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.     

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 flame technique to isolate the detonation/product interface relevant to rotating detonation engines

A novel experimental technique is proposed to study the detonation propagation in a layer of non-reacted gas weakly confined by combustion products. This problem is relevant to rotating detonation engines, where transverse detonations are confined by products of a previous rotation cycle, and other applications such as industrial safety. The experimental technique utilizes a flame ignited along the top wall in a long channel. The preferential growth of the flame along the long direction of the channel creates a finger flame and permits to create a narrow layer of unburned gas. A detonation ignited outside of this layer then propagates through the layer. This permits to conduct accurate observations of the detonation interaction with the inert gas and determine the boundary condition of the interaction. The present paper provides a proof-of-concept demonstration of the technique in a 3.4 m by 0.2 m channel, in which long finger flames were observed in ethylene-oxygen mixtures. The flame is visualized by high-speed direct luminosity over its entire travel, coupled with pressure measurements. A direct simulation of the flame growth served to supplement the experiments and evaluate the role of the induced flow by the flame growth, which gives rise to a non-uniform velocity distribution along the channel length. Detonation experiments were also performed at various layer heights in order to establish the details of the interaction. The structure was visualized using high speed Schlieren video. It was found that an inert shock always runs ahead of the detonation wave, which gives rise to a unique double shock reflection interaction.     

Computational study of NOx formation in hydrogen-fuelled pulse detonation engines

The formation of NOx in hydrogen-fuelled pulse detonation engines (PDE) is investigated numerically. The computations are based on the axisymmetric Euler equations and a detailed combustion model consisting of 12 species and 27 reactions. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation front. Computed NO concentrations are in good agreement with experimental measurements obtained at two operating frequencies and two equivalence ratios. Additional computations examine the effects of equivalence ratio and residence time on NOx formation at ambient conditions. The results indicate that NOx formation in PDEs is very high for near stoichiometric mixtures. NOx reduction requires use of lean or rich mixtures and the shortest possible detonation tube. NOx emissions for very lean or very rich mixtures are, however, fairly insensitive to residence time.     

Turbulent structures in cylindrical density currents in a rotating frame of reference

Gravity currents are flows generated by the action of gravity on fluids with different densities. In some geophysical applications, modeling such flows makes it necessary to account for rotating effects, modifying the dynamics of the flow. While previous works on rotating stratified flows focused on currents of large Coriolis number, the present work focuses on flows with small Coriolis numbers (i.e. moderate-to-large Rossby numbers). In this work, cylindrical rotating gravity currents are investigated by means of highly resolved simulations. A brief analysis of the mean flow evolution to the final state is presented to provide a complete picture of the flow dynamics. The numerical results, showing the well-known oscillatory behavior of the flow (inertial waves) and a final state lens shape (geostrophic adjustment), are in good agreement with experimental observations and theoretical models. The turbulent structures in the flow are visualized and described using, among others, a stereoscopic visualization and videos as supplementary material. In particular, the structure of the lobes and clefts at the front of the current is presented in association to local turbulent structures. In rotating gravity currents, the vortices observed at the lobes front are not of hairpin type but are rather of Kelvin-Helmholtz type.     

Rarefied molecular gas flow near the rotating cylindrical surface

An exact analytic solution of the problem of the right circular cylinder in a rarefied molecular gas is constructed in the isothermal approximation. An expression for the velocity of a rarefied molecular gas entrained by the cylinder rotated therein is obtained in the regime of a flow with slip accounting for the second-order correction in terms of the Knudsen number. A generalization of the BGK model of the Boltzmann kinetic equation accounting for the rotational degrees of freedom of gas molecules is used as the governing equation, and the diffuse reflection model is used as a microscopic boundary condition on the cylinder surface. The given approach is shown to enable the consideration of the gas flow dependence on the Prandtl number and the gas temperature.     

Critical condition of inner cylinder radius for sustaining rotating detonation waves in rotating detonation engine thruster

We describe the critical condition necessary for the inner cylinder radius of a rotating detonation engine (RDE) used for in-space rocket propulsion to sustain adequate thruster performance. Using gaseous C₂H₄ and O₂ as the propellant, we measured thrust and impulse of the RDE experimentally, varying in the inner cylinder radius r_i from 31 mm (typical annular configuration) to 0 (no-inner-cylinder configuration), while keeping the outer cylinder radius (r_o = 39 mm) and propellant injector position (r_inj = 35 mm) constant. In the experiments, we also performed high-speed imaging of self-luminescence in the combustion chamber and engine plume. In the case of relatively large inner cylinder radii (r_i = 23 and 31 mm), rotating detonation waves in the combustion chamber attached to the inner cylinder surface, whereas for relatively small inner cylinder radii (r_i = 0, 9, and 15 mm), rotating detonation waves were observed to detach from the inner cylinder surface. In these small inner radii cases, strong chemical luminescence was observed in the plume, probably due to the existence of soot. On the other hand, for cases where r_i = 15, 23, and 31 mm, the specific impulses were greater than 80% of the ideal value at correct expansion. Meanwhile, for cases r_i = 0 and 9 mm, the specific impulses were below 80% of the ideal expansion value. This was considered to be due to the imperfect detonation combustion (deflagration combustion) observed in small inner cylinder radius cases. Our results suggest that in our experimental conditions, r_i = 15 mm was close to the critical condition for sustaining rotating detonation in a suitable state for efficient thrust generation. This condition in the inner cylinder radius corresponds to a condition in the reduced unburned layer height of 4.5–6.5.     

