Propagation mechanism of dust detonations

This paper summarizes the studies on dust detonations at the Stosswellenlabor of RWTH Aachen since 1987. The onset and propagation mechanism of heterogeneous dust detonations are similar to those of marginal gas phase detonations. A self-sustained dust detonation has transverse wave structures that provide the coupling between shock and reaction. Large transition distances and transverse wave spacings require large sized tubes for the propagation of self-sustained dust detonations. The Hugoniot analysis of the Chapman-Jouguet detonation predicts equilibrium detonation states being in reasonable agreement with the self-sustained dust detonations observed. Shock matching calculations at the triple point adequately determine the wave structures of those stable dust detonations.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Shock wave attenuation in partially confined channels

An approximate analytical solution is presented for the attenuation of planar shock waves in channels with perforated walls. The problem is considered as quasi-one-dimensional. Good agreement is found between the theoretical results and available experimental data regarding the rate of shock wave attenuation within the range of initial shock Mach numbers between 1.1 and 4 and perforation ratios between 4.5 × 10^–3 and 0.53. A correlation for the discharge coefficient of a single hole perforation is presented which gives quantitatively good agreement with particular experimental observations.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Interaction of a reflected shock from a concave wall with a flame distorted by an incident shock

Observations are presented from calculations where a laminar spherical CH₄/air flame was perturbed successively by incident and reflected shock waves reflected from a planar or concave wall. The two-dimensional axi-symmetric Navier–Stokes equations with detailed chemistry were used. The computational results were qualitatively validated with experiments which were performed in a standard shock tube arrangement. Under the influence of the incident shock wave, a Richtmyer–Meshkov instability is induced in the flame, and the distorted flame finally takes the form of two separated elliptical burning bubbles in the symmetric cross plane. Then, under subsequent interactions with the shock wave reflected from the planar or the concave wall, the flame takes a mushroom-like shape. Transverse waves produced by the shock reflection from the concave wall can compress the flame towards the axis, and the focusing shock generated on the concave wall will lead to a larger mushroom-like flame than that induced by the planar reflection.      

Aerodynamic force measurement using 3-component accelerometer force balance system in a hypersonic shock tunnel

A new three-component accelerometer force balance has been designed, calibrated and tested in hypersonic shock tunnel (HST2) of Indian Institute of Science. The newly designed balance is able to measure aerodynamic forces (within test time of one millisecond) on test models at angles of attack from 0 to 12°. Two models, a blunt cone with after body and a blunt cone with after body and frustum are used to establish the accuracy of the force balance. The tests were conducted for the above two configurations with a constant Mach number of 8 and total enthalpy of 2.0 MJ/kg. The effectiveness of the balance is demonstrated by comparing the forces and moments of measured data with AGARD models. The flow fields around the test model are simulated using a 3D axisymmetric Navier–Stokes solver and the simulated results were compared with the measured values. Measured and computed force data are matched within ±10% for two different models tested here. The accuracy of the force balance is also estimated with the Newtonian theory and the values are approximately ±10% for the axial component and ±8% for the normal and pitching moment components.      

Shock structure in bubbly liquids: comparison of direct numerical simulations and model equations

Shock wave structure in a bubbly mixture composed of a cluster of gas bubbles in a quiescent liquid with initial void fractions around 10% inside a 3D rectangular domain excited by a sudden increase in the pressure at one boundary is investigated using the front tracking/finite volume method. The effects of bubble/bubble interactions and bubble deformations are, therefore, investigated for further modeling. The liquid is taken to be incompressible while the bubbles are assumed to be compressible. The gas pressure inside the bubbles is taken uniform and is assumed to vary isothermally. Results obtained for the pressure distribution at different locations along the direction of propagation show the characteristics of one-dimensional unsteady shock propagation evolving towards steady-state. The steady-state shock structures obtained by the present direct numerical simulations, which show a transition from A-type to C-type steady-state shock structures, are compared with those obtained by the classical Rayleigh–Plesset equation and by a modified Rayleigh–Plesset equation accounting for bubble/bubble interactions in the mean-field theory.      

Shock pattern in the plume of rocket nozzles: needs for design consideration

For ideal nozzles, basically two different types of shock structures in the plume may appear for overexpanded flow conditions, a regular shock reflection or a Mach reflection at the nozzle centreline. Especially for rocket propulsion, other nozzle types besides the ideal nozzles are often used, including simple conical, thrust-optimized or parabolic contoured nozzles. Depending on the contour type, another shock structure may appear: the so-called cap-shock pattern. The exact knowledge of the plume pattern is of importance for mastering the engine operation featuring uncontrolled flow separation inside the nozzle, appearing during engine start-up and shut-down operation. As consequence of uncontrolled flow separation, lateral loads may be induced. The side-load character strongly depends on the nozzle design, and is a key feature for the nozzle’s mechanical structure layout. It is shown especially for the VULCAIN and VULCAIN 2 nozzle, how specific shock patterns evolve during transients, and how - by the nozzle design - undesired flow phenomena can be avoided.     

An extension of CVDV model to Zeldovich exchange reactions for hypersonic non-equilibrium air flows

A new preferential vibration-dissociation-exchange reactions coupling model – labelled CVDEV – resulting from an extension of the well-known Treanor and Marrone CVDV model, has been derived to take into account the coupling between the vibrational excitation of the and molecules and the two Zeldovich exchange reactions. Analytical expressions for the exchange reactions coupling factor and for the average vibrational energy lost – or gained – by a molecule through an exchange reaction have been developed. The influence of such a coupling has been shown by means of numerical simulations of hypersonic air flows through normal and bow shock waves. Code-to-code comparisons between our model and other recent approaches have been conducted. The infrared radiation of nitric oxide behind a normal shock wave resulting from computations with the CVDEV model has been compared with other coupling model results and to recent shock tube experimental data. These comparisons have shown a good agreement of our model results with the experimental data. In this context, the results show the prominent influence of vibration coupling on the first Zeldovich reaction, and the absence of vibration coupling effects on the second Zeldovich reaction. Received 30 June 1997 / Accepted 3 December 1997