Session T21: Compressible Flows III

Stability of reactive shocks in the generalized Noh problem

D'yakov-Kontorovich (DK) instability is the name of the instability associated with steady shock waves. Despite the extensive literature accumulated since the pioneering works in the 1950s, the stability of steady shocks is still an open question when realistic boundary conditions are considered. There is just one explicit dispersion relationship known so far that applies only to isolated shocks, for which the DK instability reduces to a non-decaying oscillating regime accompanied by a spontaneous acoustic emission (SAE). However, the consideration of a supporting mechanism modifies the shock dynamics in this unstable range. We derive an explicit equation that determines the stability limits and the growth rate of perturbations for steady expanding shocks provided by the generalized Noh problem, i.e., non-isolated conditions. The dispersion equation is presented in terms of fundamental parameters describing the shock and geometry parameters. Within the SAE conditions used by Bates and Montgomery in a van der Waals gas, we find that cylindrical and spherical expanding shocks become literally unstable for sufficiently high mode numbers. Counterintuitively, it is found that the effect of exothermicity or endothermicity across the shock is stabilizing or destabilizing, respectively.   

Explosively-driven shock wave propagation around geometrical arrays

Explosively-driven shockwave propagation around geometrical arrays was studied using quantitative schlieren imaging.  The experiments were performed in transparent acrylic with various density inclusions incorporated.  Quantitative schlieren allowed visualization of shock reflection and diffraction patterns and measurement of local densities. Each sample was made with a 30° triangular shape connected a square base of 31.75 mm (1.25 in) in length. Inclusions of 6.35 mm (0.25 in) in diameter were placed on the base of the sample. Exploding bridgewires and detonators were used as explosive sources, which were initiated flush to the vertex angle of the acrylic plate to produce a shockwave.  High-speed refractive imaging was used to visualize and track the complexity of the shockwave propagating around the inclusions. Varied geometrical arrays were used to produce controlled shock wave interactions.    

Persistence of shock asymmetries in asymmetric charge detonations

True spherical explosive charges are extremely difficult to manufacture. This study aims to determine if a more manufacturable shape charge can be used as an approximation of a spherical charge. The hydrocode CTH was used to model the three-dimensional expansion of a PETN spherical charge and one-gram PETN pellets with increasing degrees of asymmetries. The center-initiated spherical charge is used as a baseline for ideal spherical gas expansion and shock wave propagation. The asymmetric charges explore charge geometry and initiation location and the resulting gas expansion and shock wave motions. The control data is compared to the asymmetrical charges to determine the persistence of shock wave asymmetries.   The results here show that a moderately asymmetric charge, which is easier to manufacture, can be a good approximation to a spherical charge after a few diameters of shock wave and product gas expansion.  Asymmetrical charges impact the strength and shape of late-time shock wave features like the secondary shock wave.    

High-resolution background-oriented schlieren (BOS) imaging of large-scale field explosions

Background oriented schlieren (BOS) processing techniques are used to extract quantitative data of explosively-driven shocks from high-speed images. The explosive events utilize natural backgrounds and are recorded with high-resolution high-speed cameras with varied settings. The images are post-processed with optical flow processing techniques. Optical flow processing methods are utilized to enhance the flow visualization behind the shock wave to extract quantitative refractive field and density information. The optical flow processing has not previously been applied to explosively-driven flows. Optical flow combined with BOS image subtraction processing and automated shock wave detection methods allow the extraction of the position and velocity of the shock waves from the BOS images of the explosively-driven shocks.   

2-D and 3-D Direct Numerical Simulations of a Shock Interaction with a Cloud of Particles

The present study explores the effect of viscosity, particle volume fraction, and shock strength on the long-term “steady-state” drag experienced by a cloud of particles under shock-wave loading. This study aims to extract drag statistics, such as mean, standard deviation, and explore the correlation with post-shock fluid statistics. Based on the statistics and correlation studies we highlight the dominant physical mechanisms responsible for long-term drag experienced by the particles. The differences between drag-statistics for 2-D and 3-D clouds of particles are illustrated and the viability of a multi-fidelity drag model is explored based on results from high and low-fidelity 2-D and 3-D simulations, respectively. We also investigate the importance of unclosed terms from the averaged governing equations.   

Joule Heating Driving Hydrodynamic Explosions from an Electrostatic Discharge Event

An electrostatic discharge (ESD) spark in ambient air involves electric fields strong enough to ionize air; it also creates enough Joule heating to generate a shock wave. Modeling this transient process requires an intricate coupling between Joule heating and hydrodynamic flow, with spatial and time-dependent feedback between the plasma kinetics of the ESD spark creating Joule heating and fluid flow. Within this work, a Joule heating source modeling plasma chemistry is parameterized and mapped via a high-fidelity shock-physics code to obtain physical characteristics on fluid flow, simulating an 'infinite' axial line source explosion. Shockwave generation, propagation, and energy consumption exemplify hydrodynamic phenomena observed and calculated. Energy consumption by the hydrodynamics is 'earmarked' for advection away from the axial line source, and is guaranteed to be unavailable for other physical processes within the ESD event. Comparison to experimental validation data is performed and theoretical verification over a complete range of shock regimes is executed. Excellent agreement between hydrodynamic flow generated by simulation and collected from experiment in the strong and intermediate shock regimes is observed, substantiating the assumed form of the heat source.   

