Future High-Efficient Engines with Solid Oxide Fuel Cell–Gas Turbine Coupling: System Modeling and Comparison of Directly and Indirectly Coupled SOFC-GT Systems ^†

Abstract

Aviation demand is projected to surpass 8 billion passengers per year by 2040, increasing the climate burden of kerosene-fueled propulsion. Conventional engines emit CO₂ and non-CO₂ species such as nitrogen oxides and soot, which significantly contribute to global warming. Hydrogen-based propulsion combining Solid Oxide Fuel Cells (SOFCs) with a Gas Turbine (SOFC–GT) can offer a carbon-neutral alternative with the potential for higher efficiencies than current turbofan and turboprop systems. In an SOFC–GT concept, waste heat from the SOFC is recovered in the turbine cycle, while the electrical output drives an electric motor, forming a hybrid turbomachinery–electric powertrain. Achieving SOFC operating temperatures of 650–800 °C at cruise conditions represents a key thermodynamic challenge, as compressor outlet conditions are insufficient. Two architectures are analyzed: direct coupling, where SOFC requirements define turbomachinery operation, and indirect coupling, which introduces air bypasses to increase flexibility. The results show that direct coupling enables higher cycle efficiency, whereas indirect coupling improves off-design operability at the expense of performance. Cross-validation of independent simulation frameworks strengthens the reliability of the findings and provides a foundation for evaluating SOFC–GT propulsion feasibility.

1. Introduction

The global transition toward sustainable energy sources places significant pressure on the aerospace sector to develop highly efficient, low-emission propulsion systems [1,2,3]. Solid Oxide Fuel Cell–Gas Turbine (SOFC-GT) hybrid cycles have emerged as a highly promising candidate, offering the potential for substantial efficiency improvements over conventional gas turbines (GTs) due to the synergistic operation of the fuel cell integrated in the gas turbine system. The integration of these two systems allows for high thermal efficiencies, particularly since the high efficiency of the SOFC enables optimal performance especially with a relatively low turbine inlet temperature (TIT), a characteristic that fundamentally diverges from conventional GT design philosophy as demonstrated in previous work of the authors [4].

Current research efforts are intensely focused on either stationary systems or aviation auxiliary power units (APU) [5,6]. Although studies on SOFC-GT systems for primary aircraft propulsion are increasing [7,8,9], the field remains small, primarily because the gravimetric power density of state-of-the-art SOFC stacks is still low for weight-sensitive applications such as aviation. However, ongoing SOFC development offers a promising outlook for future power densities [10]. Still, it is reasonable to assume that, in the near future, the gravimetric power density of SOFCs will remain lower than that of conventional gas turbine systems. SOFCs are therefore the critical factor in total weight, though determining mass requires more detailed analyses of the designed system, particularly in the context of multipoint analysis rather than the design point analysis performed here. Nevertheless, it can be deduced from this, however, that the power share (PS) between the SOFC’s electrical power and the mechanical power generated by the turbine is a critical initial indicator for a qualitative estimate of the system weight. Thus, a system with a high electrical power share corresponds to a higher system weight under the current assumption of a low gravimetric power density of the SOFC. However, if the SOFC’s power density exceeds that of the gas turbine system, this analysis would no longer apply and the aforementioned effects would be inverted.

Previous work focused on the fundamental system characteristics of SOFC-GT hybrid cycle using high-temperature heat exchangers, showing that the utilization of the cathode’s outlet gas is a promising system architecture regarding efficiency and, e.g., heat exchanger size. Based on this study, the primary aim of the following investigations is to systematically investigate the additional design flexibility and efficiency trade-offs introduced by directly versus indirectly coupled SOFC-GT configuration with an air bypass shown in Figure 1 for an aircraft’s cruise point. The work focuses specifically on how different constraints within the system dictate the minimum achievable power share in the directly coupled system. Subsequently, the analysis examines the use of an air bypass mechanism to enable indirect coupling between SOFC and GT, providing system designers with the flexibility to select lower PS operating points, a necessity imposed by current SOFC power density limitations, and quantifying the associated efficiency penalty.

Figure 1. Schematic overview and comparison between (a) directly coupled SOFC-GT architecture and (b) indirect-coupled architecture with air bypass.

The key findings demonstrate that the directly coupled configuration invariably yields the highest overall efficiency but is constrained by a minimum power share threshold. The indirect coupling, facilitated by the bypass, offers a crucial short-to-medium-term solution by providing essential design flexibility across a wider range of PS values, thereby mitigating the current weight challenges posed by heavy SOFCs. Furthermore, our analysis highlights the significant implications of the coupling configuration on the system’s mass flow response to off-design conditions, underscoring the necessity of integrated thermal and flow control strategies for maintaining SOFC integrity. A detailed analysis can be found in the full-paper [11].

