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Research Papers

Study of Unforced and Modulated Film-Cooling Jets Using Proper Orthogonal Decomposition—Part II: Forced 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 Journalof Turbomachinery. Manuscript received October 6, 2011; final manuscript received October 29, 2011; published online November 1, 2012. Editor: David Wisler.

J. Turbomach 135(2), 021038 (Nov 01, 2012) (14 pages) Paper No: TURBO-11-1221; doi: 10.1115/1.4006600 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). In forced experiments, average blowing ratios of 0.3 and 0.4 were investigated with a duty cycle of 50% and pulsing frequencies of St = 0.016 and 0.159. Time-resolved flow rate measurements during the experiments provided precise knowledge of the instantaneous jet blowing ratio and adequate inlet boundary conditions for large eddy simulations. The dynamics of the vortical structures generated during the transient parts of the forcing cycle as well as their impact on film cooling performance were investigated with respect of the forcing parameters. At the considered blowing ratios, a starting ring vortex was consistently generated at the transition from low to high blowing ratio. Ingestion of cross-flow fluid at the transition from high to low blowing ratio was also observed and had a negative impact on film cooling performance. All studied cases exhibited an overall decrease in coverage regardless of pulsing parameters over their corresponding steady jet cases at fixed mass flow rate. Comparisons between pulsed and steady jets at constant pressure supply (same high blowing ratio) did exhibit some film-cooling improvement with pulsing. 3D Proper orthogonal decomposition was performed on LES results at distinct forcing frequencies to provide an analysis of dominant modes in the velocity and temperature fields. Significantly different results were obtained depending on the forcing frequency.

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References

Figures

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Fig. 1

Experimental setup

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Fig. 2

Phase Averaged ηarea (top), relative coverage coefficient fluctuation for η = 0.1, 0.2, 0.3, and 0.5 (center), blowing ratio (bottom) for Case I at (a) St = 0.016 and (b) St = 0.159

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Fig. 3

Instantaneous reactive Mie scattering visualizations in the plane Yj = 0 (left) and temperature field from LES (right) at (a) t* = 4, (b) t* = 9, (c) t* = 13, (d) t* = 53, (e) t* = 57, (f) t* = 69, and (g) t* = 97 for Case I at St = 0.016

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Fig. 4

Instantaneous wall adiabatic effectiveness and Laplacian of the pressure iso-surfaces from LES for Case I (top) and Case II (bottom) at St = 0.016 at t* = 99, 6, 12, 21, 34, 56, 67, and 87%

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Fig. 5

Temperature field and 2D U-W streamlines for (a) Case I and (b) Case II at t* = 56%

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Fig. 6

Reactive Mie scattering visualizations for Case I at St = 0.08 at (a) t* = 13%, (b) t* = 43%, (c) t* = 60%, and (d) t* = 90%

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Fig. 7

Instantaneous wall adiabatic effectiveness and Laplacian of the pressure iso-surfaces from LES for Case I (left) and Case II (right) at St = 0.159 during a forcing cycle

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Fig. 8

Spanwise averaged center line (top) and (bottom) adiabatic effectiveness from LES for the forced inclined jet for (a), (b) Case I and (c), (d) Case II

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Fig. 9

Mean flow (0th POD Mode) and first significant velocity POD modes for Case I at St = 0.016 (a)-(c) Mode 0, (e)-(f) Mode 1, (g)-(i) Mode 2, (j)-(l) Mode 6. Slices at Xj = 6 (left), Xj = 10.6 (right) with U-velocity contours and V-W streamlines. Q-Criterion iso-surfaces (right) from corresponding POD modes colored by U-velocity and mean wall temperature contours (gray scale).

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Fig. 10

Mean flow and first significant velocity POD modes for Case I at St = 0.016; (a) Mode 0, (b) Mode 1, (c) Mode 2, (d) Mode 6. Slices at Yj = 0 with V-velocity contours and U-W streamlines.

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Fig. 11

Mean flow and first significant velocity POD modes for Case I at St = 0.016; (a) Mode 0, (b) Mode 1, (c) Mode 2, (d) Mode 6. Slices at Zj = 0.25 with W-velocity contours and U-V streamlines.

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Fig. 12

POD decomposition metrics for Case I at St = 0.016. (a) Temperature and velocity POD modes eigenvalues and cumulative energy; (b) Velocity POD coefficients a2nVel versus a2n-1Vel; (c) Temperature POD coefficients a2nT versus a2n-1T. For n = 1 (square), n = 2 (triangle), n = 3 (diamond). Open symbols correspond to full time sequence POD. Arrow points toward t* = 0 in the time sequence.

