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.

References

References
1.
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
.
2.
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
.
3.
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
.
4.
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
.
5.
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
.
6.
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
.
7.
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
.
8.
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
.
9.
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
.
10.
Dick
,
E.
, and
Kubacki
,
S.
,
2017
, “
Transition Models for Turbomachinery Boundary Layer Flows: A Review
,”
Int. J. Turbomach., Propul. Power
,
2
(
2
), p.
4
.
11.
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
.
12.
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
.
13.
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
.
14.
Mayle
,
R. E.
,
1991
, “
The Role of Laminar-Turbulent Transition in Gas Turbine Engines
,”
ASME J. Turbomach.
,
113
(
4
), pp.
509
537
.
15.
Hatman
,
A.
, and
Wang
,
T.
,
1999
, “
A Prediction Model for Separated-Flow Transition
,”
ASME J. Turbomach.
,
121
(
3
), pp.
594
602
.
16.
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
.
17.
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
.
18.
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
.
19.
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
.
20.
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
.
21.
Talan
,
M.
, and
Hourmouziadis
,
J.
,
2002
, “
Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow
,”
Flow Turbul. Combust.
,
69
(
3/4
), pp.
207
227
.
22.
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
.
23.
Wieneke
,
B.
,
2015
, “
PIV Uncertainty Quantification From Correlation Statistics
,”
Meas. Sci. Technol.
,
26
(
7
), p.
074002
.
24.
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
.
25.
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
.
26.
Alam
,
M.
, and
Sandham
,
N.
,
2000
, “
Direct Numerical Simulation of ‘Short' Laminar Separation Bubbles With Turbulent Reattachment
,”
J. Fluid Mech.
,
410
, pp.
1
28
.
27.
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
.
28.
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.
29.
Bellows
,
W.
, and
Mayle
,
R.
,
1986
, “
Heat Transfer Downstream of a Leading Edge Separation Bubble
,”
ASME J. Turbomach.
,
108
(
1
), pp.
131
136
.
30.
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
.
You do not currently have access to this content.