THE COMPLETION OF THE MATHEMATICAL MODEL BY PARAMETER IDENTIFICATION FOR SIMULATING A TURBOFAN ENGINE [308040]

Topical Issues in Aircraft Health Management with Applications to Jet Engines

Sorin BERBENTE1,2, Irina-Carmen ANDREI*1, Gabriela STROE2

*Corresponding author

1INCAS ‒ National Institute for Aerospace Research “Elie Carafoli”

B-dul Iuliu Maniu 220, Bucharest 061126, Romania

[anonimizat], [anonimizat], [anonimizat]

2University “POLITEHNICA” [anonimizat],

Gh. Polizu Street 1-7, Sector 1, Bucharest, 011061, Romania

[anonimizat]

Abstract: Aircraft Health Management Technology for jet engines represents a [anonimizat] a [anonimizat], increasing the engines durability and life cycle.

[anonimizat]’s, [anonimizat], while improving system’s affordability and safety. [anonimizat], [anonimizat]. Modern control for Aircraft Health Management Technology is based on improved control techniques and therefore provides improved aircraft propulsion system performances.

The study presented in this paper approaches a [anonimizat], that is the intelligent control; [anonimizat], being focused on engine controllers which are designed to match certain operability and performance constraints.

Automated Engine Health Management has the capacity to significantly reduce the maintenance effort and propulsion systems’ logistical footprint.

In order to prioritize and resolve problems in the field of support engineering there are required more detailed data on equipment reliability and failures detection and management; [anonimizat].

Key Words: [anonimizat], [anonimizat]

1. INTRODUCTION

Aircraft Health Management Technology for jet engines includes a [anonimizat], for all the jet engine running regimes and flight regimes supposed by the flight envelope and the aircraft’s flight missions.

From the jet engine’s [anonimizat], which further is based on Engine Condition Monitoring ECM.

[anonimizat].

By the means of the AHM and consequently EHM & ECM, a [anonimizat], namely: [anonimizat], [anonimizat]. [anonimizat]ency, increasing the engines durability and life cycle.

The importance of AHM & EHM can be highlighted from the economic stand point; thus, the financial impact can be tough, with severe effects acting on both those directly involved and indirectly, on potential beneficiaries of the aviation industry. Just as an example, DHL as a beneficiary of aviation operational services, estimates that the costs of an aircraft on ground AOG can rise up to 925000 euro per day, [1-2].

Another example, which highlights the importance of AHM & EHM from the financial point of view, is the structure of an airline’s operating costs, as indicated in Table 1:

Table 1 – Operating Costs of a commercial airline

The technology actually involved in AHM & EHM is high-end and in order to enable an improved level of performance that far exceeds that of today’s, the propulsion systems must be compliant with terms of reduction of harmful emissions, maximization of fuel efficiency and minimization of noise, while improving system’s affordability and safety.

Aircraft Health Management Technology includes multiple goals of aircraft propulsion control, diagnostics problems, prognostics realized, and their proper integration in control systems. Modern control for Aircraft Health Management Technology is based on improved control techniques and therefore provides improved aircraft propulsion system performances.

2. ENGINE HEALTH MONITORING EHM CURRENT STATUS AND PROSPECTIVES

The concept of Engine Health Monitoring EHM consists in four pillars, as explained in Fig. 1. The first EHM pillar originates from the jet engine post-design offline evaluation.

Intended as the first stage of EHM, the jet engine offline evaluation consisted in completing the next three steps, but without any engine monitoring at all:

As scheduled by the Engine’s Maintenance Management EMM, there were mandatory standard visits in the maintenance unit/ shop;

Based on the restrictions imposed by the Exhaust Gas Temperature EGT (i.e. the redline EGT which limits the maximum take-off EGT) and Life Limited Parts LLP’s, the concept “fly to failure” supposes that certain parts and/ or assemblies must be removed, at specified time intervals;

Unscheduled engine removals can be performed anytime provided that the aircraft and/ or jet engine is under the condition of the force majeure clause FMC.

The second EHM pillar refers to the diagnostics and consists in a reactive system based on limited data collection. In principle, there are two steps to be fulfilled:

Tailored solutions (i.e. workscoping) based on Engine Trend Monitor ETM results;

Unscheduled removals are limited, as number, due to certain prohibitive costs and delays in activities involved and connected to aircraft operation.

The current status of the EHM is represented by the achievement of the second EHM pillar. Up to present, EHM # 1 – Offline and EHM # 2 – Diagnostics are in current use.

