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Impact of nozzles on a valveless pulse detonation rocket engine without the purge process
Applied Thermal Engineering 100 (2016) 1161–1168
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Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g
Research Paper
Impact of nozzles on a valveless pulse detonation rocket engine without the purge process Qibin Zhang, Wei Fan *, Ke Wang, Wei Lu, Yeqing Chi, Yongjia Wang School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China
H I G H L I G H T S
• • •
The average thrust of a valveless PDRE with different nozzles was measured. The impact of nozzles on the operation of a valveless PDRE was investigated. The impact of nozzles on the propulsion performance of a valveless PDRE was investigated.
A R T I C L E
I N F O
Article history: Received 8 November 2015 Accepted 28 February 2016 Available online 7 March 2016 Keywords: Detonation Rocket engine Valveless mode Nozzle Frequency
A B S T R A C T
To investigate the impact of exit nozzles on the operation and the propulsive performance of a valveless pulse detonation rocket engine (PDRE) without the purge process, experiments have been carried out under wide operating frequencies. Gasoline and oxygen-enriched air were used as fuel and oxidizer. Two detonation tubes and twenty-one nozzles with different shapes were employed in this study. It was observed that both the contraction ratio and the expansion ratio have an influence on the performance of the PDRE. Nozzles with converging sections decrease the highest operating frequency of the valveless PDRE, even if it cannot operate normally with nozzles whose contraction ratios are larger than four. The expansion ratio almost has no impact on the operation of the valveless PDRE, but the thrust decreases when the expansion ratios of diverging nozzles are larger than five. Most converging nozzles increase the thrust of the valveless PDRE, especially when the fill fractions were greater than one, while most diverging nozzles increase the thrust when the fill fractions were smaller than one. A maximum thrust increase of 25% has been obtained when nozzles were utilized. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction It is realized that the detonation wave has a rapid heat release rate and the pressure and temperature increase sharply after it; thus, detonation has the potential to produce greater thermal efficiency if employed in propulsion systems [1–7]. The application of detonation in propulsion has attracted extensive attentions and many efforts have been made on relative studies in the past few decades [2–15]. One of the applications based upon detonations is the pulse detonation rocket engine (PDRE). As one kind of propulsion device, the PDRE has great potentials but there are also many challenges. It would definitely be an effective way to gain a better performance when employing exit nozzles. However, how to design optimized nozzles is one big challenge because of the unsteady blowdown process caused by repetitive detonations. As the traditional design of nozzles is no longer applicable for the PDRE, many researchers begin to explore an alternative method [16–18]. To
* Corresponding author. Tel.: +86 29 88431116; fax:+86 29 88431116. E-mail address: [email protected] (W. Fan). http://dx.doi.org/10.1016/j.applthermaleng.2016.02.135 1359-4311/© 2016 Elsevier Ltd. All rights reserved.
establish an appropriate design model, the impact of nozzles on operations of the PDRE should be investigated in more detail. Many attempts including numerical simulations and experimental studies have been carried out to solve this problem [17–26]. The review by Kailasanath [19] on the investigations of the nozzles of a pulse detonation engine (PDE) and numerical simulations of the effects of diverging nozzles on the PDE performance carried out by Yungster [20] both indicate positive effects of exit nozzles on the PDE operation, but much of previous research has focused on numerical and theoretical analysis, while more experimental data are required. The relationships among geometry (e.g., nozzle length, contraction ratio, and expansion ratio), operational conditions (e.g., backpressure, operating frequency, and fill fraction), and propulsive performance (e.g., thrust and specific impulse) have been investigated [17,18,21–24]. Barbour and Hanson [17] proposed an analytical model for diverging nozzles in single-cycle mode and it indicates that the optimized area ratio is related to the ambient to plateau pressure ratio. Owens and Hanson [18] carried out another study on the unsteady nozzles based on single-cycle operations; the optimal contraction and expansion area ratios were evaluated by
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using a quasi-one-dimensional Euler model with detailed finiterate chemistry, and the experimental results showed that the optimized diverging nozzle is necessary to produce the largest specific impulse. As demonstrated by a number of studies [20,25,26], the effects of nozzles are different for single-cycle and multi-cycle operations and also for low-frequency and high-frequency operations. Experimental study of bell-shaped nozzles on the performance of a twophase and multi-cycle PDRE was carried out by Yan et al. [26], and it was observed that both the contraction and expansion ratios and the fill fraction have a strong influence on the performance, and the converging-diverging nozzles might be the optimum choice for a valved PDRE. However, the maximum operating frequency was only limited to 40 Hz in their work. A valveless PDRE utilizing liquid fuels without the purge process has been developed by Wang et al. [27], and it resulted in a wider operating frequency range with a maximum of 110 Hz. Due to the high-frequency operation achieved under this operating mode, to study the impact of nozzles on the PDRE under wider operating frequencies becomes possible. The aim of this work is to investigate the impact of nozzles on a valveless PDRE without the purge process under high operating frequencies (up to 100 Hz). Converging, diverging and convergingdiverging nozzles were all tested in this study. 2. Experimental setup 2.1. Supply system The supply system utilized in the current study is shown schematically in Fig. 1. Oxygen-enriched air and gasoline were used as oxidizer and fuel, respectively. In order to avoid premixing, the oxidizer and fuel were absolutely separated before being injected into the detonation tube. A check valve was used to prevent flashback to the oxidizer passage. Two solenoid valves were employed for turning on/off the fuel and oxidizer supplying before or after each operation, and the periodic supply was realized by the pressure oscillations inside the detonation tube. 2.2. Detonation tubes Schematic of the detonation tubes used in this study is shown in Fig. 2. The detonation tubes were both straight tubes with one end closed, and they had an inner diameter of d, and comprised an injection and ignition section (with a length of l1), a deflagrationto-detonation transition (DDT) section (with a length of l2) and a
Fig. 2. Schematic of the detonation tube.
measurement section (with a length of l3). The injection and ignition section was located near the tube close end, and one pressure transducer (p0) was employed to record the pressure history near the close end of the detonation tube with a length of l4 away from the close end. A spark plug with an ignition energy of about 50 mJ was used to ignite the mixture injected into the detonation tube, and it was l5 away from pressure transducer p0. A typical Shchelkin spiral was employed to accelerate the DDT process. Three pressure transducers, i.e., p 1 , p 2 and p 3 , were located along the measurement section to record the pressure histories and they were l6, (l6 + l7) and (l6 + l7 + l8) away from the spark plug, respectively. The measure errors caused by the sensors employed in this investigation are between ±3%. The pressure signals obtained by these transducers were processed by a signal conditioner module, and then recorded by a multi-channel data acquisition system. A sampling rate of 200 kHz was utilized. To investigate the nozzle impact on a PDRE with more data, two detonation tubes with diameters 30 and 24 mm were employed in this study. Parameters of the detonation tubes are shown in Table 1. The thrust test bench of Ref. [28] was used in this study. 2.3. Exit nozzles Twelve cone-shaped and nine bell-shaped exit nozzles were tested in this study. The cone-shaped nozzles had three types, such as converging, diverging and converging-diverging nozzles. The bellshaped nozzles were all converging-diverging ones. Configurations of the nozzles used in this work are shown in Fig. 3 and the detailed parameters of these nozzles are shown in Table 2. The bellshaped nozzles are the same as those utilized in Ref. [26], and they are used to compare the different impacts they have on the PDRE in valved and valveless modes. Nozzles BCD1~BCD9 almost have no impact on the operation of a valved PDRE in Ref. [26], but the valveless PDRE can operate only when employing nozzles BCD3 and BCD4 in a reduced operating frequency range. It is believed that the contraction sections have a great influence on the operation of the valveless PDRE without the purge process. Hence, the contraction ratios of the new designed nozzles (C1~C4, D1~D4 and CD1~CD4) are almost smaller than three. As the blowdown process of PDREs
Fig. 3. Configurations of the exit nozzles (C: converging nozzle; D: diverging nozzle; CD: converging-diverging nozzle; BCD: bell-shaped converging-diverging nozzle).
