Performance analysis and dynamic modeling of a single-spool turbojet engine

Irina-Carmen Andrei, Adrian Toader, Gabriela Stroe, and Florin Frunzulica

Citation: AIP Conference Proceedings 1798, 020005 (2017); doi: 10.1063/1.4972597

View online: http://dx.doi.org/10.1063/1.4972597
View Table of Contents: http://aip.scitation.org/toc/apc/1798/1
Published by the American Institute of Physics

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 Performance Analysis and Dynamic Modeling of a Single-
Spool Turbojet Engine

Irina-Carmen Andrei1,a) Adrian Toader1, b) Gabriela Stroe2,c) Florin Frunzulica2, d)

1
INCAS ࣓ The National Institute for Aerospace Research “Elie Carafoli”
B-dul Iuliu Maniu 220, Sector 6, Bucharest, 061126, Romania
2
“POLITEHNICA” University of Bucharest, Faculty of Aerospace Engineering,
Str. Gh. Polizu 1-7, Sector 1, Bucharest, 011061, Romania

a)
Corresponding author: andrei.irina@incas.ro
b)
toader.adrian@incas.ro
c)
ing.Stroe@yahoo.com
d)
ffrunzi@yahoo.com

Abstract. The purposes of modeling and simulation of a turbojet engine are the steady state analysis and transient
analysis. From the steady state analysis, which consists in the investigation of the operating, equilibrium regimes and it is
based on appropriate modeling describing the operation of a turbojet engine at design and off-design regimes, results the
performance analysis, concluded by the engine's operational maps (i.e. the altitude map, velocity map and speed map)
and the engine's universal map. The mathematical model that allows the calculation of the design and off-design
performances, in case of a single spool turbojet is detailed. An in house code was developed, its calibration was done for
the J85 turbojet engine as the test case. The dynamic modeling of the turbojet engine is obtained from the energy balance
equations for compressor, combustor and turbine, as the engine's main parts. The transient analysis, which is based on
appropriate modeling of engine and its main parts, expresses the dynamic behavior of the turbojet engine, and further,
provides details regarding the engine's control. The aim of the dynamic analysis is to determine a control program for the
turbojet, based on the results provided by performance analysis. In case of the single-spool turbojet engine, with fixed
nozzle geometry, the thrust is controlled by one parameter, which is the fuel flow rate. The design and management of
the aircraft engine controls are based on the results of the transient analysis. The construction of the design model is
complex, since it is based on both steady-state and transient analysis, further allowing the flight path cycle analysis and
optimizations. This paper presents numerical simulations for a single-spool turbojet engine (J85 as test case), with
appropriate modeling for steady-state and dynamic analysis.

1. PERFORMANCE ANALYSIS OF SINGLE-SPOOL TURBOJET ENGINE

Performance analysis of a turbojet engine, also referred as thermodynamic analysis refers to the completion of
the following steps: 1- A preparatory of input data, which consists in the complete definition of engine design
parameters; for certain cases, jet engines catalogues do not provide such information, therefore parameter
identification is compulsorily; 2- Calculating at SLS, ISA conditions ("fixed point", defined by altitude H = 0 [km]
and flight velocity V = 0 [m/s]) of the engine's performances: Thrust [N] (1), Specific Thrust [Ns/kg] (2), Specific
Fuel Consumption [kg/Nh] (3) and the determination the engine's thermodynamic cycle (i.e. the Brayton cycle);
‫ ܨ‬ൌ ‫ܨ‬௦௣ ή  ‫ܯ‬ሶ௔ ǡ ሾܰሿ ;ϭͿ

ICNPAA 2016 World Congress

AIP Conf. Proc. 1798, 020005-1–020005-8; doi: 10.1063/1.4972597
Published by AIP Publishing. 978-0-7354-1464-8/$30.00

