Experimental research on the instability propagation characteristics of liquid kerosene rotating detonation wave

In order to study the instability propagation characteristics of the liquid kerosene rotating detonation wave(RDW),a series of experimental tests were carried out on the rotating detonation combustor(RDC)with air-heater.The fuel and oxidizer are room-temperature liquid kerosene and preheated oxygenenriched air,respectively.The experimental tests keep the equivalence ratio of 0.81 and the oxygen mass fraction of 35%unchanged,and the total mass flow rate is maintained at about 1000 g/s,changing the total temperature of the oxygen-enriched air from 620 K to 860 K.Three different types of instability were observed in the experiments:temporal and spatial instability,mode transition and re-initiation.The interaction between RDW and supply plenum may be the main reason for the fluctuations of detonation wave velocity and pressure peaks with time.Moreover,the inconsistent mixing of fuel and oxidizer at different circumferential positions is related to RDW oscillate spatially.The phenomenon of single-double-single wave transition is analyzed.During the transition,the initial RDW weakens until disappears,and the compression wave strengthens until it becomes a new RDWand propagates steadily.The increased deflagration between the detonation products and the fresh gas layer caused by excessively high temperature is one of the reasons for the RDC quenching and re-initiation.

Periodic oscillation and fine structure of wedge-induced oblique detonation waves

An oblique detonation wave for a Mach 7 inlet flow over a long enough wedge of 30 turning angle is simulated numerically using Euler equation and one-step rection model.The fifth-order WENO scheme is adopted to capture the shock wave.The numerical results show that with the compression of the wedge wall the detonation wave front structure is divided into three sections：the ZND model-like strcuture,single-sided triple point structure and dual-headed triple point strucuture.The first structure is the smooth straight,and the second has the characteristic of the triple points propagating dowanstream only with the same velocity,while the dual-headed triple point structure is very complicated.The detonation waves facing upstream and downstream propagate with different velocities,in which the periodic collisions of the triple points cause the oscillation of the detonation wave front.This oscillation process has temporal and spatial periodicity.In addition,the triple point trace are recorded to obtain different cell structures in three sections.

The criterion of the existence or inexistence of transverse shock wave at wedge supported oblique detonation wave

A simplified theoretic method and numerical simulations were carried out to investigate the characterization of propagation of transverse shock wave at wedge supported oblique detonation wave.After solution validation,a criterion which is associated with the ratio Φ （u 2 /u CJ） of existence or inexistence of the transverse shock wave at the region of the primary triple was deduced systematically by 38 cases.It is observed that for abrupt oblique shock wave （OSW）/oblique detonation wave （ODW） transition,a transverse shock wave is generated at the region of the primary triple when Φ 〈 1,however,such a transverse shock wave does not take place for the smooth OSW/ODW transition when Φ 〉 1.The parameter Φ can be expressed as the Mach number behind the ODW front for stable CJ detonation.When 0.9 〈 Φ 〈 1.0,the reflected shock wave can pass across the contact discontinuity and interact with transverse waves which are originating from the ODW front.When 0.8 〈 Φ 〈 0.9,the reflected shock wave can not pass across the contact discontinuity and only reflects at the contact discontinuity.The condition （0.8 〈 Φ 〈 0.9） agrees well with the ratio （D ave /D CJ） in the critical detonation.

Experimental study on propagation characteristics of rotating detonation wave with kerosene fuel-rich gas

In this study, kerosene fuel-rich gas produced by the combustion in the gas generator was used as the fuel and oxygen-rich air was used as the oxidant to investigate the propagation characteristics of the rotating detonation wave (RDW). The initiation of the kerosene fuel-rich gas and propagation process of the RDW were analyzed. The influences of the oxygen content in the oxidizer, kerosene mass flow rate of the gas generator, and temperature of the kerosene fuel-rich gas on the propagation process of the RDW were studied. The experimental results revealed that the propagation velocity of the RDW could be improved by increasing the three parameters mentioned above with the kerosene mass flow rate as the strongest factor. The minimum oxygen content that could successfully initiate and maintain the stable propagation of the RDW was 32%, achieving the RDW velocity of 1141.9 m/s. The RDW mainly propagated as two-counter rotating waves and a single wave when the equivalent ratios were 0.62–0.79 and 0.85–0.87, respectively. The highest RDW velocity of 1637.2 m/s was obtained when the kerosene mass flow rate, oxygen content, and equivalent ratio were 74.6 g/s, 44%, and 0.87, respectively.

