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Effect of convex wall curvature on three-dimensional behavior of film cooling jet

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Abstract

The flow characteristics of film coolant issuing into turbulent boundary layer developing on a convex surface have been investigated by means of flow visualization and three-dimensional velocity measurement. The Schlieren optical system with a spark light source was adopted to visualize the jet trajectory injected at 35° and 90° inclination angles. A five-hole directional pressure probe was used to measure three-dimensional mean velocity components at the injection angle of 35°. Flow visualization shows that at the 90° injection, the jet flow is greatly changed near the jet exit due to strong interaction with the crossflow. On the other hand, the balance between radial pressure gradient and centrifugal force plays an important role to govern the jet flow at the 35° injection. The velocity measurement shows that at a velocity ratio of 0.5, the curvature stabilizes downstream flow, which results in weakening of the bound vortex structure. However, the injectant flow is separated from the convex wall gradually, and the bound vortex maintains its structure far downstream at a velocity ratio of 1.98 with two pairs of counter rotating vortices.

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Abbreviations

D :

Inner diameter of the injection pipe

J :

Momentum flux ratio,J=ρ jU2 j/ρ∞U2 pw

Pr :

Total pressure outside the boundary layer

P sw :

Static pressure at the wall

P t :

Total pressure

R :

Velocity ratio,R=U j/UPw

rw :

Radius of curved wall

ReD :

Injection pipe flow Reynolds number,Re D= UjD/v

RePw :

Crossflow Reynolds number,Re pw= UpwD/v

U, V, W :

x, y and z-components of mean velocity

U e :

Mean velocity at the jet exit without crossflow

U j :

Mean velocity averaged across the jet exit,\(U_j = \frac{4}{{\pi D^2 }}\int_0^{D/2} {U_e 2\pi rdr} \)

U p :

Potential velocity in thex-direction

U pw :

Potential velocity at curved wall in thex-direction

x,y,z :

Coordinates in the streamwise, radial and spanwise directions

α :

Inclination angle of the injection pipe

δ :

Boundary layer thickness

δ* :

Displacement thickness,\(\delta ^* \equiv \int_0^\infty {(1 - \tfrac{U}{{U_p }})dy} \)

θ :

Momentum thickness,\(\theta \equiv \int_0^\infty {\tfrac{U}{{U_p }}(1 - \tfrac{U}{{U_p }})dy} \)

ν :

Kinematic viscosity

ρ j :

Injectant density

ρ :

Crossflow fluid density

Φ j :

Mean vorticity flux

Ω j :

Spatially averaged mean vorticity over cross-section of the injection pipe

Φ x :

Streamwise mean vorticity

References

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Author information

Correspondence to Sang Woo Lee or Joon Sik Lee or Keon Kuk.

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Lee, S.W., Lee, J.S. & Kuk, K. Effect of convex wall curvature on three-dimensional behavior of film cooling jet. KSME International Journal 16, 1121–1136 (2002). https://doi.org/10.1007/BF02984432

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Key Words

  • Film Cooling Jet
  • Convex Wall
  • Velocity Ratio
  • Injection Angle
  • Flow Visualization
  • Three-Dimensional Velocity Measurement