**1. Introduction**

Fuel cell-powered airplanes provide the potential to significantly reduce global greenhouse gas emissions in aviation [1,2]. The requirements related to system mass and volumespecific energy density, power and security are very demanding compared to conventional fields of fuel cell application [3–5].

One of the biggest differences compared to automotive applications is the greater variation in ambient conditions. While the pressure on the ground is around 1 bar(a), depending on the location and weather, ambient pressure during flight decreases significantly with higher flight altitudes. According to the International Standard Atmosphere [6], ambient pressure is decreased to 0.26 bar(a) at a height of 10 km, which is typical for long-range flights [7]. Temperature also decreases with altitude. For the mentioned altitude of 10 km, temperature decreases to −50 ◦C.

The performance of fuel cells increases with higher operation pressures. Lee et al. [2] simulated a pressurized air-cooled fuel cell stack and found an improvement in stack power by pressurizing the inlet air up to 5 atm. The lower air velocity resulting from higher air pressure mitigated the electrolyte dehydration. Pressurization also led to a more uniform current density distribution through reduced reactant depletion. Furthermore, the activation overpotential and the ohmic losses were reduced with increased pressure. These results are confirmed by other studies [4,5,8–10].

The changes in inlet conditions during flight affect the air supply to the fuel cell system. In order to ensure stable and powerful operation, an air supply system is needed that enables control of the inlet pressure of the stack. In an all-electric system an electrical

**Citation:** Schröter, J.; Frank, D.; Radke, V.; Bauer, C.; Kallo, J.; Willich, C. Influence of Low Inlet Pressure and Temperature on the Compressor Map Limits of Electrical Turbo Chargers for Airborne Fuel Cell Applications. *Energies* **2022**, *15*, 2896. https:// doi.org/10.3390/en15082896

Academic Editors: Bahman Shabani and Mahesh Suryawanshi

Received: 21 March 2022 Accepted: 11 April 2022 Published: 15 April 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

turbo charger is typically used to adjust the pressure level [8,11–13], but it is necessary to take into account the varying performance of a given turbo charger depending on the inlet conditions [9,14].

Kurzke et al. [15–17] used the corrected mass flow and speed to predict compressor maps of conventional gas turbines for flight-relevant conditions from known lines in the compressor map, obtained at standard conditions. They stated that the analytical prediction of the pressure ratio is difficult and therefore used empirical data for their model. The predictions matched well with their measured compressor maps. Leufven et al. [18] also used the corrected mass flow and speed correction derived from dimensionless numbers to predict the compressor map for a gas turbine. Their model fit well with the measured data from their gas turbine test bench.

Not much attention has been paid thus far to the effects of ambient pressure and temperature changes on the limits due to power and the maximum speed of electric driven turbo chargers, as the relevance of this topic only recently arose with the growing interest in pressurized PEM fuel cells in recent years. The limiting factors for the compressor maps of gas turbines and electrical compressors are not necessarily the same, because the power sources for driving the compression are different. Gas turbines use the expansion of the exhaust gas in a turbine, while electric compressors use an electric motor. Therefore, there is a need to investigate the effects that limit the operation of electrical turbo compressors for low inlet pressures and temperatures, as this is relevant for airborne fuel cell applications.

This work investigates the shift of the compressor map and its limitations for electrically driven turbo chargers, aiming at an application in a fuel cell air supply in aviation. The focus lays on applying and confirming mass flow and speed correction in order to predict altitude dependent compressor map shifts. For this reason, the Rotrex EK10AA and the Fischer 150k fuel cell air compressor are used as representatives of commercially available electrical turbo chargers and are evaluated experimentally under simulated flight conditions in a climate chamber. The influences of pressure and temperature changes are tested separately as well as in combination, as occurs during real flight conditions. The experimental data is compared to analytical data obtained via a developed software tool which calculates corrected mass flow and corrected speed from compressor maps at ground conditions. This comparison shows in which cases the mass and speed correction terms, known from gas turbines, correctly describe the compressor map shift of electrical turbo chargers, and can be used for predictions of the compressor map changes for high altitudes. The results also show that for electrical compressors, whose performance is limited by the inverter power, the performance at high altitude is underestimated when using the mass and speed correction terms.

#### **2. Operational Map of Electrical Turbo Compressors**

### *2.1. Compressor Map Limits*

The typical compressor map of an electrical turbo compressor shows the pressure ratio between in and outlet pressure over the air mass flow. This map is in principle limited by four relevant effects [19–25]: the surge limit, the choke limit, the speed limit and the power limit.

The surge line limits the compressor map at low mass flows and high pressure ratios. This limit is relevant for every turbo compressor. At the surge limit, a stall of the flow occurs which leads to an air oscillation and reversed flow that can cause severe damage to the compressor, especially in cases of air bearing.

