Session G35: Compressible Flow III: Explosions and Shock Focusing

On the Stability of Ionizing Shocks in Monatomic Gases

Prior work by our group demonstrates the use of a collisional-radiative model in reproducing the correct steady-state shock structure of ionizing shocks in monatomic gases.\footnote{Le, H. P., et al., Bull. Am. Phys. Soc. \textbf{57}, 17 (2012)} In this presentation, we report on time dependent calculations of ionizing shock flows, which reveal additional physical phenomena arising from the unsteadiness and non-linear wave coupling between convection and kinetics. The observed phenomena are similar to instabilities often seen in gaseous detonations.\footnote{Cole, L. K., et al., Combust. Sci. Technol. \textbf{184}, 1502-1525 (2012)} The present model also takes into account radiative heat losses and radiation transport, which result in a reduction in the shock velocity and precursor effects. The latter phenomena may be important at high shock velocities, and are being investigated in detail.   

Modeling Gas-Dynamic Effects in Shock-Tubes for Reaction-Kinetic Measurements

Accurate chemical kinetic models are pivotal for characterizing the effects of new fuel compositions on existing propulsion systems and for developing future combustion technologies. Shock-tube facilities remain invaluable for providing detailed information about ignition delay times, extinction limits, and species time histories for the development and validation of reaction mechanisms. However, viscous and heat transfer effects along the shock-tube wall introduce variations of the thermodynamic state behind the reflected shock wave, thereby affecting the reaction kinetics being measured. These effects have been countered experimentally by the use of driver inserts, extended shock-tube diameters, and the dilution of the test gas. To assist with the design of driver inserts and the selection of operating conditions, a low-order one-dimensional model is developed and compared to two-dimensional Unsteady-Favre-Averaged-Navier-Stokes (UFANS) models as well as experimental data. This model is shown to give accurate predictions of the gas-dynamics in shock-tubes at a computationally efficient cost.   

Shock wave control using liquid curtains

The effectiveness of a planar wall of liquid as a blast mitigation device is examined using a shock tube and a custom-designed and -built shock test chamber. Experimental data collection methods being used include high-speed schlieren photography and high-frequency pressure sensors. During the relevant shock interaction time periods, the liquid-gas interface is examined to determine its effect on shock waves. The characteristic quantities that reflect these effects include reflected-to-incident shock strength ratio, transmitted-to-incident shock strength ratio, transmitted and reflected impulse, and peak pressure reduction. These parameters are examined for correlations to incident wave speed, liquid mass, liquid density, and liquid viscosity. Initial results have been obtained that show a correlation between fluid mass and peak pressure reduction. More experiments are being performed to further explore this relationship as well as examine the effects of altering the other parameters such as liquid-gas interface geometry and using dilatant fluids.   

Explosive-driven shock wave interaction with a propane flame

Experiments were performed to analyze the interaction of an explosively driven shock wave and a propane flame. A 30 gram explosive charge was detonated at one end of a shock tube with a 3 m length and 0.6 m diameter to produce a shock wave which propagated down the tube and out into the atmosphere. A propane flame source was positioned at various locations outside of the shock tube to investigate the flame response to different strength shock waves. Retroreflective shadowgraph imaging with a high-speed digital camera was used to visualize the shock wave motion and flame response. The explosively driven shock tube was shown to produce a repeatable shock wave and a large vortex ring. Digital streak images show the shock wave and vortex ring expansion and propagation throughout the field of view. The high-speed shadowgraph images 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 propane flame.   

Analysis of shock wave propagation from explosives using computational simulations and artificial schlieren imaging

Computational simulations of explosions are performed using the hydrocode CTH and analyzed using artificial schlieren imaging. The simulations include one and three-dimensional free-air blasts and a confined geometry. Artificial schlieren images are produced from the density fields calculated via the simulations. The artificial schlieren images are used to simulate traditional and focusing schlieren images of explosions. The artificial schlieren images are compared to actual high-speed schlieren images of similar explosions. Computational streak images are produced to identify time-dependent features in the blast field. The streak images are used to study the interaction between secondary shock waves and the explosive product gas contact surface.   

