Reflected Shock Waves Research Articles

The reflection of a planar impulsive shock wave at a liquid–gas interface

The reflection of a shock pulse at a liquid–gas interface occurs in many applications, from lithotripsy to underwater explosions and additive manufacturing. In linear theory, reflection and transmission at an interface depend only on the impedance difference, but this does not hold for a nonlinear pulse. This work develops an analytical framework for computing the reflection and transmission coefficients for an impulsive shock wave at a liquid–gas interface. The problem is treated analytically by considering idealised pulses and solving a series of consecutive Riemann problems. These correspond to the initial interaction with the interface and important subsequent wave interactions that enable a complete description of the process to be obtained. Comparisons with numerical and existing analytical approaches are made for the case of a water–air interface. In the acoustic limit, the method produces results identical to those of linear acoustic theory. As the pulse strength increases, the proposed method agrees well with numerical simulation results, whereas existing analytical methods that consider only the interface fail. We detail how a reflecting pulse can put water into tension without any incident negative pressure. It is further shown that the magnitude of the reflection coefficient decreases with increasing incident shock pressure, and the reflected pulse widens. Reflections of pulses with positive and negative pressures temporarily create negative pressure regions with greater magnitude than the incident pulse. Finally, we consider non-idealised waves. Comparisons with simulations show that the reflection characteristics can be explained qualitatively using the analytical method, and the reflection coefficients are predicted accurately.

Pseudosteady shock refractions over an air–water interface

Shock refraction in a gas–liquid interface is ubiquitous in nature and engineering. This study investigates the shock refraction phenomena in air–water interfaces for various inclination angles. The interface inclination angles are achieved using a tiltable vertical shock tube. The time-resolved schlieren images are compared with numerical simulations performed using the BlastFoam solver in the OpenFOAM software. The stiffened gas equation of state is used to model water in the simulations. The shock polar analysis using modified shock relations for a stiffened gas is used to elucidate the refraction patterns. A regular refraction pattern with a reflected shock wave and a bound precursor refraction with a regular reflection are observed experimentally for the first time in an air–water system. Further, a new free precursor refraction pattern with a Mach reflection is observed. The transition criteria and the corresponding boundaries for each refraction pattern are demarcated in the ( $M_S, \theta _w^c$ )-plane. The refraction sequence and the range for various incident shock strength regimes are also identified.

Investigation on the integrated characteristics of n-decane/air rotating detonation combustor and supersonic turbine

In this study, the two-dimensional numerical simulations are conducted to study the flow field characteristics, turbine performance and loss mechanism of integrated system of rotating detonation combustor and supersonic turbine under two different directions of detonation wave propagation. The results indicate that the propagation direction of RDW affects the incident angle between OSW and guide vanes, resulting in different operating modes for aligned and unaligned modes. OSW in the turbine cascade undergoes the leading-edge shock, blade surface reflection and trailing edge diffraction. The backward-propagating rake-type shock envelope is formed due to leading-edge shock of the rotor. In misaligned mode, the stator has higher damping of both pressure and temperature. The stator significantly improves the circumferential uniformity of both velocity and pressure, particularly when operating in aligned mode. The total pressure loss in aligned mode is less, therefore the turbine achieves higher rim work and efficiency. The viscosity is one of the main sources of loss in the flow field. The reflected shock waves at the leading edge of the rotor and in the stator cascade are the primary factors contributing to the leading-edge vortices on the stator vanes.

Analysis of the effects of combined suction on hypersonic inlet starting performance

