Fluid dynamics of rotating detonation engines with hydrogen and hydrocarbon fuels

Rotating detonation engines (RDE’s) represent a logical step from pulsed detonation engine concepts to a continuous detonation engine concept for obtaining propulsion from the high efficiency detonation cycle. The hydrogen/air and hydrogen/oxygen RDE concepts have been most extensively studied, however, being able to use hydrocarbon fuels is essential for practical RDE’s. The current paper extends our hydrogen/air model to hydrocarbon fuels with both air and pure oxygen as the oxidizer. Before beginning the RDE calculations, several detonation tube results are summarized showing the ability of the code to reproduce the correct detonation velocity and CJ properties. In addition, a calculation capturing the expected irregular detonation cell patterns of ethylene/air is also shown. To do the full range of fuels and oxidizers, we found the use of temperature-dependent thermodynamic properties to be essential, especially for hydrocarbon/oxygen mixtures. The overall results for air-breathing RDE’s with hydrocarbons ranged from 1990 to 2540 s, while in pure oxygen mode the specific impulse varied from 700 to 1070 s. These results were between 85% and 89% of the expected ideal detonation cycle results, and are in line with previous hydrogen/air estimates from our previous work. We conclude from this that hydrocarbon RDE’s are viable and that the basic flow-field patterns and behaviors are very similar to the hydrogen/air cases detailed previously.     

Experimental study of internal flow structures in cylindrical rotating detonation engines

The internal flow structures of detonation wave were experimentally analyzed in an optically accessible hollow rotating detonation combustor with multiple chamber lengths. The cylindrical RDC has a glass chamber wall, 20 mm in diameter, which allowed us to capture the combustion self-luminescence. A chamber 70 mm in length was first tested using C₂H₄O₂ and H₂–O₂ as propellants. Images with a strong self-luminescence region near the bottom were obtained, confirming the small extent of the region where most of the heat release occurs as found in our previous research. Based on the visualization experiments, we tested RDCs with shorter chamber walls of 40 and 20 mm. The detonation wave was also observed in the shorter chambers, and its velocity was not affected by the difference in chamber length. Thrust performance was also maintained compared to the longer chamber, and the short cylindrical RDC had the same specific impulse tendency as the cylindrical (hollow) or annular 70-mm chamber RDC. Finally, we calculated the pressure distributions of various chamber lengths, and found they were also consistent with the measured pressure at the bottom and exit. We concluded that the short-chamber cylindrical RDC with equal length and diameter maintained thrust performance similar to the longer annular RDC, further expanding the potential of compact RDCs.     

Particle path tracking method in two- and three-dimensional continuously rotating detonation engines

The particle path tracking method is proposed and used in two-dimensional（2D） and three-dimensional（3D） numerical simulations of continuously rotating detonation engines（CRDEs）. This method is used to analyze the combustion and expansion processes of the fresh particles, and the thermodynamic cycle process of CRDE. In a 3D CRDE flow field, as the radius of the annulus increases, the no-injection area proportion increases, the non-detonation proportion decreases, and the detonation height decreases. The flow field parameters on the 3D mid annulus are different from in the 2D flow field under the same chamber size. The non-detonation proportion in the 3D flow field is less than in the 2D flow field. In the 2D and 3D CRDE, the paths of the flow particles have only a small fluctuation in the circumferential direction. The numerical thermodynamic cycle processes are qualitatively consistent with the three ideal cycle models, and they are right in between the ideal F–J cycle and ideal ZND cycle. The net mechanical work and thermal efficiency are slightly smaller in the 2D simulation than in the 3D simulation. In the 3D CRDE, as the radius of the annulus increases, the net mechanical work is almost constant, and the thermal efficiency increases. The numerical thermal efficiencies are larger than F–J cycle, and much smaller than ZND cycle.     

