Transverse Detonation Waves Research Articles

Numerical study on detonation initiation by multiple hot spots

Detonation initiation is important not only for the development of advanced detonation engines and but also for the control of accidental explosion. There are mainly two types of detonation initiation, i.e., direct initiation and indirect initiation. This work focuses on direct detonation initiation which has a short initiation distance but requires large amount of energy deposition. Specially, we investigate the reduction in the critical initiation energy through replacing the single hot spot by multiple hot spots. The transient detonation initiation process in a stoichiometric H2/O2/Ar mixture is examined through two-dimensional simulations considering detailed chemistry. It is found that under the same initiation energy, detonation initiation fails for a single large hot spot while successful detonation initiation can be achieved by employing six small hot spots. The collisions among adjacent transverse detonation waves induce new local explosions, which play a pivotal role in detonation initiation. To further assess the impact of wave collision, we change the hot spot energy used in the multiple hot spot configuration. For relatively low initiation energy, the blast wave quickly decays and decouples with the reaction zone. Consequently, the collision among transverse shock waves cannot induce new local explosion and detonation initiation fails. Increasing the initiation energy can enhance the blast wave and is favorable to the formation of local explosion, facilitating the rapid detonation initiation. Furthermore, the influence of hot spot number on detonation initiation is assessed. Interestingly the hot spot number is found to have non-monotonic effect on detonation initiation. Splitting a single hot spot into multiple hot spots enhances detonation initiation since the wave collision helps to induce local explosion. However, as the hot spot number increases, the energy of each hot spot is decreased and becomes excessively dispersed, which results in relatively weak blast wave and thereby weak wave interaction. Consequently, local explosion cannot be triggered and detonation initiation fails for relatively large hot spot numbers. This study provides insights on promoting detonation initiation through multiple hot spots.

Hybrid conservative central/WENO finite difference scheme for two-dimensional detonation problems

In the present work, a hybrid finite difference scheme is proposed and tested for the study of two-dimensional detonation problems. The hybrid scheme consists of a fifth-order weighted essentially nonoscillatory (WENO) method for discontinuous regions and a fourth or sixth-order robust conservative central finite difference scheme for the remaining domain. An arbitrary shock sensor is used to identify the discontinuities. The proposed shock sensor is based on the absolute value of the density gradient with an arbitrary threshold computed at each time step using a fast image segmentation technique. The sensor is complemented with a Ducros sensor to avoid the selection of vortices as discontinuities. The hybrid scheme is tested for several benchmark examples, including a two-dimensional transverse detonation wave, detonation wave diffraction, and a multiple obstacles test case. The obtained results show that the proposed sensor detects discontinuities adequately and the hybrid schemes give the same results as the fifth-order WENO in faster computational time.

REALIZATION OF CONTINIOUSLY ROTATING DETONATION FOR SYNGAS-AIR MIXTURES

Numerical simulation of continuously rotating detonations (CRD) of stoichiometric two-fuel mixture with air has been carried out for the cylindrical annular detonation chamber (DC) of the rocket-type engine. Thesyngas (1 - α)óO + αH2, a binary mixture of hydrogen H2 and carbon monoxide CO, is taken as a fuel. The global flow structure in the DC and the detailed structure of the transverse detonation wave (TDW) front in thecontinuously rotating regime have been studied. Integral characteristics of the detonation process - the distribution of average values of static and total pressure along the length of the DC - and the value of specific impulse on the DC exit have been obtained. The regions of existence of stable CRD regime in coordinates “stagnation pressure pm - stagnation temperature Tm” in the injection manifold (receiver) have been determined. The minimal values of the DC length and radius for CRD for some regions at the pm-Tm plane have been found.

