A numerical study of two-and three-dimensional detonation dynamics of pulse detonation engine by the CE/SE method

In this paper, the CE/SE method is developed to simulate the two- and three-dimensional flow-field of Pulse Detonation Engine (PDE). The conservation equations with stiff source terms for chemical reaction are solved in two steps. The detailed analysis of computational results of a PDE with a single detonation tube and a PDE with five detonation tubes are given in this paper. Complex wave systems are observed inside and outside a PDE. For a PDE with 5 detonation tubes, there is a big bow shock produced from a number of little shocks near the open ends of tubes. A lot of vortexes interact with shocks and a large expansion wave propagates forward and backward with respect to the PDE in a semi-oval shape.

Acoustic characteristics of pulse detonation engine with ellipsoidal reflector

Acoustic characteristics of a pulse detonation engine（PDE） with and without an ellipsoidal reflector are numerically and experimentally investigated. A two-dimensional（2 D） non-splitting unstructured triangular mesh Euler solver based on the space-time conservation element and solution element（CE/SE） method is employed to simulate the flow field of a PDE.The numerical results clearly demonstrate the external flow field of the PDE. The effect of an ellipsoidal reflector on the flow field characteristic near the PDE exit is investigated. The formation process of reflected shock wave and reflected jet shock are reported in detail. An acoustic measurement system is established for the PDE acoustic testing. The experimental results show that the ellipsoidal reflector changes the sound waveform and directivity of PDE sound. The reflected shock wave and reflected jet shock result in two more positive pressure peaks in the sound waveform. The ellipsoidal reflector changes the directivity of PDE sound from 20 to 0. It is found that the peak sound pressure level（PSPL） and overall sound pressure level（OASPL） each obtain an increment when the PDE is installed with a reflector. The maximum relative increase ratio of PSPL and OASPL are obtained at the focus point F2, whose values are 6.1% and 6.84% respectively. The results of the duration of the PDE sound indicate that the reflecting and focusing wave generated by the reflector result in the increment of A duration and B duration before and near focus point F2. Results show that the ellipsoidal reflector has a great influence on the acoustic characteristic of PDE sound. The research is helpful for understanding the influence of an ellipsoidal reflector on the formation and propagation process of PDE sound.

Acoustic characteristics of pulse detonation engine sound propagating in enclosed space

Acoustic characteristics of pulse detonation engine(PDE)sound propagating in enclosed space are numerically and experimentally investigated.The finite element software LS-DYNA is utilized to numerically simulate the PDE sound propagating in enclosed space.Acoustic measurement systems are established for testing the PDE sound in enclosed space,and the time-frequency characteristics of PDE sound in enclosed space are reported in detail.The experimental results show that the sound waveform of PDE sound in enclosed space are quite different from those in open space,and the reflection and superposition of PDE sound on the walls of enclosed space results in the sound pressure oscillating obviously.It is found that the peak sound pressure level(PSPL)and overall sound pressure level(OASPL)of PDE sound in enclosed space are higher than those in open space and their difference increases with the rise of propagation distance.The results of the duration of PDE sound indicate that the A duration of PDE sound in enclosed space is higher than that in open space except at measuring points located at 2-m and 5-m while the B duration is higher at each of all measuring points.Results show that the enclosed space has a great influence on the acoustic characteristic of PDE sound.This research is helpful in performing PDE experiments in enclosed laboratories to prevent the PDE sound from affecting the safety of laboratory environment,equipment,and staffs.

Experimental study of the influence of annular nozzle on acoustic characteristics of detonation sound wave generated by pulse detonation engine

Acoustic characteristics of the detonation sound wave generated by a pulse detonation engine with an annular nozzle,including peak sound pressure, directivity, and A duration, are experimentally investigated while utilizing gasoline as fuel and oxygen-enriched air as oxidizer. Three annular nozzle geometries are evaluated by varying the ratio of inner cone diameter to detonation tube exit diameter from 0.36 to 0.68. The experimental results show that the annular nozzles have a significant effect on the acoustic characteristics of the detonation sound wave. The annular nozzles can amplify the peak sound pressure of the detonation sound wave at 90° while reducing it at 0° and 30°. The directivity angle of the detonation sound wave is changed by annular nozzles from 30° to 90°. The A duration of the detonation sound wave at 90° is also increased by the annular nozzles. These changes indicate that the annular nozzles have an important influence on the acoustic energy distribution of the detonation sound wave, which amplify the acoustic energy in a direction perpendicular to the tube axis and weaken it along the direction of the tube axis.

