Mach Wave Research Articles

An image processing method for visualizing the Mach reflection process.

Abstract In near-ground explosions, Mach reflection occurs, generating Mach waves with considerable destructive power. Consequently, the propagation of these waves is a critical focus in the study of such detonations. This study presents a visualization method for the Mach reflection process based on image processing. By employing image processing techniques, the trajectories of the triple points are obtained, allowing for the analysis of their movement under varying explosive charges and heights. Results indicate that the interaction between detonation products and air, coupled with multiple reflections of rarefaction waves within the detonation products, leads to the convergence of these rarefaction waves at the explosion center, forming new shock waves. These shock waves, upon interacting with the ground, reflect again, resulting in multiple peaks in the overpressure time curves at measurement points. Additionally, it was observed that a smaller scaled height of the explosive charge results in a more curved Mach stem. For a constant explosive height, increasing the explosive quantity only marginally increases the height of the Mach stem. This research provides valuable insights into the Mach reflection phenomena in near-ground explosions.

Dynamic interaction patterns of oblique detonation waves with boundary layers in hypersonic reactive flows

Due to their high thermal cycle efficiency and compact combustor, oblique detonation engines hold great promise for hypersonic propulsion. Previous numerical simulations of oblique detonation waves have predominantly solved the Euler equations, disregarding the influence of viscosity and boundary layers. This work aims to study how the interaction between the oblique detonation wave and the boundary layer influences the detonation wave structures in confined spaces. Two-dimensional numerical simulations considering detailed chemistry are performed in a stoichiometric H2/air mixture. The results indicate that the wedge-induced oblique detonation wave generates a strong adverse pressure gradient upon impacting the upper wall, leading to boundary layer separation. The separation zone subsequently induces an oblique shock wave near the upper wall, and an increase in separation angle will cause the transition from an oblique shock wave to an oblique detonation wave. The formation of the separation zone reduces the actual flow area and may even lead to flow choking; its obstructive effect is similar to that of the Mach stem in inviscid flow. To establish a connection between the viscous recirculation zone and the inviscid Mach stem, we introduce a dimensionless parameter, η, based on the inviscid assumption. It is defined as the ratio of the inviscid Mach stem height to the channel entrance height. This parameter can be used to identify three wave systems in a viscous flow field: separation shock-dominated wave systems, separation detonation-dominated wave systems, and unstable Mach stem-dominated wave systems. Among these, the appearance of detonation Mach stems leads to flow choking, and the shock-detonation wave system continually moves upstream, ultimately causing the failure of the oblique detonation combustion. The findings of this study provide new insights into the investigation of the influence of viscosity on the flow structure of oblique detonation waves.

Convective Mach Number and Full-Scale Supersonic Jet Noise Directivity

This paper examines the connection of convective Mach number definitions to maximum noise radiation angle for a T-7A-installed GE F404 jet engine. Definitions include those corresponding to Kelvin–Helmholtz (K-H) and supersonic instability (SI) Mach waves, and an empirical formulation. Under convectively supersonic conditions without an afterburner (AB), only K-H waves are present. At AB, SI Mach waves may exist, but at shallow angles outside the main radiation lobe. Evidence suggests that Mach wave radiation from faster-than-ordinary K-H waves could stem from shock-cell velocity fluctuations. The empirical convective Mach number indicates decreasing effective convective velocity from ∼80 to ∼60% of fully expanded velocity as engine power increases to AB. This convective velocity decreases with frequency, especially for those whose maximum source locations occur between the potential and supersonic core tips. Additionally, a new definition of supersonic-jet convective Mach number, dependent solely on the jet acoustic Mach number, ∼Mac, has been derived from wide-ranging jet data. This definition describes the F404 maximum noise radiation angle from intermediate thrust through AB within 2°. Relating this expression to K-H Mach waves for an isothermal jet indicates the relative unimportance of temperature in determining maximum radiation angle for heated supersonic jets, including military jet aircraft and rockets.

