Hybridisation and electric machine

Due to the hybridisation of the N1 shaft, less fuel flow is required for the same thrust. On the one hand, the HPC thus operates at lower mass flows and pressure ratios. On the other hand, the speed of the LP- system is kept constant, so the LPC is throttled by the lower mass flows of the HPC. Based on this, only 1 and 2 MW electric machine (EM) will be investigated (Schuchard et al., 2023).

The power management and distribution (PMAD) system, responsible for distributing power to electrical equipment such as controls, inverters, and cables, is modelled at a constant efficiency of 97%. The efficiency of the electric machine in converting from electrical to mechanical energy is plotted against speed N and torque τ in a characteristic map. This is given in Figure 3 for an EM with a maximum continuous power of 1 MW.

Figure 3.

Efficiency of the electric machine as a function of torque and speed.

The EM designed by means of a finite element method is of a 9-phase design and has a power density of 6.86 kW/kg. The total weight of the electrical machine is 145.7 kg. The 9 phases are divided into three 3-phase systems each, which are necessary for the torque generation. The redundant design increases the reliability of the electrical machine because failures in one of the three 3-phase systems, which according to He et al. (2014) can account for up to 66% of the total faults, can be compensated for by the other two 3-phase systems. The main cause of the failures is due to increased partial discharge activity (Hanisch and Henke, 2022). The electric machine can basically be operated at all operating points within the characteristic diagram in Figure 3. In the control strategy presented here is operated at maximum torque τ which is available depending on the current speed in order to provide maximum electrical support. Therefore, the design of the electric machine focuses on high efficiency under full load. To investigate the effects of different levels of electrical support, a second electric machine with 2 MW is being developed. The increased power is achieved by geometrically scaling the second machine at constant voltage and current density. The total weight of the 2 MW machine is 256.7 kg. The axial length increases by 19% from 218.1 mm to 259.6 mm and the diameter increases by 23% from 357.7 mm to 438.7 mm.

It should be noted that the parallel hybrid-electric architecture is a complex system and requires a multi-disciplinary approach for accurate analysis. The interaction between the conventional engine and the electric motor, as well as the PMAD system, must be considered. Furthermore, the electrical components’ impact on the engine’s performance, fuel consumption, and emissions must be evaluated. This necessitates the development of sophisticated mathematical models that can capture the system’s dynamic behaviour, as well as the aerothermal and mechanical characteristics of the various components.

Unsteady propulsion performance simulation

In general, the equations of motion are used to model the performance of aircraft engine as well as the temporal and spatial aerothermodynamic properties in the gas path and the system behaviour of the solid components. The equations of motion are divided into the continuity, momentum, and energy equations (Liepmann and Roshko, 2001). The focus of the modelling is on the overall system performance, which considers only the 1D flows in the gas path. The system of differential equations 1 describes the conversation of mass, momentum, and energy with the cross-section A, density ρ, velocity u, internal energy E, pressure p as well as the bleed mass flow m˙bleed, momentum F and the heat flux Q˙.

Due to the complexity of the equations of motion, various numerical approaches are used to solve the differential equation system. In general, the methods can be classified into stationary and unsteady models. The unsteady models can also be divided further into transient and dynamic methods. Essentially, transient effects are observed on time scales of seconds to minutes, while gas dynamics are on the order of milliseconds (Garrard, 1995). For the unsteady performance simulation, a steady-state initial point is required. Therefore, an iterative process, based on the constant-mass-flow (CMF) method is used (Kurzke and Halliwell, 2018; Goeing et al., 2023). The unsteady performance of the parallel hybrid-electric turbofan engine is simulated with a dynamic approach and the transient CMF method.

Dynamic model

Based on the governing equation system 1, an ordinary differential equation system is spatially discretised (see Equations 2–6), which represents the quasi 1D gas path and describes the dynamic approach Sugiyama et al. (1989). The component characteristics are included via the surface forces FP and FT. The pressure ratio π and efficiency η are imposed on the compressor and turbine volumes, while the burner efficiency and pressure losses are imposed on the combustor volume. The energy and momentum contributions of gravitational forces have been neglected and the frictional shear stress tensor is replaced by the Fanning and Darcy friction coefficient λ. The values in the control volumes are described with the incoming (.)in and outcoming (.)out values.

Furthermore, the heat flux between components and gas path are characterised by the Q˙ in Equation 6. The Q˙ represents the heat transfer rate per unit time and depends on the product of surface area S, the convective heat transfer coefficient α and the difference between wall temperature Tw and gas temperature T (Li et al., 2022). In this study, only heat fluxes in the control volumes of the combustion chamber, HPT and LPT are considered:

Finally, the change in rotational speed is determined based on the applied torques of the turbines τT and compressors τC and the moment of inertia J. Furthermore, the EM supports the turbines:

This system was implemented in MATLAB/-Simulink 2019a. The ordinary differential equation system is solved using a variable-order method, which sets the time step with a relative tolerance of 1⋅10−6.

