The nature of shock waves in soap films is investigated theoretically and experimentally. For one-dimensional flows in soap films, the basic normal shock relations and Rankine-Hugoniot equations are derived. At low concentrations, the results are similar to those of compressible gases. On short time scales, soap films are analogous to compressible gases of \gamma = 1.0. The role of pressure in gases is played by surface tension in the film and that of compressibility by Gibbs or Marangoni elasticity, depending on the time scales of the film stretching. The thickness of the film is an active scalar which responds to the dynamics of the film motion in a manner similar to shallow water flows. A series of experiments is performed. The bursting of plane vertical soap films is studied by means of the high-speed flash photography and the line scan CCD imaging technique. An aureole and a shock wave preceding the expanding hole are clearly observed. The analogy between thickness jumps in soap films and shock waves in gases are then investigated experimentally. Photographs of supersonic flows over blunt bodies are presented. The results suggest the feasibility of the soap film shock tube.
[Hj.02] The Navier-Stokes Shock Profile for a Discrete-Velocity Gas
Balu T. Nadiga (Los Alamos National Lab), C. David Levermore (University of Arizona)
In kinetic theory of gases the Chapman-Enskog (CE) expansion gives an expression for the first order nonequilibrium fluxes in terms of variables conjugate to the conserved variables. For classical monatomic gases these conjugate variables can be simply expressed in terms of the conserved hydrodynamic densities. In contrast, this relationship is not simple for a discrete-velocity gas, i.e., the Navier-Stokes (NS) equation for a discrete-velocity gas is generally not a simple system for \rho, \rho\u, and \rho (e+u^2/2). In such a case, the direct use of conjugate variables is natural. In this talk, we present the CE expansion for a nine-velocity gas with the above choice of variables in the context of a 1D shock wave, and compare the resulting NS shock profile to the full Boltzmann profile. The conjugate variables and the discrete-velocity gas also prove to be useful tools in evaluating various high-order moment closures proposed for the transitional regimes.
[Hj.03] Interaction of Normal Shock Waves with Turbulent Jets
James C. Hermanson (Worcester Polytechnic Institute), Baki M. Cetegen (University of Connecticut)
The changes in the structure and mixing of a turbulent jet due to the passage of a normal shock wave were examined experimentally. An axisymmetric jet (1.1 mm i.d.) of pure air, helium, or carbon dioxide was centered along the axis of an air shock tube 5 x 5 cm square in cross section. The shock propagation was in the same direction as the jet flow. Planar Mie scattering imaging using pulsed laser illumination was performed over a downstream distance of roughly 60 jet diameters by seeding the jet with mineral oil smoke. For the air jet, there was little change in the spatial probability density function (pdf) of the mixed fluid, indicating little increase in mixing due to the shock/jet interaction. For the helium jet, there was a distinct shift in the pdf towards lower concentrations (more mixing) with shock passage. The images for the helium jet with shock interaction also showed a marked change in turbulent structure, leading to large-scale vortical structure not apparent for the case of the air jet. The carbon dioxide jet exhibited less mixing enhancement than the helium jet, and no marked changes in structure compared with the air jet.
[Hj.04] Using an Open-ended Shock Tube to Remove Particles from Surfaces
G.T. Smedley, D.J. Phares, R.C. Flagan (California Institute of Technology, Pasadena, CA 91125)
Experiments have been conducted to examine the dependence of particle removal from a surface on the impingement angle and height above the surface of the exit of a small shock tube. Minute particles of polystyrene (<10\mu m diameter) were manufactured and deposited on freshly cleaned glass substrates by gravitational settling. Dark field microscopy in conjunction with image processing is used to determine the extent of particle removal resulting from each firing of the shock tube. The removal threshold and angular distribution of shock strength are determined by curve fits of a hemispherical-shock model to the particle removal data.
[Hj.05] Numerical Simulation of Droplet Combustion
Kazuto Kuzuu (Institute of Computational Fluid Dynamics, JAPAN), Kuwahara Kunio (The Institute of Space and Astronautical Science, JAPAN)
The combusting flow around a droplet was investigated through a direct numerical simulation method. Calculation was based on the three-dimensional full Navier-Stokes equations coupled with a single step chemical reaction model. The droplet was liquid octane, and the composition of free stream gas was equal to that of air. The temperature of the droplet was assumed to be constant, and then we considered only a gas-phase combustion process. Calculations were carried out under some free stream conditions, velocity and temperature. From our results, we observed some characteristic behaviors about droplet combustion.