2. Methodology

The modeling approach follows previous work [4], integrated in a Matlab/Simulink R2024a framework, and is based on a one-dimensional SOFC model adapted from Hollmann et al. [12,13], using experimentally derived area specific resistance (ASR) correlations of an electrolyte supported stack from [14]. The active cell area is assumed to be 127.8 cm². The operating conditions of the fuel cell will remain constant within this study by fixing the current density to 0.2 A/cm², the fuel utilization to 80% and a temperature difference ($\Delta$T) to 150 K between the inlet and outlet. Since the temperature difference of the SOFC is an important metric for ensuring safe operating conditions for the SOFC, the air mass flow of the system is defined in the design in such a way that the excess air provides exactly the cooling effect required to maintain the $\Delta$T.

The turbomachinery is based on lumped zero-dimensional models with constant isentropic efficiencies. Based on the baseline engine from [15], the compressor has an efficiency of 86%, the high-pressure turbine (HPT) 88%, and the low-pressure turbine (LPT) 90%. The pressure ratio of the compressor is set constant to 25 as a result of [4]. The combustion chamber is modeled assuming a complete fuel burn. Cooling of the combustion chamber as well as of the HPT inlet is initially neglected. A combined pressure loss of the combustion chamber and the SOFC is assumed to be 5% of the respective SOFC inlet pressure. As no turbomachinery maps are considered within the scope of this study, a constant pressure ratio between the LPT outlet and ambient of 1.1 is assumed. The outlet pressure of the HPT is manipulated in order to ensure power balance between the compressor and HPT.

Heat exchangers are modeled using the number of transfer units (NTU) method [16] in counter-flow configuration and scaled to achieve the target SOFC inlet temperature of 700 °C. Power electronics and the electric motor are modeled with constant efficiencies of 98% and 95%, respectively, resulting in a total electrical efficiency of 93%. Thermal management components to reject low-temperature heat are not included.

An aircraft similar to the ATR-72 is assumed, requiring 1200 kW shaft power per engine and an additional 60 kW power off-take directly from the SOFC during cruise. Flight conditions correspond to FL250 (7.6 km, ISA), with 39,200 Pa ambient pressure, 240 K temperature, and Mach 0.44. The system’s thermal efficiency

$${\eta }_{\mathrm{sys}}={\displaystyle \frac{\left|P_{\mathrm{out}}\right|}{{\dot{m}}_{\mathrm{fuel}}·LH{V}_{\mathrm{fuel}}}}={\displaystyle \frac{\left|P_{\text{E-Motor}}\right|+\left|P_{\mathrm{LPT}}\right|}{{\dot{m}}_{\mathrm{fuel}}·LH{V}_{\mathrm{fuel}}}}$$

(1)

is defined as the ratio of total output shaft power to the chemical power supplied by the fuel mass flow and the corresponding lower heating value (LHV). The resulting electrical power share

$$PS=P_{\text{E-Motor}}/P_{\mathrm{out}}$$

(2)

is the ratio between the mechanical output power of the electrical motor and the LPT. For the directly coupled system, the number of SOFC cells is scaled in order to reach the target system output power as both SOFC and GT power scale with the number of cells. For the indirect coupled system, the number of cells is scaled to reach the target electrical power share, which defines the required SOFC air mass flow due to the cooling constraint. To reach the total system output power, additional fuel is added to the combustion chamber together with an increased air mass flow through the bypass defined by the air bypass ratio

$$\mathrm{ABR}={\dot{m}}_{\mathrm{air}, \mathrm{bypass}}/{\dot{m}}_{\mathrm{air}, \mathrm{SOFC}}.$$

(3)

3. Results

The subsequent analysis focuses on the distinct operational characteristics of the so-called “Directly Coupled” and “Indirectly Coupled” hybrid system configurations. As explained in previous work, the electrical power share is a result of the operating conditions of the system, where the maximum electrical power share results from the SOFC exhaust utilization by the gas turbine and directly depends on the turbine inlet temperature resulting from the SOFC operating constraints. Since electrochemical conversion is inherently more efficient than hydrogen combustion and subsequent conversion in a gas turbine, SOFC-GT systems with high electrical power shares yield the highest system efficiency. This results in the general characteristic that SOFC-GT systems with high electrical power shares are most efficient. Still, considering the propulsion system on aircraft level, the trade-off between engine weight and efficiency must be taken into account addressed with the analysis of the power share. For constant operating conditions of the fuel cell, the electrical power share can be decreased by increasing the turbine inlet temperature (TIT) by injecting additional fuel to the combustion chamber as shown in Figure 2. However, this is limited as maximum temperatures needs to be accounted as material or design limitations. Here, the maximum TIT is considered to be 1400 K. As shown, under the given operating conditions and the maximum temperature of 1400 K, the minimum resulting power share is 49%. Even if the consideration of higher maximum TIT would lead to lower power shares, additional fuel injection eventually leads to unburned hydrogen after the combustion chamber, represented by the visible drop of temperature. Contrary to classical gas turbine development, this results in a decrease of thermal efficiency with higher turbine inlet temperatures, showing the unique characteristic of directly coupled SOFC-GT systems.

