the second examined compressor, the Fischer 150k, the power limit, which is implemented in the inverter controller, limits part of the operation map of the compressor. In this case, the correction terms Equations (5) and (7) cannot be used to describe the operation range. Figure 6 shows the experimentally obtained values of the pressure ratio over the corrected air mass flow for different inlet pressures.

It can be observed that the compressor map at high inlet pressures was limited at higher air mass flows and pressures by the maximum power that the motor can provide. Once this power limit was reached, further acceleration of the impeller was prevented by the inverter. As mentioned previously, the power limit becomes less important with lower inlet pressures since the power depends on the air mass flow [9], which decreases with low inlet pressures. It can be seen from Figure 6 that at inlet pressures lower than 700 mbar(a), the compressor map of the investigated Fischer 150k was no longer determined by the motor power and the speed limit became the only relevant limit.

For the examined Fischer 150k, the power limit also depends on the pressure ratio since it varied between 4.5 and 5.3 kW during the measurements. Higher power was achieved at higher pressure ratios.

**Figure 6.** Corrected pressure ratios over corrected air mass flow for the measurements with the Fischer 150k compressor, for inlet pressures of 940, 900, 800, 700 and 600 mbar(a), corrected for 20 ◦C and 940 mbar(a). Dashed lines indicate the power limit.

#### *4.5. Prediction of the Compressor Map*

Using the mass and speed correction terms, the behavior of a compressor map without a power limit at even higher altitudes can be predicted. Based on Equations (5) and (7), a software tool (see Supplementary Material) was implemented in OriginLab to predict the changes of the absolute compressor map with altitude. The corresponding inlet pressure and temperature values are calculated according to the International Standard Atmosphere. The known surge and speed limits, often given in compressor data sheets, can be entered as data points and the mass and speed correction are used to calculate the new pressure and mass flow points for the desired altitude. For the speed correction, a linear fit through the origin is assumed. The error made by this assumption is less than 5% for the investigated compressors which is negligible compared to measurement errors. The resulting compressor map for the desired altitude is plotted automatically. The software tool is published together with this study.

Figure 7 shows the measured, as well as predicted values for the maximum reachable outlet pressure, the corresponding mass flow and the maximum possible air mass flow over altitude for the Rotrex EK10AA compressor, which is not limited by power.

It can be seen that the operation range regarding outlet pressure and air mass flow significantly decreases when going to higher altitudes. At and altitude of 5000 m, the point of maximum outlet pressure decreased from 2500 mbar(a) at 50 g/s to 1450 mbar(a) at 29 g/s compared to ground level. Going up to 10,000 m, which corresponds to −50 ◦C and 264 mbar(a), the maximum outlet pressure decreased further to 780 mbar(a) at 15 g/s. Furthermore, the maximum possible air mass flow decreased from 98 g/s at 0 m, to 55 g/s at 5000 m and to 29 g/s at 10,000 m. The measured points are in good agreement with the predicted points for the Rotrex EK10AA compressor.

The tool only works fine if the input operation map is not limited by the power, because in that case the speed limit is not determining the boundaries of the operational map. However, the maximum power can also be entered into the tool to calculate the power limit. To simplify the calculation, a constant efficiency of 60% [9] was assumed, which can

also be changed if necessary. The calculation of the power limit is only relevant for two cases: 1. If the speed limit is known and used as input and a power limit is implemented afterwards. 2. If the input reference compressor map is taken at low pressures without the presence of the power limit, but the performance at higher inlet pressures for which the power limit is relevant, is of interest.

**Figure 7.** Predicted maximum pressure ratio with corresponding air mass flow and maximum air mass flow for the Rotrex EK10AA; measurement data are plotted in stars for comparison.

Figure 8 shows the measured compressor limit at 600 m as well as the measured and calculated limits for 4000 m. This change in altitude corresponds simultaneously to a change in pressure and temperature. Since the 600 m curve was measured closer to the surge limit than the 4000 m curve, the calculated curve for 4000 m contains points with a lower mass flow than the measured curve.