Constant mass flow method

The transient CMF method is illustrated by the flowchart in Figure 4. Based on a steady-state operation point, a global cycle process calculation is performed. In contrast to the steady-state CMF method, an imbalance between the compressor and turbine torque is allowed (Palmer and Cheng-Zhong, 1985; Kurzke and Halliwell, 2018) to compute the change in rotational speed (see Equation 8). The iteration variables are varied until the steady state continuity equation and expansion conditions are satisfied within the time step. The momentum equation is not included. Once the steady state target functions have converged, the transient operating point is reached, and the rotational speeds for the next time step are integrated from the time-dependent power difference. The new time step is initiated by changing the fuel flow m˙f. The corresponding turbine entry temperature (TET) is iterated by energy conservation within the combustor. The operating point at time t is not dependent on time t−1, except for the iterated TET and integrated rotational speeds, which are used as input parameters for the global iteration process for the next time step. No length-specific quantities are required, making it a 0D method. A time step study was conducted for the CMF methods, which showed convergence at dt = 0.001 s.

Figure 4.

Flow chart of the transient constant mass flow method.

Based on the energies in the gas path and materials, the heat fluxes and thus the temperatures are updated after each iteration (Walsh and Fletcher, 2004). Thus, the information is not fed back during one iteration and does not affect the transient cycle process. Compared to the dynamic approach, aerothermodynamic interdependencies within the gas path as well as with the entire thermodynamic cycle are not taken into account.

The performance maps of the components are used form Goeing et al. (2020) and the models are validated in Goeing et al. (2021). Although the methods access the same gas tables, performance maps and correction models, parameter errors exist due to the different solution approaches. This maximum parameter error is 0.2% (Lück et al., 2022).

For further use, the surge margin SM between surge line SL and the operating point OP at constant rotational speed is defined as follows (Kurzke and Halliwell, 2018):

The deviation δ between the dynamic approach and the CMF-method is calculated as follows:

Aerothermodynamic interdependencies

Firstly, this section explains the aerodynamic interdependencies that exist in a conventional aircraft engine. For this purpose, the CMF method is compared to the dynamic approach, with a particular focus on the HPC without hybridisation and heat flux. Figure 6a shows the predicted time-dependent operating line. The dashed blue line represents the dynamic approach, while the blue solid line shows the CMF method. The curves are presented in the HPC performance map, which depicts the black speed curves in terms of pressure ratio π over corrected mass flow rate m˙corr.,HPC. It can be observed that the dynamic approach is below the CMF method during acceleration and above during the deceleration. This can be attributed to the volume storage effect that is taken into account by the dynamic model (Hashmi et al., 2021). The system responds more slowly due to volume storage, resulting in a flattening of the operational line.

Figure 6.

Numerical comparison of the HPC operating line. Left: operating line simulated by the dynamic approach and the CMF method. Right: deviation of the pressure ratio, mass flow and SM between the dynamic approach and the CMF method.

In Figure 6b the deviations δ of π in dark blue, m˙ in blue and SM in light blue between the dynamic and CMF-model are shown. Furthermore, the time points of the extreme values of the FAR are marked with the solid black line. It can be observed that the maximum deviations appear between the solid and dashed lines in the acceleration and at the black line in the deceleration. Furthermore, the deviations increase up to 3% (Q4) in pressure, 5% (Q4) in mass flow rate and decrease until −8% (Q1) in the SM. The deviations are greater during acceleration than during deceleration. Particularly noticeable is that the impact of system inertia increases up to the maximum FAR, and thus is not solely responsible for the maximum deviations that occur after the solid black line.

The impact of the volume storage effect on the cycle process is particularly evident in the case of the FAR, which is shown in Figure 7a for the different components over time. The profiles demonstrate that the results of the dynamic model have significantly higher FAR in the combustor (FAR₄), high-pressure turbine (FAR₄₁), and low-pressure turbine (FAR₄₅), than the results of the CMF method. The direct influence of volume storage reduces the mass flow rate during acceleration. This reduction in mass flow rate increases the FAR. This aerothermodynamic interdependence is only captured by the dynamic model, resulting in the CMF method predicting a smaller FAR (see magnification). Furthermore, the relative deviations of FAR₄, FAR₄₁ and FAR₄₅ of are shown in Figure 7b. As expected, the different variations of the FAR behave similarly and are significantly influenced by the core mass flow.

Figure 7.

Numerical comparison of FAR. Left: FAR simulated by the dynamic approach and the CMF method. Right: deviation of the FAR between the dynamic approach and the CMF method.

Figure 8 illustrates the process of fuel mass flow rate changes, using the example of control volumes of the turbines and the entire cycle process within one time step. Changing the fuel flow leads to a new Tt4, which in turn changes the pressure, density, and mass flow rate due to the equations of motion and the ideal gas law. This also affects the entire cycle process, leading to changes in FAR and operating point.

Figure 8.

Aerothermodynamic Interdependence during a time step inside the turbines.

