Propagation of converging and diverging shock waves under isothermal condition

In this article the flows of perfect gas behind converging and diverging strong shock waves under isothermal condition in the cases of spherical and cylindrical symmetry are examined. A diverging shock wave is formed by energy supply according to a power law. These waves propagate in a uniform medium at rest and all conservation laws hold at the fronts of these shock waves. It was established that in the case of converging waves for any value of the ratios of specific heats the solution of the problem under consideration exists and is unique. When the problem has more than one solution. In the case of diverging shock waves the solution exists and is unique for any from the interval and any value of power in the energy input law. Received 4 August 1996 / Accepted 28 May 1996     

Investigations involving shock waves generation and shock pressure measurement in direct ablation regime and confined ablation regime

Recent investigations involving shock waves generation and shock pressure measurement in direct ablation regime and confined ablation regime for aluminium, copper, titanium and steel (40C130) materials are reported. Experimental measurements demonstrated that in direct ablation regime the peak pressures typically are less than 10 Pa when the incident laser intensity is about 10 W/cm and the time duration of the applied pressure is roughly equal to the laser pulse duration. It is shown that confinement of the surface with a transparent overlayer provided an effective method of enhancing laser-induced shock waves pressure in the target material with an order of magnitude for same laser intensity. Also, in this second regime, the pressure is applied over a period much longer than the laser-pulse duration. As an application measurements of the hardness of target surface before and after laser irradiation in direct ablation regime and confined ablation regime are given, and it is shown that the maximum value of surface hardness is obtained in confined ablation regime. Received 10 March 2001 / Accepted 13 April 2001     

Test-time extension behind reflected shock waves using CO2–He and C3H8–He driver mixtures

To study combustion chemistry at low temperatures in a shock tube, it is of great importance to increase experimental test times, and this can be done by tailoring the interface between the driver and driven gases. Using unconventional driver-gas tailoring with the assistance of tailoring curves, shock-tube test times were increased from 1 to 15 ms for reflected-shock temperatures below 1,000 K. Provided in this paper is the introduction of tailoring curves, produced from a one-dimensional perfect gas model for a wide range of driver gases and the production and demonstration of successful driver mixtures containing helium combined with either propane or carbon dioxide. The He/CO₂ and He/C₃H₈ driver mixtures provide a unique way to produce a tailored interface and, hence, longer test times, when facility modification is not an option. The tailoring curves can be used to guide future applications of this technique to other configurations. Nonreacting validation experiments using driver mixtures identified from the tailoring curves were performed over a range of reflected-shock temperatures from approximately 800 to 1,400 K, and some examples of ignition-time experiments that could not have otherwise been erformed are presented.     

Computational study of reacting flow establishment in expansion tube facilities

We study the temporal evolution of the combustion flowfield established by the interaction of ram accelerator-type projectiles with an explosive gas mixture accelerated to hypersonic speeds in an expansion tube. The Navier-Stokes equations for a chemically reacting gas mixture are solved in a fully coupled manner using an implicit, time accurate algorithm. The solution procedure is based on a spatially second order, total variation diminishing scheme and a temporally second order, variable-step, backward differentiation formula method. The hydrogen-oxygen-argon chemistry is modeled with a 9-species, 19-step mechanism. The accuracy of the solution method is first demonstrated by several benchmark calculations. Numerical simulations of expansion tube flowfields are then presented for two different geometries: an axisymmetric projectile and a ram accelerator configuration. The development of the shock-induced combustion process is followed. The temporal variations of the calculated thrust and drag forces on the ram accelerator projectile are also presented. In the axisymmetric projectile case, which was designed to ensure combustion only in the boundary layer, the radial extent of the flame front during the initial transient phase was surprisingly large. In the ram accelerator configuration the flame propagated upstream along both the projectile and tube wall boundary layers, resulting in unstart. Received 25 September 1996 / Accepted 15 January 1997     

