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Structure of three-dimensional conical oblique detonation waves
Abstract
This study investigates the structure of conical detonations in premixed ethylene–air mixtures through two complementary approaches. First, a control volume-based model identifies the weakly overdriven region for stable wave formation, showing dependence on the inflow Mach number and highlighting the impact of incomplete heat release. Second, high-fidelity simulations with multistep chemical kinetics capture the formation of surface instabilities and the nature of the detonation waves. The thermodynamic analysis tool, validated against experimental data, computes detonation polars using a multi-species gas description and provides crucial insights into post-detonation properties and deflection angles for various cone half-angles. The results indicate that the regime of weakly overdriven detonations is confined by flow conditions and turning angles, with net heat release diminishing as these parameters increase. For the highest Mach number and turning angle considered, the heat release is observed to be less than 25% of the reaction enthalpy for the mixture. High-fidelity simulations corroborate the thermodynamic analysis and further demonstrate the formation of cellular instabilities on the detonation surface. For a conical system characterized by significant isentropic expansion and weaker initial shock compared to two-dimensional wedges, transverse waves reflecting off the cone surface lead to the formation of triple points, which catalyze instabilities. The overall detonation structure in conical systems is similar to that of two-dimensional wedge-based oblique detonations and planar cellular detonations.
... Over the last decade, significant research efforts have focused on the development of detonation-based propulsion and power generation technologies, including rotating detonation engines (RDEs) [1,2], pulse detonation engines (PDEs) [3,4], linear or reflective detonation engines [5,6], and oblique detonation wave engines (ODWEs) [7][8][9]. While most studies have focused on gaseous fueling, practical detonation engines must be able to leverage the higher energy densities of liquid fuels. ...
... The solver is a multi-phase adaptation of an in-house compressible reacting flow solver [35], which has been extensively used to simulate high-speed flows [7,[36][37][38][39][40]. Block-structured adaptive mesh refinement is handled by the AMReX framework [41]. ...
Detonation-based propulsion devices, such as rotating detonation engines (RDEs), must be able to leverage the higher energy densities of liquid fuels in order for them to be utilized in practical contexts. This necessitates a comprehensive understanding of the physical processes and timescales that dictate the shock-induced breakup of liquid droplets. These processes are difficult to probe and quantify experimentally, often limiting measurements to macroscopic properties. Here, fundamental mechanisms in such interactions are elucidated through detailed numerical simulation of Mach 2 and 3 shock waves interacting with 100 m water droplets. Using a thermodynamically consistent two-phase formulation with adaptive mesh refinement, the simulations capture droplet surface instabilities and atomization into secondary droplets in great detail. The results show that droplet breakup occurs through a coupled multi-stage process, including droplet flattening, formation of surface instabilities and piercing, and the shedding of secondary droplets from the ligaments of the deformed primary droplet. When considering the dimensionless timescale of Ranger and Nicholls (), these processes occur at similar rates for the different shock strengths. The PDFs for the Sauter mean diameters of secondary droplets are bimodal log-normal distributions at . Modest differences in the degree and rate of liquid mass transfer into droplets less than 5 m in diameter are hypothesized to partially derive from differences in droplet surface piercing modes. These results are illustrative of the complex multi-scale processes driving droplet breakup and have implications for the ability of shocks to effectively process liquid fuels.
... This allows spatiotemporally-evolving flow features to be captured via user-defined refinement criteria. This solver, as well as its gas-phase predecessors [58,60], have been extensively utilized to study high-speed reacting flows [11,15,50,[61][62][63][64][65][66]. ...
Canonical jet in supersonic crossflow studies have been widely used to study fundamental physics relevant to a variety of applications. While most JISC works have considered gaseous injection, liquid injection is also of practical interest and introduces additional multiscale physics, such as atomization and evaporation, that complicate the flow dynamics. To facilitate further understanding of these complex phenomena, this work presents multiphase simulations of reacting and non-reacting JISC configurations with freestream Mach numbers of roughly 4.5. Adaptive mesh refinement is used with a volume of fluid scheme to capture liquid breakup and turbulent mixing at high resolution. The results compare the effects of the jet momentum ratio and freestream temperature on jet penetration, mixing, and combustion dynamics. For similar jet momentum ratios, the jet penetration and mixing characteristics are similar for the reacting and non-reacting cases. Mixing analyses reveal that vorticity and turbulent kinetic energy intensities peak in the jet shear layers, where vortex stretching is the dominant turbulence generation mechanism for all cases. Cases with lower freestream temperatures yield negligible heat release, while cases with elevated freestream temperatures exhibit chemical reactions primarily along the leading bow shock and within the boundary layer in the jet wake. The evaporative cooling quenches the chemical reactions in the primary atomization zone at the injection height, such that the flow rates of several product species plateau after x/d=20. Substantial concentrations of final product species are only observed along the bow shock-due to locally elevated temperature and pressure-and in the boundary layer far downstream-where lower flow velocities counteract the effects of prolonged ignition delays. This combination of factors leads to low combustion efficiency at the domain exit.
