Abstract
The hydrodynamic effects of a jet in a swirling cross-flow problem, which is related to gas turbine blades film cooling, were numerically simulated using large eddy simulation with artificial inflow boundary conditions. The purpose of this study is to investigate the effects of swirling flow on a jet effusing from an inclined hole in a rotating channel. The finite volume method and the unsteady PISO algorithm were applied on a non-uniform staggered grid. The work is naturally divided into two main parts. The first part (the swirl flow generator), is a channel rotates axially to generate a turbulent swirling flow at different values of swirl number (SN) of 0.0, 0.15, 0.3, and 0.5 while the second part (test section), is a channel rotating about a parallel axis to investigate the interaction of a square jet with the turbulent swirling flow, generated by the first part, for the prediction of the film cooling under rotating conditions. Four different values of rotation number (Ro) were applied to the test section. The air jet was injected at 30 deg in the streamwise direction, at a velocity ratio of 1.0 and a jet Reynolds number of 4,700, based on the hole width and the jet exit velocity. It was found that the swirling flows primarily displayed the velocity profile of a forced vortex. Weak reverse flow was observed near the main vortex core, which moved in the direction of the swirl and deformed the kidney shape of the Counter Rotating Vortex Pair. As SN increases (SN > 0), the jet trajectory twists in an increasingly x-axis direction due to the centrifugal force effects of the swirl flow, and shifts from the centreline of the channel to the right-hand side (Z/D =+ 1.5). Also, it was shown that rotation has a strong impact on the mixing behaviour and film cooling effectiveness. Finally, it was concluded that the film cooling decreases rapidly as SN increases.
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Abbreviations
- C s :
-
Smagorinsky model constant.
- d :
-
Film hole width, mm.
- DR :
-
Density ratio.
- M w :
-
Gas molecular weight.
- P :
-
Pressure, N.m −2.
- Pr :
-
Prandtl Number.
- Pr t :
-
Turbulent Prandtl Number.
- R :
-
Universal gas constant.
- Re :
-
Reynolds number.
- Ro :
-
Rotation number.
- SGS :
-
Sub grid-scale.
- SN :
-
Swirl number.
- t :
-
Time, s.
- T :
-
Local fluid temperature, K.
- u τ :
-
Friction velocity, m/s.
- u + :
-
Velocity normalized by friction velocity.
- u, v, w :
-
Dimensional velocity components, m /s.
- VR :
-
Velocity ratio.
- X :
-
Spatial vector.
- x, y, z :
-
Dimensional coordinates in streamwise, normal, and spanwise directions, respectively, m.
- y + :
-
Dimensionless wall distance.
- Δ:
-
Filter width.
- Δt :
-
Time step, s.
- Δx,Δy,Δz :
-
Mesh spacing in the x, y, z directions, m.
- η :
-
Local film cooling effectiveness.
- \(\bar {{\eta }}\) :
-
Spanwise-averaged film cooling effectiveness.
- ρ :
-
Fluid density, kg/m 3.
- τ w :
-
Wall shear stress, N.m −2.
- μ :
-
Dynamic viscosity, N⋅s/m 2.
- μ s g s :
-
Sub-grid scale eddy viscosity, N⋅s/m 2
- v :
-
Kinematics viscosity, m 2 /s.
- Ω:
-
7 Rotating speed, rad/s
- i,j,k :
-
directions i,j,k.
- rms :
-
Root mean square.
- ∞ :
-
Free stream.
- - :
-
Filtered (LES) quantity.
- ‵ :
-
Fluctuating quantity.
- <>:
-
Time averaging.
- <<>>:
-
Time and spatial averaging.
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Al-Zurfi, N., Turan, A. A Numerical Simulation of the Effects of Swirling Flow on Jet Penetration in a Rotating Channel. Flow Turbulence Combust 94, 415–438 (2015). https://doi.org/10.1007/s10494-014-9586-9
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DOI: https://doi.org/10.1007/s10494-014-9586-9