An improved efficient adaptive method for large-scale multi-explosives explosion simulations

Shock wave caused by a sudden release of high-energy, such as explosion and blast, usually affects a significant range of areas. The utilization of a uniform fine mesh to capture sharp shock wave and to obtain precise results is inefficient in terms of computational resource. This is particularly evident when large-scale fluid field simulations are conducted with significant differences in computational domain size. In this work, a variable-domain-size adaptive mesh enlargement (vAME) method is developed based on the proposed adaptive mesh enlargement (AME) method for modeling multi-explosives explosion problems. The vAME method reduces the division of numerous empty areas or unnecessary computational domains by adaptively suspending enlargement operation in one or two directions, rather than in all directions as in AME method. A series of numerical tests via AME and vAME with varying nonintegral enlargement ratios and different mesh numbers are simulated to verify the efficiency and order of accuracy. An estimate of speedup ratio is analyzed for further efficiency comparison. Several large-scale near-ground explosion experiments with single/multiple explosives are performed to analyze the shock wave superposition formed by the incident wave, reflected wave, and Mach wave. Additionally, the vAME method is employed to validate the accuracy, as well as to investigate the performance of the fluid field and shock wave propagation, considering explosive quantities ranging from 1 to 5 while maintaining a constant total mass. The results show a satisfactory correlation between the overpressure versus time curves for experiments and numerical simulations. The vAME method yields a competitive efficiency, increasing the computational speed to 3.0 and approximately 120,000 times in comparison to AME and the fully fine mesh method, respectively. It indicates that the vAME method reduces the computational cost with minimal impact on the results for such large-scale high-energy release problems with significant differences in computational domain size.

Unsteady relationships between instantaneous surface heat flux, instantaneous surface temperature, and tracked shock wave phenomena

Investigated are unsteady relationships between surface heat flux variations, surface temperature fluctuations, and tracked shock wave phenomena. The level of coherence and time lag between events at different flow locations are used to quantify the associated interactions at different frequencies. With this approach, time-varying surface heat flux and surface temperature fluctuations are used to track events at different flow locations relative to unsteadiness associated with the test section inlet and relative to unsteadiness associated with different shock wave phenomena. Employed for the investigation is a specialty test section with an inlet Mach number of 1.54, which contains a normal shock wave, a lambda foot (which is comprised of an upstream oblique shock wave leg, and a downstream oblique shock wave leg), and a flow separation zone beneath the lambda foot. High and low unsteady Mach wave intensity levels are produced at the test section inlet by different numbers and different amounts of unsteadiness of families of intersecting and interacting Mach waves, as these are located within and just downstream of the test section entrance. When correlated with respect to normal shock wave tracked locations, values and magnitudes of the most highly correlated frequency bands are different depending upon the level of test section inlet unsteady Mach wave intensity, and the location where unsteady flow events originate. With low freestream unsteady Mach wave intensity at the test section inlet, unsteady events are generally present at normal shockwave locations prior to times when their influences are present at thin film temperature and heat flux gage surface locations. The presence of high unsteady Mach wave intensity at the test section inlet produces an environment wherein the low Mach wave intensity inlet flow is overwhelmed by highly active Mach wave fluctuations, when they are present, such that the normal shock wave is no longer a primary originating source of flow unsteadiness.