Reheat effect on the improvement in efficiency of the turbine driven by pulse detonation

Due to the strong unsteadiness of pulse detonation,large flow losses are generated when the detonation wave interacts with the turbine blades,resulting in low turbine efficiency.Considering that the flow losses are dissipated into the gas as heat energy,some of them can be recycled during the expansion process in subsequent stages by the reheat effect,which should be helpful to improve the detonationdriven turbine efficiency.Taking this into account,this paper developed a numerical model of the detonation chamber coupled with a two-stage axial turbine,and a stoichiometric hydrogen-air mixture was used.The improvement in turbine efficiency attributable to the reheat effect was calculated by comparing the average efficiency of the stages with the efficiency of the two-stage turbine.The research indicated that the first stage was critical in suppressing the flow unsteadiness caused by pulse detonation,which stabilized the intake condition of the second stage and consequently allowed much of the flow losses from the first stage to be recycled,so that the efficiency of the two-stage turbine was improved.At a 95%confidence level,the efficiency improvement was stable at 4.5%—5.3%,demonstrating that the reheat effect is significant in improving the efficiency of the detonation-driven turbine.

Experimental Investigation of Nozzle Effects on Thrust and Inlet Pressure of an Air-breathing Pulse Detonation Engine

Nozzle effects on thrust and inlet pressure of a multi-cycle air-breathing pulse detonation engine （APDE） are investigated experimentally. An APDE with 68 mm in diameter and 2 050 mm in length is operated using gasoline/air mixture. Straight nozzle, converging nozzle, converging-diverging nozzle and diverging nozzle are tested. The results show that thrust augmentation of converging-diverging nozzle, diverging nozzle or straight nozzle is better than that of converging nozzle on the whole. Thrust augmentation of straight nozzle is worse than those of converging-diverging nozzle and diverging nozzle. Thrust augmentations of diverging nozzle with larger expansion ratio and converging-diverging nozzle with larger throat area range from 20% to 40% on tested frequencies and are better than those of congeneric other nozzles respectively. Nozzle effects on inlet pressure are also researched. At each frequency it is indicated that filling pressures and average peak pressures of inlet with diverging nozzle and converging-diverging nozzle with large throat cross section area are higher than those with straight nozzle and converging nozzle Pressures near thrust wall increase in an increase order from without nozzle, with diverging nozzle, straight nozzle and converging-diverging nozzle to converging nozzle.

A technique for promoting detonation transmission from a confined tube into larger area for pulse detonation engine applications

A simple method of detonation transmission from a small tube to a large area is presented.This technique involves placing obstacles which create slight blockages at the exit of the confined tube before the planar detonation emerges into the larger space,thereby generating flow instability to promote the detonation transmission.In this experimental study two mixtures of undiluted stoichiometric acetylene-oxygen and acetylene-nitrous oxide are examined.These mixtures can be characterized by a cellular detonation front that is irregular and representative of those potentially used in practical aerospace applications.The blockage ratio imposed by the obstacles is varied systematically to identify the optimal condition under which a significant reduction in critical pressure for transmission can be obtained.A new perturbation configuration for practical use in propulsion and power systems is also introduced and results are in good agreement with those obtained using thin needles as the blockage ratio is kept constant.

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

In order to test the feasibility of a new thrust stand system based on impulse thrust mea- surement method, a liquid-fueled pulse detonation engine （PDE） is designed and built. Thrust per- formance 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.

Effect of inlet-valve structures on thrust of airbreathing pulse detonation engines

Experimental studies were conducted in order to improve the understanding of the thrust generation and the pressure/flame reverse propagation of the air-breathing pulse detonation engines(APDEs)with self-designed inlets and valves structures.The present experimental research utilized a gasoline/air APDE(with 68 mm inner-diameter,2050 mm length and maximum operating frequency not less than 40 Hz which was as a benchmark structure)at different operating frequencies,with freestream air inflow of 1.1 atm and 0℃.The theoretical equivalence ratio of gasoline/air was 1.Two kinds of inlets with centerbody or without were considered and combined with two kinds of self-designed valves(the elastic-valve and the convergent aero-valve)specially designed for comparative experiments.During the test,the inflow parameters,the pressure along the longitudinal direction inside the engine and the thrust force were measured for the APDE operating characteristic analysis,including the detonation combustion,the aerodynamic drag,the pressure/flame reverse propagation and the thrust generation.The research results indicate that:The inlet centerbody does not increase drag but plays a positive effect on airflow stability and operation matching.The elastic-valve and the convergent aero-valve,though increase the inlet aerodynamic drag,have obvious effects on suppressing the detonation wave and pressure forward propagation,resulting in effective thrust increase.Effects of the convergent aero-valve are the best when the flow choked,while the effects of elastic-valve are better and continuously stable in a wider range of frequency.The wmaximum nondimensional thrust increases with the elastic-valve is reached about 1.12 at the frequency of 8-9 Hz,and about 0.97 with the convergent aero-valve at the frequency of 7 Hz.The maximum fuel specific impulse is 2514.6 s when using the convergent aerovalve.And this study provides technical reserve for the APDE optimization design.

