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Thermodynamic performance analysis of turbofan engine with a pulse detonation duct heater
Aerospace Science and Technology 23 (2012) 206–212
Contents lists available at ScienceDirect
Aerospace Science and Technology www.elsevier.com/locate/aescte
Thermodynamic performance analysis of turbofan engine with a pulse detonation duct heater Chen Wenjuan, Fan Wei ∗ , Qiu Hua, Qin Hongqiang, Yan Chuanjun School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 21 April 2011 Received in revised form 4 July 2011 Accepted 18 July 2011 Available online 22 July 2011 Keywords: Specific thrust Specific fuel consumption Pulse Detonation Combustor Turbofan engine Bypass duct Exhaust method
The potential performance gain of utilizing pulse detonation combustion in the bypass duct of a turbofan engine was investigated in this study. Pulse detonation turbofan engine concepts were studied and their performances were assessed. There were six cases according to different bypass ratio, different exhaust methods and with Pulse Detonation Combustor (PDC) in bypass duct or not. Four study combinations were established to compare the performance of different cases. The specific thrust (F s ), specific fuel consumption (sfc) of conventional turbofan engines and the new pulse detonation turbofan engine concepts were calculated and compared on design point and with the change of flight Mach number or altitude. The nozzle performance was considered in the present work. The calculation methods of PDC in bypass duct with different exhaust methods were explored. And the calculation methods of PDC adopted in this research could be a reference for other hybrid propulsion system with PDC. © 2011 Elsevier Masson SAS. All rights reserved.
1. Introduction With the gradual maturity of Pulse Detonation Combustor (PDC) technology, it is inevitable to apply PDC to engineering practice. Based on advantages of PDC, many researchers are attempting to apply pulse detonation combustion to gas turbine engines. PDC is attempted to replace conventional combustor [7], afterburners [4] and even if to be used in the bypass duct of a turbofan engine [5], which form new hybrid propulsion systems. The concept of these systems is combined pulse detonation combustion with conventional gas turbine engine. The conventional constant pressure combustion is transformed into constant volume detonation combustion. Pressure rise across PDC results in thrust augmentation. On the given thrust, the new hybrid propulsion system can reduce the number of compressor and turbine stages thereby increase the thrust-weight ratio of the engine. The new engine has higher thermal cycle efficiency, higher power extraction efficiency of turbine machine and so on. To give an insight into the advantages of this engine and compare it with conventional engine, it is necessary to develop calculation method of thermodynamic performance of this new engine. Thermodynamic performance analysis on turbofan engine with pulse detonation combustion in bypass duct is presented in this paper. Few literatures are reported in this field. Just Mawid and Sekar et al. [5] utilize pulse detonation combustion in the bypass
*
Corresponding author. Tel.: +13659256862; fax: +029 88492748. E-mail address: [email protected] (W. Fan).
1270-9638/$ – see front matter doi:10.1016/j.ast.2011.07.002
© 2011 Elsevier Masson
SAS. All rights reserved.
duct of a turbofan engine. The performance of the new concept engine is assessed using multidimensional CFD analysis. It is shown that significant performance gains can be obtained by using the pulse detonation turbofan engine concept as compared with the conventional afterburning turbofan engine. But each component of the engine, different bypass ratio, nozzle performance and exhaust method are not considered in the calculation model. In this paper, the nozzle performance is considered. At a given velocity or altitude, thermodynamic performance of each component of the engine is calculated. The performance of turbofan engines equipped with PDC in bypass duct is compared with those of conventional turbofan engines in four combinations as follows: Combination 1: Case A (baseline): A high bypass ratio separate exhaust turbofan engine with design point: Ma0 = 0.8, H = 9.0 km, standard atmosphere, compression ratio of fan π f = 2.35, total compression ratio πc = 16.45, T t4 = 1800 K, bypass ratio B = 5.0. Case B: Incorporate bypass PDC to Case A. Combination 2: Case C (baseline): A low bypass ratio mixed exhaust turbofan engine with afterburner off with design point: Ma0 = 1.6, H = 11 km, standard atmosphere, compression ratio of fan π f = 3.8, total compression ratio πc = 17, T t4 = 1800 K, bypass ratio B = 0.4. Case D: Incorporate bypass PDC to Case C. Combination 3: Case E (baseline): A low bypass ratio mixed exhaust turbofan engine with afterburner on with design point: Ma0 = 1.6,
W. Chen et al. / Aerospace Science and Technology 23 (2012) 206–212
207
Nomenclature Fs sfc cp c pg
γ Ma0 H
πc Ma22 T t22 pt22 T 22 p 22 c 22 pb Tb
γb T t5II pt5II T 5II p 5II Ma5II L0 Hf k kg T t9II pt9II T 9II p 9II Ma9II a9II c 9II r
δc δc f
specific thrust specific fuel consumption constant pressure specific heat capacity constant pressure specific heat capacity of burned gas specific heat ratio flight Mach number flight altitude total compression ratio Mach number after fan total temperature after fan total pressure after fan static temperature after fan static pressure after fan airstream velocity after fan pressure of C–J detonation wave temperature of C–J detonation wave specific heat ratio of C–J detonation wave total temperature on 5II section total pressure on 5II section static temperature on 5II section static pressure on 5II section Mach number on 5II section theory air mass low heating value of fuel specific heat ratio specific heat ratio of burned gas total temperature on 9II section in detonation process total pressure on 9II section in detonation process static temperature on 9II section in detonation process static pressure on 9II section in detonation process Mach number on 9II section in detonation process sonic velocity on 9II section in detonation process airstream velocity on 9II section in detonation process gas constant total pressure recovery coefficient of nozzle after detonation chamber total pressure recovery coefficient of detonation chamber
T t9II f pt9II f T 9II f p 9II f Ma9II f a9II f c 9II f p0 c0 F sI F sII F sIIa F sIIb t cycle ta tb
τa τb t1 t2
t3 t fill L U CJ
α β0 c3 f f0
β δ1 δ2 B T t3 AB
total temperature on 9II section in filling process total pressure on 9II section in filling process static temperature on 9II section in filling process static pressure on 9II section in filling process Mach number on 9II section in filling process sonic velocity on 9II section in filling process airstream velocity on 9II section in filling process atmospheric pressure airstream velocity on 0 section specific thrust of engine core specific thrust of bypass duct specific thrust of bypass duct in detonation process specific thrust of bypass duct in filling process a cycle period time of detonation process time of filling process time coefficient of detonation process time coefficient of filling process spread time of detonation wave time of the first expansion wave arriving thrust wall after detonation wave arriving detonation chamber exit pressure relaxation time of detonation chamber filling time length of detonation tube velocity of C–J detonation wave normalized factor in t 2 normalized factor in t 3 sonic velocity after Taylor wave fuel gas ratio of combustor total fuel gas ratio relative air mass of plane citing relative cooling air mass of high pressure turbine relative cooling air mass of low pressure turbine bypass ratio total temperature on combustor entrance afterburner
H = 11 km, standard atmosphere, compression ratio of fan π f = 3.8, total compression ratio πc = 17, T t4 = 1800 K, bypass ratio B = 0.4. Case F: Incorporate bypass PDC to Case E. Combination 4: Case D and Case E.
