Shock Structure Research Articles

Numerical investigations of shock/boundary-layer interaction and control for Mach 2.5 flow in an axisymmetric inlet

The present work investigates the application of vortex generators for separation control in axisymmetric isolator flows. Reynolds-Averaged Navier-Stokes computations were performed to simulate a Mach 2.5 flow past a half-isolator geometry with a 20∘ axisymmteric compression ramp based on the experiments of Funderburk and Narayanaswamy at North Carolina State University. Single vortex generator and a vortex generator array placed upstream of the shock-induced separation region were investigated. Near wall streamlines, surface pressure contours and density contours on crosswise planes were compared with experiments for flow control using a single vortex generator. Results indicate that the present computations are able to capture the wake and shock structures, and also predict reduction in the streamwise extent of flow separation downstream of the device trailing edge. Finally, the effects of the shape/orientation (forward facing/backward facing) of a single vortex generator, and the design of an array of three vortex generators (with devices of similar and mixed orientations) on the flow separation were also investigated. Contours of near-surface streamwise velocity showed that device orientation had a strong effect on separation control, which is attributed to the differences in the primary streamwise vortices shed in the two cases. Further, the overall reduction in the footprint of separated flow was determined to be most with the use of an array of vortex generators with mixed orientations.

Improvement of durability of membrane electrode assembly by frame sealing structure in temperature shock

Improvement of durability of membrane electrode assembly by frame sealing structure in temperature shock

Mach reflection and pressure/heating loads on V-shaped blunt leading edges with variable cross-sections and crotches

The primary Mach Reflection (MR) and pressure/heating loads on V-shaped Blunt Leading Edges (VBLEs) with variable elliptic cross-sections and conic crotches are theoretically investigated in this study. The simplified continuity method is used to forecast the shock configurations. The theoretical predictions and the numerical simulations for the Mach stem and the triple point as well as the curved shock accord well. Based on the theoretical model, an analysis of the impact of the axial ratio a/b of the cross-sectional shape and the eccentricity e of the crotch sweep path on shock structures is carried out. The shock configurations obtained from the theoretical model enable the derivation of the transition boundaries between the primary MR and the same family Regular Reflection (sRR). It is found that the increase of a/b and e can both facilitate the primary MR to sRR transition. The resulting transition and the corresponding generation of the wall pressure and heat flux are then investigated. The results indicate that higher values of the ratio a/b can significantly reduce the wall pressure and heating loads by inducing the primary MR to sRR transition. Conversely, the increase in the eccentricity e results in increased loads, despite causing the same transition.

Shocks in the warm neutral medium

Context. Atomic and molecular line emissions from shocks may provide valuable information on the injection of mechanical energy into the interstellar medium (ISM), the generation of turbulence, and the processes of phase transition between the warm neutral medium (WNM) and the cold neutral medium (CNM). Aims. In this series of papers, we investigate the properties of shocks propagating in the WNM. Our objective is to identify the tracers of these shocks, use them to interpret ancillary observations of the local diffuse matter, and provide predictions for future observations. Methods. Shocks propagating in the WNM are studied using the Paris-Durham shock code, a multi-fluid model built to follow the thermodynamical and chemical structures of shock waves at steady-state in a plane-parallel geometry. The code, designed to take into account the impact of an external radiation field, is updated to treat self-irradiated shocks at intermediate (30 < VS < 100 km s−1) and high velocity (VS ⩾ 100 km s−1), which emit ultraviolet (UV), extreme-ultraviolet (EUV), and X-ray photons. The couplings between the photons generated by the shock, the radiative precursor, and the shock structure are computed self-consistently using an exact radiative-transfer algorithm for line emission. The resulting code is explored over a wide range of parameters (0.1 ⩽ nH ⩽ 2 cm−3, 10 ⩽ VS ⩽ 500 km s−1, and 0.1 ⩽ B ⩽ 10 μG), which covers the typical conditions of the WNM in the solar neighborhood. Results. The explored physical conditions lead to the existence of a diversity of stationary magnetohydrodynamic solutions, including J-type, CJ-type, and C-type shocks. These shocks are found to naturally induce phase transition between the WNM and the CNM, provided that the postshock thermal pressure is higher than the maximum pressure of the WNM and that the maximum density allowed by magnetic compression is greater than the minimum density of the CNM. The input flux of mechanical energy is primarily reprocessed into line emissions from the X-ray to the submillimeter domain. Intermediate- and high-velocity shocks are found to generate a UV radiation field that scales as VS3 for VS < 100 km s−1 and as VS2 at higher velocities, and an X-ray radiation field that scales as VS3 for VS ⩾ 100 km s−1. Both radiation fields may extend over large distances in the preshock depending on the density of the surrounding medium and the hardness of the X-ray field, which is solely driven by the shock velocity. Conclusions. This first paper presents the thermochemical trajectories of shocks in the WNM and their associated spectra. It corresponds to a new milestone in the development of the Paris-Durham shock code and a stepping stone for the analysis of observations that will be carried out in forthcoming works.

