Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-21T17:07:04.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent flow through a rectangular duct with a partially blocked exit

Published online by Cambridge University Press:  14 November 2007

T. Y. HSU ,
H. ELORANTA ,
P. SAARENRINNE  and
T. WEI
T. Y. HSU
Affiliation:
Department of Mechanical, Aerospace & Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
H. ELORANTA
Affiliation:
Energy and Process Engineering, Tampere University of Technology, Tampere, Finland
P. SAARENRINNE
Affiliation:
Energy and Process Engineering, Tampere University of Technology, Tampere, Finland
T. WEI
Affiliation:
Department of Mechanical, Aerospace & Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper contains data on and insights into the origins of turbulence associated with a partial blockage at the exit of a two-dimensional, laminar, horizontal duct flow. In essence, this is the upstream approach region of the forward-facing step problem. This work was motivated by the need to identify and control unsteady streamwise vortices generated in the headbox (i.e. contraction section) of an industrial paper machine. The duct was 57.2 cm wide × 10.16 cm high, with up to a 50 % blockage. Experiments were scaled to match Reynolds numbers found in paper machines; exit velocities were as large as 200 cm s−1. The goal of the research was to map the flow at the exit and to examine the response of the flat-plate turbulent boundary layer on the opposing wall under the partial blockage. Laser-induced fluorescence (LIF) and digital particle image velocimetry (DPIV) were used to examine flow in three orthogonal planes at various stations upstream of the duct exit. Mean and instantaneous DPIV vector fields clearly show that an unsteady spanwise vortex forms in the corner formed by the top nozzle wall and partial blockage which, in turn, gives rise to turbulent streamwise vortices.