Experimental Investigation on Performance of Pulse Detonation Rocket Engine Model

The PDRE test model used in these experiments utilized kerosene as the fuel, oxygen as oxidizer, and nitrogen as purge gas. The solenoid valves were employed to control intermittent supplies of kerosene, oxygen and purge gas. PDRE test model was 50 mm in inner diameter by 1.2 m long. The DDT （deflagration to detonation transition） enhancement device Shchelkin spiral was used in the test model. The effects of detonation frequency on its time-averaged thrust and specific impulse were experimentally investigated. The obtained results showes that the time-averaged thrust of PDRE test model was approximately proportional to the detonation frequency. For the detonation frequency 20 Hz, the time-averaged thrust was around 107 N, and the specific impulse was around 125 s. The nozzle experiments were conducted using PDRE test model with three traditional nozzles. The experimental results obtained demonstrated that all of those nozzles could augment the thrust and specific impulse. Among those three nozzles, the convergent nozzle had the largest increased augmentation, which was approximately 18%, under the specific condition of the experiment.

Application of Two-dimensional Viscous CE/SE Method in Calculation of Two-phase Detonation

The method of two-dimensional viscous space-time conservation element and solution element (CE/SE) can be used to calculate the gas-liquid two-phase interior flow field in pulse detonation engine (PDE). In this paper, the evolution of the detonation wave and the distribution of its physical parameters were analyzed. The numerical results show that the change of axial velocity of gas is the same as that of detonation pressure. The larger the liquid droplet radius is, the longer the time to get stable detonation wave is. The calculated results coincide with the experimented results better.

The Advantages of Non-Thermal Plasma for Detonation Initiation Compared with Spark Plug

In this paper,the characteristics of detonation combustion ignited by AC-driven non-thermal plasma and spark plug in air/acetylene mixture have been compared in a doubletube experiment system.The two tubes had the same structure,and their closed ends were installed with a plasma generator and a spark plug,respectively.The propagation characteristics of the flame were measured by pressure sensors and ion probes.The experiment results show that,compared with a spark plug,the non-thermal plasma obviously broadened the range of equivalence ratio when the detonation wave could develop successfully,it also heightened the pressure value of detonation wave.Meanwhile,the detonation wave development time and the entire flame propagation time were reduced by half.All of these advantages benefited from the larger ignition volume when a non-thermal plasma was applied.

Interaction Dynamics Characteristics of Detonation Waves with Coolant Flow in a Hydrogen Fuelled Detonation Chamber

To analyze the dynamic interaction between detonation waves and coolant flow in a hydrogen fuelled detonation chamber,a hydrogen fuelled detonation chamber with a cooled liner was designed and a simulation model was established.An explicit high-resolution total variation diminishing(TVD)scheme was developed to solve the two-dimensional Euler equations implemented with an augmented reduced mechanism of the hydrogen/air mixture.A point-implicit method was used to solve the numerical stiffness of the chemical reaction source term.The interaction between detonative was and coolant flow were presented.The interaction dynamics between detonation waves and coolant flow in a detonation chamber were investigated.The results indicated that there were some negative interaction effects between detonation waves and coolant flow.

The Feasibility of Applying AC Driven Low-Temperature Plasma for Multi-Cycle Detonation Initiation

Ignition is a key system in pulse detonation engines （PDE）. As advanced ignition methods, nanosecond pulse discharge low-temperature plasma ignition is used in some combustion systems, and continuous alternating current （AC） driven low-temperature plasma using dielectric barrier discharge （DBD） is used for the combustion assistant. However, continuous AC driven plasmas cannot be used for ignition in pulse detonation engines. In this paper, experimental and numerical studies of pneumatic valve PDE using an AC driven low-temperature plasma igniter were described. The pneumatic valve was jointly designed with the low-temperature plasma igniter, and the numerical simulation of the cold-state flow field in the pneumatic valve showed that a complex flow in the discharge area, along with low speed, was beneficial for successful ignition. In the experiments ethylene was used as the fuel and air as oxidizing agent, ignition by an AC driven low-temperature plasma achieved multi-cycle intermittent detonation combustion on a PDE, the working frequency of the PDE reached 15 Hz and the peak pressure of the detonation wave was approximately 2.0 MPa. The experimental verifications of the feasibility in PDE ignition expanded the application field of AC driven low-temperature plasma.