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Fig. 13

Mean temperature field (0th POD mode) and first significant temperature POD modes for Case I at St = 0.016 (a)-(c) Mode 0, (d)-(f) Mode 1, (g)-(i) Mode 2, (j)-(l) Mode 10. Slices at Xj = 6 (left), Xj = 10.6 (center) with temperature contours. Iso-temperature surfaces (right) computed from the corresponding POD modes and mean wall temperature contours (gray scale).

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Fig. 14

Mean temperature field and first significant temperature POD modes for Case I at St = 0.016 from LES; (a) Mode 0, (b) Mode 1, (c) Mode 2, (d) Mode 10. Slices at Yj = 0 with temperature contours.

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Fig. 15

Mean temperature field and first significant temperature POD modes for Case I at St = 0.016 from LES; (a) Mode 0, (b) Mode 1, (c) Mode 2, (d) Mode 10. Slices at Zj = 0 with temperature contours.

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Fig. 16

Temporal evolution of the POD modes coefficients ai for the velocity (top) and temperature (middle) decompositions along with forcing blowing ratio profile (bottom) at (a) St = 0.016 and (b) St = 0.159

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Fig. 17

Phase distribution of the minima (diamonds) and maxima (squares) associated with the POD modes coefficients ai for the velocity (top) and temperature (middle) along with forcing signal (bottom)

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Fig. 18

Reconstructed temperature field for multiple values of Nr at four different phase locations

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Fig. 19

Error on the reconstructed velocity field for different Nr values estimated with phase averaged fluctuation of kinetic energy. Maximum value (white) is 9%.

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Fig. 20

Error on the reconstructed temperature field for different values of Nr estimated using the total value of the temperature. Maximum value (white) is 9%.

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Fig. 21

Mean flow (0th POD Mode) and first significant velocity POD modes for Case I at St = 0.159 (a)-(c) Mode 0, (d)-(f) Mode 1, (g)-(i) Mode 3, (j)-(l) Mode 5. Slices at Xj = 6 (left), Xj = 10.6 (center) with U-velocity contours and V-W streamlines. Q Criterion iso-surfaces (right) computed from corresponding POD modes and correlated mode (white) colored by the corresponding U-velocity and mean wall temperature contours (gray scale).

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Fig. 22

Mean flow and first significant velocity POD modes for Case I at St = 0.159 (a) Mode 0, (b) Mode 1, (c) Mode 3, (d) Mode 5. Slices at Yj = 0 with V-velocity contours and U-W streamlines.

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Fig. 23

Mean flow and first significant velocity POD modes for Case I at St = 0.159 (a) Mode 0, (b) Mode 1, (c) Mode 3, (d) Mode 5. Slices at Zj = 0.25 with W-velocity contours and U-V streamlines.

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Fig. 24

POD decomposition metrics for Case I at St = 0.159 from LES (a) POD modes eigen alues and cumulative energy for temperature and velocity; (b) Velocity POD coefficients a2nVel versus a2n-1Vel; (c) Temperature POD coefficients a2nTemp versus a2n-1Temp. For n = 1 (squares), n = 2 (triangle), n = 3 (diamond), n = 4 (circle), n = 5 (X). Open symbols correspond to full time sequence POD. Arrow points toward t* = 0 in the time sequence.

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Fig. 25

Mean temperature field (0th POD mode) and first significant temperature POD modes for Case I at St = 0.159 (a)-(c) Mode 0, (d)-(f) Mode 1, (g)-(i) Mode 3, (j)-(l) Mode 5. Slices at Xj = 6 (left), Xj = 10.6 (center) with temperature contours. Iso-T surfaces (right) computed from corresponding pairs of POD modes (transparent) and mean wall temperature contours (gray scale).

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Fig. 26

Mean temperature field and first significant temperature POD modes for Case I at St = 0.159 (a) Mode 0, (b) Mode 1, (c) Mode 3, (d) Mode 5. Slices at Yj = 0 with temperature contours.

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Fig. 27

Mean temperature field and first significant temperature POD modes for Case I at St = 0.159 (a) Mode 0, (b) Mode 1, (c) Mode 3, (d) Mode 5. Slices at Zj = 0 with temperature contours.

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Fig. 28

Reconstructed temperature field for multiple values of Nr at different phase location t*

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Fig. 29

Error on the reconstructed velocity field for different Nr values estimated using the phase averaged fluctuation of kinetic energy. Maximum value (white) is 6%.

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Fig. 30

Error on the reconstructed temperature field for different values of Nr estimated using the total value of the temperature. Maximum value (white) is 6%.

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