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Thrust measurement method verification and analytical studies on a liquid-fueled pulse detonation engine

Lu Jie, Zheng Longxi, Wang Zhiwu, Peng Changxin, Chen Xinggu

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S1000-9361(14)00071-5 http://dx.doi.org/10.1016/j.cja.2014.04.001 CJA 274

Received Date: 5 June 2013

Revised Date: 27 November 2013

Accepted Date: 14 January 2014

Please cite this article as: L. Jie, Z. Longxi, W. Zhiwu, P. Changxin, C. Xinggu, Thrust measurement method verification and analytical studies on a liquid-fueled pulse detonation engine, (2014), doi: http://dx.doi.org/10.1016/ j.cja.2014.04.001

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Chinese Journal of Aeronautics 24 (2014) xx-xx

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Thrust measurement method verification and analytical studies on a liquid-fueled pulse detonation engine

LU Jie, ZHENG Longxi , WANG Zhiwu, PENG Changxin, CHEN Xinggu

School of Power and Energy, Northwestern Polytechnical University, Xi'an 710072, China Received 5 June 2013; revised 27 November 2013; accepted 14 January 2014

Abstract

In order to test the feasibility of a new thrust stand system based on impulse thrust measurement method, a liquid-fueled pulse detonation engine (PDE) is designed and built. Thrust performance of the engine is obtained by direct thrust measurement with a force transducer and indirect thrust measurement with an eddy current displacement sensor (ECDS). These two sets of thrust data are compared with each other to verify the accuracy of the thrust performance. Then thrust data measured by the new thrust stand system are compared with the verified thrust data to test its feasibility. The results indicate that thrust data from the force transducer and ECDS system are consistent with each other within the range of measurement error; Though the thrust data from the impulse thrust measurement system is a litter lower than that from the force transducer due to the axial momentum losses of the detonation jet, the impulse thrust measurement method is valid when applied to measure the averaged thrust of PDE. Analytical models of PDE are also discussed in this paper. The analytical thrust performance is higher than the experimental data due to ignoring the losses during the deflagration to detonation transition process. Effect of equivalence ratio on the engine thrust performance is investigated by utilizing the modified analytical model. Thrust reaches maximum at the equivalence ratio of about 1.1.

Keywords: Pulse detonation engine; Liquid fuel; Thrust measurements; Impulse method; Analytical model; Equivalence ratio

1. Introduction1

Pulse detonation engines (PDEs) are exciting propulsion devices which obtain thrust by generating detonations intermittently. 1 Thrust performance is the most important parameter of PDEs. Measuring the time-resolved thrust of PDEs has been proved complicated due to their periodic operating characteristics. However, the averaged thrust measurements of PDEs had been performed by using different methods. 2-8

Typically, there are three kinds of methods to carry out the averaged thrust measurements of PDEs. The first one is direct thrust measurement method which is performed by attaching the PDE on a translating frame mounted on bearings and taking the measurement with a force transducer. This method requires special attention, because the firing frequency can excite resonances in the thrust stand structures and a typical improvement is to place a spring damper system between the force transducer and the translating frame. The second one is indirect measurement method: the thrust measurement system includes an integrated spring damper system and a linear variable differential transducer (LVDT). When the engine is fired, the spring will be compressed by the thrust generated by the engine. The thrust is proportional to the displacement of the engine which can be recorded by the LVDT. The third one is ballistic pendulum method. The PDE is horizontally hanged up by wires. A video camera is used to record the ballis-

* Corresponding author. Tel.: +86-29-88492414. E-mail address: zhenglx@nwpu.edu.cn

tic pendulum deflection during operation. Although the ballistic pendulum method offers better accuracy, it is typically limited to a single impulse measurement. 8

Impulse method is an indirect thrust measurement method which uses a flat plate of large area to receive the total impulse of the jet, if there are no axial momentum losses, the thrust exerted to the plate is equal to the thrust produced by the thruster. 9 Paxson et al. 10 utilized a thrust plate to investigate an unsteady ejector performance driven by a gasoline-fueled pulsejet. Mizukaki 11 also developed a baffle plate for force measurements of high-temperature, supersonic impulse jet. But studies about utilizing the impulse method to obtain the averaged thrust of PDE have rarely been reported, only Wilson et al. 12 carried out a thrust augmentation measurement of a PDE driven ejector by

utilizing the thrust plate. He found that when the thrust plate was directly placed in front of a load cell, the load cell signal was strongly oscillatory, and extracting the DC component from it proved unreliable. Finally, He used a video camera to measure the pendulum deflection of the thrust plate which was suspended by four wires and positioned downstream of the PDE exit.