On the role of transverse detonation waves in the re-establishment of attenuated detonations in methane–oxygen

This investigation concerns the problem of detonation attenuation in stoichiometric methane-oxygen and its re-establishment following its interaction with obstacles, using high resolution numerical simulation. The main focus was on the role of the transverse detonation on the re-establishment of the detonation wave, and the importance of applying a numerical combustion model that responds appropriately to the thermodynamic state behind the complex shock wave dynamics. We applied an efficient thermochemically derived four-step global combustion model using an Euler simulation framework to investigate the critical regimes present. While past attempts at using one- or two- step models have failed to capture transverse detonations, for this scenario, our simulations have demonstrated that the four-step combustion model is able to capture this feature. We thus suggest that to correctly model detonation re-initiation in characteristically unstable mixtures, an applied combustion model should contain at least an adequate description to permit the correct ignition and state variable response when changes in temperature and pressure occur, i.e., behind shocks. Our simulations reveal that (1) there is a relationship between the critical outcomes possible and the mixture cell size, and (2) while pockets of unburned gas may exist when a detonation re-initiates, it is not the direct rapid consumption of these pockets that gives rise to transverse detonations. Instead, the transverse detonations are initiated through pressure amplification of reaction zones at burned/unburned gas interfaces whose combustion rates have been enhanced through Richtmyer–Meshkov instabilities associated with the passing of transverse shock waves, or by spontaneous ignition of hot spots, which can form into detonations through the Zeldovich gradient mechanism. In both situations, non-uniform ignition delay times are found to play a role. Finally, we found that the transverse detonations are in fact Chapman–Jouguet detonations, but whose presence contributes to overdriving the re-initiated detonation along the Mach stem.

On the propagation stability of droplet-laden two-phase rotating detonation waves

The propagation characteristics and stability of droplet-laden two-phase rotating detonation waves are studied by theoretical analysis and numerical simulations. The stability criterion of rotating detonation waves is proposed for an annular combustor fueled by liquid kerosene, which combines the pre-evaporation equivalence ratio φpre and a dimensionless parameter Δ. The latter one is defined as the ratio of the droplet evaporation distance LE to the detonation wave front height LD. The maximum droplet diameter as well as the stability boundary for the rotating detonation wave without pre-evaporation is found theoretically. Furthermore, numerical simulations are conducted on the two-phase rotating detonation waves produced by kerosene droplets and high-temperature air by means of the Eulerian-Lagrangian method. The effects of initial droplet diameter d0 and φpre on the propagation characteristics of rotating detonation waves are analyzed. The mechanism of detonation instability and wave-quenching as d0 and φpre exceed the stability boundary is explored. Results show that for φpre = 0, the droplet evaporation becomes longer and the rotating detonation wave tends to be less stable as Δ gradually increases. The unburned reactant pockets are generated at the detonation front and are consumed by the transverse detonation waves. When Δ is approximately equal to 1.0, the insufficient evaporation leads to the formation of local larger unburned reactant pockets. If the unburned reactant zones gradually enlarge, the flame and shock wave will be decoupled, and the detonation quenched soon. Increasing φpre can significantly improve the propagation stability of detonation wave for Δ ∼ O(1.0). The stability regime of droplet-laden two-phase rotating detonation waves is obtained and the above stability criterion is verified based on the simulation cases. The conclusion will inspire the optimization design of the liquid-fuel rotating detonation engine.

Numerical simulation of similarities between rotating detonation and high-frequency combustion instability under two mixing schemes

This paper presents an experimental study on rotating detonations in a hollow combustor with the slit-orifice nozzle. The experimental results reveal that the propagation speed of detonation waves increases with the rise of mass flow rates and is greater than the Chapman–Jouguet detonation speed (VC−J). Furthermore, numerical simulations of rotating detonation in a non-premixed three-dimensional cylindrical combustor have been conducted based on a multispecies reacting code. The influence of two mixing schemes—that is, slit-orifice and coaxial injector—on detonation waves are studied to determine whether the characteristics of detonation waves tend toward high-frequency combustion instability due to changes in the mixing scheme. It is found that the slit-orifice scheme’s detonation speed, pressure, and temperature are significantly higher than those of the coaxial injector scheme. In particular, the detonation speed of the former reaches 124% of the VC−J, while that of the latter is only 80.5% of the theoretical value. The numerical results reveal that the low-speed detonation is caused by the deterioration of the hydrogen (H2)/air mixing conditions. Moreover, the flow-field structures of two mixing schemes were comparable, both containing transverse detonation waves, oblique shocks, contact surfaces, and wedge-shaped reactant regions. Furthermore, the Rayleigh index analysis showed that the unsteady heat release was in phase with the pressure fluctuations, amplifying the pressure. Therefore, it is suggested that high-frequency combustion instability may be a manifestation of rotating detonation waves under poor mixing conditions.