New prospects and consequent advantages can be foreseen and/ or expected from the future EHM third and fourth pillars: EHM # 3 – Prognostics and EHM # 4 – Business Intelligence.

The third EHM pillar EHM # 3 – Prognostics consists on a pro-active system based on predictive algorithms and associated periodically inspections and verifications, i.e. snapshots. The steps of EHM # 3 – Prognostics refer to:

Enhanced identification of the upcoming problems, by the means of a better monitoring and earlier detection;

Continuously improving the maintenance planning and the solution tailoring, by integrating as feedback the solutions to the problems occurred in the past.

The fourth EHM pillar EHM # 4 – Business Intelligence refers to Big Data Analytics based on continuous data stream, that is all-encompassing engine data and beyond. The steps of EHM # 4 – Business Intelligence consist in:

Precise forecast for engine Maintenance, Repair and Overhaul MRO cost, scrap rates and removal times;

Optimized management of both aircraft and engine fleet and operations;

Engine Trend Monitor ETM becomes a major fleet planning tool.

The necessity of EHM & ECM is justified by the goals foreseen, operational and financial benefits. The operational goals are of utmost interest. The most significant operational goals refer to:

1/ the detection of the potential failures in order to avoid or to reduce secondary damages;

2/ the continuous improvement of the fleet management (focused mainly on the removal and spare engine planning.

The Engine Condition Monitoring ECM provides important operational and financial benefits, with significant impact, as follows:

Minimizing the unscheduled downtime and optimizing on-wing times,

Supports early line maintenance decisions in order to avoid secondary damages and aircrafts on ground AOG’s situations,

Supports performance prediction and optimum aircraft operational planning,

Allows the enhancement of the engine removal planning and the optimization of the spare engine management,

Allows the optimization of the maintenance planning for off-wing situations

Optimizes the core engine cleaning, which generates increased fuel efficiency and consequently the reduction of the overall fuel consumption,

Contributes to reducing the environmental impact, due to increased fuel efficiency and less overall fuel consumption.

The main goal and benefit of the Engine Condition Monitoring ECM is the cost reduction, from the most important key points: 1/ operational, 2/ financial, 3/ Maintenance, Repair and Overhaul MRO; the appropriate actions are summarized in Table 2.

Table 2 – Cost reduction as the main goal of ECM Engine Condition Monitoring

3. REPRESENTATIVE CASES OF JET ENGINES

The types of jet engines are: the turbojet, the turbofan engine, the turboprop and the mixed flows turbofan engine. This study focuses on the categories of jet engines used as propulsion systems in purpose to power commercial airliners, civil airplanes and military aircraft (combat, fighter or multirole aircraft) that are as presented in Fig. 2 – Fig. 6: the turbojet, the turbofan (equiv. high-bypass turbofan), the mixed flows turbofan (equiv. low-bypass turbofan), the twin spool or triple spool constructions for turbojet and turbofan engines. The commercial airliners can be powered by pairs of 2, 4 or 6 high by pass turbofan engines (which are also referred as un-mixed flows turbofan engines); e.g. the A380 aircraft powered by 4 Rolls Royce Trent 900 turbofan engines. In current use are also other types of turbofan engines, such as CF6-50/80 C2, V2500 IAE, PW 2000, CFM 56-3/58/7, CF 34-8/10, GE 90-110B/115B that can be mentioned [3-8].

The turbofan engines are designed such that to provide lower fuel consumption, while for the military applications, the turbojet and the mixed flows turbofan engines are designed such that to provide high levels of thrust.

A comparison of the turbojet engine architecture points out the single-spool construction, Fig. 2.a, versus twin-spool construction, Fig. 2.b, which is more advantageous due to the increased adaptability to the aircraft flight regimes and enabling a safer operation, due to removing the engine’s operating line from the surge line. The most efficient configuration is the triple-spool turbofan engine, Fig. 2.d, 2.f, for the same reasons as above: engine featuring adaptability and enhanced safety during all operational sequences.

Considering the clarity and accuracy as mandatory for any technical study, the proper use of terms and definitions must be mastered. For this reason, from the engine’s architectural standpoint, the references related to Fig. 2d, 2f are: Turbofan engine = High-bypass Turbofan = Distinct Flows Turbofan = Turbofan with Distinct Core and Bypass Flows = Turbofan, while the references related to Fig. 2c, 2e are: Mixed Flows Turbofan engine = Low-bypass Turbofan = Mixed Flows Turbofan, had to be introduced.