Abstract Taking a two-dimensional inlet (Case 1) as the original inlet, the combined suction schemes are designed and their influences on the self-starting ability of the inlet are studied. The flow fields at the design point and the self-starting progress of the inlets are calculated by the numerical simulation method. The results show that the three-slot combination scheme (Case 2) leads to the reduction of the mass flow rate of the throat at the design point by 1.15% and the increase of the total pressure recovery coefficient by 6.73%. The self-starting Mach number of the inlet decreases from 4.6 to 3.2, which indicates that the self-starting ability is improved significantly by the three-slot combination scheme. In order to illustrate the role of each slot in improving the self-starting ability, three two-slot combination schemes, which are called Case 3, Case 4, and Case 5, are set up by closing Slot 1, Slot 2, and Slot 3 in turn and their self-starting processes are simulated. The results indicate that the self-starting Mach numbers of Case 3, Case 4, and Case 5 are 3.6, 4.1, and 4.5 respectively, which are 0.4, 0.9, and 1.3 higher than that of Case 2 respectively. Slot 3 has the greatest influence on the self-starting ability. When the incoming Mach number rises to 4.2, a closed separation zone is induced between Slot 2 and the throat by the reflected shock wave on the cowl side of Case 5. Due to the lack of lip overflow, which is an important flow regulation mechanism, the separation zone has a strong self-sustaining ability, and the inlet keeps unstart until the incoming Mach number rises to 4.5. In addition, in the absence of Slot 1 or Slot 2, the large-scale separation zone will not disappear until the incoming flow pressure increases to a certain value.

Explosive characteristics of premixed hydrogen-air subjected to various concentration gradients

In this research, different concentrations of hydrogen-air were charged into separate compartments of a 4.7 m pipe with a circular cross-section. The high-speed laser schlieren technique and overpressure detection technique were employed to accurately acquire the kinetic parameters of the explosive flow field, i.e., the evolution of the flame morphology, the flame propagation velocity and the shock wave overpressure. Two concentration gradients of 15 %-17 % and 15 %-25 % were programmed for the experiment. Affected by R-T, D-L, and multidimensional shock wave perturbations, the flame morphology exhibits fingertip, planar, cellular, tulip, and twisted tulip structures. Prolonging the gas diffusion time, the mean flame speeds were observed to be 10 m/s and 20 m/s after 10 min of diffusion for 15 %-17 % and 15 %-25 %, respectively, smaller than 45 m/s and 150 m/s at uniform concentrations. Besides, with the prolongation of diffusion time, the flame rarely backflows, and the velocity is more homogeneous and stable. Furthermore, as the ignition position approaches the concentration gradient, the flame is “driven” by the reflected shock wave upstream coupled with the effect of the elevated gas concentration, which significantly enhances the propagation velocity and overpressure.

Numerical investigation of dual‐source gas explosion dynamics in h‐type tunnels under varied enclosed situations

AbstractTo further investigate the propagation characteristics of shock waves and flame waves in H‐type tunnel gas explosions, numerical simulation studies were conducted on a dual‐source gas explosion model using Fluent software. Three distinct operational conditions were designed and modeled, leading to the following outcomes. The shock wave flow field parameters from dual sources (with equal source energy) are symmetrically distributed in the H‐type tunnel, with high pressure and low flow velocity in the connecting roadway between the two shock waves. Under different conditions, the pressure is generally higher in closed tunnels (fully closed greater than semi‐closed) and lower in open tunnels. The largest overpressure in non‐explosion areas occurs at the closed ends and in the connecting roadway, while the areas bearing the greatest impulse are the shock wave reflection zones and pressure coupling regions. In closed conditions, the flame wave first moves forward and then propagates backward after the explosion, influenced by reflected waves and pressure differences between the ends and the tunnel. In open conditions, the pressure in the flame zone is lower than at both ends, inhibiting the forward propagation of the flame wave.

Numerical study of bifurcation structures in reflected shock-wave/laminar-boundary-layer interaction within an end-wall tube

Abstract The primary aim of this study is to analyze the unsteady characteristics of the interaction between a reflected shock wave and a laminar boundary layer in an end-wall shock tube. Our direct numerical simulations at shock Mach numbers of Ms=1.9, 2.5, and 3.5 using a fifth-order WENO scheme and three-step Runge-Kutta time integration method revealed inhomogeneity and anisotropy in the shock bifurcation. Surprisingly, the upper and lower bifurcated structures maintain a notably asymmetric flow during the forward propagation of the reflected shock bifurcation. The inverse flow in the bifurcation resembles a crooked earthworm structure, exhibiting high-frequency oscillations indicative of instability. However, at higher shock intensities, the earthworm transforms into a stable strip-like configuration, facilitating the entrapment of inverse flow and leading to rapid bifurcation height growth and early convergence. Additionally, isolated islands with high density, temperature, and pressure emerge in the transitional region behind the bifurcated shocks, due to variations in wave propagation speed.

