Sharp critical thresholds in a hyperbolic system with relaxation

<p style='text-indent:20px;'>We propose and study a one-dimensional <inline-formula><tex-math id="M1">\begin{document}$ 2\times 2 $\end{document}</tex-math></inline-formula> hyperbolic Eulerian system with local relaxation from critical threshold phenomena perspective. The system features dynamic transition between strictly and weakly hyperbolic. For different classes of relaxation we identify intrinsic <b>critical thresholds</b> for initial data that distinguish global regularity and finite time blowup. For relaxation independent of density, we estimate bounds on density in terms of velocity where the system is strictly hyperbolic.</p>

Local Film Thickness During Transient Voiding of a Liquid-Filled Channel

Using a recently developed method, measurements were obtained of local film thicknesses during transient voiding of a liquid-filled channel. The liquid film remaining on the channel walls was found to vary in thickness over a range of 0.015–0.15 times channel diameter. In a Lagrangian coordinate system, the film thickness at a fixed distance from the head of the void was found to increase with increasing void acceleration. In an Eulerian system, the film thickness at a fixed location on the channel wall was found to decrease with increasing acceleration, when measured at the same time after passage of the head of the void. In all cases, film thickness monotonically decreased with increasing distance from the head of the void. Complete film breakage (dryout) was not observed in these experiments. These experimental measurements of local film thicknesses during transient voiding conditions are pertinent to thermal analyses for reactor safety studies.

A Systematic Exposition of the Conservation Equations for Blast Waves

In order to provide a rational background for the analysis of experimental observations of blast wave phenomena, the conservation equations governing their nonsteady flow field are formulated in a general manner, without the usual restrictions imposed by an equation of state, and with proper account taken, by means of source terms, of other effects which, besides the inertial terms that conventionally dominate these equations, can affect the flow. Taking advantage of the fact that a blast wave can be generally considered as a spatially one-dimensional flow field whose nonsteady behavior can be regarded, consequently, as a function of just two independent variables, two generalized blast wave coordinates are introduced, one associated with the front of the blast wave and the other with its flow field. The conservation equations are accordingly transformed into this coordinate system, acquiring thereby a comprehensive character, in that they refer then to any frame of reference, being applicable, in particular, to problems involving either space or time profiles of the gas-dynamic parameters in the Eulerian system, or time profiles in the Lagrangian system.