Bradford Sturtevant

Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities

The interaction of a plane weak shock wave with a single discrete gaseous inhomogeneity is studied as a model of the mechanisms by which finite-amplitude waves in random media generate turbulence and intensify mixing. The experiments are treated as an example of the shock-induced Rayleigh-Taylor instability. or Richtmyer-Meshkov instability, with large initial distortions of the gas interfaces. The inhomogeneities are made by filling large soap bubbles and cylindrical refraction cells (5 cm diameter) whose walls are thin plastic membranes with gases both lighter and heavier than the ambient air in a square (8.9 cm side shock-tube text section. The wavefront geometry and the deformation of the gas volume are visualized by shadowgraph photography. Wave configurations predicted by geometrical acoustics, including the effects of refraction, reflection and diffraction, are compared to the observations. Departures from the predictions of acoustic theory are discussed in terms of gasdynamic nonlinearity. The pressure field on the axis of symmetry downstream of the inhomogeneity is measured by piezoelectric pressure transducers. In the case of a cylindrical or spherical volume filled with heavy low-sound-speed gas the wave which passes through the interior focuses just behind the cylinder. On the other hand, the wave which passes through the light high-sound-speed volume strongly diverges. Visualization of the wavefronts reflected from and diffracted around the inhomogeneities exhibit many features known in optical and acoustic scattering. Rayleigh-Taylor instability induced by shock acceleration deforms the initially circular cross-section of the volume. In the case of the high-sound-speed sphere, a strong vortex ring forms and separates from the main volume of gas. Measurements of the wave and gas-interface velocities are compared to values calculated for one-dimensional interactions and for a simple model of shock-induced Rayleigh-Taylor instability. The circulation and Reynolds number of the vortical structures are calculated from the measured velocities by modeling a piston vortex generator. The results of the flow visualization are also compared with contemporary numerical simulations.

The focusing of weak shock waves

This paper reports an experimental investigation, using shadowgraphs and pressure measurements, of the detailed behaviour of converging weak shock waves near three different kinds of focus. Shocks are brought to a focus by reflecting initially plane fronts from concave end walls in a large shock tube. The reflectors are shaped to generate perfect foci, aretes and caustics. It is found that, near the focus of a shock discontinuity, a complex wave field develops, which always has the same basic character, and which is always essentially nonlinear. A diffracted wave field forms behind the non-uniform converging shock; its compressive portions steepen to form diffraction shocks, while diffracted expansion waves overtake and weaken the diffraction shocks. The diffraction shocks participate in a Mach reflexion process near the focus, whose development is determined by competition between the convergence of the sides of the focusing front and acceleration of its central portion. In fact, depending on the aperture of the convergence and the strength of the initial wave, the three-shock intersections of the Mach reflexions either cross on a surface of symmetry or remain uncrossed. In the former case, which is observed if the shock wave is relatively weak, the wavefronts emerge from focus crossed and folded, in accordance with the predictions of geometrical acoustics theory. In the latter, the strong-shock case, the fronts beyond focus are uncrossed, as predicted by the theory of shock dynamics. It is emphasized that in both cases the behaviour at the focus is nonlinear. The overtaking of the diffraction shocks by the diffracted expansions limits the amplitude of the converging wave near focus, and is the mechanism by which the maximum amplification factor observed at focus is determined. In all cases, maximum pressures are limited to rather low values.

Rapid evaporation at the superheat limit

In an experimental investigation of the transient processes that occur when a single droplet of butane at the superheat limit vaporizes explosively, short-exposure photographs and fast-response pressure measurements have been used to construct a description of the complete explosion process. It is observed that only a single bubble forms within the drop during each explosion, and that the growth proceeds on a microsecond time scale. An interfacial instability driven by rapid evaporation has been observed on the surface of the bubbles. It is suggested that the Landau mechanism of instability, originally described in connection with the instability of laminar flames, also applies to rapid evaporation at the superheat limit. The photographic evidence and the pressure data are used to estimate the evaporative mass flux across the liquid-vapour interface after the onset of instability. The ;ate of evaporation is shown to be two orders of magnitude greater than would be predicted by conventional bubble-growth theories that do not account for the effects of instability. An estimate of the mean density within the bubbles during the evaporative stage indicates that it is more than one half of the critical density of butane. Additional interesting dynamical effects that are observed include a series of toroidal waves that form on the interface between the butane vapour and the external host liquid in the bubble column apparatus after the bubble has grown large enough to contact the outer edge of the drop, and violent oscillations of the bubble that occur on a millisecond time scale, after evaporation of the liquid butane is complete, that cause the disintegration of the bubble into a cloud of tiny bubbles by Rayleigh-Taylor instability.

Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface

Results of flow visualization experiments of an impulsively accelerated plane interface between air and SF6 are reported. The shock tube used for the experiments has a larger test section than in previous experiments. The larger extent of uniform test flow relative to nonuniform boundary-layer flow permits unambiguous interpretation of flow-visualization photographs, and the influence of shock-wave/boundary-layer interactions is no longer dominant. The strong wall vortex observed in previous studies is not observed in these experiments. It is found that the thin membrane, which forms the initially plane interface, has a significant influence on the initial growth rate of the interface thickness. However, the measured growth rates after the first reflected shock are independent of membrane configuration and are in good agreement with analytical predictions.

Fracture mechanics model of stone comminution in ESWL and implications for tissue damage

Focused shock waves administered during extracorporeal shock-wave lithotripsy (ESWL) cause stone fragmentation. The process of stone fragmentation is described in terms of a dynamic fracture process. As is characteristic of all brittle materials, fragmentation requires nucleation, growth and coalescence of flaws, caused by a tensile or shear stress. The mechanisms, operative in the stone, inducing these stresses have been identified as spall and compression-induced tensile microcracks, nucleating at pre-existing flaws. These mechanisms are driven by the lithotripter-generated shock wave and possibly also by cavitation effects in the surrounding fluid. In this paper, the spall mechanism has been analysed, using a cohesive-zone model for the material. The influence of shock wave parameters, and physical properties of stone, on stone comminution is described. The analysis suggests a potential means to exploit the difference between the stone and tissue physical properties, so as to make stone comminution more effective, without increasing tissue damage.

In vitro study of the mechanical effects of shock-wave lithotripsy

Impulsive stress in repeated shock waves administered during extracorporeal shock-wave lithotripsy (ESWL) causes injury to kidney tissue. In a study of the mechanical input of ESWL, the effects of focused shock waves on thin planar polymeric membranes immersed in a variety of tissue-mimicking fluids have been examined. A direct mechanism of failure by shock compression and an indirect mechanism by bubble collapse have been observed. Thin membranes are easily damaged by bubble collapse. After propagating through cavitation-free acoustically heterogeneous media (liquids mixed with hollow glass spheres, and tissue) shock waves cause membranes to fail in fatigue by a shearing mechanism. As is characteristic of dynamic fatigue, the failure stress increases with strain rate, determined by the amplitude and rise time of the attenuated shock wave. Shocks with large amplitude and short rise time (i.e., in uniform media) cause no damage. Thus the inhomogeneity of tissue is likely to contribute to injury in ESWL. A definition of dose is proposed which yields a criterion for damage based on measurable shock wave properties.

Performance data of the new free-piston shock tunnel T5 at GALCIT

A new free piston shock tunnel has been constructed at the Graduate Aeronautical Laboratories at Caltec. Compression tube length is 30 m and diameter 300 mm. Shock tube length is 12 m and diameter 90 mm. Piston mass is 150 kg and maximum diaphragm burst pressure is 130 MPa. Special features of this facility are that the pressure in the driver gas is monitered throughout the compression process until well after diaphragm rupture, and that the diaphragm burst pressure can be measured dynamically. An analysis of initial performance data including transient behavior of the flow over models is presented.

