0
Research Papers

Optimization of Forcing Parameters of Film Cooling Effectiveness

[+] Author and Article Information
Hessam Babaee

Department of Mechanical Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: hbabae1@lsu.edu

Sumanta Acharya

Professor
Department of Mechanical Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: acharya@tigers.lsu.edu

Xiaoliang Wan

Assistant Professor
Department of Mathematics,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: xlwan@math.lsu.edu

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 4, 2013; final manuscript received August 18, 2013; published online November 28, 2013. Editor: Ronald Bunker.

J. Turbomach 136(6), 061016 (Nov 28, 2013) (10 pages) Paper No: TURBO-13-1178; doi: 10.1115/1.4025732 History: Received August 04, 2013; Revised August 18, 2013

An optimization strategy is described that combines high-fidelity simulations with response surface construction, and is applied to pulsed film cooling for turbine blades. The response surface is constructed for the film cooling effectiveness as a function of duty cycle, in the range of DC between 0.05 and 1, and pulsation frequency St in the range of 0.2–2, using a pseudospectral projection method. The jet is fully modulated and the blowing ratio, when the jet is on, is 1.5 in all cases. Overall 73 direct numerical simulations (DNS) using spectral element method were performed to sample the film cooling effectiveness on a Clenshaw–Curtis grid in the design space. The geometry includes a 35-degree delivery tube and a plenum. It is observed that in the parameter space explored a global optimum exists, and in the present study, the best film cooling effectiveness is found at DC = 0.14 and St = 1.03. In the same range of DC and St, four other local optimums were found. The physical mechanisms leading to the forcing parameters of the global optimum are explored and ingestion of the crossflow into the delivery tube is observed to play an important role in this process. The gradient-based optimization algorithms are argued to be unsuitable for the current problem due to the nonconvexity of the objective function.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Bogard, D. G., and Thole, K. A., 2006, “Gas Turbine Film Cooling,” J. Propul. Power, 22(2), pp. 249–270. [CrossRef]
Bunker, R. S., 2005, “A Review of Shaped Hole Turbine Film-Cooling Technology,” ASME J. Heat Transfer, 127, pp. 441–453. [CrossRef]
Lutum, E., and Johnson, B. V., 1999, “Influence of the Hole Length-to-Diameter Ratio on Film Cooling With Cylindrical Holes,” ASME J. Turbomach., 121(2), pp. 209–216. [CrossRef]
Acharya, S., Tyagi, M., and Hoda, A., 2006, “Flow and Heat Transfer Predictions for Film Cooling,” Ann. N.Y. Acad. Sci., 934(1), pp. 110–125. [CrossRef]
Acharya, S., and Tyagi, M., 2003, “Large Eddy Simulation of Film Cooling Flow From an Inclined Cylindrical Jet,” ASME Paper No. GT2003-38633. [CrossRef]
Iourokina, I., and Lele, S., 2005, “Towards Large Eddy Simulation of Film-Cooling Flows on a Model Turbine Blade With Free-Stream Turbulence,” AIAA Paper No. 2005-670. [CrossRef]
Peet, Y., and Lele, S. K., 2008, “Near Field of Film Cooling Jet Issued Into a Flat Plate Boundary Layer: LES Study,” ASME Paper No. GT2008-50420. [CrossRef]
Guo, X., Schroder, W., and Meinke, M., 2006, “Large-Eddy Simulations of Film Cooling Flows,” Comput. Fluids, 35(6), pp. 587–606. [CrossRef]
Renze, P., Schroder, W., and Meinke, M., 2008, “Large-Eddy Simulation of Film Cooling Flows at Density Gradients,” Int. J. Heat Fluid Flow, 29(1), pp. 18–34. [CrossRef]
Coulthard, S. M., Volino, R. J., and Flack, K. A., 2007, “Effect of Jet Pulsing on Film Cooling—Part I: Effectiveness and Flow-Field Temperature Results,” ASME J. Turbomach., 129(2), pp. 232–246. [CrossRef]
Ekkad, S. V., Ou, S., and Rivir, R. B., 2006, “Effect of Jet Pulsation and Duty Cycle on Film Cooling From a Single Jet on a Leading Edge Model,” ASME J. Turbomach., 128(3), pp. 564–571. [CrossRef]
El-Gabry, L. A., and Rivir, R. B., 2012, “Effect of Pulsed Film Cooling on Leading Edge Film Effectiveness,” ASME J. Turbomach., 134(4), p. 041005. [CrossRef]
Muldoon, F., and Acharya, S., 2009, “DNS Study of Pulsed Film Cooling for Enhanced Cooling Effectiveness,” Int. J. Heat Mass Transfer, 52(13–14), pp. 3118–3127. [CrossRef]
Bidan, G., Vezier, C., and Nikitopoulos, D. E., 2013, “Study of Unforced and Modulated Film-Cooling Jets Using Proper Orthogonal Decomposition—Part II: Forced Jets,” ASME J. Turbomach., 135(2), p. 021038. [CrossRef]
Warburton, T., 1999, “Spectral/hp Methods on Polymorphic Multi-Domains: Algorithms and Applications,” Ph.D. thesis, Brown, Providence, RI.
Karniadakis, G. E., Israeli, M., and Orszag, S. A., 1991, “High-Order Splitting Methods for the Incompressible Navier–Stokes Equations,” J. Comput. Phys., 97(2), pp. 414–443. [CrossRef]
Karniadakis, G. E., and Sherwin, S. J., 2005, Spectral/hp Element Methods for Computational Fluid Dynamics, Oxford University Press, New York.
Xiu, D., 2007, “Efficient Collocational Approach for Parametric Uncertainty Analysis,” Comm. Comp. Phys., 2(2), pp. 293–309.
Clenshaw, C. W., and Curtis, A. R., 1960, “A Method for Numerical Integration on an Automatic Computer” Numerische Mathematik, 2(1), pp. 197–205. [CrossRef]
Battles, Z., and Trefethen, L., 2004, “An Extension of Matlab to Continuous Functions and Operators,” SIAM J. Comput., 25(5), pp. 1743–1770. [CrossRef]
Bidan, G., Vezier, C., and Nikitopoulos, D. E., 2013, “Study of Unforced and Modulated Film-Cooling Jets Using Proper Orthogonal Decomposition—Part I: Unforced Jets,” ASME J. Turbomach., 135(2), p. 021037. [CrossRef]
Smirnov, A., Shi, S., and Celik, I., 2001, “Random Flow Generation Technique for Large Eddy Simulations and Particle-Dynamics Modeling,” ASME J. Fluids Eng., 123(2), pp. 359–371. [CrossRef]
Sau, R., and Mahesh, K., 2008, “Dynamics and Mixing of Vortex Rings in Crossflow,” J. Fluid Mech., 604, pp. 389–409. [CrossRef]
Haven, B. A., and Kurosaka, M., 1997, “Kidney and Anti-Kidney Vortices in Crossflow Jets,” J. Fluid Mech., 352(1997), pp. 27–64. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Three-dimensional schematic of the jet in crossflow

