Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

Uniformly valid analytical solution to the problem of a decaying shock wave

An explicit representation of an analytical solution to the problem of decay of a plane shock wave of arbitrary strength is proposed. The solution satisfies the basic equations exactly. The approximation lies in the (approximate) satisfaction of two of the Rankine-Hugoniot conditions. The error incurred is shown to be very small even for strong shocks. This solution analyses the interaction of a shock of arbitrary strength with a centred simple wave overtaking it, and describes a complete history of decay with a remarkable accuracy even for strong shocks. For a weak shock, the limiting law of motion obtained from the solution is shown to be in complete agreement with the Friedrichs theory. The propagation law of the non-uniform shock wave is determined, and the equations for shock and particle paths in the (x, t)-plane are obtained. The analytic solution presented here is uniformly valid for the entire flow field behind the decaying shock wave.

Adiabatic compression testing - part I : historical development and evaluation of fluid dynamic processes including shock-wave considerations

Adiabatic compression testing of components in gaseous oxygen is a test method that is utilized worldwide and is commonly required to qualify a component for ignition tolerance under its intended service. This testing is required by many industry standards organizations and government agencies. This paper traces the background of adiabatic compression testing in the oxygen community and discusses the thermodynamic and fluid dynamic processes that occur during rapid pressure surges. This paper is the first of several papers by the authors on the subject of adiabatic compression testing and is presented as a non-comprehensive background and introduction.

Oblique-Shock-Wave/Boundary-Layer Interaction Using Near-Wall Reynolds-Stress Models

A synthesis is presented of the predictive capability of a family of near-wall wall-normal free Reynolds stress models (which are completely independent of wall topology, i.e., of the distance fromthe wall and the normal-to-thewall orientation) for oblique-shock-wave/turbulent-boundary-layer interactions. For the purpose of comparison, results are also presented using a standard low turbulence Reynolds number k–ε closure and a Reynolds stress model that uses geometric wall normals and wall distances. Studied shock-wave Mach numbers are in the range MSW = 2.85–2.9 and incoming boundary-layer-thickness Reynolds numbers are in the range Reδ0 = 1–2×106. Computations were carefully checked for grid convergence. Comparison with measurements shows satisfactory agreement, improving on results obtained using a k–ε model, and highlights the relative importance of redistribution and diffusion closures, indicating directions for future modeling work.

Influence of inflow turbulence in shock-wave/turbulent-boundary-layer interaction computations

The influence of inflow turbulence on the results of Favre–Reynolds-averaged Navier–Stokes computations of supersonic oblique-shock-wave/turbulent-boundary-layer interactions (shock-wave Mach-number MSW ∼2.9), using seven-equation Reynolds-stress model turbulence closures, is studied. The generation of inflow conditions (and the initialization of the flowfield) for mean flow, Reynolds stresses, and turbulence length scale, based on semi-analytic grid-independent boundary-layer profiles, is described in detail. Particular emphasis is given to freestream turbulence intensity and length scale. The influence of external-flow turbulence intensity is studied in detail both for flat-plate boundary-layer flow and for a compression-ramp interaction with large separation. It is concluded that the Reynolds-stress model correctly reproduces the effects of external flow turbulence.

The jump in vorticity across a shock wave in relativistic hydrodynamics

Using the singular surface theory, an expression for the jump in vorticity across a shock wave of arbitrary shape propagating in a uniform, perfect fluid occupying the space-time of special relativity, has been derived. It has been shown that the jump in vorticity across a shock of given strength and curvature depends only on the velocity of the medium ahead of the shock.

Electron temperature distribution across a shock wave in a partially ionized gas

The electron temperature structure in a weakly ionized plasma is studied allowing the degree of ionization to vary across the shock wave. The values of the electron temperature and the downstream equilibrium temperature obtained with variable ionization are less than those for frozen ionization. The electron temperature rises sharply behind the shock for variable ionization while a gradual increase is predicted by frozen ionization.

Exact traveling- wave solution for model geophysical systems

Exact traveling-wave solutions of time-dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs.

Schlieren visualization of shock wave phenomena over a missile-shaped body at hypersonic Mach numbers

The flow over a missile-shaped configuration is investigated by means of Schlieren visualization in short-duration facility producing free stream Mach numbers of 5.75 and 8. This visualization technique is demonstrated with a 41 degrees full apex angle blunt cone missile-shaped body mounted with and without cavity. Experiments are carried out with air as the test gas to visualize the flow field. The experimental results show a strong intensity variation in the deflection of light in a flow field, due to the flow compressibility. Shock stand-off distance measured with the Schlieren method is in good agreement with theory and computational fluid dynamic study for both the configurations. Magnitude of the shock oscillation for a cavity model may be greater than the case of a model without cavity. The picture of visualization shows that there is an outgoing and incoming flow closer to the cavity. Cavity flow oscillation was found to subside to steady flow with a decrease in the free stream Mach number.

