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Research Papers

Study of Unforced and Modulated Film-Cooling Jets Using Proper Orthogonal Decomposition—Part I: Unforced Jets

[+] Author and Article Information
Guillaume Bidan

e-mail: gbidan3@lsu.edu

Clementine Vézier

e-mail: clemvezier@gmail.com

Dimitris E. Nikitopoulos

e-mail: medimi@lsu.edu
Turbine Innovation and Energy Research
(TIER) Center
Mechanical Engineering Department,
Louisiana State University,
Baton Rouge, LA 70803

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received October 6, 2011; final manuscript received October 29, 2011; published online November 8, 2012. Editor: David Wisler.

J. Turbomach 135(2), 021037 (Nov 08, 2012) (11 pages) Paper No: TURBO-11-1220; doi: 10.1115/1.4006599 History: Received October 06, 2011; Revised October 29, 2011

The effects of jet flow-rate modulation were investigated in the case of a 35 deg inclined jet in cross-flow over a flat plate using Mie scattering visualizations, time-resolved flow rate records, and large eddy simulations (LES). An unforced jet study was conducted over a wide range of blowing ratios to provide a baseline for comparison to the pulsed results. The two distinct and well known steady jet regimes (attached jet with high film cooling performance for BR < 0.4 and detached jet with poor film cooling performance for BR > 1.0) were related to the dynamics of characteristic vortical structures, significant in the transition from one regime to the other. Similarity of the inclined jet results with a past vertical jet study are also put in perspective when comparing wall adiabatic effectiveness results. 3D proper orthogonal decomposition (3D-POD) was performed on LES results of an unforced case at BR = 0.15 to provide an analysis of dominant modes in the velocity and temperature fields. Error calculations on the reconstructed fields provided an estimation of the number of modes necessary to obtain satisfactory reconstruction while revealing some of the shortcomings associated with POD.

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References

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Figures

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Fig. 1

Experimental setup

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Fig. 2

LES domain and applied boundary conditions

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Fig. 3

Experimental (symbols) and LES (solid line) time averaged streamwise velocity profiles at (a) BR = 0.150, (b) BR = 1.0 at Xj = 0, 2, 5, and 9

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Fig. 4

Experimental Mie scattering visualizations in the plane Yj = 0 at (a) BR = 0.15; (b) BR = 0.4; (c) BR = 0.75; (d) BR = 1.1

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Fig. 5

Laplacian of the pressure iso-surfaces at BR = 0.300 from LES and instantaneous wall temperature

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Fig. 6

Experimental Mie scattering visualizations on a plane inclined at −30 deg with respect to the Y-Z plane for (a) BR = 0.15; (b) BR = 0.75

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Fig. 7

Laplacian of the pressure iso-surfaces from LES colored with spanwise vorticity contours (black: negative, white: positive) at (a),(b) BR = 0.15; (c),(d) BR = 0.4; (e),(f) BR = 0.75; (g),(h) BR = 1.2 and instantaneous temperature contours in the planes Zj = 0 (left) and Yj = 0 (right)

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Fig. 8

Wall adiabatic effectiveness contours from LES at (a) BR = 0.15; (b) BR = 0.3; (c) BR = 0.4; (d) BR = 0.75; (e) BR = 1.0; (f) BR = 1.2

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Fig. 9

(a) Spanwise averaged adiabatic effectiveness and (b) centerline adiabatic effectiveness from LES for the inclined jet (solid line, filled symbols) and the vertical jet (open symbols)

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Fig. 10

(a) Area averaged adiabatic effectiveness for the inclined jet (solid line) and the vertical jet (dashed line) and (b) coverage coefficient for thresholds η = 0.1, 0.2, 0.3, 0.5

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Fig. 11

Mean flow (0th POD mode) and first three velocity POD modes at BR = 0.15 (a)-(c) mode 0; (d)-(f) mode 1; (g)-(i) mode 2; (j)-(l) mode 3. Slices at Xj = 6 (left), Xj = 10.6 (center) with U velocity contours and V-W streamlines. Q-criterion iso-surfaces (right) computed from the corresponding POD modes colored by U velocity and mean wall temperature contours (gray scale).

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Fig. 12

Mean flow and first three velocity POD modes at BR = 0.15 (a) mode 0; (b) mode 1; (c) mode 2; (d) mode 3. Slices at Yj = 0 with V velocity contours and U-W streamlines.

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Fig. 13

Mean flow and first three velocity POD modes at BR = 0.15 (a) mode 0; (b) mode 1; (c) mode 2; (d) mode 3. Slices at Zj = 0.25 with W velocity contours and U-V streamlines.

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Fig. 14

POD decomposition metrics for BR = 0.15 (a) POD modes eigenvalues and cumulative temperature and velocity energies; (b) first two velocity POD coefficients a1Vel and a2Vel; (c) first two temperature POD coefficients a1Temp and a2Temp

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Fig. 15

Mean temperature field (0th POD mode) and first significant temperature POD modes at BR = 0.15 (a)-(c) mode 0; (d)-(f) mode 1; (g)-(i) mode 2; (j),(k) mode 5. Slices Xj = 6 (left), Xj = 10.6 (center) with temperature contours. Iso-temperature surfaces (right) computed from corresponding POD modes and mean wall temperature contours (gray scale).

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Fig. 16

Mean temperature field and first significant temperature POD modes at BR = 0.15 (a) mode 0; (b) mode 1; (c) mode 2; (d) mode 5. Slices Yj = 0 with temperature contours.

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Fig. 17

Mean temperature field and first significant temperature POD modes at BR = 0.15 (a) mode 0; (b) mode 1; (c) mode 2; (d) mode 5. Slices Zj = 0 with temperature contours.

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Fig. 18

Reconstructed velocity field for multiple values of Nr. Stream traces correspond to in-plane velocity, contours to streamwise velocity.

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Fig. 19

Reconstructed temperature field for multiple values of Nr

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Fig. 20

Average TKE error of the reconstructed fields for various values of Nr. Max. contour value 1 (white).

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Fig. 21

Average temperature error of the reconstructed field at various Nr values. Max. contour value: 7 × 10− 3 (white)

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