Research Papers

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

[+] Author and Article Information
M. Dellacasagrande

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

R. Guida

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

D. Lengani

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

D. Simoni

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

M. Ubaldi

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

P. Zunino

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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Volino, R. J. , 2002, “ Separated Flow Transition Under Simulated Low-Pressure Turbine Airfoil Conditions—Part 1: Mean Flow and Turbulence Statistics,” ASME J. Turbomach., 124(4), pp. 645–655. [CrossRef]
Yarusevych, S. , Kawall, J. G. , and Sullivan, P. E. , 2008, “ Separated-Shear-Layer Development on an Airfoil at Low Reynolds Numbers,” AIAA J., 46(12), pp. 3060–3069. [CrossRef]
Simoni, D. , Ubaldi, M. , and Zunino, P. , 2016, “ A Simplified Model Predicting the Kelvin–Helmholtz Instability Frequency for Laminar Separated Flows,” ASME J. Turbomach., 138(4), p. 044501. [CrossRef]
Diwan, S. S. , and Ramesh, O. , 2009, “ On the Origin of the Inflectional Instability of a Laminar Separation Bubble,” J. Fluid Mech., 629, pp. 263–298. [CrossRef]
McAuliffe, B. R. , and Yaras, M. I. , 2010, “ Transition Mechanisms in Separation Bubbles Under Low- and Elevated-Freestream Turbulence,” ASME J. Turbomach., 132(1), p. 011004. [CrossRef]
Lengani, D. , Simoni, D. , Ubaldi, M. , Zunino, P. , and Bertini, F. , 2017, “ Experimental Investigation on the Time-Space Evolution of a Laminar Separation Bubble by Proper Orthogonal Decomposition and Dynamic Mode Decomposition,” ASME J. Turbomach., 139(3), p. 031006. [CrossRef]
Marxen, O. , and Henningson, D. S. , 2011, “ The Effect of Small-Amplitude Convective Disturbances on the Size and Bursting of a Laminar Separation Bubble,” J. Fluid Mech., 671, pp. 1–33. [CrossRef]
Simoni, D. , Ubaldi, M. , Zunino, P. , Lengani, D. , and Bertini, F. , 2012, “ An Experimental Investigation of the Separated-Flow Transition Under High-Lift Turbine Blade Pressure Gradients,” Flow Turbul. Combust., 88(1–2), pp. 45–62. [CrossRef]
Lardeau, S. , Leschziner, M. , and Zaki, T. , 2012, “ Large Eddy Simulation of Transitional Separated Flow Over a Flat Plate and a Compressor Blade,” Flow Turbul. Combust., 88(1–2), pp. 919–944.
Dick, E. , and Kubacki, S. , 2017, “ Transition Models for Turbomachinery Boundary Layer Flows: A Review,” Int. J. Turbomach., Propul. Power, 2(2), p. 4. [CrossRef]
Steelant, J. , and Dick, E. , 1996, “ Modelling of Bypass Transition With Conditioned Navier–Stokes Equations Coupled to an Intermittency Transport Equation,” Int. J. Numer. Methods Fluids, 23(3), pp. 193–220. [CrossRef]
Langtry, R. B. , and Menter, F. R. , 2009, “ Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes,” AIAA J., 47(12), pp. 2894–2906. [CrossRef]
Howard, R. , Alam, M. , and Sandham, N. , 2000, “ Two-Equation Turbulence Modelling of a Transitional Separation Bubble,” Flow, Turbul. Combust., 63(1/4), pp. 175–191. [CrossRef]
Mayle, R. E. , 1991, “ The Role of Laminar-Turbulent Transition in Gas Turbine Engines,” ASME J. Turbomach., 113(4), pp. 509–537. [CrossRef]
Hatman, A. , and Wang, T. , 1999, “ A Prediction Model for Separated-Flow Transition,” ASME J. Turbomach., 121(3), pp. 594–602. [CrossRef]