Fig. 1. Schematic of the experimental setup.
Table 1 Parameters of the detonation tubes. Parameters
d/mm
l1/mm
l2/mm
l3/mm
l4/mm
l5/mm
l6/mm
l7/mm
l8/mm
Tube A Tube B
30 24
160 110
260 230
360 320
20 20
80 40
500 330
70 70
70 70
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Table 2 Parameters of the exit nozzles (di: inlet diameter; lc: converging section length; ld: diverging section length; dt: throat diameter; rc: contraction ratio; do: outlet diameter; re: expansion ratio). di/mm
number
lc/mm
ld/mm
dt/mm
rc
do/mm
re
30
C1 C2 D1 D2 CD1 CD2 BCD1 BCD2 BCD3 BCD4 BCD5 BCD6 BCD7 BCD8 BCD9 C3 C4 D3 D4 CD3 CD4
30 30 – – 30 30 31 31 31 10 31 31 31 31 31 24 24 – – 24 24
– – 30 30 52 52 34 34 34 64 39 37 43 47 76 – – 24 24 41.5 41.5
17 21 – – 17 21 13 15 18 19.9 13 13 13 13 13 14 17 – – 14 17
3.1 2.0 – – 3.1 2.0 5.3 4.0 2.8 2.3 5.3 5.3 5.3 5.3 5.3 2.9 2.0 – – 2.9 2.0
– – 60 67 38 47 29 33.6 36 63 31 36 41 45 71 – – 48 54 30 38
– – 4.0 5.0 5.0 5.0 5.0 5.0 4.0 10.0 6.0 8.0 10.0 12.0 30.0 – – 4.0 5.1 4.6 5.0
24
is highly unsteady, the velocity of the products is relatively low in the end of the blowdown process. In order to avoid over-expansion, expansion ratios of the new designed nozzles were controlled between four and five. 3. Results and discussion In this study, gasoline and the oxygen-enriched air (the volume percentage of oxygen is 40%) were utilized as fuel and oxidizer, while the equivalence ratio was 1.5. The PDRE cannot operate normally in high frequencies (actually no more than 100 Hz when using tube B without nozzles) in this study because the fill fraction is too low to generate detonations; hence, the highest operating frequency of a PDRE is limited by the mass flow rate of the fresh mixture. The same supply system is utilized for tubes A and B, which means that the maximum mass flow rate for these two tubes is consistent. As the volume of tube B is smaller than tube A, the fill fraction of tube B is larger than tube A when operating in the same frequency. It means that tube B has the ability to obtain a higher maximum operating frequency than tube A. 3.1. Impact on the operating frequency When nozzles were utilized, experiments of the impact on the operating frequency range of a valveless PDRE without the purge process were carried out. All the tests were carried out more than 1 s. Some of the pressure profiles obtained with nozzles on are shown in Fig. 4, and the maximum operating frequencies are summarized in Fig. 5. As shown in Figs. 4 and 5, most exit nozzles employed in this work have an influence on the operations, and the valveless PDRE even could not operate normally when nozzles BCD1, BCD2, and BCD5~9 were utilized. These nozzles are all convergingdiverging ones, and their contraction ratios are all greater than four. As these nozzles had no influence on the operation of a traditional PDRE in Ref. [26], it means that the valveless PDRE has a more rigorous limit on the contraction ratio of exit nozzles. While converging and converging-diverging nozzles were employed in a PDRE, there would be reflected shock waves when detonation waves passing by the nozzle throat and the reflected waves would disturb the periodic supply in the close end created by pressure oscillations inside the detonation tube. Since the operation of a valveless
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PDRE without the purge process greatly depends on the flow field produced by the pressure oscillations and the vaporization of the liquid fuel [27], the reflected shock waves induced by exit nozzles with converging sections when the detonation waves pass through will damage the sustainable operation, and even lead to failures of detonation formation. On the other hand, it causes difficulty to the exhaust process when the nozzle throat is too small (rc ≥ 4). If the products cannot be exhausted in time, the fresh fuel–oxidizer mixture cannot be injected into the detonation tube effectively; thus, the fill fraction of the next cycle will be reduced to a quite low level. As a result, there is not enough fresh detonative mixture injected in and the detonation wave cannot be produced due to the failure of the DDT process. Subsequently, pressure oscillations created by detonations disappear and the fresh fuel–oxidizer mixture will flow into the detonation tube continuously and deflagrations occur. The contraction ratios of nozzles that disturbed the normal operation were all greater than four, which means that the suitable contraction ratios should be controlled below this for the valveless PDRE in this study. Without exit nozzles, the detonation tubes A and B can, respectively, operate stably up to 70 and 100 Hz. The operating frequency might be varied when utilizing exit nozzles, especially for the nozzles with small throats. As shown in Fig. 5a, the maximum operating frequencies when nozzles C2 and CD2 (rc = 2.0) are utilized are 30 and 20 Hz, while that for nozzles C1 and CD1 (rc = 3.1) is 10 Hz; the maximum operating frequency when nozzles C4 and CD4 (rc = 2.0) are utilized is 70 Hz, while that for nozzles C3 and CD3 (rc = 2.9) is 60 Hz. It means that when nozzles with small throats are utilized, the operating frequency range will become narrower, and the smaller throat corresponds to a narrower operating frequency range. As shown in Fig. 5a, the maximum operating frequency of converging-diverging nozzles is the same as the corresponding converging ones in most cases, e.g., those for nozzles CD4 and C4 is 70 Hz, while 10 Hz for nozzles CD1 and C1, and 60 Hz for nozzles CD3 and C3. The converging-diverging nozzles in this study have the same contraction ratio with the corresponding converging nozzles, such as CD1 and C1, CD2 and C2, CD3 and C3, and CD4 and C4. It means that the diverging sections of nozzles almost have no impact on the operation of the valveless PDRE, but there also exists another case, e.g., the maximum operating frequencies for nozzles CD2 and C2 are 20 and 30 Hz, respectively. The maximum operating frequencies were 30 and 40 Hz when bell-shaped nozzles BCD3 (rc = 2.8) and BCD4 (rc = 2.3) were used. Compared to nozzles C2 and CD2, nozzles BCD3 and BCD4 both have smaller throats but the same or greater operating frequencies were available. It may be because the inner surface of the bell-shaped nozzles is well designed in hydrodynamics. As shown in Fig. 5b, the maximum operating frequencies are both 100 Hz when nozzles D4 (re = 5.1) and D3 (re = 4.0) are utilized, while it is 60 Hz for nozzle D1 (re = 4.0) and D2 (re = 5.0). It indicates that the diverging nozzles have the widest operating frequency range in this study and the expansion ratio almost has no impact on the operations. It is observed that exit nozzles with converging sections really have an influence on the operation of a valveless PDRE without the purge process. The operating frequency range is getting narrower and that is mainly induced by the converging section, which not only slows down the exhaust process but also produces reflected shock waves. It is believed that the diverging section almost has no influence on the operating frequency. 3.2. Impact on the pressure inside the detonation tube The pressure history of an individual detonation wave and the reflected shock wave when nozzle C1 was utilized at 10 Hz is shown in Fig. 6. The pressure spikes obtained by transducers p1, p2 and p3 are 4.2, 3.4, and 4.8 MPa, respectively, and the time cost for the
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Fig. 4. Pressure profiles obtained with nozzles.
