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

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.

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Fig. 1

Three-dimensional schematic of the jet in crossflow

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Fig. 2

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

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Fig. 4

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

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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

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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

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Fig. 11

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

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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

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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

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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.

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Fig. 5

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

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Fig. 6

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

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Fig. 7

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

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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.

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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.




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