Nicholas Apazidis

On generation and convergence of polygonal-shaped shock waves

A process of generation and convergence of shock waves of arbitrary form and strength in a confined chamber is investigated theoretically. The chamber is a cylinder with a specifically chosen form of boundary. Numerical calculations of reflection and convergence of cylindrical shock waves in such a chamber filled with fluid are performed. The numerical scheme is similar to the numerical procedure introduced by Henshaw et al . (1986) and is based on a modified form of Whithams theory of geometrical shock dynamics (1957, 1959). The technique used in Whitham (1968) for treating a shock advancing into a uniform flow is modified to account for non-uniform conditions ahead of the advancing wave front. A new result, that shocks of arbitrary polygonal shapes may be generated by reflection of cylindrical shocks off a suitably chosen reflecting boundary, is shown. A study is performed showing the evolution of the shock fronts shape and Mach number distribution. Comparisons are made with a theory which does not account for the non-uniform conditions in front of the shock. The calculations provide details of both the reflection process and the shock focusing.

Experimental determination of self-similarity constant for converging cylindrical shocks

Guderley’s self-similarity solution r = r0(1 – t/t0)α for strong converging cylindrical shocks is investigated experimentally for three different gases with adiabatic exponents γ = 1.13; 1.40; and 1.66 and various values of the initial Mach number. Corresponding values of the similarity exponent α which determines the strength of shock convergence are obtained for each gas thus giving the variation of α with γ. Schlieren imaging with multiple exposure technique is used to track the propagation of a single shock front during convergence. The present experimental results are compared with previous experimental, numerical, and theoretical investigations.

Temperature distribution and heat transfer in a particle-fluid flow past a heated horizontal plate

Abstract The temperature distribution in a laminar two-phase flow of a particle-fluid mixture over a heated horizontal plate is considered. Analytical expressions for the temperature fields and heat fluxes in each phase are obtained. It is found that the temperature distribution in a two-phase mixture flow differs from the corresponding single-phase case. Temperature profiles of the phases are independent of the distance along the plate and controlled by such mixture parameters as the particle size and concentration, the density ratio between the phases and the value of the Prandtl number. Moreover, the temperature fields of the phases in the mixture flow are independent of the horizontal velocity components and have a structure similar to that of a velocity profile of a single-phase flow over a flat plate at zero incidence with uniform suction.

Thermal radiation from a converging shock implosion

High energy concentration in gas is produced experimentally by focusing cylindrical shock waves in a specially constructed shock tube. The energy concentration is manifested by the formation of a hot gas core emitting light at the center of a test chamber at the instant of shock focus. Experimental and numerical investigations show that the shape of the shock wave close to the center of convergence has a large influence on the energy concentration level. Circular shocks are unstable and the resulting light emission varies greatly from run to run. Symmetry and stability of the converging shock are achieved by wing-shaped flow dividers mounted radially in the test chamber, forming the shock into a more stable polygonal shape. Photometric and spectroscopic analysis of the implosion light flash from a polygonal shock wave in argon is performed. A series of 60 ns time-resolved spectra spread over the 8 μs light flash shows the emission variation over the flash duration. Blackbody fits of the spectroscopic data...

Energy concentration by spherical converging shocks generated in a shock tube

Spherical converging shock waves are produced in a conventional shock tube with a circular cross-section. Initially, plane shocks are transformed into the shape of a spherical cap by means of a smoothly convergent cross-section. The wall shape in the transformation section is designed to gradually change the form of the shock wave until it approaches a spherical shape. Thereafter, the shock enters a conical section where it converges towards the apex of the cone. Numerical calculations with the axisymmetric Euler equations show that the spherical form is only slightly dependent on the initial Mach number of the plane shock within the range 1.5 < MS < 5.5, and is preserved to a close vicinity of the focal point. The test gas is heated to very high temperatures as a result of shock convergence and emits a bright light pulse at the tip of the test section. The light radiation is collected by optical fibers mounted at the tip of the convergence chamber and investigated by photometric and spectroscopic measure...

Influence of bubble expansion and relative velocity on the performance and stability of an airlift pump

Abstract An airlift pump which raises liquid by means of compressed air introduced near the lower end of the eduction pipe is an example of a self-control system. It has been shown by Hjalmars (1973) that an occasionally observed breakdown in the self-control mechanism, which leads to instability, is due to the fact that the control mechanism is delayed, with the effect that a small, time-dependent perturbation of the stationary flow satisfies a differential equation with delayed argument. This investigation was carried out with the assumption of a single-phase flow of an ideal incompressible liquid. The aim of the present study is to consider the stability conditions of an airlift pump within the frame of a more general flow model, namely a separate two-phase flow of compressible gas and incompressible liquid, which takes into account the effects of the expasion of gas bubbles during their lift and of the relative velocity, i.e. the difference in the velocity of gas bubbles and the liquid.

Light emission during shock wave focusing in air and argon

The light emission from a converging shock wave was investigated experimentally. Results show that the shape of the shock wave close to the center of convergence has a large influence on the amou ...

On two-dimensional laminar flows of a particulate suspension in the presence of gravity field

Abstract Three simple two-dimensional streaming motions of a mixture of solid particles with a continuous carrier fluid, or gas, in the presence of the gravity field are considered. These include flow of a mixture over an infinite stationary rigid plane perpendicular to the direction of the gravity field, flow near an oscillating rigid plane and flow in a mixture induced by a suddenly accelerated plane. The nature of the boundary conditions at the interface between a layer of sediment settling on the rigid boundary and the mixture above it suggests an introduction of the independent variables that enable simple analytical expressions for the solutions of the first two flows and a numerical solution by means of a Laplace transform in the last case.

Turning Points of the Spherical Pendulum and the Golden Ratio.

We study the turning point problem of a spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To put our result in perspective we briefly discuss its relevance in physics.

Shock dynamics of strong imploding cylindrical and spherical shock waves with real gas effects

Strong cylindrical and spherical shock implosion in a monatomic gas is considered A simple solution is obtained by Whithams geometrical shock dynamics approach modified to account for the real gas ...