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.

AN APPROXIMATE ANALYTICAL SOLUTION OF THE CYLINDRICAL DETONATION WAVE GENERATED BY THE LINEAR EXPLOSION

The solution of the cylindrical detonation wave generated by the linear explosion was obtained by numerical method in ref. [1.].In this paper, when the ratio of specific heat by using the enlargement coordinate method, the first-order analytical solutions are obtained. The perturbation parameter is The correction of these solutions is checked at the end of this paper.

MBDA R&T EFFORT ON PULSED AND CONTINUOUS DETONATION WAVE ENGINES

The continuous detonation wave engine（CDWE）can be considered to reduce the environmental conditions generated by pulsed detonation engine（PDE）while reducing the importance of initiation issue and simplifying some integration aspects.Specific experimental programs are performed by MBDA and Lavrentiev Institute to study CDWE operating mode and to address some key points for the feasibility of an operational rotating wave engine for space launcher.It is found that such engine can deliver impressive thrust in a very small package（275 daN for internal diameter of 50 mm and length of 100 mm,kerosene-oxygen engine）and that can be increased with the use of a diverging nozzle.Due to the geometry of the combustion chamber,a plug or aerospike nozzle seems to be the best design,the thrust vectoring capability of this engine（with the local change of the mass flow rate）being a way to solve the problem of attitude control.The heat fluxes are very high but located mostly near the injection wall.This point will help the gasification of the liquid component injected inside the combustion chamber.Some preliminary tests are performed to evaluate the capability of C/SiC composite materials to sustain the very severe mechanical environment generated by the rotating detonation waves.Beyond these first steps,a large scale ground demonstrator allowing to address all issues for a continuous detonation rocket engine using LH2/LOx mixture is designed by MBDA.As the first step toward the development of this large scale engine,a small scale demo is tested in Spring 2010.

Investigation of hot jet on active control of oblique detonation waves

The hot jet injection is utilized to actively control the oblique detonation wave,such as initiating and stabilizing an oblique detonation wave at a desired position that is shorter than the length of induction zone,and adjust the height of the oblique detonation wave at the exit of combustor when the oblique detonation wave engine is working on off-design flight conditions.The fifth order Weighted Essentially Non-Oscillatory(WENO)scheme and a two-step reversible reaction mechanism of the stoichiometric H_2/Air are adopted in the simulations.With the help of hot jet injection,the transition from inert oblique shock wave to the oblique detonation wave immediately occurs near the position of hot jet injection,and consequently the length of combustor can be reduced.The angle of oblique detonation wave also decreases as the hot jet injection approaches the nose of wedge.Additionally,the height of the oblique detonation wave at the exit of combustor can be flexibly adjusted,and also depends on the injection position and the strength of the hot jet.If the velocity of the hot jet is too weak to directly trigger the overall oblique detonation wave at the position of injection,increasing the injection pressure will improve the strength of the hot jet and results in a successful transition.

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.

Effects of total pressures and equivalence ratios on kerosene/air rotating detonation engines using a paralleling CE/SE method

In this paper,the kerosene/air rotating detonation engines(RDE)are numerically investigated,and the emphasis is laid on the effects of total pressures and equivalence ratios on the operation characteristics of RDE including the initiation,instabilities,and propulsive performance.A hybrid MPI t OpenMP parallel computing model is applied and it is proved to be able to obtain a more effective parallel performance on high performance computing(HPC)systems.A series of cases with the total pressure of 1 MPa,1.5 MPa,2 MPa,and the equivalence ratio of 0.9,1,1.4 are simulated.On one hand,the total pressure shows a significant impact on the instabilities of rotating detonation waves.The instability phenomenon is observed in cases with low total pressure(1 MPa)and weakened with the increase of the total pressure.The total pressure has a small impact on the detonation wave velocity and the specific impulse.On the other hand,the equivalence ratio shows a negligible influence on the instabilities,while it affects the ignition process and accounts for the detonation velocity deficit.It is more difficult to initiate rotating detonation waves directly in the lean fuel operation condition.Little difference was observed in the thrust with different equivalence ratios of 0.9,1,and 1.4.The highest specific impulse was obtained in the lean fuel cases,which is around 2700 s.The findings could provide insights into the understanding of the operation characteristics of kerosene/air RDE.

