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Energies 2018, 11, 217 10 of 26 model is chosen. Equations (5) and (6), which are taken from [56], are varied using more detailed and reliable data achieved from GasTurb [57] modeling: T = k1P0σk2 /MNk3 , (5) PSFC=c 1−c P ×10−3[1−M c3], (6) 120N where T and PSFC are available operating thrust and power specific fuel consumption at desired given condition, P0 is the sea level maximal power, σ is the air density ratio (operating flight altitude to sea level), which represents the impact of flight altitudes. ki and ci are to-be-determined factors. It has to be noted that ki and ci can be selected based on thrust output requirement, which depends on flight altitudes and Mach numbers. The values of ci can be selected by detailed engine modeling with a typical combination of {2.88, 0.025, 0.2}, as suggested by Howe [56]. In this model, higher drag parameters caused by idling propellers are neglected, which could be achieved by introducing a blade folding mechanism [13]. The described input parameters and models are taken for a first initial aircraft sizing, which delivers minimal power-to-weight and weight-to-wing-ratios (Figure 3). On this basis the components are sized including geometric information such as the vertical tail sizing, which is effected by the different HEA configurations and the wingtip propeller. Performance estimations are iterated over the flight mission. The resulting MTOW converges for each OAD process until an optimal design is found. A coding for the simulation results is introduced to distinguish between the HEA configurations. RTP-x-y is used to describe the HEA strategy of the regional turbo-prop with the DoH x and the battery strategy parameter y. RTP-0-0 represents a conventional aircraft and RTP-1-1 is a FEA. For the following analysis resolutions of 0.01 for both hybridization and battery strategy parameter are applied. 3.4. Validation and Verification Due to the very limited data of turboprop aircraft available in literature, the ATR-42 aircraft is chosen to verify the validity of the calculation methods. Details about performance and dimensions can be found in [58]. The mass breakdown data of ATR-42 are derived from [59]. As presented in Table 2, the modeling results show very good accuracy for most components. Table 2. Simulation tool validation: Comparison of the simulated ATR-42 data with reference data. Parameters Passenger number Design range (NM) MTOW (kg) OWE (kg) Wing mass (kg) Fuselage mass (kg) Vertical tail plane mass (kg) 4. Results Original Data ATR-42 48 800 16,150 10,253 1565 2587 322 Calculated Data 48 800 16,132 9266 1558 2394 319 Deviation (%) 0 0 −0.11 −9.63 −0.45 −7.46 −0.93 The simulation results of the battery performance and its influence on the OAD are investigated in this section. The results of the HEA configurations with HP = [0.1, 0.9] are pictured in heat maps. The DoH is shown on the x-axis and the battery strategy parameter on the y-axis. A color scale is given for the values of the parameters. A scale limit is introduced for each parameter as these can exceed reasonable magnitudes for some HEA configurations. The OAD parameters correlate with each other and a significant growth of one parameter has a reinforcing effect on others. The limits are set, when the exponential growth of the parameters increases critically. This is decided for each parameter individually. Values beyond these limits are displayed in white. Since the conventional RTP-0-0 andPDF Image | Design of Operation Strategies for Hybrid Electric Aircraft
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