Rotor-Stator Interaction in Turbomachines

Doctoral Thesis

“UNSTEADY ROTOR-STATOR
INTERACTION IN AN AXIAL
TURBOMACHINE”

D. Jesús Manuel Fernández Oro

Dtor: Prof. Carlos Santolaria Morros
23/11/2011

Table of Contents

“Unsteady Rotor-Stator Interaction in an Axial Turbomachine”.
Rotor- Turbomachine”
Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo.
Gijó April, 2/64

Table of Contents

1.- Introduction

2.- Axial Turbomachine

3.- Experimental Work

Facilities Results

4.- Numerical Work

Methodology Results

5.- Deterministic
Analysis

6.- Conclussions &
Future Work

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1.- Introduction
UNSTEADY This unsteady pressure field is
TURBOMACHINERY a consequence of the blades
FLOW motion of the rotor.

 
Dh0 P     Why Unsteady
     T v   f v    q Flow Analysis?
Dt t

1.- Even, an inviscid, adiabatic flow (reversible) is exchanging enthalpy
(work) due to the existence of an unsteady pressure field.

2.- Mechanical vibrations and unsteady forces also appear due to the
time variations of the pressure field.

3.- Aerodynamically generated noise is associated to the pressure
fluctuations inside the turbomachine.

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1.- Introduction
ROTOR-STATOR INTERACTION TURBOMACHINERY
Turbomachinery flows are highly UNSTEADY
unsteady because of the relative MECHANISMS
motion of rotor and stator stages. In
general, unsteadiness may be viewed
as a combination of two processes:
TIME PERIODIC Chaotic, aperiodic
Chaotic,
the INVISCID POTENTIAL EFFECT phenomena
PHENOMENA
and the PERIODIC PASSING OF
WAKES generated by the upstream
blade rows. The former is due to the Turbulence

relative motion of the rotors with Related to Speed Non related to
respect to the stators, and this effect
stators Rotation Speed Rotation
Transitional
becomes stronger when the gap Operation –
between rotor and stator is small. Vortex Speed Range
shedding Variations
The latter arises from the interaction
Stable Unstable
of the blade boundary layers with the
Operation Operation
vortices shed from the blunt trailing
edge of upstream blade rows, and Rotating
from the variation of the angle of ROTOR-STATOR
ROTOR- Stall
INTERACTION
attack at the leading edge due to the
wake velocity deficit. All these
unsteady features and the Potential Origin
interaction between them make the
simulation of unsteady Boundary Layer Which Unsteady
turbomachinery flows a highly
challenging task. (C.HIRSCH) Shock Waves Flow Analysis?

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1.- Introduction
ROTOR-STATOR
INTERACTION
• Wake Decay (Mixing Loss)
PERIODIC PASSING • Wake Transport (Chopping effects, Redistribution of Moment,
OF WAKES Hot Spots)
• Wake Recovery (Wake Stretching)
INVISCID
POTENTIAL EFFECT

Vortex shedding

Rotor 1

Stator 2

Stator wakes Rotor 2

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1.- Introduction
ROTOR-STATOR
INTERACTION

PERIODIC PASSING
OF WAKES
• Axial gap variations. Pitch effect.
• Circunferential variations in total pressure due to the blades
INVISCID
POTENTIAL EFFECT downstream response.
• Time circunferential variations and response to an uniform inlet
conditions.

  
 
t t  
“A steady flow pattern in a relative frame of
reference with a velocity gradient in the
tangential direction generates an unsteady
absolute flow pattern”. (Lyman, 1993)
The static pressure field upstream and downstream of a blade row
is varying circumferentially (and radially) due to the blade load.
load
This causes a flow defect, which is felt as unsteady pressure waves
by the relative moving blade rows. (Jöcker, 2002)
(J cker,

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1.- Introduction How Unsteady Flow?

Mathematical Models For
TURBOMACHINERY Turbomachinery Flows
FLOW SCALES

Blade-passing
frequencies

Spectral Gap
Averaging Technique
Segregation

Ensemble Average
Energy

Turbulence Time Average
scales
Passage Average
Frequency
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1.- Introduction
DETERMINISTIC FLOW INSIDE A
1. Ensemble-average TURBOMACHINE (Adamzcyk, 1986)

2
M
1
 f  r , , z ,   m  1 ; t1  t  T  t1
e
f  lim  t
M  M
m 1 
2. Time-average
1
H G  r , , z , t dt
1 T
0 H G  r , , z, t   f  r , , z, t  dt
T
 
t
f  e

T T 0

3. Passage-to-passage average
1 2
  gl  r , , z d
L

1 N 1
 2 n   2 n  2
l 1

 G  r ,  N , z   f t  r ,  N , z  l j
0
f ap

N     G  r , , z    l 1 gl  r , , z 
n0 L

• Aperiodic Term: Indexing contribution of different blade row stages.
stages.
URANS • DETERMINISTIC TERM: Rotor-Stator Interaction at one stage.
Rotor- stage.
Equations • Reynolds Stresses: Stochastic unresolved flow-field.
flow- field.

