Incident Shock Wave Research Articles

On the interphase and intra-phase interaction of particles and gas in a layer of granular materials behind shock wave

The work is devoted to the analysis of physical mechanisms of lifting a layer of granular material in the flow behind shock wave. Based on experimental data physical processes are considered behind a shock wave traveling above a dust layer, leading to its rise: the escape of single particles from the layer and the formation of an intermediate layer or fluidized bed between a dense layer and a suspension, the collision of particles in the fluidized bed and its ascent, the influence of a dense suspension on the flow behind the shock wave, and the effect of unsteady flow on the rise of the layer. A physical model of the process is proposed that allows predicting the rate and height of the rise of a layer of granular material at an early stage of interaction with the flow behind incident shock wave.

Long-duration blast loading & response of steel column sections at different angles of incidence

This paper reports experimental results pertaining to the effects of planar long-duration blast waves interacting with steel I-section column elements about different angles of incidence. Long-duration blast waves are typically defined by a positive pressure phase duration in excess of 100 ms, characteristic of very large explosion events such as industrial accidents. Blasts of this magnitude result in large impulses and dynamic pressures with the potential to exert high drag forces on column elements within an open frame structure. Due to relatively small dimensions in comparison to the blast wavelength, individual column elements are predominantly subjected to translational drag loading. Blast drag loading is complex to characterise, generally requiring approximation using drag coefficients, although proposed values in literature display inconsistency and typically lack provision for multi-axis interaction with I-shape geometries. Four full-scale long-duration experiments investigated blast interaction and elastic structural response of two steel I-section columns as a function of orientation to the incident shock wave. Drag coefficients were calculated as a function of I-section orientation using experimental pressure data and compared to values proposed in literature. It was found that drag coefficients proposed in literature have the potential to under-predict drag loading for certain oblique I-section orientations examined in these experiments. Importantly, intermediate oblique I-section orientations recorded higher loading and exhibited higher drag coefficients compared to orthogonal orientations, resulting in larger structural elastic response. Results from this experimental work have confirmed that I-section columns are axis-sensitive to blast wave direction giving rise to varying magnitudes of drag loading and structural response.

A theoretical model to estimate inactivation effects of OH radicals on marine Vibrio sp. in bubble-shock interaction

A theoretical model for estimating inactivation effects on marine Vibrio sp. is developed from the viewpoint of the chemical action of the OH radicals induced by interaction of bubbles with shock waves. It consists of a biological probability model for cell viability and a bubble dynamic model for its collapsing motion due to the shock pressures. The biological probability model is built by defining a sterilized space of the OH radicals. To determine the radius of the sterilized space, the Herring equation is solved in the bubble dynamic model in consideration of the effect of the heat conductivity and mass transportation. Furthermore, the pressure waveform of incident shock wave used in the model is obtained with the pressure measurement. On the other hand, a bio-experiment of marine Vibrio sp. is carried out using a high-voltage power supply in a cylindrical water chamber. Finally, the viability ratio of marine bacteria estimated by the theoretical model is examined under the experimental conditions of this study. In addition, we also discuss the influence of bubble initial size for predicting the inactivation effects.

Steady Mach reflection with two incident shock waves

Mach reflection in steady supersonic flow with two incident shock waves is studied. The second incident shock wave is produced by an additional deflection of the wedge lower surface, at some point ensuring that the two incident shock waves would intersect at the reflecting surface in case of normal reflection. Both theory and computational fluid dynamics (CFD) are used to study the flow structure and the influence of the second incident shock wave. The overall flow configuration, in case of Mach reflection, is shown to be composed of a triple shock structure, a shock/shock interaction structure and a shock/slipline reflection structure. Similar phenomenon, triggered by a high downstream pressure, has been observed before numerically, but not studied theoretically. The second incident shock wave reflects over the slipline to deflect the slipline more towards the reflecting surface, increasing thus the Mach stem height, advancing the transition of regular reflection to Mach reflection of the first incident shock wave, and causing an inverted Mach reflection below the usual von Neumann condition. A Mach stem height model built for a weak second incident shock wave is used to study the influence of the second incident shock wave on the Mach stem height. Both theory and CFD predict a maximum of the Mach stem height at some additional wedge deflection angle.