This paper is aimed at developing and calibrating an averaged thrust measurement system that can be used to measure the thrust of a pulse detonation turbine engine. 13-14 The commonly used methods such as measurements with a force transducer or LVDT are not practical for such a complex experimental installation, so the impulse method is chosen for its convenience and relative simplicity. To achieve the goal of this research, a new thrust stand system based on impulse method is built up. To verify the feasibility of the thrust stand system, a liquid-fueled PDE is manufactured and the thrust data of the PDE at different operating frequencies are obtained with two different methods: direct thrust measurements with a force transducer and indirect thrust measurements with an eddy current displacement sensor (ECDS). After the accuracy of the thrust data is confirmed, the engine thrust data at different operation frequencies are measured by the force transducer and the impulse method synchronously to test the reliability of the new thrust stand system. Analytical thrust performance is also discussed in this paper. The analytical model is based on an updated numerical analysis carried out by Endo-Fujiwara. 15-17 A modification is conducted on this analytical model to consider the effect of droplets resistance and heat transfer on the tube on the detonation wave velocity. What's more, the thrust data obtained from the modified analytical model are compared with experimental results.

2. Experimental setup

2.1. Liquid-fueled PDE system

A schematic of liquid-fueled PI chamber, ignition chamber, and det length of 0.175 m, 0.160 m, and 1.270

. is shown in Fig. 1. The PDE consists of three different sections: mixing on chamber. All three sections have the same diameter of 0.06 m, with the , respectively. The shchelkin type spiral is welded in the detonation chamber to accelerate the deflagration-to-detonation transition process. A twin-fluid air-assist atomizer is installed in the center of the thrust wall. Air is introduced into the engine in radial direction through flexible pipes at the engine head. A spark plug is mounted in the middle of the ignition chamber. Two high-frequency piezoelectric static pressure sensors are installed near the exit of the detonation chamber to verify the successful initiation of detonation wave. Another high-frequency piezoelectric static pressure sensor is placed at the tube head to obtain pressure history at the thrust wall. The PDE system is mounted on the moving frame which is supported by four ball bearings. The engine can slide on stainless steel rails only in axial direction. The force transducer or spring is connected to a rigid thrust block and the moving system.

Fig. 1 Schematic diagram of the liquid-fueled PDE system. 2.2. Thrust measurement systems

Three kinds of thrust measurement systems are integrated together to carry out thrust measurements of a liquid-fueled PDE: direct thrust measurement with a force transducer, indirect thrust measurement with ECDS and impulse method with a flat plate. The force transducer is mounted on the thrust block and the moving frame is connected to the force transducer through a spring which has a stiffness of 240 N/mm. A Kistler force sensor with the sensitive degree of 3.682 pC/N and the maximal measurement range of ±10000 N is chosen for the direct thrust measurement method. A CWY-D0-812504 type ECDS is mounted on the fixed frame to measure the relative displacement of the engine, which is proportional to the thrust. These two kinds of thrust measurement methods are compared with each other to confirm the accuracy of the thrust generated by the engine.

For the impulse method, a new thrust measurement system is designed and built. A schematic of the system is shown in Fig. 2. The flat plate has a diameter of 0.4 m which is connected to a force transducer through the strut. The strut and its connection components are supported by four ball bearings which can slide along the rails. A Kistler force sensor with the sensitive degree of 3.678 pC/N and the maximal measurement range of ±10000 N is chosen for impulse method. The rest parts of the thrust stand system are designed as a rigid component so that the whole system can undertake the impulse of the supersonic jet produced by the engine. What's more, the height of the lower part of the system is adjustable to meet the needs of thrust measurements. During operation, the thrust measurement system is placed downstream of the engine. The centerline of the flat plate is consistent with the centerline of the engine. The distance between the engine exit and the flat plate is 0.350 m. This distance is chosen to ensure that the plate is not so close as to alter the back pressure of the jet or too far to receive the total impulse of the jet.

