Shock wave focusing using geometrical shock dynamics

A finite-difference numerical method for geometrical shock dynamics has been developed based on the analogy between the nonlinear ray equations and the supersonic potential equation. The method has proven to be an efficient and inexpensive tool for approximately analyzing the focusing of weak shock waves, where complex nonlinear wave interactions occur over a large range of physical scales. The numerical results exhibit the qualitative behavior of strong, moderate, and weak shock focusing observed experimentally. The physical mechanisms that are influenced by aperture angle and shock strength are properly represented by geometrical shock dynamics. Comparison with experimental measurements of the location at which maximum shock pressure occurs shows good agreement, but the maximum pressure at focus is overestimated by about 60%. This error, though large, is acceptable when the speed and low cost of the method is taken into consideration. The error is primarily due to the under prediction of disturbance speed on weak shock fronts. Adequate resolution of the focal region proves to be particularly important to properly judge the validity of shock dynamics theory, under-resolution leading to overly optimistic conclusions

Highly focused supersonic microjets

The paper describes the production of thin, focused microjets with velocities up to 850 m/s by the rapid vaporization of a small mass of liquid in an open liquid-filled capillary. The vaporization is caused by the absorption of a low-energy laser pulse. A likely explanation of the observed phenomenon is based on the impingement of the shock wave caused by the nearly-instantaneous vaporization on the free surface of the liquid. An experimental study of the dependence of the jet velocity on several parameters is conducted, and a semi-empirical relation for its prediction is developed. The coherence of the jets, their high velocity and good reproducibility and controllability are unique features of the system described. A possible application is to the development of needle-free drug injection systems which are of great importance for global health care.Comment: 10 pages, 11figure

Highly focused supersonic microjets

The paper describes the production of thin, focused microjets with velocities up to 850 m/s by the rapid vaporization of a small mass of liquid in an open liquid-filled capillary. The vaporization is caused by the absorption of a low-energy laser pulse. A likely explanation of the observed phenomenon is based on the impingement of the shock wave caused by the nearly-instantaneous vaporization on the free surface of the liquid. An experimental study of the dependence of the jet velocity on several parameters is conducted, and a semi-empirical relation for its prediction is developed. The coherence of the jets, their high velocity and good reproducibility and controllability are unique features of the system described. A possible application is to the development of needle-free drug injection systems which are of great importance for global health care.Comment: 10 pages, 11figure

Shock dynamics in non-uniform media

The theory of shock dynamics in two dimensions is reformulated to treat shock propagation in a non-uniform medium. The analysis yields a system of hyperbolic equations with source terms representing the generation of disturbances on the shock wave as it propagates into the fluid non-uniformities. The theory is applied to problems involving the refraction of a plane shock wave at a free plane gaseous interface. The ‘slow–fast’ interface is investigated in detail, while the ‘fast–slow’ interface is treated only briefly. Intrinsic to the theory is a relationship analogous to Snell's law of refraction at an interface. The theory predicts both regular and irregular (Mach) refraction, and a criterion is developed for the transition from one to the other. Quantitative results for several different shock strengths, angles of incidence and sound-speed ratios are presented. An analogy between shock refraction and the motion of a force field in unsteady one-dimensional gasdynamics is pointed out. Also discussed is the limiting case for a shock front to be continuous at the interface. Comparison of results is made with existing experimental data, with transition calculations based on three-shock theory, and with the simple case of normal interaction

Techniques for Generating Centimetric Drops in Microgravity and Application to Cavitation Studies

This paper describes the techniques and physical parameters used to produce stable centimetric water drops in microgravity, and to study single cavitation bubbles inside such drops (Parabolic Flight Campaigns, European Space Agency ESA). While the main scientific results have been presented in a previous paper, we shall herein provide the necessary technical background, with potential applications to other experiments. First, we present an original method to produce and capture large stable drops in microgravity. This technique succeeded in generating quasi-spherical water drops with volumes up to 8 ml, despite the residual g-jitter. We find that the equilibrium of the drops is essentially dictated by the ratio between the drop volume and the contact surface used to capture the drop, and formulate a simple stability criterion. In a second part, we present a setup for creating and studying single cavitation bubbles inside those drops. In addition, we analyze the influence of the bubble size and position on the drop behaviour after collapse, i.e. jets and surface perturbations

An investigation of shock strengthening in a conical convergent channel

The behaviour of an initially plane, strong shock wave propagating into a conical convergence is investigated experimentally and theoretically. In the experiment a 10° half-angle cone is mounted on the end of a pressure-driven shock tube. Shock waves with initial Mach numbers varying from 6.0 to 10·2 are generated in argon a t a pressure of 1·5 Torr. During each run local shock velocities a t several positions along the cone axis are measured using a thin multi-crystal piezoelectric probe inserted from the vertex. This technique produces accurate velocity data for both the incident and reflected shock waves. In the corresponding analysis, a simplified characteristics method is used to obtain an approximate solution of the axisymmetric diffraction equations derived by Whitham (1959). Both the shock velocity measurements and the axisymmetric diffraction solution confirm that the incident shock behaviour is dominated by cyclic diffraction processes which originate at the entrance of the cone. Each diffraction cycle is characterized by Mach reflexion on the cone wall followed by Mach reflexion on the axis, These cycles evidently persist until the shock reaches the cone vertex, where the measured velocity has increased by as much as a factor of three. Real-gas effects, enhanced in the experiment by increasing the initial Mach number and decreasing the pressure, apparently alter the shock wave behaviour only in the region near the vertex. Velocity measurements for the reflected shock within the cone show that the shock velocity is nearly constant throughout most of the convergence length

Geometrical shock dynamics for magnetohydrodynamic fast shocks

We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as ϵ^(-1), where ϵ is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock