Density Variation with Time and Radius in a Miniature Shock Tube Using X-ray Densitometry

The growth of cold side-wall boundary layer behind the reflected shock in a miniature high repetition rate shock tube was investigated by analyzing the data obtained from the X-ray densitometry experiments performed at Advanced Photon Source (Argonne National Laboratory). The complete analysis of the experimental data was performed by using a custom written Python code. The data obtained from several line-of-sight measurements helped in obtaining time resolved densities using the Beer’s law which were path length averaged measurements. The magnified effect of the boundary layer growth was observed early in the end wall pressure traces due to the small bore of the miniature shock tube (12.7 mm). Further analysis of temperature profile based on the isentropic assumption and distribution along the path length accounting for hot core gas region and cold boundary layer region was performed. This led to the estimation thermal boundary layer growth as a function time. In addition to this analysis, the radially resolved densities were obtained by performing the Abel Inversion technique (Onion Peeling) using the path length averaged line-of–sight density measurements. The increase in the density as the side wall approached resulted in estimation of boundary layer thickness by choosing the location of 101% centerline density. Various boundary layer thickness calculations were performed and compared, leading to the formation of a base boundary layer estimation model in order to support newer models accounting for other factors such as viscous effects. In addition to this a comprehensive uncertainty analysis was performed to estimate the range of experimental and calculated densities obtained from ideal normal shock equations.