Session H2: Compressible Flows I

Bulk Viscosities of Low-Pressure Gases

We provide estimates of the bulk viscosity of ideal gases using Tisza's formula and published values of the rotational and vibrational relaxation times. It is shown that, unlike the shear viscosities, the bulk viscosities take on a wide variety of numerical values and temperature variations. Common fluids having bulk viscosities which are hundreds to thousands of times larger than their shear viscosities are identified. We argue that the temperature variation of the bulk viscosity of many fluids will have a local maximum.   

The Inviscid and Boundary Layer Approximations in Fluids with Large Bulk Viscosities

We re-examine the structure of classical inviscid steady flow over a finite body in Navier-Stokes fluids having bulk viscosities which are large compared to their shear viscosities. When the ratio of bulk to shear viscosity is of the order of the square root of the Reynolds number both the inviscid flow and boundary layer require corrections on the order of the inverse square root of the Reynolds number.   

Detailed Simulations of Incident Shock Wave Development and Boundary Layer Growth in Shock Tube Facilities

The boundary layer growth after the incident shock in shock-tube systems results in the attenuation of the incident shock, which leads to uncertainties in measurements. Apart from few computational investigations, the current understanding about the boundary layer dynamics in shock tubes is largely derived from asymptotic analysis. To address this, detailed numerical simulations in realistic shock-tube systems at relevant operating conditions were conducted to quantify direct contributions of the boundary layer development on the incident shock wave and resulting deviations from ideal shock tube conditions. Both 3D results in cylindrical coordinates and 2D axis-symmetry results were compared with theoretical formulations for boundary layer developments. From this study, detailed characterization of boundary layer growth in realistic shock tube systems was obtained to validate potential models.   

Simulations of the Formation and Hydrodynamic Penetration of Micro-Shaped Charge Jets

An explosively formed shape charge jet can be generated by the action of a detonation in explosive charge that surrounds a hollow cone of metal, embedded in the explosive, that collapses the cone on the central axis in order to form a forward-going jet of metal. We discuss the results of a series of multi-material simulations for very small charges and cones, for which the thickness of the metal (copper) cone is less than 1/100th of an inch. We look at the ability of these micro-shaped charge jets ability to penetrate aluminum target blocks and compare against experiment. We examine the effects of shape defects in the cone liner and how they affect the penetration depth. The LLNL multi-physics hydrodynamic code ALE3D is used to carry out the simulations.   

Underwater shock focusing by composite structures

Underwater explosions are threats to the structural integrity of naval vessels. In particular, if a convergent section is present on the vessel, the shock wave can focus and produce extremely high pressures near the focal region. Based on previous research on converging shock waves, a logarithmic spiral duct is considered to be an efficient shape to focus shock waves onto the focal region. Here, underwater shock tests on logarithmic spiral-shaped structures made of plastic, metal and fiber composites are conducted. High-speed schlieren photography is used to visualize the shock waves. Simultaneously, ultrafast pressure readings are recorded by laboratory- made pressure sensors, which are able to measure pressures up to 10 GPa. Comparisons between the various types of surrounding materials will be presented. The results can explore the use of composite materials in future marine applications.   

Large-Eddy Simulation of an over-expanded planar nozzle

Large-eddy simulation (LES) of an over-expanded planar nozzle is performed to elucidate the complex interaction between the turbulent boundary layer, the internal shock wave and the separated shear layer downstream of the shock. This numerical simulation seeks to model one the experiments of Papamoschou et.al. and shed light on the underlying physics of the shock-boundary layer interaction and the Free-Shock Separation (FSS) which is present in over-expanded supersonic nozzles. Simulation results compare well with those obtained from the experiment despite the modeling approximations. The LES captures the unsteady fluctuation of the shock wave as it interacts with the incoming turbulent boundary layer and the separated shear layer downstream. The richness of the simulation data allow for a more in-depth exploration of the underlying physics and have informed development of a reduced order model for approximating the large-scale dynamics of the complex system.   

Creating sharp features by colliding shocks on ion bombarded surfaces

When a surface is bombarded with ions, it erodes at different rates depending on the slope of the surface, and intricate patterns can evolve. On large scales the surface slope evolves according to a conservation law, which can form shocks, while the type of shocks which can occur are governed by the small-scale fourth-order surface diffusion. As in thin film flows, undercompressive shocks (which violate the Lax entropy condition) can occur, and appear to dominate the dynamics when the initial surface contains slopes which are large enough. We show that when two undercompressive shocks moving in opposite directions collide, they form a shock which is undercompressive from both sides. In the height variable this is a stationary, knife-edge like ridge with steep sides; interestingly the slopes are much larger than any contained in the initial surface patterning. This suggests a possible method to pattern surfaces on the small scale more cheaply than by conventional methods: by patterning the surface initially on the macroscale to have slopes of O(1), and then bombarding it with ions, the surface may spontaneously develop features which are much smaller and steeper.   

The Structure of Shock Waves in Liquids

This talk presents solutions of the Navier-Stokes equations that model shock waves in liquids, including water and mercury. One-dimensional jump functions are computed to describe the viscous microstructure of hydrodynamic shocks, which are not isentropic. Empirical equations of state in polynomial form are applied to the conservation laws to derive the physical flow microstructure for shock compressions and pressures up to 2.0 and 50.0 kbars, respectively. Traveling wave solutions are found for the Navier-Stokes equations by integrating the equations of motion along characteristic lines, where the shock wave jump functions are the solution of a two point boundary value problem. The empirical equations of state yield increasing shock wave jump functions for density and pressure. The solution method presented is applicable to arbitrary liquids that behave as Newtonian fluids for one-dimensional planar shock waves.   

Simulation of Deformation, Momentum and Energy Coupling Particles Deformed by Intense Shocks

Modern energetic materials have embedded solids and inerts in an explosive matrix. A detonation in condensed phase materials, generates intense shocks that deform particles as the incident shock diffracts around them. The post-shock flow generates a wake behind the particle that is influenced by the shape changes of the particle. The gasdynamic flow in the explosive products and its interaction with the deformation of the particle must be treated simultaneously. Direct numerical simulations are carried out that vary the particle-to-surrounding density and impedance ratios to consider heavier and lighter particle. The vorticity deposited on the interface due to shock interaction with the particle, the resulting particle deformation and the net momentum and energy transferred to the particle, on the acoustic and longer viscous time scale are considered. The LLNL multi-physics hydrodynamic code ALE3D is used to carry out the simulations.   

Particle Motion Measurements Following the Impingement of a Planar Shock on a Dense Particle Field

The shock-induced dispersal of a dense field of particles is studied using a recently developed multiphase shock tube. The particle field is generated by a gravity-fed method that results in a spanwise curtain of 100-micron spherical particles with a volume fraction of about 20 percent. The facility drives a planar shock into the particle curtain producing interactions at incident shock Mach numbers of 1.66, 1.92, and 2.02. The gas-particle momentum transfer is calculated using a control volume technique that utilizes pressure measurements made upstream and downstream of the interaction along with the method of characteristics. High-speed schlieren imaging reveals the complex wave structure associated with the interaction and also provides a measure of the particle field motion. Particle drag estimates are made using the schlieren imaging and the control volume technique. Furthermore, the trajectories of the upstream and downstream edges of the particle field at different Mach numbers are shown to be similar when normalized by the velocity of the flow induced by the incident shock.