Characteristics of Supersonic Sweeping Jet with Geometry Variation of Actuator Exits

Supersonic sweeping jets (SWJs) have demonstrated their effectiveness across a variety of scenarios, particularly in aeronautic applications (e.g., lift enhancement). An experimental study is conducted to investigate the characteristics of SWJs emitted from actuators with different spreading angle θ and exit length l. Schlieren visualization is used to capture the near- and far-field SWJs at nozzle pressure ratios (NPRs) ranging from 1.6 to 6.9. The results show that as NPR increases the SWJs become underexpanded when l≠0. Different θ have an impact on the shock structure and the law of the spreading angle of jet control area α changing with NPR. When θ is approximately 100 deg, α increases at first and then decreases with increasing NPR, reaching up to 90 deg at high NPRs. When θ is about 50 deg, α remains roughly constant and equal to θ. Internal flow measurements reveal that flow attachment caused by the Coanda effect plays a significant role in the mechanism that leads to a change in α. Proper orthogonal decomposition is applied to analyze the spatial and temporal patterns. Far-field measurements show multiple sound waves propagating upstream and downstream, which generated by the supersonic SWJs.

Schlieren-Based Analysis of Supersonic Multistream Control Using Data-Driven and Filtering Techniques

Synchronized time-resolved schlieren and far-field pressure measurements were used to examine control of a supersonic multi-aperture rectangular single- expansion ramp nozzle with an aft deck. The design contains core (Mach 1.6) and bypass (sonic) streams mixing behind a splitter plate, generating a high-frequency tone. Control was applied through splitter-plate trailing-edge spanwise waviness (passive), spanwise-arranged microjet blowing actuators (active), and their combination (hybrid). Passive and hybrid control successfully alleviate the tone, whereas active control amplifies and alters the tone frequency. Time-averaged schlieren data show changes to mean shock structures with control. Spectral proper orthogonal decomposition (SPOD) spectra from the raw schlieren data are consistent with the far-field measurements and reveal coherent structural details. Radiation associated with high-frequency structures is inhibited by passive and hybrid control that enhance mixing, but not by active control. Momentum potential theory filtering prior to SPOD application augments the analysis by isolating irrotational content, providing additional clues on acoustic vs hydrodynamic mechanisms. The results indicate shock–shear-layer interaction and shedding as sources of low- and high-frequency content, respectively. As such, through suitable processing, relatively easy-to-obtain high-speed schlieren provides a powerful tool to assess complex flow-control physics.

Enhancing transonic compressor rotor efficiency by flow analysis-driven blade section modification

Abstract Transonic axial compressors are widely used in aero-engines and gas turbines, and their efficiency has a significant influence on the equipment energy utilization rate and fuel cost. In this research, blade section modification based on flow analysis is carried out on the Rotor 67 for improving efficiency. First, the numerical calculation method used is verified with experimental data to ensure the accuracy of the simulation. Then, according to the analysis of simulated flow field and shock structure, the blade section shapes are altered to optimize the blade passage wide distribution for the sections from hub to mid-span. In addition, the blade surface angle is altered to reduce the supersonic flow expansion angle for decreasing shock strength. With these optimizations, the efficiency of modified transonic rotor increases by 0.9 percentage at the design point and 1.0 percentage at near stall point (N = 1.0), respectively. Slightly higher efficiency at off-design speeds (N = 0.9 and 0.8) are also obtained, with maintaining the stall margin.

