1 Introduction

To reach aviation’s long-term emission reduction targets motivated by the European Commission [1] and specified by ACARE [2], significant improvements along the entire efficiency chain of the air transport system are required. Within the framework of the German national aeronautical research program (LuFo-V-2) funded by the “Bundesministerium für Wirtschaft und Energie” the project “Technologien für REvolutionäre ArbeitsProzesse” (TREVAP) investigated technologies for revolutionary thermodynamic cycle designs. One particularly promising option for significant thermal efficiency enhancement beyond the Joule–Brayton cycle engines, which is part of the TREVAP research activities, is the so-called Composite Cycle Engine (CCE). It features a piston engine in the high pressure part of a turbo engine architecture behind the intermediate pressure compressor and before the Joule combustion chamber. This allows to benefit from the partially isochoric combustion during closed volume combustion and the higher permissible peak temperatures and pressures. The CCE concept is initially discussed in [3, 4] by Kaiser et al. and combines the high efficiency potentials of the Seiliger cycle, as present in piston engines, with the high specific power capability of gas turbine systems. In Fig. 1, the innovative thermodynamic cycle characteristics of a CCE are shown.

Fig. 1
figure 1

Enthalpy over entropy diagram of the Composite Cycle and conventional Joule–Brayton Cycle [5]

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Assuming the same technology levels, the CCE concept offers double digit fuel burn reduction potential above advance geared turbofan technology [3, 4], meeting in example the ARCARE targets specified in [2] for entry into service in year 2035 [3]. The technology may be combined synergistically with annexed technology such as intercooling [5,6,7], adaptive geometries [8], or boundary layer ingestion [9] to achieve emission reduction targets for year 2050.

Beside the piston engines approach, further technology concepts for realizing combustion with pressure gain, in example wave rotor combustors [10], pulsed detonation tubes [11] or nutating discs [11], are currently under investigation to increase thermal efficiency of aircraft propulsion systems.

In this paper, different piston engine concepts, in particular two- and four-stroke reciprocating piston engines as well as rotary engines as presented by Whurr [12] and Nickl et al. [5], are evaluated within a CCE architecture. Each piston engine configuration offers specific advantages, which mostly are connected with dedicated technological challenges. For example, the power-to-weight ratio of two-stroke reciprocating engines is supposed to be better than for four-stroke engines, while cooling demand and wall temperatures are more challenging due to the missing scavenging cycle. In Fig. 2, conceptual sketches of promising CCE engine architectures, which are investigated in this study, are illustrated. All investigated piston engine configurations are fueled with direct injected kerosene and operated with the Seiliger cycle process, which features a partially isochoric and partially isobaric combustion characteristic. As kerosene is very similar to diesel, it is used in piston engines as well [13].

Fig. 2
figure 2

Basic conceptual sketches of promising CCE concepts—a reciprocating piston compressors and engines (2-/4-stroke), b rotary piston engine in coaxial arrangement

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To identify the most fuel-efficient concept, thermodynamic cycle studies will be presented that integrate crank angle-resolved thermodynamic models of the piston engines in a turbo engine syntheses framework. A technology level representing entry into service in year 2035+ is assumed for all components. The CCEs are sized to deliver 22-MW shaft output power on the low-pressure spool under take-off conditions. Beside thermodynamic efficiency, the final rating of the different piston options will also include quantitative assessments of piston system weights and NOx emissions as well as qualitative evaluation of technological challenges and integration aspects for each concept.

2 Methods

For the investigation of the piston engines, parametric models are used to identify performance relevant parameters and geometric dimensions. The models provide crank angle-resolved data, which can be transformed to time-resolved data, to consider the non-stationary operation mode. Additionally, interactions of the piston system and the turbo engine components can be investigated using such models. Following, the methodology of piston engine performance modeling is described in detail. Furthermore, assumptions on weight, emission and cooling demand are presented.