The choke limit depends on the geometry of the compressor and is only relevant for some compressors. Once the air flowing through the blades and volute reaches the speed of sound, it cannot be further accelerated. Therefore, the maximum possible mass flow is reached in this point and the choke line limits the compressor map at higher mass flows.

The speed limit protects the compressor from structural damages by limiting the maximum impeller speed through the implementation of the inverter control. The speed limit therefore limits the compressor map at higher pressure ratios and at higher mass flows.

The power limit is only relevant for some electrical turbo chargers and depends on the manufacturer's technical configuration of the motor. If the power limit is reached, the inverter or the electrical motor prevents a further acceleration of the impeller. For some turbo charger/inverter combinations a minimum voltage is needed to reach a certain speed. Often a maximum current limit is implemented into the system for thermal reasons. As the inlet pressure decreases, the air mass flow also decreases, and therefore less power is required for compression [9]. This means that the power limit becomes less important at lower inlet pressures. In this case, the speed limit might become the relevant limit of the compressor map.

### *2.2. Compressor Map Prediction according to Corrected Mass Flow*

The considered application for electrical turbo chargers in this work is the supply of air to a fuel cell in aviation. For this reason, the absolute compressor outlet pressure, which correlates to the fuel cell inlet pressure, is the variable of interest. The term absolute compressor map is used in this work to describe a map of the absolute outlet pressure of the turbo charger over the mass flow.

The prediction of the absolute compressor map for gas turbines in literature [15,17,18,20,21] is usually done with the help of a universal compressor map showing the pressure ratio over the air mass flow for defined standard conditions and the formula for mass flow correction Equation (5), assuming Mach similarity.

The Mach number in flow direction *Mf* is the ratio of flow velocity *v* to the speed of sound *c*.

$$M\_f = \frac{v}{c} = \frac{v}{\sqrt{\kappa R\_S T}} \to \ v = M\_f \sqrt{\kappa R\_S T} \tag{1}$$

where *c* is expressed through the adiabatic index for air *κ* = 1.4, the specific gas constant for air *Rs* = 287 *<sup>J</sup> kg*· *<sup>K</sup>* ; and the air temperature.

The density of air *ρ* can be calculated from the ideal gas law with the pressure *p*; the gas constant *Rs*; and the air temperature *T*.

$$
\rho = \frac{p}{R\_S T} \tag{2}
$$

Using the cross sectional area A, Equations (1) and (2) the air mass flow through the compressor can be expressed according to Equation (3).

$$
\dot{m} = \rho A v = \frac{p}{R\_s T} A \left( M\_f \sqrt{\kappa R\_s T} \right) \tag{3}
$$

Comparing the air mass flow for two different inlet temperatures and pressures indexed "0" and "1" leads to

$$\frac{\dot{m}\_1}{\dot{m}\_0} = \frac{\frac{p\_1}{R\_S T\_1} A \left(M\_f \sqrt{\kappa R\_S T\_1}\right)}{\frac{p\_0}{R\_S T\_0} A \left(M\_f \sqrt{\kappa R\_S T\_0}\right)} = \frac{p\_1 \sqrt{T\_0}}{p\_0 \sqrt{T\_1}}\tag{4}$$

$$
\dot{m}\_1 = \dot{m}\_0 \frac{p\_1 \sqrt{T\_0}}{p\_0 \sqrt{T\_1}} \tag{5}
$$

Equation (5) is named mass flow correction and can be used to predict the compressor behavior for varying inlet conditions. The mass flow correction is combined with a speed correction for varying inlet temperatures, also derived from Mach similarity. For the speed correction, the radial Mach number is the relevant parameter [20]. In this case, the flow velocity *v* in Equation (1) can be expressed by the radius *r* times the rotation speed to get an expression for the radial Mach number *Mr*.

$$M\_r = \frac{v}{c} = \frac{r\omega}{\sqrt{\kappa R\_S T}}\tag{6}$$

Comparing two different inlet temperatures and rearranging Equation (6) to be similar to Equation (4) leads to the speed correction Equation (7),

$$
\omega\_1 = \frac{\omega\_0 \cdot \sqrt{T\_1}}{\sqrt{T\_0}} \tag{7}
$$

where *ω*<sup>1</sup> is the assigned speed for *T*1, taking the speed *ω*<sup>0</sup> at temperature *T*<sup>0</sup> as the reference point. Varying inlet pressures do not affect the corrected speed.

