Research Papers

Numerical Investigation of Compound Angle Effusion Cooling Using Differential Reynolds Stress Model and Zonal Detached Eddy Simulation Approaches

[+] Author and Article Information
G. Arroyo-Callejo

Moissy-Cramayel 77550, France
e-mail: gustavo.arroyo-callejo@onera.fr

E. Laroche, P. Millan

ONERA—The French Aerospace Lab,
Toulouse 31055, France
e-mail: emmanuel.laroche@onera.fr

F. Leglaye

Moissy-Cramayel 77550, France
e-mail: francois.leglaye@snecma.fr

F. Chedevergne

ONERA—The French Aerospace Lab,
Toulouse 31055, France
e-mail: francois.chedevergne@onera.fr

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received June 8, 2015; final manuscript received March 7, 2016; published online April 19, 2016. Assoc. Editor: Kenichiro Takeishi.

J. Turbomach 138(10), 101001 (Apr 19, 2016) (11 pages) Paper No: TURBO-15-1109; doi: 10.1115/1.4033016 History: Received June 08, 2015; Revised March 07, 2016

Effusion cooling is one of the most effective and widespread techniques to prevent combustor liner from being damaged. However, most recent developments in combustion techniques, resulting from increasingly stricter air pollution regulations, have highlighted the necessity of reducing the amount of air available for effusion cooling while keeping an adequate level of protection. Adoption of compound angles in effusion cooling is increasingly recognized by jet engine manufacturers as a powerful solution to meet new combustor requirements. Therefore, understanding the flow behavior and developing methods able to provide accurate estimates of wall temperatures is of a major importance. This study assesses the capability of a high-level Reynolds-averaged Navier–Stokes (RANS) method, differential Reynolds stress model (DRSM), in conjunction with a generalized gradient diffusion hypothesis (GGDH), and of a hybrid RANS–large eddy simulations (LES) method, zonal detached eddy simulation (ZDES), to predict overall film effectiveness. Both approaches are compared with the experimental data from Zhang et al. (2009, “Cooling Effectiveness of Effusion Walls With Deflection Hole Angles Measured by Infrared Imaging,” Appl. Therm. Eng., 29(5), pp. 966–972) and with a classical well-known RANS model (k–ω shear-stress transport (SST) model). Despite the fact that some discrepancies are found, both approaches have proved suitable and reliable for predicting wall temperatures (relative errors of about 5%). Moreover, a new method to deal with ZDES length scales for unstructured grids is proposed. ZDES applicability and its general advantages and drawbacks are also discussed. Finally, an in-depth analysis of the film structure is carried out on the basis of the ZDES simulations. The principal structures are identified (an asymmetric main vortex (AMV) and a counter rotating vortex pair, CRVP), and the film formation mechanisms are presented. Significant spanwise-homogeneous distributions of surface overall film cooling effectiveness are observed.

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Fig. 1

Schematic depiction of the row pattern

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Fig. 2

Sketch of the computational domain and boundary conditions. PBCs stand for periodic boundary conditions.

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Fig. 3

Schematic depiction of Ritter's method. P is a vertex, C is the circle center, and r is the radius of the circle.

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Fig. 4

Schematic representation of LΩ and SΩ for a four-vertex cell element

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Fig. 5

Close-up of the “medium” computational grid

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Fig. 6

Span-averaged overall film cooling effectiveness (η¯f) of the k−ω SST, DRSM/GGDH, and ZDES methods along the plate. Experimental data are only available between x/d=0 and x/d=80.

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Fig. 7

Overall film cooling effectiveness (ηf) contours for both numerical methods (DRSM/GGDH and ZDES) compared to experimental data. Vm arrow represents the main flow direction.

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Fig. 8

ZDES time-averaged heat transfer coefficient (h) between the sixth and the seventh row (left). Streamlines from the sixth row (right). Vm arrow represents the main flow direction.

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Fig. 9

ZDES overall film cooling effectiveness (ηf) along lines of constant z crossing even (A) and odd (C) rows and the centerline (B)

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Fig. 10

Blending function of ZDES calculations (f) in the plane of symmetry of a perforation at the nineth row. Contours represent effectiveness to visualize the zonal modeling compared to the flow structure.

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Fig. 11

ZDES iso-contours of Q-criterion present in the steady-state field (Q·d2/Vm,∞2 equal to 11.5 and 1.15). Vm arrow represents the main flow direction.

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Fig. 12

ZDES dimensionless vorticity normal to the centerline plane field (Ωn·d/Vm,∞) of the instantaneous solution at the symmetry plane of the nineth row. Vorticity is normal to the symmetry plane.

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Fig. 13

Power spectral densities at the upstream shear layer of the first and the fifth row

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Fig. 14

ZDES time-averaged effectiveness (η) isolines and contours of the film. Only the injection side (y > 0) is plotted. Streamwise planes (yz) are positioned at the center of the odd rows. Vm arrow represents the main flow direction.

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Fig. 15

ZDES time-averaged effectiveness (η) isolines of the film. Only the injection side (y > 0) is plotted. Streamwise planes (yz) are positioned at the center of the odd rows. Vm arrow represents the main flow direction.

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Fig. 16

ZDES snapshot of iso-contours of Q-criterion present in the instantaneous field (Q·d2/Vm,∞2=0.5). Only the injection side (y > 0) is plotted. Contours represent effectiveness.

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Fig. 17

Thickness of the compound angle plate compared with Miron's axial correlation [52]




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