detonation wave to pass through them are Δt12 and Δt23, which are 0.034 and 0.036 ms, respectively. The distances between the transducers are Δd12 and Δd23, which are both 70 mm; hence, the average velocities are v12 = 2058.82 m/s and v23 = 1944.44 m/s. The pressure and velocity calculated by CEA (Chemical Equilibrium with Applications) codes are 2.87 MPa and 2100.9 m/s in the present experiments. Because the actual pressure and temperature of the fuel– oxidizer mixture were hard to be determined, the initial pressure and temperature employed in the calculation were 1 atm and
298.5 K, same as the ambient pressure and temperature. As there is no purge process under the valveless mode, the blowdown time is reduced compared with the valved mode with the purge process in the same operating conditions, which leads to a higher initial pressure in the next cycle. Therefore, the spike pressures obtained in this case were greater than the C-J values. When employing nozzle C1 and other nozzles, the pressures and velocities all exceeded 80% of the C-J values, which indicated fully developed detonations were obtained considering liquid fuel was utilized.
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As illustrated in Fig. 6, there are smaller pressure spikes created by the reflected shock waves after main spikes. The pressure of the reflected shock wave is lower than 2.0 MPa, and the velocities of the reflected shock wave between transducers p3, p2 and p1 are v32 and v21, which are 1590.91 and 1186.44 m/s, respectively. The pressure and velocity of the reflected shock wave are both lower than those of the detonation wave, so the reflected shock wave can be distinguished from the detonation wave easily. The reflected shock wave has been observed on a solenoid valved PDRE with nozzles that have throats [26], but this has a greater influence on the operations of a valveless PDRE. Besides inducing the reflected shock waves when converging and converging-diverging nozzles were utilized, the pressure inside the detonation tube was increased. Shown in Fig. 7 are the pressure histories obtained with and without nozzle C1 at 10 Hz. In order to smoothen the curves, the raw pressure data were reconstructed by the arithmetic method, which was written as
xk =
1 i +9 ∑ xi (k = 1, 11, 21…) 10 i=k
(1)
As shown in Fig. 7, the pressure increased when a nozzle with a converging section was employed. That is because the throat makes it difficult to exhaust the burned gases in time, and the pressure inside the detonation tube decreases slowly. On the other hand, as the products cannot be exhausted in time the initial pressure of the detonative mixture in the next cycle will be increased slightly, and this would lead to a greater pressure after detonations. Eventually, it brought an enhancement of the propulsive performance when nozzle C1 was employed in tube A. The impact of nozzles on the thrust of a PDRE will be discussed in the following section. 3.3. Impact on the thrust
Fig. 5. The maximum operating frequencies (MOFs) obtained with different nozzles.
Fig. 6. Pressure profiles obtained with nozzle C1 employed.
3.3.1. Thrust without nozzles The thrust produced without nozzles was measured and shown in Fig. 8. The thrust data were normalized by the raw thrust at 10 Hz. As illustrated in Fig. 8, the variation of the dimensionless thrust with the operating frequency can be divided into three stages, i.e., linear increase, nonlinear increase and quick decrease, which is consistent with the results obtained in Ref. [28] and is due to the fill conditions. The fill fraction varied with the operating frequency in the current study due to the supply capacity of the system, and the fact is that the fill fraction decreases with the increase of the operating frequency. The relationship of the fill fraction and the operating frequency in a valveless PDRE without the purge process has been described in Ref. [28]. In this study, the fill fraction under different operating frequencies is shown in Table 3. 3.3.2. Thrust with nozzles The thrust with nozzles in a wide operating frequency range was obtained, and it was also normalized by the raw thrust without nozzles at 10 Hz. Fig. 9 shows the dimensionless thrust with nozzles. As the operating frequency range of tube B was wider than that of tube A, more thrust data were obtained when utilizing tube B. Therefore, the tendency described was mainly based on the data of tube B, while the data of tube A were used as a supplement and a validation. It was observed that when nozzles were utilized, the tendency of the generated thrust with the operating frequency was different from the case without nozzles. When converging nozzles were installed on tube B, the thrust increased with the operating frequency (i.e., 10~60 Hz for nozzle C3 and 10~70 Hz for nozzle C4). And the thrust obtained with nozzle C3 was greater than the case with nozzle C4 below 40 Hz, while the situation inversed between 50 and 60 Hz. Nozzle C3 has a larger
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Fig. 7. Pressure histories obtained with and without nozzle C1.
contraction ratio (i.e., a smaller throat) than nozzle C4 and a smaller throat extends the blowdown time, which maintains the pressure inside the detonation tube at a relatively high level for a longer time and results in a greater propulsive performance. When the operating frequency was increased to 50 and 60 Hz, the time for each cycle decreased and a longer blowdown time corresponding to a greater contraction ratio would lead to the reduction of the actual fill fraction to partial fill conditions. In this case, the influence of nozzles C3 and C4 on the thrust differs from that obtained below 40 Hz. While diverging nozzles were utilized the thrust increased with the operating frequency first (i.e., 10~90 Hz for nozzle D3 and 10~80 Hz for nozzle D4) and then decreased with the operating frequency (i.e., 90~100 Hz for nozzle D3 and 80~100 Hz for nozzle D4). There is an inflexion of the thrust variation, and the inflexion when utilizing nozzle D3 is greater than that of nozzle D4. It may be because the expansion ratio of nozzle D3 is more appropriate to obtain a better propulsive performance than that of nozzle D4 in the current cases. When utilizing converging-diverging nozzles, the thrust increases with the operating frequency between 10 and 70 Hz.