Zonal flow induced by longitudinal librations of a rotating cylindrical cavity

Longitudinal librations represent oscillations about the axis of a rotating axisymmetric fluid filled cavity. An analytical theory is developed for the case of a cylindrical cavity in the limit when the libration frequency is small in comparison with the rotation rate, but large in comparison with the inverse of the spin-up time. It is shown that through the nonlinear advection in the Ekman layers the librations cause the fluid to rotate more slowly.     

Experimental investigation of in-duct insertion loss of catalysts in internal combustion engines

Acoustic performance characteristics of catalysts in the exhaust system are important in the development of predictive tools for the breathing system of internal combustion engines. To understand the wave attenuation behavior of these elements with firing engines, dynamometer experiments are conducted on a 3.0L V-6 engine with two different exhaust systems: one with the catalysts on the cross-over pipe, and the other that replaces the catalysts with equal length straight pipes. The instantaneous crank-angle resolved pressure data are acquired at wide open throttle and 500 rpm intervals over the operating range of the engine (from 1000 to 5000 rpm) at various locations in both exhaust systems. The effect of the catalyst is then isolated and discussed in terms of insertion loss at critical locations in the exhaust system. The analysis is presented both in terms of time-domain and order-domain. The predictive capability of a finite-difference based time-domain nonlinear approach is also demonstrated as applied to large amplitude waves in the exhaust system of firing engines.     

Transverse wave generation mechanism in rotating detonation

Detonation engines are expected to be included in a number of aerospace thrusters in the future. Several types of detonation engines are currently under examination, including the rotating detonation engine (RDE). Although the RDE has been explored experimentally, its rotating detonation propagation mechanism is not well understood. This paper clarifies the detonation mechanism and dynamics of the RDE by 2D and 3D simulation using compressible Euler equations with a full chemical reaction mechanism of H₂/O₂ and H₂/Air, especially from the triple-point and transverse detonation points of view. A total variation diminishing (TVD) scheme is used for the mixture of H₂/Air, and an advection upwind splitting method difference vector (AUSMDV) scheme is used for the mixture of H₂/O₂. The use of an AUSMDV scheme provides a much clearer detonation structure than does the TVD scheme. We focus on the complex interaction mechanism of the detonation front and burned mixture gases. We found out that at this interaction point, an unreacted gas pocket appears and ignites periodically to generate transverse waves at the detonation front and maintain detonation propagation.     

涡轮导向器对旋转爆轰波传播特性影响的实验研究

为了研究涡轮导向器对旋转爆轰波传播特性的影响,以氢气为燃料,空气为氧化剂,在不同当量比下开展了实验研究.基于高频压力传感器及静态压力传感器的信号,详细分析了带涡轮导向器的旋转爆轰燃烧室的工作模式以及涡轮导向器对非均匀不稳定爆轰产物的影响.实验结果表明:在当量比较低时,爆轰燃烧室以快速爆燃模式工作;逐渐增大当量比,爆轰燃烧室开始以不稳定旋转爆轰模式工作;继续增大当量比,爆轰燃烧室以稳定旋转爆轰模式工作,且旋转爆轰波的传播速度和稳定性均随当量比的增大逐渐提高.爆轰波下游的斜激波与涡轮导向器相互作用,涡轮导向器对压力振荡的幅值具有明显的抑制作用,但对压力振荡频率的影响较小.随着当量比的增大,涡轮导向器上下游的静压均同时增大,经过涡轮导向器的作用,涡轮下游静压明显降低.     

Stabilization mechanisms of longitudinal pulsations in rotating detonation combustors

This work investigates the stabilization mechanisms of two types of longitudinal pulsations in rotating detonation combustors. The first type is linked to operating modes with two counter-rotating waves in combustors with open outlets and appears as a minor peak in the pressure spectrum. The second type is observed as pulsed operation of the combustor when the outlet is restricted. Different combustor lengths are studied and the susceptibility to these longitudinal pulsations is investigated. Pressure measurements along the length of the combustor and around the perimeter are used to identify the operating mode and to describe the propagation and stabilization mechanisms of the two longitudinal modes. The results show that both modes are linked to the longitudinal acoustic resonance of the combustor. The length-to-perimeter ratio and the mass flux are identified as the driving parameters for the existence of these longitudinal modes. The first mode is shown to be an acoustic resonance supported by the intersections of counter-rotating waves. The second mode is controlled by the reflection of an explosion induced shock wave propagating through a high velocity bulk flow.     

Mixing and detonation structure in a rotating detonation engine with an axial air inlet

High-fidelity simulations of an experimental rotating detonation engine with an axial air inlet were conducted. The system operated with hydrogen as fuel at globally stoichiometric conditions. Instantaneous data showed that the detonation front is highly corrugated, and is considerably weaker than an ideal Chapman–Jouguet wave. Regions of deflagration are present ahead of the wave, caused by mixing with product gases from the previous cycle, as well as the injector recovery process. It is found that as the post-detonation high pressure flow expands, the injectors recover unsteadily, leading to a transient mixing process ahead of the next cycle. The resulting flow structure not only promotes mixing between product and reactant gases, but also increases likelihood of autoignition. These results show that the detonation process is very sensitive to injector design and the transient behavior during the detonation cycle. Phase-averaged statistics and conditionally averaged data are used to understand the overall reaction structure. Comparisons with available experimental data on this configuration show remarkable good agreement of the predicted reacting flow structure.