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## Summary

The periodic and transient character of pressure gain, almost isochoric combustion in gas turbine processes leads to highly transient boundary conditions for all subcomponents of the system. The resulting interactions must be assessed in terms of their significance for the overall engine, in order to be able to make a statement about the intended efficiency gain and the reliable operating behaviour. This holistic view is the content of this subproject. The aim of the subproject is to enable a detailed energetic and exergetic analysis of a dynamic gas turbine process with pressure gain combustion (PGC) under consideration of the effects of transient and gas-dynamic effects on the characteristic operating parameters of the individual components.

## 1st funding period 2016 - 2020

A three-stage concept has been developed for the analysis of gas turbine processes with PGC. This is based on a stepwise increase in the level of detail of the cycle simulations. The three different modeling levels are 0D, hybrid and 1D, which are explained in the following

**0D-Modelling - Thermodynamic Analyses**

In a first stage, 0D models of the gas turbine components were used. For PGC, previously published approaches were initially used. In the course of the project, these were adapted and an own model of pressure gain combustion was developed (Mix-x model in Figure 1).

These models assume a stationary operating behaviour. This results in an equivalent thermodynamic outlet state of the combustion chamber depending on the inlet conditions and fuel input. A comparison of the individual models is shown in Figure 1. Here the achieved pressure ratio over the combustion chamber is shown as a function of the temperature ratio over the combustion chamber. The 0D models are computationally very favourable and thus allow extensive parameter studies as well as an optimisation of the gas turbine architecture, among other things, by means of a genetic algorithm. For the optimization studies, a model was used that adjusts the cooling air mass flow in such a way that a given blade temperature is not exceeded. From the optimizations, design rules for the gas turbine could be derived. This shows that a higher specific output is achieved by PGC. However, maximum efficiency is achieved at almost identical machine mass flow (see Fig. 2). The compressor pressure ratio is reduced according to the additional pressure increase in the combustion chamber.

**Hybrid Modelling**

The second step of the investigations is based on hybrid process models, which represent the combustion processes in a very detailed and time-resolved manner and represent the remaining components by 0D models. For the computation of the two combustion processes (Pulsed Detonation Combustion (PDC) and Shockless Explosion Combustion (SEC)) an adapted version of the 1D-solver of the Euler equations developed in the 1st phase of the SFB in subproject A03 was used. This solver provides the thermodynamic conditions at the exit of the combustion chamber as a function of time over a complete cycle of the combustion processes (filling, ignition, blowing out and purging). For each time step, the mass increment leaving the combustion chamber is determined and separately expanded in the turbine (see Fig. 3). The isentropic efficiency of the turbine was calculated for each mass increment based on its state variable (pressure) from a generic turbine map to determine the work done. The total turbine power was calculated by integrating the incremental work. Thus, the influence of gas dynamic phenomena in the combustion chambers could be investigated and first design rules for the turbine could be derived.

- Figure 3: Concept of hydrid modelling and thermal efficiency of the simple gas turbine cycle with SEC as a function of compressor pressure ratio and static or total quantities at turbine inlet
- © TUB

The 1D simulation also allows a detailed analysis of the entropy generation in the individual sub-processes of combustion, as well as the resulting pressure and suction waves within the combustion chamber.

**1D-Modelling**

The second step of the investigations is based on hybrid process models, which represent the combustion processes in a very detailed and time-resolved manner and represent the remaining components by 0D models. For the computation of the two combustion processes (Pulsed Detonation Combustion (PDC) and Shockless Explosion Combustion (SEC)) an adapted version of the 1D-solver of the Euler equations developed in the 1st phase of the SFB in subproject A03 was used. This solver provides the thermodynamic conditions at the exit of the combustion chamber as a function of time over a complete cycle of the combustion processes (filling, ignition, blowing out and purging). For each time step, the mass increment leaving the combustion chamber is determined and separately expanded in the turbine (see Fig. 3). The isentropic efficiency of the turbine was calculated for each mass increment based on its state variable (pressure) from a generic turbine map to determine the work done. The total turbine power was calculated by integrating the incremental work. Thus, the influence of gas dynamic phenomena in the combustion chambers could be investigated and first design rules for the turbine could be derived.