This study reports the first experiments of a large-scale hydrogen-fueled oblique detonation engine model conducted in a hypersonic wind tunnel. The stabilization characteristic of oblique detonation wave, the specific combustion mode and the corresponding flow structures are emphasized. Results show that by adjusting the geometry of the combustor in different tests, two stabilized oblique detonation combustion modes relevant to the two theoretical branches of oblique detonation at a given wedge angle, referred to as the strong oblique detonation mode and the weak oblique detonation mode, respectively, are consequently implemented in the combustor.
Significance
There is now an intensifying international effort to develop robust propulsion systems for hypersonic and supersonic flight. Such a system would allow flight through our atmosphere at very high speeds and allow efficient entry and exit from planetary atmospheres. The possibility of basing such a system on detonations, the most powerful form of combustion, has the potential to provide higher thermodynamic efficiency, enhanced reliability, and reduced emissions. This work reports a significant step in attaining this goal: the discovery of an experimental configuration and flow conditions that generate a stabilized oblique detonation, a phenomenon that has the potential to revolutionize high-speed propulsion of the future.
High-fidelity simulations of turbulent flames are computationally expensive when using detailed chemical kinetics. For practical fuels and flow configurations, chemical kinetics can account for the vast majority of the computational time due to the highly non-linear nature of multi-step chemistry mechanisms and the inherent stiffness of combustion chemistry. While reducing this cost has been a key focus area in combustion modeling, the recent growth in graphics processing units (GPUs) that offer very fast arithmetic processing, combined with the development of highly optimized libraries for artificial neural networks used in machine learning, provides a unique pathway for acceleration. The goal of this paper is to recast Arrhenius kinetics as a neural network using matrix-based formulations. Unlike ANNs that rely on data, this formulation does not require training and exactly represents the chemistry mechanism. More specifically, connections between the exact matrix equations for kinetics and traditional artificial neural network layers are used to enable the usage of GPU-optimized linear algebra libraries without the need for modeling. Regarding GPU performance, speedup and saturation behaviors are assessed for several chemical mechanisms of varying complexity. The performance analysis is based on trends for absolute compute times and throughput for the various arithmetic operations encountered during the source term computation. The goals are ultimately to provide insights into how the source term calculations scale with the reaction mechanism complexity, which types of reactions benefit the GPU formulations most, and how to exploit the matrix-based formulations to provide optimal speedup for large mechanisms by using sparsity properties. Overall, the GPU performance for the species source term evaluations reveals many informative trends with regards to the effect of cell number on device saturation and speedup. Most importantly, it is shown that the matrix-based method enables highly efficient GPU performance across the board, achieving near-peak performance in saturated regimes.
The purpose of this paper is twofold. First, the application of high-order methods in combination with the popular HLLC Riemann solver demonstrates that the grid-aligned shock instability can strongly affect simulation results when the grid resolution is increased. Beyond the well-documented two-dimensional behavior, the problem is particularly troublesome with three-dimensional simulations. Hence, there is a need for shock-stable modifications of HLLC-type solvers for high-speed flow simulations.
Second, the paper provides a stabilization of the popular HLLC flux based on a recently proposed mechanism for grid aligned-shock instabilities [Fleischmann et al., JCP 401(2020): 109004]. The instability was found to be triggered by an inappropriate scaling of acoustic and advection dissipation for local low Mach numbers. These low Mach numbers occur during the calculation of fluxes in transverse direction of the shock propagation, where the local velocity component vanishes. A centralized formulation of the HLLC flux is provided for this purpose, which allows for a simple reduction of nonlinear signal speeds. In contrast to other shock-stable versions of the HLLC flux, the resulting HLLC-LM flux reduces the inherent numerical dissipation of the scheme.
The robustness of the proposed scheme is tested for a comprehensive range of cases involving strong shock waves. Three-dimensional single- and multi-component simulations are performed with high-order methods to demonstrate that the HLLC-LM flux also copes with latest challenges of compressible high-speed computational fluid dynamics.
