Showing papers in "Shock Waves in 2016"

Detonation propagation in hydrogen-air mixtures with transverse concentration gradients

Abstract: The influence of transverse concentration gradients on detonation propagation in $$\hbox {H}_2$$ –air mixtures is investigated experimentally in a wide parameter range. Detonation fronts are characterized by means of high-speed shadowgraphy, OH* imaging, pressure measurements, and soot foils. Steep concentration gradients at low average $$\hbox {H}_2$$ concentrations lead to single-headed detonations. A maximum velocity deficit compared to the Chapman–Jouguet velocity of 9 % is observed. Significant amounts of mixture seem to be consumed by turbulent deflagration behind the leading detonation. Wall pressure measurements show high local pressure peaks due to strong transverse waves caused by the concentration gradients. Higher average $$\hbox {H}_2$$ concentrations or weaker gradients allow for multi-headed detonation propagation.

Role of inlet reactant mixedness on the thermodynamic performance of a rotating detonation engine

Abstract: Rotating detonation engines have the potential to achieve the high propulsive efficiencies of detonation cycles in a simple and effective annular geometry. A two-dimensional Euler simulation is modified to include mixing factors to simulate the imperfect mixing of injected reactant streams. Contrary to expectations, mixing is shown to have a minimal impact on performance. Oblique detonation waves are shown to increase local stream thermal efficiency, which compensates for other losses in the flow stream. The degree of reactant mixing is, however, a factor in controlling the stability and existence of rotating detonations.

Curved shock theory

Abstract: Curved shock theory (CST) is introduced, developed and applied to relate pressure gradients, streamline curvatures, vorticity and shock curvatures in flows with planar or axial symmetry. Explicit expressions are given, in an influence coefficient format, that relate post-shock pressure gradient, streamline curvature and vorticity to pre-shock gradients and shock curvature in steady flow. The effect of pre-shock flow divergence/convergence, on vorticity generation, is related to the transverse shock curvature. A novel derivation for the post-shock vorticity is presented that includes the effects of pre-shock flow non-uniformities. CST applicability to unsteady flows is discussed.

Large-eddy and unsteady RANS simulations of a shock-accelerated heavy gas cylinder

Abstract: Two-dimensional numerical simulations of the Richtmyer–Meshkov unstable “shock-jet” problem are conducted using both large-eddy simulation (LES) and unsteady Reynolds-averaged Navier–Stokes (URANS) approaches in an arbitrary Lagrangian–Eulerian hydrodynamics code. Turbulence statistics are extracted from LES by running an ensemble of simulations with multimode perturbations to the initial conditions. Detailed grid convergence studies are conducted, and LES results are found to agree well with both experiment and high-order simulations conducted by Shankar et al. (Phys Fluids 23, 024102, 2011). URANS results using a k–L approach are found to be highly sensitive to initialization of the turbulence lengthscale L and to the time at which L becomes resolved on the computational mesh. It is observed that a gradient diffusion closure for turbulent species flux is a poor approximation at early times, and a new closure based on the mass-flux velocity is proposed for low-Reynolds-number mixing.

Vorticity dynamics after the shock–turbulence interaction

Abstract: The interaction of a shock wave with quasi-vortical isotropic turbulence (IT) represents a basic problem for studying some of the phenomena associated with high speed flows, such as hypersonic flight, supersonic combustion and Inertial Confinement Fusion (ICF). In general, in practical applications, the shock width is much smaller than the turbulence scales and the upstream turbulent Mach number is modest. In this case, recent high resolution shock-resolved Direct Numerical Simulations (DNS) (Ryu and Livescu, J Fluid Mech 756:R1, 2014) show that the interaction can be described by the Linear Interaction Approximation (LIA). Using LIA to alleviate the need to resolve the shock, DNS post-shock data can be generated at much higher Reynolds numbers than previously possible. Here, such results with Taylor Reynolds number approximately 180 are used to investigate the changes in the vortical structure as a function of the shock Mach number, $$M_{s}$$ , up to $$M_{s}=10$$ . It is shown that, as $$M_{s}$$ increases, the shock interaction induces a tendency towards a local axisymmetric state perpendicular to the shock front, which has a profound influence on the vortex-stretching mechanism and divergence of the Lamb vector and, ultimately, on the flow evolution away from the shock.