020005-1
 ே௦
‫ܨ‬௦௣ ൌ ݉௚ ή ܿହ െ ܸǡ ቂ ቃ ;ϮͿ
௞௚
ଷ଺଴଴ή௠೎ ௞௚
‫ܥ‬௦௣ ൌ ǡ ቂ ቃ ;ϯͿ
ிೞ೛ ே௛
3- Calculating the engine's performances at different flight regimes and rotor speed, usually expressed as ENGINE's
OPERATING MAPS (i.e. ALTITUDE MAP, VELOCITY MAP, SPEED MAP).
4- Calculating of the ENGINE's UNIVERSAL MAP.
The results obtained from the thermodynamic analysis allow the calculation of the flight envelope and are
preparatory input data for dynamic modeling and simulation of a turbojet engine.
The relations (4) - (34) ordered as algorithm entries represent the basis for computing the turbojet engine
performances (1) - (3).
• SLS, ISA conditions: ‫݌‬଴ ൌ ͳǤͲͳ͵ʹͷሾܾܽ‫ݎ‬ሿ (4.1), ܶ଴ ൌ ʹͺͺሾ‫ܭ‬ሿ (4.2) and ݅଴ ൌ ‫ܥ‬௣ ή ܶ଴ ሾ݇‫ܬ‬Ȁ݇݃ሿ, (5)
• conditions at engine inlet (intake) - station 0 (SLS) or H (flight) :
if H = 0 [km] then ‫݌‬ଵ‫ כ‬ൌ  ߪௗ௔
‫כ‬
ή ‫݌‬଴ ሾܾܽ‫ݎ‬ሿ, (6.1), ܶଵ‫ כ‬ൌ ܶ଴ ሾ‫ܭ‬ሿ (7.1), and ݅ଵ‫ כ‬ൌ ‫ܥ‬௣ ή ܶଵ‫ כ‬ሾ݇‫ܬ‬Ȁ݇݃ሿ (8),
if H > 0 then ‫݌‬ଵ ൌ ‫݌‬ு  ή ‫݌‬଴ ሾܾܽ‫ݎ‬ሿ (6.2), ܶଵ‫ כ‬ൌ ܶு‫ כ‬ሾ‫ܭ‬ሿ (7.2) and ݅ଵ‫ כ‬ൌ ‫ܥ‬௣ ή ܶଵ‫ כ‬ሾ݇‫ܬ‬Ȁ݇݃ሿ (8),
‫כ‬ ‫כ‬

் ହǤଶହହଷ
where ܶு ൌ ܶ଴ െ ͸Ǥͷ ή ‫ܪ‬ሾ݇݉ሿǡ ሾ‫ܭ‬ሿ (9) and ‫݌‬ு ൌ ‫݌‬଴ ή ቀ ಹ ቁ (10)
்బ
௏మ ሺ௞ିଵሻ
and ܶு‫ כ‬ൌ ܶு ൅  (11) or ܶு‫ כ‬ൌ ܶு ή ቀͳ ൅ ή ‫݄ܿܽܯ‬ଶ ቁ (12)
ଶή஼೛ ଶ
ೖషభ
ሺ௞ିଵሻ ቀ ቁ
ೖ
and ‫݌‬ு‫ כ‬ൌ ‫݌‬ு ή ቀͳ ൅ ή ‫݄ܿܽܯ‬ଶ ቁ  (13)
ଶ
ೖషభ ೖషభ ೖషభ
‫כ‬ ቀ ቁ ቀ ቁ
௣ಹ ்‫כ‬ ೖ ሺ௞ିଵሻ ೖ ቀ ቁ
• dynamic pressure ratio: ߨௗ‫ כ‬ൌ ൌ  ቀ ಹቁ ൌ ቀͳ ൅ ή ‫݄ܿܽܯ‬ଶ ቁ  ൌ  ൫ȣሺ‫݄ܿܽܯ‬ሻ൯ ೖ  (14)
௣ಹ ்ಹ ଶ
‫כ‬ ‫כ‬
• conditions at compressor inlet - station ͳ : ‫݌‬ଵ‫כ‬ ൌ ߪௗ௔ ή  ‫݌‬ு‫( כ‬15), ܶଵ‫כ‬ ൌ  ܶு‫ כ‬ (16), ݅ଵ‫כ‬ ൌ  ݅ு‫כ‬ (17)
ೖషభ
ቆሺగ೎‫ כ‬ሻ ೖ ିଵቇ
௜‫כ‬
• conditions at combustor inlet - station ʹ‫ כ‬: ‫݌‬ଶ‫ כ‬ൌ ߨ௖‫ כ‬ή  ‫݌‬ଵ‫( כ‬18), ݅ଶ‫ כ‬ൌ  ݅ଵ‫ כ‬ή ቌͳ ൅ ቍ (19), ܶଶ‫ כ‬ൌ ஼మ (20)
ఎ೎‫כ‬ ೛