Diaphragmless shock wave generators for industrial applications of shock waves

The prime focus of this study is to design a 50 mm internal diameter diaphragmless shock tube that can be used in an industrial facility for repeated loading of shock waves. The instantaneous rise in pressure and temperature of a medium can be used in a variety of industrial applications. We designed, fabricated and tested three different shock wave generators of which one system employs a highly elastic rubber membrane and the other systems use a fast acting pneumatic valve instead of conventional metal diaphragms. The valve opening speed is obtained with the help of a high speed camera. For shock generation systems with a pneumatic cylinder, it ranges from 0.325 to 1.15 m/s while it is around 8.3 m/s for the rubber membrane. Experiments are conducted using the three diaphragmless systems and the results obtained are analyzed carefully to obtain a relation between the opening speed of the valve and the amount of gas that is actually utilized in the generation of the shock wave for each system. The rubber membrane is not suitable for industrial applications because it needs to be replaced regularly and cannot withstand high driver pressures. The maximum shock Mach number obtained using the new diaphragmless system that uses the pneumatic valve is 2.125 +/- 0.2%. This system shows much promise for automation in an industrial environment.

A study of shock wave interaction with a rotating cylinder

Shock wave reflection over a rotating circular cylinder is numerically and experimentally investigated. It is shown that the transition from the regular reflection to the Mach reflection is promoted on the cylinder surface which rotates in the same direction of the incident shock motion, whereas it is retarded on the surface that rotates to the reverse direction. Numerical calculations solving the Navier-Stokes equations using extremely fine grids also reveal that the reflected shock transition from RRdouble right arrowMR is either advanced or retarded depending on whether or not the surface motion favors the incident shock wave. The interpretation of viscous effects on the reflected shock transition is given by the dimensional analysis and from the viewpoint of signal propagation.

Development of micro-shock wave assisted dry particle and fluid jet delivery system

Small quantity of energetic material coated on the inner wall of a polymer tube is proposed as a new method to generate micro-shock waves in the laboratory. These micro-shock waves have been harnessed to develop a novel method of delivering dry particle and liquid jet into the target. We have generated micro-shock waves with the help of reactive explosive compound high melting explosive (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) and traces of aluminium] coated polymer tube, utilising 9 J of energy. The detonation process is initiated electrically from one end of the tube, while the micro-shock wave followed by the products of detonation escape from the open end of the polymer tube. The energy available at the open end of the polymer tube is used to accelerate tungsten micro-particles coated on the other side of the diaphragm or force a liquid jet out of a small cavity filled with the liquid. The micro-particles deposited on a thin metal diaphragm (typically 100-mu m thick) were accelerated to high velocity using micro-shock waves to penetrate the target. Tungsten particles of 0.7 mu m diameter have been successfully delivered into agarose gel targets of various strengths (0.6-1.0 %). The device has been tested by delivering micro-particles into potato tuber and Arachis hypogaea Linnaeus (ground nut) stem tissue. Along similar lines, liquid jets of diameter 200-250 mu m (methylene blue, water and oils) have been successfully delivered into agarose gel targets of various strengths. Successful vaccination against murine salmonellosis was demonstrated as a biological application of this device. The penetration depths achieved in the experimental targets are very encouraging to develop a future device for biological and biomedical applications.

Theoretical-experimental study of shock wave-assisted metal forming process using a diaphragmless shock tube

The use of high-velocity sheet-forming techniques where the strain rates are in excess of 10(2)/s can help us solve many problems that are difficult to overcome with traditional metal-forming techniques. In this investigation, thin metallic plates/foils were subjected to shock wave loading in the newly developed diaphragmless shock tube. The conventional shock tube used in the aerodynamic applications uses a metal diaphragm for generating shock waves. This method of operation has its own disadvantages including the problems associated with repeatable and reliable generation of shock waves. Moreover, in industrial scenario, changing metal diaphragms after every shot is not desirable. Hence, a diaphragmless shock tube is calibrated and used in this study. Shock Mach numbers up to 3 can be generated with a high degree of repeatability (+/- 4 per cent) for the pressure jumps across the primary shock wave. The shock Mach number scatter is within +/- 1.5 per cent. Copper, brass, and aluminium plates of diameter 60 mm and thickness varying from 0.1 to 1 mm are used. The plate peak over-pressures ranging from 1 to 10 bar are used. The midpoint deflection, circumferential, radial, and thickness strains are measured and using these, the Von Mises strain is also calculated. The experimental results are compared with the numerical values obtained using finite element analysis. The experimental results match well with the numerical values. The plastic hinge effect was also observed in the finite element simulations. Analysis of the failed specimens shows that aluminium plates had mode I failure, whereas copper plates had mode II failure.

Micro-shock wave assisted bacterial transformation

A gene is a unit of heredity in a living organism. It normally resides on a stretch of DNA that codes for a type of protein or for an RNA chain that has a function in the organism. All living things depend on genes, as they specify all proteins and functional RNA chains. Genes hold the information to build and maintain an organism’s cells and pass genetic traits to offspring. The gene has to be transferred to bacteria or eukaryotic cells for basic and applied molecular biology studies. Bacteria can uptake exogenous genetic material by three ways: conjugation, transduction and transformation. Genetic material is naturally transferred to bacteria in case of conjugation and transferred through bacteriophage in transduction. Transformation is the acquisition of exogenous genetic material through cell wall. The ability of bacteria of being transformed is called competency and those bacteria which have competency are competent cells. Divalent Calcium ions can make the bacteria competent and a heat shock can cause the bacteria to uptake DNA. But the heat shock method cannot be used for all the bacteria. In electroporation, a brief electric shock with an electric field of 10-20kV/cmmakes pores in the cell wall, facilitates the DNA to enter into the bacteria. Microprecipitates, microinjection, liposomes, and biological vectors are also used to transfer polar molecules like DNA into host cells.