Statistical Measurement of Critical Tube Diameter

Qualitative association of gaseous detonation phenomenon with “dynamic parameters” such as cell size and critical diameter has been a successful endeavor in detonation research for the last three decades. [1] Attempts to perform more quantitative correlation are complicated by the fact that soot foil records are difficult to characterize with a single cell dimension, often with considerable interpretation “by eye” required to extract data from a foil. Classification of cellular regularity, for example, is made by comparison of foils to those obtained by Strehlow in an early publication [2]. The technique of performing digital image analysis on foils [3,4] shows promise, but the nuances of foil preparation mean that it is unlikely that a given result can be reproduced by different researchers. The mechanism by which a detonation writes on a foil is still under investigation, and precisely what a smoked foil measures remains a subject of discussion. [5] This paper proposes a new technique to provide an extremely precise quantification of detonation wave dynamics based on the critical diameter experiment. In the critical diameter experiment, a detonation wave emerges from a tube into an unconfined environment. The detonation either successfully transitions to a spherical detonation and continues to propagate or fails with the combustion front decoupling from the shock. The tube diameter which delimits these two outcomes is the critical diameter dc. For a wide range of hydrocarbon/oxygen and hydrocarbon/oxygen/diluent (including hydrocarbon/air) mixtures, the critical diameter has been shown to be approximately 13 times the detonation cell size λ (dc ≈ 13 λ). For mixtures exhibiting highly “regular” cellular structure, such as hydrogen-oxygen (or acetylene-oxygen) heavily diluted with argon, the dc ≈ 13 λ criterion has been shown to break down, with the critical diameter being 25-30 λ. [6] This points to two different mechanisms of transition in critical diameter experiments, as discussed further in [7]. The current investigation seeks to measure critical diameter with greater precision than previously obtained via a statistically significant number of repeated measurements. This permits the “fuzziness” of the critical diameter to be measured. This can be understood by considering a mixture that has a critical diameter of, for example, 100 mm: If the tube diameter is reduced to 99 mm, will the detonation always fail upon emerging, and then if increased to 101 mm, will the detonation always continue to propagate upon emerging from the tube? Rather, it is anticipated that there is a distribution of probabilities around the critical diameter, where the outcome of an experiment continuously varies from 0% of repeated experiments resulting in detonation to 100% successful transition as the tube diameter is increased. Measurement of the width of the “sharpness” or “fuzziness” of this transition (this is more properly referred to as the “variance” or “statistical dispersion”) may provide a new means to quantify the regularity or irregularity of detonation phenomenon. While repeated experiments with different sized tubes is conceptually the most straightforward experiment to visualize, it is more convenient to vary other experimental parameters, such as mixture composition or initial pressure. For this study, the tube diameter is fixed and the pressure is varied. Since cell size and critical diameter are known to follow an inverse linear dependence when plotted on a log-log graph, it is possible to relate the variance of critical pressure with a fixed tube diameter to the variance of the tube diameter at a fixed pressure. Despite the fact that measurements like this have not been previously reported for gaseous detonation phenomenon, statistical measurements of critical gap thickness tests are routinely performed for condensed explosives using the so-called “Bruceton Up-Down” technique [8].