Design and characterization of a research electrohydraulic lithotripter patterned after the Dornier HM3

An electrohydraulic lithotripter has been designed that mimics the behavior of the Dornier HM3 extracorporeal shock wave lithotripter. The key mechanical and electrical properties of a clinical HM3 were measured and a design implemented to replicate these parameters. Three research lithotripters have been constructed on this design and are being used in a multi-institutional, multidisciplinary research program to determine the physical mechanisms of stone fragmentation and tissue damage in shock wave lithotripsy. The acoustic fields of the three research lithotripters and of two clinical Dornier HM3 lithotripters were measured with a PVDF membrane hydrophone. The peak positive pressure, peak negative pressure, pulse duration, and shock rise time of the focal waveforms were compared. Peak positive pressures varied from 25 MPa at a voltage setting of 12 kV to 40 MPa at 24 kV. The magnitude of the peak negative pressure varied from 2 7t o212 MPa over the same voltage range. The spatial variations of the peak positive pressure and peak negative pressure were also compared. The focal region, as defined by the full width half maximum of the peak positive pressure, was 60 mm long in the axial direction and 10 mm wide in the lateral direction. The performance of the research lithotripters was found to be consistent at clinical firing rates ~up to 3 Hz!. The results indicated that pressure fields in the research lithotripters are equivalent to those generated by a clinical HM3 lithotripter.

Earthquakes, volcanoes, and rectified diffusion

Rectified diffusion is a mechanism by which a strain wave can rapidly pump volatiles into a bubble and therefore increase the pressure in a closed system. The dynamic strain of either distant regional tectonic earthquakes or local volcanic tremor can be translated to static strain inside a magma chamber via this process. We formulate a theory appropriate to the conditions of a magma chamber and calculate the increased pressure using realistic physical parameters. For a basaltic system initially at 130 MPa pressure, the excess pressure from rectified diffusion is between 0.4 and 4 MPa for a regional M≥8 earthquake. The pressure from rectified diffusion is often significantly above the static stress caused by deformation for documented cases of triggered eruptions and thus presents a more viable mechanism for triggering. Prolonged tremor can have a similar effect since the total pressure added increases linearly with the duration of the excitation.

Mechanical haemolysis in shock wave lithotripsy (SWL): I. Analysis of cell deformation due to SWL flow-fields

This work analyses the interaction of red blood cells (RBCs) with shock-induced and bubble-induced flows in shock wave lithotripsy (SWL), and calculates, in vitro, the lytic effects of these two flows. A well known experimentally observed fact about RBC membranes is that the lipid bilayer disrupts when subjected to an areal strain (deltaA/A)c of 3%, and a corresponding, critical, isotropic tension, Tc, of 10 mN m(-1) (1 mN m(-1) = 1 dyne cm(-1)). RBCs suspended in a fluid medium tend to deform in accordance with the deformation of the surrounding fluid medium. The fluid flow-field is lytically effective if the membrane deformation exceeds the above threshold value. From kinematic analysis, motion of an elementary fluid particle can always be decomposed into a uniform translation, an extensional flow (e.g. -->uinfinity(x, y, z) = (k(t)x, -k(t)y, 0)) along three mutually perpendicular axes, and a rigid rotation of these axes. However, only an extensional flow causes deformation of a fluid particle, and consequently deforms the RBC membrane. In SWL, a fluid flow-field, induced by a non-uniform shock wave, as well as radial expansion/implosion of a bubble, has been hypothesized to cause lysis of cells. Both the above flow-fields constitute an unsteady, extensional flow, which exerts inertial as well as viscous forces on the RBC membrane. The transient inertial force (expressed as a tension, or force/length), is given by Tiner approximately rhor(c)3k/tau, where tau is a timescale of the transient flow and r(c) is a characteristic cell size. When the membrane is deformed due to inertial effects, membrane strain is given by deltaA/A approximately ktau. The transient viscous force is given by Tvisc approximately rho(nu/tau)1/2r(c)2k, where rho and nu are the fluid density and kinematic viscosity. For the non-uniform shock, the extensional flow exerts an inertial force, Tiner approximately 64 mN m(-1), for a duration of 3 ns, sufficient to induce pores in the RBC membrane. For a radial flow-field, induced by bubble expansion/implosion, the inertial forces are of a magnitude 100 mN m(-1), which last for a duration of 1 micros, sufficient to cause rupture. Bubble-induced radial flow is predicted to be lytically more effective than shock-induced flow in typical in vitro experimental conditions.