and multiplied by their time coefficients respectively, then added to deduce the total thrust. In Case D with mixed exhaust the averaged total temperature and total pressure at detonation tube exit are calculated by energy conservation equation and isentropic relation respectively. The PDC calculation methods in this paper can be a reference for other hybrid propulsion system with PDC.
Two PDC calculation methods are used in engines with different exhaust modes respectively. Calculation in Case B with separate exhaust involves detonation process and filling process. Thrusts in two processes are obtained by momentum theorem respectively,
2. Ideal cycle and operation processes The characteristic sections of Case B, Case D and Case F are shown in Fig. 1, Fig. 2 and Fig. 3 respectively.
Fig. 1. Characteristic sections of Case B.
208
W. Chen et al. / Aerospace Science and Technology 23 (2012) 206–212
Fig. 2. Characteristic sections of Case D.
Fig. 3. Characteristic sections of Case F.
Fig. 4. Ideal cycle of Case B on p–v diagrams: (a) core; (b) bypass.
p–v diagrams of ideal cycle of Case B are shown in Fig. 4. Fig. 4(a) shows ideal cycle of the core flow. Point 0 represents ambient air pressure that is compressed along the line 0-2-22-2.5-3 by the intake, fan and compressor in sequence. 0-3 is an isentropic compression process. From 3 to 4 heat is added to the air by introducing and burning fuel at constant pressure, thereby considerably increasing the volume of air. From 4 to 9 the gases resulting from combustion expand through the turbine and nozzle to atmosphere. 4-9 is an isentropic expansion process. Fig. 4(b) shows ideal cycle of the bypass. From 0 to 22 air is compressed by the intake and the fan. From 22 to 4 air is heated by pulse detonation combustion. 4 -9II is an isentropic expansion process in bypass duct. 9II-0 gases resulting from combustion expand through PDC nozzle progresses in atmosphere. p–v diagrams of ideal cycle of Case D are shown in Fig. 5. There is a mixing process after point 5 comparing with Case B, which is also shown in Fig. 2. Figs. 5(a) and 5(b) show ideal cycle of the core of Case D and the bypass respectively. 5I-6 is a constant pressure endothermic process and 5II-6 is a constant pressure exothermic process. 6-9 is an isentropic expansion process. p–v diagrams of ideal cycle of Case F are shown in Fig. 6. Comparing with Case D, there is a constant pressure combustion process by afterburner in Case F. As shown in Fig. 6(a), (b), 6-7 is a constant pressure endothermic process and 7-9 is an isentropic expansion process. 3. Thermodynamic performance analysis method To establish performance calculation model, it was assumed that: (1) airstream is perfect gas, and is in quasi-steady state and one-dimensional when flowing through every part; (2) the c p and γ of the airstream are different respectively when they flow in
Fig. 5. Ideal cycle of Case D on p–v diagrams: (a) core; (b) bypass.
Fig. 6. Ideal cycle of Case F on p–v diagrams: (a) core; (b) bypass.
different components. But they are constant in each component respectively when flowing in intake, fan, compressor, combustor, turbines and nozzle, whereas changed in PDC and mixing chamber. It was assumed that the flight Mach number Ma0 , flight altitude H and efficiency or loss coefficient of each component are known. The operation parameters (such as pressure, temperature and so on) on each section of the core were calculated as an adiabatic process according to the above ideal cycle. And it was supposed that the gas expand completely through nozzle. The performance parameters of Case A, Case C, and the core of Case B were calculated by performance analysis method of the traditional turbofan engine [2,3]. The part of the core of Case D which was before mixing chamber was also calculated by traditional method. The bypass of Case B, Case D and Case F and the part of Case D and Case F after mixing chamber were related to detonation combustion. So the key technologies were calculating the parameters of exit of PDC
W. Chen et al. / Aerospace Science and Technology 23 (2012) 206–212
and treating with the correlation between deflagration and detonation. Detonation calculation in Case B included detonation process and filling process. It was supposed that the Mach number after fan Ma22 is equal to 0.5, which is combined with total temperature and total pressure after fan (tt22 , pt22 ) to calculate static temperature t 22 , static pressure p 22 and airstream velocity c 22 . Detonation parameters (p b , tb , γb ) were obtained by the calculation method of equilibrium composition of combustion products [6]. In detonation process averaged velocity at the detonation tube exit was obtained from detonation parameters and thermodynamics relations (1)–(11):
p 5II = p 22 T 5II Tb
=
(1)
p 5II
γbγ−1
pb
(3)
T t9II = T t5II
(4)
2
Ma5II =