Adaptive unified gas-kinetic scheme for diatomic gases with rotational and vibrational nonequilibrium

Multiscale nonequilibrium physics at large variations of local Knudsen number are encountered in applications of aerospace engineering and micro-electro-mechanical systems, such as high-speed flying vehicles and low pressure of the encapsulation. An accurate description of flow physics in all flow regimes within a single computation requires a genuinely multiscale method. The adaptive unified gas-kinetic scheme (AUGKS) is developed for such multiscale flow simulation. The AUGKS applies discretized velocity space to accurately capture the non-equilibrium physics in the multiscale UGKS, and adaptively employs continuous distribution functions following Chapman–Enskog expansion to efficiently recover near-equilibrium flow region in GKS. The UGKS and GKS are dynamically connected at the cell interface through the fluxes from the discretized and continuous gas distribution functions, which avoids any buffer zone between them. In this study, the AUGKS with rotation and vibration non-equilibrium is developed based on a multiple temperature relaxation model. The real gas effect in different flow regimes has been properly captured. To capture aerodynamic heating accurately, the heat flux modifications from the rotation and vibration modes are also included in the current scheme. Unstructured discrete particle velocity space is adopted to further improve the computational performance of the AUGKS. Numerical tests, including Sod tube, normal shock structure, high-speed flow around the two-dimensional cylinder and three-dimensional sphere and space vehicles, and an unsteady nozzle plume flow from the continuum flow to the background vacuum, have been conducted to validate the current scheme. In comparison with the original UGKS, the current scheme speeds up the computation, reduces the memory requirement, and maintains the equivalent accuracy for multiscale flow simulation, which provides an effective tool for nonequilibrium flow simulations, especially for the flows at low and medium speed.

Gradient-Based Monte Carlo Methods for Relaxation Approximations of Hyperbolic Conservation Laws

Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes, inspired by vortex methods for the Navier–Stokes equations. Such methods, referred to as gradient random walk methods, were extensively studied in the ’90s and have several interesting features, such as being grid-free, automatically adapting to the solution by concentrating elements where the gradient is large, and significantly reducing the variance of the standard random walk approach. In this work, we revive these ideas by showing how to generalize the approach to a larger class of partial differential equations, including hyperbolic systems of conservation laws. To achieve this goal, we first extend the classical Monte Carlo method to relaxation approximation of systems of conservation laws, and subsequently consider a novel particle dynamics based on the spatial derivatives of the solution. The methodology, combined with asymptotic-preserving splitting discretization, yields a way to construct a new class of gradient-based Monte Carlo methods for hyperbolic systems of conservation laws. Several results in one spatial dimension for scalar equations and systems of conservation laws show that the new methods are very promising and yield remarkable improvements compared to standard Monte Carlo approaches, either in terms of variance reduction as well as in describing the shock structure.

Design and Evaluation of a Hypersonic Waverider Vehicle Using DSMC

This work investigates the aerodynamic performance of a hypersonic waverider designed to operate at Mach 7, focusing on optimizing its design through advanced computational methods. Utilizing the Direct Simulation Monte Carlo (DSMC) method, the three-dimensional flow field around the specifically designed waverider was simulated to understand the shock wave interactions and thermal dynamics at an altitude of 90 km. The computational approach included detailed meshing around the vehicle’s critical leading edges and the use of three-dimensional iso-surfaces of the Q-criterion to map out the shock and vortex structures accurately. Additional simulation results demonstrate that the waverider achieved a lift–drag ratio of 2.18, confirming efficient aerodynamic performance at a zero-degree angle of attack. The study’s findings contribute to the broader understanding of hypersonic flight dynamics, highlighting the importance of precise computational modeling in developing vehicles capable of operating effectively in near-space environments.