The numerical simulation of supersonic flow over a cone is carried out to investigate oblique detonation waves. A three-dimensional (3D) conical oblique detonation wave is studied by changing the heat release. It is found that the formation of a conical oblique detonation wave shifts from a moderate transition to an abrupt transition and the frontal structure also changes from smooth to cellular features. Moreover, the conical oblique detonation wave approaches detachment as heat release increases. A comparison of oblique detonation waves attached to a 2D wedge and a 3D cone demonstrates that, for a fixed heat release, a cone is able to moderate the transition significantly, and that detaching behavior is also delayed significantly due to curvature as heat release changes. The critical heat release for detachment of the conical oblique detonation wave is much larger than that of the wedge-induced oblique detonation wave. Moreover, we assess the difference in angles of oblique detonation waves produced by wedges and cones and find that the angle is much smaller than that of wedge-induced oblique detonation wave because of flow divergence caused by the curvature (curved front in the circumference direction of the cone).
The formation and structure of oblique detonation waves initiated by semi-infinite wedges and cones are presented. For wedge or cone angles less than the deflection angle required for an oblique Chapman-Jouguet (CJ) detonation, different wave structures have been previously reported. Using the method of characteristics and numerical simulations, it is shown that, for such low wedge or cone angles, a CJ oblique detonation is eventually initiated following an induction process. It its thus demonstrated that shock-induced combustion with the reaction front remaining uncoupled to the oblique shock in the far field is not a valid solution. Simulations with semi-infinite cones reveal that the effect of the front curvature around the cone axis allows oblique detonations to be formed at angles lower than that of a planar CJ oblique detonation.
Initiation of detonation by a hypersonic conical projectile launched into a combustible gas mixture is investigated. From analytic considerations of the flowfield, energetic and kinetic limits are proposed to predict the conditions required to initiate an oblique detonation wave in the mixture. To experimentally investigate these limits, projectiles with cone half angles varying from 15° to 60° were launched into a stoichiometric mixture of hydrogen/oxygen with 70% argon dilution at initial pressure between 10 and 200kPa. The projectiles were launched from a combustion-driven gas gun at velocities as great as 2.5km/s (corresponding to 150% of the Chapman Jouguet velocity). Pictures of the flowfields generated by the projectiles were taken via schlieren photography. Five combustion regimes could be observed about the projectile ranging from a prompt and delayed oblique detonation wave formation, combustion instabilities, a wave splitting, and an inert shock wave. The two theoretical limits provide a means to interpret the observed flowfield regimes and are in satisfactory agreement with the experimental results.
Wave combustors, which include the Oblique Detonation Wave Engine (ODWE), are attractive propulsion concepts for hypersonic flight. These engines utilize oblique shock or detonation waves to rapidly mix, ignite, and combust the air-fuel mixture in thin zones in the combustion chamber. Benefits of these combustion systems include shorter and lighter engines which will require less cooling and can provide thrust at higher Mach numbers than conventional scramjets. The wave combustor's ability to operate at lower combustor inlet pressures may allow the vehicle to operate at lower dynamic pressures which could lessen the heating loads on the airframe. The research program at NASA-Ames includes analytical studies of the ODWE combustor using CFD codes which fully couple finite rate chemistry with fluid dynamics. In addition, experimental proof-of-concept studies are being carried out in an arc heated hypersonic wind tunnel. Several fuel injection designs were studied analytically and experimentally. In-stream strut fuel injectors were chosen to provide good mixing with minimal stagnation pressure losses. Measurements of flow field properties behind the oblique wave are compared to analytical predictions.
Gaseous cellular detonation is unsteady, and its propagation dynamics in a uniform mixture have been widely studied, but there are few works on cellular detonations in continuously disturbed media. Based on two fundamental propagation modes: stable (with regular cells) or unstable (with irregular cells), this study uses the Euler equations coupled with a two-step chemical reaction model to investigate two-dimensional cellular detonations with longitudinal disturbances. Disturbed detonations are generated by introducing a longitudinal sinusoidal density disturbance whose bifurcation parameter is the disturbance wavelength λ. The detonation cell distributions and propagation features are analyzed by recording the maximum local pressure and presenting the frequency spectrum of the averaged cell pressure. It is observed that the ratio of longitudinal disturbance wavelength λ to reaction zone width WR plays an important role in cell morphology. For regular detonations, the cell scale changes periodically with the disturbance cycle, and the fundamental frequency of the averaged pressure signals is consistent with the disturbance frequency when this ratio is much greater than 1. If the ratio has a single-digit value, the original coupling relationship of shock waves and reaction fronts is destroyed and rebuilt, leading to an intermittent and local detonation decoupling and reinitiation. The size of newly formed large cells reaches about 3–6 times the size of the undisturbed cell. However, there are different cell-size spectra for stable and unstable detonations attributed to different transverse wave regularities. By introducing acoustic impedance analyses, the interaction of the detonation wave and varying density interface is presented, and the role of a sinusoidal density disturbance in wave dynamics is discussed.
