Session D03: Shock Waves & Explosions

Lie Symmetry Analysis of Shock Problems Using Generalized Functions

Lie symmetry analysis depends on the calculation of derivatives to find and use the symmetries.  Solutions to hydrodynamic shock problems have discontinuities which mean that the usual derivative cannot be calculated.  The solution is to use symmetry analysis in the smooth regions between shocks and stitch them together using the Hugoniot jump conditions, which must also satisfy the symmetry conditions.  In this work we use generalized functions to express the solution and then calculate the derivatives using generalized derivatives.  This provides a concise framework for analyzing shock problems.  We demonstrate the method on the Noh and shock tube problems.   

A small-disturbance model for transonic flow of a real gas around a thin airfoil

A small-disturbance model for a steady transonic flow of a real gas around a thin airfoil is presented. The model explores the nonlinear interactions among the near-sonic speed of the flow, the small thickness ratio and angle of attack of the airfoil, and the upstream properties of the gas. The flow thermodynamic properties are described by a general equation of state. The asymptotic analysis provides the similarity parameters that govern the flow problem. Also, the flow field can be described by a transonic small-disturbance (TSD) equation. The approach is applied to the perfect gas, van der Waals and Redlich-Kwong gas models and the relationships between these cases are explored. An iterative numerical scheme that is based on the Murman & Cole's (1971) method for the solution of the TSD equation is developed. The computed results describe the effect of the upstream flow pressure and temperature on the fields of flow properties and the on aerodynamic performance of airfoils.
  

Shock wave propagation and reflections in confined two- and three-dimensional geometries

Explosively driven shock propagation was studied using a miniature shock demonstrator made from laser cut acrylic sheets to model various geometries in two and three dimensional space.  Shock waves are produced using an electric spark gap on a detonator header which is driven by an FS-17 fire set.  The spark causes an air shock which propagates through the demonstrator.  Shock reflection, diffraction, and complex interactions are studied in the transition from two to three-dimensional space.  The propagation is quantified in terms of velocity throughout the geometries.  In addition, piezoelectric pressure gauges are used to measure static and reflected pressures at various locations in the geometries.  The demonstrator is placed within a schlieren imaging system to obtain high speed images of the shock propagation caused by the explosive events.   

Dynamics and attenuation of shock waves launched in liquid jets by X-ray laser pulses

Chemical and biological experiments performed at X-ray laser facilities embed the samples in liquid microjets to enable rapid sequential X-ray probing of fresh samples. The absorption of intense X-ray laser pulses generates shock waves that travel along the liquid jets, and may damage samples in MHz repetition rate experiments. We imaged optically these shock waves and determined their properties up to ~40 ns of travel along liquid water microjets with 14 or 20 µm diameters. The shock pressure was evaluated from the shock velocity and was found to decay rapidly from peak pressures around 1 GPa to pressures below 100 MPa; the latter value still exceeds the Vickers hardness of lysozyme protein crystals. The reflection of the shock at the surface of the jets leads to cavitation and to the generation of additional pressure waves, leading to a complex shock structure that is related to, yet different from, the one observed in supersonic gas jets.