On the propagation mechanism of a detonation wave in a round tube with orifice plates

Abstract: This study deals with the investigation of the detonation propagation mechanism in a circular tube with orifice plates. Experiments were performed with hydrogen air in a 10-cm-inner-diameter tube with the second half of the tube filled with equally spaced orifice plates. A self-sustained Chapman–Jouguet (CJ) detonation wave was initiated in the smooth first half of the tube and transmitted into the orifice-plate-laden second half of the tube. The details of the propagation were obtained using the soot-foil technique. Two types of foils were used between obstacles, a wall-foil placed on the tube wall, and a flat-foil (sooted on both sides) placed horizontally across the diameter of the tube. When placed after the first orifice plate, the flat foil shows symmetric detonation wave diffraction and failure, while the wall foil shows re-initiation via multiple local hot spots created when the decoupled shock wave interacts with the tube wall. At the end of the tube, where the detonation propagated at an average velocity much lower than the theoretical CJ value, the detonation propagation is much more asymmetric with only a few hot spots on the tube wall leading to local detonation initiation. Consecutive foils also show that the detonation structure changes after each obstacle interaction. For a mixture near the detonation propagation limit, detonation re-initiation occurs at a single wall hot spot producing a patch of small detonation cells. The local overdriven detonation wave is short lived, but is sufficient to keep the global explosion front propagating. Results associated with the effect of orifice plate blockage and spacing on the detonation propagation mechanism are also presented.

Structure of an oblique detonation wave induced by a wedge

Abstract: The structure of an oblique detonation wave (ODW) induced by a wedge is investigated via numerical simulations and Rankine–Hugoniot analysis. The two-dimensional Euler equations coupled with a two-step chemical reaction model are solved. In the numerical results, four configurations of the Chapman–Jouguet (CJ) ODW reflection (overall Mach reflection, Mach reflection, regular reflection, and non-reflection) are observed to take place sequentially as the inflow Mach number increases. According to the numerical and analytical results, the change of the CJ ODW reflection configuration results from the interaction among the ODW, the CJ ODW, and the centered expansion wave.

Shock Hugoniot and equations of states of water, castor oil, and aqueous solutions of sodium chloride, sucrose and gelatin

Abstract: This paper reports a result of experiments for the determination of reliable shock Hugoniot curves of liquids, in particular, at relatively low pressure region, which are needed to perform precise numerical simulations of shock wave/tissue interaction prior to the development of shock wave related therapeutic devices. Underwater shock waves were generated by explosions of laser ignited 10 mg silver azide pellets, which were temporally and spatially well controlled. Measuring temporal variation of shock velocities and over-pressures in caster oil, aqueous solutions of sodium chloride, sucrose and gelatin with various concentrations, we succeeded to determine shock Hugoniot curves of these liquids and hence parameters describing Tait type equations of state.

AEROFROSH: a shock condition calculator for multi-component fuel aerosol-laden flows

Abstract: This article introduces an algorithm that determines the thermodynamic conditions behind incident and reflected shocks in aerosol-laden flows. Importantly, the algorithm accounts for the effects of droplet evaporation on post-shock properties. Additionally, this article describes an algorithm for resolving the effects of multiple-component-fuel droplets. This article presents the solution methodology and compares the results to those of another similar shock calculator. It also provides examples to show the impact of droplets on post-shock properties and the impact that multi-component fuel droplets have on shock experimental parameters. Finally, this paper presents a detailed uncertainty analysis of this algorithm’s calculations given typical experimental uncertainties.

Visualization of deflagration-to-detonation transitions in a channel with repeated obstacles using a hydrogen–oxygen mixture

Abstract: The deflagration-to-detonation transition in a 100 mm square cross-section channel was investigated for a highly reactive stoichiometric hydrogen oxygen mixture at 70 kPa. Obstacles of 5 mm width and 5, 10, and 15 mm heights were equally spaced 60 mm apart at the bottom of the channel. The phenomenon was investigated primarily by time-resolved schlieren visualization from two orthogonal directions using a high-speed video camera. The detonation transition occurred over a remarkably short distance within only three or four repeated obstacles. The global flame speed just before the detonation transition was well below the sound speed of the combustion products and did not reach the sound speed of the initial unreacted gas for tests with an obstacle height of 5 and 10 mm. These results indicate that a detonation transition does not always require global flame acceleration beyond the speed of sound for highly reactive combustible mixtures. A possible mechanism for this detonation initiation was the mixing of the unreacted and reacted gas in the vicinity of the flame front convoluted by the vortex present behind each obstacle, and the formation of a hot spot by the shock wave. The final onset of the detonation originated from the unreacted gas pocket, which was surrounded by the obstacle downstream face and the channel wall.