In this paper, we investigate the formation and development characteristics of oblique detonation wave in stoichiometric hydrogen-oxygen mixtures diluted with argon using Euler equations coupled with the 19-step or 34-step chemical reaction model. The novelty of this work lies in the study of differences in the characteristics of the initiation region and the formation processes of oblique detonation by different chemical kinetic processes. The formation processes of radicals in the induction region and heat release region for the oblique detonation flow field are emphatically analyzed, and the differences in the sensitivity on the key chemical reaction channels to radicals are also discussed. The results show that under the action of 19-step mechanism, the oblique detonation forms relatively early, the wave morphology of the flow field is complex, and the type of the initiation region is abrupt transition. While for the 34-step mechanism, the structure of flow field is simple with smooth transition type. The existence of transverse wave in the mainstream region contributes a lot to the formation of a sonic region and the abrupt transition structure. The chemical kinetic process directly affects the flow field structure of oblique detonation, and H2O2 plays an important role on triggering and accelerating the exothermic process. The radicals of H, O and H2O2 have different properties in different chemical reaction models.
Previous studies of a high-speed blunt projectile in a combustible mixture found two oscillating unsteady combustion modes induced by the curved shock, referred to as high- and low-frequency modes. A new unsteady combustion mode is observed in the present study. The frequency reaches approximately twice the high frequency and is referred to as the super-high frequency to maintain consistency with the terminology used in previous works. The super-high-frequency mode appears in cases of a small sphere diameter, and with a proper diameter, an intermediate mode arises with the co-existence of both high and the super-high frequencies. An analysis of pressure and temperature gradients along the stagnation streamline attributes the oscillation of combustion to the interaction of compression and entropy waves between the shock and flame front. If the compression/entropy waves affect the flame front of the next cycle, the high-frequency mode arises; this is consistent with the results of previous works. However, weakened compression/entropy waves in cases of a small sphere diameter only affect the flame front of every other cycle, leading to the super-high-frequency mode.
The understanding of oblique detonation dynamics has both inherent basic research value for high-speed compressible reacting flow and propulsion application in hypersonic aerospace systems. In this study, the oblique detonation structures formed by semi-infinite cones are investigated numerically by solving the unsteady, two-dimensional axisymmetric Euler equations with a one-step irreversible Arrhenius reaction model. The present simulation results show that a novel wave structure, featured by two distinct points where there is close-coupling between the shock and combustion front, is depicted when either the cone angle or incident Mach number is reduced. This structure is analyzed by examining the variation of the reaction length scale and comparing the flow field with that of planar, wedge-induced oblique detonations. Further simulations are performed to study the effects of chemical length scale and activation energy, which are both found to influence the formation of this novel structure. The initiation mechanism behind the conical shock is discussed to investigate the interplay between the effect of the Taylor-Maccoll flow, front curvature, and energy releases from the chemical reaction in conical oblique detonations. The observed flow fields are interpreted by means of the energetic limit as in the critical regime for initiation of detonation.
Operator splitting is a numerical method of computing the solution to a differential equation. The splitting method separates the original equation into two parts over a time step, separately computes the solution to each part, and then combines the two separate solutions to form a solution to the original equation. A canonical example is splitting of diffusion terms and convection terms in a convection-diffusion partial differential equation. Related applications of splitting for reaction-diffusion partial differential equations in chemistry and in biology are emphasized here. The splitting idea generalizes in a natural way to equations with more than two operators. In all cases, the computational advantage is that it is faster to compute the solution of the split terms separately, than to compute the solution directly when they are treated together. However, this comes at the cost of an error introduced by the splitting, so strategies have been devised to control this error. This chapter introduces splitting methods and surveys recent developments in the area. An interesting perspective on absorbing boundary conditions in wave equations comes via Toeplitz-plus-Hankel splitting. One recent development, balanced splitting, deserves and receives special mention: it is a new splitting method that correctly captures steady state behavior.