Negative LIF Development For H2 Jet Characterization: Influence Of Tracers

This study focuses on the development of a new laser diagnostic based on Laser Induced Fluorescence by seeding the gas (N2) in which hydrogen is injected with fluorescent tracer. In this paper, three tracers were characterized, two aromatic compounds (toluene and difluorobenzene) and one ketone (acetone). The first part of this study compared the fluorescence of both aromatic compounds without injecting H2 . More particularly the influence of a temperature variation on the quantum yield and cross section absorption was regarded. It appeared that difluorobenzene was more suitable LIF measurement than toluene as it has a higher quantum yield that is less dependent to temperature variation. Then, Negative LIF was tested using two different tracers (difluorobenzene and acetone) and considering three different post-processing methods to consider the temperature variation inside the hydrogen jet: no temperature correction, temperature calculated based on a CFD RANS simulation, temperature calculated via an isentropic expansion and adiabatic mixture hypothesis. Results evidence that the first and the third methods presents respectively a lower and upper limit for the hydrogen mole fraction when the second method is biased by the presence of shock and expansion structures near the injector nozzle. Finally, it appears that, with the proper temperature correction, difluorobenzene and acetone yield similar results, despite the fact the acetone fluorescence needing more amplification to be captured, the signal to noise ratio is lower than for aromatic compounds.

An Experimental Investigation On The Effect Of Laser Energy Deposition In An Over-Expanded Jet

The shock train structure of a supersonic over-expanded jet is the product of the interaction between the jet flow at the nozzle exit and the ambient environment. Although the effect of flow disturbances on the performance of the supersonic inlets has been studied in detail, a limited understanding of the shock train dynamics subject to flow disturbances is available for over-expanded jets. This experimental investigation focuses on understanding the influence of perturbations due to short-duration energy deposition on the shock train structure and its dynamics in an axisymmetric over-expanded Mach 2.52 jet. The flow is perturbed by laser-induced breakdown, creating a shock wave and a high-temperature plasma zone in the shock train. A high-speed self-aligning focusing schlieren system is used to visualize the flow structure variations by measuring the shock angles and Mach disk height and width to characterize the shock train dynamics and the flow structure recovery process. The response of jet flow to the perturbation at the nozzle exit and the pre-reflection point is found to be similar, however, the response of the supersonic jet to the post-reflection energy deposition is significantly different. The damping ratio for the pre-reflection point and nozzle exit cases found are nearly constant for all scenarios whereas it is linearly dependent on the jet chamber pressure for the post-reflection cases. The frequency of the oscillations is found to be the same for all cases and irrespective of the chamber pressure, laser energy, and deposition location, approximately 10 kHz. The transition from Mach to regular reflection and vice versa are observed at a chamber pressure of Pc = 689 kPa. Any perturbation to the shock structure of a supersonic over-expanding jet at close to the steady-state bifurcation condition between Mach and regular reflection will exhibit Mach-to-regular transition or vice versa.

Effects of the droplet size and engine size on two-phase kerosene/air rotating detonation engines in flight operation conditions

The numerical and experimental research of rotating detonation engines is usually conducted in ground environmental conditions. Although many breakthroughs have been made, there are still deficiencies in understanding engines operating in real flight conditions. In order to reveal the effect of engine size and initial kerosene droplet size on the rotating detonation engines in flight conditions, the Eulerian-Lagrangian model is adopted, and a series of two-phase kerosene/air rotating detonation cases are simulated in the conditions of Mach 5 and 24 km altitude. When 5 μm and 10 μm droplets are adopted, the RDE behaves like gaseous rotating detonations with clear cellular structures. When the 20 μm and 30 μm droplets are adopted, the rotating detonation waves tend to be divided into two layers and form the λ-shaped shock structure. The results indicate that droplet size and engine size influence detonation wave propagation and flow field mainly through droplet heat absorption and evaporation height. Increasing the engine sizes can promote the two-phase rotating detonation and broaden the initial diameter range capable of obtaining rotating detonation waves. However, as droplet size increases, the fresh mixture layer becomes stratified, with an upper layer predominantly comprising fuel vapor and a lower layer of fuel droplets, which results in an λ-shaped shock structure at the detonation front. The flight operation condition brings in differences in features such as detonation wave height and velocity deficit. The detonation height in flight conditions is higher than that in ground conditions. The most velocity deficit in flight conditions observed in our study is below 15 %, which is lower than the results (22.5 %) in ground operating conditions. These results indicate that the optimal design of the rotating detonation engine must consider the real operation conditions and the effect of engine sizes and droplet sizes.