These aerothermodynamic interdependencies become significantly more complex due to further secondary effects. Using heat transfer as an example, this section illustrates how the heat fluxes Q˙ change between the gas and wall material due to a change in the fuel mass flow rate. The heat flux, in turn, interacts with the wall temperature. A new wall temperature, in turn, leads to a new heat flux and a new gas temperature (yellow circles in Figure 8). This gas temperature also affects the control volume of the turbines and influences the operating point. This impact of the heat flux will be investigated in the next section.

Heat fluxes

To advance the exploration of aerothermodynamic interdependencies, the convective heat transfer within the turbines of an aircraft engine, specifically between the gas path and materials is considered. For this purpose, the same surrogate models and correlations for discs, blades, and housings are used in the CMF method and in the dynamic model (Stephan et al., 2019; Li et al., 2022). In Figure 9a, the temperature profiles of the miscellaneous components are shown, while the box plot of relative temperature deviations is displayed in Figure 9b. The results of the deviation between the CMF and dynamic model with heat convection are illustrated in yellow and compared to the box plots from the previous subsection without heat fluxes in the same figure in blue. The temperature profiles can be qualitatively divided into temperatures upstream and downstream of the combustor. The predicted temperatures of both methods simulate qualitatively comparable profiles. The largest discrepancies are visible in Tt5, due to the largest heat flux. In the box plot of Figure 9b, the difference between the two Tt5. values is particularly evident, and the modelled heat fluxes are the cause of the discrepancies. On the one hand, the heat flux dampens the discrepancies, with the range of deviations (Q1 until Q4) without heat flux being 5% and with heat flux being 3%. On the other hand, the box width (Q2 until Q3) and average |δ¯| increase significantly. Similar trends can be observed for Tt4. and Tt45, with the box shape of Tt4 approaching that without heat convection. This damping effect depends on the heat fluxes, which are strongest in the LPT. Moreover, it becomes apparent that the mean deviations in the entire cycle process increase due to the aerothermodynamic interdependencies. This effect leads to a significant increase in the compressor's temperature, particularly noticeable in the LPC, whose temperature deviation range (Q1 until Q4) increases from 0.7% to 2.1%.

Figure 9.

Numerical comparison of temperatures with and without heat flux. Left: temperatures simulated by the dynamic approach and the CMF method. Right: deviation of the temperatures between the dynamic approach and the CMF method.

Level of hybridisation

In this section the influence of hybridisation on the aerothermodynamic interdependence is examined in this section without heat transfer. For this purpose, the operating strategy shown in Figure 5b is used and connected to the 1 MW or 2 MW motors (see Figure 3). Due to the hybridisation of the aircraft engine, the LPC represents a critical component. The performance is examined more closely in Figure 10. In Figure 10a, the unsteady operating line during the manoeuvre of the LPC can be seen. The conventional aircraft engine without an electric motor is represented in blue, with 1 MW hybridisation in green, and with 2 MW in purple. The dynamic model is shown with the dashed lines and the CMF method with the solid lines. The diagram shows that the steady-state operating points are throttled at 103 kN by hybridisation, while the operating characteristics are identical at 11 kN (here, the EM is switched off). The use of the EM during time-dependent operation changes the unsteady operating characteristics and operates closer to the stability line. In Figure 10b, the differences of the SM between the CMF and the dynamic model are displayed. The plots exhibit a qualitatively similar behaviour. However, the box plots in the middle of the diagram demonstrate that the Q1 until Q4 and the median deviations increase due to the hybridisation. It is evident that the deviations in acceleration are particularly pronounced during engagement of the EM [also visible in the magnification of diagram (a)]. The deviations increase due to the control with the N1 rotational speed as well as with the interaction with the HPC, which is less stressed due to hybridisation.

Figure 10.

Impact of hybridisation on the LPC. Left: operating line during the transient manoeuvres of different aircraft configurations. Right: deviation of the SMLPC between the dynamic approach and the CMF method.

Finally, in Figure 11, the box plots of the deviations from the surge margin in diagram (a) as well as the thrust and rotational speeds in diagram (b) are shown. The results show the deviation with heat flux enabled for different levels of hybridisation. The deviations of the SM between the dynamic and CMF method increase in the LP-System and decrease in the HPC (see Figure 11a). This can be justified by the control strategy, as well as by the reduced stress on the HPC due to the hybridisation, which results in a smaller fuel flow step (see Figure 5). Furthermore, the diagram (a) shows that the LPC is most sensitive to the interactions and exhibits deviations of up to −13% (Q1). Also the aerothermodynamic interdependencies of the heat transfer increase the deviation significantly (compared to Figures 6 and 10).

Figure 11.

Numerical comparison between the dynamic approach and the CMF method with heat flux and different levels of hybridisation.

The influence of the control strategy on the deviation is also visible in diagram (b). While the deviations of N1 and the thrust increase slightly, the rational speed N2 decreases. The quantity of thrust displays the most significant deviations, as it is an integral parameter that reacts most sensitively to the interactions.