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Research Papers

Correlations for the Prediction of Intermittency and Turbulent Spot Production Rate in Separated Flows

[+] Author and Article Information
M. Dellacasagrande

DIME,
Universitá di Genova,
Genova 16145, Italy
e-mail: matteo.dellacasagrande@edu.unige.it

R. Guida

DIME,
Universitá di Genova,
Genova 16145, Italy
e-mail: roberto.guida@edu.unige.it

D. Lengani

DIME,
Universitá di Genova,
Genova 16145, Italy
e-mail: davide.lengani@edu.unige.it

D. Simoni

DIME,
Universitá di Genova,
Genova 16145, Italy
e-mail: daniele.simoni@unige.it

M. Ubaldi

DIME,
Universitá di Genova,
Genova 16145, Italy
e-mail: marina.ubaldi@unige.it

P. Zunino

DIME,
Universitá di Genova,
Genova 16145, Italy
e-mail: pietro.zunino@unige.it

1Corresponding author.

Manuscript received July 18, 2018; final manuscript received November 16, 2018; published online January 16, 2019. Editor: Kenneth Hall.

J. Turbomach 141(3), 031003 (Jan 16, 2019) (8 pages) Paper No: TURBO-18-1164; doi: 10.1115/1.4042066 History: Received July 18, 2018; Revised November 16, 2018

Experimental data describing laminar separation bubbles developing under strong adverse pressure gradients, typical of ultra-high-lift turbine blades, have been analyzed to define empirical correlations able to predict the main features of the separated flow transition. Tests have been performed for three different Reynolds numbers and three different free-stream turbulence intensity levels. For each condition, around 4000 particle image velocimetry (PIV) snapshots have been acquired. A wavelet-based intermittency detection technique, able to identify the large scale vortices shed as a consequence of the separation, has been applied to the large amount of data to efficiently compute the intermittency function for the different conditions. The transition onset and end positions, as well as the turbulent spot production rate, are evaluated. Thanks to the recent advancements in the understanding on the role played by Reynolds number and free-stream turbulence intensity on the dynamics leading to transition in separated flows, guest functions are proposed in the paper to fit the data. The proposed functions are able to mimic the effects of Reynolds number and free-stream turbulence intensity level on the receptivity process of the boundary layer in the attached part, on the disturbance exponential growth rate observed in the linear stability region of the separated shear layer, as well as on the nonlinear later stage of completing transition. Once identified the structure of the correlation functions, a fitting process with own and literature data allowed us to calibrate the unknown constants. Results reported in the paper show the ability of the proposed correlations to adequately predict the transition process in the case of separated flows. The correlation for the spot production rate here proposed extends the correlations proposed in literature for attached (by-pass like) transition process, and could be used in γ–Reϑ codes, where the spot production rate appears as a source term in the intermittency function transport equation.

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Figures

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Fig. 1

Test section and PIV field of view

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Fig. 2

Normalized mean streamwise velocity u¯/U0 (top), rms of streamwise velocity fluctuations u′rms/U0 (middle) and rms of normal to the wall velocity fluctuations v′rms/U0 (bottom) for the reference case (low Re and low Tu, on the left column) for higher Tu (in the middle column) and for higher Re (on the right column)

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Fig. 3

Effects of Reynolds number and Tu level variation on the normal to the wall velocity fluctuations rms v′rms/U0

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Fig. 4

Time-resolved sequence of perturbation velocity maps with superimposed the wavelet energy density contour for the reference case Re = 40,000 and Tu = 0.65%

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Fig. 5

Comparison between the intermittency curves computed at (a) Re = 40,000, (b) 75,000, and (c) 90,000 and different Tu levels

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Fig. 6

(a) Dispersion of the transition onset Reynolds number Rest as a function of the new defined variable Reϑs0.65/Tu0.5. (b) Comparison between fitting curves obtained from the correlations of Mayle [14] (black straight line), Suzen at al. [30] (dash-dot lines) and from Eq. (4) (dashed lines).

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Fig. 7

(a) Dispersion of the transition length Reynolds number ReL as a function of the new defined variable Reϑs0.84/Tu0.15. (b) Comparison between fitting curves obtained from the correlation of Mayle [14] (black line) and from Eq. (5) at different Tu levels (dashed lines).

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Fig. 8

(a) Dispersion of the spot production rate as a function of ReL obtained from Eq. (5) and (b) Spot production rate obtained from Eq. (7) at different Tu levels compared with previous studies and Mayle's correlation [14]

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