A turbulent boundary layer was initiated on the duct wall opposite the blockage, upstream of a two-dimensional contraction. Results show that even though the acceleration parameter, K, exceeded the nominal critical level of 3.0 × 10−6 for relaminarization beneath the blockage, the flow did not reach a quasi-laminar state. In addition, there did not appear to be direct interaction between unsteady vortex formation at the partial blockage on the upper wall and bottom-wall turbulent boundary layer structures.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 592 , 10 December 2007 , pp. 51 - 78
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Badri Narayanan, M. A. & Ramjee, V. 1969 On the criteria for reverse transition in a two-dimensional boundary layer. J. Fluid Mech. 35, 225.CrossRefGoogle Scholar
Blackwelder, R. F. & Eckelmann, H. 1979 Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech., 94, 577.Google Scholar
Blackwelder, R. F. & Kovasznay, L. S. G. 1972 Large-scale motion of a turbulent boundary layer during relaminarization. J. Fluid Mech. 53, 61.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775.CrossRefGoogle Scholar
Eloranta, H. 2000 Near-wall coherent flow structures in the papermachine headbox slice. MS Thesis, Tampere University of Technology.Google Scholar
Eloranta, H. 2005 Fluid mechanics of the papermaking machine headbox – instabilities and disturbances in the slice chamber. PhD. Dissertation, Institute of Energy and Process Engineering, Tampere University of Technology, Finland.Google Scholar
Escudier, M. P., Abdel-Hameed, A., Johnson, M. W. & Sutcliffe, C. J. 1998 Laminarisation and re-transition of a turbulent boundary layer subjected to favourable pressure gradient. Exps. Fluids 25, 491.CrossRefGoogle Scholar
Fernholz, H. H. & Warnack, D. 1998 The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 1. The turbulent boundary layer. J. Fluid Mech. 359, 329.Google Scholar
Görtler, H. 1940 Uber eine driedimensionale instabilität laminarer grenzschichten an konkaven wanden. Math. Phys. Kl 2, 1 (also NASA TM 1375 (1954)).Google Scholar
Grega, L. M., Hsu, T. Y. & Wei, T. 2002 Vorticity transport in a corner formed by a solid wall and a free surface. J. Fluid Mech. 465, 331.Google Scholar
Grega, L. M., Wei, T., Leighton, R. I. & Neves, J. C. 1995 Turbulent mixed-boundary flow in a corner formed by a solid wall and a free surface. J. Fluid Mech. 294, 17.Google Scholar
Hsu, T. Y. 2000 Turbulent secondary flow in the mixed boundary corner formed by a horizontal free surface and a vertical solid wall. MS Thesis, Rutgers, The State University.Google Scholar
Hsu, T. Y. 2002 Hydrodynamics of paper making: streamwise vortices generated in upstream of a 2-D Jet Nozzle. PhD Dissertation, Rutgers; The State University of New Jersey, USA.Google Scholar
Hsu, T. Y., Grega, L. M., Wei, T., & Leighton, R. I. 2000 Turbulent kinetic energy transport in a corner formed by a solid wall and a free surface. J. Fluid Mech. 410, 343.CrossRefGoogle Scholar
Hsu, T. Y. & Wei, T. 2004 Generation of streamwise vortices in a slice knife model: Can streaks be generated at the slice exit? TAPPI J. 3, 3.Google Scholar
Jones, W. P. & Launder, B. E. 1972 Some properties of sink-flow turbulent boundary layers. J. Fluid Mech. 56, 337.Google Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 50, 133.Google Scholar
Mei, R. W. & Plotkin, A. 1986 Navier-Stokes solutions for laminar incompressible flows in forward-facing step geometrices. AIAA J. 24, 1106.CrossRefGoogle Scholar
Morel, T. 1977 Design of two-dimensional wind tunnel contractions. Trans. ASME: J. Fluids Engng 99, 371.Google Scholar
Moretti, P. H. & Kays, W. M. 1965 Heat transfer in turbulent boundary layer with varying free-stream velocity and varying surface temperature – an experimental study. Intl J. Heat Mass Transfer 8, 1187.Google Scholar
Myose, R. Y. & Blackwelder, R. F. 1991 Controlling the spacing of streamwise vortices on concave walls. AIAA J. 29, 1901.Google Scholar
Myose, R. Y. & Blackwelder, R. F. 1994 On the role of the outer region in the turbulent-boundary-layer bursting process. J. Fluid Mech. 259, 345.Google Scholar
Narasimha, R. & Sreenivansan, K. R. 1979 Relaminarization of fluid flows. Adv. Appl. Mech. 19, 221.CrossRefGoogle Scholar
Piomelli, U., Balaras, E. & Pascarelli, A. 2000 Turbulent structures in accelerating boundary layers. J. Turbulence, http://jot.iop.org/, 1/2000.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601.CrossRefGoogle Scholar
Rothenflue, J. A. & King, P. I. 1996 Three-dimensional velocity measurements within Görtler vortices. AIAA J. 34, 1736.CrossRefGoogle Scholar
Shah, P., Atsavapranee, P., Hsu, T. Y., Wei, T. & McHugh, J. 1999 Turbulent transport in the core of a trailing delta wing vortex. J. Fluid Mech. 387, 151.Google Scholar
Shah, P. N., Atsavapranee, P., Wei, T. & McHugh, J. 2000 The role of turbulent elongational stresses on deflocculation in paper sheet formation. TAPPI J. 83, 70.Google Scholar
Sherman, F. S. 1990 Viscous Flow. McGraw-Hill.Google Scholar
Smith, C. R. & Schwartz, S. P. 1983 Observation of streamwise rotation in the near-wall region of turbulent boundary layer. Phys. Fluids 26, 241.Google Scholar
Smith, G. B. 1992 Turbulent cascade to small scales during the off-axis collision of two vortex rings. MS Thesis, Rutgers, The State University of New Jersey.Google Scholar
Soderberg, L. D. & Alfredsson, P. H. 1997 Experiments concerning the creation of streaky structures inside a plane water jet. Proc. 1997 TAPPI Engineering Conference, p. 1205.Google Scholar
Spalart, P. R. 1986 Numerical study of sink-flow boundary layers. J. Fluid Mech. 172, 328.Google Scholar
Sreenivasan, K. R. 1982 Laminarescent, relaminarizing and retransitional flows. Acta Mech. 44, 1.Google Scholar
Swearingen, J. D. & Blackwelder, R. F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255.Google Scholar
Talamelli, A., Fornaciari, N., Westin, K. J. A. & Alfredson, P. H. 2002 Experimental investigation of streaky structures in a relaminarizing boundary layer. J. Turbulence http://jot.iop.org/, 3/2002, 018, 13 p.Google Scholar
Warnack, D. & Fernholz, H. H. 1998 The effects of a favourable pressure gradient and of the Reynolds number on anincompressible axisymmetric turbulent boundary layer. Part 2. The boundary layer with relaminarization. J. Fluid Mech. 359, 357.Google Scholar
Wei, T. & Smith, C. R. 1986 Secondary vortices in the wake of circular cylinders. J. Fluid Mech. 169, 513.CrossRefGoogle Scholar
Willert, C. E. & Gharib, M. 1991 Digital particle image velocimetry. Exps. Fluids 10, 181.CrossRefGoogle Scholar