#### **3. Experimental Setup**

To validate the developed equation, experimental tests were performed with an EK10AA turbo charger (Rotrex A/S, Ishøj, Denmark) [23] and an EMTC-150K AIR (FIS-CHER Fuel Cell Compressor AG, Herzogenbuchsee, Switzerland) [21] in a custom-made climate chamber [26]. The test bench setup, shown in Figure 1, was similar to the one described in [9]. Filtered ambient air was compressed with the specified electrical turbo charger. The heated air was cooled with an air-to-liquid intercooler before it passed the mass flow control valve. Sensors measured the compressors' static in- and outlet pressures (PT0517 and PT5504, ifm electronic GmbH, Essen, Germany) and temperatures (HFM5, Robert Bosch GmbH, Germany and TM4101 ifm electronic GmbH, Essen, Germany) as well as the air mass flow (HFM5, Robert Bosch GmbH, Gerlingen, Germany). Compressor speed and the state of the throttle valve were set manually in the control software. Each curve was recorded at its respective compressor speed. The maximum possible speed was 140 krpm for the Rotrex and 150 krpm for the Fischer compressor.

**Figure 1.** Schematic of the test bench setup, including air filter, compressor with inverter, intercooler, mass flow control valve and sensors.

According to Bernoulli's principle Equation (8), the dynamic pressure *pdyn* calculated from mass flow and density was added to the measured static pressure *psta* to obtain the total pressure *ptot*.

$$p\_{tot} = p\_{sta} + p\_{dyn} = p\_{stat} + \frac{1}{2} \cdot \frac{R\_S \cdot T \cdot \dot{m}^2}{p\_{sta} \cdot \pi^2 \cdot r^4} \tag{8}$$

Compressor outlet pressures were measured for inlet pressures of 940, 700 and 500 mbar(a) ± 20 mbar and inlet temperatures of −10, 5, 20 and 40 ◦C e 4˙ ◦C. In a further experiment, variation of inlet pressure and temperature were combined according to Table 1 to simulate the operating conditions of real flight altitudes.


**Table 1.** Values used for simulated altitude, oriented towards the international standard atmosphere.

#### **4. Results and Discussion**

#### *4.1. Pressure and Temperature Dependence of the Compressor Map*

For the following considerations, the measurements with the Rotrex EK10AA turbo compressor were evaluated because its compressor map is not determined by the power limit. Figure 2 shows the measured outlet pressures over the air mass flow for varying compressor inlet pressures (940 mbar, 700 mbar and 500 mbar) and rotational speeds of 120 and 140 krpm. These speeds were chosen because they represent the upper, applicationrelevant part of the compressor map. The observed shifts in pressure and mass flow for constant speed were valid for lower speeds in the same way. Points close to the surge line were avoided and only tested for the combined pressure and temperature variations since it was not clear how much mechanical overstressing the compressor could handle.

**Figure 2.** Absolute compressor map for 940, 700 and 500 mbar(a); inlet pressure and compressor speeds of 140 and 120 krpm; and 20 ◦C inlet temperature.

Figure 2 shows clearly that decreasing the inlet pressure led to a decrease in measured outlet pressure for the same air mass flow over the full compressor map, as was expected. For 140 krpm and an inlet pressure decrease from 940 mbar(a) to 700 mbar(a), the outlet pressure was reduced by more than 500 mbar for all mass flows. Further lowering to 500 mbar(a) inlet pressure led to an additional decrease of about 600 mbar for the same mass flow. The maximum air mass flow provided by the compressor also changed with inlet

pressure. The maximum air mass flow reduced from 90 g/s for 940 mbar(a) inlet pressure to 69 g/s for 700 mbar(a) and 47 g/s for 500 mbar(a). A similar behavior of outlet pressure and mass flow reduction was observed for all compressor speeds. The absolute outlet pressure difference for varying inlet pressures was smaller for lower compressor speeds. For example, for 120 krpm and 50 g/s, the difference between 940 mbar(a) and 700 mbar(a) was 560 mbar, compared to 700 mbar for 940 mbar(a) inlet pressure. The reason for this was a lower compression ratio at lower speeds and a resulting lower absolute difference.

Figure 3 shows the outlet pressure curves for rotational speeds of 120 and 140 krpm for four different air inlet temperatures (−10 ◦C, 5 ◦C, 20 ◦C and 40 ◦C).

**Figure 3.** Absolute compressor map for varying inlet temperatures of −10 ◦C (dark blue), 5 ◦C (light blue), 20 ◦C (black) and 40 ◦C (red) and varying compressor speeds of 120 krpm (empty points) and 140 krpm (filled points).

From the measured curves, it can be seen that lower inlet temperatures enabled higher compressor outlet pressures. For the maximum compressor speed, a 50 K temperature decrease from 40 ◦C to −10 ◦C led to a higher outlet pressure of about 400 mbar for all mass flows. Furthermore, the maximum possible mass flow increased from 86 g/s to 92 g/s. These influences of the inlet temperature were also confirmed by the measurements for 5 ◦C and 20 ◦C. For lower compressor speeds, the difference in absolute outlet pressure again decreased because of the lower pressure ratios, as described for varying inlet pressures.

Figures 2 and 3 show that the inlet pressure and temperature both have a significant influence on the compressor outlet pressure and need to be considered for a fuel cell system in airplane applications.