kg − 1
pt5II = p 5II 1 +
T t5II T 5II
kg − 1 2
−1 Ma25II
(5)
k k−g 1 g
(6)
pt9II = δc pt5II Ma9II =
kg − 1
T 9II = T t9II a9II =
(7) 2
τa = ta /t cycle
(22)
τb = tb /t cycle
(23)
ta = t 1 + t 2 + t 3
(24)
tb = t fill
(25)
t 1 = L /U CJ
(26)
t 2 = α L /c 3
(27)
t 3 = β0 L /c 3
(28)
t fill = L /c 22
1+
pt9II
k g −1 kg
p 9II kg − 1 2
−1
(8)
k g rT 9II
(9)
pt5II pb
=
T t5II
(12)
p 9II f = p 0
(13)
T 9II f = T 22
Ma9II f a9II f =
(14) p 9II f
k −1 k
p 22
k−k 1 2 p t9II f = −1 k−1 p 9II f krT 9II f
c 9II f = a9II f Ma9II f
(15)
(30)
b
(31)
Tb
Fs =
f0 +
1 − β0
1+ B
c9 +
B 1+ B
c 9II − c 0
In Case B:
F sII =
1+
1 L0
c 9II − c 0
+ (c 9II f − c 0 ) Fs =
U CJ c 3
[c 3 + (α + β)U CJ ]c 22 + U CJ c 3
(34) (35)
1+ B
(33)
[c 3 + (α + β)U CJ ]c 22 [c 3 + (α + β)U CJ ]c 22 + U CJ c 3
F sI + B F sII
Fs = 1 + f0 −
(32)
β0 c9 − c0 1+ B
(36)
In all cases:
sfc =
3600 f 0 Fs
(37)
4. Results and discussion
(16) (17) (18)
Thus thrust was obtained by momentum theorem in two processes respectively by (19), (20):
F sIIa = (1 + 1/ L 0 )c 9II − c 0
(19)
F sIIb = c 9II f − c 0
(20)
In two processes the thrust was multiplied by its time coefficient (τa , τb ) respectively, then total thrust in bypass duct of Case B was obtained by (21):
F sII = F sIIa τa + F sIIb τb
c 22
(29)
γ γ−b 1
In Cases C–F:
pt9II f = δc f pt22
+
Performance parameters F s and sfc were computed by the following relations [2,3]: In Case A:
(11)
Averaged velocity at detonation tube exit in filling process was calculated by thermodynamics relations (12)–(18):
T t9II f = T t22
c3
1
In Case D and Case F the averaged total temperature and total pressure at detonation tube exit were calculated by energy conservation (3) and isentropic relation (31):
(10)
c 9II = a9II Ma9II
+
α+β
F sI = 1 + (1 − β0 − δ1 − δ2 ) f − β0 c 9 − c 0
Ma29II
1 U CJ
(2)
T t5II c pg (1 + 1/ L 0 ) = c p T t22 + H f / L 0
where
t cycle = ta + tb = L
b
209
(21)
The current work was composed of four parts: the performance compare of Case A and Case B, Case C and Case D, Case E and Case F, Case D and Case E respectively. The specific thrust (F s ), specific fuel consumption (sfc) of them were calculated and compared on design point and with the change of flight Mach number or altitude. 4.1. Combination 1: Case A and Case B Design point conditions are as follows: Ma0 = 0.8, H = 9.0 km, standard atmosphere, compression ratio of fan π f = 2.35, total compression ratio πc = 16.45, T t4 = 1800 K, bypass ratio B = 5.0. Under these conditions, results are obtained in Table 1. In Table 1, it is revealed that F s of Case B is 2.002 times of that of Case A, and sfc is added by 423.3%. So for a high bypass ratio separate exhaust turbofan engine, after incorporating PDC into the bypass duct, F s increases and sfc ascends more on design point.
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Fig. 7. Velocity characteristic curves of Case A and Case B: (a) averaged thrust; (b) specific fuel consumption. Table 1 F s and sfc of Case A and Case B on design point.
F s (N · s/kg) sfc (kg/(N · h))
Case A
Case B
262 0.0823
524 0.4306
Table 2 F s and sfc of Cases C–F on design point.
F s (N · s/kg) sfc (kg/(N · h))
Case C
Case D
Case E
Case F
637 0.1287
1044 0.1456
1089 0.1815
1220 0.1160
4.1.1. Performance comparison of Case A and Case B with the change of flight Mach number Fig. 7 shows the velocity characteristic of Case A and Case B. With the increase of Ma0 , F s declines and sfc raises. And the curves are smooth and the amplitude of variation is not wide. It indicates that two kinds of engine can work well in wide Mach number range. Case B can improve F s effectively, but sfc is very high. 4.1.2. Performance comparison of Case A and Case B with the variation of altitude The altitude characteristics of Case A and Case B are shown in Fig. 8. With the increase of H , F s ascends and sfc falls, and the changes are slight. It is indicated that the performances of Case A and Case B are steady in wide altitude range. Compared with Case A, the law of altitude characteristics of Case B is coincident with that of velocity characteristics, and the altitude characteristic curves are smoother. Combining the two kinds of characteristics, it is concluded that for a high bypass ratio separate exhaust turbofan engine, after incorporating PDC into the bypass duct, F s improves well and sfc ascends consumedly. 4.2. Combinations 2, 3 and 4: Case C and Case D, Case E and Case F, Case D and Case E Design point conditions are as follows: Ma0 = 1.6, H = 11 km, standard atmosphere, compression ratio of fan π f = 3.8, total compression ratio πc = 17, T t4 = 1800 K, bypass ratio B = 0.4. Under these conditions, results are obtained in Table 2. As shown in Table 2, on design point: (1) Compared with Case C, F s adds by 63.77% and sfc adds by 13.16% in Case D respectively. The advantage of Case D is evident in Combination 2.
