Oblique shock train motion based on schlieren image processing

In this paper, shock train motion in a Mach number 2.7 duct is studied experimentally, and large numbers of schlieren images are obtained by a high-speed camera. An image processing method based on Maximum Correlation Detection (MCD) is proposed to detect shock train motion from the schlieren images, based on which the key structures, e.g., separation positions and separation shock angles on the top and bottom walls, can be analysed in detail. The oscillations of the shock train are generated by rhombus and ellipse shafts at various excitation frequencies. According to the analysis of MCD results, the distributions of the frequency components of shock train oscillation generated by the two shafts are distinctly different, in which the motion generated by the ellipse shaft is much smoother; shock train motion is mainly characterized by the oscillation of separation position while the separation shock strength is not so sensitive to downstream disturbance; there is a hysteresis loop relation between the downstream pressure and separation position.     

1-D dusty photo-ionization models of WR planetary nebulae NGC 2452 and IC 2003

We report dusty photo-ionization models for two Planetary Nebulae NGC 2452 and IC 2003, which have [WR] type central stars, using 1D photo-ionization code Cloudy17.02. We used the medium resolution optical spectra and archival IRAS photometry to constrain our models. The physical size of the ionized nebula derived using accurate distance measurements and absolute H$\beta$ flux available in the literature were used as additional constrains. We examine the importance of photo-electric heating and found that models with and without considering photo-electric heating do not make significant difference for both PNe for the MRN grain size distribution considered in this study. We derive the nebular elemental abundances of these PNe by the empirical method as well as by making dusty photo-ionization models. The values of N/O ratios for both PNe obtained from our models are lower than their respective values arrived using empirical methods. The central stars are assumed to be black bodies and the photospheric temperatures derived respectively for NGC 2452 and IC 2003 from their best fit models are 182 kK and 155 kK and their respective luminosities are 630$L_{\odot }$ and 1015$L_{\odot }$. We propose that both the PNe were resulted from low-mass progenitors of mass $?$2.8 M_⊙.