Shock Angle Research Articles

Multidimensional Numerical Modeling of Combustion Dynamics in a Non-Premixed Rotating Detonation Engine With Adaptive Mesh Refinement

Abstract In the present work, a novel computational fluid dynamics (CFD) methodology was developed to simulate full-scale non-premixed rotating detonation engines (RDEs). A unique feature of the modeling approach was the incorporation of adaptive mesh refinement (AMR) to achieve a good trade-off between model accuracy and computational expense. Unsteady Reynolds-averaged Navier–Stokes (RANS) simulations were performed for an Air Force Research Laboratory (AFRL) non-premixed RDE configuration with hydrogen as fuel and air as the oxidizer. The finite-rate chemistry model, along with a ten-species detailed kinetic mechanism, was employed to describe the H2-Air combustion chemistry. Three distinct operating conditions were simulated, corresponding to the same global equivalence ratio of unity but different fuel/air mass flowrates. For all conditions, the capability of the model to capture essential detonation wave dynamics was assessed. An exhaustive verification and validation study was performed against experimental data in terms of a number of waves, wave frequency, wave height, reactant fill height, oblique shock angle, axial pressure distribution in the channel, and fuel/air plenum pressure. The CFD model was demonstrated to accurately predict the sensitivity of these wave characteristics to the operating conditions, both qualitatively and quantitatively. A comprehensive heat release analysis was also conducted to quantify detonative versus deflagrative burning for the three simulated cases. The present CFD model offers a potential capability to perform rapid design space exploration and/or performance optimization studies for realistic full-scale RDE configurations.

Backstreaming Pickup Ions

Abstract Ions that are reflected at the shock front and escape back into the upstream region can play the role of ions that start to be accelerated by a diffusive shock acceleration mechanism. Backstreaming ions have been shown to be generated from a superthermal tail of the solar wind at sufficiently high upstream temperatures. The number of such ions was found to be low and they were not found at shock angles exceeding 50°. The mechanism of production is multiple reflection when an ion changes the direction of motion inside the ramp for the first time, due to the cross-shock potential. Since pickup ions (PUIs) constitute a strongly superthermal population of protons a substantially stronger production of backstreaming PUIs can be expected. We study the reflection of PUIs in a planar stationary shock front using test particle analysis. The used model is inspired by the observed profile of the termination shock. The influence of magnetic compression, the shock angle, and the overshoot are analyzed. It is found that generation of backstreaming PUIs in this shock is substantially more efficient than the generation of backstreaming protons from thermal solar wind. The fraction of backstreaming PUIs rapidly increases with the increase of magnetic compression and the decrease of the shock angle. Overshoot enhances production of backstreaming PUIs and allows it for larger shock angles. No backstreaming ions have been found for shock angles larger than 60°. The results of the test particle analysis are supported by full-particle simulations.

Visible Light Refraction Effects on High-Speed Stereo Digital Image Correlation Measurement of a Thin Panel in Mach 2 Flow

This study utilized a Mach 2 wind tunnel, Research Cell 19 (RC-19), where the panel specimen became part of the test section top wall. Two stereo digital image correlation (3D-DIC) systems simultaneously acquired displacement measurements both with and without flow by filming the front and back sides of the panel. The two DIC results were then compared to note if any changes between the two measurements could be attributed to light refraction distortions. Various flow conditions were investigated including varying stagnation pressures and multiple shock angles to characterize and quantify potential distortions over a range of conditions. Previous work showed that the distortions were largely quasi-static in nature which had little or no bearing on vibration measurement however, static deflections caused by thermal gradients and less than ideal boundary conditions could be important for finite element model updating. Current results indicate that distortions at the shock wave foot were present in the DIC displacement results however, the level of distortion could be considered the same magnitude of typical sources of measurement noise and not significant.

On the conservative property of particle-based Fokker–Planck method for rarefied gas flows

The Fokker–Planck-type approximation of the full Boltzmann equation has aroused intense research interest due to its potential for the stochastic particle simulation of rarefied gas flows. The ellipsoidal statistical Fokker–Planck (ES-FP) model treats the evolution of molecular velocity as a continuous stochastic process, and it satisfies the basic requirements for a proper gas-kinetic model including the H-theorem and an adjustable Prandtl number. The ES-FP model can be numerically implemented with computational particles in a Monte Carlo manner. Two different particle ES-FP schemes are presented. The first scheme utilizes the exact stochastic integral solution of the Langevin equations corresponding to the ES-FP equation and couples free-molecular moves and intermolecular collisions. The second scheme is designed to enforce the conservation of momentum and energy during the numerical simulation based on the decoupled algorithm and the analysis of the specific conditions for the conservative property. Numerical tests are conducted to demonstrate the performances of different schemes. In the simulation of a homogeneous gas system, the ES-FP scheme without enforcement of conservation leads to unphysical variation in the momentum and loss in energy, whereas the conservative ES-FP scheme strictly maintains the momentum and energy of the system. For the Mach 6 flows over the leading edge of a flat plate and over a round-nosed blunt body, the non-conservative ES-FP scheme underestimates the shock angle and the shock standoff distance, makes inaccurate predictions of aerodynamic force and heating, and produces low-temperature anomalies in front of the shock waves. In comparison with the results given by the direct simulation Monte Carlo method, the results of the conservative ES-FP simulations show satisfactory accuracy for the flow fields as well as the distributions of pressure, friction, and heat flux on the wall surfaces.

Ionization and dissociation effects on boundary-layer stability

Abstract

Foreign object damage simulation of aero-engine blade

To study the anti-foreign object damage (FOD) ability of aero-engine compressor blades, finite element model of compressor blades was established. Blades damage was evaluated with different steel ball diameters and shock angles. Results show that the damage width and depth becomes bigger with the steel ball’s diameter increases. The damage width doesn’t change apparently with the shock angles, and the damage width nearly equals to the steel ball diameter. The damage depth mostly becomes smaller with the increase of shock angle.

Energetic Ion Reflections at Interplanetary Shocks: First Observations From ARTEMIS

AbstractInterplanetary shocks accelerate charged particles and have significant space weather effects. The widely accepted categorization of shocks uses the upstream plasma beta (βu), the shock angle (θBn), and the shock Mach number (M, i.e., the fast magnetosonic Mach number). In addition, two critical Mach numbers (Mc) classify shocks based on whether shock dissipation is provided by electron resistivity and conductance alone or also requires ion viscosity. The two critical Mach numbers were defined in studies by Edmiston and Kennel and by Kennel in the 1980s. The corresponding two transition points from subcritical to supercritical are referred to as critical Mach numbers Mc (EK84) and Mc(K87), respectively. In this study, we use the critical Mach numbers and magnetic overshoot as identifiers of supercritical shocks. When the ratio of M/Mc ≥ 1, and/or an overshoot presents, a shock is categorized as a supercritical shock. We found that in more than 80% of supercritical shocks (with M/Mc(K87) ≥ 1), in addition to the regular ion reflection around the magnetic foot, there is another group of ion reflections: energetic ion reflections (EIRs). Typically, regularly reflected ions range from ~1–4 keV, staying at or around the foot, while EIR ions range from ~4–25 keV (or higher), running minutes upstream of the shock, perhaps as a result of ion backstreaming and escaping. EIR is a newly discovered feature observed by Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) at supercritical interplanetary shocks, occurring even when θBn > 60°, which is excluded by simulations due to a strong suppression of the backstreaming reflection in such circumstances. The close correlation between EIR occurrence and the critical Mach number Mc(K87) revealed that the conceptual ion viscosity in the magnetohydrodynamics (MHD)‐derived criticality has a root in kinetic microphysics.

Investigations of a novel boundary condition approach for the accurate prediction of hypersonic oblique shocks in mesh-free Lagrangian simulations

The mesh-free Smoothed-particle hydrodynamic (SPH) method, with boundary condition and artificial viscosity modifications, is used to model oblique shock waves in inviscid, compressible (super- and hypersonic) flow. The boundary modifications include simple particle reflection at walls and the artificial viscosity modifications include a novel compression switch. It is shown the Lagrangian SPH particle method can be used to accurately capture not only the shock angle but also the jump conditions of the flow across the oblique shock, including post-shock temperature, density, pressure, Mach, and velocity. The validation shown includes compression corner angles for air, at M = 5, at 10-25 degrees—those possibly found in real hypersonic flight—as well as stretch cases of supersonic (M = 2) flow and CO2 as the working fluid.

