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In this study, the three-dimensional non-premixed two-phase kerosene/air rotating detonation engines with different isolator configurations and throat area ratios are simulated by the Eulerian-Lagrangian method. The effects of the divergence, straight, and convergence isolators on the rotating detonation wave dynamics and the upstream oblique shock wave propagation mechanism are analyzed. The differences in the rotating detonation wave behaviors between ground and flight operations are clarified. The results indicate that the propagation regimes of the upstream oblique shock wave depend on the isolator configurations and operation conditions. With a divergence isolator, the airflow is accelerated throughout the isolator and divergence section, leading to a maximum Mach number (∼1.8) before the normal shock. The total pressure loss reaches the largest, and the detonation pressure drops. The upstream oblique shock wave can be suppressed within the divergence section with the divergence isolator. However, for the straight and convergence isolators, the airflow in the isolator with a larger ψ1 (0.3 and 0.4) can suffer from the disturbance of the upstream oblique shock wave. The critical incident angle is around 39° at ground operation conditions. The upstream oblique shock wave tends to be suppressed when the engine operates under flight operation conditions. The critical pressure ratio βcr0 is found to be able to help in distinguishing the propagation regimes of the upstream oblique shock wave. Slightly below or above the βcr0 can obtain different marginal propagation results. The high-speed airflow in the divergence section affects the fuel droplet penetration distance, which deteriorates the reactant mixing and the detonation area. Significant detonation velocity deficits are observed and the maximum velocity deficit reaches 26%. The results indicate the engine channel design should adopt different isolator configurations based on the purpose of total pressure loss or disturbance suppression. This study can provide useful guidance for the channel design of a more complete two-phase rotating detonation engine.

The regimes of development of a 500 ns sliding surface discharge are experimentally studied in time-dependent supersonic air flows in the channel of shock tube with a rectangular cross-section. The Mach numbers of the shock waves were from 2.30 to 5.00 at the initial air pressures from 2 to 100 Torr and the Mach numbers in the flow were from 1.18 to 1.66. A 100 mm-long sliding surface discharge was initiated at a given moment of time in different stages of the time-dependent supersonic flow after plane shock wave diffraction on an obstacle and in a quasistationary flow past the obstacle in the presence of an inclined shock wave. The discharge current and spatial radiation characteristics were analyzed. The high-speed shadowgraphy of the flow fields was carried out at the frequency up to 525 000 frames per second. The numerical modeling of the channel flow was performed within the framework of the Navier–Stokes equations. The comparison of the experimental and numerical results made it possible to establish the correlation between the parameters of a low-density zone formed as a result of the interaction between the oblique shock wave and a boundary layer and the regime in which the discharge current proceeds. The flow structure in the channel is analyzed after the discharge initiation, when a near-semi-cylindrical shock wave is formed. The comparison of the experimental and numerical results shows the thermal energy released in the discharge current region amounts to from 0.15 to 0.36 J.

This article presents the results of simulation for a special type of vortex tubes – self-vacuuming vortex tube (SVT), for which extreme values of temperature separation and pressure drop are realized. The main results of this study are the flow structure in the SVT and energy loss estimations on oblique shock waves, gas friction, instant expansion and organization of vortex bundles in SVT.

This article presents the results of simulation for a special type of vortex tubes - self-vacuuming vortex tube (SVVT), for which extreme values of temperature separation and vacuum are realized. The main results of this study are the flow structure in the SVVT and energy loss estimations on oblique shock waves, gas friction, instant expansion and organization of vortex bundles in SVVT.

The mechanism of turbulence amplification in shock-wave/boundary layer interactions is reviewed, and a new turbulence amplification mechanism is proposed based on the analysis of data from direct numerical simulation of an oblique shock-wave/flat-plate boundary layer interaction at Mach 2.25. In the upstream part of the interaction zone, the amplification of turbulence is not essentially shear driven, but induced by the interaction of the deceleration of mean flow with streamwise velocity fluctuations, which causes a rapid increase of turbulence intensity in the near-wall region. In the downstream part of the interaction zone, the high turbulence intensity is mainly due to the free shear layer generated in the interaction zone. During the initial stage of turbulence amplification, the characteristics of wall turbulence, including compact velocity streaks, streamwise vortices and an anisotropic Reynolds stress, are well preserved. The mechanism proposed explains the high level of turbulence in the near-wall region observed in some experiments and numerical simulations.