PANS Equations + ˆˆ

Closure requirements Rij   ui u j   ui u j   uiuj
 ˆˆ

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1.- Introduction

OBJECTIVES OVERVIEW

1.- Analysis of the unsteady scenario inside an axial turbomachine

2.- Both numerical and experimental characterization of the flow
patterns

3.- Segregation of instantaneous turbulent phenomena through a
time average for every rotor phase

4.- Identification of dynamic unsteadiness sources, either generated
by rotor blades or generated by stator vanes

5.- Analysis of these dynamics phenomena (axial gap influence, mass
flow rate variations) associated to blade passing frequency (BPF)

6.- Deterministic analysis of the flow: wake transport, wake
convection and wake recovery

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FAN characteristics: STATOR characteristics:
• Tip diameter: 820 mm • 13 Inlet Guide Vanes (IGV’s)
1-STAGE • Hub diameter: 380 mm • British Circular Profile C1
AXIAL • Rotation Speed: 2400 rpm
BLOWER • Design Flow Rate: 18 m3/s ROTOR characteristics:
• Design Pressure: 1200 Pa • 9 Blades (127 mm – chord)
• Stator-Rotor Configuration • NACA 65 Profile

Rear View

Front View

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STATOR Geometrical ROTOR Geometrical
Parameters Parameters

• 13 Inlet Guide Vanes • 9 Blades (127 mm – chord)
• British Circular Profile C1 • NACA 65 Profile

D (mm)  380  490  600  710  820 D(mm)  380  490  600  710  820
β1 0º 0º 0º 0º 0º β3 59,61º 62,01º 64,7º 67,18º 69,36º
β2 31,17º 24,84º 20,73º 17,81º 15,68º β4 47,73º 54,82º 60,07º 64,06º 67,16º
 1,71 1,37 1,14 0,98 0,86  1,35 1 0,79 0,65 0,55
b/l 3% 3% 3% 3% 3% b/l 12 % 10,49 % 9,43 % 8,63 % 8%
i - 0,47º - 0,82º - 0,93º - 0,93º - 0,88º i 4,08º 2,45º 1,28º 0,52º 0,03º
 18,12º 14,93º 12,97º 11,66º 10,78º  10,96º 7,17º 5º 3,71º 2,9º
 37,18º 31,51º 27,81º 25,2º 23,21º  13,76º 9,46º 7,43º 6,38º 5,75º
º 18,12º 14,93º 12,97º 11,66º 10,78º º 48,64º 54,84º 59,7º 63,47º 66,46º
 5,54º 5,85º 6,15º 6,45º 6,75º  5,97º 4,71º 4,08º 3,78º 3,57º
β 31,17º 24,84º 20,73º 17,81º 15,68º β 11,88º 7,19º 4,63º 3,12º 2,2º

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2.- Axial Turbomachine Test Facility

Regulation Cone Venturi Nozzle Hub

BS 848 (1980) – Motor
“Methods of Testing
Performance”. Fans Inlet
for General Purposes.
British Standard
Institution.

Stabilization Duct

L = 20 D

Stator Rotor

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3.- Experimental Work Methodology

MEASUREMENT TYPES

1.-Pressure Five Hole Probe 2.- Hot Wire Anemometry 3.- Piezoelectric transducer

• Steady measurements • Unsteady measurements • Unteady measurements
• Average velocity maps and • Instantaneous velocity maps • Instantaneous Pressure signals
pressure distributions • High Frequency Response: up to • High Frequency Acquiring: up to
• No BPF Response (0.36 KHz) 30 KHz 100 KHz

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1.- PRESSURE FIVE
HOLE PROBE