Effects of internal intervention in tubes on shock wave attenuation, formation and propagation of flame during high-pressure hydrogen release

Experiments on the impacts of the combination of fin structure and expansion chamber on shock wave attenuation, hydrogen ignition, and flame characteristics during high-pressure hydrogen release were carried out. The fin is a four-edged platform hollowed out on all sides. The inflated upper and lower tube walls are located 85, 95, and 105 mm away from the nickel burst disk. With the incident shock wave traveling through the fin, the reflected shock and the superposition of multiple reflected shock waves appear, and the reflected shock wave intensity can equal that of the release pressure. The decrease of the incident shock wave intensity behind the fin leads to the decrease of the non-uniformity of the mixed layer temperature, further causing the decrease of the flame propagation velocity. The presence of fins increases the probability of ignition in the fin region and the critical release pressure for ignition is significantly lower than that in the barrier free tube, mainly because the fin inside intensifies the hydrogen/air mixture, resulting in a lower minimum ignition energy required for self-ignition. Furthermore, the decrease of flame propagation velocity leads to the increase of hydrogen consumption inside the tube and the decrease of shock overpressure outside.

Influence of the shock wave-turbulence interaction on the swirl distortion in hypersonic inlet

This study uses the Large Eddy Simulation (LES) technique to conduct an exhaustive analysis of the flow characteristics within the Rectangular-to-Elliptical shape Transition (REST) inlet under Mach 6 conditions. It mainly focuses on investigating the influence of the shock wave-turbulence interaction on the swirl distortion at the inlet exit. At the design condition, characterized by 0° Attack and 0° Sideslip, the incident shock wave at the inlet lip undergoes multiple reflections within the boundary layer of the domain wall, culminating in the formation of turbulent structures. The first reflected shock wave has the highest energy, exerting a significant impact on the boundary layer and the exit swirl distortion. On the contrary, the energy of the incident shock wave is progressively reduced due to repeated reflections, which results in reducing the exit swirl distortion. Under off-design conditions, characterized by 6° Attack and 0° Sideslip as well as 6° Attack with 6° Sideslip, variations in the incoming flow make the incident shock wave move inward, decreasing the frequency of shock wave reflections and even significantly reducing the reflected shock waves under conditions of 6° Attack and 6° Sideslip. However, this results in significantly increasing the exit swirl angle and distortion intensity. The obtained results demonstrate that changes in the incoming flow conditions significantly affect the level of exit swirl distortion by modulating the shock wave-turbulence interaction, especially in terms of the positioning of the incident shock wave and the quantity of reflected shock waves. In addition, this paper studies the wall heat transfer coefficient of the inlet. The obtained results show that the interaction between shock waves and the boundary layer significantly affects the heat transfer coefficient. This study provides a foundation for the comprehension and prediction of the performance of hypersonic inlets across a spectrum of flight conditions, and for the guidance of the design and optimization of such inlets.

Experiment and kinetics study on OH∗ chemiluminescence up to 3150 K in hydrogen combustion behind reflected shock waves

Chemiluminescence of OH∗ is commonly employed as an optical indicator for the combustion process. It is widely recognized that the generation of OH∗ in hydrogen flames is primarily governed by the reaction H + O + M=>OH∗+M. In this study, the time histories of OH∗ chemiluminescence from the A→X band around 308 nm were recorded behind reflected shock waves for stoichiometric and lean H2/O2 mixtures highly diluted in argon over the temperature range of 1130–3150 K and at the pressure of approximately 0.9 atm. Based on the time histories of OH∗ chemiluminescence, the best-fit reaction rate coefficient for the reaction H + O + M=>OH∗+M was determined as k = 3.17 × 1027exp(-121968 cal mol−1/RT) + 2.25 × 1017exp(-4246 cal mol−1/RT) cm6 mol−2 s−1 over the temperature range studied. Furthermore, by using the current rate coefficient in mechanism predictions, the predicted time histories and relative peak intensities of OH∗ chemiluminescence are in good agreement with experimental results reported in literature.