Tandem shock waves in medicine and biology: a review of potential applications and successes

Abstract: Shock waves have been established as a safe and effective treatment for a wide range of diseases. Research groups worldwide are working on improving shock wave technology and developing new applications of shock waves to medicine and biology. The passage of a shock wave through soft tissue, fluids, and suspensions containing cells may result in acoustic cavitation i.e., the expansion and violent collapse of microbubbles, which generates secondary shock waves and the emission of microjets of fluid. Cavitation has been recognized as a significant phenomenon that produces both desirable and undesirable biomedical effects. Several studies have shown that cavitation can be controlled by emitting two shock waves that can be delayed by tenths or hundreds of microseconds. These dual-pulse pressure pulses, which are known as tandem shock waves, have been shown to enhance in vitro and in vivo urinary stone fragmentation, cause significant cytotoxic effects in tumor cells, delay tumor growth, enhance the bactericidal effect of shock waves and significantly increase the efficiency of genetic transformations in bacteria and fungi. This article provides an overview of the basic physical principles, methodologies, achievements and potential uses of tandem shock waves to improve biomedical applications.

A numerical investigation of the prompt oblique detonation wave sustained by a finite-length wedge

Abstract: The prompt oblique detonation wave (PODW) sustained by a finite-length wedge is investigated by numerical simulation. The numerical results show that it is possible to stabilize a PODW on a finite-length wedge shorter than the induction length of the mixture behind the inert shock by numerically imposing a premature initiation of combustion in the initial flow field. The fully coupled and the partially coupled PODWs are observed in the numerical results. For the fully coupled PODW, the upstream facing transverse waves (UF TW) are swept downstream and consequently a fully coupled PODW can persist. For the partially coupled PODW, the UF TWs propagate upstream and the downstream facing transverse waves are weakened by the expansion wave emanating from the corner. As a result, a partially coupled PODW forms. Further, it is found that the stability of the partially coupled PODW is weak. The configuration of the partially coupled PODW can be altered by local explosions occurring downstream.

Shock wave reflection induced detonation (SWRID) under high pressure and temperature condition in closed cylinder

Abstract: Super-knock is one of the major obstacles for improving power density in advanced internal combustion engines (ICE). This work studied the mechanism of super-knock initiation using a rapid compression machine that simulated conditions relevant to ICEs and provided excellent optical accessibility. Based on the high-speed images and pressure traces of the stoichiometric iso-octane/oxygen/nitrogen combustion under high-temperature and high-pressure conditions, it was observed that detonation was first initiated in the near-wall region as a result of shock wave reflection. Before detonation was initiated, the speed of the combustion wave front was less than that of the Chapman–Jouguet (C–J) detonation speed (around 1840 m/s). In the immediate vicinity of the initiation, the detonation speed was much higher than that of the C–J detonation.

Shock wave emission during the collapse of cavitation bubbles

Abstract: Shock wave emission induced by intense laser pulses is investigated experimentally. The present work focuses on the conditions of shock wave emission in glycerine and distilled water during the first bubble collapse. Experimental investigations are carried out in liquids as a function of temperature and viscosity. Comparison is made with the theoretical work of Poritsky (Proc 1st US Natl Congress Appl Mech 813–821, 1952) and Brennen (Cavitation and bubble dynamics, Oxford University Press 1995). To the best knowledge of the authors, this is the first experimental verification of those theories.

The GraVent DDT database

Abstract: An open-access online platform containing data from experiments on deflagration-to-detonation transition conducted at the Institute of Thermodynamics, Technical University of Munich, has been developed and is accessible at http://www.td.mw.tum.de/ddt . The database provides researchers working on explosion dynamics with data for theoretical analyses and for the validation of numerical simulations.