(2) Compared with Case E, F s increases and sfc decreases a lot in Case F. So for a low bypass ratio mixed exhaust turbofan engine with afterburner on, after incorporating PDC into the bypass duct, the performance improved effectively. (3) Compared with Case E, F s and sfc both reduce a little in Case D. So for a low bypass ratio mixed exhaust turbofan engine, compared with afterburner on, incorporating PDC into the bypass duct has no obvious advantage on performance. 4.2.1. Performance comparison of Cases C–F with the change of flight Mach number The velocity characteristics of Cases C–F are shown in Fig. 9. It is indicated that with the increase of flight Mach number F s descends and sfc rises. Compared with Case C, F s improves effectively and sfc increases a little in Case D. So in Combination 2, Case D has some advantages in velocity characteristics. In wide Mach number range, compared with Case E, F s enhances and sfc cuts down in Case F. So in Combination 3, Case F improves performance effectively in velocity characteristics. In Combination 4, when Ma0 is less than 1.15, F s in Case D is higher than that in Case E. And when Ma0 is more than 1.15, the situation is opposite. sfc in Case D is much lower than that in Case E. So compared with Case E, Case D has some advantages in velocity characteristics. 4.2.2. Performance comparison of Cases C–F with the variation of altitude The altitude characteristics of Cases C–F are shown in Fig. 10. It is coincident with velocity characteristic that: (1) In Combination 2: Compared with Case C, F s improves effectively and sfc increases a little in Case D. (2) In Combination 3: Compared with Case E, F s enhances and sfc cuts down in Case F. (3) In Combination 4: F s in Case D is close to that in Case E and sfc is much lower than that of Case E. When altitude is less than 11 km, in four cases with the increase of altitude F s ascends and sfc falls because the atmosphere temperature drops resulting in the decreasing of T t3 ; when altitude is equal to or more than 11 km, with the increase of altitude in Case C and Case E the change stops because the atmosphere temperature does not change resulting in constant T t3 and in Case D and Case F F s ascends and sfc descends slightly due to pulse detonation combustion. Compared the four cases in Figs. 9 and 10, Case F has the highest F s and the lowest sfc. So for low bypass ratio mixed exhaust turbofan engines, Case F has the best performance.
W. Chen et al. / Aerospace Science and Technology 23 (2012) 206–212
211
Fig. 8. Altitude characteristic curves of Case A and Case B: (a) averaged thrust; (b) specific fuel consumption.
Fig. 9. Velocity characteristic curves of Cases C–F: (a) averaged thrust; (b) specific fuel consumption.
Fig. 10. Altitude characteristic curves of Cases C–F: (a) averaged thrust; (b) specific fuel consumption.
5. Validation
The baseline cases Case A, Case C and Case E are corresponding to high bypass ratio turbofan engine, low bypass ratio turbofan engine with AB off and with AB on respectively. Case A and M45H-01 are in the same engine family. Case C, Case E and A-31 are in the same engine family. Table 3 shows the cruising parameters of Case A and M45H-01 [1]. It is revealed that the parameters of Case A are reasonable, so the calculation methods should be appropriate.
Table 3 Cruising parameters of Case A and M45H-01.
Ma0 H (km)
πc B F s (N · s/kg) sfc (kg/(N · h))
Case A
M45H-01
0.8 9 16.45 5 262 0.0823
0.6 6 16 3 119 0.0723
Table 4 shows the cruising parameters of Case C, Case E and low bypass ratio turbofan engine A-31 [1]. Case C and Case E
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W. Chen et al. / Aerospace Science and Technology 23 (2012) 206–212
Table 4 Cruising parameters of Case C, Case E and A-31 .
Ma0 H (km)
πc B F s (N · s/kg) sfc (kg/(N · h))
Case C
Case E
A-31 AB OFF
AB ON
1.6 11 17 0.4 637 0.1287
1.6 11 17 0.4 1089 0.1815
Cruising Cruising 23.8 0.6 680 0.0795
Cruising Cruising 23.8 0.6 1095 0.2000
correspond to A-31 with AB off and with AB on respectively. Compared their cruising parameters correspondingly, it is revealed that the parameters of Case C and Case E are reasonable, so the calculation methods should be appropriate. 6. Conclusions In this paper, for turbofan engine, six cases (Cases A–F) according to different bypass ratio, different exhaust methods and with PDC in bypass duct or not were investigated. Performance calculation model corresponding to each case was established. Four study combinations were established to compare the performance of different cases. The specific thrust (F s ), specific fuel consumption (sfc) of conventional turbofan engines and the new pulse detonation turbofan engine concepts were calculated and compared with the change of flight Mach number or altitude. Finally it was concluded that: (1) In all cases, with the increase of flight Mach number, F s decreases and sfc increases; and with the increase of flight altitude, F s rises and sfc declines. (2) For a high bypass ratio separate exhaust turbofan engine, after incorporating PDC into the bypass duct, F s improves well and sfc ascends consumedly. (3) For a low bypass ratio mixed exhaust turbofan engine with AB off, after incorporating PDC into the bypass duct, F s improves
effectively and sfc increases a little, so the performance improves. (4) For a low bypass ratio mixed exhaust turbofan engine with AB on, after incorporating PDC into the bypass duct, F s augments and sfc falls off a lot, so the performance improved effectively. (5) For a low bypass ratio mixed exhaust turbofan engine, compared with AB on, incorporating PDC into the bypass duct has some advantages on performance. (6) So for low bypass ratio mixed exhaust turbofan engines, Case F (with AB on and incorporating PDC into the bypass duct) has the best performance. Acknowledgements The authors wish to thank the National Natural Science Foundation of China through Grant No. 50976094, the Doctoral Program Foundation of Education Ministry of China (20096102110022) and the Doctorate Foundation of Northwestern Polytechnical University (CX200909) for financial supports of this work. References [1] C.D. Fang, The World Aircraft Engines Handbook, Aviation Industry Press, Beijing, 1996 (in Chinese). [2] X.C. Lian, H. Wu, The Principles of Aero-Engine (the second volume), National Defence Polytechnical Publishing Company Press, Beijing, 2001, pp. 62–63 (in Chinese). [3] X.C. Lian, H. Wu, The Principles of Aero-Engine, Northwestern Polytechnical University Press, Xi’an, 2005, pp. 152–161 (in Chinese). [4] M.A. Mawid, T.W. Park, Towards replacement of turbofan engines afterburners with pulse detonation devices, AIAA-2001-3470. [5] M.A. Mawid, T.W. Park, B. Sekar, C. Arana, Application of pulse detonation combustion to turbofan engines, Journal of Engineering for Gas Turbines and Power 125 (January 2003) 270–283. [6] B.J. McBride, S. Gordon, Computer program for calculation of complex chemical equilibrium compositions and applications, NASA Reference Publ. 1311, June 1996. [7] D.P. Petters, J.L. Felder, Engine system performance of pulse detonation concepts using the NPSS program, AIAA-2002-3910.