Gostelow, J. , Blunden, A. , and Walker, G. , 1994, “ Effects of Free-Stream Turbulence and Adverse Pressure Gradients on Boundary Layer Transition,” ASME J. Turbomach., 116(3), pp. 392–404. [CrossRef]
Samson, A. , and Sarkar, S. , 2016, “ Effects of Free-Stream Turbulence on Transition of a Separated Boundary Layer Over the Leading-Edge of a Constant Thickness Airfoil,” ASME J. Fluids Eng., 138(2), p. 021202. [CrossRef]
Pacciani, R. , Marconcini, M. , Arnone, A. , and Bertini, F. , 2014, “ Predicting High-Lift Low-Pressure Turbine Cascades Flow Using Transition Sensitive Turbulence Closures,” ASME J. Turbomach., 136(5), p. 051007. [CrossRef]
Simoni, D. , Lengani, D. , Ubaldi, M. , Zunino, P. , and Dellacasagrande, M. , 2017, “ Inspection of the Dynamic Properties of Laminar Separation Bubbles: Free-Stream Turbulence Intensity Effects for Different Reynolds Numbers,” Exp. Fluids, 58(6), p. 66. [CrossRef]
Simoni, D. , Lengani, D. , and Guida, R. , 2016, “ A Wavelet-Based Intermittency Detection Technique From PIV Investigations in Transitional Boundary Layers,” Exp. Fluids, 57(9), p. 145. [CrossRef]
Talan, M. , and Hourmouziadis, J. , 2002, “ Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow,” Flow Turbul. Combust., 69(3/4), pp. 207–227. [CrossRef]
Sciacchitano, A. , Neal, D. R. , Smith, B. L. , Warner, S. O. , Vlachos, P. P. , Wieneke, B. , and Scarano, F. , 2015, “ Collaborative Framework for PIV Uncertainty Quantification: Comparative Assessment of Methods,” Meas. Sci. Technol., 26(7), p. 074004. [CrossRef]
Wieneke, B. , 2015, “ PIV Uncertainty Quantification From Correlation Statistics,” Meas. Sci. Technol., 26(7), p. 074002. [CrossRef]
Marxen, O. , Rist, U. , and Wagner, S. , 2004, “ Effect of Spanwise-Modulated Disturbances on Transition in a Separated Boundary Layer,” AIAA J., 42(5), pp. 937–944. [CrossRef]
Yang, Z. , and Voke, P. R. , 2001, “ Large-Eddy Simulation of Boundary-Layer Separation and Transition at a Change of Surface Curvature,” J. Fluid Mech., 439, pp. 305–333. [CrossRef]
Alam, M. , and Sandham, N. , 2000, “ Direct Numerical Simulation of ‘Short' Laminar Separation Bubbles With Turbulent Reattachment,” J. Fluid Mech., 410, pp. 1–28. [CrossRef]
Marxen, O. , Lang, M. , and Rist, U. , 2013, “ Vortex Formation and Vortex Breakup in a Laminar Separation Bubble,” J. Fluid Mech., 728, pp. 58–90. [CrossRef]
Volino, R. J. , and Hultgren, L. S. , 2000, “ Measurements in Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions,” ASME Paper No. 2000-GT-0260.
Bellows, W. , and Mayle, R. , 1986, “ Heat Transfer Downstream of a Leading Edge Separation Bubble,” ASME J. Turbomach., 108(1), pp. 131–136. [CrossRef]
Suzen, Y. , Huang, P. , Ashpis, D. , Volino, R. , Corke, T. , Thomas, F. , Huang, J. , Lake, J. , and King, P. , 2007, “ A Computational Fluid Dynamics Study of Transitional Flows in Low-Pressure Turbines Under a Wide Range of Operating Conditions,” ASME J. Turbomach., 129(3), pp. 527–541. [CrossRef]


Grahic Jump Location
Fig. 1

Test section and PIV field of view

Grahic Jump Location
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)

Grahic Jump Location
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%

Grahic Jump Location
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).

Grahic Jump Location
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).

Grahic Jump Location
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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