Shock waves in porous media

The experimental data [1, 2] on the effect of the parameters of plane incident shock waves and the characteristics of a porous medium on the attenuation and reflection of waves from a rigid obstacle are examined. The propagation of waves with a pressure jumps of up to ΔP/P0 = 20 (P0 = 0.1 MPa) in polyurethane foam blocks with a density of 20 kg/m3 and 35 kg/m3 and a length of up to 0.8 m, tightly adjacent to the walls and the end face of the driven section of the shock tube is studied. At lengths of the porous block greater than the extent of the shock wave, the porous block effectively attenuated the shock wave. For a wave of limited duration with a triangular pressure profile, a stronger attenuation of the wave in the polyurethane foam block was observed in comparison with that for an extended wave pulse. The reflection pressures of the waves in polyurethane foam with pressure jumps of ΔP/P0 ≥ 12 exceed the reflection pressures of shock waves in air. The degree of attenuation or amplification of a wave depends on the material density and the ratio of the lengths of the foamed polyurethane block and the pressure pulse.

Numerical investigation of an interaction between shock waves and bubble in a compressible multiphase flow using a diffuse interface method

The shock-bubble interaction in a compressible multiphase flow was investigated using a diffuse interface method (DIM) consisting of seven equations. To achieve detailed flow structures and mass transfer information, high-order numerical schemes, including the fifth-order MLP and a modified HLLC Riemann solver, were implemented. The numerical methods were verified via a flow structure comparison of the high-pressure water and low-pressure air shock tubes. A two-dimensional air-helium shock-bubble interaction at the incident shock wave condition (Mach number 1.22) was numerically solved and verified using the experimental results. A very detailed deformation was observed, so unsteady shock patterns such as the incident, transmitted, and reflected shocks could be identified. In addition, the air–water shock-bubble interaction at the same Mach number condition (1.22) was analyzed via the observation of detailed flow structures such as the reflection and transmitted shock inside and outside of the water bubble.

Numerical Study on Liquid Droplet Internal Flow Under Shock Impact

The establishment of an internal flowfield inside a single water droplet subjected to shock-wave impact is numerically and theoretically investigated. The main focus is on the description of the droplet internal flow pattern, which is believed to be one of the dominant factors in initial droplet deformation. The droplet internal flow pattern holds steady for quite a long time after the incident shock passage, and a saddle point is observed for the first time. Accordingly, the saddle point inside the droplet flow is used as a characteristic point to describe the internal flow. Cases of different incident shock strengths are tested, and a theoretical prediction is proposed to delineate the correlation between the saddle point steady position and the strength of the incident shock wave. The numerical cases are found to be in good agreement with the prediction. The present study helps to complete the understanding of the overall droplet aerobreakup phenomenon.

Numerical study of three-dimensional developments of premixed flame induced by multiple shock waves

The three-dimensional interactions of a perturbed premixed flame interface with a planar incident shock wave and its reflected shock waves are numerically simulated by solving the compressible, reactive Navier–Stokes equations with the high-resolution scheme and a single-step chemical reaction. The effects of the initial incident shock wave strength (Mach number) and the initial perturbation pattern of interface on the interactions are investigated. The distinct properties of perturbation growth on the flame interface during the interactions are presented. Our results show that perturbation growth is mainly attributed to the flame stretching and propagation. The flame stretching is associated with the larger-scale vortical flow due to Richtmyer–Meshkov instability while the flame propagation is due to the chemical reaction. The mixing properties of unburned/burned gases on both sides of the flame are quantitatively analyzed by using integral and statistical diagnostics. The results show that the large-scale flow due to the vortical motion always plays a dominating role during the reactive interaction process; however, the effect of chemistry becomes more important at the later stage of the interactions, especially for higher Mach number cases. The scalar dissipation due to the molecular diffusion is always small in the present study and can be negligible.

Numerical investigation on the interaction of planar shock wave with an initial ellipsoidal bubble in liquid medium

This paper performs numerical investigations on the interaction of shock wave with an ellipsoidal bubble in liquid medium. The governing equations, including the conservative Euler equations and the non-conservative transport equation of the liquid volume fraction, are discretized based on the finite volume method. A tangent of hyperbola for interface capturing (THINC) interface reconstruction scheme is employed for the phasic densities and the liquid volume fraction to maintain the interface sharpness. The major-axis (z-axis) of the bubble is parallel to the incident planar shock wave. Different collapse behaviors are observed for two ellipsoidal geometries, named as the disk-like bubble and rugby-like one. Different collapse patterns of an initial ellipsoidal bubble are presented and the manifestation is that the transverse jets pierce the bubble differently, classified as along the centerline, off-centerline along the circumferential direction or along the meridian line if the aspect ratio is varied. For the disk-like bubble, it presents the strongest collapsing process under certain eccentricity, characterized by the highest water hammer pressure under the same incident shock strength. The second sheeting jet is an important factor that leads to the collapse of the remaining bubbles pierced by the first transverse jet.