All the data are monitored and collected through DEWE3020 high-speed data acquisition system for a total of 16 channels and the Sampling rates is 200 kHz.

Fig. 2 Schematic diagram of impulse thrust measurement system.

2.3. Rig operation

Before operation, all of the thrust measurement systems are calibrated by a pulley-cable system. The PDE is tested from 10 Hz to 30 Hz. When the PDE is in normal operation, baseline thrust of the engine is obtained by the direct thrust measurement method. After that, the spring is placed between the thrust block and the moving frame. Displacement of the engine is recorded by the ECDS system. Then the thrust is obtained by transforming the measured displacement into thrust and compared with that obtained by the force transducer. Confirmed with the PDE thrust performance obtained by the force transducer and ECDS system, the ECDS system is removed and the impulse thrust measurement system is placed downstream of the engine. Thrust performance of the PDE is obtained by the force transducer and the impulse thrust measurement system at the same time. In order to improve the accuracy of the measured averaged thrust data, all the averaged thrust data are obtained by time averaging the total thrust signal over the steady state period. What's more, all the tests at different ignition frequencies are repeated three times to reduce errors. The experimental conditions are shown in Table 1.

Table1 Mass flow rate of air and fuel at different frequency

Frequency(Hz) Mass flow rate of air (kg/h) Mass flow rate of gasoil (ml/s)

10 260 6.4

15 370 8.3

20 492 11.1

25 535 13.1

30 621 16.1

3. Experimental results

3.1. Verification of detonation wave formation

For detonation in gaseous fuels, the forming of the detonation wave can be determi shock wave, the peak pressure and the rise time of the peak pressure. But in two-ph compared to the Chapman-Jouguet (C-J) detonation velocity was observed. 18 Wall before the C-J plane, and energy loss due to rearward propagating waves hav

velocity of leading nation, a velocity deficit incomplete combustion en proposed as reasons for the

velocity deficits. 19 Therefore, peak pressure is used as the main criterion for verification of the detonation wave in two-phase detonation. However, the experimentally measured detonation wave velocity can be another reference criterion to judge whether fully developed detonation waves are obtained or not.

Fig. 3 shows the pressure profiles at PCB2 when the engine is operated at frequencies of 10 Hz, 20 Hz, and 30 Hz. Under the current experimental conditions, the ambient temperature and pressure are 285 K and 0.098 MPa, respectively. Gasoil and air are injected into the detonation chamber at nearly equivalence ratio of one. The C-J pressure and velocity of gasoline and air mixture calculated by the NASA CEA400 code 20 are 1.91 MPa and 1796.4 m/s, respectively. It can be seen from Fig. 3 that the pressure spikes are much higher than the theoretical value. This can be explained as follows: the C-J pressure calculated by the NASA CEA400 code is based on one-dimension structure of the detonation wave. Whereas the detonation wave has three-dimensional unsteady structure and there exist triple points in the detonation wave front. When the detonation wave propagates in the tube, the collision between the shock waves may cause the peak pressure captured by the pressure sensors greater than the C-J pressure. In addition, the Von-Neumann spike in the detonation wave front is about twice of the C-J pressure, which is easier to be captured by the pressure sensors due to the prolonged length of reaction zone in two-phase detonation.

The velocity of the detonation wave can be determined by measuring the elapsed time that a detonation wave travels across two successive pressure transducer ports with a fixed distance. In the present research, The averaged wave velocities between PCB1 and PCB2 are 1289.5 m/s, 1249.6 m/s, 1271.3 m/s, 1280.1 m/s, 1268.4 m/s with the frequency from 10 Hz to 30 Hz, which are 71.8%, 69.6%, 70.8%, 71.3%, and 70.6% of C-J detonation wave speed respectively. Therefore we can consider that the detonation waves are successfully obtained in all the tests.

0 0.5 1.0 1.5 2.0

rime (s)

(a) Pressure profile at operating frequency of 10 I Iz

Fig. 3 Pressure profile at PCB2 under different operation frequencies.