Continuous Detonation of CH4/H2–Air Mixtures in an Annular Combustor with Varied Geometry

Regimes of continuous detonation of CH4/H2–air mixtures with mass fractions of H2 in the fuel equal to 0–1/5 are obtained in an annular combustor 503 mm in diameter with variation of the combustor geometry. The influence of the combustor geometry on the velocity and number of transverse detonation waves, pressure in the combustor, and specific impulse is considered. It is found that three-fold constriction of the combustor exit cross area allows obtaining two-wave regimes of continuous spin detonation in the pure methane–air mixture. Based on stagnation pressures measured at the combustor exit, the specific impulses in the case of continuous detonation are determined for different compositions of the fuel.

Continuous detonation of a hydrogen–oxygen gas mixture in a 100-mm plane-radial combustor with exhaustion toward the periphery

Regimes of continuous spin detonation and continuous multifront detonation in a hydrogen–oxygen mixture are obtained in a plane-radial combustor with an inner diameter of 100 mm and exhaustion toward the periphery. The fuel-lean limits of detonation in terms of the specific flow rate of the mixture are determined. For continuous spin detonation, transverse detonation waves and the flow in their vicinity in the combustor plane are reconstructed. The detonation wave is found to be significantly curved because of the increase in the tangential component of the velocity along the combustor radius. It is demonstrated that the scale effect is manifested only in the number of rotating waves. However, their velocity increases with increasing the combustor size. The velocity deficit of continuous detonation is 20–40% as compared to the velocity of the ideal Chapman–Jouguet detonation. (The smaller value corresponds to the fuel-lean mixture.)

MHD effects in continuous spin detonation

Conversion possibility of the chemical energy of combustion products of a hydrogen–oxygen mixture into electrical energy with the use of continuous spin detonation has been demonstrated for the first time in an MHD system. The specific conductivity of detonation products in the region of rotation of the detonation front was measured to be ~3 · 10–2 Ω–1 m–1. The structure of transverse detonation waves was examined, their velocity was measured (2220 ± 50 m/s), and the flow in their vicinity was studied.

Detonation of a hydrogen-oxygen gas mixture in a plane-radial combustor with exhaustion toward the periphery in the regime of oxygen ejection

The results of experimental study concerning a continuous spin detonation of hydrogen-oxygen mixture in a flow-through plane-radial combustor with a diameter of 10 cm and with exhaustion toward the periphery in the regime of oxygen ejection are presented. In the experiment, the regimes of continuous spin detonation with one and two transverse detonation waves rotating with velocity D = 1.3÷1.43 and 1.45÷1.54 km/s, measured relative to the inner cylindrical surface of the combustor, respectively, and two near-sonic waves rotating with velocities of about 0.7 km/s have been observed. The waves of pulse combustion with frequencies of 4.4 – 3.6 kHz have been found for the first time. The structure of waves and flow in their vicinity has been studied.

Continuous Detonation of Methane/Hydrogen–Air Mixtures in an Annular Cylindrical Combustor

Regimes of continuous detonation of methane/hydrogen–air mixtures in spin and opposing transverse detonation waves are obtained for the first time in a flow-type annular cylindrical combustor 503 mm in diameter. A two-component (methane/hydrogen) fuel with the H2 mass fractions of 1/9 to 1/2 in the range of specific flow rates of the mixture from 64 to 1310 kg/(s ·m2) and the fuel-to-air equivalence ratio ϕ = 0.78–1.56 is considered. In methane/hydrogen–air mixtures with two compositions of the fuel (CH4 + 8H2 and CH4 + 4H2), one-wave and two-wave regimes of continuous spin detonation are obtained; the frequency of rotation of transverse detonation waves is 0.56–1.66 kHz at ϕ = 0.78–1.02. For the fuel compositions CH4 + 2H2 and CH4 + 1.5H2, continuous multifront detonation with two opposing transverse detonation waves rotating with the frequency of 0.86–1.34 kHz at ϕ = 1.0–1.23 is obtained. For the CH4 + H2 + air mixture, both combustion in the chamber and continuous spin detonation outside the combustor with transverse detonation waves rotating with the frequency of 1.01–1.1 kHz are observed. The lean limits of continuous detonation are obtained in terms of the specific flow rate of the mixture: 64, 100, 200, and 790 kg/(s · m2) for the fuel compositions CH4 + 8H2, CH4 + 4H2, CH4 + 2H2, and CH4 + 1.5H2, respectively, for the mass fraction of hydrogen in the methane/hydrogen fuel of ≈0.16. Violation of regularity of the continuous detonation wave structure and the wave velocity with a decrease in the fraction of hydrogen in the two-component fuel is detected.