• conditions at turbine inlet - station ͵‫ כ‬: ‫݌‬ଷ‫ כ‬ൌ ߪ௖௔

‫כ‬
ή  ‫݌‬ଶ‫( כ‬21),ή ܶଷ‫ כ‬allows specific enthalpy ݅ଷ‫ כ‬ൌ ‫ܥ‬௣௚  ή ܶଷ‫( כ‬22)
ሺ௜య‫ି כ‬௜మ‫ כ‬ሻ
• fuel flow coefficient (from energy balance eqn. in combustor): ݉௖ ൌ (23)
൫క೎ೌ ή௉೎೔ ି௜య‫ כ‬൯
• burned gas flow coefficient (from mass balance eqn. in combustor): ݉௚ ൌ ͳ ൅  ݉௖ (24)
ெሶ
• definition of fuel flow coefficient: ݉௖ ൌ  ெሶ೎  (25)
ೌ
ெሶ೒
• definition of burned gas flow coefficient: ݉௚ ൌ   (26)
ெሶೌ
௜ర‫כ‬ ఋ೟‫כ‬
• conditions at turbine exit - station Ͷ‫ כ‬: ݅ସ‫ כ‬ൌ  ݅ଷ‫ כ‬െ  ݈௧‫( כ‬27), ܶସ‫ כ‬ൌ (28); ‫݌‬ସ‫ כ‬ൌ  (29),
஼೛೒ ௣య‫ כ‬
• where ߜ௧‫ כ‬ is the pressure ratio in turbine, and it comes out from the expression of specific work in
ೖ೒
‫כ‬ ିቀ ቁ
௟೟̴೔೏ ೖ೒షభ
turbine. ߜ௧‫כ‬ ൌ  ቀͳ െ ቁ (30)
௜య‫כ‬
• conditions at nozzle exit - station ͷ:
• case: full exhaust nozzle expansion: ‫݌‬ହ ൌ ‫݌‬ு (31) , then the thrust obtained is maximum
ೖ೒
ଶ ቀ ቁ
ೖ೒షభ
• case: partial exhaust nozzle expansion: ‫݌‬ହ ൌ  ‫݌‬௖௥ ൏ ‫݌‬ு (32), ‫݌‬௖௥ ൌ  ቀ௞௚ାଵቁ ή ‫݌‬ସ‫( כ‬33)
• velocity of expelled gas ܿହ [m/s], (34):
ೖషభ
ೖ೒షభ
ିቀ ቁ ሺగ೎‫ כ‬ሻ ೖ ିଵ
ܿହ  ൌ  ߮௔௥ ή ඨʹ ή ൝൤݅ଷ‫ כ‬ή ሺͳ െ ߨௗ‫ כ‬ή ߪௗ௔
‫כ‬ ‫ כ‬ሻ
ή ߨ௖‫ כ‬ή ߪ௖௔ ೖ೒ ൨ െ ݅ଵ‫ כ‬ή ൥ ൩ൡ (34)
ఎ೎‫ כ‬ήఎ೟‫ כ‬ήఎ೘

