The unsteady blade row interaction (UBRI) is inherent and usually has a large effect on performance in multistage axial compressors. The effect could be considered by using the average-passage equation system (APES) in steady-state environment by introducing the deterministic correlations (DC). How to model the DC is the key in APES method. The primary purpose of this study is to develop a DC model for compressor routine design. The APES technique is investigated by using a 3D viscous unsteady and time-averaging Computational fluid dynamics (CFD) flow solver developed in our previous studies. Based on DC characteristics and its effects on time-averaged flow, an exponential decay DC model is proposed and implemented into the developed time-averaging solver. Steady, unsteady, and time-averaging simulations are conducted on the investigation of the UBRI and the DC model in the first transonic stage of NASA 67 and the first two stages of a multistage compressor. The DC distributions and mean flow fields from the DC model are compared with the unsteady simulations. The comparison indicates that the proposed model can take into account the major part of UBRI and provide significant improvements for predicting compressor characteristics and spanwise distributions of flow properties in axial compressors, compared with the steady mixing plane method.

References

References
1.
Scillitoe
,
A. D.
,
Tucker
,
P. G.
, and
Adami
,
P.
,
2017
, “
Numerical Investigation of Three-Dimensional Separation in an Axial Flow Compressor: The Influence of Freestream Turbulence Intensity and Endwall Boundary Layer State
,”
ASME J. Turbomach.
,
139
(
2
), p.
021011
.
2.
Liu
,
Y. W.
,
Yan
,
H.
,
Lu
,
L. P.
, and
Li
,
Q. S.
,
2017
, “
Investigation of Vortical Structures and Turbulence Characteristics in Corner Separation in a Linear Compressor Cascade Using DDES
,”
ASME J. Fluids Eng.
,
139
(
2
), p.
021107
.
3.
Yan
,
H.
,
Liu
,
Y. W.
,
Li
,
Q. S.
, and
Lu
,
L. P.
,
2018
, “
Turbulence Characteristics in Corner Separation in a Highly Loaded Linear Compressor Cascade
,”
Aerosp. Sci. Technol.
,
75
, pp.
139
154
.
4.
Spalart
,
P. R.
,
2012
, “
Reflections on RANS Modelling
,”
Progress in Hybrid RANS-LES Modelling
,
Springer-Verlag
,
Berlin
, pp.
7
24
.
5.
Denton
,
J. D.
,
2010
, “
Some Limitations of Turbomachinery CFD
,”
ASME
Paper No. GT2010-22540.
6.
Liu
,
Y. W.
,
Yu
,
X. J.
, and
Liu
,
B. J.
,
2008
, “
Turbulence Models Assessment for Large-Scale Tip Vortices in an Axial Compressor Rotor
,”
J. Propul. Power
,
24
(
1
), pp.
15
25
.
7.
Liu
,
Y. W.
,
Yan
,
H.
,
Liu
,
Y. J.
,
Lu
,
L. P.
, and
Li
,
Q. S.
,
2016
, “
Numerical Study of Corner Separation in a Linear Compressor Cascade Using Various Turbulence Models
,”
Chin. J. Aeronaut.
,
29
(
3
), pp.
639
652
.
8.
Adamczyk
,
J. J.
,
2000
, “
Aerodynamic Analysis of Multistage Turbomachinery Flows in Support of Aerodynamic Design
,”
ASME J. Turbomach.
,
122
(
2
), pp.
189
217
.
9.
Liu
,
Y. W.
,
Lu
,
L. P.
,
Fang
,
L.
, and
Gao
,
F.
,
2011
, “
Modification of Spalart-Allmaras Model With Consideration of Turbulence Energy Backscatter Using Velocity Helicity
,”
Phys. Lett. A
,
375
(
24
), pp.
2377
2381
.
10.
Lee
,
K. B.
,
Wilson
,
M.
, and
Vahdati
,
M.
,
2017
, “
Validation of a Numerical Model for Predicting Stalled Flows in a Low-Speed Fan—Part I: Modification of Spalart–Allmaras Turbulence Model
,”
ASME J. Turbomach.
,
140
(
5
), p.
051008
.
