Session L5: Compressible Flow: Shock Waves

Optical diagnostics of turbulent mixing in explosively-driven shock tube

Explosively-driven shock tube experiments were performed to investigate the turbulent mixing of explosive product gases and ambient air. A small detonator initiated Al / I$_{\mathrm{2}}$O$_{\mathrm{5}}$ thermite, which produced a shock wave and expanding product gases. Schlieren and imaging spectroscopy were applied simultaneously along a common optical path to identify correlations between turbulent structures and spatially-resolved absorbance. The schlieren imaging identifies flow features including shock waves and turbulent structures while the imaging spectroscopy identifies regions of iodine gas presence in the product gases. Pressure transducers located before and after the optical diagnostic section measure time-resolved pressure. Shock speed is measured from tracking the leading edge of the shockwave in the schlieren images and from the pressure transducers. The turbulent mixing characteristics were determined using digital image processing. Results show changes in shock speed, product gas propagation, and species concentrations for varied explosive charge mass.   

An experimental study of shock wave propagation through a polyester film

A polyester film is available in a variety of uses such as packaging, protective overlay, barrier protection, and other industrial applications. In the current study, shock tube experiments are performed to study the influence of a polyester film on the propagation of a planar shock wave. A conventional shock tube is used to create incident shock Mach numbers of $M_{s}=$ 1.34 and 1.46. A test section of the shock tube is designed to hold a 0.009 mm, 0.127 mm, 0.254 mm, or 0.508 mm thick polyester film (Dura-Lar). High-temporal resolution schlieren photography is used to visualize the shock wave mitigation caused by the polyester film. In addition, four pressure transducers are used to measure the elapsed time of arrival and overpressure of the shock wave both upstream and downstream of the test section. Results show that the transmitted shock wave in the polyester film is clearly observed and the transmitted shock Mach number is decreased by increasing film thickness.   

Direct Numerical Simulation of a normal shock train with thermal nonequilibrium

The role of a normal shock train in a supersonic engine is to convert a sufficient amount of the incoming kinetic energy into internal energy by the entrance of the combustor, in order to guarantee flame ignition. It comprises a succession of compression and expansion waves attached to a turbulent boundary layer. When the molecular collisional process is not fast enough compared to convective and turbulent timescales, thermal nonequilibrium becomes important, which could alter the energy conversion process. By changing the local thermophysical properties and density, nonequilibrium can change the shock structures leading to changes in the energy conversion process. Here, direct numerical simulations are used to study the effect of such nonequilibrium on a Mach 2.0 rectangular isolator. A one-dimensional time-averaged analysis is used to quantify this effect on the pressure work and turbulent kinetic energy evolution.   

Numerical Study of Shock Wave Attenuation Using Logarithmic Spiral Liquid Sheet.

Research of shock wave attenuation has drawn much attention due to its military and civilian applications. One method to attenuate shock waves is to use water to block the shock wave propagation path and allow the shock wave to lose energy by breaking up the water sheet. We propose a way by holding a water sheet in logarithmic spiral shape, which has the ability of focusing the incident shock wave to its focal region. In addition, the shock wave will break up the bulk water and thus lose energy. The process of shock wave reflecting off and transmitting through the water sheet is numerically modeled using Euler equations and stiffened gas equation of state. In this study, the shock focusing ability of a logarithmic spiral water sheet is compared for various logarithmic spiral sheets. Further, the attenuation effect is quantified by the measurement of pressure impulse and peak pressure behind the transmitted and reflected shock waves.   

Material Point Methods for Shock Waves

Particle methods are often the choice for problems involving large material deformation with history dependent material models. Often large deformation of a material is caused by shock loading, therefore accurate calculation of shock waves is important for particle methods. In this work, we study four major versions (original MPM, GIMP, CPDI, and DDMP) of material point methods, using a weak one-dimensional isothermal shock of ideal gas as an example. The original MPM fails. With a small number of particles, the GIMP and the CPDI methods produce reasonable results. However, as the number of particles increases these methods do not converge and produce pressure spikes. With sparse particles, DDMP results are unsatisfactory. As the number of particles increases, DDMP results converge to correct solutions, but the large number of particles needed for an accurate result makes the method very expensive to use in shock wave problems. To improve the numerical accuracy while preserving the convergence, conservation, and smoothness of the DDMP method, a new numerical integration scheme is introduced. The improved DDMP method is only slightly more expensive than the original DDMP method, but accuracy improvements are significant as shown by numerical examples.   

The role of statistical fluctuations on the stability of shockwaves through gases with activated inelastic collisions

The present study addresses the stability of piston driven shock waves through a system of hard particles subject to activated inelastic collisions. Molecular Dynamics (MD) simulations have previously revealed an unstable structure for such a system in the form of high density non-uniformities and convective rolls within the shock structure. The work has now been extended to the continuum level by considering the Euler and Navier-Stokes equations for granular gases with a modified cooling rate to include an impact threshold necessary for inelastic collisions. We find that the pattern formations produced in MD can be reproduced at the continuum level by continually perturbing the incoming density field. By varying the perturbation amplitude and wavelength, we find that fluctuations consistent with the statistical fluctuations seen in MD yield similar instabilities to those previously observed. While the inviscid model predicts a highly chaotic structure from these perturbations, the inclusion of viscosity and heat conductivity yields equivalent wavelengths of pattern formations to those seen in MD, which is equal to the relaxation length scale of the dissipative shock structure.   

Regularized Moment Equations and Shock Waves for Rarefied Granular Gas

It is well-known that the shock structures predicted by extended hydrodynamic models are more accurate than the standard Navier-Stokes model in the rarefied regime, but they fail to predict continuous shock structures when the Mach number exceeds a critical value. Regularization or parabolization is one method to obtain smooth shock profiles at all Mach numbers. Following a Chapman-Enskog-like method [H. Struchtrup, 2004, Phys. Fluids], we have derived the ``regularized`` version 10-moment equations (``R10'' moment equations) for inelastic hard-spheres. In order to show the advantage of R10 moment equations over standard 10-moment equations, the R10 moment equations have been employed to solve the Riemann problem of plane shock waves for both molecular and granular gases. The numerical results are compared between the 10-moment and R10-moment models and it is found that the 10-moment model fails to produce continuous shock structures beyond an upstream Mach number of $1.34$, while the R10-moment model predicts smooth shock profiles beyond the upstream Mach number of $1.34$. The density and granular temperature profiles are found to be asymmetric, with their maxima occurring within the shock-layer [Reddy \& Alam, 2015, J Fluid Mech, vol. 779, R2].   

Existence of solutions to the Guderley implosion problem in arbitrary media

It is known classically that in an ideal gas, there exist self-similar, spherical, converging shock solutions, but much less is understood about the existence of such solutions in compressible flow of real materials. On the other hand, it has recently been pointed out that there exist self-similar solutions for the Euler equations regardless of the equation of state closure model, which suggests the possibility that the Guderley problem might be solvable in general. In this work, we rigorously determine what properties are required of an equation of state in order for an exact, self-similar Guderley flow to be realized, including a generic solution procedure in the cases where existence holds. Among other contexts, this result is of great practical interest for the verification of codes intended to treat shock propagation in a wide variety of real materials.