STEAM INDUCED SHOCKWAVE INTERACTION WITH A SUBMERGED PLATE CONFIGURED AT A RANGE OF INCLINATIONS FROM VERTICAL

Interaction of shock wave and the shear induced vortex across the steam-water layer has been vital in several transportation and chemical industrial processes. Experiments were conducted using a facility including a rectangular chamber, which housed a shock tube in it. Steam was injected into the tube to induce shock wave by bursting the Aluminum diaphragm disk and the shock wave surrounding by the steam-water shear layer induced vortex, exited the shock tube and struck the rectangular steel plate. PIV setup along with the pressure and acoustic emissions sensors were used to characterize the propagation and impingement of the shock wave on the plate as well as the behavior of the reflected shock wave and the vortex ring. In case of a vertical rectangular steel sheet stationed in front of the exit of the shock tube, the central part of the shock wave was found to interact with the central part of the vortex structure and the external part of the shock wave came into contact with the outer part of the vortex structure. Whereas in case of inclined sheet, the shockwave reflected from the sheet, came into collision with the rebound shockwave as well as with the lower portion of the vortex ring largely. However, with the further variation in the angle of inclination (i.e. 30o and larger) fromvertical axis, no further appreciable change was observed in the flow profile except the vortex ring interacted earlier with the rebounded shockwave in the lower region within the neighborhood of the plate than the interaction of the vortex ring with the rebounded shock wave in the upper region of the inclined plate. The pressure and acoustic emission measurements were symmetric with the vertical plate, however, the pressure data was asymmetric when the plate was inclined from vertical. When the angle of inclination changes to 30 degrees from the vertical, the flow becomes more asymmetric as the shockwave and the consequent vortices impinged on the surface of the plate much earlier than the 15 degrees’ inclination case.

Numerical Simulation of Weak Shock Wave Reflection in Water Media

Abstract Shock wave reflection (SWR) is an interesting physical phenomenon that plays an important role in the ocean engineering. The existing research mainly focused on the gas SWR. Compared with the gas SWR, the water SWR has distinctive features. This article uses numerical methods to study the reflection mode and regularity inside a gas-filled and water-filled wedge. Specifically, we use the fifth-order weighted essentially nonoscillatory method in space and the third-order Runge–Kutta (RK) method in time to solve the compressible Euler equations. The ideal gas equation of state and water equation of state are also considered in the simulations. We developed a numerical solver using the Fortran language based on these equations and numerical methods. The reliability and accuracy of the developed program were validated by the existing theoretical solution and experiment data. Results show that the reflections are different in gas and water media. Regular reflection (RR) and Mach reflection are observed in a gas-filled wedge. However, only the RR is observed in a water-filled wedge for the weak water shock. Besides, it is found that the reflected shock (RS) wave in water is straighter than that in gas medium. Under the same pressure condition, the curvature of the RS wave is larger in a gas medium. The difference in SWR mode can be attributed to the difference in compressibility between the gas and water. It is found that there is a significant increase in temperature behind the incidence shock in the gas due to its high compressibility, which causes the change of local wave speed especially near the reflected wave. However, the temperature and wave speed are approximately constant during the SWR process in water. These distinctions can well explain the difference in SWR modes between gas and water.

Chemiluminescence during the high-temperature pyrolysis and oxidation of ammonia

Chemiluminescent emissions from NH2*, NH*, NO*, and OH* during the pyrolysis and oxidation of ammonia (NH3) are quantitatively characterized to gain insight into their reaction mechanisms. Time profiles of light emitted from high-temperature reactions of NH3/Ar and NH3/O2/Ar mixtures have been measured behind reflected shock waves at temperatures of 2300–2600 K and pressures of 1.6–1.9 bar in a high-repetition-rate shock tube. The emission intensities have been calibrated based on the well-characterized OH* chemiluminescence in a hydrogen-oxygen system and converted to photon emission rates for quantitative comparison with kinetic simulations. A kinetic model describing the pyrolysis and oxidation of ammonia and reactions of excited species has been constructed by combining the reaction mechanisms proposed in recent modeling studies. With only modest updates of the thermodynamic functions and the rate constants for the formation and quenching of excited species, the observed chemiluminescence profiles could be reasonably reproduced, with a few exceptions. The rate of production analysis indicates that NH2* is produced by the reaction of NH3 with H as well as thermal excitation of NH2, that the energy transfer reactions from 3N2 to NH and NO are responsible for the formation of NH* and NO*, respectively, and that the formation of OH* is competitively contributed by the reactions of H with N2O, 3N2 with OH, and NH with NO. Remaining discrepancies between the experiment and modeling are noted, and potential directions for further model improvement are discussed.