The influence of altitude, flight Mach number and rotor speed on inlet air flow rate (35) and compressor pressure
ratio (40) - (43) is given below. Airflow rate (35) is influenced by the change of altitude and flight Mach number, by
the means of the variation of compressor pressure ratio, dynamic pressure ratio and the ratio of static pressures at
altitude H [km] versus SLS:
గ‫כ‬ ௣
‫ܯ‬௔ ൌ  ‫ܯ‬ሶ௔ ή ‫כ‬೎ ή ߨௗ‫ כ‬ή ಹ 
଴
(35)
గ೎ బ ௣బ

020005-2
 • specific work on compression (36) changes with the square of rotor speed (37), which represents the ratio
of speeds at operating versus nominal engine regime:
݈௖‫ כ‬ൌ  ݈௖‫ כ‬଴ ή ݊തଶ (36)
௡
݊ത ൌ (37)
௡ಿೀಾ೔೙ೌ೗
• the relations between specific work of compressor, compressor pressure ratio, intake enthalpy and rotor
speed, are (38) for SLS, ISA conditions and (39) for the flight at altitude:
ೖషభ
൫గ೎‫ כ‬బ ൯ ೖ ିଵ
݈௖‫ כ‬଴ ൌ ݅଴ ή ൭ ൱ (38)
ఎ೎‫ כ‬బ
ೖషభ
ቆሺగ೎‫ כ‬ሻ ೖ ିଵቇ
݈௖‫כ‬ ൌ  ݅ு‫כ‬ ή  ቌͳ ൅ ቍ (39)
ఎ೎‫כ‬

• the influence of altitude, flight Mach number and rotor speed on compressor pressure ratio is expressed by
relations (40) - (43); the ratio of compressor efficiencies at operating regime versus nominal can be taken
about 1.0, as initial approximation or in case that the universal compressor map is not available.
ೖ
ೖషభ ቀೖషభቁ
௜బ ఎ೎‫כ‬
ߨ௖‫כ‬ ൌ  ቈͳ ൅ ቆ൫ߨ௖‫ כ‬଴ ൯ ೖ െ ͳቇ ή ‫כ‬
ଶ
ή ݊ത ή ቉ (40)
௜ಹ ఎ೎‫ כ‬బ
ೖ
ೖషభ ቀ ቁ
ೖషభ
௜బ ఎ೎‫כ‬
ߨ௖‫כ‬ ൌ  ቈͳ ൅ ቆ൫ߨ௖‫ כ‬଴ ൯ ೖ െ ͳቇ ή ‫כ‬
ଶ
ή ݊ത ή ቉ (41)
௜ಹ ఎ೎‫ כ‬బ
ೖ
ೖషభ ቀೖషభቁ
௜బ
ߨ௖‫ כ‬ൌ  ቈͳ ൅ ቆ൫ߨ௖‫ כ‬଴ ൯ ೖ െ ͳቇ ή ‫כ‬ ή ݊തଶ ቉ (42)
௜ಹ
ೖ
ቀ ቁ
௟೎̴೔೏ ೖషభ
ߨ௖‫ כ‬ൌ  ൤ͳ ൅ ‫כ‬ ή ݊തଶ ൨  (43)
௜ಹ

The Engine Operating Maps EOM's are defined by the Altitude Map, Table 1, Velocity Map, Table 2 and Rotor
Speed Map, Table 3.

Table 1 - Definition of Altitude Map

Thrust ‫ ܨ‬ൌ ݂ሺ‫ܪ‬ሻ‫ۀ‬ቚ ௏ୀ଴ ሾܰሿ
௡Ψୀଵ
Specific thrust ‫ܨ‬௦௣ ൌ ݂ሺ‫ܪ‬ሻ‫ۀ‬ቚ ௏ୀ଴ ே௦
ቂ ቃ
௡Ψୀଵ ௞௚
Specific fuel ‫ܥ‬௦௣ ൌ ݂ሺ‫ܪ‬ሻ‫ۀ‬ቚ ௏ୀ଴ ௞௚
ቂ ቃ
consumption ௡Ψୀଵ ே௛