Due to the reduced cross section, the turbojet engines and the mixed flows turbofan engines are preferred as propulsion systems for the military aircraft (combat/ fighter/ multirole). The thrust of both turbojet and mixed flows turbofan engines can be significantly increased, for short periods of time, by the means of the reheat engine cycle; such engines are equipped with afterburners (i.e. afterburn units). In Fig. 3 is shown the J-85 GE-17A Turbojet Engine [1,6].

The General Electric J-85 family is based on a small single-shaft turbojet engine, that in military versions is produced with afterburning variants, while civilian models, known as the CJ610, are supplied without an afterburner; the CF700 adds a rear-mounted fan for improved fuel economy. The J-85 turbojet engine was developed initially for the ADM-20 Quail (i.e. a large decoy missile) and further found applications in other light-jet applications including the supersonic Northrop F-5/T-38 family, as well as in commercial CJ610.

In Fig. 4 is detailed the cutaway view of the afterburning J-79 GE Turbojet Engine [7].

The General Electric J79 basic solution is an axial-flow turbojet engine, which was developed for reliable Mach 2 performance, powering the Convair B-58 bomber.

The J79 was used to power a variety of fighter and bomber aircraft (such as: Convair B-58 Hustler, Lockheed F-104 Starfighter, McDonnell F-4 Phantom II; North American RA-5 Vigilante, IAI Kfir) and a supersonic cruise guided missile (i.e. SSM-N-9 Regulus II).

The commercial version of General Electric J79, designated the CJ805, powered the Convair 880, while an aft-turbofan derivative, the CJ805-23, powered the Convair 990 airliners and a single Sud Aviation Caravelle demonstrated the benefits of a bypass engine over the existing Avon turbojet.

The gas generator of the J79 was developed as a stationary 10MW-class free-turbine turboshaft engine for naval power, power generation, and industrial use, called the LM1500. The J79 was replaced from powering fighter aircraft by afterburning turbofans (such as the Pratt & Whitney TF30 used in the F-111 and F-14) and newer generation turbofans (e.g. the Pratt & Whitney F100 used in the F-15 Eagle), which give better cruise fuel efficiency by-passing air around the core of the engine.

In Fig. 5 is shown a cutaway view of the Rolls-Royce Trent 900 high-bypass turbofan engine, which was designed to power the Airbus A380, competing with the Engine Alliance GP7000. Producing between up to 374 [kN], the Trent 900 has the three shaft architecture of the Rolls-Royce Trent family with a 2.95 [m] fan, and it has the overall pressure ratio of 37-37 and bypass ratio about 8.5-8.7.

Latest advances in science and technology enabled highly efficient solutions for innovative constructions of turbofan engines. The improvements are targeted for lowering fuel consumption, weight reduction, environment friendly by reducing CO and NO emissions and noise levels.

In Fig. 6 are highlighted advanced technology elements, summarized in case of the Rolls Royce Trent XWB engine [11], as follows: Integrated Intelligent Engine Health Monitoring, Bearing Load Management, Advanced Materials, Full 3D Aerodynamic Compressors, Blisk Technology, Hollow Lightweight Titanium Fan System, Turbine End Wall Profiling, Soluble Core HP Turbine Blades, Low Emissions Combustor.

In Fig. 7 are exemplified innovative technology concepts, which in case of the Rolls Royce BR725 Engine designed to power the G650 Gulfstream, such as: new swept fan blades, Trent technology tailored for increased bypass ratio and increased diameter, improved HPC with 5 stages of Blisk, smoke free combustor, new 3 stage LPT, 16 lobe mixer for minimal jet noise.

In Fig. 8 is presented the F100 PW 220E Reheated Mixed Flows Turbofan Engine, powering the F16 Fighting Falcon [9-11]. The Pratt & Whitney F100 Mixed Flows Turbofan Engine (company designation JTF22) is an afterburning turbofan engine manufactured by Pratt & Whitney purposed to power the F-15 Eagle and F-16 Fighting Falcon. Other applications are as follows:

1/ the F401 engine for Rockwell XFV-12 prototype supersonic VTOL fighter;

2/ the F100 for powering: General Dynamics F-16 Fighting Falcon, McDonnell Douglas F-15 Eagle, McDonnell Douglas F-15E Strike Eagle, Northrop Grumman X-47B, Vought YA-7F;

3/ the F401 for powering: Grumman F-14B Tomcat (planned; test aircraft only), Rockwell XFV-12, Vought Model 1600 (proposed).