To demonstrate heat addition to supersonic flow by shock-induced combustion three test series were carried out. Spherical and conical projectiles were shot into explosive mixtures of hydrogen/air and hydrogen/oxygen at pressures between 186 and 422 Torr. The models had a diameter of 15 mm and reached velocities from 1600 m/sec which corresponds to the Mach numbers 4.0-6.5. The chemical reaction was caused and stabilized by the bow wave originating at the tip of the model moving at supersonic speed. When spherical projectiles are fired into a hydrogen/air mixture the reaction wave is pulsating as long as the model velocity is inferior to the detonation velocity of the explosive mixture. These instabilities could be explained by the induction time and it was also possible to measure the corresponding distance directly from the photographs. With hydrogen/oxygen mixture a self-sustained detonation could be initiated when the model velocity reached a certain limit. Theoretical considerations on heat addition by a deflagration front in a conical stream-the only case of non adiabatic cone flow to be considered here-give an information on the possible flow regimes depending on the deflection angle in the deflagration zone. The existence of such a deflagration front could be proved by experiment. In some cases it was possible to calculate the second Damköhler parameter for heat release. These values varied from 0.5 to 4.4.
We report on a series of experiments performed to characterize oblique detonation wave engine combustor flows. The Caltech T-5 shock tunnel facility was used to provide flows at stagnation enthalpies and pressures representative of the flow into the combustor section of a hypersonic air-breathing oblique detonation wave engine. A hydrogen injection system located within the T-5 nozzle was designed to provide coflowing jets of hydrogen to premix with the T-5 flow upstream of a wedge model placed in the test section. Pressure transducers were placed in the wedge model and Resonant Holographic Interferometry was used to image the concentration of OH in the flow. Hydrogen was injected into T-5 air flow and compared with similar, but nonreacting shots using T-5 nitrogen flow. The total enthalpy and total pressure of the T-5 flow was varied from conditions that resulted in little chemical reaction to conditions that resulted in nearly complete combustion of the hydrogen/air mixture ahead of the wedge model.
A predictive capability for conical oblique detonation waves (ODWs) is discussed with particular attention given to the special case of an axisymmetric conical projectile, which yields necessary conditions for attached waves. A multidimensional numerical model was used to study the influence of a finite Damkoehler number (Da) and viscosity on the formation of a conical ODW. The ODW is predicted for Da on the order of 10, and is found to be important in the ODW formation. For a Da of 1, shock induced combustion is predicted. Simulations of the experimental geometry showed general agreement with experimental flow features, but underpredicted the shock angle. It is suggested that this difference may be caused by inadequate boundary layer resolution, lack of grid orthogonality at the cone surface, and an inappropriate chemical mechanism. 15 refs.
The effect of confinement on the initiation of detonation waves by supersonic projectiles is investigated. For experiments in a large diameter detonation chamber, the projectile bow shock cannot reach the tube wall during the experimental test time, making the experiment effectively unconfined. In this case, a projectile is capable of direct initiation only, wherein the combustion sufficiently couples to the projectile bow shock to propagate as a free-running detonation. If the dimensions of the detonation chamber are reduced to the order of the projectile diameter, multiple bow shock reflections and boundary layer growth can promote ignition and the confinement of the chamber wall can assist in the initiation of detonation via deflagration to detonation transition (DDT) mechanisms. This paper reports an experimental examination into the effect of confinement. Spheres with a diameter of 1.27 cm were fired into a stoichiometric mixture of hydrogen and oxygen diluted with argon. The mixture was contained in a tube 3.81 cm in diameter. Combustion waves were observed to form in the wake of the sphere and eventually overtake the sphere. This result is in contrast with prior experiments in an 18 cm diameter detonation chamber with the same mixture and sphere size. In the large chamber, only direct initiation from the sphere itself was observed. The results indicate that initiation in a confined environment can be realized under a much wider range of conditions (lower projectile Mach numbers and mixture pressures) than in an unconfined environment. The relevance of
The structure of oblique detonation waves stabilized on a hypersonic wedge in mixtures characterized by a large activation energy is investigated via steady method of characteristics (MoC) calculations and unsteady computational flowfield simulations. The steady MoC solutions show that, after the transition from shock-induced combustion to an overdriven oblique detonation, the shock and reaction complex exhibit a spatial oscillation. The degree of overdrive required to suppress this oscillation was found to be nearly equal to the overdrive required to force a one-dimensional piston-driven detonation to be stable, demonstrating the equivalence of two-dimensional steady oblique detonations and one-dimensional unsteady detonations. Full unsteady computational simulations of the flowfield using an adaptive refinement scheme showed that these spatial oscillations are transient in nature, evolving in time into transverse waves on the leading shock front. The formation of left-running transverse waves (facing upstream) precedes the formation of right-running transverse waves (facing downstream). Both sets of waves are convected downstream away from the wedge in the supersonic flow behind the leading oblique front, such that the mechanism of instability must continuously generate new transverse waves from an initially uniform flow. Together, these waves define a cellular structure that is qualitatively similar to a normal propagating detonation.