3.2. Baseline thrust

rements

The baseline thrust is obtained by the force transducer. Fig. 4 shows the thrust profiles recorded by the force transducer when the PDE is operated at the frequencies of 10 Hz and 15 Hz. It suggests that the PDE remains in a steady state and the transient thrust exhibits significant cyclical characteristics. What's more, negative thrust and cyclical oscillations are observed from the transient thrust profiles. These are determined by the operating characteristics of the force transducer and dynamic characteristics of the thrust stand. The force transducer and the thrust stand can be simplified as a single freedom mass-spring-damped vibration system. When the engine is fired, the vibration system is undertaken the strong pulse thrust produced by the engine. If the vibration system is under-damped, the output signal of the system would exhibits oscillations and negative values. However, the integration results of the input and output signals over one cycle time are the same. 21 Therefore, the direct thrust measurement method with force transducer is an averaged thrust measurement method. Fig. 5 shows an enlarged thrust profile when the engine operated at frequency of 10 Hz, together with the synchronized pressure profile at the engine head obtained by PCB0 (which is represented by p0 in Fig.5). Theoretically speaking, the peak pressure at the engine head represents the peak thrust generated by the engine. But the peak value of thrust profile is a litter lagged behind the peak value of the pressure at the engine head. It indicates that the thrust profile obtained by the force transducer is different from the real transient thrust produced by the engine.

Hence, the averaged thrust is the key parameter that needs to be taken care of. When the thrust profile is integrated over different cycle time scales, the averaged thrust signal as a function of time can be obtained. Typical averaged thrust signals over three cycle time to five cycle time are presented in Fig. 6. As the integral time interval become longer, the averaged thrust is approaching a quasi-steady level. So all the averaged thrust data presented below are obtained by integrating the transient thrust profile over more than 50 cycle time (> 1.5 s) when the PDE is operated at steady state.

Fig. 4 Thrust profiles when the engine is operated at different frequencies.

Fig. 5 Comparison between the thrust profile and the pressure profile at the engine head.

Averaged thrust history over different time scales when PDE is operated at 25 Hz.

between the force transducer and ECDS results

fy the fidelity of the PDE thrust data at different operating frequencies, the engine thrust performance obtained by the force transducer and the ECDS system are compared at operation frequencies from 10 Hz to 30 Hz. Fig. 7 shows the averaged thrust as a function of operation frequency. Obviously, the averaged thrust of the engine increases with the increasing of frequency and there is a quasi-linear relationship between the averaged thrust and operation frequency. What' more, the thrust obtained by the force transducer are higher than that from the ECDS system. The maximum difference is about 7 N. For the thrust measurements with the force transducer, the engine is fixed to the thrust block, and the static friction between the ball bearings and the stainless steel rails is the main source of measurement error, but for the ECDS system, the drag resistance caused by the fuel and air pipes become obvious when the engine is moving back and forth due to the deformation of the spring during operation. However, the thrust data from two thrust measurement methods are consistent with each other within the range of measurement error. It demonstrates that the averaged thrust data are reliable.

Frequency

Fig. 7 Averaged thrust as a function of operation frequenc;

3.4. Comparison between the force transducer and impulse measurement system results

Confirmed with the correctness of the thrust data, the PDE system is used to test the feasibility of utilizing the impulse method to conduct the averaged thrust measurement of the PDE. The impulse thrust measurement system is placed downstream of the engine to obtain the averaged thrust performance of the engine at the operation frequencies from 10 Hz to 30 Hz. The averaged thrust data as a function of frequency is presented in Fig. 8. Two sets of thrust data are given: thrust data from the force transducer and thrust data from the impulse thrust measurement system. As expected, the thrust data obtained by the two methods are different at each operating frequencies. The maximum difference between the two sets of data is about 9 N. But the trend of that the thrust increased with the increasing of frequency is good fitting together. The thrust from the impulse thrust measurement system is lower than that from the force transducer. The reason is that the axial momentum received by the flat plate is less than the axial momentum exhaust from the engine exit. Two factors lead to this phenomenon, one is the momentum loss of the detonation jet in the axial direction before the jet reaches the flat plate: when the detonation jet exhausts from the detonation chamber, it degenerates into a spherical shock wave and a decoupled combustion wave, as the spherical shock wave propagates toward the flat plate, small part of the products alter to the radial direction, therefore the axial momentum received by the flat plate would be reduced; another is the interaction between the detonation jet and flat plate: when the shock wave reflects from the plate, it will also cause axial momentum loss of the jet. Even though the impulse thrust measurement system underestimates the averaged thrust, it is valid when applied to measure the averaged thrust of PDE, but care must be taken to know limits of its accuracy and to avoid possible sources of measurement error.

