Showing papers on "Rarefaction published in 1984"

A unified description of two-layer flow over topography

Abstract: Observations of the flow of a two-layer fluid resulting from the motion of a towed streamlined two-dimensional obstacle are described in some detail. The experiments were designed to further our understanding of the factors governing the nature and magnitude of upstream disturbances in the general flow of stratified fluid over two-dimensional topography, and predictions for arbitrary two-dimensional flows are made from the results of these experiments. In particular, the relationship between uniformly stratified flow and single-layer flow over topography is suggested. Most of the observed features of interest in these experiments are nonlinear in character. Relatively complete descriptions of the observed flows are presented over a wide range of parameter values, and the phenomena observed include upstream undular and turbulent bores, bores with zero energy loss, ‘rarefactions’ (in which the interface height changes monotonically over a transition region of continuously increasing length), and downstream hydraulic drops and jumps. Their properties are shown to be broadly consistent with predictions from a two-layer hydrostatic model based on continuity and momentum considerations, which employs jump criteria and rarefaction equations where appropriate. Bores occur because of nonlinear steepening when the layer containing the obstacle is thinner than the other, and rarefactions occur when this layer thickness is comparable with or greater than that of the other layer. The speed and amplitude of the upstream bores are governed by nonlinear effects, but their character is determined by a balance between nonlinear steepening, wave dispersion and interfacial friction when the bore is non-turbulent. Experimental evidence is presented for two types of hysteresis or ‘multiple equilibria’ - situations where two different flow states may exist for the same external steady conditions. In the first of these hysteresis types, the upstream flow may be supercritical or consist of an upstream bore state. It is analogous to the type anticipated for single-layer flow by Baines & Davies (1980) and described numerically by Pratt (1983), but it is only found experimentally for part of the expected parameter range, apparently because of interfacial stress effects. The second hysteresis type is new, and involves the presence or absence of a downstream hydraulic drop and following jump.

The forward‐reverse shock pair at large heliocentric distances

Abstract: An unsteady one-dimensional numerical magnetohydrodynamic (MHD) model is developed in order to study the essential physical processes involved in the development of the forward-reverse shock pair in the heliosphere. In the model, MHD shocks are treated as boundary surfaces which divide the domain of interest in the r-t plane into several flow regions. The positions of the shock boundary surfaces between two neighboring flow regions are determined by shock speed. On the basis of integrations of the model, it is found that the strong MHD disturbances generated in a corotating interaction region (CIR) propagate at a fast speed relative to the moving material, and that the wave propagation speed is greater in CIR than in its surroundings. This causes disturbances in CIR to pile up and form a shock pair. The newly formed shock pair will in turn propagate outward from the leading edge to interact with ambient rarefaction regions. This interaction accounts for the double sawtooth configuration observed in velocity profiles of shock pairs. It is also demonstrated that the merging of two shocks produces a stronger shock and constant surface on its backside. Computer generated velocity profiles based on the model are presented.

Direct simulation of transitional flow for hypersonic reentry conditions

Abstract: This paper presents results of flowfield calculations for typical hypersonic reentry conditions encountered by the nose region of the Space Shuttle Orbiter. Most of the transitional flow regime is covered by the altitude range of 150 to 92 km. Calculations were made with the Direct Simulation Monte Carlo (DSMC) method that accounts for translational, rotational, vibrational, and chemical nonequilibrium effects. Comparison of the DSMC heating results with both Shuttle flight data and continuum predictions showed good agreement at the lowest altitude considered. However, as the altitude increased, the continuum predictions, which did not include slip effects, departed rapidly from the DSMC results by overpredicting both heating and drag. The results demonstrate the effects of rarefaction on the shock and the shock layer, along with the extent of the slip and temperature jump at the surface. Also, the sensitivity of the flow structure to the gas-surface interaction model, thermal accommodation, and surface catalysis are studied.

Diffraction characteristics of laser‐induced acoustic waves in liquids

Abstract: The effect of diffraction on the temporal shape of laser‐excited plane acoustic waves propagating in liquids is studied both theoretically and experimentally. Two different boundary conditions corresponding to a constrained and a free surface of the liquid are considered. The main features are the development of a rarefaction zone behind the pure compression pulse in the first case and the appearance of a second compression zone following the original compression/rarefaction signal in the second case. Experiments have been performed in distilled water with a hybrid CO2 laser and piezoelectric detection of the acoustic transients. A good agreement between theory and experiment is found.

Chapter II : 18 – THE VELOCITY OF SOUND BEHIND STRONG SHOCK WAVES IN 2024 Al*

Abstract: Rarefaction waves were produced by impacting a target with a thin plate. An optical technique was used to determine where the rarefaction from the back surface of the impactor overtook the shock wave induced in a step wedge target. Bromoform was placed on the front surface. When the shock reached the liquid it radiated steadily until the rarefaction from the impactor overtakes it. The times when this occurred were used to determine where the rarefaction just overtook the shock in the target, and thus the sound velocity. The leading edge of this rarefaction wave travels at longitudinal sound velocity in solids. This velocity increases smoothly with pressure until shock heating causes the material to melt. The data indicate that melting on the Hugoniot of 2024 Al begins at about 125 GPa and is completed at 150 GPa.

Structure of self-similar rarefaction waves and expansion adiabats of substances

Abstract: The author sets forth two modifications in direct recording of flow parameters for rarefaction waves in a high pressure domain: recording the pressure or mass flow rate on the particular trajectory, and plotting the particle displacements or successive locations of the front of opposite rarefaction waves at a fixed time. Through a series of equations for the dependencies involved in this process, he discovers the simplest way to determine the adiabat of substance expansion from the experimental profile of centered rarefaction waves.

The effect of equilibrium modeling of saturated quartz in energy coupling calculations

Abstract: The effect of the quartz-stishovite phase transition on the on-axis ground shock in energy coupling is studied both analytically and numerically using an equation – of – state that assumes thermodynamic equilibrium. The qualitative behavior of the ground shock is predicted analytically; in particular, it is shown that a rarefaction shock is generated in the phase transition region (due to the anomalous nature of the isentropes) that severely modifies the ground shock. General agreement with detailed numerical results is obtained.