A diffuse interface Lox/hydrogen transcritical flame model

We present a diffuse-interface all-pressure flame model that transitions smoothly between subcritical and supercritical conditions. The model involves a non-equilibrium liquid/gas diffuse interface of van der Waals/Korteweg type embedded into a non-ideal multicomponent reactive fluid. The multicomponent transport fluxes are evaluated in their thermodynamic form in order to avoid singularities at thermodynamic mechanical stability limits. The model also takes into account condensing liquid water in order to avoid thermodynamic chemical instabilities. The resulting equations are used to investigate the interface between cold dense and hot light oxygen as well as the structure of diffusion flames between cold dense oxygen and gaseous-like hydrogen at all pressures, either subcritical or supercritical.     

Sensitizing gaseous detonations for hydrogen/ethylene-air mixtures using ozone and H2O2 as dopants for application in rotating detonation engines

The effect of ozone and hydrogen peroxide as dopants on hydrogen-air and ethylene-air detonations was investigated with one-dimensional ZND calculations. Also, the effects of dopants were studied numerically with argon and helium as diluents with an aim to reduce the temperature of detonation products while maintaining a detonation wave of sufficient strength such that its propagation is stable near its propagation limits. The primary goal of the present investigation is to isolate the chemical kinetic effects from fluid and gas dynamic effects by altering the ignition chemistry of an unburned mixture without significantly changing its thermodynamic and physical properties. The ZND calculations demonstrate that the addition of O₃ and H₂O₂ in small quantities will substantially reduce the induction length (Δ_i) and time (τ_i), even with higher diluent percentages of argon and helium, making it a viable solution for reducing the operating temperatures of rotating detonation engines (RDEs). The effects of O₃ and H₂O₂ are also studied numerically at lower equivalence ratios for H₂/C₂H₄-air detonations with an aim to reduce the post-detonation temperatures below 2000 K for its application in practical engine cycles. Also, the efficacy of CF₃I, as an ignition promoter at small quantities, is studied numerically for hydrogen-air detonations, and its performance is compared with O₃ and H₂O₂.     

The effects of flame generated turbulence for turbulent-induced deflagration to detonation transition

The turbulent deflagration to detonation transition (DDT) process occurs when a subsonic flame interacts with intense turbulence resulting in spontaneous acceleration and the onset of DDT. The mechanisms that govern the spontaneous ignition are deduced intricately in numerical simulations. This work experimentally explores the conditions that are known precursors to detonation initiation. More specifically, the experiment presented investigates the role of flame-generated compression as a cycle that continuously amplifies until a hotspot forms on the flame front and ignites. The study quantifies the compression comparatively against other flame regimes through ultra-high speed pressure measurements while qualitatively detailing flame generated compression through density gradients via schlieren imaging. Additionally, flow field measurements are quantified throughout the flow using simultaneous particle image velocimetry (PIV) and OH* chemiluminescence. The turbulence fluctuations and flame speeds are extracted from these measurements to identify the reactant conditions where flame-generated compression begins. Collectively, these simultaneous high-speed measurements provide detailed insight into the flame and flow field characteristics where the runaway process occurs. This work ultimately documents direct flow field measurements to extract the contribution of flame-generated turbulence on the turbulent deflagration to detonation transition process.     

Experimental observations of flame acceleration and transition to detonation following shock-flame interaction

Observations are presented from experiments where laminar flame bubbles were perturbed successively by incident and reflected shock waves. Significant flame acceleration was observed in many instances, with the flame closely coupled to the reflected shock wave. The coupled waves are interpreted using a generalized Hugoniot analysis. As the incident shock velocity increased, detonation emerged near the highly convolved reaction zone. Prior to detonation the external visual attributes of the combustion fronts appear identical to turbulent combustion. However, they cannot be due to classical isotropic turbulence. The overall conclusion is that the observed enhancement of combustion is driven by chemi-acoustic interactions and related gas-dynamic effects. An analysis of the prevailing thermodynamic states suggests that thermal auto-ignition chemistry could also play a significant role prior to the onset of detonation.     

An engineering method for calculating the parameters and characteristics of pulse detonation engines

Theoretical fundamentals for calculating the thermodynamic cycle of engines with fuel detonation (FD cycle), which is realized in the thrust units of pulse detonation engines (PDE), are presented. A system of equations for calculating the parameters of the detonation waves under various conditions of their initiation is derived. These equations were used to examine how various factors influence the parameters of detonation waves and, consequently, the work of the cycle, thermal efficiency, and the specific parameters of the PDE. It was demonstrated that the maximum thermal efficiency of the FD cycle virtually coincides with the minimum losses caused by the irreversibility of heat input into the detonation wave. It was established that the losses are substantially dependent on the temperature of the working substance (compressed air or heated gas) supplied into the thrust units, more specifically, they decrease with increasing temperature.     