Contents lists available at ScienceDirect
Aerospace Science and Technology www.elsevier.com/locate/aescte
Thermodynamic performance analysis of turbofan engine with a pulse detonation duct heater Chen Wenjuan, Fan Wei ∗ , Qiu Hua, Qin Hongqiang, Yan Chuanjun School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 21 April 2011 Received in revised form 4 July 2011 Accepted 18 July 2011 Available online 22 July 2011 Keywords: Specific thrust Specific fuel consumption Pulse Detonation Combustor Turbofan engine Bypass duct Exhaust method
The potential performance gain of utilizing pulse detonation combustion in the bypass duct of a turbofan engine was investigated in this study. Pulse detonation turbofan engine concepts were studied and their performances were assessed. There were six cases according to different bypass ratio, different exhaust methods and with Pulse Detonation Combustor (PDC) in bypass duct or not. Four study combinations were established to compare the performance of different cases. The specific thrust (F s ), specific fuel consumption (sfc) of conventional turbofan engines and the new pulse detonation turbofan engine concepts were calculated and compared on design point and with the change of flight Mach number or altitude. The nozzle performance was considered in the present work. The calculation methods of PDC in bypass duct with different exhaust methods were explored. And the calculation methods of PDC adopted in this research could be a reference for other hybrid propulsion system with PDC. © 2011 Elsevier Masson SAS. All rights reserved.
1. Introduction With the gradual maturity of Pulse Detonation Combustor (PDC) technology, it is inevitable to apply PDC to engineering practice. Based on advantages of PDC, many researchers are attempting to apply pulse detonation combustion to gas turbine engines. PDC is attempted to replace conventional combustor [7], afterburners [4] and even if to be used in the bypass duct of a turbofan engine [5], which form new hybrid propulsion systems. The concept of these systems is combined pulse detonation combustion with conventional gas turbine engine. The conventional constant pressure combustion is transformed into constant volume detonation combustion. Pressure rise across PDC results in thrust augmentation. On the given thrust, the new hybrid propulsion system can reduce the number of compressor and turbine stages thereby increase the thrust-weight ratio of the engine. The new engine has higher thermal cycle efficiency, higher power extraction efficiency of turbine machine and so on. To give an insight into the advantages of this engine and compare it with conventional engine, it is necessary to develop calculation method of thermodynamic performance of this new engine. Thermodynamic performance analysis on turbofan engine with pulse detonation combustion in bypass duct is presented in this paper. Few literatures are reported in this field. Just Mawid and Sekar et al. [5] utilize pulse detonation combustion in the bypass
*
Corresponding author. Tel.: +13659256862; fax: +029 88492748. E-mail address: [email protected] (W. Fan).
1270-9638/$ – see front matter doi:10.1016/j.ast.2011.07.002
© 2011 Elsevier Masson
SAS. All rights reserved.
duct of a turbofan engine. The performance of the new concept engine is assessed using multidimensional CFD analysis. It is shown that significant performance gains can be obtained by using the pulse detonation turbofan engine concept as compared with the conventional afterburning turbofan engine. But each component of the engine, different bypass ratio, nozzle performance and exhaust method are not considered in the calculation model. In this paper, the nozzle performance is considered. At a given velocity or altitude, thermodynamic performance of each component of the engine is calculated. The performance of turbofan engines equipped with PDC in bypass duct is compared with those of conventional turbofan engines in four combinations as follows: Combination 1: Case A (baseline): A high bypass ratio separate exhaust turbofan engine with design point: Ma0 = 0.8, H = 9.0 km, standard atmosphere, compression ratio of fan π f = 2.35, total compression ratio πc = 16.45, T t4 = 1800 K, bypass ratio B = 5.0. Case B: Incorporate bypass PDC to Case A. Combination 2: Case C (baseline): A low bypass ratio mixed exhaust turbofan engine with afterburner off with design point: Ma0 = 1.6, H = 11 km, standard atmosphere, compression ratio of fan π f = 3.8, total compression ratio πc = 17, T t4 = 1800 K, bypass ratio B = 0.4. Case D: Incorporate bypass PDC to Case C. Combination 3: Case E (baseline): A low bypass ratio mixed exhaust turbofan engine with afterburner on with design point: Ma0 = 1.6,
W. Chen et al. / Aerospace Science and Technology 23 (2012) 206–212
207
Nomenclature Fs sfc cp c pg
γ Ma0 H
πc Ma22 T t22 pt22 T 22 p 22 c 22 pb Tb
γb T t5II pt5II T 5II p 5II Ma5II L0 Hf k kg T t9II pt9II T 9II p 9II Ma9II a9II c 9II r
δc δc f
specific thrust specific fuel consumption constant pressure specific heat capacity constant pressure specific heat capacity of burned gas specific heat ratio flight Mach number flight altitude total compression ratio Mach number after fan total temperature after fan total pressure after fan static temperature after fan static pressure after fan airstream velocity after fan pressure of C–J detonation wave temperature of C–J detonation wave specific heat ratio of C–J detonation wave total temperature on 5II section total pressure on 5II section static temperature on 5II section static pressure on 5II section Mach number on 5II section theory air mass low heating value of fuel specific heat ratio specific heat ratio of burned gas total temperature on 9II section in detonation process total pressure on 9II section in detonation process static temperature on 9II section in detonation process static pressure on 9II section in detonation process Mach number on 9II section in detonation process sonic velocity on 9II section in detonation process airstream velocity on 9II section in detonation process gas constant total pressure recovery coefficient of nozzle after detonation chamber total pressure recovery coefficient of detonation chamber
T t9II f pt9II f T 9II f p 9II f Ma9II f a9II f c 9II f p0 c0 F sI F sII F sIIa F sIIb t cycle ta tb
τa τb t1 t2
t3 t fill L U CJ
α β0 c3 f f0
β δ1 δ2 B T t3 AB
total temperature on 9II section in filling process total pressure on 9II section in filling process static temperature on 9II section in filling process static pressure on 9II section in filling process Mach number on 9II section in filling process sonic velocity on 9II section in filling process airstream velocity on 9II section in filling process atmospheric pressure airstream velocity on 0 section specific thrust of engine core specific thrust of bypass duct specific thrust of bypass duct in detonation process specific thrust of bypass duct in filling process a cycle period time of detonation process time of filling process time coefficient of detonation process time coefficient of filling process spread time of detonation wave time of the first expansion wave arriving thrust wall after detonation wave arriving detonation chamber exit pressure relaxation time of detonation chamber filling time length of detonation tube velocity of C–J detonation wave normalized factor in t 2 normalized factor in t 3 sonic velocity after Taylor wave fuel gas ratio of combustor total fuel gas ratio relative air mass of plane citing relative cooling air mass of high pressure turbine relative cooling air mass of low pressure turbine bypass ratio total temperature on combustor entrance afterburner
H = 11 km, standard atmosphere, compression ratio of fan π f = 3.8, total compression ratio πc = 17, T t4 = 1800 K, bypass ratio B = 0.4. Case F: Incorporate bypass PDC to Case E. Combination 4: Case D and Case E.