An Analytic Analysis of Aluminum Gap Experiments: Extending Curved Shock Theory to Linear D - u Materials

A detonation wave propogating through a rate stick is known to have visible curvature,and thus a shock wave propogated into an Aluminum gap from a detonation also has visible curvature. As the shock passes from the Aluminum gap back into the explosive, a regularly reflected shock forms driven by the reflection points moving radially outward as the incident wave collides with the interface. In order to relate the curvatures of the incident and reflected shock waves, we extend Sannu Molder's theory of curved shocks (CST) to materials with linear shock speed - particle speed relationships, which include many common metals such as Aluminium. Our presentation of the curved shock equations for this class of materials introduces the possibility of new benchmark solutions for experiments of this kind.   

Generalized Supersonic Flow Characteristics for 2D Rotational, Non-Isentropic Flow with Application to Influence of Confinement on Detonation Propagation

Detonations are supersonic waves consisting of a lead shock driven by energy release from reacting flow. In high explosives, the structure of the reaction zone is strongly influenced by the effects of surrounding (strong or weak) confinement. The high detonation pressures (tens of GPa) generated causes the material confinement to deflect, inducing a multi-D structure to the detonation reaction zone and thereby influencing both the rate of propagation and confinement push. Structurally, a multi-D sonic plane in the frame of the detonation shock separates regions of subsonic and supersonic flow and defines the boundary of influence that can affect detonation propagation. However, we have recently discovered that information flow from the confinement boundaries is able to propagate through the supersonic flow region and impact the sonic boundary, thus influencing the detonation driving zone structure. In order to analyze this information flow, we have constructed a 2D characteristic flow analysis that applies generally to rotational, non-isentropic flow. We apply this construction to analyze the influence of confinement boundaries on detonation propagation in 2D planar and circular arc geometries.   

Partial Cavity Shedding Mechanisms on a Pitching Hydrofoil

Unsteadiness in the incoming flow can affect the formation and dynamics of a partial cavity. On hydrofoils experiencing partial cavitation, either a liquid re-entrant flow or a propagating bubbly shock wave can cause periodic shedding of vapor clouds. In this study, cavitation dynamics on a plano-convex hydrofoil are studied at both stationary and pitching conditions at maximum pitching rates on the order of 10,000 deg/s^2. The effect of flow unsteadiness achieved by pitching the hydrofoil is examined using time resolved X-ray densitometry and high-speed cinematography. In addition, synchronized unsteady surface pressure and cavity static pressure measurements are also measured. The effect of pitching motion on the shedding mechanisms and cavity topology at various angular accelerations is discussed.   

Protein molecular deformation and protein crystal damage induced by shock waves traveling in liquid microjets

Femtosecond crystallography studies done at X-ray laser facilities are an emerging method that provides new insights into the biological function of complex proteins. Second-generation X-ray lasers enable acquisition rates exceeding a million diffraction images per second, and to supply fresh protein crystals at these rates, they must be carried by high-velocity liquid microjets. These microjets also guide the shock waves generated by previous X-ray pulses. The effect of shocks generated by previous X-ray pulses on lysozyme and carboxyhemoglobin crystals was investigated experimentally. The molecular structure of the lysozyme did not change after shocks with amplitudes up to 140 MPa, but the quality of diffraction data decreased for shocks above 30−45 MPa, indicating crystal damage. In contrast, the molecular structure of carboxyhemoglobin changed after shocks ranging from 35 to 70 MPa. These results suggest the shocks induced brittle failure in lysozyme but plastic deformation in carboxyhemoglobin, and were used to estimate under what conditions X-ray laser crystallography data is likely to be affected by such shocks.   

Effect of evaporation and surface tension on shock droplet interactions using detailed numerical simulations

Evaporation plays an important role in liquid fuel droplet combustion [1] and is dictated by several factors including the particle size, gas temperature and shock strength. The size distribution of droplets is governed by breakup and coalescence processes, which are highly sensitive to surface tension. Extreme conditions encountered in combustion and detonations pose significant challenges to experimental investigations of these processes. In this work, we describe results from detailed numerical simulations of the evolution of a JP-10 liquid droplet in a heated air environment processed by an impinging shock wave. Simulations were performed for different shock Mach numbers and droplet diameters to isolate the effects of surface tension and evaporation on droplet breakup. A fifth order in space, WENO code, IMPACT was used to solve the Euler equations in Cartesian geometry with Adaptive Mesh Refinement and coupled to third-order Runge-Kutta scheme for time integration. The Level set method was used to track the interface between the liquid and gaseous phases and the Ghost Fluid Method (GFM), integrated with a multi-medium Riemann solver [2] was used to couple the two phases.   

Resolvent analysis of planar supersonic impinging jet

Supersonic jets impinging on a ground surface are important in vertical takeoff/landing operations. A major determinant of the dynamics is a resonant feedback loop between the ground and the nozzle, producing intense noise tones. An examination of these dynamics in the context of input-output characteristics has the potential to guide noise mitigation strategies. To this end, we employ resolvent analysis on an LES time-mean flow of an under-expanded Mach 1.27 planar jet at Reynolds number of 579,320, impinging on the ground surface 4 diameters downstream. The resolvent analysis is performed over frequency (St), and spanwise wavenumber (β) ranges of 0.1≤ St ≤ 1.05 and 0 ≤ β ≤ 10π, respectively. The gain-peak resides in the 0.35 ≤ St ≤ 0.5 and 2π ≤ β ≤ 4π ranges. Key conclusions are that the energy amplification mechanics is dominated by Kelvin–Helmholtz type of response. The corresponding forcing is essentially white noise around the nozzle. At St~0.45, the KH types of response exhibit symmetric structures at β = 0, π, 3π, 4π, 5π and 6π with higher energy amplification compared to the antisymmetric counterparts at other cases of β. The physical insights provided by the resolvent analysis aid flow control that targets noise mitigation.