A study of conical and curved shock waves via the streamline transformation method

The axisymmetric conical and curved shock waves are studied theoretically via the streamline transformation method (STM), which integrates the differential geometries of streamlines into the conservation laws and solves the flow field geometrically. Under the condition of a straight shock wave, the governing equation is significantly simplified, from which the assumptions of the conical flow and geometric self-similarity are mathematically proved. The simplified equation is also demonstrated as equivalent to the classical Taylor–MacColl equation. The flow mechanism after a conical shock wave is discussed from a geometric perspective, where the key factor is the dimensionless lateral distance between symmetric planes. The corresponding geometric and flow parameters, e.g., the distance between streamlines, the streamline curvature, and the Mach number, are computed for the demonstration of this mechanism. In the flow field over a circular cone, the isentropic compression is modeled geometrically. Due to the isentropic compression, the conical shock wave remains approximately a Mach wave at small semi-angles and the detachment is suspended at large semi-angles. For the axisymmetric curved shock wave, the flow field is computed directly by the streamline transformation method, where both the concave and convex shock waves are considered. Along the wall streamline, an explicit proportional relation between the shock curvature and the orthogonal derivatives of flow parameters is also provided and verified numerically. These results are applicable in the theoretical analysis and inverse design of axisymmetric shock waves.

Experimental and theoretical analysis of charge length on single-hole vibration amplitude from underground deep-hole blasting

Deep-hole blasting, characterized by large diameter and long charge length, is a prevalent practice in large-scale underground mining. However, the increasing charge length in each borehole, together with the growing charge weight, necessitates a heightened focus on the induced vibration effects. Understanding the impact of long charge length on induced vibration in comparison with traditional vibration characteristics is crucial for the safety control of deep-hole blasting. Therefore, experiments involving 6 charge lengths and 4 monitoring stations were conducted in an underground mine to clarify the variation of waveform and peak particle velocity (PPV). The entire borehole waveform superposed by the short charge elements was theoretically calculated and compared with the measured waveforms. The exact full-field model was further used to gain a comprehensive understanding of the effect of charge length and the related parameters of initiation positions and velocity of detonation (VoD). The experimental data and model analysis allow the following conclusions: (1) the effect of charge length on amplitude is highly dependent on the Mach wave, irrespective of varying initiation positions and VoDs; (2) an increase in the charge length does not necessarily lead to an increase of the PPV in the far-field, but it would result in a faster attenuation rate below a certain length; (3) given a constant charge weight, a greater length-to-diameter ratio of the explosive column results in a smaller vibration amplitude; (4) the appropriate duration of the explosive pressure should be considerably longer than the actual duration for investigating blast vibration.

Electron Heating in High Mach Number Collisionless Shocks.

The energy partition in high Mach number collisionless shock waves is central to a wide range of high-energy astrophysical environments. We present a new theoretical model for electron heating that accounts for the energy exchange between electrons and ions at the shock. The fundamental mechanism relies on the difference in inertia between electrons and ions, resulting in differential scattering of the particles off a decelerating magnetically dominated microturbulence across the shock transition. We show that the self-consistent interplay between the resulting ambipolar-type electric field and diffusive transport of electrons leads to efficient heating in the magnetic field produced by the Weibel instability in the high Mach number regime and is consistent with fully kinetic simulations.

Acoustic resolvent analysis of turbulent jets

Abstract We perform a resolvent analysis of a compressible turbulent jet, where the optimisation domain of the response modes is located in the acoustic field, excluding the hydrodynamic region, in order to promote acoustically efficient modes. We examine the properties of the acoustic resolvent and assess its potential for jet-noise modelling, focusing on the subsonic regime. Resolvent forcing modes, consistent with previous studies, are found to contain supersonic waves associated with Mach wave radiation in the response modes. This differs from the standard resolvent in which hydrodynamic instabilities dominate. We compare resolvent modes with SPOD modes educed from LES data. Acoustic resolvent response modes generally have better alignment with acoustic SPOD modes than standard resolvent response modes. For the optimal mode, the angle of the acoustic beam is close to that found in SPOD modes for moderate frequencies. However, there is no significant separation between the singular values of the leading and sub-optimal modes. Some suboptimal modes are furthermore shown to contain irrelevant structure for jet noise. Thus, even though it contains essential acoustic features absent from the standard resolvent approach, the SVD of the acoustic resolvent alone is insufficient to educe a low-rank model for jet noise. But because it identifies the prevailing mechanisms of jet noise, it provides valuable guidelines in the search of a forcing model (Karban et al. in J Fluid Mech 965:18, 2023). Graphical abstract