Investigation on onset of shock-induced separation

A great number of experimental data indicating shock wave/boundary layer interactions in internal or external supersonic flows were reviewed to make clear the mechanism of the interaction and to decide the onset of shock-induced separation. The interesting conclusions were obtained for the considerably wide range of flow geometries that the onset of separation is independent of the flow geometries and the boundary layer Reynolds number. It is found that the pressure rise necessary to separate the boundary layer in supersonic external flows could be applied to such internal flows as overexpanded nozzles or diffusers. This is due to the fact that the separation phenomenon caused by shock wave/boundary layer interactions is processed through a supersonic deceleration. The shock-induced separation in almost all of interacting flow fields is governed by the concept of free interaction, and the onset of shock-induced separation is only a function of the Mach number just upstream of shock wave. However, physical scales of the produced separation are not independent of the downstream flow fields.     

Interaction of a shock wave with a loose dusty bulk layer

The interaction of a planar shock wave with a loose dusty bulk layer has been investigated both experimentally and numerically. Experiments were conducted in a shock tube. The incident shock wave velocity and particle diameters were measured with the use of pressure transducers and a Malvern particle sizer, respectively. The flow fields, induced by shock waves, of both gas and granular phase were visualized by means of shadowgraphs and pulsed X-ray radiography with trace particles added. In addition, a two-phase model for granular flow presented by Gidaspow is introduced and is extended to describe such a complex phenomenon. Based on the kinetic theory, such a two-phase model has the advantage of being able to clarify many physical concepts, like particulate viscosity, granular conductivity and solid pressure, and deduce the correlative constitutive equations of the solid phase. The AUSM scheme was employed for the numerical calculation. The flow field behind the shock wave was displayed numerically and agrees well with our corresponding experimental results.      

Shock wave diffraction on multi-facetted and curved walls

The two-dimensional diffraction of a shock wave over a wall made up of a series of plane and/or curved sections is considered. The analysis is based on the theory presented by, for the interaction of an originally plane shock wave with a corner. A method is presented by which the shock profile may be determined for a wall of any shape and for any incident Mach number, in regions where the characteristics form a simple wave. Comparisons are made between experimental measurements and theoretical predictions for convex walls consisting of a number of facets, and for circular arcs, for a range of incident shock wave Mach numbers. It is shown that the theory gives a satisfactory prediction of the wave shape, which improves as the Mach number increases. Modifications in the flow field behind the shock, compared to that for a simple corner made up of two plane walls is discussed, particularly relating to flow separation. For circular arc concave walls a inverse Mach reflection results experimentally, leading to regular reflection, for which the theory is of no use. PACS 47.40.Nm     

Interaction of shock waves during the passage of a disrupted meteoroid through the atmosphere

The motion of fragments following disintegration of a meteoroid during its flight through the Earth's atmosphere is investiated. Shock wave configurations, aerodynamical forces and moments acting on each fragment and the trajectories of the pieces are determined for hypothetical initial configurations. The results of numerical simulations show that a meteoroid's breakup may lead to both increase and decrease of the total cross section, drag forces and energy release in the atmosphere. As a consequence the emitted radiation varies.     

Tomographic reconstruction of shock layer flows

The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw. 8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution (Faletič in Tomographic reconstruction of shock layer flows, 2005). This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research, Canberra, Australia, March 1–3, 2006.     

Three-dimensional effects on line-of-sight visualization measurements of supersonic and hypersonic flow over cylinders

Flow visualization experiments were performed for supersonic and hypersonic nitrogen test gas flows over a cylinder. The results were used to quantify the influence of three-dimensional effects on optical line-of-sight visualization measurements. Images of cylindrical models of varying aspect ratios (length to diameter) were taken. Shock stand-off distance measurements for the models were compared with a two-dimensional approximation and numerical simulations. For aspect ratios of two and above, the two-dimensional approximation was acceptable within experimental uncertainty. The measured shock stand-off decreased by less than 5% from an asymptotic value for an infinite length cylinder. For smaller aspect ratios, a correction factor for the shock stand-off needs to be applied if comparisons between the two-dimensional approximation and experimental measurements are to be drawn. An estimate of this correction factor has been derived from an empirical fit to the available data.