Nozzle CD3 performs better than nozzle CD4 during 10~60 Hz, and the reason is consistent with the case utilizing converging nozzles during 10~40 Hz, while a better combination of the contraction and expansion ratios makes it possible for nozzle CD3 to maintain its advantage during 50~60 Hz. However, neither nozzle CD3 nor CD4 has a better performance than converging nozzles in the same operating frequencies. Fig. 10 provides a summary of the thrust increment obtained by tube B with nozzles. It indicates that some of the nozzles can produce positive thrust increment at suitable operating frequencies. As shown in Fig. 10, the maximum thrust increment is about 25% with nozzle C3 at 10 Hz. It may be because the detonation tube can be fully filled in each cycle in a low operating frequency, and in this case the converging nozzle can maintain the pressure inside the detonation tube in a relatively high level for a longer time. Some nozzles could not bring positive thrust increment in this work, such as nozzle D3 at 30 Hz, nozzle D4 at 40 Hz, nozzle CD4 at 20 Hz and so on. It might be because the supply and initial conditions in the present study were not the appropriate ones for these nozzles to produce their
Table 3 The fill fraction under different operating frequencies. Operating frequency/Hz
10
20
30
40
50
60
70
80
90
100
Fill fraction of tube A Fill fraction of tube B
2.11 5.45
1.41 4.35
1.05 2.17
0.84 1.45
0.70 1.09
0.60 0.87
0.51 0.72
– 0.62
– 0.54
– 0.48
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Fig. 8. Dimensionless thrust obtained without nozzles.
best performances. The impacts of nozzles on the thrust increment were different at different operating frequencies. In low operating frequencies (10~40 Hz), the converging nozzles performed best, e.g., the thrust increment utilizing nozzle C3 was positive with an average increase of 12.25%, while that of nozzle CD3 was 1.5%, and −5.625% for nozzle D3. That means nozzles that have converging section can improve the thrust if the detonation tube is fully filled. In medium operating frequencies (50~70 Hz), the converging nozzles also presented the best performance but the thrust increment decreased compared to that in low operating frequencies. It even brought a negative increment in some cases, e.g., the average thrust increment produced by nozzle C4 at this stage was only 2%, which was lower than an average increment of 8.25% in low operating frequency stage. Reflected shock waves and the partial fill effect decreased the thrust when converging and converging-diverging nozzles were utilized in this operating regime. In high operating frequencies (80~100 Hz), most nozzles with small throats lead to operation failures, but the PDRE could still operate utilizing the diverging nozzles and a positive average thrust increment was obtained. According to the results, it is believed that nozzles with different shapes are appropriate in different operating frequencies to
Fig. 9. Dimensionless thrust obtained with nozzles.
increase the propulsive performance of a PDRE, e.g., converging and converging-diverging nozzles should be employed in low and medium operating frequencies (<70 Hz for tube B and <30 Hz for tube A), while diverging nozzles are suggested in high operating frequencies (>70 Hz for tube B and >30 Hz for tube A). 4. Conclusions Experiments were carried out to investigate the impact of nozzles on a PDRE operating in the valveless mode without the purge process. Cone-shaped and bell-shaped exit nozzles were employed in this test, and different nozzle configurations, e.g., converging, diverging and converging-diverging nozzles, were all considered. Experimental results indicate that the converging section has a great impact on the operation of the valveless PDRE. The reflected shock waves induced by the throat of a nozzle would disturb the sustainable operation of the valveless PDRE, and it may lead to failures of the operation when the contraction ratio is too large (rc ≥ 4). The converging section also slows down the exhaust process
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Subscripts c Converging d Diverging cd Converging-diverging e Expansion i Inlet t Throat o Outlet References
Fig. 10. The thrust increment of tube B with nozzles.
inside the detonation tube, and then the pressure decreases slowly. As the valveless PDRE greatly depends on the flow field produced by pressure oscillations inside the tube, the contraction ratio should be controlled in a relatively low level (rc ≤ 3.1). When employing nozzles with converging sections, the highest operating frequency of the valveless PDRE would be decreased, for example, tube B can only operate up to 70 Hz with nozzle C3, while it is 100 Hz without nozzles. Although the expansion ratio almost has no impact on the operations of a PDRE, it should also be limited in a suitable range as too big an expansion ratio will lead to over-expansion of the burned gases and may decrease the propulsive performance, for example, nozzle D3 (re = 4) brings more thrust increment than nozzle D4 (re = 5). According to the impact of nozzles on the propulsive performance, converging nozzles are suggested to be used when the fill fraction is larger than one, while diverging nozzles are suggested when the fill fraction is smaller than one. Convergingdiverging nozzles are disadvantageous compared to converging nozzles in this study, which may be caused by the limited experimental conditions. However, it is believed that converging-diverging nozzles with adjustable geometries may have the potential to produce an increased performance, and further studies will be carried out in future. Acknowledgements The authors wish to thank the National Natural Science Foundation of China (91441201, 51176158, and 51376151) and the Doctoral Program Foundation of the Ministry of Education of the People’s Republic of China (20126102110029) for financial support of this work. The authors wish to thank Le Jin and Yongjian Zhang for their assistance in carrying out these experiments. Nomenclature l p d r MOF
Length Pressure transducer Diameter Area ratio Maximum operating frequency
[1] J.H.S. Lee, The Detonation Phenomenon, Cambridge University Press, 2008. [2] Y.B. Zeldovich, To the question of energy use of detonation combustion, J. Propul. Power 22 (2006) 588–592. [3] E. Wintenberger, J.E. Shepherd, Stagnation Hugoniot analysis for steady combustion waves in propulsion systems, J. Propul. Power 22 (2006) 835–844. [4] E. Wintenberger, Application of steady and unsteady detonation waves to propulsion (Ph.D. thesis), California Institute of Technology, Pasadena, California, 2004. [5] P. Wolanski, Detonative propulsion, Proc. Combust. Inst. 34 (2013) 125–158. [6] K. Kailasanath, Recent developments in the research on pulse detonation engines, AIAA J. 41 (2003) 145–159. [7] G.D. Roy, S.M. Frolov, A.A. Borisov, D.W. Netzer, Pulse detonation propulsion: challenges, current status, and future perspective, Prog. Energy Combust. Sci. 30 (2004) 545–672. [8] W. Fan, C.J. Yan, X.Q. Huang, Q. Zhang, L.X. Zheng, Experimental investigation on two-phase pulse detonation engine, Combust. Flame 133 (2003) 441–450. [9] J.A. Nicholls, H.R. Wilkinson, R.B. Morrison, Intermittent detonation as a thrust-producing mechanism, Jet Propul. 27 (1957) 534–541. [10] J.B. Hinkey, T.R.A. Bussing, L. Kaye, Shock tube experiments for the development of a hydrogen-fueled pulse detonation engine, AIAA Paper 1995-2578, 1995. [11] S. Stanley, K. Burge, D. Wilson, Experimental investigation of pulse detonation wave phenomenon as related to propulsion application, AIAA Paper 1995-2580, 1995. [12] M.J. Aarnio, J.B. Hinkey, T.R.A. Bussing, Multiple cycle detonation experiments during the development of a pulse detonation engine, AIAA Paper 1996-3263, 1996. [13] J.B. Hinkey, J.T. Williams, S.E. Henderson, T.R.A. Bussing, Rotary-valved, multi-cycle, pulse detonation engine experimental demonstration, AIAA Paper 1997-2046, 1997. [14] K. Kailasanath, Liquid-fueled detonations in tubes, J. Propul. Power 22 (2006) 1261–1268. [15] Z. Wang, Y. Zhang, J. Huang, Z. Liang, L. Zheng, J. Lu, Ignition method effect on detonation initiation characteristics in a pulse detonation engine, Appl. Therm. Eng. 93 (2016) 1–7. [16] H. Qiu, C. Xiong, W. Fan, One-dimensional unsteady design method for pulsed detonation engine nozzles, Proc. Inst. Mech. Eng. G J. Aerosp. Eng. 228 (2014) 2496–2507. [17] E.A. Barbour, R.K. Hanson, Analytic model for single-cycle detonation tube with diverging nozzles, J. Propul. Power 25 (2009) 162–172. [18] Z.C. Owens, R.K. Hanson, Single-cycle unsteady nozzle