Session X15: Shock Waves and Explosions

Shock wave propagation from a shotgun shell

Shotgun shell blanks with no projectiles are used to produce shock waves which are used for seismic mapping in geologic materials.  The shock wave produced by the shotgun shell is examined here to understand its propagation in air, solid PMMA, and through a granular sand material.   Schlieren imaging techniques and ultra high-speed cameras are implemented to visualize the wave propagation.  Quantitative tools including quantitative schlieren, Photon Doppler Velocimetry (PDV), and accelerometers are used to characterize the shock wave density and particle velocity at various distances from the source in each propagation medium.  The pressure-time history in the shotgun shell case is measured and used to further understand the shock wave source.  The measurement suite allows characterization of the shock wave propagation in the near and far fields which is critical for its use as a seismic mapping source.    

Experimental Examination of Shock Wave Phenomena in Ducts with Abrupt Area Expansions

This experimental study explores the shock wave and flow field evolution as the shock propagates far downstream from an abrupt area expansion. Close to the expanded region's entrance, intricate phenomena arise, including the formation of a substantial vortex near the expansion corner, which eventually evolves into a steady shear layer. As the shock wave progresses beyond the expansion, it initially undergoes regular reflection from the walls and subsequently transitions to Mach reflection. This results in a series of reflected shock waves propagating slower than the incident shock wave, inducing significant pressure fluctuations behind the shock wave. These fluctuations persist for an extended duration, increasing in number and reducing in strength as the shock wave front advances further downstream until eventually they reach a uniform strength. The reflection pattern behind the incident shock wave effectively divides the region into two distinct parts: a highly transient region characterized by strong shock waves and pressure fluctuations and a steady-state region. Notably, the study highlights the extended duration of the highly transient region and its growth as the shock wave front moves downstream, an aspect not extensively reported in previous research.   

Dynamic Shock Waves transitions in Unsteady Supersonic Flows

Predicting the shock reflections and the shock wave interactions holds paramount importance in the design and operation of various engineering applications, including supersonic and hypersonic vehicles, explosion gas dynamics, and shock wave focusing. The dynamic transition between Regular Reflection (RR) and Mach Reflection (MR) phenomena significantly affects the functionality and design of supersonic and hypersonic air-breathing vehicles. Consequently, this study investigates the dynamic transition between RR and MR in unsteady supersonic flow using a two-dimensional moving wedge, wherein the trailing edge moves upstream along the x-direction with a velocity, V(t), while considering different free-stream Mach numbers. The transient simulation is carried out using an unsteady compressible inviscid flow solver, employing the Arbitrary Lagrangian-Eulerian (ALE) technique to simulate the wedge motion. The transition from RR to MR is defined using sonic and detachment criteria. The study's results shed light on the impact of the moving wedge rate on the dynamic shock system.   

Application of stochastic data assimilation to a non-reacting shock tube configuration

An ensemble-based data assimilation method is presented for uncertainty reduction in a stochastically represented non-reacting shock tube calculation. Two modifications on the traditional ensemble Kalman filter (EnKF) are used. The first, a normal-score ensemble Kalman filter (NS-EnKF), is used to assimilate non-Gaussian distributed quantities, and the second, a feature-informed ensemble Kalman filter (FI-EnKF), enables tracking of global features. The methods are applied independently and in sequence to assimilate temporally evolving fluid states with noisy pressure observations, improving estimates of the true system state. Results are compared to the traditional EnKF and experimental shock tube data.   

Quantification of the perturbations in an explosive gas cloud during expansion using edge tracking and image processing.

The expansion of explosively driven product gases from perturbed C-4 spheres was investigated using high-speed photography and image processing. Spherical charges constructed of 105 g and 880 g of C-4 were used as explosive sources. Each mass explosive charge was tested in three surface geometry variants: baseline smooth, perturbed with 10/π cycles/rad ripples, and perturbed with 20/π cycles/rad ripples. Each test sample was initiated using RP-83 EBW detonators and the explosion was recorded using a Shimadzu HPV-X2 camera. The high-speed video frames were then processed to assemble digital streak images using various streak angles. Radial expansion velocities were extracted from binarized frames. The perturbations on the spheres translated to ripples on the gas clouds for both sphere sizes with the initial perturbations dominating early time gas expansion, resulting in distinct regions of faster and slower radial expansion. For the smooth samples, the edge of the fireball had no discernable structure to its turbulence. At 10/π cycles/rad, the surface of the fireball began to expand noticeably faster where perturbations were initially present. The 20/π cycles/rad samples also displayed faster local expansion at perturbation areas albeit with less clear distinction between ripples than for the 10/π cycles/rad samples.   

Analytical linear theory for Richtmyer-Meshkov instability in shock-flame interactions

Shock-flame interactions play a critical role in various combustion applications, including flame acceleration and control in supersonic propulsion systems. In safety combustion technology, understanding shock-flame catch-up is particularly important as the post-interaction flow field can lead to deflagration-to-detonation transition. The increased flame surface and temperature resulting from the interaction contribute to enhanced flame speed. This work aims to quantify the deformation rate of the flame surface and burning velocity caused by a planar shock crossing a corrugated laminar flame from behind. During the interaction, a pair of corrugated transmitted and reflected shocks are generated, resembling the canonical Ricthmyer-Meshkov instability (RMI). At times significantly shorter than the characteristic flame burning time, the flame front deforms as an inert interface dominated by the RMI. To understand this phenomenon better, we employ a comprehensive, fully-analytical linear theory that explicitly describes the flame growth rate. Our analytical approach accounts for the unbalanced shock-generated tangential velocities across the flame interface, obtaining both transient and asymptotic growth rates and providing a comprehensive analysis of the flame evolution during the interaction process.   

