Riemann shock tube: 1D normal shocks in air, simulations and experiments

Abstract

This paper presents numerical simulation of the evolution of one-dimensional normal shocks, their propagation, reflection and interaction in air using a single diaphragm Riemann shock tube and validate them using experimental results. Mathematical model is derived for one-dimensional compressible flow of viscous and conducting medium. Dimensionless form of the mathematical model is used to construct space-time finite element processes based on minimization of the space-time residual functional. The space-time local approximation functions for space-time p-version hierarchical finite elements are considered in higher order H k,p (¯ e xt ) spaces that permit desired order of global differentiability of local approximations in space and time. The resulting algebraic systems from this approach yield unconditionally positive-definite coefficient matrices, hence ensure unique numerical solution. The evolution is computed for a space-time strip corresponding to a time increment t and then time march to obtain the evolution up to any desired value of time. Numerical studies are designed using recently invented hand-driven shock tube (Reddy tube) parameters, high/low side density and pressure values, highand low-pressure side shock tube lengths, so that numerically computed results can be compared with actual experimental measurements. Introduction, literature review and scope of workIn compressible flows, shocks naturally form due to the existence of the compression wave, and the process of piling up of these waves to eventually form a shock. Numerical simulation of flows with shocks can be viewed in many ways depending upon what outcome is of interest. The first group of numerical methods are shock fitting or shock capturing methods. In these methods one does not pay attention to the evolution of shock but is rather interested in the shock relations; hence, the name 'shock fitting' or 'shock capturing.' The conditions behind and ahead of the shock are used to transition in some manner and then marched during evolution. Obviously, these methods can describe neither the evolution of the shock nor the physics in the shock region. The second group of methods are those in which shock evolution is considered but with much higher viscosity than the actual viscosity of the medium so that extremely small shock widths with actual viscosity can be avoided. These methods work well in predicting shock relations and some aspects of other features like shock reflection, shock interaction and so on, as long as the diffused shock width is much smaller than the spatial dimension of the domain. In this approach, with much increased shock width, one could study flows over large objects since shock structure is no longer a microprocess. In the third group of methods one studies the true evolution, propagation, reflection and inter-

Streamer properties and associated x-rays in perturbed air

“…They do not investigate We propose here to perform an experiment involving a shock tube (see e.g. [75,76] for a discussion of the set-up and comparisons with numerical models). The shock tube is divided into a driver and driven section by a membrane.…”

Validation of a blast induced neurotrauma model using modified Reddy tube in rats: A pilot study

“…The details of the working of the Reddy tube has been described elsewhere. 3,4 However, a brief description of Reddy Tube is given below for making the paper self contained. It is a simple tube consisting of two sections (a high pressure-driver section, and a low pressure-driven section) separated by a diaphragm, generally made of a sheet of tracing paper of 90/95 grade.…”

“…The blast waves and pressure recordings have been shown to be reproducible. 3,4 Due to the small opening of 29 mm diameter only the head of the rat is exposed to the blast beyond which the pressure falls rapidly therefore the body is not exposed to the blast. The blast pressure curve follows the Friedlander distribution.…”