phenomena in pulse detonation engines, J. Propul. Power 23 (2007) 325–337. [19] K. Kailasanath, A review of research on pulse detonation engine nozzles, AIAA Paper 2001-3932, 2001. [20] S. Yungster, Analysis of nozzle effects on pulse detonation engine performance, AIAA Paper 2003-1316, 2003. [21] E.A. Barbour, Z.C. Owens, C.I. Morris, R.K. Hanson, The impact of convergingdiverging nozzle on PDE performance and its associated flowfield, AIAA Paper 2004-867, 2004. [22] E.A. Barbour, R.K. Hanson, A pulsed detonation tube with a converging-diverging nozzle operating at different pressure ratios, AIAA Paper 2005-1307, 2005. [23] E.A. Barbour, R.K. Hanson, Chemical nonequilibrium, heat transfer, and friction in a detonation tube with nozzles, J. Propul. Power 26 (2010) 230–239. [24] M. Cooper, J.E. Shepherd, The effect of transient nozzle flow on detonation tube impulse, AIAA Paper 2004-3914, 2004. [25] D. Allgood, E. Gutmark, J. Hoke, Performance measurements of multicycle pulse-detonation-engine exhaust nozzles, J. Propul. Power 22 (2006) 70–77. [26] Y. Yan, W. Fan, K. Wang, Y. Mu, Experimental investigation of the effect of bell-shaped nozzles on the two-phase pulse detonation rocket engine performance, Combust. Explos. Shock Waves 47 (2011) 335–342. [27] K. Wang, W. Fan, W. Lu, F. Chen, C.J. Yan, Study on a liquid–fueled and valveless pulse detonation rocket engine without the purge process, Energy 71 (2014) 605–614. [28] K. Wang, W. Fan, W. Lu, Q.B. Zhang, F. Chen, C.J. Yan, et al., Propulsive performance of a pulse detonation rocket engine without the purge process, Energy 79 (2015) 228–234.
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Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g
Research Paper
Impact of nozzles on a valveless pulse detonation rocket engine without the purge process Qibin Zhang, Wei Fan *, Ke Wang, Wei Lu, Yeqing Chi, Yongjia Wang School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China
H I G H L I G H T S
• • •
The average thrust of a valveless PDRE with different nozzles was measured. The impact of nozzles on the operation of a valveless PDRE was investigated. The impact of nozzles on the propulsion performance of a valveless PDRE was investigated.
A R T I C L E
I N F O
Article history: Received 8 November 2015 Accepted 28 February 2016 Available online 7 March 2016 Keywords: Detonation Rocket engine Valveless mode Nozzle Frequency
A B S T R A C T
To investigate the impact of exit nozzles on the operation and the propulsive performance of a valveless pulse detonation rocket engine (PDRE) without the purge process, experiments have been carried out under wide operating frequencies. Gasoline and oxygen-enriched air were used as fuel and oxidizer. Two detonation tubes and twenty-one nozzles with different shapes were employed in this study. It was observed that both the contraction ratio and the expansion ratio have an influence on the performance of the PDRE. Nozzles with converging sections decrease the highest operating frequency of the valveless PDRE, even if it cannot operate normally with nozzles whose contraction ratios are larger than four. The expansion ratio almost has no impact on the operation of the valveless PDRE, but the thrust decreases when the expansion ratios of diverging nozzles are larger than five. Most converging nozzles increase the thrust of the valveless PDRE, especially when the fill fractions were greater than one, while most diverging nozzles increase the thrust when the fill fractions were smaller than one. A maximum thrust increase of 25% has been obtained when nozzles were utilized. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction It is realized that the detonation wave has a rapid heat release rate and the pressure and temperature increase sharply after it; thus, detonation has the potential to produce greater thermal efficiency if employed in propulsion systems [1–7]. The application of detonation in propulsion has attracted extensive attentions and many efforts have been made on relative studies in the past few decades [2–15]. One of the applications based upon detonations is the pulse detonation rocket engine (PDRE). As one kind of propulsion device, the PDRE has great potentials but there are also many challenges. It would definitely be an effective way to gain a better performance when employing exit nozzles. However, how to design optimized nozzles is one big challenge because of the unsteady blowdown process caused by repetitive detonations. As the traditional design of nozzles is no longer applicable for the PDRE, many researchers begin to explore an alternative method [16–18]. To
* Corresponding author. Tel.: +86 29 88431116; fax:+86 29 88431116. E-mail address: [email protected] (W. Fan). http://dx.doi.org/10.1016/j.applthermaleng.2016.02.135 1359-4311/© 2016 Elsevier Ltd. All rights reserved.
establish an appropriate design model, the impact of nozzles on operations of the PDRE should be investigated in more detail. Many attempts including numerical simulations and experimental studies have been carried out to solve this problem [17–26]. The review by Kailasanath [19] on the investigations of the nozzles of a pulse detonation engine (PDE) and numerical simulations of the effects of diverging nozzles on the PDE performance carried out by Yungster [20] both indicate positive effects of exit nozzles on the PDE operation, but much of previous research has focused on numerical and theoretical analysis, while more experimental data are required. The relationships among geometry (e.g., nozzle length, contraction ratio, and expansion ratio), operational conditions (e.g., backpressure, operating frequency, and fill fraction), and propulsive performance (e.g., thrust and specific impulse) have been investigated [17,18,21–24]. Barbour and Hanson [17] proposed an analytical model for diverging nozzles in single-cycle mode and it indicates that the optimized area ratio is related to the ambient to plateau pressure ratio. Owens and Hanson [18] carried out another study on the unsteady nozzles based on single-cycle operations; the optimal contraction and expansion area ratios were evaluated by
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using a quasi-one-dimensional Euler model with detailed finiterate chemistry, and the experimental results showed that the optimized diverging nozzle is necessary to produce the largest specific impulse. As demonstrated by a number of studies [20,25,26], the effects of nozzles are different for single-cycle and multi-cycle operations and also for low-frequency and high-frequency operations. Experimental study of bell-shaped nozzles on the performance of a twophase and multi-cycle PDRE was carried out by Yan et al. [26], and it was observed that both the contraction and expansion ratios and the fill fraction have a strong influence on the performance, and the converging-diverging nozzles might be the optimum choice for a valved PDRE. However, the maximum operating frequency was only limited to 40 Hz in their work. A valveless PDRE utilizing liquid fuels without the purge process has been developed by Wang et al. [27], and it resulted in a wider operating frequency range with a maximum of 110 Hz. Due to the high-frequency operation achieved under this operating mode, to study the impact of nozzles on the PDRE under wider operating frequencies becomes possible. The aim of this work is to investigate the impact of nozzles on a valveless PDRE without the purge process under high operating frequencies (up to 100 Hz). Converging, diverging and convergingdiverging nozzles were all tested in this study. 2. Experimental setup 2.1. Supply system The supply system utilized in the current study is shown schematically in Fig. 1. Oxygen-enriched air and gasoline were used as oxidizer and fuel, respectively. In order to avoid premixing, the oxidizer and fuel were absolutely separated before being injected into the detonation tube. A check valve was used to prevent flashback to the oxidizer passage. Two solenoid valves were employed for turning on/off the fuel and oxidizer supplying before or after each operation, and the periodic supply was realized by the pressure oscillations inside the detonation tube. 2.2. Detonation tubes Schematic of the detonation tubes used in this study is shown in Fig. 2. The detonation tubes were both straight tubes with one end closed, and they had an inner diameter of d, and comprised an injection and ignition section (with a length of l1), a deflagrationto-detonation transition (DDT) section (with a length of l2) and a
Fig. 2. Schematic of the detonation tube.