Table 2 - Definition of Velocity Map

Thrust ‫ ܨ‬ൌ ݂ሺܸሻ‫ۀ‬ቚ ுୀ଴ ‫ ܨ‬ൌ ݂ሺ‫ܯ‬ሻ‫ۀ‬ቚ ுୀ଴ ሾܰሿ
௡Ψୀଵ ௡Ψୀଵ
‫ܨ‬௦௣ ൌ ݂ሺܸሻ‫ۀ‬ቚ ுୀ଴ ‫ܨ‬௦௣ ൌ ݂ሺ‫ܯ‬ሻ‫ۀ‬ቚ ுୀ଴ ே௦
Specific thrust ቂ ቃ
௡Ψୀଵ ௡Ψୀଵ ௞௚
Specific fuel ‫ܥ‬௦௣ ൌ ݂ሺܸሻ‫ۀ‬ቚ ுୀ଴ ‫ܥ‬௦௣ ൌ ݂ሺ‫ܯ‬ሻ‫ۀ‬ቚ ுୀ଴ ௞௚
ቂ ቃ
consumption ௡Ψୀଵ ௡Ψୀଵ ே௛

Table 3 - Definition of Velocity Map

Thrust ‫ ܨ‬ൌ ݂ሺ݊ሻ‫ۀ‬ቚுୀ଴  ‫ ܨ‬ൌ ݂ሺΨ݊ሻ‫ۀ‬ቚ ுୀ଴  ሾܰሿ
௏ୀ଴ ெୀ଴
‫ܨ‬௦௣ ൌ ݂ሺ݊ሻ‫ۀ‬ቚுୀ଴  ‫ܨ‬௦௣ ൌ ݂ሺΨ݊ሻ‫ۀ‬ቚ ுୀ଴  ே௦
Specific thrust ቂ ቃ
௏ୀ଴ ெୀ଴ ௞௚
Specific fuel ‫ܥ‬௦௣ ൌ ݂ሺ݊ሻ‫ۀ‬ቚுୀ଴  ‫ܥ‬௦௣ ൌ ݂ሺΨ݊ሻ‫ۀ‬ቚ ுୀ଴  ௞௚
ቂ ቃ
consumption ௏ୀ଴ ெୀ଴ ே௛

020005-3
The Engine Universal Map EUM is defined either as in Table 4.1, expressing thrust parameter and specific fuel
consumption parameter as functions of flight Mach number, for different values of speed parameter, or equivalent,
as specified in Table 4.2.

Table 4.1 - Engine Universal Map - definition #1

‫ܨ‬
ൌ  ݂ሺ‫ܯ‬ሻ‫ۀ‬
Thrust parameter ‫݌‬ଵ‫כ‬ ೙
ተ ୀ௖௢௡௦௧Ǥ
ට೅‫כ‬భ

‫ܥ‬௦௣
ൌ ݂ሺ‫ܯ‬ሻ‫ۀ‬
Specific fuel consumption parameter ඥܶଵ‫כ‬ ተ
೙
ୀ௖௢௡௦௧Ǥ
ට೅‫כ‬భ
௡
Speed parameter ൌ ܿ‫ݐ݊ܽݐݏ݊݋‬
ඥ்భ‫כ‬

Table 4.2 - Engine Universal Map - definition #2

‫ܨ‬ ݊
Thrust parameter ൌ  ݂ ቆ ‫ כ‬ቇቝ
‫݌‬ଵ‫כ‬ ඥܶଵ ȁெୀ௖௢௡௦௧Ǥ
‫ܥ‬௦௣ ݊
Specific fuel consumption parameter ൌ ݂ቆ ቇቝ
ඥܶଵ‫כ‬ ඥܶଵ‫כ‬ ȁெୀ௖௢௡௦௧Ǥ
Flight Mach number ‫ ܯ‬ൌ ܿ‫ݐ݊ܽݐݏ݊݋‬

2. DYNAMIC MODELING OF A TURBOJET ENGINE

The dynamic modeling of a single-spool turbojet engine is based on the energy balance equations for the main
engine parts, such as the compressor, combustor and turbine, as shown in Figure 1.

