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Physics of Fluids / Volume 24 / Issue 1 / ARTICLES / Laminar Flows

Phys. Fluids 24, 013601 (2012); http://dx.doi.org/10.1063/1.3673568 (25 pages)

Uniformly valid asymptotic flow analysis in curved channels

M. Zagzoule1, P. Cathalifaud1, J. Cousteix2, and J. Mauss1

1Université de Toulouse, INPT, UPS, CNRS, IMFT, F-31400 Toulouse, France
2ONERA - The French Aerospace Lab, ISAE, F-31055 Toulouse, France

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(Received 14 July 2010; accepted 28 November 2011; published online 6 January 2012)

The laminar incompressible flow in a two-dimensional curved channel having at its upstream and downstream extremities two tangent straight channels is considered. A global interactive boundary layer (GIBL) model is developed using the approach of the successive complementary expansions method (SCEM) which is based on generalized asymptotic expansions leading to a uniformly valid approximation. The GIBL model is valid when the non dimensional number μ = δmath is O(1) and gives predictions in agreement with numerical Navier-Stokes solutions for Reynolds numbers Re ranging from 1 to 104 and for constant curvatures δ = math ranging from 0.1 to 1, where H is the channel width and Rc the curvature radius. The asymptotic analysis shows that μ, which is the ratio between the curvature and the thickness of the boundary layer of any perturbation to the Poiseuille flow, is a key parameter upon which depends the accuracy of the GIBL model. The upstream influence length is found asymptotically and numerically to be O(math).

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. FORMULATION
    1. General equations
    2. Fully established flow
  3. OVERALL PRESENTATION OF THE METHOD
  4. ASYMPTOTIC ANALYSIS
    1. The equations
    2. Using the SCEM
    3. Euler equations
    4. The pressure
  5. THE GIBL
    1. General formulation
    2. A simplified model
    3. Numerical procedure
  6. RESULTS
    1. Shear stress
    2. Pressure distribution
    3. Velocity profiles and upstream influence length
  7. CONCLUSION

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KEYWORDS and PACS

Keywords

boundary layers, channel flow, laminar flow, Navier-Stokes equations, numerical analysis

PACS

  • 47.15.Rq

    Laminar flows in cavities, channels, ducts, and conduits

  • 47.60.Dx

    Flows in ducts and channels

  • 47.15.Cb

    Laminar boundary layers

  • 47.10.ad

    Navier-Stokes equations

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3673568

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    B. Snyder and C. Lovely, “A computational study of developing 2-d laminar-flow in curved channels,” Phys. Fluids A: Fluid Dyn. 2(10), 1808 (1990)PFADEB000002000010001808000001.


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