A direct numerical simulation of an oblique shock wave impinging on a turbulent boundary layer at Mach number 2.28 is carried out at moderate Reynolds number, simulating flow conditions similar to those of the experiment by Dupont et al. (J. Fluid Mech., vol. 559, 2006, pp. 255–277). The low-frequency shock unsteadiness, whose characteristics have been the focus of considerable research efforts, is here investigated via the Morlet wavelet transform. Owing to its compact support in both physical and Fourier spaces, the wavelet transformation makes it possible to track the time evolution of the various scales of the wall-pressure fluctuations. This property also makes it possible to define a local intermittency measure, representing a frequency-dependent flatness factor, to pinpoint the bursts of energy that characterise the shock intermittency scale by scale. As a major result, wavelet decomposition shows that the broadband shock movement is actually the result of a collection of sparse events in time, each characterised by its own temporal scale. This feature is hidden by the classical Fourier analysis, which can only show the time-averaged behaviour. Then, we propose a procedure to process any relevant time series, such as the time history of the wall pressure or that of the separation bubble extent, in which we use a condition based on the local intermittency measure to filter out the turbulent content in the proximity of the shock foot and to isolate only the intermittent component of the signal. In addition, wavelet analysis reveals the intermittent behaviour also of the breathing motion of the recirculation bubble behind the reflected shock, and allows us to detect a direct, partial correspondence between the most significant intermittent events of the separation region and those of the wall pressure at the foot of the shock.

We use resolvent analysis to develop a physics-based, open-loop, unsteady control strategy to attenuate pressure fluctuations in turbulent flow over a rectangular cavity with a length-to-depth ratio of $6$ at a Mach number of $1.4$ and a Reynolds number based on cavity depth of $10\\,000$. Large-eddy simulations (LES) of the baseline uncontrolled flow reveal the dominance of Rossiter modes II and IV that generate high-amplitude unsteadiness via trailing-edge impingement and oblique shock waves that obstruct the free stream. To suppress the oscillations, we introduce three-dimensional unsteady blowing along the cavity leading edge. We leverage resolvent analysis as a linear model with respect to the baseline flow to guide the selections of the optimal spanwise wavenumber and frequency of the unsteady actuation input for a fixed momentum coefficient of 0.02. Instead of choosing the most amplified resolvent forcing modes, we seek a disturbance that yields sustained amplification of the primary response mode-based kinetic energy distribution over the entire cavity length. This necessary but not sufficient guideline for effective mean flow modification is evaluated using LES of the controlled cavity flows. The most effective control case reduces the pressure root mean square level up to $52\\,\\%$ along cavity walls relative to the baseline and is approximately twice that achievable by comparable steady blowing. Dynamic mode decomposition on the controlled flows confirms that the optimal actuation input indeed suppresses the formation of the large-scale Rossiter modes. It is expected that the present flow control guideline derived from resolvent analysis will also be applicable at higher Reynolds numbers with the aid of physical insights and further validation.

This paper presents a vortex breakdown study due to the interaction between a Batchelor vortex and the crossing of oblique shock waves with Mach numbers of 3.5 and 5.0, favourable for supersonic mixing and combustion, respectively. Numerical simulations were conducted to investigate the effects of the circulation intensity and shock angle on vortex breakdown. The results indicate that a breakdown occurs at the shock angle $\\beta \\geqslant 45^\\circ$ or the vortex circulation $q = 0.32$, and the configuration is a bubble structure with a recirculation region; most of the breakdowns possess a stagnation point. Furthermore, the structure differs from that of a normal shock wave and vortex interaction because the bubble region is subsonic and does not comprise a normal shock wave on the inside. Additionally, this vortex breakdown shows that the momentum flux on the centreline decreases once at the tip of the bubble owing to a sudden drop in velocity in the subsonic region. In addition, the enstrophy production resulting from vortex stretching and tilting is found to have a significant advantage in the interaction region. Based on these results, the threshold required for a bubble vortex breakdown was theoretically derived as an inequality. The numerical simulation results support the theoretical criterion obtained from the proposed inequality. Therefore, a streamwise vortex breakdown resulting from the interaction between the vortex and intersecting oblique-shocks should be reasonably predicted.

