Effect of shock interactions on mixing layer between co-flowing supersonic flows in a confined duct

Experiments are conducted to observe the effect of shock interactions on a mixing layer generated between two supersonic streams of Mach number M1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_\mathrm {1}$$\end{document} =\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$=$$\end{document} 1.76 and M2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_\mathrm {2}$$\end{document} =\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$=$$\end{document} 1.36 in a confined duct. The development of this mixing layer within the duct is observed using high-speed schlieren and static pressure measurements. Two-dimensional, compressible Reynolds averaged Navier–Stokes equations are solved using the k-ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document} SST turbulence model in Fluent. Further, adverse pressure gradients are imposed by placing inserts of small (<7% of duct height) but finite (> boundary layer thickness) thickness on the walls of the test section. The unmatched pressures cause the mixing layer to bend and lead to the formation of shock structures that interact with the mixing layer. The mixing layer growth rate is found to increase after the shock interaction (nearly doubles). The strongest shock is observed when a wedge insert is placed in the M2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_\mathrm {2}$$\end{document} flow. This shock interacts with the mixing layer exciting flow modes that produce sinusoidal flapping structures which enhance the mixing layer growth rate to the maximum (by 1.75 times). Shock fluctuations are characterized, and it is observed that the maximum amplitude occurs when a wedge insert is placed in the M2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_\mathrm {2}$$\end{document} flow.