Hypersonic inlet flow field reconstruction dominated by shock wave and boundary layer based on small sample physics-informed neural networks

High Mach number inlets face complex challenges such as shock wave/boundary layer interference, adversely impacting the aerodynamic characteristics and stable operating boundaries. Traditional computational fluid dynamics (CFD) simulations for performance and flow field analysis are slow, and data-driven deep learning technologies struggle with predicting flow fields in complex aerodynamic phenomena like shock wave/boundary layer interactions, boundary layer separation, and Mach disks. This study introduces a rapid, robust method for reconstructing hypersonic viscous inlet flow fields using inlet geometry design parameters. This method is called shock wave and boundary layer dominated two-dimensional multiphysical field reconstruction model based on multi-scale sensory field fusion residual physical information neural network (PIMSRF_ResNet), ensuring high-precision training data. Using the optimal Pareto solution set from multi-objective optimization with a small sample intelligence method, 150 sets of multi-physics fields under Ma10 conditions with varying geometric design parameters are calculated. Compared to traditional pure data-driven models, PIMSRF_ResNet's structural similarity in the test set reaches 0.9773, with a peak signal-to-noise ratio close to 30 dB and a correlation coefficient exceeding 98%. These experimental results demonstrated that the proposed method is a promising tool for real-time prediction of complex internal flow fields dominated by high Mach number shock waves and boundary layers.

Acoustical Holography and Coherence-Based Noise Source Characterization of an Installed F404 Engine

Understanding the acoustic source characteristics of supersonic jets is vital to accurate noise field modeling and jet noise reduction strategies. This paper uses advanced, coherence-based partial field decomposition methods to characterize the acoustic sources in an installed, supersonic GE F404 engine. Partial field decomposition is accomplished using an equivalent source reconstruction via acoustical holography. Bandwidth is extended through the application of an array phase-unwrapping and interpolation scheme. The optimized-location virtual reference method is used. Apparent source distributions and source-related partial fields are shown as a function of frequency. Local maxima are observed in holography reconstructions at the nozzle lipline, distinct in frequency and space. The lowest-frequency local maximum may relate to noise generated by large-scale turbulence structures in the convectively subsonic region of the flow. Other local maxima are correlated primarily with Mach wave radiation originating from throughout the shear layer and into the fully mixed region downstream of the potential core tip. Source-elucidating decompositions show that the order and behavior of the decomposition lend to the local maxima being related to distinct subsources. Between the local maxima, however, there may be a combination of sources active, which is likely the cause of the spatiospectral lobes observed in other full-scale, supersonic jets.

Excitation and evolution of radiating modes in supersonic boundary layers. Part 2. Back effect of spontaneously radiated Mach waves

Excitation and evolution of radiating modes in supersonic boundary layers. Part 2. Back effect of spontaneously radiated Mach waves

Condensation shock topologies in carbon dioxide and a non-condensable gas mixture in supersonic nozzles

Condensation shock waves may occur in many flow expansion devices such as turbomachinery, gas ejectors, micro thrust-nozzles, and supersonic gas flow separators. However, their experimental analysis has been barely addressed as condensation shocks comprise complex phenomena such as compressible flow behavior, a shock-like phase transition, and a two-phase flow expansion. This work characterizes experimentally some condensation shock topologies of a mixture of carbon dioxide and dry air at several compositions in a Laval nozzle. Experiments were carried out in a test-rig instrumented with high-response pressure transducers installed along the Laval nozzle wall along with a Schlieren setup equipped with a high-speed video camera imaging the flow behavior within the nozzle. The nozzle wall profile was built by using the method of characteristics developed from a real equation-of-state suited for the testing mixture. Results revealed the influence of the nozzle wall profile on the condensation shock location and topology. Moreover, there types of flow behavior were captured and named as conventional, transition, and Mach wave condensation shocks. The transition from one topology to another occurred due to the interaction between cancelation waves originated from the nozzle wall and the phase-change phenomenon, giving rise to two distinct regions characterized by certain observable droplet population density. The current investigation presents an in-depth phenomenological discussion of the three types of condensation shock topologies as such assessment has not been previously developed.

