Research Papers

Modal Analysis of Inclined Film Cooling Jet Flow

[+] Author and Article Information
Prasad Kalghatgi

Department of Mechanical Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: pkalgh1@tigers.lsu.edu

Sumanta Acharya

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



Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received October 6, 2013; final manuscript received December 9, 2013; published online January 31, 2014. Editor: Ronald Bunker.

J. Turbomach 136(8), 081007 (Jan 31, 2014) (11 pages) Paper No: TURBO-13-1227; doi: 10.1115/1.4026374 History: Received October 06, 2013; Revised December 09, 2013

Thermal and hydrodynamic flow field over a flat surface cooled with a single round inclined film cooling jet and fed by a plenum chamber is numerically investigated using large eddy simulation (LES) and validated with published measurements. The calculations are done for a freestream Reynolds number Re = 16,000, density ratio of coolant to freestream fluid ρj/ρ=2.0, and blowing ratio BR=ρjV/ρV=1.0. A short delivery tube with aspect ratio l/D=1.75 and 35 deg inclination is considered. The evolution of the Kelvin–Helmholtz (K-H), hairpin and counterrotating vortex pair (CVP) vortical structures are discussed to identify their origins. Modal analysis of the complete 3D flow and temperature field is carried out using a dynamic mode decomposition (DMD) technique. The modal frequencies are identified, and the specific modal contribution toward the cooling wall temperature fluctuation is estimated on the film cooling wall. The low and intermediate frequency modes associated with streamwise and hairpin flow structures are found to have the largest contribution (in-excess of 28%) toward the wall temperature (or cooling effectiveness) fluctuations. The high frequency Kelvin–Helmholtz mode contributes toward initial mixing in the region of film cooling hole away from the wall. The individual modal temperature fluctuations on the wall and their corresponding hydrodynamic flow structures are presented and discussed.

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Fig. 1

Computational domain with plenum and crossflow

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Fig. 2

Grid independence for centerline film cooling effectiveness

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Fig. 3

Centerline and laterally averaged film cooling effectiveness

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Fig. 4

Mean velocity comparison (•U/U0(exp), ♦V/U0(exp), –U/U0, -•-V/U0)

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Fig. 5

Turbulence comparison (•U'/U0(exp), ♦V'/U0(exp), –U'/U0, -•-V'/U0)

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Fig. 6

(a) Film cooling effectiveness distribution on the surface, (b) temperature distribution at spanwise midsection (z/D = 0), and (c) temperature distribution over the cooled wall and selected crossflow planes

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Fig. 7

(a) Instantaneous flow structures (contours of temperature), (b) flow structures in delivery tube (λ2 isosurface)

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Fig. 8

Instantaneous (a) temperature, and (b) spanwise vorticity field

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Fig. 9

Evolution of K-H vortex (z = 0 plane)

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Fig. 10

Evolution of hairpin vortices (λ2 isosurface) (a) spanwise vorticity, (b) streamwise vorticity, (c) schematic

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Fig. 11

Merging of spiral vortices and CVP–time-averaged field (λ2 isosurface, contours–streamwise vorticity)

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Fig. 12

DMD domain (D) (highlighted in red)

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Fig. 13

Spectral power density of streamwise velocity and temperature at the location: x/D=0.1,y/D=0.1,z/D=0.0

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Fig. 14

DMD growth rate spectrum

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Fig. 15

DMD energy spectrum (||DM||2∀ D) over the entire domain shown in Fig. 12

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Fig. 16

DMD energy spectrum near the surface (‖DM‖2∀ cooling wall)

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Fig. 17

Mode R and evolution of hairpin vortices (λ2 isosurface). Top figure is a close up of the near-hole region.

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Fig. 18

Mean distribution and fluctuation of temperature modes on film cooling wall

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Fig. 19

Hydrodynamic modes (λ2 isosurface) for mode B

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Fig. 20

Mode G (evolution of CVP) (λ2 isosurface)

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Fig. 21

Centerline film cooling effectiveness from reconstructed thermal field

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Fig. 22

Snapshot of modal temperature variation on film cooling wall

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Fig. 23

RMS fluctuations of film cooling effectiveness due to individual modes




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