Ethylene–air detonation in water spray

Abstract: Detonation experiments are conducted in a 52 $$\hbox {mm}$$ square channel with an ethylene–air gaseous mixture with dispersed liquid water droplets. The tests were conducted with a fuel–air equivalence ratio ranging from 0.9 to 1.1 at atmospheric pressure. An ultrasonic atomizer generates a polydisperse liquid water spray with droplet diameters of 8.5–12 $$\upmu \hbox {m}$$ , yielding an effective density of 100–120 $$\hbox {g}/\hbox {m}^{3}$$ . Pressure signals from seven transducers and cellular structure are recorded for each test. The detonation structure in the two-phase mixture exhibits a gaseous-like behaviour. The pressure profile in the expansion fan is not affected by the addition of water. A small detonation velocity deficit of up to 5 % was measured. However, the investigation highlights a dramatic increase in the cell size ( $$\lambda $$ ) associated with the increase in the liquid water mass fraction in the two-phase mixture. The detonation structure evolves from a multi-cell to a half-cell mode. The analysis of the decay of the post-shock pressure fluctuations reveals that the ratio of the hydrodynamic thickness over the cell size ( $$x_{{\mathrm {HT}}}/{\lambda }$$ ) remains quite constant, between 5 and 7. A slight decrease of this ratio is observed as the liquid water mass fraction is increased, or the ethylene–air mixture is made leaner.

Analysis of small-scale scalar mixing processes in highly under-expanded jets

Abstract: In the present study, we numerically investigate turbulent scalar mixing taking place downstream of highly under-expanded jets. The focus is placed on two inter-related issues: (i) the closure of the mean scalar dissipation rate (SDR) and (ii) the turbulence–scalar interaction (TSI) term. It is indeed commonly admitted that the former, i.e., the SDR, which is defined as the product of the scalar diffusivity with the squared scalar gradient, provides a good measure of the mixing efficiency. In turbulent flows, the mean (turbulent) SDR requires a specific closure to be settled. It is generally obtained within the approximation of a linear relaxation of scalar fluctuations or linear relaxation model. We will first evaluate herein the performance of this widely used closure. The analysis is further developed by means of the consideration of the mean SDR transport equation which shows that, in gaseous conditions, the SDR is mainly driven by two terms: (i) a dissipation contribution and (ii) the third-order correlation between the velocity gradient tensor and small-scale scalar anisotropy tensor. The scalar mixing efficiency thus appears to be controlled by the latter quantity, which is often denoted as the TSI term. It can be shown that only the symmetric part (rate of strain) of the velocity gradient tensor contributes to this term; the anti-symmetric part modifies, indeed, the orientation of the scalar gradient but not its magnitude. The classical approach is to analyze this contribution in the eigenframe of the rate of strain tensor. Such analyses show that, in homogeneous isotropic turbulence, the scalar gradient tends to align with the most compressive direction, thus leading to SDR production. However, the present conditions, which are far from homogeneity and involve strong density variations, may modify this classical picture. The present study analyzes this possible influence.

Interaction theory of hypersonic laminar near-wake flow behind an adiabatic circular cylinder

Abstract: The separation and shock wave formation on the aft-body of a hypersonic adiabatic circular cylinder were studied numerically using the open source software OpenFOAM. The simulations of laminar flow were performed over a range of Reynolds numbers ( $$8\times 10^3 < Re < 8\times 10^4$$ ) at a free-stream Mach number of 5.9. Off-body viscous forces were isolated by controlling the wall boundary condition. It was observed that the off-body viscous forces play a dominant role compared to the boundary layer in displacement of the interaction onset in response to a change in Reynolds number. A modified free-interaction equation and correlation parameter has been presented which accounts for wall curvature effects on the interaction. The free-interaction equation was manipulated to isolate the contribution of the viscous–inviscid interaction to the overall pressure rise and shock formation. Using these equations coupled with high-quality simulation data, the underlying mechanisms resulting in Reynolds number dependence of the lip-shock formation were investigated. A constant value for the interaction parameter representing the part of the pressure rise due to viscous–inviscid interaction has been observed at separation over a wide range of Reynolds numbers. The effect of curvature has been shown to be the primary contributor to the Reynolds number dependence of the free-interaction mechanism at separation. The observations in this work have been discussed here to create a thorough analysis of the Reynolds number-dependent nature of the lip-shock.