Figure 2. Resulting turbine inlet temperatures with variation in power share (a) and the respective thermal efficiency (b). The grey lines indicate exceeded turbine inlet temperatures.

To enhance the design space of SOFC-GT systems, the introduction of an air bypass stream as depicted in Figure 1 enables the indirectly coupled configuration to overcome the inherent operational limits of the directly coupled system. Using the bypass allows independent control of the SOFC temperature difference ($\Delta$T) and the turbine inlet temperature. This means that the power share can now be freely modulated. Eventually, the gas turbine process can be designed independently of the fuel cell in order to reach lower electrical power shares. The following analysis shows the resulting system characteristics for the different turbine inlet temperatures while keeping the SOFC inlet and outlet temperature fixed. Starting with the turbine inlet temperature of the directly coupled system (925 K), the temperature is increased to 1200 K and 1400 K for comparison of both system configurations.

Setting the design power share is done by utilizing the air bypass by scaling the air mass flow until the required mechanical output power of the power turbine matches the targeted power share at the defined target turbine inlet temperature shown by increasing bypass ratios (Figure 3a). A switch in system characteristics can be observed. For the directly coupled variant, the air mass flow decreases with lower electrical power share. This trend results directly from the decreasing number of cells, which defines the air mass flow per cell described with the oxygen utilization. Contrary, the air mass flow increases for the indirectly coupled system due to the scaling effect on the mechanical output power. Furthermore, it becomes clear that the effect of increasing air mass flow is even reinforced at lower turbine inlet temperatures. While the directly coupled system at a turbine inlet temperature of 1400 K at lowest electrical power share (49%) requires a mass flow of 1.36 kg/s, determined by the necessary SOFC cooling, this value increases to 2.24 kg/s in the indirectly coupled system for an electrical power share of 20%. Decreasing the turbine inlet temperature to 1200 K, the required air mass flow at 20% electrical power share is 3.39 kg/s.

Figure 3. Comparison of directly and indirectly coupled SOFC-GT systems: (a) Air mass flow (solid lines) and air bypass ratio (dashed lines) and (b) resulting thermal efficiency for different maximum turbine inlet temperatures (TIT). The dashed grey line indicates exceeded maximum turbine inlet temperature in the directly coupled configuration.

However, the hereby gained design flexibility is realized at the cost of overall cycle thermal efficiency. A comparative examination of the efficiency curves (Figure 3b) reveals characteristic differences in curvature. First, it can be seen that the directly coupled system is always the most efficient as the electrochemical fuel conversion, which produces less entropy and dominates the electrical power share. This characteristic results in the highest efficiency of 63.4% at the highest possible electrical power share, meaning no additional fuel is combusted and therefore the turbine inlet temperature remains significantly lower than known from conventional gas turbine development. Accordingly, an increased turbine inlet temperature results in lower efficiency, i.e., 56.9% for a TIT of 1400 K. For even higher TIT, the characteristic efficiency decrease continues until not enough oxygen is available to completely combust the hydrogen. Although this condition is not representative for a practical design point, its inclusion in the sensitivity study demonstrates a sharp drop in overall efficiency.

Second, the directly coupled efficiency curve exhibits a distinct concave shape, whereas the indirectly coupled curve displays a convex shape. This distinction clearly illustrates a fundamental shift in system characteristics: at lower power shares, the indirectly coupled system increasingly adopts the characteristic behavior of the conventional gas turbine cycle, diverging significantly from the high-efficiency synergy of the SOFC-GT hybrid. In this GT-dominated regime, a higher turbine inlet temperature becomes advantageous for improving overall efficiency at a given, selected power share. Conversely, if the design objective is the maximization of efficiency for a defined power share, the operational domain of the Directly Coupled system prevails, where a high electrical Power Share coupled with a low turbine inlet temperature remains to be the optimal configuration.

4. Cross-Validation

In the absence of experimental reference data, the obtained results were cross-validated using two independently developed simulation frameworks. The first model, implemented in MATLAB (R2024a)/Simulink at Leibniz University Hannover (LUH), and the second, developed in Modelica (version 3.2) at the German Aerospace Center (DLR), were configured separately to ensure methodological independence and avoid cross-dependencies that could bias the comparison. This approach allows a robust consistency check of the underlying physical models and numerical solvers.

