Modeling of Film Cooling—Part II: Model for Use in Three-Dimensional Computational Fluid Dynamics

[+] Author and Article Information
André Burdet, Reza S. Abhari, Martin G. Rose

Turbomachinery Laboratory, Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology – ETH Zürich, CH-8092 Zürich, Switzerland

J. Turbomach 129(2), 221-231 (May 29, 2006) (11 pages) doi:10.1115/1.2437219 History: Received May 23, 2006; Revised May 29, 2006

Computational fluid dynamics (CFD) has recently been used for the simulation of the aerothermodynamics of film cooling. The direct calculation of a single cooling hole requires substantial computational resources. A parametric study, for the optimization of the cooling system in real engines, is much too time consuming due to the large number of grid nodes required to cover all injection holes and plenum chambers. For these reasons, a hybrid approach is proposed, based on the modeling of the near film-cooling hole flow, tuned using experimental data, while computing directly the flow field in the blade-to-blade passage. A new injection film-cooling model is established, which can be embedded in a CFD code, to lower the central processing unit (CPU) cost and to reduce the simulation turnover time. The goal is to be able to simulate film-cooled turbine blades without having to explicitly mesh inside the holes and the plenum chamber. The stability, low CPU overhead level (1%) and accuracy of the proposed CFD-embedded film-cooling model are demonstrated in the ETHZ steady film-cooled flat-plate experiment presented in Part I (Bernsdorf, Rose, and Abhari, 2006, ASME J. Turbomach., 128, pp. 141–149) of this two-part paper. The prediction of film-cooling effectiveness using the CFD-embedded model is evaluated.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Schematic of the near-hole region, with the jet intrinsic frame of reference (χ,ξ,η) on the plane of injection (top) and main geometrical parameters (bottom)

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Figure 2

Schematic of the near-hole macroflow features

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Figure 3

Schematic of the jet mixing zones just after the injection site (cross section)

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Figure 4

Schematic of the image vortex procedure to determine the coolant jet secondary flow velocity vector

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Figure 5

Velocity field, comparison between experiment (16) and model for α0=30deg and 50deg. The cross sections are located at X∕d=+1.25 and +1.0 downstream of the hole center for α0=30deg and 50deg respectively.

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Figure 6

Velocity and temperature field, comparison between the experiment (22) and model in the cross section located at X∕d=+1.0 downstream of the hole center: DR=1.17 and BR=1.35. In this plot, Z* is Y∕d and Y* is Z∕d.

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Figure 7

Example of the near-hole coolant jet boundary surface immersed in the computational mesh

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Figure 8

Computational stencil used for the implicit immersed boundary method

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Figure 9

Numerical prediction, using the film-cooling model, of the flow field near the hole exit. Contours of normalized static pressure ΔPs are represented on the flat plate (Z∕d=0.0). Normalized streamwise vorticity ωx* is shown at three different cross sections (X∕d=+2.0, +7.0, and +12.0). The freestream streamlines are represented in dark green.

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Figure 10

Comparison of numerical predictions of the near-hole normalized static pressure ΔPs

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Figure 11

Contours of normalized streamwise velocity (U∕Uf), superimposed with freestream streamlines, in the center plane Y∕d=0.0, found in the experimental measurements (16) and in the CFD prediction using the film-cooling model

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Figure 12

Contours of normalized streamwise velocity (U∕Uf), superimposed with secondary flow vectors (V∕Uf,W∕Uf), in the cross section X∕d=+4.0, found in experimental measurements (16) and in CFD prediction using the film-cooling model

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Figure 13

Contours of normalized streamwise ωx* and normal ωz* vorticity in the cross section Z∕d=+0.4; comparison between the experiment (16) (left) and CFD prediction using the film-cooling model (right)

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Figure 14

Lateral profile of normalized absolute vorticity ω, comparison between experiment (16) and CFD prediction (using the film-cooling model) for α0=30deg (left) and α0=50deg (right), at Z∕d=+0.4

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Figure 15

Predicted and measured (17) local wall adiabatic film-cooling effectiveness η for BR=0.5 (top) and BR=1.5 (bottom)

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Figure 16

Predicted and measured (17) laterally averaged wall adiabatic film-cooling effectiveness η¯

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Figure 17

Jet-solid curved cylinder analogy and forces applied to it



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