measurement section (with a length of l3). The injection and ignition section was located near the tube close end, and one pressure transducer (p0) was employed to record the pressure history near the close end of the detonation tube with a length of l4 away from the close end. A spark plug with an ignition energy of about 50 mJ was used to ignite the mixture injected into the detonation tube, and it was l5 away from pressure transducer p0. A typical Shchelkin spiral was employed to accelerate the DDT process. Three pressure transducers, i.e., p 1 , p 2 and p 3 , were located along the measurement section to record the pressure histories and they were l6, (l6 + l7) and (l6 + l7 + l8) away from the spark plug, respectively. The measure errors caused by the sensors employed in this investigation are between ±3%. The pressure signals obtained by these transducers were processed by a signal conditioner module, and then recorded by a multi-channel data acquisition system. A sampling rate of 200 kHz was utilized. To investigate the nozzle impact on a PDRE with more data, two detonation tubes with diameters 30 and 24 mm were employed in this study. Parameters of the detonation tubes are shown in Table 1. The thrust test bench of Ref. [28] was used in this study. 2.3. Exit nozzles Twelve cone-shaped and nine bell-shaped exit nozzles were tested in this study. The cone-shaped nozzles had three types, such as converging, diverging and converging-diverging nozzles. The bellshaped nozzles were all converging-diverging ones. Configurations of the nozzles used in this work are shown in Fig. 3 and the detailed parameters of these nozzles are shown in Table 2. The bellshaped nozzles are the same as those utilized in Ref. [26], and they are used to compare the different impacts they have on the PDRE in valved and valveless modes. Nozzles BCD1~BCD9 almost have no impact on the operation of a valved PDRE in Ref. [26], but the valveless PDRE can operate only when employing nozzles BCD3 and BCD4 in a reduced operating frequency range. It is believed that the contraction sections have a great influence on the operation of the valveless PDRE without the purge process. Hence, the contraction ratios of the new designed nozzles (C1~C4, D1~D4 and CD1~CD4) are almost smaller than three. As the blowdown process of PDREs
Fig. 3. Configurations of the exit nozzles (C: converging nozzle; D: diverging nozzle; CD: converging-diverging nozzle; BCD: bell-shaped converging-diverging nozzle).
Fig. 1. Schematic of the experimental setup.
Table 1 Parameters of the detonation tubes. Parameters
d/mm
l1/mm
l2/mm
l3/mm
l4/mm
l5/mm
l6/mm
l7/mm
l8/mm
Tube A Tube B
30 24
160 110
260 230
360 320
20 20
80 40
500 330
70 70
70 70
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Table 2 Parameters of the exit nozzles (di: inlet diameter; lc: converging section length; ld: diverging section length; dt: throat diameter; rc: contraction ratio; do: outlet diameter; re: expansion ratio). di/mm
number
lc/mm
ld/mm
dt/mm
rc
do/mm
re
30
C1 C2 D1 D2 CD1 CD2 BCD1 BCD2 BCD3 BCD4 BCD5 BCD6 BCD7 BCD8 BCD9 C3 C4 D3 D4 CD3 CD4
30 30 – – 30 30 31 31 31 10 31 31 31 31 31 24 24 – – 24 24
– – 30 30 52 52 34 34 34 64 39 37 43 47 76 – – 24 24 41.5 41.5
17 21 – – 17 21 13 15 18 19.9 13 13 13 13 13 14 17 – – 14 17
3.1 2.0 – – 3.1 2.0 5.3 4.0 2.8 2.3 5.3 5.3 5.3 5.3 5.3 2.9 2.0 – – 2.9 2.0
– – 60 67 38 47 29 33.6 36 63 31 36 41 45 71 – – 48 54 30 38
– – 4.0 5.0 5.0 5.0 5.0 5.0 4.0 10.0 6.0 8.0 10.0 12.0 30.0 – – 4.0 5.1 4.6 5.0
24
is highly unsteady, the velocity of the products is relatively low in the end of the blowdown process. In order to avoid over-expansion, expansion ratios of the new designed nozzles were controlled between four and five. 3. Results and discussion In this study, gasoline and the oxygen-enriched air (the volume percentage of oxygen is 40%) were utilized as fuel and oxidizer, while the equivalence ratio was 1.5. The PDRE cannot operate normally in high frequencies (actually no more than 100 Hz when using tube B without nozzles) in this study because the fill fraction is too low to generate detonations; hence, the highest operating frequency of a PDRE is limited by the mass flow rate of the fresh mixture. The same supply system is utilized for tubes A and B, which means that the maximum mass flow rate for these two tubes is consistent. As the volume of tube B is smaller than tube A, the fill fraction of tube B is larger than tube A when operating in the same frequency. It means that tube B has the ability to obtain a higher maximum operating frequency than tube A. 3.1. Impact on the operating frequency When nozzles were utilized, experiments of the impact on the operating frequency range of a valveless PDRE without the purge process were carried out. All the tests were carried out more than 1 s. Some of the pressure profiles obtained with nozzles on are shown in Fig. 4, and the maximum operating frequencies are summarized in Fig. 5. As shown in Figs. 4 and 5, most exit nozzles employed in this work have an influence on the operations, and the valveless PDRE even could not operate normally when nozzles BCD1, BCD2, and BCD5~9 were utilized. These nozzles are all convergingdiverging ones, and their contraction ratios are all greater than four. As these nozzles had no influence on the operation of a traditional PDRE in Ref. [26], it means that the valveless PDRE has a more rigorous limit on the contraction ratio of exit nozzles. While converging and converging-diverging nozzles were employed in a PDRE, there would be reflected shock waves when detonation waves passing by the nozzle throat and the reflected waves would disturb the periodic supply in the close end created by pressure oscillations inside the detonation tube. Since the operation of a valveless