4. PROBLEM STATEMENT: TURBOFAN ENGINES CONTROL FOR CIVIL AND MILITARY APPLICATIONS

The jet engine control problem for military and civil applications is customized in accordance with the type and construction of the selected engine [12-14].

Turbojet engines and turbofan engines for military applications are destined to power combat aircrafts (fighter and/ or multirole aircraft); the construction of such engines is explained in Fig. 2, while cutaway views are detailed in Fig. 3 – Fig. 8. Since the exhaust nozzle area features variable geometry, then the control is performed by the means of two variables, that is the fuel flow rate and the nozzle exhaust area ; consequently, the control vector consists of two elements [19].

In case of military afterburning turbojets and turbofans, the state vector contains the information on combustor pressure and afterburner pressure, otherwise, only the combustor pressure is referred [21].

Turbofan engines for civil applications are dedicated to power commercial airliners; since the exhaust nozzle area is fixed, then the control is performed by the means of a single variable, that is the fuel flow rate ; consequently, the control vector consists of one element.

In case of single-spool versus twin-spool and triple-spool constructions, the state vector contains information on the speed for each spool: low-pressure compressor to turbine spool, high-pressure compressor to turbine spool and fan to turbine spool [23].

Since the profile mission of a combat aircraft often requires a sudden increase of available thrust, the MFTE is equipped with an afterburner, which provides a significant augmentation of the engine’s thrust, by the means of a reheat cycle [15-18]. In case of the MFTE and the reheated MFTE respectively, for a better adaptability of the engine’s regimes to the aircraft’s flight regimes, and a safer engine operation (due to the fact that the work regimes line is shifted farther from the surge line), the geometry of the exhaust nozzle is variable [23-25].

In Fig. 8 is shown a cut view of the F100 PW 220E Reheated Mixed Flows Turbofan Engine, [9], which is powering the F16 Fighting Falcon, aircraft, in current use within the Romanian Air Force.

In case of the mixed flows turbofan engine MFTE for civil applications, the control is performed by the means of one variable: the fuel flow rate ; consequently, the control vector consists of one element [28].

The jet engine control can be described by either non-linear, linearized or linear models; in this study, a linearized mathematical model was used, expressed by the state (1) and output (2) equations, where the matrices A, B, C and D (of appropriate order) are computed for each representative operating point (of the jet engine), in accordance with the flight path and flight map [19-22].

The most complex model of the jet engine control is that used for the reheated mixed flows turbofan engine, in Table 3 being detailed the parameters which define the state vector x:

output vector y:

and control vector u:

Table 3 – Parameters defining the state vector x, output vector y and control vector u in case of the reheated mixed flows (twin spool) turbofan engine

Table 4 – Parameters defining the state vector x, output vector y and control vector u in case of a twin spool turbofan engine

In case of military turbojet and military turbofan, the control of the jet engine is enabled by two parameters:

combustor fuel flow rate [kg/s],

exhaust nozzle area [m^2], (due to the variable geometry feature of the exhaust nozzle)

Therefore, the dimension of the control vector is 2. Many types of turbojet and turbofan engines purposed as propulsion systems for military aircraft are provided with afterburners, and then for this reason, the state vector contains information regarding the pressure inside the combustor and afterburner, as indicated in Table 3. In case of turbojet and turbofan engines as prospective propulsion systems for civil use aircrafts, the exhaust nozzle is characterized by fixed geometry, and therefore, the jet engine is controlled by the means of a single parameter: combustor fuel flow rate [kg/s].

The output vector is defined in accordance with the architecture of the jet engine, namely: single-spool versus twin-spool construction, resulting the compressor surge margin (as in Table 5) or the High Pressure Compressor HPC and Low Pressure Compressor LPC surge margins (as in Table 4).

For a typical single spool turbojet engine, the linearized model contains the state equation (1) and the output equation (2), with the state vector, output vector and control vector defined as shown in Table 5.

Table 5 – Parameters defining the state vector x, output vector y and control vector u in case of a single spool turbojet engine

The problem of jet engine control can be solved if prior is set a mathematical model to describe with adequate accuracy the behaviour of the jet engine for all the operating regimes and all the flight regimes required by the flight mission profile.

