Abstract
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 \(u_1^\prime \) and less in \(u_2^\prime \) and \(u_3^\prime \), whereas the trend is reversed in a ramp-down flow. This is a reflection of the redistribution of turbulence from \(u_1^\prime \) to \(u_2^\prime \) and \(u_3^\prime \).
Similar content being viewed by others
References
Brereton, G.J., Mankbadi, R.R.: Review of recent advances in the study of unsteady turbulent internal flows. Appl. Mech. Rev. 48(4), 189–212 (1995)
Gerrard, J.H.: An experimental investigation of pulsating turbulent water flow in a tube. J. Fluid Mech. 46(01), 43–64 (1971)
Tu, S.W., Ramaprian, B.R.: Fully developed periodic turbulent pipe flow. Part 1. Main experimental results and comparison with predictions. J. Fluid Mech. 137, 31–58 (1983)
Shemer, L., Wygnanski, I., Kit, E.: Pulsating flow in a pipe. J. Fluid Mech. 153, 313–337 (1985)
Brereton, G.J., Reynolds, W.C., Jayaraman, R.: Response of a turbulent boundary layer to sinusoidal free-stream unsteadiness. J. Fluid Mech. 221(–1), 131–159 (1990)
Scotti, A., Piomelli, U.: Numerical simulation of pulsating turbulent channel flow. Phys. Fluids 13(5), 1367–1384 (2001)
Tardu, S.F., Da Costa, P.: Experiments and modeling of an unsteady turbulent channel flow. AIAA J. 43(1), 140–148 (2005)
Tuzi, R., Blondeaux, P.: Intermittent turbulence in a pulsating pipe flow. J. Fluid Mech. 599, 51–79 (2008)
He, S., Jackson, J.D.: An experimental study of pulsating turbulent flow in a pipe. Eur. J. Mech. B, Fluids 28(2), 309–320 (2009)
Maruyama, T., Kuribayashi, T., Mizushina, T.: Structure of the turbulence in transient pipe flows. J. Chem. Eng. Jpn. 9(6), 431–439 (1976)
Greenblatt, D., Moss, E.A.: Rapid temporal acceleration of a turbulent pipe flow. J. Fluid Mech. 514, 65–75 (2004)
He, S., Jackson, J.D.: A study of turbulence under conditions of transient flow in a pipe. J. Fluid Mech. 408, 1–38 (2000)
He, S., Ariyaratne, C., Vardy, A.E.: A computational study of wall friction and turbulence dynamics in accelerating pipe flows. Comput. Fluids 37(6), 674–689 (2008)
Ariyaratne, C., He, S., Vardy, A.E.: Wall friction and turbulence dynamics in decelerating pipe flows. J. Hydraul. Res. 48, 810–821 (2010)
Chung, Y.M.: Unsteady turbulent flow with sudden pressure gradient changes. Int. J. Numer. Methods Fluids 47(8–9), 925–930 (2005)
Kim, J., Moin, P.: Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59(2), 308–323 (1985)
Orlandi, P.: Fluid Flow Phenomena: A Numerical Toolkit. Kluwer, Dordrecht (2001)
Kim, J., Moin, P., Moser, R.: Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166 (1987)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Seddighi, M., He, S., Orlandi, P. et al. A Comparative Study of Turbulence in Ramp-Up and Ramp-Down Unsteady Flows. Flow Turbulence Combust 86, 439–454 (2011). https://doi.org/10.1007/s10494-011-9341-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10494-011-9341-4