An experimental study of shock wave reflection over non-Newtonian liquid wedges

An experimental investigation of the reflection of a planar shock wave over different density liquid wedges was performed by means of an angled shock tube. The goal is to find a transition criterion between regular reflection (RR) and irregular reflection (IR). The shock tube can be rotated to any angle between the horizontal and vertical planes for various impact media. The reflection of the oblique shock wave for different wedges was visualized using the shadowgraph and schlieren techniques. Previous research by Ben-Dor et al. (1987) conducted different types of reflecting solid conditions and Takayama et al. (1989) investigated a similar experiment with a nonsolid reflecting surface. Motivated by the previous work, we undertook a series of shock tube experiments where both Newtonian and non-Newtonian liquids were used to form a wedge for a shock wave to impact. Shear-thickening materials, such as a water-cornstarch mixture, or similar suspensions, could potentially be utilized to protect soldiers and other high-risk personnel from impacts. Results show that, for both a water-cornstarch and ballistic gelatin sample, the detachment angle at which the RR transitions to an IR was different from those of a solid and water.   

A Comparison of Numerical and Experimental Results of Passive Shock Wave Attenuation in Two-Dimensional Ducts

The study of shock wave attenuation has drawn much attention in shock wave area. One of the common ways to attenuate shock waves is to arrange multiple obstacles to block the propagation path of the shock wave. We propose an arrangement of the obstacles by placing the square or cylinder shaped obstacles along the outline of a logarithmic spiral curve, taking advantage of its ability of collecting the incident shock wave to its focal region. We simulated the process of the shock wave passing through these arrangements using the Euler equations of gas dynamics. Then, to validate the numerical results, we present corresponding experiments under the same initial conditions. Results show that the numerical and experimental methods agree well, and that placing obstacles along a logarithmic spiral curve can effectively attenuate the transmitted shock waves.   

Geometrical shock dynamics, formation of singularities and topological bifurcations of converging shock fronts

We are concerned with singularities of the shock fronts of converging perturbed shock waves. Our considerations are based on Whitham's theory\footnote{G.B. Whitham, {\it Linear and Nonlinear Waves}, (John Wiley \& Sons, 1974).} of geometrical shock dynamics. The recently developed method of local analysis\footnote{J. Eggers and M. A. Fontelos, {\it Panoramas et Synth\`eses}, {\bf 38}, 69 (2013).} is applied in order to determine generic singularities. In this case the solutions of partial differential equations describing the geometry of the shock fronts are presented as families of smooth maps with state variables and the set of control parameters dependent on Mach number, time and initial conditions. The space of control parameters of the singularities is analysed, the unfoldings describing the deformations of the canonical germs of shock front singularities are found and corresponding bifurcation diagrams are constructed.   

Simulations on shock focusing effects of multiple munitions using Euler equations and geometrical shock dynamics

Shock propagation effects from single or multiple munitions onto a specified target and its surroundings have been explored. The results of a single blast wave with fixed energy, $E$, was compared to that of $N$ multiple blast waves, each with energy $E/N$ and placed in specific geometrical patterns around the intended target. The intention is to increase the severe conditions at the target area while simultaneously reduce collateral damage. Simulations using the Euler equations with a Godunov scheme have been used to study the dynamics of the shock waves. Results show that multiple munitions generate a coalesced shock front that eventually forms a polygonal converging shock, which reconfigures during propagation towards the target. In order to further study this phenomenon, an approach based on Whitham's theory of geometrical shock dynamics (GSD) has been implemented. In GSD, the motion of the converging shock is computed independent of the flow field behind the shock. Hence, the scheme is efficient and inexpensive and can be used to further analyze the shock focusing effects based on initial location of individual munitions. Results from both simulations will be presented and optical configurations will be discussed.   

Stochastic analysis and robust optimization for a converging shock wave experimental setting

The efficient generation of ultrahigh pressure is one of the key issues in research related to high energy density physics, as for example Inertial Confinement Fusion reactions. In order to create more stable converging shock configurations, recently, it has been proposed to shape the shock front by the means of obstacles. Such polygonal-shaped shocks are expected to be less sensitive to external disturbances that circular ones, but at the same time obstacles produce a loss of energy during the focusing process of the shocks. The aim of this work is to perform a robust shape optimization of the obstacles by taking into account several experimental uncertainties, thus yielding a more stable and efficient shock configuration. For this purpose, both inviscid and viscous turbulent solvers are coupled with a Polynomial Chaos method. This analysis allows estimating the variability of the maximal temperature and energy. Finally, obstacle shape is optimized in order to maximize the energy concentration and thus provide useful remarks for improving the experience. The effect of neglecting viscous terms in the optimization process is also investigated.