Experimental investigation into effects of combustor structure on characteristics of rotating detonation of cracked kerosene gas

This study examines the influence of the structure of the combustor on the propagation of rotating detonation waves (RDWs) of cracked kerosene gas (CKG) by using oxygen-rich air, with mass fractions of oxygen of 36% and 48%, as the oxidant while maintaining stable values of the state parameters of CKG. The experimental results showed that the structure of the combustor played a key role in the initiation and stable propagation of CKG, and suitable values of its width and the width of its outlet promoted the stable self-sustained propagation of the RDWs. Combustors of 8 and 14 mm width failed to initiate with 36% oxygen-rich air and without blockage ratio. In the combustors of 20 and 26 mm width, as the blockage ratio increased, the modes of propagation of the RDW included a single stable RDW, intermittent single RDW, and four, six, and eight counter-rotating RDWs. With the further increase in the blockage ratio, the reflected shock wave at the end of the combustor was enhanced, resulting in an increase in the number of RDW wave heads. As a result, the height of the fresh fuel layer was decreased, the mixing time was decreased and led to a decrease in the RDW velocity. The increase in the width of the combustor was conducive to the radial and axial diffusion of fuel and oxidizer in the combustor, which led to an obvious increase in the propagation velocity of RDW. In the 26 mm width combustor, the maximum RDW velocity is 1769 m/s.

Numerical study on flame acceleration and deflagration-to-detonation transition affected by the solid obstacles with different shapes

To investigate which shape of solid obstacles is most optimal in terms of detonation-assisting capability within a closed channel, this study utilizes the Large Eddy Simulation (LES) method, based on the OpenFOAM platform, to conduct a detailed numerical study on the effects of different shaped obstacles (rectangular, rhombus, trapezoidal, circular, triangular) on flame acceleration and detonation initiation processes. The results show that the obstacles arranged in the middle of the combustion chamber can create more passages and local flames. Meanwhile, changes in the shape of obstacles can also produce different vortex structures and recirculation zones. These differences affect the flame surface area and the total combustion heat release rate, thereby affecting the flame acceleration effect. Judging from the results, triangular obstacles have the best flame acceleration effect, followed by rhombus, trapezoid, rectangle, and circular obstacles. In terms of detonation initiation, the obstacles with a slope can induce vortex to detach earlier, which produce a better vortex-flame interaction. Simultaneously, the slope can reflect the shock wave more frequently, creating more favourable conditions for the formation of Mach reflection and Mach stem. Based on this, it is found that trapezoidal and triangular obstacles have better detonation-assisting capability. Additionally, it is found that the stronger the leading shock wave and the shorter the distance between it and the flame front, the better the detonation initiation effect. In general, the types of detonation initiation in this study all belong to the shock detonation transition (SDT). However, the detonation initiation process can be further classified into two categories: (I) Detonation induced by shock wave reflection; (II) Detonation triggered by shock wave focusing.

Ignition of Aged Lubricants in a Shock Tube

Abstract Lubricants experience harsh conditions which result in degradation of the oil. To imitate similar conditions, Mobil DTE 732, a common gas turbine lubricating oil, was subjected to high temperatures for an extended period of time, until thermal degradation occurred, indicated through the creation of coke. Samples were taken throughout this process, with the sample that was tested having been exposed for 78 hours. Utilizing an endwall injector system, the samples were ignited behind reflected shock waves in the High-Pressure Shock Tube at Texas A&M University. The injector system utilizes the incident wave to increase the temperature of the lubricant past its vaporization temperature, thereby vaporizing the fuel prior to the arrival of the reflected shock. Using this system, the base Mobil DTE 732 and the 78-hour sample produced from the coking test were tested at 1.06 to 1.58 atm and between 1171 and 1373 K. The ignition delay times of the samples were recorded utilizing pressure rise and hydroxyl chemiluminescence located in the sidewall of the shock tube. Upon the analysis of the results, there were negligible changes in the ignition behavior of the fuel, based on ignition delay time. However, changes in the combustion behavior were experienced, such as an absence of two-stage ignition and lower viscosity for the post-coke sample.