Fracture mechanism of a cylindrical shell cut by circumferential detonation collision

The failure mechanism of a cylindrical shell cut into fragments by circumferential detonation collision was experimentally and numerically investigated.A self-designed detonation wave regulator was used to control the detonation and cut the shell.It was found that the self-designed regulator controlled the fragment shape.The macrostructure and micro-characteristics of fragments revealed that shear fracture was a prior mechanism,the shell fractured not only at the position of detonation collision,but the crack also penetrated the shell at the first contact position of the Chapmen-Jouguet(C-J)wave.The effects of groove number and outer layer thickness on the fracture behavior were tested by simulations.When the thickness of the outer layer was 5e18 mm,it has little effect on fragmentation of the shell,and shells all fractured at similar positions.The increase of the groove number reduced the fracture possibility of the first contact position of the C-J wave.When the groove number reached 7 with a 10 mm outer layer(1/4 model),the fracture only occurred at the position of detonation collision and the fragment width rebounded.

Detonation initiated disintegration of coal particle due to the maxi- mum strain energy theory

Fragmentation behaviour of coal particles subjected to detonation wave is being studied. Detonation wave is initiated by a plasma cartridge at one end of a detonation tube. Coal particles are subjected to a shock whose temperature depends on the Mach number of the detonation wave. Temperature shock is found to generate thermal stresses which may fragment the coal particles. A non-dimensional mathematical model for the heat transfer process in the coal particle is proposed. Thermal stresses are calculated at various times and radii while maximum strain energy theory is used to understand the failure behavior viz., the time, temperature and location of fracture. A physical model for coal particle fragmentation when subjected to detonation wave is also proposed. The study suggests that detonation combustion of coal is qualitatively different from conventional method.

Theoretical approach to one-dimensional detonation instability

Detonation instability is a fundamental problem for understanding the microbehavior of a detonation front. With the theoretical approach of shock dynamics, detonation instability can be mathematically described as a second-order ordinary difference equation. A one-dimensional detonation wave can be modelled as a type of oscillators. There are two different physical mechanisms controlling the behaviors of a detonation. If the shock Mach number is smaller than the equilibrium Mach number, the fluid will reach the sonic speed before the end of the chemical reaction. Then, thermal chock occurs, and the leading shock becomes stronger. If the shock Mach number is larger than the equilib- rium Mach number, the fluid will be subsonic at the end of the chemical reaction. Then, the downstream rarefaction waves propagate upstream, and weaken the leading shock. The above two mechanisms are the basic recovery forces toward the equilibrium state for detonation sustenance and propagation. The detonation oscillator concept is helpful for understanding the oscillating and periodic behaviors of detonation waves. The shock dynamics theory of detonation instability gives a description of the feedback regime of the chemical reaction, which causes variations of the leading shock of the detonation. Key words detonation wave, detonation instability, shock wave, chemical reaction

IMPLICIT TVD SCHEMES APPLIED TO GAS-DROPLET DETONATION CALCULATION

In order to investigate parameters of FAE (fuel air explosive) explosion, the two-phase gas-droplet conservation equations with two-dimensional axial symmetry in the Euler coordinate were used. High-resolution implicit TVD ( total variation diminishing) schemes were applied to gas phase equations and MacCormack schemes to liquid equations. The formation and propagation of gas-droplet detonation wave were simulated numerically. The simulation results and the others are compared with a good agreement.