Continuous spin detonation of a syngas-air mixture in a plane-radial vortex combustor

Continuous spin detonation in syngas-air mixtures with three different syngas compositions [CO]/[H2] = 1/3, 1/2, and 1/1 is experimentally studied in a flow-type radial vortex combustor 500 mm in diameter. It is found that all these mixtures with three syngas compositions can be effectively burned in air in the detonation regime. Transverse detonation waves of identical structure are detected. The limits of existence of continuous detonation in terms of the specific flow rates of the mixtures (minimum values) are determined.

Modeling Of Transverse Detonation Waves In A Flat-Radial Annular Channel

Acoustic properties of two regions of gases with different temperatures arising at the initial stage of evolution of transverse detonation waves in annular channel were examined. Mechanics of acoustic vibrations and waves are studied using both numeric and analytical and methods. Rotating circumferential waves at boundary surface of two gases with different temperatures were discovered and rotation velocities of these waves were determined.

Scaling factor in continuous spin detonation of syngas–air mixtures

Multiwave regimes of continuous spin detonation in syngas–air mixtures in a flow-type annular cylindrical combustor 503 mm in diameter are obtained. Experiments are performed for mixtures of carbon oxide and hydrogen with the ratio of the components equal to 1/3, 1/2, or 1/1. The varied parameters are the flow rates of air and syngas, the ratio of these flow rates, and the combustor length. Scalability of the continuous spin detonation process is demonstrated: at identical values of the specific flow rate of air and the combustor expansion ratio, the number of transverse detonation waves increases with increasing combustor diameter. In the examined ranges of combustor lengths and specific flow rates of air, the frequency of these waves is independent of the combustor length, except for narrow regions where the number of waves (and, correspondingly, the flow regime) changes. The structures of transverse detonation waves in regular regimes are almost identical for all examined syngas compositions. It is shown that detonation can be initiated by a jet of combustion products. The minimum diameters of the detonation chamber for different flow rates of the mixture are estimated.

Pressure measurement by fast-response piezo-electric sensors during continuous spin detonation in the combustor

Pressure profiles in a transverse detonation wave propagating in a plane-radial vortex chamber during continuous spin detonation of a mixture consisting of lignite, syngas, and air are measured by specially designed and fabricated high-frequency pressure sensors based on TsTS-19 piezo-ceramics. Pressure levels in the detonation wave front relative to the mean static pressure are determined. It is demonstrated that these levels decrease toward the combustor center (by a factor of 20 and lower) as the wave intensity (velocity) decreases. Pressure oscillations behind the wave front testify to a complex gas-dynamic pattern of the processes in the wave region. A chemical reaction region is detected behind the wave front; its length is approximately 8% of the period between the waves.

Моделирование поперечных детонационных волн в плоскорадиальном кольцевом канале

Моделирование поперечных детонационных волн в плоскорадиальном кольцевом канале

Detonation combustion of a hydrogen–oxygen mixture in a plane–radial combustor with exhaustion toward the center

Regimes of continuous spin detonation in a plane–radial combustor with an external diameter of 80 mm with peripheral injection of a hydrogen–oxygen mixture in the range of specific flow rates of the mixture 3.6–37.9 kg/(s ·m2) are obtained for the first time. Depending on the diameter of the exit orifice in the combustor (40, 30, or 20 mm), specific flow rate of the mixture, its composition, and counterpressure, one to seven transverse detonation waves with a frequency from 6 to 60 kHz are observed. It is found that the number of detonation waves increases, while their intensity decreases owing to reduction of the exit orifice diameter or to an increase in the counterpressure. The flow structure in the region of detonation waves is analyzed. The domain of detonation regimes in the coordinates of the fuel-to-air equivalence ratio and specific flow rate of the mixture is constructed. A physicomathematical model of continuous spin detonation in a plane–radial combustor is formulated. For parameters of hydrogen and oxygen injection into the combustor identical to experimental conditions, the present simulations predict similar parameters of detonation waves, in particular, the number of waves over the combustor circumference and the wave velocity.