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PDRE without the purge process greatly depends on the flow field produced by the pressure oscillations and the vaporization of the liquid fuel [27], the reflected shock waves induced by exit nozzles with converging sections when the detonation waves pass through will damage the sustainable operation, and even lead to failures of detonation formation. On the other hand, it causes difficulty to the exhaust process when the nozzle throat is too small (rc ≥ 4). If the products cannot be exhausted in time, the fresh fuel–oxidizer mixture cannot be injected into the detonation tube effectively; thus, the fill fraction of the next cycle will be reduced to a quite low level. As a result, there is not enough fresh detonative mixture injected in and the detonation wave cannot be produced due to the failure of the DDT process. Subsequently, pressure oscillations created by detonations disappear and the fresh fuel–oxidizer mixture will flow into the detonation tube continuously and deflagrations occur. The contraction ratios of nozzles that disturbed the normal operation were all greater than four, which means that the suitable contraction ratios should be controlled below this for the valveless PDRE in this study. Without exit nozzles, the detonation tubes A and B can, respectively, operate stably up to 70 and 100 Hz. The operating frequency might be varied when utilizing exit nozzles, especially for the nozzles with small throats. As shown in Fig. 5a, the maximum operating frequencies when nozzles C2 and CD2 (rc = 2.0) are utilized are 30 and 20 Hz, while that for nozzles C1 and CD1 (rc = 3.1) is 10 Hz; the maximum operating frequency when nozzles C4 and CD4 (rc = 2.0) are utilized is 70 Hz, while that for nozzles C3 and CD3 (rc = 2.9) is 60 Hz. It means that when nozzles with small throats are utilized, the operating frequency range will become narrower, and the smaller throat corresponds to a narrower operating frequency range. As shown in Fig. 5a, the maximum operating frequency of converging-diverging nozzles is the same as the corresponding converging ones in most cases, e.g., those for nozzles CD4 and C4 is 70 Hz, while 10 Hz for nozzles CD1 and C1, and 60 Hz for nozzles CD3 and C3. The converging-diverging nozzles in this study have the same contraction ratio with the corresponding converging nozzles, such as CD1 and C1, CD2 and C2, CD3 and C3, and CD4 and C4. It means that the diverging sections of nozzles almost have no impact on the operation of the valveless PDRE, but there also exists another case, e.g., the maximum operating frequencies for nozzles CD2 and C2 are 20 and 30 Hz, respectively. The maximum operating frequencies were 30 and 40 Hz when bell-shaped nozzles BCD3 (rc = 2.8) and BCD4 (rc = 2.3) were used. Compared to nozzles C2 and CD2, nozzles BCD3 and BCD4 both have smaller throats but the same or greater operating frequencies were available. It may be because the inner surface of the bell-shaped nozzles is well designed in hydrodynamics. As shown in Fig. 5b, the maximum operating frequencies are both 100 Hz when nozzles D4 (re = 5.1) and D3 (re = 4.0) are utilized, while it is 60 Hz for nozzle D1 (re = 4.0) and D2 (re = 5.0). It indicates that the diverging nozzles have the widest operating frequency range in this study and the expansion ratio almost has no impact on the operations. It is observed that exit nozzles with converging sections really have an influence on the operation of a valveless PDRE without the purge process. The operating frequency range is getting narrower and that is mainly induced by the converging section, which not only slows down the exhaust process but also produces reflected shock waves. It is believed that the diverging section almost has no influence on the operating frequency. 3.2. Impact on the pressure inside the detonation tube The pressure history of an individual detonation wave and the reflected shock wave when nozzle C1 was utilized at 10 Hz is shown in Fig. 6. The pressure spikes obtained by transducers p1, p2 and p3 are 4.2, 3.4, and 4.8 MPa, respectively, and the time cost for the
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Fig. 4. Pressure profiles obtained with nozzles.
detonation wave to pass through them are Δt12 and Δt23, which are 0.034 and 0.036 ms, respectively. The distances between the transducers are Δd12 and Δd23, which are both 70 mm; hence, the average velocities are v12 = 2058.82 m/s and v23 = 1944.44 m/s. The pressure and velocity calculated by CEA (Chemical Equilibrium with Applications) codes are 2.87 MPa and 2100.9 m/s in the present experiments. Because the actual pressure and temperature of the fuel– oxidizer mixture were hard to be determined, the initial pressure and temperature employed in the calculation were 1 atm and
298.5 K, same as the ambient pressure and temperature. As there is no purge process under the valveless mode, the blowdown time is reduced compared with the valved mode with the purge process in the same operating conditions, which leads to a higher initial pressure in the next cycle. Therefore, the spike pressures obtained in this case were greater than the C-J values. When employing nozzle C1 and other nozzles, the pressures and velocities all exceeded 80% of the C-J values, which indicated fully developed detonations were obtained considering liquid fuel was utilized.
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As illustrated in Fig. 6, there are smaller pressure spikes created by the reflected shock waves after main spikes. The pressure of the reflected shock wave is lower than 2.0 MPa, and the velocities of the reflected shock wave between transducers p3, p2 and p1 are v32 and v21, which are 1590.91 and 1186.44 m/s, respectively. The pressure and velocity of the reflected shock wave are both lower than those of the detonation wave, so the reflected shock wave can be distinguished from the detonation wave easily. The reflected shock wave has been observed on a solenoid valved PDRE with nozzles that have throats [26], but this has a greater influence on the operations of a valveless PDRE. Besides inducing the reflected shock waves when converging and converging-diverging nozzles were utilized, the pressure inside the detonation tube was increased. Shown in Fig. 7 are the pressure histories obtained with and without nozzle C1 at 10 Hz. In order to smoothen the curves, the raw pressure data were reconstructed by the arithmetic method, which was written as
xk =
1 i +9 ∑ xi (k = 1, 11, 21…) 10 i=k
(1)
As shown in Fig. 7, the pressure increased when a nozzle with a converging section was employed. That is because the throat makes it difficult to exhaust the burned gases in time, and the pressure inside the detonation tube decreases slowly. On the other hand, as the products cannot be exhausted in time the initial pressure of the detonative mixture in the next cycle will be increased slightly, and this would lead to a greater pressure after detonations. Eventually, it brought an enhancement of the propulsive performance when nozzle C1 was employed in tube A. The impact of nozzles on the thrust of a PDRE will be discussed in the following section. 3.3. Impact on the thrust
Fig. 5. The maximum operating frequencies (MOFs) obtained with different nozzles.
Fig. 6. Pressure profiles obtained with nozzle C1 employed.