Another interesting phenomenon is that the variation amplitude of the averaged thrust data over one cycle time is different. For the impulse thrust measurement system, it is more likely to approach the quasi-state and the variation amplitude is lower than the data from the force transducer which can be noted in Fig. 9. This may due to the attenuation of the detonation wave when it exhausts from the detonation chamber.

100 i-

- Force transducer result

- Impulse method result

Fig. 8

Frequency (Hz)

Comparison between averaged thrust of the force transducer results and impulse method results.

Time (s)

Fig. 9 Comparison of averaged thrust over one cycle time between the force transducer re;

4. Analytical model

mpulse method results.

The analytical model is based on an updated numerical analysis conducted by Endo-Fujiwara. In this model, the PDE is simplified as a straight tube with a fixed cross section, the decay portion of the pressure history at the thrust wall is analytically formulated without any empirical parameters. Only parts of the model are presented here, detail of the model can be found on the published literature.

4.1. Simplified analytical model

The impulse per unit cross section per one cycle of a

a simpl:

plified PI

rs. Only pa

PDE can be calculated by Eq. (1).

<4+Fti(sa1,sa2))( P3- ax

where p3 is the plateau pressure; p1 is the initial pressure of the reactants; tCJ is the time for the detonation wave propagates from the thrust wall to the exit. Parameters in Eq. (1) are calculated by the following equations.

iklMj +k2 k2 +1V2-« kMaJ +1 lkk~

kMaj + k f kMaJ+k k2 +1 ^-1

kMh2 +1 2k,

P3 = 4A1P1

y fill ^ ^CJ

where k1, k2 is the specific-heat ratio of reactants and products respectively; MaCJ is the detonation Mach number;

DCJ is the velocity of the detonation wave. These parameters are calculated by the NASA CEA400 code; Vml is the filling velocity which can be determined by the air mass flow rate of the engine; Ltube is the length of the engine. The averaged thrust of the PDE at different operation frequency is obtained by Eq. (7).

Favg 1 cycle ^trustf (7)

where Atrust is the thrust wall area; f is the operating frequency.

4.2. Modified analytical model

For a liquid-fueled PDE, the detonation velocity can be affected by many factors such as the diameter of the droplets and their distribution. These factors will result in losses of performance. In order to include the losses related to the two-phase factors, a modification is conducted to the detonation velocity according to the work in the literature of Refs. 22, 23. The relationship between the gas-phase detonation velocity DCJ and spray detonation velocity DCJ,S is given by the following equation:

DJ={1+3[Cd + 2( k22 -1) CH].[ R X*]}-05 (8) Dcj Rl(1+FAR)

where CD is drag coefficient; CH is heat transfer coefficient; FAR is the fuel air ratio; Rh is the hydraulic diameter; XR is the reaction zone width which can be decided based on experimental results or by the semi-empirical Eq. (9).

X R =-

f d_ ?

do DCJ f ^0.5

where d is droplet diameter and the subscript 0 means the initial droplet diameter; pis density, subscript l means the liquid fuel, g means gas fuel; C2 is the sound speed of products.

For the two-phase detonation, the reaction zone width is longer than that of the gas-phase detonation. The width will be prolonged by the evaporation and mixing process of the fuel in the reaction zone, which can be concluded from Eq. (9).

4.3. Comparison between analytical model and experimental results

Table 2 gives the calculated detonation velocity of gasoil-air reactants in gas-phase and the modified result from Eq. (8) under the experimental condition; experimental result is also included here for comparison. The theoretical detonation velocity of gasoil and air mixture in two-phase model are in agreement with the experimental results, but much lower than the gas-phase detonation velocity.