Fig. 1 - Schematic diagram of a turbojet engine, main parts and stations, S. Zak, [3]

At each engine section are written the corrected parameters, such as the corrected mass flow rate (48), corrected
engine speed (49) and mass flow parameter (52) - (54), which are based on dimensionless ratios of pressure,
temperature and density (44) - (46), with the consideration of the reference ISA parameters (47):
௣
ߜ ൌ௣  (44)
బ
்
ߠ ൌ  (45)
்బ
ఘ
ߪ ൌఘ  (46)
బ
ଷ
‫݌‬଴ ൌ ͳǤͲͳ͵ʹͷሾܾܽ‫ݎ‬ሿ ܶ଴ ൌ ʹͺͺǤͳͷሾ‫ܭ‬ሿ ߩ଴ ൌ ͳǤʹʹͷሾ݇݃Ȁ݉ ሿ (47)
ඥఏ೔
݉ሶ௖௜ ൌ  ݉ሶ௜ ή  (48)
ఋ೔
௡
݊௖௜ ൌ  (49)
ඥఏ೔
From the one-dimensional mass flow equation (50) and the modeling equation of a perfect gas (51), the mass
flow parameter defined by relation (52), one can express the relation (53) for computing the mass flow rate ݉ሶ using
the MFP function (54):

020005-4
݉ሶ௖௜ ൌ ߩ ή ‫ ܣ‬ή ܸ (50)
‫ ݌‬ൌ ߩ ή ܴ ή ܶ (51)
௠ሶ ξ் ‫כ‬
‫ ܲܨܯ‬ൌ  ή  (52)
஺ ௣‫כ‬
௣‫ כ‬ή஺
݉ሶ ൌ  ή ‫ܲܨܯ‬ሺ‫݄ܿܽܯ‬ሻ (53)
ξ் ‫כ‬
ೖశభ
௞ ሺ௞ିଵሻ ିቀ ቁ
ଶ మήሺೖషభሻ
‫ܲܨܯ‬ሺ‫݄ܿܽܯ‬ሻ ൌ ට ή ‫ ݄ܿܽܯ‬ή ቀͳ ൅ ή ‫ ݄ܿܽܯ‬ቁ ή (54)
ோ ଶ

The energy balance equations are written for the compressor model (55), combustor (56) and turbine (57):

ௗ்మ‫כ‬ ଵ
ൌ ή ൣ݉ଶ‫ כ‬ή ൫‫ܥ‬௣ ή ܶଵ‫ כ‬െ ܶଶ‫ כ‬൯൧ െ ሺ݉ଶ‫ כ‬൅ ‫݈݀ܤ‬ሻ ή ܴ ή ܶଶ‫ כ‬ (55)
ௗ௧ ெమ ή஼ೡ
ௗ்య‫כ‬ ଵ
ൌ ή ൣ݉ଶ‫ כ‬ή ൫‫ܥ‬௣ ή ܶ௕ െ ‫ܥ‬௩ ή ܶଷ‫ כ‬൯൧ െ ݉௙ ή ሺ‫ ܨܸܪ‬ή ߟ௕ െ ‫ܥ‬௩ ή ܶଷ‫ כ‬ሻ െ  ݉ଷ‫ כ‬ή ܴ ή ܶଶ‫ כ‬ (56)
ௗ௧ ெయ ή஼ೡ
ௗ்ర‫כ‬ ଵ
ௗ௧
ൌெ ή ൣ݉ଶ‫ כ‬ή ൫‫ܥ‬௣ ή ܶଷ‫כ‬ െ ‫ܥ‬௩ ή ܶସ‫ כ‬൯൧ െ ݉ସ‫ כ‬ή ܴ ή ܶଶ‫ כ‬ (57)
ర ή஼ೡ

Note that in eqn. (55), ,ass flow rate and the shaft speed for the compressor are represented in the compressor
performance map, with the consideration of Bld [kg/s] - compressor bleed flow rate.