As shown in Figure 4 and Table 1, both models exhibit excellent agreement across key system-level quantities such as the air mass flow rate, bypass ratio, and overall thermal efficiency. For higher turbine inlet temperatures, the mean deviation between the two simulations remains below 0.5% for both air mass flow and thermal efficiency, confirming a high degree of numerical consistency. At low turbine inlet temperatures (925 K), the deviation of air mass flow remains below 2.5%. The maximum deviation of the resulting thermal efficiency is 2.60%. The latter arises from differences in heat transfer correlations and SOFC parameterization. The increasing discrepancies at lower turbine inlet temperature indicate that the main variations stem from the SOFC model itself.

Figure 4. Cross-validation comparison of (a) air mass flow and (b) thermal efficiency.

Table 1. Cross-validation results for mass flow and efficiency deviations.

TIT in K	Mean $\mathsf{\Delta }{\dot{\mathit{m}}}_{\mathbf{air}}$	Max. $\mathsf{\Delta }{\dot{\mathit{m}}}_{\mathbf{air}}$	Mean $\mathsf{\Delta }{\mathsf{\eta }}_{\mathbf{sys}}$	Max. $\mathsf{\Delta }{\mathsf{\eta }}_{\mathbf{sys}}$
925	2.20%	2.28%	2.06%	2.60%
1200	0.30%	0.38%	0.38%	0.52%
1400	0.35%	0.41%	0.45%	0.50%

This cross-validation strengthens the credibility of both frameworks and provides valuable insight into numerical sensitivities and parameter dependencies. Minor deviations, for example, can reveal differences in property databases, discretization strategies or heat transfer correlations. The cross-validation approach therefore establishes a solid foundation for future integration studies with experimental validation once test data become available.

5. Discussion and Outlook

Solid Oxide Fuel Cell–Gas Turbine (SOFC-GT) hybrid systems represent a highly promising alternative for future aircraft propulsion concepts due to their exceptional overall efficiency of possibly more than 60%. However, the current technological limitation lies in the low gravimetric power density of SOFC stacks. This increased efficiency is due to the high efficiency of electrochemical fuel conversion and the synergy with the re-utilization of the high temperature waste heat of the SOFC. Consequently, the chosen electrical power share (PS) between fuel cell and turbines becomes a critical design variable directly influencing the overall system weight. As demonstrated in the results, directly coupled SOFC-GT systems impose a non-negotiable minimum PS that cannot be undercut for the directly coupled configuration under the given assumptions. If system weight constraints necessitate designing the engine below this minimum PS, the introduction of a bypass mechanism, which enables indirect coupling, becomes a valuable design choice.

While the bypass reduces the system’s efficiency compared to the purely directly coupled optimum, the resulting hybrid still offers a significant efficiency increase over a conventional gas turbine system. Crucially, the bypass introduces flexibility in the PS design point, allowing engine designers to strategically trade off system efficiency for favorable weight adjustment. It is unequivocally confirmed that the directly coupled system always yields the highest overall efficiency. Therefore, the indirectly coupled SOFC-GT system is not the long-term optimal solution but rather a short-to-medium-term alternative that provides essential PS flexibility, even with moderate SOFC power density. With continued advancements in SOFC power density, the long-term objective remains the implementation of the directly coupled configuration to achieve maximum efficiency gains in propulsion technology.

Beyond providing design flexibility, the introduction of a bypass also offers significant potential advantages concerning the Off-Design performance and control of the system. Given that the highest air preheating demand occurs at the cruise flight phase (due to lower ambient temperature), only the cruise point was considered for the system design analysis presented here. However, it is well known that the resulting air mass flow differs significantly between various operational points along the flight phases. Since the mass flow in the directly coupled system dictates the thermal management of the fuel cell stack, the ability to regulate it becomes paramount. An insufficient mass flow rate would lead to an increase in the temperature difference ($\Delta$T) across the SOFC, resulting in detrimental thermo-mechanical stresses that can cause cell failure. Conversely, a higher mass flow rate would decrease the $\Delta$T, mitigating thermal stress but potentially increasing the internal resistance of the SOFC, which could cause a corresponding voltage drop. A detailed, transient analysis of the off-design mass flow management and its effect on SOFC integrity is therefore required.

As a final outlook for subsequent studies, the behavior of alternative system configurations should be considered. While the current analysis exclusively focused on utilizing the cathode exhaust gas for preheating the incoming air, the thermodynamic properties suggest that employing the exhaust gas from the Low-Pressure Turbine (LPT) might offer an attractive alternative for heat integration.