Measurement Set-Up
Set-

Measurement Chain Calibration Set-Up
Set-

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2.- HOT WIRE
ANEMOMETRY

Calibration Set-Up
Set-

Probe repairing
Measurement Set-Up
Set- equipment

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3.- TRANSDUCER
PRESSURE

Measurement Points

Measurement
Equipment

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• Upstream and downstream rotor measurements.
• Circunferential sectors used as “Windows”.
MEASUREMENT • Tangential direction: Stator pitch = 360º/13  28º.
LOCATIONS • Spanwise: From hub to tip.
• Spatial discretization: 15x15 = 225 points/window.
• Temporal discretization: 36 KHz (100 instants/passage)

Circunferential sector

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MEASUREMENT AXIAL BLOWER PERFORMANCE CURVE
STRATEGIES 2500 60

50
2000

1.- Working Point Variations

Total Efficiency (%)
40

Pressure (Pa)
1500

30

N) Nominal Flow Rate (Qn): 1000
20

16.5 m3/s 500
10

P) -15% Nominal Flow Rate 0 0

(0.85Qn): 13.5 m3/s 0 2 4 6 8 10
Flow Rate (m3/s)
12 14 16 18

Static Pressure, Ps Dinamic Pressure, Pd Total Pressure, Pt Numerical Points Efficiency

S) -30% Nominal Flow Rate
(0.7Qn): 11.5 m3/s
Axial Gap
2.-Axial Gap Modification

1.25G) Upper Axial Gap: 100 mm

G) Lower Axial Gap: 80 mm

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3.- Experimental Work Results

EXPERIMENTAL
RESULTS

PASSAGE- PHASE-AVERAGED
AVERAGED FLOW FLOW

• Averaged Results • Instantaneous Results
• Mean DHW & FHP • DHW & Transducer

STEADY UNSTEADY
Characteristics Characteristics

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3.- Experimental Results FHP

PASSAGE-AVERAGED FLOW

ADIM. AXIAL VELOCITY
• Between the rows (D), at
nominal flow rate, there is a
rate,
perfect homogenetation of
the flow, just broken by
flow,
stator wakes. Both axial
wakes.
gaps.
gaps.
• Rotor downstream (R), the
stator wakes are clearly
present, more diffused and
present,
advected, but perfectly
advected,
visible.
• Boundary layer zones: For
zones:
(D), wide boundary at tip.
tip.
Instead, for (R), the hub
Instead,
boundary layer seems to be
thicker.
thicker.
• FIRST RESULTS !!

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3.- Experimental Results DHW

STATOR Downstream ROTOR Downstream

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ADIM. TANGENTIAL VELOCITY

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PHASE-AVERAGED FLOW

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PHASE-AVERAGED FLOW

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PHASE-AVERAGED FLOW

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PHASE-AVERAGED FLOW

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3.- Experimental Results PT

PHASE-AVERAGED FLOW

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4.- Numerical Work Methodology

NUMERICAL
METHODOLOGY

TWO- THREE-
DIMENSIONAL (2D) DIMENSIONAL (3D)

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TWO-DIMENSIONAL DOMAIN (2D) URANS Sliding Mesh Technique

• Spatial Discretization: up to 350,000 cells. 12,000 cells/passage. Hybrid
mesh. O-Grid around the blades. Grid accuracy analysis.
• Temporal Discretization: 5.34*10-5 s. 468 time steps/rotor rev. (13x9x4).
• Numerical Scheme: SIMPLE algorithm for pressure-velocity coupling, upwind
discretizations and second order implicit scheme for the time dependent term.
• Turbulence modeling: LES-(k-ε)RSM comparison.

Nº de celdas por canal Nº de celdas por canal
0 2500 5000 7500 10000 12500 0 2500 5000 7500 10000 12500
-600 500 18.4 1250
-700 450
18.2 1200
400

Fluctuación Pres (Pa)
-800
350 18.0
-900
Stat Pres (Pa)

Caudal (m3/s)
1150
Pres_med (ajuste) 300

AP (Pa)
-1000 17.8
Pres_med 250 1100
-1100 Pres_desv (ajuste) 17.6
200
-1200 Pres_desv Q (ajuste) 1050
150
17.4 Q
-1300 100 AP (ajuste) 1000
-1400 50 17.2 AP
-1500 0 17.0 950
0 50000 100000 150000 200000 250000 300000 0 50000 100000 150000 200000 250000 300000
Núm ero de celdas
Núm ero de celdas

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THREE-DIMENSIONAL DOMAIN (3D) URANS Sliding Mesh Technique

• Spatial Discretization: up to 1,800,000 cells. 3,000 cells/passage 3D. Hybrid
mesh. O-Grid around the blades. [100x35x25].
• Temporal Discretization: 1.068*10-4 s. 234 time steps/rotor rev. (13x9x2).
• Numerical Scheme: SIMPLE algorithm for pressure-velocity coupling, upwind
discretizations and second order implicit scheme for the time dependent term.
• Turbulence modeling: LES-(k-ε)RSM comparison.