Study on blast-induced vibration of single-hole cylindrical charge

It is essential to study the blast-induced vibration of cylindrical charge so as to reduce ground vibration level and protect the surrounding environment. In this paper, the Heelan model is used to study the generation and propagation mechanisms of blasting vibration induced by single-hole cylindrical charge. It shows that the superposition of vibration waves induced by explosives in different positions of the cylindrical charge causes the increase of peak particle velocity ( PPV) in the region along the propagation direction of detonation waves. The vector peak particle velocity ( VPPV) versus distance for different stemming lengths ( SL) indicates that the linear attenuation between the VPPV and the exponential of distance appears only over a certain distance. Hence, the traditional formula for PPV prediction is suitable just in the middle and far field, not in the near field. The influences of charge length, detonation velocity and initiation pattern on the blast vibration are also investigated. The generation of Mach waves is determined by the relationship of scale between velocity of detonation ( VoD), P-wave velocity, and S-wave velocity. Over a certain value, the charge length doesn’t affect maximum VPPV, but affects the range of VPPV with relatively large values. Moreover, the bottom and top detonator positions have similar consequences on vibration control in the far field as the influence of limited charge length on blast vibration can be ignored. The VPPV of the middle initiating is almost twice as much as the other two detonator positions in the far field. Thus, in practical blasting, the middle initiating needs to be avoided.

A photographic analysis of Mach wave radiation from a rocket plume

At 7:30 AM on October 6, 2020 Space-X launched a Falcon-9 rocket from pad 39A at Kennedy Space Center. Photographer Trevor Mahlmann had positioned his camera in the location where the rocket would pass in front of the rising sun and took a series of images of that encounter. These images are visually stunning, but they are also scientifically useful. The high-intensity sound and shock waves originating in the plume are imaged by passing in front of the sun, particularly near the edge of the sun. This can be considered a background-oriented schlieren system. The sound from a supersonic rocket plume is thought to be due to Mach wave radiation, but the details are not yet well understood. We are analyzing these images to determine the position and radiation characteristics of the sound source in the plume. The results of this analysis will be presented.

A study of rocket launch directivity and the potential correlation of various parameters

A rocket launch produces sound that is highly directional. This radiation is presumed to be due to Mach wave radiation, but the production mechanism is poorly understood. Previous research has shown that launch vehicle sound directivity peaks at an angle near 65° relative to the plume for most large rockets during early stages of the launch, yet limited attention has been given to the physical parameters involved in this sound production. This study explores the influence of some additional parameters that are not usually considered, such as ambient atmospheric pressure effects and the launch vehicle's Mach number on a rocket's directivity. Drawing parallels with similar studies on military jets, we aim to compare results and further our understanding of rocket acoustics, contributing to improved modeling precision.

Three-dimensional numerical simulations of oblique internal solitary wave-wave interactions in the South China Sea

Satellite images show that the oblique internal solitary wave-wave interactions frequently occur in the South China Sea, especially in the periphery of Dongsha Island. Depending on the amplitudes and angles of initial oblique waves, theoretical works illustrated that the evolution pattern falls into different regimes characterised by the respective four-fold augmentation of wave amplitudes (relative to the initial waves) and occurrence of Mach stem waves in the interaction region. Nevertheless, these results were based on the reduced theories rooted from the primitive Navier-Stokes equations and the disparities induced by these simplifications with the scenarios in realistic ocean are still unclear. To fill this research gap, three-dimensional numerical simulations in the South China Sea are used to evaluate the oblique internal solitary wave-wave interactions. It is found that transformations between mode-1 and mode-2 waves occur near the Dongsha Island when two waves obliquely collide, together with a small portion of energy is converted into higher modes, most of which is dissipated locally due to their unstable vertical structures. This conclusion has been seldom reported in previous studies (if any). These oblique interactions are essentially nonlinear and impacted by the dynamical factors, such as varying depth, background current, etc., exhibiting complicated variations of waveforms and energy, which, further, enhance the mixing at local sites in the mechanism of both shear and convective instabilities indicated by the Richardson number.

