Graphical Abstract Figure
Graphical Abstract Figure
Close modal

Abstract

The use of a vortex lattice method (VLM) is investigated on a tip-leakage flow single-blade configuration (NACA 0012) for a wide range of tip gaps. The aim is to estimate the circulation of the tip-leakage vortex (TLV) detaching from the blade. The evaluation of that circulation without adding viscous effects to the potential method is comparable with the experimental measurements for the largest gaps but requires a diffusive model for the smaller gaps. A new diffusive model is constructed and integrated to the VLM, yielding a very good match with the experiment on the circulation for the whole tip gap range. This result indicates that for thin blades, the development of the TLV can be described in two stages: (i) a potential formation and (ii) a viscous diffusion leading to a decay once the vortex is detached from the blade.

References

1.
Denton
,
J.
,
1993
, Loss Mechanisms in Turbomachines, Technical Report, The American Society of Mechanical Engineers, New York.
2.
Courtiade
,
N.
, and
Ottavy
,
X.
,
2013
, “
Experimental Study of Surge Precursors in a High-Speed Multistage Compressor
,”
ASME J. Turbomach.
,
135
(
6
), p.
061018
.
3.
Vo
,
H. D.
,
Tan
,
C. S.
, and
Greitzer
,
E. M.
,
2008
, “
Criteria for Spike Initiated Rotating Stall
,”
ASME J. Turbomach.
,
130
(
1
), p.
011023
.
4.
Storer
,
J.
, and
Cumpsty
,
N.
,
1994
, “
An Approximate Analysis and Prediction Method for Tip Clearance Loss in Axial Compressors
,”
ASME J. Turbomach.
,
116
(
4
), pp.
648
656
.
5.
Smith
,
L. H. Jr.
,
1970
, “Casing Boundary Layers in Multistage Axial-Flow Compressors,”
Flow Research on Blading
,
L. S.
Dzung
, ed.,
Elsevier
,
New York
, pp.
275
304
.
6.
Koch
,
C. C.
, and
Smith
,
L. H.
,
1976
, “
Loss Sources and Magnitudes in Axial-Flow Compressors
,”
J. Eng. Power
,
98
(
3
), pp.
411
424
.
7.
Khalid
,
S. A.
,
Khalsa
,
A. S.
,
Waitz
,
I. A.
,
Tan
,
C. S.
,
Greitzer
,
E. M.
,
Cumpsty
,
N. A.
,
Adamczyk
,
J. J.
, and
Marble
,
F. E.
,
1999
, “
Endwall Blockage in Axial Compressors
,”
ASME J. Turbomach.
,
121
(
3
), pp.
499
509
.
8.
Lakshminarayana
,
B.
, and
Horlock
,
J. T.
,
1965
,
Leakage and Secondary Flows in Compressor Cascades
,
HM Stationery Office
,
London, UK
.
9.
Nikolos
,
I. K.
,
Douvikas
,
D. I.
, and
Papailiou
,
K. D.
,
1995
, “
Theoretical Modelling of Relative Wall Motion Effects in Tip Leakage Flow
,” In Turbomachinery, Vol.
1
,
American Society of Mechanical Engineers
, p.
V001T01A017
.
10.
Rains
,
D. A.
,
1954
, “
Tip Clearance Flows in Axial Compressors and Pumps
,” Ph.D. thesis,
California Institute of Technology
,
Pasadena, CA
.
11.
Chen
,
G. T.
,
Greitzer
,
E. M.
,
Tan
,
C. S.
, and
Marble
,
F. E.
,
1990
, “
Similarity Analysis of Compressor Tip Clearance Flow Structure
,” In ASME 1990 International Gas Turbine and Aeroengine Congress and Exposition,
American Society of Mechanical Engineers
, p.
V001T01A049
.
12.
Brandt
,
H.
,
Fottner
,
L.
,
Saathoff
,
H.
, and
Stark
,
U.
,
2002
, “
Effects of the Inlet Flow Conditions on the Tip Clearance Flow of an Isolated Compressor Rotor
,”
Proceedings of the ASME Turbo Expo 2002: Power for Land, Sea, and Air. Volume 5: Turbo Expo 2002, Parts A and B
,
Amsterdam, The Netherlands
,
June 3–6
,
ASME
, pp.
1123
1132
.
13.
Riéra
,
W.
,
Marty
,
J.
,
Castillon
,
L.
, and
Deck
,
S.
,
2016
, “
Zonal Detached-Eddy Simulation Applied to the Tip-Clearance Flow in an Axial Compressor
,”
AIAA J.
,
54
(
8
), pp.
2377
2391
.
14.
Gourdain
,
N.
,
Wlassow
,
F.
, and
Ottavy
,
X.
,
2012
, “
Effect of Tip Clearance Dimensions and Control of Unsteady Flows in a Multi-stage High-Pressure Compressor
,”
ASME J. Turbomach.
,
134
(
5
), p.
051005
.
15.
Montsarrat
,
C.
,
2021
, “
Tip-Leakage Flow Modelling in Axial Compressors
,” Ph.D. thesis,
Université de Lyon
,
Ecully, France
.
16.
Yamada
,
K.
,
Furukawa
,
M.
,
Tamura
,
Y.
,
Saito
,
S.
,
Matsuoka
,
A.
, and
Nakayama
,
K.
,
2016
, “
Large-Scale DES Analysis of Stall Inception Process in a Multi-stage Axial Flow Compressor
,” In Turbomachinery, Vol.
2D
,