Multi-frame visualization for detonation wave diffraction

When a detonation wave emerges from a tube into unconfined space filled with a gas mixture, detonation wave diffraction occurs due to abrupt changes in the cross-sectional area. In the present study, we focused on the local explosion in reinitiation and propagation of a transverse detonation wave by performing comprehensive and direct observation with high time resolution visualization in a two-dimensional rectangular channel. Using the visualization methods of shadowgraph and multi-frame, short-time, open-shutter photography, we determined where the wall reflection point is generated, and also determined where the bright point is originated by the local explosion, and investigated the effects of the deviation angle and initial pressure of the gas mixture. We found that the reinitiation of detonation had two modes that were determined by the deviation angle of the channel. If the deviation angle was less than or equal to 30\(^{\circ }\), the local explosion of reinitiation might occur in the vicinity of the channel wall, and if the deviation angle was greater than or equal to 60\(^{\circ }\), the local explosion might originate on the upper side of the tube exit. With a deviation angle greater than 60\(^{\circ }\), the position of the wall reflection point depended on the cell width, so the radial distance of the wall reflection point from the apex of the tube exit was about 12 times the cell width. Similarly, the bright point (local explosion point) was located a distance of about 11 times the cell width from the apex of the tube exit, with a circumferential angle of 48\(^{\circ }\).

Effect of combustor geometry on continuous spin detonation in syngas–air mixtures

Regimes of continuous detonation burning of syngas–air mixtures in transverse (spinning) detonation waves in a flow-type annular cylindrical combustor are considered. Mixtures of carbon oxide and hydrogen in proportions of 1/1, 1/2, and 1/3 are used. The varied parameters are the combustor geometry and the fuel injection system, as well as the flow rates of air and syngas. The influence of additional supply of air to the products on the detonation wave parameters, pressure in the combustor, and specific impulse is determined. The range of realization of continuous spin detonation of the syngas–air mixture in terms of specific flow rates of the mixture is expanded from 25 to 786 kg/(s ·m2). It is shown that additional supply of air increases the pressure in the combustor, the thrust, and the number of detonation waves, but decreases the detonation wave velocity. The flow structure in the domain of detonation waves is studied. For some values of the combustor expansion coefficient, a chart of detonation regimes in the coordinates of the fuel-to-air equivalence ratio and specific flow rate of air is constructed, and the specific impulse of the thrust force is calculated.

Spinning detonation, cross-currents, and the Chapman–Jouguet velocity

AbstractInterestingly, the Chapman–Jouguet detonation velocity ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}D_{CJ}$) based on a one-dimensional and steady model compares well with the measured data. For the spinning detonation, in particular, this agreement is particularly notable, since the flow is highly three-dimensional and unsteady; perpendicular to the leading shock front, a transverse detonation wave (TDW) spins periodically. In the wake of this TDW, a secondary flow, called here the cross-current, appears which is orthogonal to the leading shock. Despite the presence of these cross-currents, the $D_{CJ}$ agreement remains remarkably satisfactory, and we investigate the reason for this, for spinning detonation in a tube. First, we focus on the origin of the cross-current. The cross-current, driven by the shock pressure, arises initially across a warped shock frontal surface, and both its sign and magnitude depend on the local slopes of the shock surface. The cross-current undergoes further pressure-driven transitions, with its magnitude eventually diminishing downstream and reducing the flow to a quasi-one-dimensional one. Second, regarding the unsteadiness, under the assumptions that the TDW spins at constant angular wave speed and the flow is steady in the frame rotating with it, the unsteady energy equation becomes integrable, resulting in the invariance of the so-called rothalpy. Also, in the integral forms of the mass and momentum balance, the unsteady terms drop out. Taken together, in the far field the governing equations are reduced to being one-dimensional and steady. From these the $D_{CJ}$ follows immediately, which appears to be the reason for the enduring usefulness of the $D_{CJ}$. The results of the analysis are confirmed with computational fluid dynamics (CFD). Additionally, the area-averaged flow profiles are found to display more than a passing resemblance to the Zeldovitch–Von Neumann–Doering (ZND) model.