In this study, numerical simulations using the inviscid Euler equations with one-step Arrhenius chemistry model are carried out to investigate the effects of activation energy and wedge angle on the stability of oblique detonation surfaces. Two kinds of cellular structure are studied, one is featured by a single group of transverse waves traveling upstream, referred to as LRTW (left-running transverse waves), and the other is featured by additional RRTW (right-running transverse waves). The present computational simulation reveals the formation of un-reacted gas pockets behind the cellular oblique detonation. Numerical smoked foil records are produced to show the emergence of the two types of transverse waves and the evolution of the unstable cellular structure of the oblique detonation. The transverse wave dynamics, including the colliding, emerging and splitting types, are found to be similar to the normal detonation propagation, demonstrating the instability mechanism is originated from the inherent instability of cellular detonations. Statistical analysis on the cellular structure is carried out to observe quantitatively the influences of activation energy and wedge angle. Results from the parametric study show that high activation energy and low wedge angle are favorable to the LRTW formation. However, the condition for the RRTW formation is more complex. In the case of low activation energy, small wedge angle is beneficial to the RRTW formation, as to the LRTW formation. In contrary, for high activation energy, there appears one moderate wedge angle favoring the RRTW formation and giving the shortest length between the onset of both LR and RR transverse waves. For quantitative comparison, we analyze the variation of two distances with the wedge angle, one is between the detonation initiation and LRTW formation points, and the other between LRTW and RRTW formation points. Results show the latter is relatively less pronounced than the former, indicating the RRTW formation depends mainly on the activation energy and the generation of LRTW.
Oblique detonation waves are simulated to study the induction zone structures with different incident Ma numbers. Three kinds of shock configurations are observed at the end of the induction zone, which are the λ-shaped shock, the X-shaped shock and the Y-shaped shock. The X-shaped and Y-shaped shocks appear when the incident Ma is low, and the Y-shaped shock associated with the complicated unstationary process. The induction zone length reaches the maximum value when the X-shaped shock changes into the Y-shaped shock, which indicates different mechanisms deciding the induction zone. The oblique shock wave dominates the induction zone when the incident Ma is high, while the oblique detonation wave dominates the induction zone when the incident Ma is low.
Oblique detonation waves are simulated to study the evolution of their morphology as gasdynamic and chemical parameters are varied. Although two kinds of transition pattern have previously been observed, specifically an abrupt transition and a smooth one, the determining factors for the transition pattern are still unclear. Numerical results show that the transition pattern is influenced by the inflow Mach number, chemical activation energy and heat release. Despite the fact that these parameters were known to influence the detonation instability, the transition pattern variation cannot be predicted according to the instability criterion. In this study, the difference in the oblique shock and detonation angles is proposed as the criterion to determine the transition pattern with the aid of shock-polar analysis. It is found that the smooth transition will appear when the angle difference is small, while the abrupt transition will occur when the difference is large. The shift from the smooth transition to the abrupt transition occurs when the angle difference is about –. The previously proposed criterion using the characteristic time ratio is also examined and compared with the present angle difference criterion, and the latter is proved to provide better results.
A survey of propulsion based on detonation of chemical systems is provided in this paper. After a short historical review, basic schematics of engines utilizing detonation as the combustion mechanism are described. Possible improvement of propulsive efficiency due to detonative combustion which results in a significant pressure increase is presented, and a comparison of deflagrative and detonative combustion is discussed. Basic research on Pulsed Detonation Engines (PDE) and rotating detonations in cylindrical and disk-like chambers for different mixtures is presented. Basic principles of engines utilizing Standing Detonation Waves as well as Ram Accelerators are also provided. Detailed descriptions of PDE as well as Rotating Detonation Engines (RDE) are given. Different implementations of the PDE concept are presented and experimental and theoretical results to date are reviewed. Special attention is given to RDE, since rotating detonation can be applied to all kinds of propulsive engines including rocket, ramjet, turbine, and combined-cycle engines. A survey of detonative propulsion research carried out at different laboratories is presented, and possible future applications of such propulsion systems are discussed. A short note on detonative propulsion using non-chemical energy sources is also given.