Wave Interactions for Chaplygin Gas with Combustion

The elementary wave interactions for the Chapman-Jouguet model with combustion are investigated. We obtain the unique solution of the initial value problem under the global entropy conditions. We analyze the elementary wave interactions in the phase plane and construct uniquely the solution of this initial value problem. It is found that the combustion wave solution of the corresponding Riemann may be extinguished after perturbation which shows that the unburnt gas is unstable.

Air-Decking Technique in Bench Blasting

The mechanism and the design parameters of blasting with air-decking are studied. The theory of detonation waves is used to investigate the processes of the one-dimensional plane detonation wave within a borehole. The interac- tion of the rarefaction wave with an interface and reflection on a rigid wall is also analyzed. The same courses of the shock wave are also investigated. This decides the distribution of the pressure of the explosion products changing with time along the borehole. Based on the above theoretical analysis, two conditions should be met for a reasonable range of values of the air-decking ratio in blasting rock. First, the rarefaction wave from the contact interface between detonation products and air reaches the bottom earlier than that of the reflected shock wave from the end of the stemming. Second, the reflected shock wave reaches the contact interface between the detonation products and air earlier than that of the reflected rarefaction wave from the bottom of the borehole. Finally, the reasonable value of the air-decking ratio must be decided theoretically in air-decking blasting. For different explosives, the reasonable range of air-decking ratio varies from 0.15 to 0.4. This result is well consistent with what was obtained by previous researchers.

Generalized Riemann problem for gas dynamic combustion

The generalized Riemann problem for gas dynamic combustion in a neighborhood of the origin t 0 in the （x, t） plane is considered. Under the modified entropy conditions, the unique solutions are constructed, which are the limits of the selfsimilar Zeldovich-von Neumann-Dring （ZND） combustion model. The results show that, for some cases, there are intrinsical differences between the structures of the perturbed Riemann solutions and the corresponding Riemann solutions. Especially, a strong detonation in the corresponding Riemann solution may be transformed into a weak deflagration coalescing with the pre-compression shock wave after perturbation. Moreover, in some cases, although no combustion wave exists in the corresponding Riemann solution, the combustion wave may occur after perturbation, which shows the instability of the unburnt gases.

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.

THE ASYMPTOTIC LIMIT FOR A COMBUSTION MODEL IN REGARD TO INFINITE REACTION RATE

The Zeldovich-von Neumann-Doring model and the Chapman-Jouguet model for a simplified combustion model-Majda＇s model is studied.The author proves a uniform maximum norm estimate,then proves that as the rate of chemical reaction tends to infinity the solutions to the Zeldovich-von Neumann-Doring model tend to that of the Chapman-Jouguet model.The type of combustion waves is studied.This result is compared with the result of the projection and finite difference method for the same model.

Numerical Investigation of the Influence of Fuel Concentration Gradient on Propane/Oxygen Detonation Propagation

In this paper,one-and two-dimensional numerical simulations are carried out to study the effects of fuel concentration gradients(such as steep,intermediate and shallow)on the detonation wave behavior.The equivalent ratio range of detonation propagation,the quenching mechanism and the change of cell size are discussed in detail.The simulation results show,as the fuel concentration gradient increases,the detonation wavefront decays faster and decouples into a leading shock and a following flame at equivalence ratios of 0.68,0.64 and 0.62,respectively.Moreover,there are two modes of the quenching mechanism.One occurs in the steep gradient that the detonation wave fails rapidly.The O_(2)in front of the detonation wave passes through the detonation wave and forms some unburned O_(2)pockets.The unburned pockets are affected by the marginal walls and reduce the heat release.The other occurs in the intermediate and shallow gradients that more triple points will survive in the flow field,which leads to a difference in the propagation speed of the detonation wavefront.This makes the detonation wavefront bent and deformed.The unburned O_(2)pockets are affected by the strong instability near the triple points and show different distribution characteristics compared with the steep gradient,which may be helpful to the detonation propagation.In addition,as the fuel concentration gradient increases,the triple points moving toward the wall gradually disappear while the triple points that move toward the center can continue to survive,which leads to the gradual increase in cell size and irregularity of the cell structure.