Resolvent analysis is used to study the low-frequency behaviour of the laminar oblique shock wave/boundary layer interaction (SWBLI). It is shown that the computed optimal gain, which can be seen as a transfer function of the system, follows a first-order low-pass filter equation, recovering the results of Touber & Sandham (J. Fluid Mech., vol. 671, 2011, pp. 417–465). This behaviour is understood as proceeding from the excitation of a single stable, steady global mode whose damping rate sets the time scale of the filter. Different Mach and Reynolds numbers are studied, covering different recirculation lengths $L$. This damping rate is found to scale as $1/L$, leading to a constant Strouhal number $St_{L}$ as observed in the literature. It is associated with a breathing motion of the recirculation bubble. This analysis furthermore supports the idea that the low-frequency dynamics of the SWBLI is a forced dynamics, in which background perturbations continuously excite the flow. The investigation is then carried out for three-dimensional perturbations for which two regimes are identified. At low wavenumbers of the order of $L$, a modal mechanism similar to that of two-dimensional perturbations is found and exhibits larger values of the optimal gain. At larger wavenumbers, of the order of the boundary layer thickness, the growth of streaks, which results from a non-modal mechanism, is detected. No interaction with the recirculation region is observed. Based on these results, the potential prevalence of three-dimensional effects in the low-frequency dynamics of the SWBLI is discussed.

We present wall-modelled large-eddy simulations (WLES) of oblique shock waves interacting with the turbulent boundary layers (TBLs) (nominal $\\def \\xmlpi #1{}\\def \\mathsfbi #1{\\boldsymbol {\\mathsf {#1}}}\\let \\le =\\leqslant \\let \\leq =\\leqslant \\let \\ge =\\geqslant \\let \\geq =\\geqslant \\def \\Pr {\\mathit {Pr}}\\def \\Fr {\\mathit {Fr}}\\def \\Rey {\\mathit {Re}}\\delta _{99}=5.4\\ \\mathrm{mm}$ and ${\\mathit{Re}}_{\\theta }\\approx 1.4\\times 10^4$ ) developed inside a duct with an almost-square cross-section ( $45\\ \\mathrm{mm}\\times 47.5\\ \\mathrm{mm}$ ) to investigate three-dimensional effects imposed by the lateral confinement of the flow. Three increasing strengths of the incident shock are considered, for a constant Mach number of the incoming air stream $M\\approx 2$ , by varying the height (1.1, 3 and 5 mm) of a compression wedge located at a constant streamwise location that spans the top wall of the duct at a 20° angle. Simulation results are first validated with particle image velocimetry (PIV) experimental data obtained at several vertical planes (one near the centre of the duct and three near one of the sidewalls) for the 1.1 and 3 mm-high wedge cases. The instantaneous and time-averaged structure of the flow for the stronger-interaction case (5 mm-high wedge), which shows mean flow reversal, is then investigated. Additional spanwise-periodic simulations are performed to elucidate the influence of the sidewalls, and it is found that the structure and location of the shock system, as well as the size of the separation bubble, are significantly modified by the lateral confinement. A Mach stem at the first reflected interaction is present in the simulation with sidewalls, whereas a regular shock intersection results for the spanwise-periodic case. Low-frequency unsteadiness is observed in all interactions, being stronger for the secondary shock reflections of the shock train developed inside the duct. The downstream evolution of secondary turbulent flows developed near the corners of the duct as they traverse the shock system is also studied.