Complex shock structure in multi-species dusty plasma with nonextensive electrons and two-temperature nonthermal ions

A theoretical investigation has been made to explore the behavior of nonplanar (cylindrical and spherical) electrostatic shock waves in a dusty plasma system that consists of arbitarily charged dust particles, negatively charged heavy ions following Cairn’s distribution, positively charged ions with two different temperatures, and nonextensive electrons. The reductive perturbation technique is used to derive a modified Burgers equation analytically. Analytical analysis shows that the characteristics of the nonplanar shock waves, including their polarity, amplitude, width, and phase speed, undergo significant alterations due to factors such as the charges on dust particles, the number density of particles, the temperatures of heavy and light ions, nonextensive electron behavior, and dust kinematic viscosity. Furthermore, this study found shock structures with either a positive or negative potential, depending on the critical value of the proportion of ions to the density of dust particles. The findings maybe useful in understanding the characteristics of shock waves both in space plasma environments and laboratory plasmas.

Inner structures of rapid free-surface granular avalanche over a small bump obstacle: Expansion fan, oblique shock wave, and contact anisotropy

This study investigates the inner flow characteristics of a rapid granular avalanche passing over a small bump obstacle fixed on an inclined chute using the discrete element method. Both the cross-sectional mean flow properties, such as free-surface height, mean flow velocity, and mean stresses, and the inner local flow properties, including granular temperature, coordination number, pressure, contact force orientation, and granular fabrics, were comprehensively investigated. Upstream of the obstacle, a wide compression region where mean stresses strengthen and exhibit anisotropy was observed. Employing the kinetic theory of granular gas, we revealed a smooth supersonic-to-subsonic transition near the obstacle, a phenomenon distinct from typical gas dynamics. These upstream flow phenomena are attributed to the generation of stream-wise-oriented contact force chains as the flow impacts the obstacle. Downstream of the obstacle, a complex non-monotonic expansion–compression–expansion process was observed. We demonstrated that this non-monotonic flow process reflects an inner gasdynamic-like phenomenon characterized by an expansion fan followed by an oblique shock wave. Moreover, the force chains and the inner shock structure were found to significantly influence the evolution of stream-wise velocity profiles. These findings underscore the significance of inner flow structures in shaping the dynamics of granular avalanche flow interacting with obstacles.

A fluid approach to cosmic-ray modified shocks

A study of cosmic ray modified shock structures is presented for a system of four fluids consisting upon cosmic rays, thermal plasmas, forward and backward propagating self-excited Alfvén waves. A fluid model is employed to study the energy exchange mechanisms for the shock formation where cosmic rays, forward and backward propagating Alfvén waves are taken massless fluids in the comparison of thermal plasmas. This work may help to understand theoretical and observational perspective of the processes involved in supernova environment.

Detached Eddy Simulations of a Reaction Control Jet from an Axi-Symmetric Body in a Supersonic Crossflow

The introduction of a control jet into a supersonic cross flow yields a substantial region of separated flow, manifesting in the vicinity of the injection site. This, in turn, alters the distribution of pressure on the primary body, thereby influencing the effectiveness of the injected jet’s capacity to produce the desired control forces and moments. In the context of an axi-symmetric parent body, this disruption typically leads to a reduction in effectiveness, owing to the overflow of the shock structures encompassing the parent body. The present study investigates the injection of a reaction control jet into a supersonic crossflow using different Detached Eddy Simulation (DES) techniques. The side jet is injected from an orifice on an axi-symmetric parent body, which is aligned with the crossflow direction. The effects of the side jet on the flow field are analysed in terms of general flow features and spectral behaviour of pressure and turbulent kinetic energy. The DES results are compared with those obtained from RANS using various turbulence models. The overall effect of a transient interaction pulse is characterized using URANS and two different DES models.