Transformation of detonation waves at the interface between bubble media

The passage of detonation waves through the interface between bubble media is studied experimentally. Data are obtained for the structure, velocity, and pressure of an incident detonation wave and a wave transmitted through the interface.     

爆轰波在炸药-金属界面上的折射分析

针对爆轰波在炸药-金属界面上折射时由实验获得的金属折射冲击波压力与经典爆轰波极曲线理论预测的压力存在显著差异这一问题, 本文展开了进一步的理论和数值模拟分析研究. 首先通过分析指出经典爆轰波极曲线理论的缺陷, 并对爆轰波极曲线理论进行了改进, 改进爆轰波极曲线理论给出了炸药爆轰波折射类型以及折射冲击作用点处的压力值. 然后发展了一个基于次特征理论来数值求解爆轰反应流动控制方程的二阶中心型Lagrange方法, 并数值模拟了一个典型的炸药爆轰波折射实验. 改进爆轰波极曲线理论和数值模拟分析结果表明, 爆轰波折射类型有三种:反射冲击波的正规折射、带Mach反射的非正规折射、无反射波的正规折射, 并且金属折射冲击波压力值随入射角增大而单调减小.     

An equation of state for the detonation product of copper oxide/aluminum nanothermite composites

An equation of state (EOS) for the detonation product of the copper oxide/aluminum (CuO/Al) nanothermite composites is developed based on the Chapman–Jouguet (CJ) theory and the nanothermite detonation experiment. The EOS is implemented into a coupled computational fluid dynamics and computational solid dynamics code through the material point method for the model-based simulations of the detonation response of the CuO/Al nanothermite material placed in a small well. The simulations demonstrate the validity of the formulated EOS to catch the essential feature of the detonation response of the CuO/Al nanothermite. The EOS parameters are determined by comparing simulated and experimentally measured pressure–time histories.     

Effects of heat loss and viscosity friction at walls on flame acceleration and deflagration to detonation transition

The coupled effect of wall heat loss and viscosity friction on flame propagation and deflagration to detonation transition(DDT) in micro-scale channel is investigated by high-resolution numerical simulations.The results show that when the heat loss at walls is considered, the oscillating flame presents a reciprocating motion of the flame front.The channel width and Boit number are varied to understand the effect of heat loss on the oscillating flame and DDT.It is found that the oscillating propagation is determined by the competition between wall heat loss and viscous friction.The flame retreat is led by the adverse pressure gradient caused by thermal contraction, while it is inhibited by the viscous effects of wall friction and flame boundary layer.The adverse pressure gradient formed in front of a flame, caused by the heat loss and thermal contraction, is the main reason for the flame retreat.Furthermore, the oscillating flame can develop to a detonation due to the pressure rise by thermal expansion and wall friction.The transition to detonation depends non-monotonically on the channel width.     

Changes in the product composition during the detonation of an unconfined volume of a combustible mixture

For a model problem the solution to which describes the main features of changes in the parameters of the medium in the detonation of an unconfined gas mixture charge of in the air, direct numerical simulation, without of simplifying assumptions on changes in the composition of the mixture, was performed to study changes in the composition of the detonation products, determine the limits of applicability of the chemical equilibrium mixture model, and verify a previously obtained sufficient condition of applicability of the chemical equilibrium mixture model. The results of determining the limits of applicability of the chemical equilibrium mixture model previously obtained using an approximate method were confirmed.     

A second-order accurate material-order-independent interface reconstruction technique for multi-material flow simulations

A new, second-order accurate, volume conservative, material-order-independent interface reconstruction method for multi-material flow simulations is presented. First, materials are located in multi-material computational cells using a piecewise linear reconstruction of the volume fraction function. These material locator points are then used as generators to reconstruct the interface with a weighted Voronoi diagram that matches the volume fractions. The interfaces are then improved by minimizing an objective function that smoothes interface normals while enforcing convexity and volume constraints for the pure material subcells. Convergence tests are shown demonstrating second-order accuracy. Static and dynamic examples are shown illustrating the superior performance of the method over existing material-order-dependent methods.     