RSM LES Exp

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4.- Numerical Work Results

NUMERICAL
RESULTS

PASSAGE- PHASE-AVERAGED
AVERAGED FLOW FLOW

• Two-dimensional • Two-dimensional
Averaged Results Instantaneous Results
• Three-dimensional • Three-dimensional
Averaged Results Instantaneous Results

STEADY UNSTEADY
Characteristics Characteristics

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4.- Numerical Results 3D


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ADIM. TANGENTIAL VELOCITY

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AZIMUT ANGLE

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PHASE-AVERAGED FLOW

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PHASE-AVERAGED FLOW

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PHASE-AVERAGED FLOW

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PHASE-AVERAGED FLOW

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PHASE-AVERAGED FLOW

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PHASE-AVERAGED FLOW

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PHASE-AVERAGED FLOW

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UNSTEADY FORCES

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OUTLET PLANE PERTURBATIONS INLET PLANE
PROPAGATION

Tyler and Sofrin Rule

Axial Velocity at
Inlet/Outlet planes

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PERTURBATIONS PROPAGATION

(FIXED) (MOVING)

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5.- Deterministic Analysis

TURBO NAVIER-STOKES GENERAL
MACHINERY PURPOSE

PASSAGE-TO-PASSAGE REYNOLDS
AVERAGE AVERAGE

PANS EQUATIONS RANS EQUATIONS
-Passage-to-passage Average -Reynolds Average

CLOSURE
Navier-Stokes- Navier-Stokes-

ˆˆ


Rij   ui u j   ui u j   uiuj
ˆ
ˆ  ij   uiuj

SOLUTION

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• Aperiodic Term: Indexing contribution of different blade row
Term:
ˆˆ
 stages.
stages.
Rij   ui u j   ui u j   uiuj
 ˆˆ
 • DETERMINISTIC TERM: Rotor-Stator Interaction at one stage.
Rotor- stage.
• Reynolds Stresses: Stochastic unresolved flow-field.
Stresses: flow- field.

N
1
1.- Ensemble Average (Phase) ui (r ,  , z , t ) 
e

N
 u ( r ,  , z , )
i 1
i

2.- Passage-to-passage Average

Fixed Reference Frame Moving Reference Frame

TR NR TS NS
1 1 1 1
u u
t(S ) t (R)
(r , , z )   ui (r ,  , z, t )  dt  (r , , z,  ) (r , , z )   ui (r ,  , z , t )  dt  (r ,  , z, nS )
e e e R e e e
ui i n ui i
TR 0
NR n 1 TS 0
NS n 1

TR TS
1  u e (r , , z , t )  u e t ( S ) (r , , z )    u e (r , , z , t )  u e t ( S ) (r , , z )   dt 1  u e (r , , z, t )  u e t ( R ) (r , , z )    u e (r , , z , t )  u e t ( R ) (r , , z )   dt
  i   j    i   j 
Det ( S ) Det ( R )
R R
       
ij i j ij i j
TR 0
TS 0
NR

 ui e (r , , z,nR )  ui e (r , , z )   ui e (r , , z,nR )  ui e (r , , z ) 
NS

 u (r ,  , z )   ui e (r ,  , z, nS )  ui e (r , , z ) 
1 t(S ) t(S ) 1 t (R) t (R)
  e
(r ,  , z, nS )  ui e
NR 
n 1 
 
  
 NS 

n 1
i  
  


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5.- Deterministic Analysis – Exp.

DETERMINISTIC STRESS TENSOR Fixed Frame Tax-ax

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DETERMINISTIC STRESS TENSOR Fixed Frame Tcirc-circ

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DETERMINISTIC STRESS TENSOR Fixed Frame Tax-circ

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5.- Deterministic Analysis – Num.