and multiplied by their time coefficients respectively, then added to deduce the total thrust. In Case D with mixed exhaust the averaged total temperature and total pressure at detonation tube exit are calculated by energy conservation equation and isentropic relation respectively. The PDC calculation methods in this paper can be a reference for other hybrid propulsion system with PDC.
Two PDC calculation methods are used in engines with different exhaust modes respectively. Calculation in Case B with separate exhaust involves detonation process and filling process. Thrusts in two processes are obtained by momentum theorem respectively,
2. Ideal cycle and operation processes The characteristic sections of Case B, Case D and Case F are shown in Fig. 1, Fig. 2 and Fig. 3 respectively.
Fig. 1. Characteristic sections of Case B.
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Fig. 2. Characteristic sections of Case D.
Fig. 3. Characteristic sections of Case F.
Fig. 4. Ideal cycle of Case B on p–v diagrams: (a) core; (b) bypass.
p–v diagrams of ideal cycle of Case B are shown in Fig. 4. Fig. 4(a) shows ideal cycle of the core flow. Point 0 represents ambient air pressure that is compressed along the line 0-2-22-2.5-3 by the intake, fan and compressor in sequence. 0-3 is an isentropic compression process. From 3 to 4 heat is added to the air by introducing and burning fuel at constant pressure, thereby considerably increasing the volume of air. From 4 to 9 the gases resulting from combustion expand through the turbine and nozzle to atmosphere. 4-9 is an isentropic expansion process. Fig. 4(b) shows ideal cycle of the bypass. From 0 to 22 air is compressed by the intake and the fan. From 22 to 4 air is heated by pulse detonation combustion. 4 -9II is an isentropic expansion process in bypass duct. 9II-0 gases resulting from combustion expand through PDC nozzle progresses in atmosphere. p–v diagrams of ideal cycle of Case D are shown in Fig. 5. There is a mixing process after point 5 comparing with Case B, which is also shown in Fig. 2. Figs. 5(a) and 5(b) show ideal cycle of the core of Case D and the bypass respectively. 5I-6 is a constant pressure endothermic process and 5II-6 is a constant pressure exothermic process. 6-9 is an isentropic expansion process. p–v diagrams of ideal cycle of Case F are shown in Fig. 6. Comparing with Case D, there is a constant pressure combustion process by afterburner in Case F. As shown in Fig. 6(a), (b), 6-7 is a constant pressure endothermic process and 7-9 is an isentropic expansion process. 3. Thermodynamic performance analysis method To establish performance calculation model, it was assumed that: (1) airstream is perfect gas, and is in quasi-steady state and one-dimensional when flowing through every part; (2) the c p and γ of the airstream are different respectively when they flow in
Fig. 5. Ideal cycle of Case D on p–v diagrams: (a) core; (b) bypass.
Fig. 6. Ideal cycle of Case F on p–v diagrams: (a) core; (b) bypass.
different components. But they are constant in each component respectively when flowing in intake, fan, compressor, combustor, turbines and nozzle, whereas changed in PDC and mixing chamber. It was assumed that the flight Mach number Ma0 , flight altitude H and efficiency or loss coefficient of each component are known. The operation parameters (such as pressure, temperature and so on) on each section of the core were calculated as an adiabatic process according to the above ideal cycle. And it was supposed that the gas expand completely through nozzle. The performance parameters of Case A, Case C, and the core of Case B were calculated by performance analysis method of the traditional turbofan engine [2,3]. The part of the core of Case D which was before mixing chamber was also calculated by traditional method. The bypass of Case B, Case D and Case F and the part of Case D and Case F after mixing chamber were related to detonation combustion. So the key technologies were calculating the parameters of exit of PDC
W. Chen et al. / Aerospace Science and Technology 23 (2012) 206–212
and treating with the correlation between deflagration and detonation. Detonation calculation in Case B included detonation process and filling process. It was supposed that the Mach number after fan Ma22 is equal to 0.5, which is combined with total temperature and total pressure after fan (tt22 , pt22 ) to calculate static temperature t 22 , static pressure p 22 and airstream velocity c 22 . Detonation parameters (p b , tb , γb ) were obtained by the calculation method of equilibrium composition of combustion products [6]. In detonation process averaged velocity at the detonation tube exit was obtained from detonation parameters and thermodynamics relations (1)–(11):
p 5II = p 22 T 5II Tb
=
(1)
p 5II
γbγ−1
pb
(3)
T t9II = T t5II
(4)
2
Ma5II =
kg − 1