11.
Kim
,
S.
,
Pullan
,
G.
,
Hall
,
C. A.
,
Grewe
,
R. P.
,
Wilson
,
M. J.
, and
Gunn
,
E.
,
2018
, “
Stall Inception in Low Pressure Ratio Fans
,”
ASME
Paper No. GT2018-75153.
12.
Tang
,
Y. M.
,
Liu
,
Y. W.
, and
Lu
,
L. P.
,
2018
, “
Solidity Effect on Corner Separation and Its Control in a High-Speed Low Aspect Ratio Compressor Cascade
,”
Int. J. Mech. Sci.
,
142–143
, pp.
304
321
.
13.
Erdos
,
J. I.
,
Alzner
,
E.
, and
McNally
,
W.
,
1977
, “
Numerical Solution of Periodic Transonic Flow Through a Fan Stage
,”
AIAA J.
,
15
(
11
), pp.
1559
1568
.
14.
Rai
,
M. M.
,
1987
, “
Navier-Stokes Simulations of Rotor/Stator Interaction Using Patched and Overlaid Grids
,”
J. Propul. Power
,
3
(
5
), pp.
387
396
.
15.
Giles
,
M. B.
,
1988
, “
Calculation of Unsteady Wake/Rotor Interaction
,”
J. Propul. Power
,
4
(
4
), pp.
356
362
.
16.
Hall
,
K. C.
,
Thomas
,
J. P.
, and
Clark
,
W. S.
,
2002
, “
Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique
,”
AIAA J.
,
40
(
5
), pp.
879
886
.
17.
Adamczyk
,
J. J.
,
1985
, “
Model Equations for Simulating Flows in Multistage Turbomachinery
,”
ASME
Paper No. 85-GT-26.
18.
Adamczyk
,
J. J.
,
Mulac
,
R. A.
, and
Celestina
,
M. L.
,
1986
, “
A Model for Closing the Inviscid Form of the Average Passage Equation System
,”
ASME J. Turbomach.
,
108
(
2
), pp.
180
186
.
19.
Rhie
,
C. M.
,
Gleixner
,
A. J.
,
Spear
,
D. A.
,
Fischberg
,
C. J.
, and
Zacharias
,
R. M.
,
1998
, “
Development and Application of a Multistage Navier-Stokes Solver—Part I: Multistage Modeling Using Body forces and Deterministic Stresses
,”
ASME J. Turbomach.
,
120
(
2
), pp.
205
214
.
20.
Li
,
Y. G.
, and
Tourlidakis
,
A.
,
2001
, “
Influence of Deterministic Stresses on Flow Prediction of a Low-Speed Axial Flow Compressor Rear Stage
,”
IMechA
,
215
(
5
), pp.
571
583
.
21.
Sondak
,
D. L.
,
Dorney,D
,
J.
, and
Davis
,
R. L.
,
1996
, “
Modeling Turbomachinery Unsteadiness With Lumped Deterministic Stresses
,”
AIAA
Paper No. 96-2570.
22.
He
,
L.
,
1996
, “
Modeling Issues for Computation of Unsteady Turbomachinery Flows
,”
Unsteady Flows in Turbomachines
(Von Karman Inst. Lecture Series 1996-05),
Von Karman Institute for Fluid Dynamics
,
Rhode Saint Genese, Belgium
.
23.
Hall
,
E. J.
,
1997
, “
Aerodynamic Modeling of Multistage Compressor Flow Fields. Part II: Modeling Deterministic Stresses
,”
ASME
Paper No. 97-GT-345.
24.
Van de Wall
,
A. G.
,
1999
, “
A Transport Model for the Deterministic Stresses Associated With Turbomachinery Blade Row Interactions
,” Ph.D. thesis, Case Western Reserve University.
25.
Charbonnier
,
D.
, and
Leboeuf
,
F.
,
2004
, “
Steady Flow Simulation of Rotor-Stator Interactions With a New Unsteady Flow Model
,”
AIAA
Paper No. 2004-3754.
26.
Stollenwerkl
,
S.
, and
Kugeler
,
E.