2.1 Thermodynamics

For piston compressor and the different piston engines, the same methodology of thermodynamic process modeling is used in principle. Differences occur during combustion and the related heat transfers. No spatial resolution of thermodynamic states in the piston volume is used, which means that cycle parameters only vary in time. For each crank angle position, chamber geometry as well as mass and energy balance are computed as illustrated in Fig. 3. The cycle calculation iterates until end conditions match the starting values. The adoption of dimensionless formulated correlations based on characteristic numbers (Nusselt, Reynolds, Prandtl) allows variations of the actual piston geometry, and therefore ensures scalability.

Fig. 3
figure 3

Schematic illustration of thermodynamic piston cycle modeling

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The scavenging characteristic of the piston system during mass exchange results from inlet end exhaust valve modeling. The valves are assumed to be located at the cylinder head. Therefore, valve areas scale with piston diameter and are set to maximum feasible values for given piston diameters. For each piston, two inlet and two exhaust valves are modeled. Valve timings are defined according to crank angle with sinusoidal valve area opening and closing characteristics. Within the valve model, mass flow always develops in direction of negative pressure gradient to consider backflows through the valves. At each crank angle position, chamber surface areas for heat transfer calculations are derived from the piston geometry. By assuming stationary wall temperatures and using heat transfer correlations, based on dimensionless Nusselt number correlations to ensure scalability, for piston engines given in [14, 15], heat transfer from piston chamber volume to the walls (cyclinder head, cylinder side wall and the piston) is determined. The heat transfer model is illustrated in Fig. 4. It considers convection at the inner piston wall, heat conduction through the wall and convection and radiation at the outer piston casing. For heat transfer at the outer wall, surrounding air flow with Mach number 0.1 and piston inlet conditions are assumed.

Fig. 4
figure 4

Schematic illustration of heat transfer modeling at the piston walls

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The heat transfer model was calibrated and verified with data from NASA-CR188232 report [16]. The time-resolved rate of heat release during combustion is given by the Wiebe function [17]. Increased heat transfer as a result of enhanced turbulence due to combustion is also covered by the heat transfer correlations.

Overall thermodynamic cycle modeling and thermodynamic state parameters were verified with NASA-CR188232 report [16] and NASA-CR185155 [18]. In Fig. 5, crank angle-resolved piston chamber pressure is shown for the current piston model. The calculated pressure matches the reference data with minor deviations in peak pressure. In Table 1, a comparison of calculated integral cycle data with reference data is illustrated. Deviations for fuel mass, mass flow, power output heat losses and exhaust temperature are less than one percent.

Fig. 5
figure 5

Verification of calculated chamber pressure and temperature of a two-stroke piston engine with reference date given in [16]

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Table 1 Verification of integral piston cycle data of thermodynamic piston cycle modeling with NASA_CR 188232 reference data
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The thermodynamic process modeling of the Wankel-type rotary engine follows the same principle as the described model for reciprocation piston engines. Rotary engine-specific functions for chamber geometry, heat transfer [19] and valve areas are used. Additionally, leakage between rotor and casing is considered. A detailed description of the adopted rotary engine model is given in [5]. In Fig. 6 important geometric parameters of Wankel-type rotary engines are depicted on the left side, in particular rotor radius R, eccentricity e, rotor thickness d and rotor combustion pocket volume VPR. At the right side, the control volume of the rotary engine model is illustrated with the considered energy flows.

Fig. 6
figure 6

Rotary piston engine—left: schematic rotor illustration with main geometric parameters [5], right: control volume with considered energy flows

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The crank angle-resolved rotary engine performance simulation model was also verified with data from literature [19]. A comparison of calculated data (orange, “RE model”) for chamber pressure, chamber temperature and heat losses for a single rotor revolution is depicted in Fig. 7. A very good match of the data given in [19] is achieved. For integral performance parameters, relative errors up to 2.5% are detected as tabulated in Table 2. These deviations result from slightly different heat transfer and valve modeling. The current model additionally considers heat input during the charging phase from the hot walls into the chamber volume and allows backflows through the valves.