Grahic Jump Location
Fig. 2

Blowing ratio signal g(t;ξ) specified as vertical velocity at the plenum inlet

Grahic Jump Location
Fig. 3

Unstructured hexahedral grid; (a) three-dimensional view; (b) x1-x3 view of the grid in the vicinity of the jet exit with spectral order m = 4

Grahic Jump Location
Fig. 4

Grid convergence study. The centerline film cooling effectiveness for cases shown in Table 1 are compared.

Grahic Jump Location
Fig. 5

Error convergence for η˜N(ξ) with increasing polynomial order

Grahic Jump Location
Fig. 6

Comparison of time-averaged u1 velocity in the midplane with experimental data [21] at BR = 0.15

Grahic Jump Location
Fig. 7

Time-averaged temperature contours for quadrature points on cooled surface (x2 = 0). Each row: constant Tp; each column: constant DC.

Grahic Jump Location
Fig. 8

Instantaneous temperature surface in the midplane (x3 = 0) with constant pulsation period of Tp = 1.16. Plenum and delivery tube are not shown.

Grahic Jump Location
Fig. 9

Instantaneous temperature surface in the midplane (x3 = 0) with constant duty cycle of DC = 0.52. Plenum and delivery tube are not shown.

Grahic Jump Location
Fig. 10

Snapshots of instantaneous temperature at x3 = 0 during one pulsation cycle with DC = 0.09, Tp = 1.16, Δton = 0.10 and Δtoff = 1.06

Grahic Jump Location
Fig. 11

Instantaneous u2-u3 velocity vector field at: left x1 = 2; right x1 = 4, at DC=0.09 and Tp = 1.16

Grahic Jump Location
Fig. 12

Snapshots of instantaneous temperature at x3 = 0 during one pulsation cycle with DC = 0.34, Tp = 1.16, Δton = 0.39 and Δtoff = 0.77

Grahic Jump Location
Fig. 13

Snapshots of instantaneous temperature at x3 = 0 during one pulsation cycle with DC = 0.09, Tp = 2.75, Δton = 0.25 and Δtoff = 2.5

Grahic Jump Location
Fig. 14

Contours of averaged film cooling effectiveness (η˜N(ξ)). Local and global maxima are shown, with P1 being the global maximum and P2 to P5 are local maxima ordered with decreasing values.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In