Experimental Study of the Ignition of a Stoichiometric Propylene–Oxygen–Argon Mixture Behind a Reflected Shock Wave

Experimental Study of the Ignition of a Stoichiometric Propylene–Oxygen–Argon Mixture Behind a Reflected Shock Wave

Numerical study on flame acceleration and deflagration-to-detonation transition: Spatial distribution of solid obstacles

This study conducts a detailed numerical investigation on the spatial distribution of solid obstacles using the large eddy simulation method. It is discovered that although flame acceleration induced by solid obstacles is dominated by factors such as flow field disturbances, vortices and recirculation zones, turbulence, flame surface areas and combustion heat release rates, etc., the characteristics of the leading shock wave are key to detonation initiation. Specifically, the intensity of the leading shock wave, its formation time, and its distance from the flame front significantly affect detonation initiation. Depending on the state of the shock wave, the detonation initiation process may occur through various mechanisms such as shock reflection, shock focusing. Overall, the types of detonation initiation in this study all belong to the shock detonation transition. However, the detonation initiation process can be further classified into two categories: (I) Detonation induced by shock wave reflection; (II) detonation triggered by shock wave focusing. Despite certain disparities in the detonation initiation process, all detonation initiation processes conform to the gradient theory, and the flame evolution processes in all cases consistently follow three stages: the laminar slow-ignition stage; the turbulent deflagration stage; the detonation initiation stage. Furthermore, the study further discerns that, compared to positioning obstacles on the wall, placing obstacles inside the combustion chamber can further augment the detonation-assisting effect. However, excessively sparse or dense spatial distributions of solid obstacles fail to yield the optimal detonation effect. An optimal distribution exists, which triggers the fastest detonation initiation.

Numerical study of perturbed shock driven instability in a dilute gas-particle mixture

The effects of particles on the Richtmyer–Meshkov (RM) instability of a flat interface driven by perturbed and reflected shock waves are numerically investigated. By utilizing three different sizes of particles (d=5μm, 20μm and 50μm) and two types of heavy gases (SF6 and CO2), the effect of the presence of particles with different sizes on the RM instability and the dynamic process of particle diffusion have been explored, respectively. The evolution of interface morphology under smaller particle (d=5μm and 20μm) conditions bears a striking resemblance to that of the condition without particles while the large particles (d=50μm) contribute to the formation of many “wrinkles” on the interface due to the large particle size and particle inertia. The addition of particles with smaller size (d=5μm and 20μm) can either slightly inhibit or promote the growth of the mixing width at the late stage of the interface evolution, depending on the extent of interface evolution. Both the particle size and the type of heavy fluid are able to influence the particle motion.

Experimental temperature- and pressure-dependent absorbance cross sections and a pseudo-line-list model for methyl formate near [formula omitted]

We first present quantitative, broadband absorbance cross sections of the C=O stretch fundamental rovibrational band of methyl formate in the 1670–1850 cm−1 range at temperatures of 300, 600, 800, and 1000 K and pressures of 1–2 atm. The title molecular spectra were additionally studied across the pressure range of 1 to 35 atm at room temperature. Elevated temperature measurements were taken in argon bath gas behind the reflected shock wave of a shock tube by a rapid-tuning, broad-scan external cavity quantum cascade laser. The room temperature cross section of methyl formate was collected to validate our method and agreed well with previous room-temperature measurements by Sharpe et al. Then, to extend the utility of the collected data across intermediate temperatures, a pseudo-line-list (PLL) absorbance model was generated through a simultaneous fit of line-by-line intensities and lower-state energies to the measured cross sections. This PLL model was able to replicate the measurements within 3% across most of the spectral range and within 8% around the extremely sharp Q-branch feature present at room temperature. Cross-validation was then performed by re-fitting the PLL excluding the 800 K data set and demonstrated that the PLL approach is effective in interpolating between measured absorption cross sections at discrete temperatures. Finally, the additional room-temperature measurements from 1 to 35 atm were collected in a high-pressure static cell in nitrogen bath gas. These measurements revealed a notable Q-branch cross section pressure dependence while the P- and R-branch wings remained largely pressure independent across this wide pressure range. The collected methyl formate cross sections comprise the latest addition to the Stanford ShockGas-IR database for mid-infrared polyatomic absorption cross sections at elevated temperatures.