,
2013
, “
Deterministic Stress Modeling for Multistage Compressor Flowfields
,”
ASME
Paper No. GT2013-94860.
27.
Liu
,
Y. W.
,
Liu
,
B. J.
, and
Lu
,
L. P.
,
2010
, “
Investigation of Unsteady Impeller-Diffuser Interaction in a Transonic Centrifugal Compressor Stage
,”
ASME
Paper No. GT2010-22737.
28.
Liu
,
Y. W.
,
Liu
,
B. J.
, and
Lu
,
L. P.
,
2012
, “
Study of Modeling Unsteady Blade Row Interaction in a Transonic Compressor Stage—Part 1: Code Development and Deterministic Correlation Analysis
,”
Acta Mech. Sin.
,
28
(
2
), pp.
281
290
.
29.
Liu
,
Y. W.
,
Liu
,
B. J.
, and
Lu
,
L. P.
,
2012
, “
Study of Modeling Unsteady Blade Row Interaction in a Transonic Compressor Stage—Part 2: Influence of Deterministic Correlations on Time-Averaged Flow Prediction
,”
Acta Mech. Sin.
,
28
(
2
), pp.
291
299
.
30.
Liu
,
B. J.
,
Zhang
,
B.
, and
Liu
,
Y. W.
,
2014
, “
Numerical Investigations of Impeller–Diffuser Interactions in a Transonic Centrifugal Compressor Stage Using Nonlinear Harmonic Method
,”
Proc. Inst. Mech. Eng., Part A
,
228
(
8
), pp.
862
877
.
31.
Liu
,
B. J.
,
Zhang
,
B.
, and
Liu
,
Y. W.
,
2015
, “
Investigation of Model Development for Deterministic Correlations Associated With Impeller-Diffuser Interactions in Centrifugal Compressors
,”
Sci. China Technol. Sci.
,
58
(
3
), pp.
499
509
.
32.
Denton
,
J. D.
,
1992
, “
The Calculation of 3D Viscous Flow Through Multistage Turbomachines
,”
ASME J. Turbomach.
,
114
(
1
), pp.
18
26
.
33.
Denton
,
J. D.
,
1986
, “
The Use of Body Force to Simulate Viscous Effects in 3D Flow Calculations
,”
ASME
Paper No. 86-GT-144.
34.
Liu
,
Y. W.
,
2009
, “
Investigations of Steady State Numerical Techniques for Predicting Flows Through Multistage Compressors
,” Ph. D. thesis, Beihang University, Beijing, China.
35.
Hathaway
,
M. D.
,
Suder
,
K. L.
,
Okiishi
,
T. H.
,
Strazisar
,
A. J.
, and
Adamczyk
,
J. J.
,
1987
, “
Measurements of the Unsteady Flow Field Within the Stator Row of a Transonic Axial-Flow Fan-Results and Discussion
,” NASA, Washington, DC, Report No. 86-C-31.
36.
Uzol
,
O.
,
Chow
,
Y.-C.
,
Katz
,
J.
, and
Meneveau
,
C.
,
2003
, “
Average Passage Flow Field and Deterministic Stresses in the Tip and Hub Regions of a Multi-Stage Turbomachine
,”
ASME J. Turbomach.
,
125
(
4
), pp.
714
725
.
37.
Poensgen
,
B.
, and
Gallus
,
H. E.
,
1990
, “
Three-Dimensional Wake Decay Inside of a Compressor Cascade and Its Influence on the Downstream Unsteady Flow Field—Part 1: Wake Decay Characteristics in the Flow Passage
,”
ASME
Paper No. 90-GT-21.
38.
Urasek
,
C.
,
Gorrell
,
W. T.
, and
Cunnan
,
W. S.
,
1979
, “
Performance of Two-Stage Fan Having Low-Aspect-Ratio First-Stage Rotor Blading
,” NASA, Washington, DC, Report No. TP-1493.
39.
Chen
,
T.
,
Vasanthakumar
,
P.
, and
He
,
L.
,
2001
, “
Analysis of Unsteady Blade Row Interaction Using Nonlinear Harmonic Approach
,”
J. Propul. Power
,
17
(
3
), pp.
651
658
.
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