3. SINGLE SPOOL TURBOJET ENGINE STATES AND CONTROL

For a typical single spool turbojet engine, the LINEARIZED MODEL contains the STATE EQUATION (58)
and the OUTPUT EQUATION (59); the matrices A, B, C, D are computed for each representative operating point,
in accordance with the flight path and flight map.
‫ݔ‬ሶ ൌ ‫ ܣ‬ή ‫ ݔ‬൅ ‫ ܤ‬ή ‫ݑ‬ (58)
‫ ݕ‬ൌ ‫ ܥ‬ή ‫ ݔ‬൅ ‫ ܦ‬ή ‫ݑ‬ (59)

The STATE VECTOR x (60) contains the compressor speed and the combustor internal pressure
‫ ݔ‬ൌ  ቀ௣௡‫ כ‬ቁ (60)
య

The CONTROL VECTOR u (61) contains the fuel flow rate (which is the only one control parameter, because
the exhaust area is fixed geometry in case of this turbojet)
‫ ݑ‬ൌ  ൫‫ܯ‬ሶ௔ ൯ (61)

The OUTPUT VECTOR y (62) gives the engine thrust, turbine inlet temperature and surge margin
்௛௥௨௦௧
‫ ݕ‬ൌ൬ ೅‫כ‬య ൰ (62)
ೞ೘

4. NUMERICAL SIMULATIONS AND CONCLUSIONS

The engine's operational maps have been calculated and are shown in Figure 1 - Altitude Map, Figure 2 -
Velocity Map and Figure 3 - Rotor Speed Map, for the J85 single-spool turbojet engine as the test case.

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 a) Thrust [N] b) Specific Thrust [N] c) Specific Fuel Consumption [kg/Nh]
FIGURE 1. Altitude Map

a) Thrust [N] b) Specific Thrust [N] c) Specific Fuel Consumption [kg/Nh]

FIGURE 2. Velocity Map

a) Thrust [N] b) Specific Thrust [N] c) Specific Fuel Consumption [kg/Nh]

FIGURE 3. Rotor Speedf Map

The numerical simulations for the dynamic analysis of the single spool turbojet engine have been carried on for
different values of fuel flow rate; for study case #1 have been considered Fuel flow rate 0.6000 Kg/s + P*(Ncmd-
N), controller proportional with speed error, P=0.000221 Kg/s/RPM.

a) State vector component Æ Rotor speed [rpm] b) Control vector Æ Fuel flow [kg/s]
FIGURE 4. Study case #1: Fuel flow rate 0.6000 Kg/s

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 The effect of fuel flow as control on engine parameters, such as flow rate, stagnation temperature and stagnation
pressure was monitored at different engine sections: - at combustor inlet, Fig. 5, at turbine inlet, Fig. 6 and at turbine
exit, Fig. 7, was simulated and shown in graphics. The effect of fuel flow control on pressure ratios p3/p4 is
presented in Fig. 8 and of pressure ratios p3/p_ref in Fig. 9. In Fig. 10 was simulated the effect of fuel flow control
on flow rate at combustor inlet, and in Fig. 11 is presented the simulation of the influence of fuel flow control on
flow rate at turbine inlet.

FIGURE 5. Effect of fuel flow control on flow rate, stagnation temperature and
stagnation pressure at combustor inlet

FIGURE 6. Effect of fuel flow control on flow rate, FIGURE 7. Effect of fuel flow control on flow rate,
stagnation temperature and stagnation pressure at turbine stagnation temperature and stagnation pressure at
inlet turbine exit

FIGURE 8. Effect of fuel flow control on pressure ratios FIGURE 9. Effect of fuel flow control on pressure ratios
p3/p4 p3/p_ref

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 FIGURE 10. Effect of fuel flow control on flow rate at FIGURE 11. Effect of fuel flow control on flow rate at
combustor inlet turbine inlet

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