Fig. 7
figure 7

Verification of the thermodynamic rotary engine model—left: pressure, middle: temperature, right: heat losses, each parameter per crank angle position

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Table 2 Verification rotary engine model—comparison of important integral performance parameters
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2.2 NOx emissions

Beside CO2 reduction targets, the European Commission also addressed NOx emissions within its Flightpath 2050 agenda. Therefore, the piston concepts were evaluated on NOx emissions, too. In general, higher temperatures during combustion result in higher NOx emissions. In piston engines, significantly higher combustion temperatures are feasible compared to conventional Joule–Brayton combustion chambers, as present in state-of-the-art aero engines. These increased combustion temperatures are enabled by the non-stationarity of the piston cycle, which means that the high temperature arises only for a very short time during the whole piston cycle. Due to the short time of residence of the peak temperature, the chemical reaction mechanism for NOx production does not reach chemical equilibrium at this point [20]. In consequence, less NOx emissions compared to stationary combustion with the same peak temperature are generated.

Formation mechanism for NOx are complex; thus, a simplified correlation for NOx emissions prediction of piston engines as presented in [21] is used. This correlation was developed for diesel piston engines with direct injection and is a lumped one step reaction model, which means that NOx emissions are estimated from theoretical adiabatic flame temperature at the top dead center of the piston engine. The correlation is given in Eq. (1). The adiabatic flame temperature Tflam is computed from combustion start temperature and the heating value of the fuel by assuming ideal stoichiometric combustion.

$${\text{EINOx}} = 1.6 \times e^{{ - \frac{{36700 {\text{K}}}}{{T_{\text{flam}} }}}}$$
(1)

2.3 Weight

Introducing piston systems in turbo engine architecture will probably increase propulsion system weight, which will reduce fuel saving potential resulting from thermodynamic cycle improvement. Therefore, weight estimation for piston components is important for propulsion system evaluation of CCEs. In this study, the weight prediction model uses geometric data of the piston and piston housing, which result from thermodynamic cycle calculation. By assuming state-of-the-art materials for the piston, the piston housing and the cylinder head, component weights of these parts are calculated. Additionally, a weight breakdown, depicted in Fig. 8, is used for piston engine weight estimation. The weight breakdown in Fig. 8 has been taken from motors in automobile application. Due to additional components in the automotive application case, like electric generator and turbo charger, the share of “other parts” is reduced for piston engines integrated in the CCE architecture.

Fig. 8
figure 8

Percentage weight brakedown for piston engine components [22]

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For weight prediction of rotary engines, a correlation published in NASA-TM-X71906 [23] is used. With this correlation, rotor and casing weight (Eqs. (2) and (3)) is determined by the use of main geometric parameters like rotor radius R, eccentricity e and the number of rotors n, the casing material properties σ (strength) and ρ (density) and the cycle peak pressure pcl. Again, these geometric data result from thermodynamic cycle calculation. The weight of cooling fins and other components is considered by calibration factors, leading to the total rotary engine weight as shown in Eq. (4).

$$m_{\text{casing}} = \frac{{\pi R^{2} \left( {1 + \left( {e/R} \right)} \right)^{2} p_{\text{cl}} }}{\sigma /\rho }\left[ {\frac{2}{3} \times nR + \left( {n + 1} \right)R\left( {1 + \left( {\frac{e}{R}} \right)} \right)} \right]$$
(2)
$$m_{\text{rotor}} = 0.5 \times V_{\text{rotor}} \times \rho_{\text{rotor}}$$
(3)
$$m_{\text{total}} = 1.18 \times (1.5 \times m_{\text{casing}} + m_{\text{rotor}} )$$
(4)

2.4 Cooling fin layout

The heat losses of the piston engine resulting from thermodynamic cycle calculation are assumed to be rejected by an air cooling system. Therefore, cooling fins were added, to increase the feasible heat transfer at the outer piston casing. A simplified approach for cooling fin design is used to get a rough estimation of the necessary volume and weight. Hence, a rectangular cooling fin profile is assumed. Figure 9 shows a section of the piston engine cylinder with a detailed zoom on the cooling fins, where main geometric parameters of the fins are illustrated.