Shock waves in sprays: numerical study of secondary atomization and experimental comparison

Abstract: Numerical modeling of the interaction between a cloud of water droplets and a planar shock wave is compared with experimental data. The mathematical model relies on an Eulerian description of the dispersed phase with the assumption of dilute flows. It is shown that the secondary atomization of the droplets strongly influences the structure of both the shock wave and the induced flow. After shock loading, the individual liquid components generate daughter droplets, and the overall interphase surface per unit volume undergoes strong variations which modify the pressure relaxation process towards a dynamic and thermal equilibrium state. The experimental data enable one to determine the best analytical formulation of the droplet number production rate. Models of droplet number production rate are compared in order to highlight this feature. The model based on the assumption of linear variation of droplet diameter with time gives the best agreement between the numerical results and the experimental data.

Effect of thermal nonequilibrium on reactions in hydrogen combustion

Abstract: The presence of shocks in scramjet internal flows introduces nonequilibrium of internal energy modes of the molecules. Here, the effect of vibrational nonequilibrium on key reactions of hydrogen–air combustion is studied. A quasi-classical trajectory (QCT) approach is used to derive reaction probability for nonequilibrium conditions using ab initio-derived potential energy surfaces. The reaction rates under nonequilibrium are studied using a two-temperature description, where the vibrational modes are assumed to be distributed according to a Boltzmann distribution at a characteristic vibrational temperature, in addition to a translational temperature describing the translational and rotational population distribution. At scramjet-relevant conditions, it is found that the nonequilibrium reaction rate depends not only on the level of vibrational excitation, but also on the reactants involved. Conventional two-temperature models for reaction rates, often derived using empirical means, were found to be inaccurate under these conditions, and modified parameters are proposed based on the QCT calculations. It is also found that models that include details of the reaction process through dissociation energy, for instance, provide a better description of nonequilibrium effects.

Numerical simulation of armored vehicles subjected to undercarriage landmine blasts

Abstract: Landmine threats play a crucial role in the design of armored personnel carriers. Therefore, a reliable blast simulation methodology is valuable to the vehicle design development process. The first part of this study presents a parametric approach for the quantification of the important factors such as the incident overpressure, the reflected overpressure, the incident impulse, and the reflected impulse for the blast simulations that employ the Arbitrary Lagrangian-Eulerian formulation. The effects of mesh resolution, mesh topology, and fluid-structure interaction (FSI) parameters are discussed. The simulation results are compared with the calculations of the more established CONventional WEaPons (CONWEP) approach based on the available experimental data. The initial findings show that the spherical topology provides advantages over the Cartesian mesh domains. Furthermore, the FSI parameters play an important role when coarse Lagrangian finite elements are coupled with fine Eulerian elements at the interface. The optimum mesh topology and the mesh resolution of the parametric study are then used in the landmine blast simulation. The second part of the study presents the experimental blast response of an armored vehicle subjected to a landmine explosion under the front left wheel in accordance with the NATO AEP-55 Standard. The results of the simulations show good agreement with the experimental measurements.

Auto-ignitions of a methane/air mixture at high and intermediate temperatures

Abstract: A rapid compression machine (RCM) and a shock tube (ST) have been employed to study ignition delay times of homogeneous methane/air mixtures at intermediate-to-high temperatures. Both facilities allow measurements to be made at temperatures of 900–2000 K, at pressures of 0.38–2.23 MPa, and at equivalence ratios of 0.5, 1.0, and 2.0. In ST experiments, nitrogen served as a diluent gas, whereas in RCM runs the diluent gas composition ranged from pure nitrogen to pure argon. Recording pressure, UV, and visible emissions identified the evolution of chemical reactions. Correlations of ignition delay time were generated from the data for each facility. At temperatures below 1300 K, a significant reduction of average activation energy from 53 to 15.3 kcal/mol was obtained. Moreover, the RCM data showed significant scatter that dramatically increased with decreasing temperature. An explanation for the abnormal scatter in the data was proposed based on the high-speed visualization of auto-ignition phenomena and experiments performed with oxygen-free and fuel-free mixtures. It is proposed that the main reason for such a significant reduction of average activation energy is attributable to the premature ignition of ultrafine particles in the reactive mixture.