It can be seen that the prediction works fine in the range of error for the part of the compressor map that is limited by the speed limit. In contrast, the power limitation of the reference curve at 600 m leads to an underestimation of the compressor map for 4000 m because the power limit is used as input, although it becomes less relevant with increased altitude. As can be seen, the measured curve is only limited by the speed limit, and the correction only works for the parts of the compressor map that are not limited by the power.

If the surge and speed limit alone define the borders of the reference compressor map, the prediction according to the mass and speed correction, work reliably. This is shown by the good agreement of measured and calculated data presented in Figure 7, as well as for the very low mass flows in Figure 8. When using the mass and speed correction terms, only the available points of the reference compressor map are corrected. If points close to the surge line are missing, the tool cannot predict these points for other inlet conditions.

**Figure 8.** Measured compressor limit at 600 m and calculated corresponding limit at 4000 m, in comparison to the measured compressor limit for a 4000 m altitude for the Fischer 150k compressor. Speed limit is plotted in the solid line and the power limit is plotted in dashed lines.

#### **5. Conclusions**

This work examined the influence of varying inlet pressure and temperature resulting from varying flight altitudes on the compressor map of two electrical turbo chargers. Two commercially available turbo compressors, the Rotrex EK10AA and the Fischer 150k, are tested in a custom-made climate chamber at different ambient temperatures, pressures and combinations of both, that simulate flight altitudes. Decreasing the inlet pressure leads to a decrease in the measured outlet pressure for the same air mass flow over the full compressor map, while lower inlet temperatures enable higher compressor outlet pressures, as is to be expected. The results of the Rotrex EK10AA were compared to the theory of corrected mass flow and speed and confirmed the applicability of corrected mass flow and corrected speed relationships for the speed and the surge limit of the compressor at varying flight altitudes. This allows the selection of electrical turbo chargers for airborne fuel cell application with only one given compressor map, which is defined by the speed, choke and surge limit. Typically, manufacturers give the map for ground conditions. From this map the behavior of the compressor for other altitudes can be predicted.

Based on this, a software tool was developed to calculate the impact of altitude on the compressor map considering the combined change in pressure and temperature, and a prediction of the compressor map for up to 10,000 m altitude was given. The maximum possible outlet pressure and air mass flow range significantly decreased for elevated flight altitudes. The maximum outlet pressure and the maximum possible air mass flow for the investigated Rotrex EK10AA compressor dropped by 70% when going from sea level to 10,000 m.

However, for some commercially available compressors, like the examined Fischer 150k, the maximum power available from the motor and inverter limits the compressor map and corrected mass flow and speed can no longer be used for the prediction of the compressor map at low inlet pressures. This power limit becomes less relevant with increasing altitude, so using the mass and speed correction theory might underestimate the performance at high altitudes. In order to reliably predict the behavior at high altitudes the compressor map that is not limited by inverter or motor power has to be known.

The results gained in this study can be used to predict the operation range of a pressurized airborne fuel cell system. Further research is necessary to examine the effect of high altitude on the efficiency and power of the compressor and the corresponding fuel cell system.

**Supplementary Materials:** The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/en15082896/s1, Video S1: Map prediction tool.

**Author Contributions:** Conceptualization, C.B. and C.W.; Data curation, Valentin Radke; Funding acquisition, C.B., J.K. and C.W.; Investigation, J.S., D.F. and V.R.; Methodology, J.S. and D.F.; Project administration, C.B.; Supervision, C.W.; Validation, J.S., D.F. and V.R.; Visualization, J.S.; Writing—original draft, J.S., D.F., V.R. and C.W.; Writing—review & editing, C.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the German Federal Ministry for Economic Affairs and Energy as part of the project HighV (20Y1701B) and the Federal Ministry for Transport and Digital Infrastructure as part of the project Go4Hy2 (03B10703A).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors want to thank Marcel Haag and Fatih Türk for their help in setting up the test bench and Florian Becker from DLR Hamburg for fruitful discussions.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **Nomenclature**