Table 2 Detonation velocity of gas-oil mixture

DCJ_DCJS_Experimental result

1793_1288__1200-1300

Fig. 10 shows the thrust data as a function of operating

frequency calculated by the two analytical models. The experimental thrust data measured by the force transducer are also presented here for comparison. Obviously, the simplified analytical model overestimates the thrust performance of a liquid-fueled PDE and the modified analytical model gives better results, which is still higher than the experimental thrust data. Two factors can be used as explanations. On the one hand, the analytical model assumes direct initiation of detonation wave, but direct initiation of detonation wave requires huge energy input and it is not practical in application. Hence a deflagration to detonation transition (DDT) process is used to initiate the detonation wave in experiments. The losses during the DDT process

are not considered in the analytical model. Cooper et al. 24 had found that the DDT process would have a negative effect on engine thrust by as much as 25%. In the present research, the data obtained by the modified analytical model is about 24.7% higher than the experimental thrust data, which is quiet close to the results of

Cooper; on the other hand, these models are based on a single cycle operation. When the engine is operated at multi-cycle model, the averaged thrust from cycle to cycle is different, which can be seen from Fig. 6. Therefore, it is still hard to accurately predict the real performance of PDE. Further efforts are still needed to put more losses into consideration.

Fig. 10

15 20 25 Frequency (Hz)

Comparison between two analytical models and experimen

tal resu

4.4. The effect of equivalence ratio on the thrust performance of a liquid-fuele I

The thrust of a liquid-fueled PDE could be optimized by changing both equivalence ratio and fill fraction. Here only the equivalence ratio is changed to see if there is any benefit by using this parameter in thrust control. Fig. 11 gives the thrust data from the modified analytical model as a function of equivalence ratio when the engine is operated at 10 Hz. The result shows that the thrust increases when the equivalence ratio changes from 0.7 to 1.1, but reaches its maximum at the equivalence ratio of about 1.1. When the equivalence ratio is further increased, the thrust is reduced. When the equivalence ratio increases from the lean fuel condition to the rich fuel condition, the strength of the detonation wave reaches its maximum value at the equivalence ratio of about 1.1. So the plateau pressure at the engine head also has a peak value at the equivalence ratio of about 1.1. The engine thrust is mainly determined by the value of the plateau pressure and its decay process. That is the reason why the thrust of the engine reaches its maximum value at the equivalence ratio of about 1.1.

Fig. 11

Equivalence ratio

Thrust performance of a liquid-fueled PDE as a function of equivalence ratio.

5. Conclusions t

(1) Thrust performance of a liquid-fueled PDE at operation frequencies from 10 Hz to 30 Hz are obtained by three thrust measurement methods: direct thrust measurement with a force transducer, indirect thrust measurement with an ECDS and impulse thrust measurement method. All the thrust data show good agreement within the range of measurement error, indicating that the impulse thrust measurement method is valid when applied to measure the averaged thrust of PDE.

(2) The averaged thrust data from the impulse thrust measurement method is lower than that from the force transducer due to the axial momentum losses of the detonation jet. Care must be taken to avoid possible sources of error when the impulse thrust measurement method is used to measure the averaged thrust of PDE.

(3) Two analytical models are used to obtain the thrust of the PDE. Analytical model is based on an updated numerical analysis by Endo-Fujiwara. A modification is conducted on this analytical model to consider the effect of droplets resistance and heat transfer to the tube on the detonation wave velocity. The data obtained by the modified analytical model is 24.7% higher than the experimental thrust data due to the losses during the DDT process.

(4) The effect of equivalence ratio on the thrust performance of a liquid-fueled PDE is investigated based on the modified analytical model. The thrust reaches the maximum at the equivalence ratio of about 1.1 and too rich or too lean will cause lose in thrust.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51306153), the Natural Science Foundation of Shanxi Province of China (No. 2010JQ7005), Doctoral Fund of Ministry of Education of China (No. 20116102120027) and Northwestern Polytechnical University Foundation for Fundamental Research (No. NPU-FFR-JCY20130129).

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Lu Jie is a Ph.D. student at School of Power and Energy, Northwestern Polytechnical University. He received the B.S.

degree from Northwestern Polytechnical University in 2011. His area of research includes combustion and flow of

aero-engine.

Zheng Longxi is a professor and Ph.D. supervisor at School of Power and Energy, Northwestern Polytechnical University. He is devoted to the study of combustion, propulsion and pulse detonation engines.