Ignition studies of undiluted diethyl ether in a high-pressure shock tube

The high ignitability of diethyl ether (DEE) reflected by a high cetane number of ∼125 leads often to unintentional far-endwall ignitions in shock tubes. This is the main reason why exclusively diluted DEE experiments with attenuated reactivity can be found in the literature. The current work deals with the ignition behavior of undiluted DEE/air mixtures at engine relevant conditions. The experiments are conducted in a high-pressure shock tube (HPST) under stoichiometric conditions comprising pressures of 18 and 40 bar and temperatures from 646 to 1058 K and 622 to 1100 K, respectively. A recently published detailed kinetic mechanism is employed for kinetic analyses and evaluation purposes. Comprehensive kinetic studies have shown that the oxidation process of DEE behind incident shock waves can proceed significantly leading even to weak and strong far-endwall ignitions. With the aid of x-t-diagrams, each influenced experiment by far-endwall ignitions could be identified and excluded from the dataset. The valid sets of data capture the ignition trend from low to high temperatures including the negative temperature coefficient region (NTC). A new oblique scaling method is introduced together with derived formulae, which enable the scaling of experimental data in the NTC region. The experimental ignition trend at both pressures and the overall ignition delay times at 18 bar are well described by the mechanism, whereas shorter ignition delays are predicted at 40 bar.

Simulations of shock wave/turbulent boundary layer interaction with upstream micro vortex generators

The streamwise breathing motion of the separation bubble, triggered by the shock wave/boundary layer interaction (SBLI) at large Mach number, is known to yield wall pressure and aerodynamic load fluctuations. Following the experiments by Wang et al. (2012), we aim to evaluate and understand how the introduction of microramp vortex generators (mVGs) upstream the interaction may reduce the amplitude of these fluctuations. We first perform a reference large-eddy simulation (LES) of the canonical situation when the interaction occurs between the turbulent boundary layer (TBL) over a flat plate at Mach number M=2.7 and Reynolds number Reθ=3600 and an incident oblique shock wave produced on an opposite wall. A high-resolution simulation is then performed including a rake of microramps protruding by 0.47δ in the TBL. The long time integration of the simulations allows to capture 52 and 32 low-frequency oscillations for the natural case and controlled SBLI, respectively. In the natural case, we retrieve the pressure fluctuations associated with the reflected shock foot motions at low-frequency characterized by StL=0.02−0.06. The controlled case reveals a complex interaction between the otherwise two-dimensional separation bubble and the array of hairpin vortices shed at a much higher frequency StL=2.4 by the mVGs rake. The effect on the map of averaged wall shear stress and on the pressure load fluctuations in the interaction zone is described, with a 20% and 9% reduction of the mean separated area and pressure load fluctuations, respectively. Furthermore, the controlled SBLI exhibits a new oscillating motion of the reflected shock foot, varying in the spanwise direction with a characteristic low-frequency of StL=0.1 in the wake of the mVGs and StL=0.05 in between.

The influence of radial entrance width of the circular cavity on incident shock wave focusing

Despite the achievement of shock wave focusing with certain reflectors, the influence of the radial entrance width of a circular cavity on the flow field has yet to be addressed. In this study, we systematically investigated the effects of the shock wave focusing process in a cavity based on the radial entrance widths. An experimental system was installed to research the evolution of the flow field under conditions with different radial entrance widths of 3.0, 11.1, 19.5, and 33.0 mm. A schlieren system was used to photograph the structures of the flow field in the cavity, and a data acquisition system was used to record the dynamic pressure histories of different points. A numerical simulation was carried out to investigate greater details of the shock wave focusing process. A third-order strong stability-preserving Runge-Kutta method, third-order weighed essential non-oscillation scheme, and an adaptive mesh refinement algorithm were adopted to simulate the shock wave reflection, diffraction, and focus process. Good agreement between the experimental and numerical results was observed. By comparing the evolution process of the flow field under the conditions of four different entrance cavity widths, we found that when the entrance width was 19.5 mm, there was the stronger intensity of the shock wave focusing in the focal region, and the larger pressure value at the apex of the cavity than the other three entrance widths, occur. This study improves our understanding of shock wave focusing.