American Society of Mechanical Engineers
, p.
V02DT44A021
.
17.
Tan
,
C.
,
Day
,
I.
,
Morris
,
S.
, and
Wadia
,
A.
,
2010
, “
Spike-Type Compressor Stall Inception, Detection, and Control
,”
Annu. Rev. Fluid. Mech.
,
42
(
1
), pp.
275
300
.
18.
Deveaux
,
B.
,
Fournis
,
C.
,
Brion
,
V.
,
Marty
,
J.
, and
Dazin
,
A.
,
2020
, “
Experimental Analysis and Modeling of the Losses in the Tip Leakage Flow of an Isolated, Non-Rotating Blade Setup
,”
Exp. Fluids
,
61
(
5
), pp.
1
23
.
19.
Cumpsty
,
N. A.
,
1989
,
Compressor Aerodynamics
,
Longman Scientific & Technical
,
Harlow, UK
.
20.
Doukelis
,
A.
,
Mathioudakis
,
K.
, and
Papailiou
,
K.
,
1998
, “
The Effect of Tip Clearance Gap Size and Wall Rotation on the Performance of a High-Speed Annular Compressor Cascade
,”
Proceedings of the ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition, Volume 1: Turbomachinery
,
Stockholm, Sweden
,
June 2–5
,
p. V001T01A011
.
21.
Kang
,
S.
, and
Hirsch
,
C. H.
,
1993
, “
Experimental Study on the Three-Dimensional Flow Within a Compressor Cascade With Tip Clearance: Part II—The Tip Leakage Vortex
,”
ASME J. Turbomach.
,
115
(
3
), pp.
444
450
.
22.
Inoue
,
M.
,
Kuroumaru
,
M.
, and
Fukuhara
,
M.
,
1986
, “
Behavior of Tip Leakage Flow Behind an Axial Compressor Rotor
,”
ASME J. Eng. Gas Turbines Power.
,
108
(
1
), pp.
7
14
.
23.
Katz
,
J.
, and
Plotkin
,
A.
,
2001
,
Low-Speed Aerodynamics
,
Cambridge University Press
,
Cambridge, UK
.
24.
Lakshminarayana
,
B.
, and
Horlock
,
J.
,
1963
, Tip-Clearance Flow and Losses for an Isolated Compressor Blade. Technical Report, Aeronautical Research Council Reports and Memoranda, London.
25.
Prandtl
,
L.
,
1919
, Tragflügeltheorie. Technical Report, Göttingen Universität, Göttingen, Germany.
26.
Montsarrat
,
C.
,
Deveaux
,
B.
,
Boudet
,
J.
,
Marty
,
J.
, and
Lippinois
,
E.
,
2020
, “
Vortex Lattice Method for the Calculation of the Tip-Leakage Flow: Evaluation on a Single Blade
,”
Proceedings of the ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. Volume 2A: Turbomachinery
,
Virtual, Online
.
Sept. 21–25
, ASME, p. V02AT32A034.
27.
Van Geffen
,
J.
, and
van Heijst
,
G. F.
,
1998
, “
Viscous Evolution of 2D Dipolar Vortices
,”
Fluid Dyn. Res.
,
22
(
4
), pp.
191
213
.
28.
Lamb
,
H.
,
1932
,
Hydrodynamics
,
Cambridge University Press
,
Cambridge, UK
.
29.
Delbende
,
I.
, and
Rossi
,
M.
,
2009
, “
The Dynamics of a Viscous Vortex Dipole
,”
Phys. Fluids
,
21
(
7
), p.
073605
.
30.
Squire
,
H. B.
,
1954
,
The Growth of a Vortex in Turbulent Flow
, Vol.
16
,
ARC
,
London, UK
.
31.
Owen
,
P. R.
,
1970
, “
The Decay of a Turbulent Trailing Vortex
,”
Aeronaut. Q.
,
21
(
1
), pp.
69
78
.
32.
Chorin
,
A. J.
,
1977
, Vortex Sheet Approximation of Boundary Layers. Technical Report, Department of Mathematics and Lawrence Berkeley Laboratory, University of California, Berkeley, CA.
33.
Porthouse
,
D. T. C.
, and
Lewis
,
R. I.
,
1981
, “
Simulation of Viscous Diffusion for Extension of the Surface Vorticity Method to Boundary Layer and Separated Flows
,”
ASME J. Mech. Eng. Sci.
,
23
(
3
), pp.
157
167
.
34.
Lewis
,
R. I.
,
1991
,
Vortex Element Methods for Fluid Dynamic Analysis of Engineering Systems
, 1st ed.,
Cambridge University Press
,
Cambridge, UK
.
35.
Deveaux
,
B.
,
2020
, “
Analyse et Contrôle De L’écoulement De Jeu D’une Aube Fixe Isolée
,” Ph.D. thesis,
HESAM Université, Ecole Nationale Supérieure d’Arts et Métiers
,
Paris, France
.
36.
Chen
,
X.
,
Koppe
,
B.
,
Lange
,
M.
,
Chu
,
W.
, and
Mailach
,
R.
,
2022
, “
Comparison of Turbulence Modeling for a Compressor Rotor at Different Tip Clearances
,”
AIAA J.
,
60
(
2
), pp.
1186
1198
.
37.
Brion
,
V.
,
2009
, “
Stabilité Des Paires De Tourbillons Contra-rotatifs: Application Au Tourbillon De Jeu Dans Les Turbomachines
,” Ph.D. thesis,
Ecole Polytechnique X
,
Palaiseau, France
.
38.
Boudet
,
J.
,
Cahuzac
,
A.
,
Kausche
,
P.
, and
Jacob
,
M. C.
,
2015
, “
Zonal Large-Eddy Simulation of a Fan Tip-Clearance Flow, With Evidence of Vortex Wandering
,”
ASME J. Turbomach.
,
137
(
6
), p.
061001
.
You do not currently have access to this content.