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A numerical study of three-dimensional backward-facing step flow

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Abstract

The laminar and turbulent flow over a backward-facing step placed in a square duct was investigated numerically. The aspect ratio of the step (step width/step height) was 3 and the area expansion ratio was 2∶3. Three-dimensional effects were significant due to the small aspect ratio. To simulate turbulent flows, both a standardk-ɛ model and a non-lineark-ɛ model were employed and the results were compared. The non-linear model was found to yield better results. From the numerical results, the existence of the corner vortex and the flow field associated with it were clarified. The reattachment length of the three-dimensional flow was found to be considerably shorter than the corresponding two-dimensional flow. The evolution of longitudinal vortices was visualized. Surface flow patterns which clearly demonstrate three-dimensional aspects of the flow were presented. Based on various data available, topological flow pattern was also sketched. To support the findings explored in the present work, expeirmental data were compared with the numerical data where applicable.

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Abbreviations

AE,AW,AN,AS,AT,AB:

Finite-difference coefficients

C1,C2,Cμ,CD,CE:

Turbulence model constants

G :

Production rate ofk

h :

Step height

k :

Turbulent kinetic energy

P :

Static pressure

Re :

Reynolds number based on step\(height\left( { = \frac{{Uoh}}{v}} \right)\)

S ϕ :

Integrated source term in finite difference equation

U, V, W :

Local velocity in each direction

\(\overrightarrow U \) :

Velocity vector

Uo :

Reference velocity in the plane of the step edge

\(\bar u',\bar v'\) :

r.m.s. value of velocity fluctuations

x, y, z :

Longitudinal, Transverse, Spanwise Coordinates

x r :

Reattachment length

Λ:

Diffusion coefficient

ε:

Dissipation rate ofk

μ:

Molecular viscosity

μt :

Turbulent viscosity

σk, σɛ :

Turbulence model constants

ϕ:

Scalar quantity

ρ:

Fluid density

τij :

Reynolds stress tensor

τiq :

Wall shear stress

F :

Foci at the surface

N :

Nodal point

S :

Saddle point

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Authors and Affiliations

  1. Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology, Kusong-Dong 373-1, Yusung-Ku, Taejon, Korea

    S. O. Park

  2. Chinhae Research Laboratory, Agency for Defense Development, Chinhae, Korea

    K. S. Lim (Senior Research Scientist)

  3. Department of Mechanical Engineering, Iowa State University, Ames, Ia, U.S.A.

    R. H. Pletcher

Authors
  1. S. O. Park
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  2. K. S. Lim
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  3. R. H. Pletcher
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Park, S.O., Lim, K.S. & Pletcher, R.H. A numerical study of three-dimensional backward-facing step flow. KSME Journal 7, 1–13 (1993). https://doi.org/10.1007/BF02953140

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  • DOI: https://doi.org/10.1007/BF02953140

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