High-speed imaging of inhomogeneous ignition in a shock tube

Homogeneous and inhomogeneous ignition of real and surrogate fuels were imaged in two Stanford shock tubes, revealing the influence of small particle fragmentation. n-Heptane, iso-octane, and Jet A were studied, each mixed in an oxidizer containing 21% oxygen and ignited at low temperatures (900–1000 K), low pressures (1–2 atm), with an equivalence ratio of 0.5. Visible images (350–1050 nm) were captured through the shock tube endwall using a high-speed camera. Particles were found to arrive near the endwalls of the shock tubes approximately 5 ms after reflection of the incident shock wave. Reflected shock wave experiments using diaphragm materials of Lexan and steel were investigated. Particles collected from the shock tubes after each experiment were found to match the material of the diaphragm burst during the experiment. Following each experiment, the shock tubes were cleaned by scrubbing with cotton cloths soaked with acetone. Particles were observed to fragment after arrival near the endwall, often leading to inhomogeneous ignition of the fuel. Distinctly more particles were observed during experiments using steel diaphragms. In experiments exhibiting inhomogeneous ignition, flames were observed to grow radially until all the fuel within the cross section of the shock tube had been consumed. The influence of diluent gas (argon or helium) was also investigated. The use of He diluent gas was found to suppress the number of particles capable of causing inhomogeneous flames. The use of He thus allowed time history studies of ignition to extend past the test times that would have been limited by inhomogeneous ignition.

Numerical investigation of the interaction between a planar shock wave with square and triangular bubbles containing different gases

The interaction between a planar shock wave and square and triangular bubbles containing either SF6, He, Ar, or CO2 is studied numerically. It is shown that, due to the existing large differences in the molecular weight, the specific heat ratio, and the acoustic impedance between these gases, different wave patterns and pressure distribution inside the bubbles are developed during the interaction process. In the case of heavy gases, the velocity of the shock wave propagating along the bubble inner surface is always less than that of the incident shock wave and higher than that of the transmitted shock wave. However, in the case of the light gas (He), the fastest one is the transmitted shock wave and the slowest one is the incident shock wave. The largest pressure jump is witnessed in the SF6 case, while the smallest pressure jump is seen in the helium case. There are also pronounced differences in the deformation of the investigated bubbles; while triangular bubbles filled with either Ar, CO2, or SF6 were deformed to a crescent shape, the helium bubble is deformed to a trapezoidal shape with three pairs of vortices emanating from its surface.

Nonequilibrium processes in meta-stable media⋆.

Meta-stable systems are those staying in the local equilibrium state: being slightly deviated from it they return to the equilibrium, but in case deviation surpasses a critical value those systems fall down to another equilibrium state. Chemically reacting gaseous mixture provides a typical example of a meta-stable system. The paper is aimed at numerical and experimental investigation of detonation initiation in hydrogen-air mixtures due to focusing of a shock wave reflected inside a wedge. Both numerical and experimental investigations were conducted. Comparison of numerical and experimental results made it possible to validate the developed 3D transient mathematical model of chemically reacting gas mixture flows incorporating hydrogen-air mixtures. Kinetic schemes and turbulence models were improved based on comparison of numerical and experimental results. Several different flow scenarios manifest in the reflection of shock waves all being dependent on the incident shock wave intensity: reflection of the shock wave with lagging behind the combustion zone, formation of a detonation wave in reflection and focusing, and intermediate transient regimes.

Shock Tube Study of Ignition-Delay Measurements and Kinetic Mechanism Research for Syngas

Ignition-delay times of syngas mixtures () were measured using a shock tube in the following conditions: temperatures of 910–1290 K, pressures of approximately 1.0 atm, an equivalence ratio of 1.0, ratios of 0.25 and 4.0, and especially Ar dilution rates of 94% and 79%. Simulating results and sensitivity analysis show that Davis Mech, NUIG Mech, and Varga Mech have more accurate computational results than GRI 3.0, SD Mech, and Li Mech at around 1000 K because for reaction the former three mechanisms have a lower reaction rate. Oxidation of occurs mainly through reactions and , whereas is the dominant reaction for the oxidation of CO. Comparative analyses of syngas with the same ratio at 94% and 79% Ar dilution rates show that heat absorption of Ar during combustion is the main cause of long ignition-delay time, although Ar also inhibits the reactivity of syngas through at 1000 K. Moreover, the pressure response curve rises slowly with 94% Ar dilution but sharply with 79% Ar dilution under low-temperature conditions, and detonation (or deflagration to detonation) can be observed under such conditions. In addition, emission was observed behind the incident shock wave when its velocity reached with 79% Ar dilution, and it was unable to measure ignition-delay time behind the reflected shock wave.

