Transitional Flows in Curved Channels

Dr. Phil Ligrani:    p_ligrani@msn.com

  • Diversity of practical applications
  • Heat transfer and flow characteristics
  • Applicable to cooling of surfaces of nozzles in rocket engines
  • Dean numbers from 50 to 1100
  • Laminar, transitional, turbulent flows
  • Dean vortex pairs along with secondary instabilities such as splitting and merging, undulating vortex pairs, twisting vortex pairs
  • New procedure to deduce forced convection Nusselt numbers from mixed convection measurements

Heat transfer in channels with transitional and turbulent flows are important for a range of practical applications, including cooling passages in gas turbine blades, internal combustion engine cooling ducts, heat exchangers, cooling systems for the nozzle walls of rocket motors, and medical treatment of the human cardiovascular system. Straight and curved channels are also interesting because they provide environments to investigate an assortment of transitional phenomena. In straight channels, these phenomena include regions of longitudinally distinct local instability referred to as “slugs” and “puffs” of turbulence. In curved channels, transition begins with the development of arrays of counter-rotating Dean vortex pairs which form across the channel span. Whether in straight or curved channels, developing transitional flow events provide the initial conditions for the turbulent flows which follow. The interactions between these transitional phenomena and the subsequently developing turbulent flows can be quite complex, especially when a curved channel segment follows a straight segment, as in the present studies.

In the present investigations, heat transfer and flow structure are obtained for a channel with a straight portion followed by a portion with mild curvature at Dean numbers from 100 to 1084. The channel aspect ratio is 40, radius ratio is 0.979, and the ratio of shear layer thickness to channel inner radius is 0.011. The data include flow visualizations, and spanwise-averaged Nusselt numbers. Also included are time-averaged turbulence structural data, time-averaged profiles and surveys of velocity components, spectra of longitudinal velocity fluctuations, and surveys of time-averaged vorticity components. Different flow events are present including laminar two-dimensional flow, Dean vortex flow, wavy Dean vortex flow (in both undulating and twisting modes), splitting and merging of Dean vortex pairs, transitional flow with arrays of Dean vortex pairs, and fully turbulent flow with arrays of Dean vortex pairs. Transitional events generally first appear in the curved portion of the channel at Dean numbers less than 350 in the form of arrays of counter-rotating Dean vortex pairs. At Dean numbers greater than 350, transitional events occur in the upstream straight portion of the channel but then continue to cause important variations in the downstream curved portion. The resulting Nusselt number variations with curvature, streamwise development, and Dean number vary significantly as they are affected by these different laminar, transitional, and turbulent flow phenomena.


Channel coordinate system and geometry

Time sequence of twenty-four smoke visualization photographs and sketches illustrating how one vortex pair may be engulfed by an adjacent vortex pair followed by the emergence of a vortex pair from the near-wall region for De =100 at a streamwise location 105 from the start of curvature. Photographs are spaced apart by 1/30 second intervals. The streamwise direction is into the plane of the plot, the concave surface is on the bottom of each photograph, and the convex surface is on the top of each photograph.


Forced convection Nusselt numbers as dependent upon x/d for Dean numbers of 218, 549, 709, 831, 905, and 1084 for the concave and convex channel surfaces.

RECENT PUBLICATIONS.

  • Flow Visualization of Dean Vortices in a Curved Channel with 40 to 1 Aspect Ratio (P. M. Ligrani and R. D. Niver), Physics of Fluids , Vol. 31, No. 12, pp. 3605-3617, December 1988.
  • Features of Wavy Vortices in a Curved Channel from Experimental and Numerical Studies (P. M. Ligrani, W. H. Finlay, W. A. Fields, S. J. Fuqua, and C. S. Subramanian), Physics of Fluids A , Vol. 4, No. 4, pp. 695-709, April 1992.
  • Surface Heat Transfer and Flow Properties of Vortex Arrays Induced Artificially and From Centrifugal Instabilities (C. S. Subramanian, P. M. Ligrani and M. F. Tuzzolo), International Journal of Heat and Fluid Flow , Vol. 13, No. 3, pp. 210-223, September 1992.
  • Transient, Oscillatory and Steady Characteristics of Dean Vortex Pairs in a Curved Rectangular Channel (P. M. Ligrani), Ordered and Turbulent Patterns in Taylor-Couette Flow (Editors: C. David Andereck and F. Hayot) , NATO Advanced Science Institutes Series Volume, Series B: Physics Vol. 297, Plenum Press Publishing Corporation, pp. 281-288, October 1992.
  • Splitting, Merging and Spanwise Wavenumber Selection of Dean Vortex Pairs (P. M. Ligrani, J. E. Longest, M. R. Kendall, and W. A. Fields), Experiments in Fluids , Vol. 18, No. 1, pp. 41-58, December 1994.
  • Effects of Dean Vortex Pairs and Transition to Turbulence on Surface Heat Transfer in a Curved Channel (P. M. Ligrani and C. R. Hedlund), 9th Couette-Taylor Workshop, University of Colorado, Boulder, Colorado, August 7-10, 1995.
  • Effects of Dean Vortex Pairs on Surface Heat Transfer in Curved Channel Flow (P. M. Ligrani, S. Choi, A. R. Schallert, and P. Skogerboe), International Journal of Heat and Mass Transfer , Vol. 39, No. 1, pp. 27-37, January 1996.
  • Mixed Convection in Straight and Curved Channels With Buoyancy Orthogonal to the Forced Flow (P. M. Ligrani and S. Choi ), International Journal of Heat and Mass Transfer , Vol. 39, No. 12, pp. 2473-2484, August 1996.
  • Heat Transfer in Curved and Straight Channels With Transitional Flow (C. R. Hedlund and P. M. Ligrani), International Journal of Heat and Mass Transfer , Vol. 41, No. 3, pp. 563-573, February 1998.
  • Transition to Turbulent Flow in Curved and Straight Channels With Heat Transfer at High Dean Numbers (P. M. Ligrani and C. R. Hedlund), International Journal of Heat and Mass Transfer , Vol. 41, No. 12, pp. 1739-1748, June 1998.
  • Effects of Curvature on Heat Transfer in Channels and Swirl Chambers (P. M. Ligrani), Recent Research Developments in Heat, Mass, & Momentum Transfer , Vol. 2-1999 , (Editor: S. G. Pandalai), Research Signpost Publishers, Vol. 2, pp. 171-183, 1999.
  • Experimental Surface Heat Transfer and Flow Structure in a Curved Channel With Laminar, Transitional, and Turbulent Flows, (P. M. Ligrani, and C. R. Hedlund), Paper 2003-GT-38734, 48th ASME Gas Turbine and Aeroengine Technical Congress, Exposition, and Users Symposium, Atlanta, Georgia, June 16-19, 2003.
  • Experimental Surface Heat Transfer and Flow Structure in a Curved Channel With Laminar, Transitional, and Turbulent Flows, (P. M. Ligrani, and C. R. Hedlund), ASME Transactions-Journal of Turbomachinery , accepted for publication, 2003, to appear, 2004.
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