Investigation of the shock formation process in double-diaphragm shock tubes

A comprehensive understanding of the shock formation process is crucial for reliable experimental data in shock tubes. Previous research primarily focused on shock tubes equipped with a single diaphragm, where its rupture leads to the formation of compression waves that accelerate and merge, eventually forming a shock wave. To achieve precise control over post-shock conditions, an additional diaphragm is often incorporated between the primary diaphragm and the driven section. Upon sudden release of the gas in the intermediate section between the two diaphragms, the primary diaphragm ruptures first, followed by the secondary diaphragm, leading to a sequence of shock front acceleration and deceleration.

In our double-diaphragm shock formation investigation, experiments covered driver pressures of 15 to 60 bar and driven pressures of 100 to 600 Torr with Ar, N2, and CO2 as driven gases. At low Mach numbers (Mach < 4), shock profiles were non-uniform, suggesting complex wave interactions. Higher Mach numbers revealed a distinctive behavior with two stages of shock deceleration. Analyzing slope differences in shock profiles provided deeper understanding of their individual contributions.

We used an in-house WENO code for 1D simulations with the intermediate section and a delayed opening of the secondary diaphragm. The results provide insights into shock formation in double-diaphragm mode of shock tube operation and help in precisely controlling shock parameters.   

Triple Point Path Prediction of Diffracted Shock Waves Through Computational Fluid Dynamics Simulations.

Explosions inside structures, civilian or military alike, are an alarming safety issue. Due to complex interactions between internal geometries and the blast wave, predicting the flow patterns with any sort of certainty is an insurmountable task. Triple points, Mach stems, reflected shocks, and diffracted shocks are some of the common complicated flow phenomena that may arise. With this work, we aim to explore the analogy of a blast wave and a diffracted shock wave by assessing the triple point (TP) path using numerical simulations. A diffracted shock may approximate a blast wave for large corner angles. This is done by using a double-bend duct geometry through Euler and turbulent simulations. The TP path is measured with the goal of sizing the height of the exit duct to allow the TP path to pass completely into the exit duct. The incident Mach number is varied along with the inlet height to generate a wide range of curves for comparison with the corner angle remaining constant. Due to our simulations lacking an incident charge mass, limited literature comparisons can be made. However, due to this, one major outcome will be a simple model that allows explosive researchers and shock diffraction researchers to address TP path outside of the existing models.   

Reducing the uncertainty of unsteady drag coefficient measurements for micron-sized particles

At Los Alamos National Laboratory’s Horizontal Shock Tube (HST) facility we are studying acceleration of shocked isolated micron-scale liquid and solid droplets in a gas. Unsteady forces on microparticles driven by a shock wave are not well understood and difficult to model, therefore standard drag coefficients may not predict the motion of particles. Our current experiments are part of an ongoing campaign to improve drag laws in this regime and performed in conjunction with validation and computational efforts. We detail the optimization of our micron-sized particle seeding systems for both liquid and solid particles, including monitoring resulting distribution. This assisted in reducing random and systematic uncertainty of resultant drag coefficient measurements. This work was done by carefully controlling and tuning liquid spray injector and particle solution concentration. Sifting of solid particles was also performed prior to injecting into test section. We minimize moisture and electrostatic forces which cause clumping by implementing a new grounded stainless-steel particle recirculation system. As final step we created synthetic data to evaluate our processing technique. As a result, we see a reduction in estimated drag which can be attributed to reduction in uncertainty.   

The fractal behavior of explosively driven product gasses with initial surface perturbation

Characterization of the interface between explosive product gases and ambient air in an explosion is a complicated task due to the turbulent mixing and inherently three-dimensional expansion of the interface. This study aims to quantify the evolution of the interface as a temporally-varying fractal dimension. The impact of dominant initial surface perturbations, represented by a sinusoidal azimuthal variation in radius, is assessed. Perturbations of 10/π cycle/rad and 20/π cycle/rad were used, and a smooth, non-perturbed case was used as a baseline measurement. On the two tested charge masses of 105 g and 880 g, the effective angular wave numbers of the perturbations varied between k = 384.6 rad/m and k = 1574 rad/m. The early time product gas, or fireball, expansion was captured using high-speed cameras. Gas interface location profiles are extracted using automated image processing algorithms. The Hausdorff dimension was estimated using boxcounting algorithms on the extracted profiles. At microsecond time scales, the gas boundary develops fractal-like properties that show similar scaling to explosive fireball radius-time scaling. Despite apparent structural differences in fireball evolution, perturbations do not appear to have a significant effect on the evolution of the fractal dimension, with variations remaining inside the measurement uncertainty for the fractal dimension.   

Analysis of high explosive burn methodologies in cylinder test simulations

High explosive (HE) detonation is typically modeled at the continuum scale with either a programmed burn or reactive burn method. Reactive burn methods use a shock induced reaction rate which controls the transition from explosive reactants to products. This requires a fine computational mesh which ideally resolves the reaction zone. In programmed burn methods, the HE lighting time and detonation velocity are determined from an evolution equation which should then be consistent with energy release from the equation of state (EOS). These methods can utilize mesh resolutions much larger than the reaction zone, but at the cost of decoupling the shock front from the reaction. This work investigates simulations of the cylinder test, which measures the expansion of an explosive-filled copper tube, using different programmed and reactive burn models. These include programmed burn with a Huygen's construction wavefront, Detonation Shock Dynamics (DSD) with a velocity-adjusted EOS or the dynamic small resolved heat release model (DASHER) model, and the Arrhenius Wescott-Stewart-Davis (AWSD) reactive burn model. DASHER is a relatively new programmed burn method which assumes that most of the chemical energy is instantaneously released at the shock and the remainder is released via the AWSD burn model. Key advantages and disadvantages of each model are discussed, with particular attention paid to the DASHER model.