Theoretical validation and experimental calibration of a variable Mach number tunnel with continuous wave-elimination

The increasing demand for wide-range aircraft techniques drives the development of variable Mach number test facilities. Existing tunnels can provide uniform flow at design case, but the imperfect wave-elimination at non-design cases leads to insufficient flow uniformity, limited variation range, and complex operation. By applying flowfield inverse design and elasticity inverse design, this paper designs a continuous wave-elimination variable Mach number nozzle. The nozzle is validated by the perfect nozzle theory. By a single jack, the nozzle can deform to the perfect nozzles with different Mach numbers, eliminating the Mach waves continuously and achieving the high-quality test flow. The numerical evaluation validates the design and supports the fabrication of continuous wave-elimination variable Mach number tunnel for the National University of Defense Technology. The flow visualizations by Schlieren and nanoparticle-tracer based planar laser scattering technique indicate no vortices or waves induced by imperfect nozzle geometry. The Mach number calibrations show that the maximum deviations are less than 0.6%, and the standard deviations meet the national advanced standards. These results show that the tunnel eliminates the Mach waves at different Mach numbers through simple operation, providing a wider variable Mach range and a higher flow quality.

Analysis of the internal flow features of a CO2 transonic nozzle and optimization of the nozzle shape profile

Two-phase flow Laval nozzles are simple and have promising applications, but the internal flow is intricate and encompasses physical phenomena like phase transition, transonic and Mach waves. Therefore, a 1D mathematical model for validating and designing a CO2 two-phase flow transonic nozzle was developed and validated based on experiments. The findings demonstrated that a grid density of 0.292 mm was appropriate and that the maximum error of the model was less than 6.0 %, with an average error of less than 2.5 %. Additionally, it was discovered that when a phase transition occurred at the nozzle throat, whether through condensation or evaporation, there was a minimum critical pressure ratio in the nozzle; when the phase transition took place in the nozzle diffusion chamber, there was a minimum total pressure ratio. Finally, the Laval nozzle was designed to utilize the isostatic pressure gradient method (IPG), which gave a more significant pressure drop than a conventional nozzle while eliminating the shock wave strings at the nozzle throat. Under the typical operating conditions of a transcritical CO2 heat pump system, the ejector performance was boosted by an average of 5.44 %.

The overall-subshear and multi-segment rupture of the 2023 Mw7.8 Kahramanmaraş, Turkey earthquake in millennia supercycle

On February 6, 2023, an Mw7.8 earthquake hit the East Anatolian Fault (EAF) and Narlı Fault (NF), followed by an Mw7.5 event on the Sürgü Fault. We combine multiple seismic datasets, global navigation satellite system recordings, and radar satellite images with finite fault inversion and slowness enhanced back-projection to study the rupture kinematics. Our analysis reveals that the rupture originated on the NF, propagating 120 km northeast at 3.05 km/s and 200 km southwest at 3.11 km/s after reaching the EAF junction, exhibiting overall subshear speeds. Further Mach wave analysis confirms the subshear rupture, matching the prediction using close-Rayleigh speeds. The unexpectedly-large slip on some EAF segments suggests a supercycle lasting ≥900 years. The EAF geometry is similar to the San Andreas-San Jacinto Fault system, while the latter has higher slip rates but without large earthquakes on its southern segments since 1857, carrying the potential of an M8 earthquake.