3.3.1. Thrust without nozzles The thrust produced without nozzles was measured and shown in Fig. 8. The thrust data were normalized by the raw thrust at 10 Hz. As illustrated in Fig. 8, the variation of the dimensionless thrust with the operating frequency can be divided into three stages, i.e., linear increase, nonlinear increase and quick decrease, which is consistent with the results obtained in Ref. [28] and is due to the fill conditions. The fill fraction varied with the operating frequency in the current study due to the supply capacity of the system, and the fact is that the fill fraction decreases with the increase of the operating frequency. The relationship of the fill fraction and the operating frequency in a valveless PDRE without the purge process has been described in Ref. [28]. In this study, the fill fraction under different operating frequencies is shown in Table 3. 3.3.2. Thrust with nozzles The thrust with nozzles in a wide operating frequency range was obtained, and it was also normalized by the raw thrust without nozzles at 10 Hz. Fig. 9 shows the dimensionless thrust with nozzles. As the operating frequency range of tube B was wider than that of tube A, more thrust data were obtained when utilizing tube B. Therefore, the tendency described was mainly based on the data of tube B, while the data of tube A were used as a supplement and a validation. It was observed that when nozzles were utilized, the tendency of the generated thrust with the operating frequency was different from the case without nozzles. When converging nozzles were installed on tube B, the thrust increased with the operating frequency (i.e., 10~60 Hz for nozzle C3 and 10~70 Hz for nozzle C4). And the thrust obtained with nozzle C3 was greater than the case with nozzle C4 below 40 Hz, while the situation inversed between 50 and 60 Hz. Nozzle C3 has a larger
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Fig. 7. Pressure histories obtained with and without nozzle C1.
contraction ratio (i.e., a smaller throat) than nozzle C4 and a smaller throat extends the blowdown time, which maintains the pressure inside the detonation tube at a relatively high level for a longer time and results in a greater propulsive performance. When the operating frequency was increased to 50 and 60 Hz, the time for each cycle decreased and a longer blowdown time corresponding to a greater contraction ratio would lead to the reduction of the actual fill fraction to partial fill conditions. In this case, the influence of nozzles C3 and C4 on the thrust differs from that obtained below 40 Hz. While diverging nozzles were utilized the thrust increased with the operating frequency first (i.e., 10~90 Hz for nozzle D3 and 10~80 Hz for nozzle D4) and then decreased with the operating frequency (i.e., 90~100 Hz for nozzle D3 and 80~100 Hz for nozzle D4). There is an inflexion of the thrust variation, and the inflexion when utilizing nozzle D3 is greater than that of nozzle D4. It may be because the expansion ratio of nozzle D3 is more appropriate to obtain a better propulsive performance than that of nozzle D4 in the current cases. When utilizing converging-diverging nozzles, the thrust increases with the operating frequency between 10 and 70 Hz.
Nozzle CD3 performs better than nozzle CD4 during 10~60 Hz, and the reason is consistent with the case utilizing converging nozzles during 10~40 Hz, while a better combination of the contraction and expansion ratios makes it possible for nozzle CD3 to maintain its advantage during 50~60 Hz. However, neither nozzle CD3 nor CD4 has a better performance than converging nozzles in the same operating frequencies. Fig. 10 provides a summary of the thrust increment obtained by tube B with nozzles. It indicates that some of the nozzles can produce positive thrust increment at suitable operating frequencies. As shown in Fig. 10, the maximum thrust increment is about 25% with nozzle C3 at 10 Hz. It may be because the detonation tube can be fully filled in each cycle in a low operating frequency, and in this case the converging nozzle can maintain the pressure inside the detonation tube in a relatively high level for a longer time. Some nozzles could not bring positive thrust increment in this work, such as nozzle D3 at 30 Hz, nozzle D4 at 40 Hz, nozzle CD4 at 20 Hz and so on. It might be because the supply and initial conditions in the present study were not the appropriate ones for these nozzles to produce their
Table 3 The fill fraction under different operating frequencies. Operating frequency/Hz
10
20
30
40
50
60
70
80
90
100
Fill fraction of tube A Fill fraction of tube B
2.11 5.45
1.41 4.35
1.05 2.17
0.84 1.45
0.70 1.09
0.60 0.87
0.51 0.72
– 0.62
– 0.54
– 0.48
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Fig. 8. Dimensionless thrust obtained without nozzles.
best performances. The impacts of nozzles on the thrust increment were different at different operating frequencies. In low operating frequencies (10~40 Hz), the converging nozzles performed best, e.g., the thrust increment utilizing nozzle C3 was positive with an average increase of 12.25%, while that of nozzle CD3 was 1.5%, and −5.625% for nozzle D3. That means nozzles that have converging section can improve the thrust if the detonation tube is fully filled. In medium operating frequencies (50~70 Hz), the converging nozzles also presented the best performance but the thrust increment decreased compared to that in low operating frequencies. It even brought a negative increment in some cases, e.g., the average thrust increment produced by nozzle C4 at this stage was only 2%, which was lower than an average increment of 8.25% in low operating frequency stage. Reflected shock waves and the partial fill effect decreased the thrust when converging and converging-diverging nozzles were utilized in this operating regime. In high operating frequencies (80~100 Hz), most nozzles with small throats lead to operation failures, but the PDRE could still operate utilizing the diverging nozzles and a positive average thrust increment was obtained. According to the results, it is believed that nozzles with different shapes are appropriate in different operating frequencies to
Fig. 9. Dimensionless thrust obtained with nozzles.
increase the propulsive performance of a PDRE, e.g., converging and converging-diverging nozzles should be employed in low and medium operating frequencies (<70 Hz for tube B and <30 Hz for tube A), while diverging nozzles are suggested in high operating frequencies (>70 Hz for tube B and >30 Hz for tube A). 4. Conclusions Experiments were carried out to investigate the impact of nozzles on a PDRE operating in the valveless mode without the purge process. Cone-shaped and bell-shaped exit nozzles were employed in this test, and different nozzle configurations, e.g., converging, diverging and converging-diverging nozzles, were all considered. Experimental results indicate that the converging section has a great impact on the operation of the valveless PDRE. The reflected shock waves induced by the throat of a nozzle would disturb the sustainable operation of the valveless PDRE, and it may lead to failures of the operation when the contraction ratio is too large (rc ≥ 4). The converging section also slows down the exhaust process
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Subscripts c Converging d Diverging cd Converging-diverging e Expansion i Inlet t Throat o Outlet References
Fig. 10. The thrust increment of tube B with nozzles.
inside the detonation tube, and then the pressure decreases slowly. As the valveless PDRE greatly depends on the flow field produced by pressure oscillations inside the tube, the contraction ratio should be controlled in a relatively low level (rc ≤ 3.1). When employing nozzles with converging sections, the highest operating frequency of the valveless PDRE would be decreased, for example, tube B can only operate up to 70 Hz with nozzle C3, while it is 100 Hz without nozzles. Although the expansion ratio almost has no impact on the operations of a PDRE, it should also be limited in a suitable range as too big an expansion ratio will lead to over-expansion of the burned gases and may decrease the propulsive performance, for example, nozzle D3 (re = 4) brings more thrust increment than nozzle D4 (re = 5). According to the impact of nozzles on the propulsive performance, converging nozzles are suggested to be used when the fill fraction is larger than one, while diverging nozzles are suggested when the fill fraction is smaller than one. Convergingdiverging nozzles are disadvantageous compared to converging nozzles in this study, which may be caused by the limited experimental conditions. However, it is believed that converging-diverging nozzles with adjustable geometries may have the potential to produce an increased performance, and further studies will be carried out in future. Acknowledgements The authors wish to thank the National Natural Science Foundation of China (91441201, 51176158, and 51376151) and the Doctoral Program Foundation of the Ministry of Education of the People’s Republic of China (20126102110029) for financial support of this work. The authors wish to thank Le Jin and Yongjian Zhang for their assistance in carrying out these experiments. Nomenclature l p d r MOF
Length Pressure transducer Diameter Area ratio Maximum operating frequency
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