Design of a pulse-type strain gauge balance for a long-test-duration hypersonic shock tunnel

Abstract: When the measurement of aerodynamic forces is conducted in a hypersonic shock tunnel, the inertial forces lead to low-frequency vibrations of the model, and its motion cannot be addressed through digital filtering because a sufficient number of cycles cannot be obtained during a tunnel run. This finding implies restrictions on the model size and mass as the natural frequencies are inversely proportional to the length scale of the model. Therefore, the force measurement still has many problems, particularly for large and heavy models. Different structures of a strain gauge balance (SGB) are proposed and designed, and the measurement element is further optimized to overcome the difficulties encountered during the measurement of aerodynamic forces in a shock tunnel. The motivation for this study is to assess the structural performance of the SGB used in a long-test-duration JF12 hypersonic shock tunnel, which has more than 100 ms of test time. Force tests were conducted for a large-scale cone with a $$10^{\circ }$$ semivertex angle and a length of 0.75 m in the JF12 long-test-duration shock tunnel. The finite element method was used for the analysis of the vibrational characteristics of the Model-Balance-Sting System (MBSS) to ensure a sufficient number of cycles, particularly for the axial force signal during a shock tunnel run. The higher-stiffness SGB used in the test shows good performance, wherein the frequency of the MBSS increases because of the stiff construction of the balance. The experimental results are compared with the data obtained in another wind tunnel and exhibit good agreement at $$M = 7$$ and $$\alpha =5^\circ $$ .

Experiments in hand-operated, hypersonic shock tunnel facility

Abstract: Experiments were conducted using the newly developed table-top, hand-operated hypersonic shock tunnel, otherwise known as the Reddy hypersonic shock tunnel. This novel instrument uses only manual force to generate the shock wave in the shock tube, and is designed to generate a freestream flow of Mach 6.5 in the test section. The flow was characterized using stagnation point pressure measurements made using fast-acting piezoelectric transducers. Schlieren visualization was also carried out to capture the bow shock in front of a hemispherical body placed in the flow. Freestream Mach numbers estimated at various points in the test section showed that for a minimum diameter of 46 mm within the test section, the value did not vary by more than 3 % along any cross-sectional plane. The results of the experiments presented here indicate that the device may be successfully employed for basic hypersonic research activities at the university level.

Numerical simulation of Mach reflection of cellular detonations

Abstract: The Mach reflection of cellular detonation waves on a wedge is investigated numerically in an attempt to elucidate the effect of cellular instabilities on Mach reflection, the dependence of self-similarity on the thickness of a detonation wave, and the initial development of the Mach stem near the wedge apex. A two-step chain-branching reaction model is used to give a thermally neutral induction zone followed by a chemical reaction zone for the detonation wave. A sufficiently large distance of travel of the Mach stem is computed to observe the asymptotic behavior in the far field. Depending on the scale at which the Mach reflection process occurs, it is found that the Mach reflection of a cellular detonation behaves essentially in the same way as a planar ZND detonation wave. The cellular instabilities, however, cause the triple-point trajectory to fluctuate. The fluctuations are due to interactions of the triple point of the Mach stem with the transverse waves of cellular instabilities. In the vicinity of the wedge apex, the Mach reflection is found to be self-similar and corresponds to that of a shock wave of the same strength, since the Mach stem is highly overdriven initially. In the far field, the triple-point trajectory approaches a straight line, indicating that the Mach reflection becomes self-similar asymptotically. The distance of the approach to self-similarity is found to decrease rapidly with decreasing thickness of the detonation front.

Numerical simulation of a compressible vortex–wall interaction

Abstract: The wall interaction of isolated compressible vortices generated from a short driver section shock tube has been simulated numerically by solving the Navier–Stokes equations in axisymmetric form. The dynamics of shock-free (incident shock Mach number $$M = 1.36$$ ) and shock-embedded $$(M = 1.57)$$ compressible vortices near the wall has been studied in detail. The AUSM+ scheme with a fifth-order upwind interpolation formula is used for the convective fluxes. Time integration is performed using a low dissipative and dispersive fourth-order six-stage Runge–Kutta scheme. The evolution of primary and wall vortices has been shown using the velocity field, vorticity field, and numerical schlierens. The vortex impingement, shocklets, wall vortices, and their lift-off are clearly identified from the wall pressure time history. It has been observed that the maximum vorticity of the wall vortices reaches close to 30 % of the primary vortex for $$M = 1.36$$ and it reaches up to 60 % for $$M = 1.57$$ . The net pressure force on the wall due to incident shock impingement is dominant compared to the compressible vortex impingement and their evolution.

