A Comparative Study of Turbulence in Ramp-Up and Ramp-Down Unsteady Flows

DNS of a turbulent channel flow subjected to a step change in pressure gradient are performed to facilitate a direct comparison between ramp-up and ramp-down flows. Strong differences are found between behaviours of turbulence in the two flows. The wall shear stress in the ramp-up flow first overshoots, and then strongly undershoots the quasi-steady value in the initial stage of the excursion, before approaching the quasi-steady value. In a strongly decelerating flow, the wall shear stress tends to first undershoot but then overshoot the quasi-steady value. ‘Slow’ response of turbulence as well as flow inertia is responsible for these behaviours. In the ramp-up flow, the response of turbulence is similar to that observed in uniformly accelerating flows from previous studies, exhibiting a three-stage development. However, the transition between the various stages is more gradual and the responding stage is much longer and slower in the flows considered here. It has been shown that the delay in the near wall region is longer than that in the buffer layer confirming that turbulence response first occurs at the location of peak turbulence production. In a strongly decelerating flow, the response of turbulence exhibits a two-stage development. In both ramp-up and ramp down flows, the energy distribution in the three components of turbulent kinetic energy deviates from that of the steady flow. In a ramp-up flow, more energy is in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u_1^\prime $\end{document} and less in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u_2^\prime $\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u_3^\prime $\end{document}, whereas the trend is reversed in a ramp-down flow. This is a reflection of the redistribution of turbulence from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u_1^\prime $\end{document} to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u_2^\prime $\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$u_3^\prime $\end{document}.