Proposals have been made to utilize stabilized oblique detonation waves (ODWs) for the propulsion of hypersonic air-breathing vehicles and hypervelocity mass launchers. There exists hypersonic flight regimes where premixing of fuel and air may be desirable or unavoidable due to finite chemical induction times. Consequently, it is essential to understand under what conditions detonations may occur in order to design supersonic combustors to either avoid or utilize them efficiently. A theoretical analysis is made of supersonic flow of a combustible gas mixture past a wedge or an inclined wall, which shows that, for approach velocities roughly 25% or more greater than the Chapman-Jouguet velocity of the reactant mixture, there exists a usefully wide range of turning angles within which ODWs may be attached or stabilized. For smaller wedge angles, either an incomplete ODW, shock-induced combustion, or no combustion at all may ensue. For larger wedge angles, the wave will detach and form an overdriven normal detonation or normal shock-induced combustion wave immediately upstream of the stagnation point, decaying off axis to either a single oblique Chapman-Jouguet wave, or bifurcating to form an oblique shock followed by a shock-induced deflagration.
Detonation structures generated by wedge-induced, oblique shocks in hydrogen–oxygen–nitrogen mixtures were investigated by time-dependent numerical simulations. The simulations show a multidimensional detonation structure consisting of the following elements: (1) a nonreactive, oblique shock, (2) an induction zone, (3) a set of deflagration waves, and (4) a ‘‘reactive shock,’’ in which the shock front is closely coupled with the energy release. In a wide range of flow and mixture conditions, this structure is stable and very resilient to disturbances in the flow. The entire detonation structure is steady on the wedge when the flow behind the structure is completely supersonic. If a part of the flow behind the structure is subsonic, the entire structure may become detached from the wedge and move upstream continuously.
We studied experimentally the shock waves and combustion waves generated by a hypersonic spherical projectile in an explosive mixture. An acetylene/oxygen mixture diluted with argon (2C2H2+5O2+7Ar) was used with various initial pressures (detonation cell sizes) to observe optically with a shadowgraph imaging system a shock-induced combustion (SIC), a stable oblique detonation wave (ODW), and a wave called a Straw Hat type consisting of a strong SIC and ODW. The criticality of stabilizing an ODW around a projectile is expressed by the ratio of the projectile diameter, d, to the cell size, λ, as d/λ=3.63–4.84. Although the Straw Hat type wave in the vicinity of criticality is an unstable phenomena, it has been mainly observed by a single frame picture to date, so that it is difficult to discuss the time history of its wave structure. In this study, it was remarkable to directly carry out continuous optical observations using a high speed video camera which can continuously film 100 pictures with a 1μs frame speed so as to allow an investigation of the sustaining mechanism of the unstable wave structure. Our results allowed the identification of an increase in unsteadiness in the relative distance between the projectile fronts and the transition points to an ODW as the time increased. They also showed local explosions in the SIC region near transition point transformed the ODW front upstream.
Applications of detonations to propulsion are reviewed. First, the advantages of the detonation cycle over the constant pressure combustion cycle, typical of conventional propulsion engines, are discussed. Then the early studies of standing normal detonations, intermittent (or pulsed) detonations, rotating detonations, and oblique shock-induced detonations are reviewed. This is followed by a brief discussion of detonation thrusters, laser- supported detonations and oblique detonation wave engines. Finally, a more detailed review of research during the past decade on ram accelerators and pulsed detonation engines is presented. The impact of the early work on these recent developments and some of the outstanding issues are also discussed. In this paper, the status of propulsion applications of detonations is reviewed. First, a cycle analysis is performed to show that the ef- é ciencyof a detonation cycleisclosetothat of the constant-volume Humphrey cycle, which is much more efécient than the constant- pressure Brayton cycle,characteristicof most conventional propul- sion systems. Other advantages of detonations are also discussed. Then a review of the early attempts to use detonations for propul- sionispresented.Aftera briefdiscussionof the possible reasonsfor the successes and failures of the early attempts, more recent work during the 1980s on oblique detonation wave engines is reviewed. This is followed by a detailedanalysis of the ram acceleratorin the detonative mode and the pulsed detonation engine, a topic of great current interest. Finally, some observations from the lessons learnt in the past and their potential implications for further development of detonations for propulsion applications are presented.