Explosive-driven shock wave and vortex ring interaction with a propane flame

Abstract: Experiments were performed to analyze the interaction of an explosively driven shock wave and a propane flame. A 30 g explosive charge was detonated at one end of a 3-m-long, 0.6-m-diameter shock tube to produce a shock wave which propagated into the atmosphere. A propane flame source was positioned at various locations outside of the shock tube to investigate the effect of different strength shock waves. High-speed retroreflective shadowgraph imaging visualized the shock wave motion and flame response, while a synchronized color camera imaged the flame directly. The explosively driven shock tube was shown to produce a repeatable shock wave and vortex ring. Digital streak images show the shock wave and vortex ring propagation and expansion. The shadowgrams show that the shock wave extinguishes the propane flame by pushing it off of the fuel source. Even a weak shock wave was found to be capable of extinguishing the flame.

Set-valued solutions for non-ideal detonation

Abstract: The existence and structure of a steady-state gaseous detonation propagating in a packed bed of solid inert particles are analyzed in the one-dimensional approximation by taking into consideration frictional and heat losses between the gas and the particles. A new formulation of the governing equations is introduced that eliminates the difficulties with numerical integration across the sonic singularity in the reactive Euler equations. With the new algorithm, we find that when the sonic point disappears from the flow, there exists a one-parameter family of solutions parameterized by either pressure or temperature at the end of the reaction zone. These solutions (termed “set-valued” here) correspond to a continuous spectrum of the eigenvalue problem that determines the detonation velocity as a function of a loss factor.

Viscous solution of the triple-shock reflection problem

Abstract: The reflection of a triple-shock configuration was studied numerically in two dimensions using the Navier–Stokes equations. The flow field was initialized using three shock theory, and the reflection of the triple point on a plane of symmetry was studied. The conditions simulated a stoichiometric methane-oxygen detonation cell at low pressure on time scales preceding ignition when the gas was assumed to be inert. Viscosity was found to play an important role on some shock reflection mechanisms believed to accelerate reaction rates in detonations when time scales are small. A small wall jet was present in the double Mach reflection and increased in size with Reynolds number, eventually forming a small vortex. Kelvin–Helmholtz instabilities were absent, and there was no Mach stem bifurcation at Reynolds numbers corresponding to when the Mach stem had travelled distances on the scale of the induction length. Kelvin–Helmholtz instabilities are found to not likely be a source of rapid reactions in detonations at time scales commensurate with the ignition delay behind the Mach stem.

Multi-frame visualization for detonation wave diffraction

Abstract: When a detonation wave emerges from a tube into unconfined space filled with a gas mixture, detonation wave diffraction occurs due to abrupt changes in the cross-sectional area. In the present study, we focused on the local explosion in reinitiation and propagation of a transverse detonation wave by performing comprehensive and direct observation with high time resolution visualization in a two-dimensional rectangular channel. Using the visualization methods of shadowgraph and multi-frame, short-time, open-shutter photography, we determined where the wall reflection point is generated, and also determined where the bright point is originated by the local explosion, and investigated the effects of the deviation angle and initial pressure of the gas mixture. We found that the reinitiation of detonation had two modes that were determined by the deviation angle of the channel. If the deviation angle was less than or equal to 30 $$^{\circ }$$ , the local explosion of reinitiation might occur in the vicinity of the channel wall, and if the deviation angle was greater than or equal to 60 $$^{\circ }$$ , the local explosion might originate on the upper side of the tube exit. With a deviation angle greater than 60 $$^{\circ }$$ , the position of the wall reflection point depended on the cell width, so the radial distance of the wall reflection point from the apex of the tube exit was about 12 times the cell width. Similarly, the bright point (local explosion point) was located a distance of about 11 times the cell width from the apex of the tube exit, with a circumferential angle of 48 $$^{\circ }$$ .