Processing of high-speed videos of shock wave boundary layer interactions

This paper presents a framework for processing high-speed videos recorded during gas experiments in a shock tube. The main objective is to study boundary layer interactions of reflected shock waves in an automated way, based on image processing. The shock wave propagation was recorded at a frame rate of 500,000 frames per second with a Kirana high-speed camera. Each high-speed video consists of 180 frames, with image size [768 times 924] pixels. An image processing framework was designed to track the wave front in each image and thereby estimate: (a) the shock position; (b) position of triple point; and (c) shock angle. The estimated shock position and shock angle were then used as input for calculating the pressure exerted by the shock. To validate our results, the calculated pressure was compared with recordings from pressure transducers. With the proposed framework, we were able to identify and study shock wave properties that occurred within less than 300, upmu hbox {sec} and to track evolveness over a distance of 100 mm. Our findings show that processing of high-speed videos can enrich, and give detailed insight, to the observations in the shock experiments.

Preferential Heating of Heavy Ions in Shocks

Abstract Observations show that postshock temperatures of heavy ions in supernovae collisionless shocks are approximately proportional to their masses. So far there is no convincing explanation of this dependence that would take into account the microphysics of the ion interaction with the electromagnetic fields inside the shock front. Here it is shown that perpendicular temperature increases due to the gyration of heavy ions starts inevitably upon crossing the shock front because of the global change of the magnetic field. An estimate for the downstream temperature as a function of the shock angle and magnetic compression is derived.

Underwater oblique shock wave reflection from submerged hydraulic structures

This paper investigates the effect of obliquity on impulse imparted to the hydraulic structures by an underwater shock wave. In this regard, the oblique shock reflection phenomenon due to a planar shock wave impingement on an inclined rigid surface is numerically modeled. Results from simulations are presented in this manuscript for different shock strengths and angles of structure obliquity. The study reveals that impulse transmitted to the structure due to oblique shock reflection is lower than that of normal incidence. In specific regimes of structure obliquity to incident shock direction, the formation of Mach-stem is observed, i.e., triple point configuration at a certain distance from the structure. Inside these regimes, the stem height decreases with the increase in structure obliquity and vice versa. Locus of the triple point has a direct implication on the magnitude of transmitted impulse, which reduces with the increase in stem height, i.e., more the locus of the triple point is away from the structure, less is the transmitted impulse. Results presented in this manuscript may help in understanding the physics of shock reflections from submerged hydraulic structures and subsequently framing mitigation strategies.

Numerical characterization of 3D nonreacting supersonic cavity combustor with inlet Mach number variation

A numerical investigation of a cavity-based supersonic combustor with non-reacting upstream hydrogen fuel injection is conducted to study the effects of inlet Mach number (Ma) on flow structure and fuel-air mixing. Three different freestream Mach number cases (1.5, 2.5 and 3.5) are investigated at a constant fuel flow rate, injected at the sonic condition by considering governing equations for compressible, turbulent flow using Shear Stress Transport (SST) k-ω model. The complex flow structure is investigated by identifying various flow features namely, upstream three-dimensional bow shock, compression waves, Mach reflection, vortex in the separated boundary layer and horseshoe vortices at the downstream of the injection port. Besides this, the flow physics involved in these complex flow features are unravelled. Moreover, the performance of the combustor is characterized quantitatively in terms of mixing efficiency, total pressure loss and coefficient of pressure. However, the mixing efficiency and total pressure loss for the operating condition of Ma = 1.5, exhibits better performance than that of the other Mach number cases (2.5, 3.5) due to decrease in inclination angle of reattachment shock from 47.6° to 29.9°. The present numerical investigation also demonstrates that the three-dimensional simulation is essential in the characterization of fuel-air mixing in supersonic cavity-based combustors.

Effects of a nonadiabatic wall on hypersonic shock/boundary-layer interactions

The effects of wall thermal conditions on the canonical case of an impinging shock wave interacting with a turbulent boundary layer is a topic that remains under explored. Direct numerical simulations are used to study the flow properties of hypersonic-shock--boundary-layer interactions with distinct wall thermal conditions and shock angles.