Fig. 9
figure 9

Cooling fin design for piston engine

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A share of the main core mass flow, which is not lead through the piston cylinder, is used as cooling fluid. Fluid velocity is set to Mach 0.1. For these conditions, rejectable heat is calculated by Eq. (5), as published in [24]

$$Q_{c} = \alpha_{\text{sum}} \times \left( {T_{w} - T_{\text{cool}} } \right) \times A_{0} \times \left[ {\left( {2l + s} \right)/\left( {b + s} \right)} \right] \times \eta_{c}$$
(5)

In Eq. (5), surface area of the cylinder without cooling fins is named with A0 and cooling fin efficiency with ƞc. In the case of rectangular cooling fin profiles this efficiency equals the value of 0.627 [25] for volumetric optimized cooling fins, which are, in a first approximation, also weight optimal. Tw and Tcool describe the involved temperatures of the wall and the surrounding cooling fluid. The heat transfer coefficient αsum considers heat conduction from the cooling fin root and convective heat transfer into the fluid. It is calculated by

$$\alpha_{\text{sum}} = \left( {\frac{{r_{o} \ln \left( {\frac{{r_{o} }}{{r_{i} }}} \right)}}{\lambda } + \alpha^{ - 1} } \right)^{ - 1} ,$$
(6)

using the cooling fin root (ri) and tip diameter (ro) as well as the heat conductivity coefficient λ of the cooling fins and the convective heat transfer coefficient α. For the finally derived piston engine design presented later on, 13 cooling fins with a depth of b = 5 mm, a vertical spacing of s = 10 mm and a fin length of l = 50 mm the heat losses resulting from thermodynamic cycle calculation can be rejected. The resulting weight of the cooling fins is 20.9 kg per cylinder.

2.5 Integration in aircraft propulsion system synthesis

For evaluation of the piston systems in a CCE architecture, the previously described performance models are integrated into the Bauhaus Luftfahrt in-house Aircraft Propulsion System Syntheses (APSS) framework. In APSS, a component-based, modular representation of the turbo engine architecture is used for power plant performance calculation. During cycle calculation iterations, common sizing and design heuristics reported in [26, 27] are applied. Following the flow path through the engine, changes in thermodynamic state variables are computed. The power request from the piston engine is given by the mechanically connected compressors. With fluid input conditions according to compressor outlet and a technologically limited maximum peak pressure in the piston engine cycle, piston systems and geometries, which are able to fulfill the performance requirements, are derived.

3 Results

Following, results from a qualitative concept analysis and piston system data calculated with the previously introduced models are presented. For the most promising concept, a detailed design of the piston components will be shown. Typical take-off conditions are used for propulsion system comparison and component sizing point.

3.1 Evaluation of piston concepts

The qualitative assessment of the piston engine concepts is based on typical characteristics of the three investigated piston systems as known in literature [28, 29] and independent of the TREVAP application case. The piston systems are evaluated on thermal and volumetric efficiency, power-to-weight ratio, thermal stresses and aspects of lubrication, sealing and cycle characteristics. On the one hand, the two-stroke engine offers a good power-to-weight ratio with small integration volume. On the other hand, low volumetric efficiency due to poor scavenging behavior and challenging thermal stresses due to burning in every revolution are connected with the two-stroke piston system. On the contrary, the four-stroke engine offers very high volumetric efficiency to the cost of higher complexity and more discrete power delivery. Further, better lubrication is achievable for this engine. The rotary engine offers best power-to-weight ratio and can be integrated coaxially to the turbo components. But sealing between the single chambers is very challenging and complex, less efficient sealing systems are in use. Additionally, lubrication of the rotor is very difficult. A significant share of the lubricant is burnt during the cycle.