pt5II = p 5II 1 +
T t5II T 5II
kg − 1 2
−1 Ma25II
(5)
k k−g 1 g
(6)
pt9II = δc pt5II Ma9II =
kg − 1
T 9II = T t9II a9II =
(7) 2
τa = ta /t cycle
(22)
τb = tb /t cycle
(23)
ta = t 1 + t 2 + t 3
(24)
tb = t fill
(25)
t 1 = L /U CJ
(26)
t 2 = α L /c 3
(27)
t 3 = β0 L /c 3
(28)
t fill = L /c 22
1+
pt9II
k g −1 kg
p 9II kg − 1 2
−1
(8)
k g rT 9II
(9)
pt5II pb
=
T t5II
(12)
p 9II f = p 0
(13)
T 9II f = T 22
Ma9II f a9II f =
(14) p 9II f
k −1 k
p 22
k−k 1 2 p t9II f = −1 k−1 p 9II f krT 9II f
c 9II f = a9II f Ma9II f
(15)
(30)
b
(31)
Tb
Fs =
f0 +
1 − β0
1+ B
c9 +
B 1+ B
c 9II − c 0
In Case B:
F sII =
1+
1 L0
c 9II − c 0
+ (c 9II f − c 0 ) Fs =
U CJ c 3
[c 3 + (α + β)U CJ ]c 22 + U CJ c 3
(34) (35)
1+ B
(33)
[c 3 + (α + β)U CJ ]c 22 [c 3 + (α + β)U CJ ]c 22 + U CJ c 3
F sI + B F sII
Fs = 1 + f0 −
(32)
β0 c9 − c0 1+ B
(36)
In all cases:
sfc =
3600 f 0 Fs
(37)
4. Results and discussion
(16) (17) (18)
Thus thrust was obtained by momentum theorem in two processes respectively by (19), (20):
F sIIa = (1 + 1/ L 0 )c 9II − c 0
(19)
F sIIb = c 9II f − c 0
(20)
In two processes the thrust was multiplied by its time coefficient (τa , τb ) respectively, then total thrust in bypass duct of Case B was obtained by (21):
F sII = F sIIa τa + F sIIb τb
c 22
(29)
γ γ−b 1
In Cases C–F:
pt9II f = δc f pt22
+
Performance parameters F s and sfc were computed by the following relations [2,3]: In Case A:
(11)
Averaged velocity at detonation tube exit in filling process was calculated by thermodynamics relations (12)–(18):
T t9II f = T t22
c3
1
In Case D and Case F the averaged total temperature and total pressure at detonation tube exit were calculated by energy conservation (3) and isentropic relation (31):
(10)
c 9II = a9II Ma9II
+
α+β
F sI = 1 + (1 − β0 − δ1 − δ2 ) f − β0 c 9 − c 0
Ma29II
1 U CJ
(2)
T t5II c pg (1 + 1/ L 0 ) = c p T t22 + H f / L 0
where
t cycle = ta + tb = L
b
209
(21)
The current work was composed of four parts: the performance compare of Case A and Case B, Case C and Case D, Case E and Case F, Case D and Case E respectively. The specific thrust (F s ), specific fuel consumption (sfc) of them were calculated and compared on design point and with the change of flight Mach number or altitude. 4.1. Combination 1: Case A and Case B Design point conditions are as follows: Ma0 = 0.8, H = 9.0 km, standard atmosphere, compression ratio of fan π f = 2.35, total compression ratio πc = 16.45, T t4 = 1800 K, bypass ratio B = 5.0. Under these conditions, results are obtained in Table 1. In Table 1, it is revealed that F s of Case B is 2.002 times of that of Case A, and sfc is added by 423.3%. So for a high bypass ratio separate exhaust turbofan engine, after incorporating PDC into the bypass duct, F s increases and sfc ascends more on design point.
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Fig. 7. Velocity characteristic curves of Case A and Case B: (a) averaged thrust; (b) specific fuel consumption. Table 1 F s and sfc of Case A and Case B on design point.
F s (N · s/kg) sfc (kg/(N · h))
Case A
Case B
262 0.0823
524 0.4306
Table 2 F s and sfc of Cases C–F on design point.
F s (N · s/kg) sfc (kg/(N · h))
Case C
Case D
Case E
Case F
637 0.1287
1044 0.1456
1089 0.1815
1220 0.1160
4.1.1. Performance comparison of Case A and Case B with the change of flight Mach number Fig. 7 shows the velocity characteristic of Case A and Case B. With the increase of Ma0 , F s declines and sfc raises. And the curves are smooth and the amplitude of variation is not wide. It indicates that two kinds of engine can work well in wide Mach number range. Case B can improve F s effectively, but sfc is very high. 4.1.2. Performance comparison of Case A and Case B with the variation of altitude The altitude characteristics of Case A and Case B are shown in Fig. 8. With the increase of H , F s ascends and sfc falls, and the changes are slight. It is indicated that the performances of Case A and Case B are steady in wide altitude range. Compared with Case A, the law of altitude characteristics of Case B is coincident with that of velocity characteristics, and the altitude characteristic curves are smoother. Combining the two kinds of characteristics, it is concluded that for a high bypass ratio separate exhaust turbofan engine, after incorporating PDC into the bypass duct, F s improves well and sfc ascends consumedly. 4.2. Combinations 2, 3 and 4: Case C and Case D, Case E and Case F, Case D and Case E Design point conditions are as follows: Ma0 = 1.6, H = 11 km, standard atmosphere, compression ratio of fan π f = 3.8, total compression ratio πc = 17, T t4 = 1800 K, bypass ratio B = 0.4. Under these conditions, results are obtained in Table 2. As shown in Table 2, on design point: (1) Compared with Case C, F s adds by 63.77% and sfc adds by 13.16% in Case D respectively. The advantage of Case D is evident in Combination 2.