[Hj.06] Interaction of a Shock with a Sinusoidally Perturbed Flame
Elaine Oran, Alexei Khokhlov (NRL)
The interaction of a shock wave and a sinusoidally perturbed premixed flame was studied using reactive 2D and 3D Navier-Stokes simulations resolved down to the viscous microscale. The chemical model reproduced the combustion properties of a mixture of stoichiometric acetylene-air. The range of Mach numbers considered (1.25 - 3.0) is too low to cause direct detonation initiation. The basic interaction is a Richtmyer-Meshkov instability that creates vorticity, increases the surface area of the flame, and increases the energy-release rate. Vortices present long after the shock wave has passed through the flame maintain a high level of energy release. 3D perturbations (of given amplitude and wavelength) grow a factor of \simeq 2 faster than comparable 2D perturbations, and the maximum energy-release rate is a factor of \simeq 2 larger in 3D. The vorticity generated is too weak to stretch and extinguish the flame locally. The maximum increase in the energy generation rate due the interaction is at most a factor of 20 to 30. To greatly increase the burning rate, multiple shock-flame interactions are required.
[Hj.07] Shock Amplification and DDT Caused by Shock-Flame Interactions
Alexei Khokhlov, Elaine Oran (NRL)
The interaction of a shock with a spherical flame in shock-tube experiments (G. Thomas et al., U. Wales Aberystywth, 1997) shows the emergence of a high-speed wave that sometimes transitions to a detonation. This interaction is simulated numerically for a stoichiometric acetylene-air mixture at 100 torr over a range of Mach numbers (1.4--1.6) by solving the reactive Navier-Stokes equations and resolving the interaction down to the viscous microscale. The shock-flame interaction increases the flame surface and significantly increases energy generation. As in the experiments, a high-speed wave emerges with a velocity approximately half of the CJ velocity. The material behind the wave is near auto-ignition conditions. For M \simeq 1.5 and higher, spontaneous ignition occurs in the wave, resulting in DDT. This scenario may be a crucial element of the DDT process.
[Hj.08] Experimental and Numerical Investigation of Double-Cone Geometries in Hypersonic Flow
T. D. Magruder, A. J. Smits (Princeton University), J. Olejniczak, M. J. Wright, G. V. Candler (University of Minnesota)
Experiments examining the shock/shock and shock/boundary layer interactions that occur in the flow over double cone geometries have been completed in a hypersonic wind tunnel at Mach 8. The flow structure was examined using schlieren and planar Rayleigh scattering, and surface pressure measurements were obtained at selected locations. The first geometry exhibited a Type VI shock interaction pattern with a small region of separation at the corner. The second model produced a Type V shock interaction with a large region of separated flow in the corner. Laminar CFD calculations were compared with experimental results, and it was found that at lower Reynolds numbers the CFD accurately predicted the shock structure, separation regions, and surface pressure. At higher Reynolds numbers, the experiments indicated transition to turbulence downstream of the shock-wave boundary-layer interaction.
[Hj.09] Flow Between Segments of a Hypersonic Projectile
David B. Goldstein, David D. Young (U. Texas at Austin)
A preliminary computational study of the unsteadiness of the flow between two segments of a hypersonic projectile is described. The stagnation pressure on the trailing segment is found to be highly oscillatory having spikes that are up to five times the mean value. The oscillations are associated with pressure waves moving upstream through a subsonic region and causing vortices to be shed in a manner similar to what is found in other hypersonic/cavity configurations. The time scale of the oscillations is determined by the smallest length between the segments. A time-average of the unsteady flowfield is significantly different than a steady-state solution. The differences indicate that unsteadiness may effect the stability of the trailing body and that the unsteady flow produces a higher drag force on the trailing body than would a truly steady flow.
[Hj.10] Electrohydrodynamic behavior of a drop in an electric field at finite electric Reynolds number
James Q. Feng (Xerox Corporation, Wilson Center for Research and Technology, 800 Phillps Road, Webster, New York 14580)
The electrohydrodynamic flow associated with a fluid drop in an electric field is a consequence of the tangential electric stress at the fluid interface. The presence of fluid flow also leads to charge convection phenomena. The relative significance of the charge convection effect is usually measured in terms of the electric Reynolds number, Re_E, defined as the ratio of the time scale for charge convection by flow and that for charge relaxation by ohmic conduction. This work presents a quantitative analysis of the charge convection effects in a framework of the leaky dielectric model at finite Re_E, which has been lacking in the previous investigations. Axisymmetric steady flows driven by an applied uniform electric field about a deformable fluid drop suspended in an immiscible fluid are studied by computational means of the Galerkin finite-element method with supplementary asymptotic analysis. According to the present results, oblate drops tend to be less deformed in an electric field when influenced by the charge convection. The prolate drops are often associated with an equator-to-pole flow, which convects charges toward the poles to enhance the prolate drop deformation. In many cases, charge convection effects are found to be significant even at apperantly rather small Re_E corresponding to the charge relaxation time scale about 10^-3 s, suggesting that many experimental results reported in the previous publications could have been influenced by charge convection effects.