DETERMINISTIC STRESS TENSOR Fixed Frame Tax-ax

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DETERMINISTIC STRESS TENSOR Fixed Frame Tcirc-circ

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DETERMINISTIC STRESS TENSOR Fixed Frame Tax-circ

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DETERMINISTIC STRESS TENSOR Blade-to-blade 2D

Tax-ax 1.25G - midspan Tax-ax 1.25G - tip

1 3
K Det   Tii
2 i 1

70
60 1.25G
G
50

Kdet (m2/s2)
Tax-circ 1.25G - hub Tax-circ 1.25G - tip 40
30
20
10
0
Hub Midspan Tip

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WAKE RECOVERY Theory

L L 1  2  0
1  2  u0   u1  v1   u0   u1  v1 
1 2 2
t 1 2 2
t

2
x1
2
x2 No Recovery
Kin1 Kex 2
 K  1  2  0
1  2  Kin1  Kex 2  Kin1 1  ex 2   Kin1  R
 Kin1  Recovery

1  (D)

2  ( R)

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5.- Deterministic Analysis Numerical

WAKE RECOVERY

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6.- Conclusions & Future Work

CONCLUSIONS

1.- Both NUMERICAL and EXPERIMENTAL studies have been realized in order to
CHARACTERIZE the UNSTEADY ROTOR-STATOR INTERACTION in an AXIAL FLOW
BLOWER.
• Intensive DHW measurements have been achieved for the experimental
methodology.
• Instantaneous numerical velocity maps were obtained through a URANS
simulation in the FLUENT code.

2.- Both ROTOR and STATOR frames of reference have been considered for a more
comprehensive understanding of the generation and transport of the unsteady flow
features.

3.- An IDENTIFICATION METHODOLOGY based on the deterministic stresses model
has been employed, so UNSTEADY SOURCES related to BLADE PASSING
FREQUENCIES have been determinated. Either interaction location, or unsteadiness
intensity have been properly segregated and estimated.

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CONCLUSIONS

4.- Characteristic POTENTIAL EFFECTS (INVISCID mechanisms) and WAKE
EFFECTS (BOUNDARY LAYER mechanisms) were observed:
• ROTOR BLOCKAGE (Potential).
• WAKE-BLADE Interaction (Radial migration of stator wakes).
• WAKE-RECOVERY Stretching (Stator wakes passing through rotor passages).
• WAKE-TIP Interaction (Maximum unsteady values at tip locations).
• WAKE-WAKE Interaction (Residual stator wakes affecting rotor wakes).

5.- GAP AXIAL MODIFICATIONS and OFF-DESIGN CONDITIONS have been included
in the study to determine the influence of these parameters. General conclusions
point out that:
• Both parameters modify WAKE-ROTOR unsteady patterns.
• WAKE-WAKE features are less affected by gap reduction and badly related to
partial load perfomance.

6.- PROPAGATION mechanisms along DUCTED FAN have been also reviewed in the
numerical modelling. The relationship between INLET and OULET perturbations and
VANE and BLADE numbers was established through TURBOFAN NOISE ANALYSIS.

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CONCLUSIONS

7.- The construction of the DETERMINISTIC STRESS TENSOR in both fixed and
moving reference frames has concluded this work. About this issue, it can be said
that:
• Deterministic unsteady features are more pronounced at the stator.
• Blade-to-blade tensor has revealed that stator wake core is unaffected by
circumferential pressure gradients generated by the rotor.
• Between the rows, similar values to Reynolds stresses are encountered for
Deterministic Stresses (former studies).
• Deterministic unsteadiness sources have been indentified, so all correlations
can be used as input data for a steady RANS simulation.

8.- WAKE RECOVERY process has been outlined, with the goal of obtaining an
estimation on the residual deterministic kinetic energy associated to stator wakes
at downstream rotor locations.

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FUTURE WORK

1.- ANALYSIS OF THE ROTOR-STATOR CONFIGURATION, as well as the former
stator-rotor stage.

2.- NUMERICAL SOLUTION ENHACEMENT through RADIAL GAP modelling. Also,
improvement of 3D meshes quality (mainly, high dense zones at blade passages), in
order to improve LES characteristics (y+ restrictions criterion)

3.- DEEPER knowledge on Deterministic Stresses Transport and Diffusion. Analysis of
other physical topics related to DST, like radial and circumferential redistribution of
the momentum, also reported in the literature.

4.- INTRODUCTION OF CLOCKING EFFECTS, through consideration of larger
machines with more than just one single stage.

5.-A few HOLYDAYS

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Doctoral Thesis

“UNSTEADY ROTOR-STATOR
INTERACTION IN AN AXIAL
TURBOMACHINE”

D. Jesús Manuel Fernández Oro

Prof. Carlos Santolaria Morros
23/11/2011

Rotor-Stator Interaction in Turbomachines

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