(2) Compared with Case E, F s increases and sfc decreases a lot in Case F. So for a low bypass ratio mixed exhaust turbofan engine with afterburner on, after incorporating PDC into the bypass duct, the performance improved effectively. (3) Compared with Case E, F s and sfc both reduce a little in Case D. So for a low bypass ratio mixed exhaust turbofan engine, compared with afterburner on, incorporating PDC into the bypass duct has no obvious advantage on performance. 4.2.1. Performance comparison of Cases C–F with the change of flight Mach number The velocity characteristics of Cases C–F are shown in Fig. 9. It is indicated that with the increase of flight Mach number F s descends and sfc rises. Compared with Case C, F s improves effectively and sfc increases a little in Case D. So in Combination 2, Case D has some advantages in velocity characteristics. In wide Mach number range, compared with Case E, F s enhances and sfc cuts down in Case F. So in Combination 3, Case F improves performance effectively in velocity characteristics. In Combination 4, when Ma0 is less than 1.15, F s in Case D is higher than that in Case E. And when Ma0 is more than 1.15, the situation is opposite. sfc in Case D is much lower than that in Case E. So compared with Case E, Case D has some advantages in velocity characteristics. 4.2.2. Performance comparison of Cases C–F with the variation of altitude The altitude characteristics of Cases C–F are shown in Fig. 10. It is coincident with velocity characteristic that: (1) In Combination 2: Compared with Case C, F s improves effectively and sfc increases a little in Case D. (2) In Combination 3: Compared with Case E, F s enhances and sfc cuts down in Case F. (3) In Combination 4: F s in Case D is close to that in Case E and sfc is much lower than that of Case E. When altitude is less than 11 km, in four cases with the increase of altitude F s ascends and sfc falls because the atmosphere temperature drops resulting in the decreasing of T t3 ; when altitude is equal to or more than 11 km, with the increase of altitude in Case C and Case E the change stops because the atmosphere temperature does not change resulting in constant T t3 and in Case D and Case F F s ascends and sfc descends slightly due to pulse detonation combustion. Compared the four cases in Figs. 9 and 10, Case F has the highest F s and the lowest sfc. So for low bypass ratio mixed exhaust turbofan engines, Case F has the best performance.
W. Chen et al. / Aerospace Science and Technology 23 (2012) 206–212
211
Fig. 8. Altitude characteristic curves of Case A and Case B: (a) averaged thrust; (b) specific fuel consumption.
Fig. 9. Velocity characteristic curves of Cases C–F: (a) averaged thrust; (b) specific fuel consumption.
Fig. 10. Altitude characteristic curves of Cases C–F: (a) averaged thrust; (b) specific fuel consumption.
5. Validation
The baseline cases Case A, Case C and Case E are corresponding to high bypass ratio turbofan engine, low bypass ratio turbofan engine with AB off and with AB on respectively. Case A and M45H-01 are in the same engine family. Case C, Case E and A-31 are in the same engine family. Table 3 shows the cruising parameters of Case A and M45H-01 [1]. It is revealed that the parameters of Case A are reasonable, so the calculation methods should be appropriate.
Table 3 Cruising parameters of Case A and M45H-01.
Ma0 H (km)
πc B F s (N · s/kg) sfc (kg/(N · h))
Case A
M45H-01
0.8 9 16.45 5 262 0.0823
0.6 6 16 3 119 0.0723
Table 4 shows the cruising parameters of Case C, Case E and low bypass ratio turbofan engine A-31 [1]. Case C and Case E
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W. Chen et al. / Aerospace Science and Technology 23 (2012) 206–212
Table 4 Cruising parameters of Case C, Case E and A-31 .
Ma0 H (km)
πc B F s (N · s/kg) sfc (kg/(N · h))
Case C
Case E
A-31 AB OFF
AB ON
1.6 11 17 0.4 637 0.1287
1.6 11 17 0.4 1089 0.1815
Cruising Cruising 23.8 0.6 680 0.0795
Cruising Cruising 23.8 0.6 1095 0.2000
correspond to A-31 with AB off and with AB on respectively. Compared their cruising parameters correspondingly, it is revealed that the parameters of Case C and Case E are reasonable, so the calculation methods should be appropriate. 6. Conclusions In this paper, for turbofan engine, six cases (Cases A–F) according to different bypass ratio, different exhaust methods and with PDC in bypass duct or not were investigated. Performance calculation model corresponding to each case was established. Four study combinations were established to compare the performance of different cases. The specific thrust (F s ), specific fuel consumption (sfc) of conventional turbofan engines and the new pulse detonation turbofan engine concepts were calculated and compared with the change of flight Mach number or altitude. Finally it was concluded that: (1) In all cases, with the increase of flight Mach number, F s decreases and sfc increases; and with the increase of flight altitude, F s rises and sfc declines. (2) For a high bypass ratio separate exhaust turbofan engine, after incorporating PDC into the bypass duct, F s improves well and sfc ascends consumedly. (3) For a low bypass ratio mixed exhaust turbofan engine with AB off, after incorporating PDC into the bypass duct, F s improves
effectively and sfc increases a little, so the performance improves. (4) For a low bypass ratio mixed exhaust turbofan engine with AB on, after incorporating PDC into the bypass duct, F s augments and sfc falls off a lot, so the performance improved effectively. (5) For a low bypass ratio mixed exhaust turbofan engine, compared with AB on, incorporating PDC into the bypass duct has some advantages on performance. (6) So for low bypass ratio mixed exhaust turbofan engines, Case F (with AB on and incorporating PDC into the bypass duct) has the best performance. Acknowledgements The authors wish to thank the National Natural Science Foundation of China through Grant No. 50976094, the Doctoral Program Foundation of Education Ministry of China (20096102110022) and the Doctorate Foundation of Northwestern Polytechnical University (CX200909) for financial supports of this work. References [1] C.D. Fang, The World Aircraft Engines Handbook, Aviation Industry Press, Beijing, 1996 (in Chinese). [2] X.C. Lian, H. Wu, The Principles of Aero-Engine (the second volume), National Defence Polytechnical Publishing Company Press, Beijing, 2001, pp. 62–63 (in Chinese). [3] X.C. Lian, H. Wu, The Principles of Aero-Engine, Northwestern Polytechnical University Press, Xi’an, 2005, pp. 152–161 (in Chinese). [4] M.A. Mawid, T.W. Park, Towards replacement of turbofan engines afterburners with pulse detonation devices, AIAA-2001-3470. [5] M.A. Mawid, T.W. Park, B. Sekar, C. Arana, Application of pulse detonation combustion to turbofan engines, Journal of Engineering for Gas Turbines and Power 125 (January 2003) 270–283. [6] B.J. McBride, S. Gordon, Computer program for calculation of complex chemical equilibrium compositions and applications, NASA Reference Publ. 1311, June 1996. [7] D.P. Petters, J.L. Felder, Engine system performance of pulse detonation concepts using the NPSS program, AIAA-2002-3910.