The numerical simulations carried on based on the jet engine’s mathematical model can provide accurate results on the performances of the studied jet engine (i.e. the thrust, specific thrust and specific fuel consumption) for the design and all the off-design regimes, for the steady state analysis [26-27].

The dynamic analysis of the jet engine highlights the jet engine’s behaviour to transient regimes and/ or non-stationary. Adequate mathematical modelling can provide proper results for the dynamic analysis and jet engine’s control.

Further, in conjunction with the Engine Condition Monitoring ECM and Engine Health Monitoring, the jet engine’s control problem (which includes algorithms, procedures and techniques) can be a solid foundation for Advanced Health Monitoring AHM.

In this context, researches regarding the mathematical modelling of turbojet, turbofan engine and mixed flows turbofan engines, targeted and customized for performance prediction at design and off-design regimes, steady state analysis and dynamic analysis, jet engines and aircraft control, optimizations, in purpose to create and develop in-house software, are of utmost interest.

5. ENGINE CONDITION MONITORING

The purpose of Engine Condition Monitoring ECM is to assess engine performances and to detect impending failures, by continuously surveying and monitoring certain key engine parameters. It uses standard aircraft and engine instrumentation for monitoring, and does not need any additional measurement equipment.

The engine control key parameters to be measured and monitored are those defining the state vector, output vector and control vector, as described in Tables 3, 4 and 5. In addition to the engine control key parameters, the Engine Condition Monitoring ECM requires other parameters, such as additional engine parameters (e.g. oil temperature, oil pressure, N1/N2 vibrations, valve solenoid positions), aircraft parameters (e.g. altitude, flight Mach number, total air temperature) as well as for the accessories to be monitored and controlled.

Engine Condition Monitoring ECM can be successfully used as a complex tool, in association with a software based on full aero-thermo-dynamic jet engine models.

Based on aircraft data acquisition systems, real-time in-flight analysis and monitoring techniques, engine stall detection, real-time thrust, the Engine Condition Monitoring ECM can provide information of the current engine operation, can prevent the occurrence of failures, can perform proper control and adjustments such that the engine runs within the safe domain.

Featuring the adaptability, the Engine Condition Monitoring ECM provides accurate results for advanced diagnosis, prognosis and analysis, based on continuous system enhancements. It can further be extended to Advanced Health Monitoring AHM.

6. CONCLUDING REMARKS

Proper data acquisition, monitoring, understanding and managing engine data, allow to perform the following tasks:

1/ accurate automatic diagnosis,

2/ prognosis,

3/ modular deterioration diagnosis.

The automatic diagnosis is based on pattern matching, which consists in the comparison of current trend pattern with historic failures stored in database; then, the numerical simulation based on a thermodynamic model, provides information and simulates failure, in order to determine root cause on module base.

The prognosis allows to improve the fleet management performance, based on Engine Trend Monitoring ETM; therefore, from each flight report is expressed a forecast, which specifies the remaining cycles or time intervals / days on-wing until a specific EGTM threshold is reached. Then, based on EGTM history, can be calculated a smoothed deterioration gradient, outliers being excluded from statistical smoothing. Eventually, the results for each engine will be included in a fleet ranking report, periodically updated.

The next step is represented by Modular Deterioration Diagnosis MDD. Based on the correlation between the engine flight hours and the influence of the Exhaust Gas Temperature EGT on the engine’s main modules (i.e. fan, LPC, HPC, HPT, LPT) diagnostics of module contribution to performance loss can be expressed, as well as prognostics of future modular behavior. The main goal of Modular Deterioration Diagnosis MDD is to optimize workscope planning for the whole engine life.

An important contribution to Business Intelligence is the Fleet Analysis FA based on Engine Trend Monitoring ETM. Basically, it pinpoints the link between cycles since on-wing installation and EGT margin loss since installation. For such approach, it is built a deterioration matrix, which allows for historic data analysis, the investigation and efficient management of the following issues:

Fleet average and single engine deterioration rates,

Shop / maintenance unit visit effects (surveillance of the regained performance),

Performance information of mature engines.

In Table 6 is presented a summarize of the integration of all the available data sources.

Table 6 – A summarize of the integration of all the available data sources

Following the integration of all the available data sources is the direct effect on the management effectiveness, especially on Fleet Management FM and Maintenance, Repair and Overhaul MRO and Operating Supplies OS Management, as detailed in Table 7.

Table 7 – Management improvements on fleet and MRO due to advanced data sources integration

Engine Trend Overhaul ETO is a continually evolving and updating process, since it must monitor, analyze and manage high amount of future incoming data.