Visualization of hypersonic incident shock wave boundary layer interaction

The incident shock interactions with the hypersonic laminar and forced turbulent boundary layer are visualized by the planar laser scattering technique. The effect of interaction strength on flow structures is also investigated. The results show that the boundary layer shape has been greatly altered by the incident shock. In both the laminar and turbulent inflows, the boundary layer thickness has an abrupt decrease at the interaction region. In laminar inflow, the boundary layer transition rapidly takes place due to the incident shock. The greater the incident shock angle, the bigger the boundary layer thickness downstream the incident shock. In turbulent inflow, the thickness downstream the shock is less than that of the inflow. Fractal analysis is firstly carried on hypersonic shock boundary layer interaction. The effect of the shock angle and inflow condition on fractal dimension is studied. The results indicate that with the stronger shock, the fractal dimension value is bigger for both laminar and forced turbulent inflows.

Prediction of liquid jet trajectory in supersonic crossflow and continuous liquid column model

The trajectory of the spray is studied theoretically and experimentally when a round liquid jet is injected into a supersonic crossflow vertically. A solid model of continuous liquid column is established in three-dimensional space. The cross-section deformation equation of the continuous liquid column along the injection direction is established using a method of micro-element analysis. The stress analysis of cross section is simplified into a two-dimensional droplet. The shape of the cross section is considered to continuously change from circular to elliptical shape. And the bow shock wave in front of the jet column is simplified into an oblique shock wave with a known shock angle. Based on this, the calculation of aerodynamic force is greatly simplified. A dimensionless parameter named effective deformation time of liquid column (the logogram is <inline-formula><tex-math id="M300">\begin{document}${t_{\rm valid}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200903_M300.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200903_M300.png"/></alternatives></inline-formula>) is defined and used to judge the end point of the liquid column quantitatively. The liquid jet trajectory and cross-section deformation can be calculated using MATLAB software. The instantaneous images of continuous liquid columns in supersonic crossflow are captured using high-spatial-resolution microscopic imaging methods. The microscopic imaging system is composed of a double pulse solid-state laser, computer, CCD camera, synchronous controller, microscope lens and laser diffuser. After passing through the laser diffuser, a plane background light with uniform distribution is formed on the scattering plate. The mean filtering method is used to filter the original image. After filtering, the range of gray distribution in the background area is obviously reduced. The distribution of gray value is more concentrated, and the background of the image is more uniform. Then the image edge detection function is used to obtain the near-field jet trajectory. The parameter variables studied include liquid injection pressure drop (1–2 MPa), liquid nozzle diameter (0.5 mm/1.0 mm), and liquid gas momentum ratio (3.32–7.27). The results show that the continuous liquid column model can better predict the jet trajectory on the center plane and the shape of the liquid column in three-dimensional space. It is indicated that the predictive result matches well with the experimental result. This study is of great significance for establishing the solid-particle coupling model of liquid jet in supersonic crossflows.

Numerical Simulation on Residual Stress Field of Flat‐Topped Laser Oblique Shocking of Ni‐Based Alloy GH4169

This paper is based on laser shock peening (LSP) system with a flat‐topped beam, using robot simulation software to determine the oblique shock angle of different areas of a certain turbine disk mortise. Three‐dimensional finite element analysis was used to study residual stress field of Ni‐based alloy GH4169 under flat‐topped laser oblique shocking. The effects of different laser energy and different shocking number on residual stress field of Ni‐based alloy GH4169 of LSP were studied. Three‐dimensional finite element analysis used super‐Gaussian beam distribution to construct spatial distribution model of shock wave induced by LSP. The simulation results were in good agreement with the experimental results. The research results will provide a theoretical basis for LSP of certain turbine disk mortise.

A case study of large-amplitude ULF waves in the Martian foreshock

Foreshock ultralow frequency (ULF) waves constitute a significant physical phenomenon in the plasma environment of terrestrial planets. The occurrence of these waves, associated with backstreaming particles reflected and accelerated at the bow shock, implies specific conditions and properties of the shock and its foreshock. Using magnetic field and ion measurements from MAVEN, we report a clear event of ULF waves in the Martian foreshock. The interplanetary magnetic field connected to the Martian bow shock, forming a shock angle of ~51°. Indicating that this was a fast mode wave is the fact that ion density varied in phase with perturbations of the wave field. The peak frequency of the waves was about 0.040 Hz in the spacecraft frame, much lower than the local proton gyrofrequency (~0.088 Hz). The ULF waves had a propagation angle approximately 34° from ambient magnetic field and were accompanied by the whistler mode. The ULF waves displayed left-hand elliptical polarization with respect to the interplanetary magnetic field in the spacecraft frame. All these properties fit very well with foreshock waves excited by interactions between solar wind and backstreaming ions through right-hand beam instability.