The instability of oblique shock wave (OSW) induced combustion is examined for a wedge with a flow turning angle greater than the maximum attach angle of the oblique detonation wave (ODW), where archival results rarely exist for this case in previous literatures. Numerical simulations were carried out for wedges of different length scales to account for the ratio of the chemical and fluid dynamic time scales. The results reveal three different regimes of combustion. (1) No ignition or decoupled combustion was observed if a fluid dynamic time is shorter than a chemical time behind an OSW. (2) Oscillatory combustion was observed behind an OSW if a fluid dynamic time is longer than a chemical time behind an OSW and the fluid dynamic time is shorter than the chemical time behind a normal shock wave (NSW) at the same Mach number. (3) Detached bow shock-induced combustion (or detached overdriven detonation wave) was observed if a fluid dynamic time is longer than a chemical time behind a NSW. Since no ignition or decoupled combustion occurs as a very slow reaction and the detached wave occurs as an infinitely fast reaction, the finite rate chemistry is considered to be the key for the oscillating combustion induced by an OSW over a wedge of a finite length with a flow turning angle greater than the maximum attach angle for an ODW. Since this case has not been previously reported, grid independency was tested intensively to account for the interaction between the shock and reaction waves and to determine the critical time scale where the oscillating combustion can be observed.
A comprehensive numerical study was carried out to investigate the unsteady cell-like structures of oblique detonation waves (ODWs) for a fixed Mach 7 inlet flow over a wedge of 30° turning angle. The effects of grid resolution and activation energy were examined systematically at a dimensionless heat addition of 10. The ODW front remains stable for a low activation energy regardless of grid resolution, but becomes unstable for a high activation energy featuring a cell-like wave front structure. Similar to the situation with an ordinary normal detonation wave (NDW), a continuous increase in the activation energy eventually causes the wave-front oscillation to transit from a regular to an irregular pattern. The wave structure of an unstable ODW, however, differs considerably from that of a NDW. Under the present flow condition, triple points and transverse waves propagate downstream, and the numerical smoke-foil record exhibits traces of triple points that rarely intersect with each other. Several instability-driving mechanisms were conjectured from the highly refined results. Since the reaction front behind a shock wave can be easily destabilized by disturbance inherent in the flowfield, the ODW front becomes unstable and displays cell-like structures due to the local pressure oscillations and/or the reflected shock waves originating from the triple points. The combined effects of various instability sources give rise to a highly unstable and complex flow structure behind an unstable ODW front.
We present new experimental results demonstrating the initiation and stabilization of an oblique detonation by a hypervelocity projectile. Projectiles 25 mm in diameter were launched at nominal velocities of 2700 m/s into stoichiometric H2-O2-N2 mixtures at pressures between 0.1 and 2.5 bar. A critical threshold in initial pressure was found to be required for the establishment of detonations. Initiation events similar to DDT in propagating waves were observed after 300 mm of travel in H2-O2 mixtures diluted with 25% N2. A more direct initiation process was observed in H2-air mixtures. A stabilized but overdriven oblique detonation was observed in a stoichiometric H2-air mixture at an initial pressure of 2.5 bar.The pressure threshold can be explained in terms of competing reaction and flow-quenching effects along a curving streamline in supersonic flow behind a curved shock wave. This competition can be characterized by a critical Damkohler number Da0, which is inversely proportional to the product of wave curvature κ and reaction zone thickness Δ. Only if the reaction zone is sufficiently thin in comparison with the projectile, Da>Da0, is it possible to obtain stabilized detonations. Otherwise, the reactions quench and the wave splits into a nonreactive shock wave followed by flamelike contact surface. The inverse pressure dependence Δ∼P0−1 of the reaction zone length and the scaling of the wave curvature κ∼1/a with the body radius a implies the standard binary scaling relationship P0a=constant for the critical conditions of stabilization for a given mixture composition characterized by a bimolecular rate-limiting step.
Stable delayed oblique detonation waves have been observed both numerically and experimentally in hydrogen-air stoichiometric mixtures for Mach numbers 6 and 7.5. The experimental results obtained using an oblique shock tube facility are compared to calculations made by solving the full conservation equations for a reactive gas. The overall flow structure obtained experimentally is compared to detailed computations of an oblique shock wave to oblique detonation-wave transition over a wedge, and resulting flow fields are analyzed on the basis of shock and detonation polars.
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