Engine Trend Monitoring ETM represents a key instrument goaled to improve engine operation and MRO – Maintenance, Repair and Overhaul; it may also provide great opportunities for fleet management improvements.

REFERENCES

[1] *** https://www.monarchaircraftengineering.com/media/glossary

[2] *** https://www.mtu.de/maintenance/commercial-aircraft-engine-services/engine-maintenance-overhaul/

[3] *** Rolls Royce, The Jet Engine, fifth edition, ISBN 0 902121 2 35, The Technical Publications Department Rolls-Royce plc, Derby, England

[4] *** Powerplant, JAA ATPL Training, JEPPESEN, Atlantic Flight Training Ltd

[5] *** https://ntrs.nasa.gov/

[6] *** https://en.wikipedia.org/wiki/Turbojet

[7] *** https://en.wikipedia.org/wiki/General_Electric_J79

[8] *** https://en.wikipedia.org/wiki/Airbus_A380

[9] *** http://www.f-16.net/f-16-news-article3930.html

[10] *** http://www.allstar.fiu.edu/aero/P&WEngines02.html

[11] Rolls Royce, Rolls Royce Technology for Future Aircraft Engines, RAeS Hamburg, Fermany, 2014

[12] L. C. Jaw, J. D. Mattingly, Aircraft Engine Controls, American Institute of Aeronautics and Astronautics Education Series, Inc. Reston, ISBN-13: 978-1600867057, ISBN-10: 1600867057.

[13] G. G. Kulikov, H. A. Thompson, Dynamic Modelling of Gas Turbines: Identification, Simulation, Condition Monitoring and Optimal Control, ISBN 1-85233-784-2, Springer Verlag, London, 2004.

[14] S. Mahmoud, D. Mc Lean, An Effective Optimal Control of an Aircraft Engine, Aeronautical Journal, January 1991, pp. 21-27.

[15] J. D. Mattingly, Elements of Propulsion and Gas Turbine and Rockets, American Institute of Aeronautics and Astronautics Education Series, Inc. Reston, VA, 2006.

[16] J. D. Mattingly, Aircraft Engine Design, American Institute of Aeronautics and Astronautics Education Series, Inc. Reston, VA, 2002.

[17] H. Cohen, G. F. C. Rogers, H. I. H. Saravanamuttoo, Gas Turbine Theory, 4 ed., Longman, Essex, 1989.

[18] W. Wisser, Generic Analysis Methods for Gas Turbine Engine Performance, The development of the gas turbine simulation program GSP, PhD Thesis, NLR and TU Delft, 2015.

[19] S. M. Eastbourn, Modeling and simulation study of a dynamic turbofan engine using Matlab Simulink, M. Sc. A.E. Dissertation, Wright State University, 2012.

[20] C. J. Daniele, S. M. Krosel, J. R. Szuch, E. J. Westerkamp, NASA Technical Memorandum 83446 (NASA – TM 83446), Digital Computer Program for Generating Dynamic Turbofan Engine Models (DIGTEM), Lewis Research Center, Cleveland, Ohio, 1983.

[21] W. C. Merrill, NASA Technical Memorandum NASA – TM X 71726, An Application of Modern Control Theory to Jet Propulsion Systems, Lewis Research Center, Cleveland, Ohio, 1975.

[22] J. Szuch, NASA Technical Memorandum TM X-3014, A generalized hybrid computer program for studying turbojet or turbofan engine dynamics, Cleveland, Ohio, 1974.

[23] ***Compressor and Turbine Maps for Gas Turbine Performance Computer Programs, Issue 3, 2013, Gas Turb GmbH.

[24] S. Farokhi, Aircraft propulsion, second edition, Wiley & Sons, 2014.

[25] F. Zare, A. Veress, K. Beneda, Simplified mathematical model for a single spool and no by-pass jet engine, RTK Conference, BME, 2013.

[26] H. Asgari, X. Chen, R. Sainudin, Modeling and simulation of gas turbines, Intl. Journal Modelling, Simulation and Control, 2013.

[27] V. Stanciu, C. Mnohoghitnei, E. Rotaru, Caracteristicile Turbomotoarelor, Editura Bren, București, 2004.

[28] S. C. Uysal, High by-pass ratio turbofan engines aero-thermodynamic design and optimization, PhD Thesis, The Graduate School of Natural and Applied Sciences, Middle East Technical University, 2014.