Multiple Osculating Cones’ Waverider Design Method for Ruled Shock Surfaces

The traditional osculating cones’ (OCs’) waverider design method is widely used in hypersonic waverider airframe design. However, it becomes ineffective when the shock strength in each osculating plane varies and the azimuthal pressure gradients appear to be important. To solve this problem, a method called the multiple osculating cones’ (multiple-OCs’) waverider design method has been developed for ruled shock surfaces. The new method discretizes the ruled shock surface into elements that can be derived from multiple locally conical flows. Multiple locally conical flows indicate that neighboring osculating planes have different shock generators. This feature not only provides a practical way to represent the azimuthal pressure gradients but also extends the variety of waverider designs. Waverider test cases at and are performed by the osculating cones with variable shock angles’ (OC-VSAs’) method and the multiple-OCs’ method, respectively. It has been shown that the multiple-OCs’ method is applicable to more generalized shock surfaces. The comparison results reveal that the waverider derived by the multiple-OCs’ method has a better agreement with the computational fluid dynamics solution than the OC-VSAs’ method. Moreover, the new method ensures a more homogeneous inlet captured flowfield on the bottom side of the waverider, which is favorable for hypersonic airframe propulsion integration.

Electron Scattering by Low-frequency Whistler Waves at Earth’s Bow Shock

Abstract Electrons are accelerated to nonthermal energies at shocks in space and astrophysical environments. While shock drift acceleration (SDA) has been considered a key process of electron acceleration at Earth’s bow shock, it has also been recognized that SDA needs to be combined with an additional stochastic process to explain the observed power-law energy spectra. Here, we show mildly energetic (∼0.5 keV) electrons are locally scattered (and accelerated while being confined) by magnetosonic-whistler waves within the shock transition layer, especially when the shock angle is large ( ). When measured by the Magnetospheric Multiscale mission at a high cadence, ∼0.5 keV electron flux increased exponentially in the shock transition layer. However, the flux profile was not entirely smooth and the fluctuation showed temporal/spectral association with large-amplitude ( ), low-frequency ( where is the cyclotron frequency), obliquely propagating ( , where is the angle between the wave vector and background magnetic field) whistler waves, indicating that the particles were interacting with the waves. Particle simulations demonstrate that, although linear cyclotron resonances with ∼0.5 keV electrons are unlikely due to the obliquity and low frequencies of the waves, the electrons are still scattered beyond 90° pitch angle by (1) resonant mirroring (transit-time damping), (2) non-resonant mirroring, and (3) subharmonic cyclotron resonances. Such coupled nonlinear scattering processes are likely to provide the stochasticity needed to explain the power-law formation.

A Study of Fluctuations in Magnetic Cloud‐Driven Sheaths

AbstractInterplanetary coronal mass ejections are at the center of the research on geomagnetic activity. Sheaths, highly fluctuating structures, which can be found in front of fast interplanetary coronal mass ejections, are some of the least known geoeffective solar transients. Using Morlet transforms, we analyzed the magnetic fluctuations in a list of 42 well‐identified and isolated magnetic clouds driving a sheath and shock (Masías‐Meza et al., 2016, https://doi.org/10.1051/0004-6361/201628571. We studied the fluctuations inside sheaths by defining two quantities: the power and the anisotropy. With a simple statistical approach we found that sheaths, in particular, those driven by a fast magnetic cloud, encountering a highly turbulent solar wind, and forming a high Alfvén Mach number shock have high levels of turbulent energy (∼10 times compared with the solar wind) as well as a low anisotropy (approximately halved compared with the solar wind) of their fluctuations. On the other hand, the effect of the shock angle and plasma beta in the solar wind are less straightforward: If the shock is quasi‐parallel or the beta in the solar wind is high, both the turbulent energy in the sheaths and the anisotropy of the fluctuations are reduced; but for quasi‐perpendicular shocks or low beta solar wind the turbulent energy and anisotropy can take any value.