On the transition from deflagration to detonation

Feedback between the turbulent-flow and deflagration-wave parameters leads to breakage of the combustion regime. Critical conditions of the development of this instability are formulated.     

论惯性积平移和旋转变换的一般形式

给出了惯性积平移变换的一般关系式和旋转变换的一般关系式,由此可以解决一切惯性积的变换问题.     

A new application of electron energy loss spectroscopy technique for a non-destructive study of the Si-SiO2 interface

Electronic structures of Si(substrate)-SiO₂ (film) interface were examined non-destructively through an application of electron energy loss spectroscopy (ELS) by utilizing variable sampling depth (10 to several tens Å) of probing electrons with different energies (200–2000 eV). The ELS measurements on Si specimens with top oxide layers explored a new feature at the energy of ～ 8 eV in the ELS spectra, which did not exist in the spectra of pure (clean) Si and thick SiO₂. The sharp interfacial structure was proposed and the possible existence of undulation in the Si-SiO₂ interface was discussed.     

Pseudo interface waves observed at the fluid/porous-medium interface. A comparison of two methods

At the fluid/porous-medium interface the pseudo-Rayleigh (pR) and pseudo-Stoneley (pSt) waves exist. The relation with the corresponding poles in the slowness plane is not unambiguous, depending on the choice of branch cuts. For a point-force excitation, the far-field Green's functions are computed using vertical branch cuts (method I) implying that the pR- and pSt-poles obey the radiation condition. Then, a separate pseudo interface wave is entirely captured by the corresponding pole residue because the loop integral along a branch cut contributes to a body wave only. When hyperbolic branch cuts are used (method II) the poles lie on the "principal" Riemann sheet. Then, also the loop integrals necessarily contribute to the pR-wave because the pR-pole is different from that in method I. They do not contribute to the pSt-wave when the pSt-pole lies on the principal Riemann sheet because the pole is identical to that in method I. When the pSt-pole has migrated to another Riemann sheet, however, the pSt-wave is fully captured by the loop integrals. In conclusion, the phase velocity and attenuation of a separate pseudo interface wave can be computed from the pole location in method I, but should be extracted from the full response in method II.     

A homogeneous superspace relevant to superconformal field theory

An infinite-dimensional homogeneous superspace, determined by the choice of annihilation operators in a superconformal field theory, is introduced. Regularization of the field theory induces a central extension for the group which acts transitively on the space, and the cocycle for the central extension is computed. The vacuum states for the theory form a line bundle over the homogeneous superspace, and the curvature of the line bundle is calculated.     

Flame acceleration and the transition to detonation of stoichiometric ethylene/oxygen in microscale tubes

Flame propagation in capillary tubes with smooth circular cross-sections and diameters of 0.5, 1.0, and 2.0 mm are investigated using high-speed photography. Flames were found to propagate and accelerate to detonation speed in stoichiometric ethylene and oxygen mixtures initially at room temperature in all three tube diameters. Ignition occurs at the midpoint along the length of the tube. We observe for the first time transition to detonation in micro-tubes. Detonation was observed with both spark and hot-wire ignition. Tubes with larger diameters take longer to transition to detonation. In fact, transition distance scales with the diameter in our 1.0 and 2.0 mm cases with spark ignition. Flame structures are observed for various stages of the process. Three types of flame propagation modes were observed in the 0.5 mm tube with spark ignition: (a) acceleration to Chapman–Jouguet (CJ) detonation speed followed by constant CJ wave propagation, (b) acceleration to CJ speed, followed by the detonation wave failure, and (c) flame acceleration to a constant speed below the CJ speed of approximately 1600 m/s. The current detonation mechanism observed in capillary tubes is applicable to predetonators for pulsed detonation, micro propulsion devices, safety issues, and addresses fundamental issues raised by recent theoretical and numerical analyses.