For quantitative evaluation of the different piston systems, integrated thermodynamic cycle calculations on propulsion system level are computed. Therefore, the project-specific application case of 22 MW shaft power on the low-pressure spool and 1.1 MW residual core flow power under typical take-off conditions (Mach number 0.25, sea level, ISA + 15) are used. The chosen conditions represent the relevant sizing point for piston engine and secondary air system, but do not indicate full fuel saving potential of CCEs in typical cruise conditions, as presented in previous assessments of integrated CCE performance [3]. Thermodynamic cycle calculations of the piston systems are operated with the previously described models. For all piston concepts, cycle peak pressure is set to 25 MPa. Table 3 lists important results from these calculations. Compared to state-of-the-art turbo engines, thermal efficiency of the CCE concepts improves between 7.9% (rotary engine) and 8.5% (four-stroke engine) for the investigated conditions. In case of the two-stroke engine, results from qualitative assessment are confirmed. High wall temperatures and poor volumetric efficiency are observed. It is found, that in case of the four-stroke engine, high volumetric efficiency and lower temperature level during the charging phase compensate for the half power output rate, leading to very similar piston diameters (assuming same number of pistons for the two- and the four-stroke engine). Due to the lower cycle temperature level, less NOx emissions are predicted for this piston mode. The rotary engine offers a substantial weight saving potential. For comparability reasons, peak pressure of 25 MPa was assumed here, too. However, this pressure level is not achieved by state-of-the-art rotary engines. Dimensions and weight saving potential become rapidly worse by assuming lower peak pressures. Therefore, the four-stroke reciprocating piston system is chosen as best option. Following, a detailed design of a four-stoke piston engine for the TREVAP application case is presented.

Table 3 Characteristic cycle data for different piston engine configurations
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3.2 Piston system design

For the preferred four-stroke piston engine, a preliminary geometric design is derived from the thermodynamic cycle calculations and the resulting performance requirements. Therefore, three piston engines in V-arrangement around the turbo engine shaft are assumed. Each piston engine consists of eight piston compressors and six lighted pistons. In total, 24 piston compressor and 18 piston engine cylinders are used. The relevant geometric data of the piston components are listed in Table 4. The piston engine cylinders have smaller inner diameters, due to cooling fins at the outer cylinder surface. All cylinders are supposed to have a stroke of 0.15 m. The piston compressors operate with a geometric compression ratio of 24 and deliver a pressure ratio of 3.92. For the piston engine, a compression ratio of 10.3 is used. The buffering volumes in front of the piston compressor and after the piston engine are sized to reduce the total pressure fluctuation at the connected turbo components to less than 1% of the corresponding mean pressure level. In Fig. 10, a possible basic arrangement of the piston components in the Composite Cycle Engine architecture is illustrated. A longitudinal and a transversal section of the engine are shown. Additionally, one piston compressor cylinder and one piston engine cylinder are depicted in detail with most important dimension data.

Table 4 Piston engine component data
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Fig. 10
figure 10

(modified from [3])

Illustration of piston engine integration and geometry.

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4 Conclusion

In the present paper, three different piston engine systems are evaluated in a CCE architecture for the TREVAP project-specific application case of a 22-MW turbo shaft engine at typical take-off conditions. In case of the conceptually promising coaxial-arranged Wankel-type rotary engine, technological challenges concerning the peak pressure level and the chamber sealing, especially at the rotor tips, are identified which might not be sufficiently solved in the near future. Shortfalls in these issues significantly worsen the thermodynamic performance. Therefore, the rotary engine concept is not viable until further technological advancements will have been achieved.

Compared to the rotary engine configuration, the reciprocating piston systems are less challenging in terms of technological requirements. For the two-stroke piston configuration, the expectation of a higher power-to-weight ratio compared to the four-stroke mode is disproved during the quantitative cycle evaluation. The poor scavenging efficiency and the higher temperature level of the two-stroke engine cycle lead to a similar needed cylinder diameter for both concepts, while assuming the same number of pistons. In consequence, the four-stroke piston mode outperforms the two-stroke piston system due to less heat losses and lower NOx emissions. The lower wall temperatures also decrease thermal load of the piston material, enabling the use of lighter materials.

A preliminary design of the selected four-stroke piston configuration consists of three piston engines in a V-arrangement around the turbo engine core with 24 piston compressors and 18 piston engine cylinders in total. All cylinders are designed to have similar outer diameters of approximately 0.3 m. While cooling fins are needed to reject the heat from the lighted cylinders, the inner diameter of the piston engine cylinders is reduced to 0.195 m.