Fluid–Structure Interactions between Oblique Shock Trains and Thin-Walled Structures in Isolators

Understanding aeroelastic issues related to isolators is pivotal for the structural design and flow control of scramjets. However, research on fluid–structure interactions (FSIs) between thin-walled structures and the isolator flow remains limited. This study delves into the FSIs between thin-walled panels and the isolator flow, as characterized by an oblique shock train, by quantitatively analyzing 11 flow parameters assessing the structural response, separation zones, shock structures, flow symmetry, and performance. The results reveal that an FSI triggers panel flutter under oblique shock train conditions, with the panel shapes exhibiting a combination of first- and second-mode responses, peaking at 0.75 of the panel length. Compared to rigid wall conditions, isolators with a flexible panel at the bottom wall experience downstream movement of the separation zones and shock structures, reduced flow symmetry, and minor changes in performance. Transient fluctuations occur due to the panel flutter. Two flexible panels at the top and bottom walls have a comparatively lesser influence on the averaged parameters but exhibit more violent transient fluctuations. Furthermore, the FSI effects under oblique shock train conditions are contrasted with those under normal shock train conditions. The flutter response under normal shock train conditions is more pronounced, with a larger amplitude and higher frequency, driven by the heightened participation of the first-mode response. The effects of FSIs under normal shock train conditions on the averaged parameters are the opposite (with a larger influence) to those under oblique shock train conditions, with significantly more drastic transient fluctuations. Overall, this study sheds light on the complex and substantial influence of FSIs on the isolator flow, emphasizing the necessity of considering FSIs in future isolator design and development endeavors.

Large-Eddy Simulations of a Supersonic Impinging Jet Using OpenFOAM

Supersonic impinging jets are a versatile configuration that can model the compressible flows of cold-spray manufacturing and vertical take-off-and landing strategy. In this work, rhoCentralFoam, solver of the OpenFOAM framework, and a large-eddy simulation formulation were used to simulate an underexpanded supersonic jet of Mach 1.45 and nozzle pressure ratio of 4, impinging on a flat wall situated at 1.5 nozzle diameters away from the jet outlet. Care was taken in the mesh construction to properly capture the characteristic standoff shock and vortical structures. The grid convergence index was evaluated with three meshes of increasing spatial resolution. All meshes can generally be considered as sufficient in terms of results focused on time-averaged values and mean physical properties such as centerline Mach number profile. However, the highest resolution mesh was found to capture fine shear vortical structures and behaviors that are absent in the coarser cases. Therefore, the notion of adequate grid convergence may differ between analyses of time-averaged and transient information, and so should be determined by the user’s intention for conducting the simulations. To guide the selection of mesh resolution, scaling analyses were performed, for which the current rhoCentralFoam solver displays a good weak scaling performance and maintains a linear strong scaling up to 4096 cores (32 nodes) for an approximately 40 million-cell mesh. Due to the internode communication bottlenecks of OpenFOAM and improvements in central processing units, this work recommends, for future scaling analyses, adopting a “cells-per-node” basis over the conventional “cells-per-core” basis, with particular attention to the interconnect speed and architecture used.

Conceptual design methodology and performance evaluation of turbine-based combined cycle inward-turning inlet with twin-design points

Turbine-based combined cycle (TBCC) engines attract intensive attention due to adequate high working efficiency within the full speed range of air-breathing vehicles. Challenges of TBCC engines lie mostly in common-used components in particular the inlet system, which needs to satisfy the mass flow distribution of different sub-engines and to reconcile the performance requirement in the full speed range. In the present work, a new conceptual design methodology of the three-dimensional inward-turning TBCC inlet with twin-design points is proposed according to the basic flow field with double incident shock waves. The shock structures and flow field parameters at the high-speed design point Ma=4 and mass flow distribution at the low-speed design point Ma=3 both can be designed by the basic flow field. On that basis, a typical inlet model is designed and the corresponding aerodynamic performance is evaluated at two design points. Simulation results prove that the shock structure, the mass flow distribution, and the averaged throat parameters of the TBCC inlet are all consistent with the basic flow field with sufficient accuracy at twin-design points, where the maximum relative error is only 6.3%. Meanwhile, the aerodynamic performance of the inlet shows that the inlet has stable and efficient operation characteristics, which fully affirms the feasibility of the design method.