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Incompressible laminar flow near a corner of 90° angle

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Abstract

Numerical integration is conducted for two-dimensional incompressible laminar flow over a 90° corner. Using Newton’s method, the Navier-Stokes equations are generated up toRe=2800, with the result that the corner generates a second bubble nearRe=800. There exist distinct patterns for the evolution of the pressure gradient and the position of a separation point. AsRe is increased the pressure gradient tends to approach zero over the recirculated region and shows sharper variations near the separation and reattachment points. Thus, these results confirm the free streamline model for separation proposed by Sychev.

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Abbreviations

i :

Index to denote the step number in ξ-direction

I :

i at the downstream edge ξ=ξ m

j :

Index to denote the step number in η-direction

J :

j atη=η m

M :

Jacobian forz→σ

p :

Non-dimensional pressure

Re :

Reynolds number

s :

Coordinate along the wall

w :

x 1+iy 1

x 1,y 1 :

Coordinate system inw-plane

x, y :

Coordnate system inz-plane

x s :

Separation point

z :

x+iy

ζ:

Vorticity

η:

Normal component of ρ

η m :

Displacement thickness of the boundary layer flow over a wedge

η m :

η at the upper edge

ξ:

Tangential component of ρ

ε m :

ξ at the downstream edge

ρ:

ξ+i η

T :

Wall shear defined as Eq. (14)

Ψ:

Stream function

Ψ:

Eq. (6)

Ψ m :

Ψ atη=η m

References

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Correspondence to Yong Kweon Suh.

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Suh, Y.K., Park, C.K. Incompressible laminar flow near a corner of 90° angle. KSME Journal 1, 121–127 (1987). https://doi.org/10.1007/BF02971655

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Key Words

  • Corner
  • Newton’s Method
  • Second Bubble
  • Separation
  • Boundary Layer
  • Free Streamline Model