Operation of a Rotary-valved Pulse Detonation Rocket Engine Utilizing Liquid-kerosene and Oxygen

The pulse detonation rocket engine （PDRE） requires periodic supply of oxidizer, fuel and purge gas. A rotary-valve assembly is fabricated to control the periodic supply in this research. Oxygen and liquid aviation kerosene are used as oxidizer and fuel respectively. An ordinary automobile spark plug, with ignition energy as low as 50 mJ, is used to initiate combustion. Steady operation of the PDRE is achieved with operating frequency ranging from 1 Hz to 10 Hz. Experimentally measured pressure is lower than theoretical value by 13% at 1 Hz and 37% at 10 Hz, and there also exists a velocity deficit at different operating frequencies. Both of these two phenomena are believed mainly due to droplet size which depends on atomization and vaporiza-tion of liquid fuel.

An improved constant volume cycle model for performance analysis and shape design of PDRE nozzle

An improved constant volume cycle （CVC） model is developed to analyze the nozzle effects on the thrust and specific impulse of pulse detonation rocket engine （PDRE）. Theoretically, this model shows that the thrust coefficient/specific impulse of PDRE is a function of the nozzle contraction/expansion ratio and the operating frequency. The relationship between the nozzle contraction ratio and the operation frequency is obtained by introducing the duty ratio, by which the key problem in the theoretical design can be solved. Therefore, the performance of PDRE can be accessed to guide the preliminary shape design of nozzle conveniently and quickly. The higher the operating frequency of PDRE is, the smaller the nozzle contraction ratio should be. Besides, the lower the ambient pressure is, the larger the expansion ratio of the nozzle should be. When the ambient pressure is 1.013 × 105 Pa, the optimal expansion ratio will be less than 2.26. When the ambient pressure is reduced to vacuum, the extremum of the optimal thrust coefficient is 2.236 9, and the extremum of the specific impulse is 321.01 s. The results of the improved model are verified by numerical simulation.

Acceleration of DDT by non-thermal plasma in a single-trial detonation tube

This paper compares the flame acceleration in single-trial dual-detonation tubes triggered by a spark plug and non-thermal plasma igniter. The low-temperature plasma was generated by an in-house novel AC-driven dielectric barrier discharge igniter, which reduces the power supply requirements and was applied in the quiescent ignition of a single-trial detonation tube. Three different types of detonation mixtures were tested with flame propagation tracked by ion probes and pressure waves recorded by high-frequency pressure transducers. The flame propagation speeds were calculated and compared based on signals from the ion probes. The detonation combustion succeeded in the dual tubes, but the deflagration-to-detonation transition could be significantly accelerated by the plasma for all mixtures, as it was shortened by more than 50% compared to that of the spark plug. The present study provides a suitable technological approach for igniters of PDEs.

Numerical simulations of cellular detonation diffraction in a stable gaseous mixture

In this paper,the diffraction phenomenon of gaseous cellular detonations emerging from a confined tube into a sudden open space is simulated using the reactive Euler equations with a two-step Arrhenius chemistry model.Both two-dimensional and axisymmetric configurations are used for modeling cylindrical and spherical expansions,respectively.The chemical parameters are chosen for a stable gaseous explosive mixture in which the cellular detonation structure is highly regular.Adaptive mesh refinement(AMR)is used to resolve the detonation wave structure and its evolution during the transmission.The numerical results show that the critical channel width and critical diameter over the detonation cell size are about 1371 and 2571,respectively.These numerical findings are comparable with the experimental observation and confirm again that the critical channel width and critical diameter differ essentially by a factor close to 2,equal to the geometrical scaling based on front curvature theory.Unlike unstable mixtures where instabilities manifested in the detonation front structure play a significant role during the transmission,the present numerical results and the observed geometrical scaling provide again evidence that the failure of detonation diffraction in stable mixtures with a regular detonation cellular pattern is dominantly caused by the global curvature due to the wave divergence resulting in the global decoupling of the reaction zone with the expanding shock front.