Eine Vordimensionierung des Plenums zwischen Verdichter und PDC, sowie eine Untersuchung der Verdichterstabilität für verschiedene PDC-Parameter, erfolgt durch eine Kopplung des 1D-Turbomaschinen-Codes mit einem 0D-Plenumsmodell (siehe Abb. 4). Die Ergebnisse werden auf der ASME GT 2020 veröffentlicht.

**Demonstrator**

The development of a demonstrator, which will enable the combination of all SFB technologies, will take into account both their different levels of maturity and the given university infrastructure. Based on the presented simulations and as a joint effort of the SFB, a concept was developed with the following objectives:

- Demonstration of a pressure gain

- Demonstration of the damping effect of the turbine and compressor plenum

- Demonstration of a strategy for the filling of several burner tubes

- Demonstration of the operation of all above mentioned components in an experimental setup

The concept for the demonstrator is shown in the following figure.

## Publications

Gray, J., J. Vinkeloe, J. Moeck, C. O. Paschereit, P. Stathopoulos, P. Berndt und R. Klein: Thermodynamic Evaluation of Pulse Detonation Combustion for Gas Turbine Power Cycles. In: In Proc. Turbo Expo 2016. ASME, jun 2016.

Neumann, N. und D. Peitsch: Introduction and Validation of a Mean Line Solver for Present and Future Turbomachines. In: Proceedings of ISABE Canberra 2019, Canberra, Australia, 22-26 September. ISABE-2019-24441, 2019.

Neumann, N. und D. Peitsch: Potentials for Pressure Gain Combustion in Advanced Gas Turbine Cycles. Applied Sciences, 9(16), 2019, ISSN 2076-3417.

Neumann, N., D. Woelki und D. Peitsch: A Comparison of Steady-state Models for Pressure Gain Combustion in Gas Turbine Performance Simulation. In: Proceedings of GPPS Beijing 2019, Beijjing, China, 16-18 September, Nr. GPPS-BJ-2019-0198. Global Power and Propulsion Society, 2019.

Rähse, T., C. Paschereit, P. Stathopoulos, P. Berndt und R. Klein: Gas dynamic simulation of shockless explosion combustion for gas turbine power cycles. In: Proceedings of the ASME Turbo Expo, Bd. 3, 2017.

Rähse, T. S., P. Stathopoulos, J. S. Schäpel, F. Arnold und R. King: On the influence of fuel stratification and its control on the efficiency of the shockless explosion combustion cycle. In: Proceedings of ASME Turbo Expo, Oslo, Norway, 2018. ASME International.

Rähse, T. S., P. Stathopoulos, F. Arnold, J. Schäpel, R. King: On the influence of fuel stratification and its control on the efficiency of the shockless explosion combustion cycle. J. Eng. Gas Turbines Power 141,1 (2018).

Stathopoulos, P.: Comprehensive Thermodynamic Analysis of the Humphrey Cycle for Gas Turbines with Pressure Gain Combustion. Energies, 11(12), 2018.

Stathopoulos, P., T. Rähse, J. Vinkeloe und N. Djordjevic: First law thermodynamic analysis of the recuperated Humphrey cycle for gas turbines with pressure gain combustion. Energy, 2019.

Stathopoulos, P., T. Rähse, J. Vinkeloe und N. Djordjevic: Steam injected Humphrey cycle for gas turbines with pressure gain combustion. Energy, 2019.

Neumann, N., T. Rähse, P. Stathopoulos und D. Peitsch: Holistic Performance Evaluation of Gas Turbines featuring Pressure Gain Combustion. In: Proceedings of DLRK 2019, Darmstadt, Germany, Deutsche Gesellschaft für Luft- Raumfahrt, 2019.

Neumann, N., D. Peitsch, A. Berthold, F. Haucke und P. Stathopoulos: Pulsed Impingement Turbine Cooling and its Effect on the Efficiency of Gas Turbines with Pressure Gain Combustion. In: Proceedings of the ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition, London, England, 22–26 June 2020 (submitted)

Dittmar, L. und P. Stathopoulos: Numerical Stability and Operational Analysis of an Axial Compressor Connected to an Array of Pulsed Detonation Tubes. In: Proceedings of the ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition, London, England, 22–26 June 2020 (submitted)