Blast from pressurized carbon dioxide released into a vented atmospheric chamber

This study describes the blast from pressurized carbon dioxide $$(\hbox {CO}_{2})$$ released from a high-pressure reservoir into an openly vented atmospheric chamber. Small-scale experiments with pure vapor and liquid/vapor mixtures were conducted and compared with simulations. A motivation was to investigate the effects of vent size and liquid content on the peak overpressure and impulse response in the atmospheric chamber. The comparison of vapor-phase $$\hbox {CO}_{2}$$ test results with simulations showed good agreement. This numerical code described single-phase gas dynamics inside a closed chamber, but did not model any phase transitions. Hence, the simulations described a vapor-only test into an unvented chamber. Nevertheless, the simulations reproduced the incident shock wave, the shock reflections, and the jet release inside the atmospheric chamber. The rapid phase transition did not contribute to the initial shock strength in the current test geometry. The evaporation rate was too low to contribute to the measured peak overpressure that was in the range of 15–20 kPa. The simulation results produced a calculated peak overpressure of 12 kPa. The liquid tests showed a significantly higher impulse compared to tests with pure vapor. Reducing the vent opening from 0.1 to $$0.01\,\hbox {m}^{2}$$ resulted in a slightly higher impulse calculated at 100 ms. The influence of the vent area on the calculated impulse was significant in the vapor-phase tests, but not so clear in the liquid/vapor mixture tests.

Interaction of a shock wave with multiple spheres suspended in different arrangements

In this study, the unsteady drag force, Fd, drag coefficient, Cd, and the relevant dynamic behaviors of waves caused by the interaction between a planar incident shock wave and a multi-sphere model are investigated by using imbedded accelerometers and a high-speed Schlieren system. The shock wave is produced in a horizontal 200 mm inner diameter circular shock tube with a 2000 mm × 200 mm × 200 mm transparent test section. The time history of Cd is obtained based on band-block and low-pass Fast Fourier Transformation filtering combined with Savitzky-Golay polynomial smoothing for the measured acceleration. The effects of shock Mach number, Ms, geometry of multi-sphere model, nondimensional distance between sphere centers, H, and channel blockage are analyzed. We find that all time histories of Cd have a similar double-peak shaped main structure. It is due to wave reflection, diffraction, interference, and convergence at different positions of the spheres. The peak Fd increases, whereas the peak Cd decreases monotonically with increasing Ms. The increase of shock strength due to shock focusing by upstream spheres increases the peak Fd of downstream spheres. Both the increase in sphere number and the decrease in distance between spheres promote wave interference between neighboring spheres. As long as the wave interference times are shorter than the peak times, the peak Fd and Cd are higher compared to a single sphere.

Numerical analysis on interactions of vortex, shock wave, and exothermal reaction in a supersonic planar shear layer laden with droplets

The analysis on the interactions of a large-scale shearing vortex, an incident oblique shock wave, and a chemical reaction in a planar shear layer is performed by numerical simulations. The reacting flows are obtained by directly solving the multi-species Navier-Stokes equations in the Eulerian frame, and the motions of individual point-mass fuel droplets are tracked in the Lagrangian frame considering the two-way coupling. The influences of shock strength and spray equivalence ratio on the shock-vortex interaction and the induced combustion are further studied. Under the present conditions, the incident shock is distorted by the vortex evolution to form the complicated waves including an incident shock wave, a multi-refracted wave, a reflected wave, and a transmitted wave. The local pressure and temperature are elevated by the shock impingement on the shearing vortex, which carries flammable mixtures. The chemical reaction is mostly accelerated by the refracted shock across the vortex. Two different exothermal reaction modes could be distinguished during the shock-vortex interaction as a thermal mode, due to the additional energy from the incident shock, and a local quasi detonation mode, due to the coupling of the refracted wave with reaction. The former mode detaches the flame and shock wave, whereas the latter mode tends to occur when the incident shock strength is higher and local equivalence ratio is higher approaching to the stoichiometric value. The numerical results illustrate that those two modes by shock-vortex interaction depend on the structure of the post-shock flame kernel, which may be located either in the vortex-braids of post-shock flows or in the shock-vortex interaction regime.

Simulation of shock-induced bubble collapse using a four-equation model

This paper presents a numerical study of the interaction between a planar incident shock wave with a cylindrical gas bubble. Simulations are performed using an inviscid compressible one-fluid solver based upon three conservation laws for the mixture variables, namely mass, momentum, and total energy along with a supplementary transport equation for the volume fraction of the gas phase. The study focuses on the maximum pressure generated by the bubble collapse. The influence of the strength of the incident shock is investigated. A law for the maximum pressure function of the Mach number of the incident shock is proposed.