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# Doctoral thesis final

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### Doctoral thesis final

1. 1. Doctoral Thesis “UNSTEADY ROTOR-STATOR INTERACTION IN AN AXIAL TURBOMACHINE” D. Jesús Manuel Fernández Oro Dtor: Prof. Carlos Santolaria Morros23/11/2011
2. 2. 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
3. 3. 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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 3/64
4. 4. 1.- Introduction UNSTEADY This unsteady pressure field isTURBOMACHINERY 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. “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 4/64
6. 6. 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 EFFECTVortex shedding Rotor 1 Stator 2 Stator wakes Rotor 2 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 6/64
8. 8. 1.- Introduction How Unsteady Flow? Mathematical Models For TURBOMACHINERY Turbomachinery Flows FLOW SCALES Blade-passing frequencies Spectral Gap Averaging Technique Segregation Ensemble AverageEnergy Turbulence Time Average scales Passage Average Frequency “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 8/64
9. 9. 1.- Introduction DETERMINISTIC FLOW INSIDE A1. 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 03. 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  “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 9/64
10. 10. 1.- IntroductionOBJECTIVES 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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 10/64 10/64
11. 11. 2.- Axial Turbomachine 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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 11/64 11/64
12. 12. 2.- Axial Turbomachine STATOR Geometrical ROTOR Geometrical Parameters Parameters• 13 Inlet Guide Vanes • 9 Blades (127 mm – chord)• British Circular Profile C1 • NACA 65 ProfileD (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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 12/64 12/64
13. 13. 2.- Axial Turbomachine Test FacilityRegulation 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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 13/64 13/64
14. 14. 3.- Experimental Work Methodology MEASUREMENT TYPES1.-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 signalspressure distributions • High Frequency Response: up to • High Frequency Acquiring: up to• No BPF Response (0.36 KHz) 30 KHz 100 KHz “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 14/64 14/64
15. 15. 3.- Experimental Work Methodology 1.- PRESSURE FIVE HOLE PROBE Measurement Set-Up Set- Measurement Chain Calibration Set-Up Set- “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 15/64 15/64
16. 16. 3.- Experimental Work Methodology 2.- HOT WIRE ANEMOMETRY Calibration Set-Up Set- Probe repairingMeasurement Set-Up Set- equipment “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 16/64 16/64
17. 17. 3.- Experimental Work Methodology 3.- TRANSDUCER PRESSURE Measurement Points Measurement Equipment “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 17/64 17/64
18. 18. 3.- Experimental Work Methodology • 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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 18/64 18/64
19. 19. 3.- Experimental Work MethodologyMEASUREMENT 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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 19/64 19/64
20. 20. 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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 20/64 20/64
21. 21. 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 !! “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 21/64 21/64
22. 22. 3.- Experimental Results DHW STATOR Downstream ROTOR Downstream “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 22/64 22/64
23. 23. 3.- Experimental Results DHW PASSAGE-AVERAGED FLOW ADIM. AXIAL VELOCITY “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 23/64 23/64
24. 24. 3.- Experimental Results DHW PASSAGE-AVERAGED FLOW ADIM. TANGENTIAL VELOCITY “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 24/64 24/64
25. 25. 3.- Experimental Results DHW PASSAGE-AVERAGED FLOW ADIM. AXIAL VELOCITY “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 25/64 25/64
26. 26. 3.- Experimental Results DHW PASSAGE-AVERAGED FLOW ADIM. AXIAL VELOCITY “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 26/64 26/64
27. 27. 3.- Experimental Results DHW PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 27/64 27/64
28. 28. 3.- Experimental Results DHW PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 28/64 28/64
29. 29. 3.- Experimental Results DHW PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 29/64 29/64
30. 30. 3.- Experimental Results DHW PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 30/64 30/64
31. 31. 3.- Experimental Results PT PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 31/64 31/64
32. 32. 4.- Numerical Work Methodology NUMERICAL METHODOLOGY TWO- THREE- DIMENSIONAL (2D) DIMENSIONAL (3D) “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 32/64 32/64
33. 33. 4.- Numerical Work MethodologyTWO-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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 33/64 33/64
34. 34. 4.- Numerical Work MethodologyTHREE-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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 34/64 34/64
35. 35. 4.- Numerical Work Results NUMERICAL RESULTS PASSAGE- PHASE-AVERAGED AVERAGED FLOW FLOW• Two-dimensional • Two-dimensionalAveraged Results Instantaneous Results• Three-dimensional • Three-dimensionalAveraged Results Instantaneous Results STEADY UNSTEADY Characteristics Characteristics “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 35/64 35/64
36. 36. 4.- Numerical Results 3D PASSAGE-AVERAGED FLOW ADIM. AXIAL VELOCITY “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 36/64 36/64
37. 37. 4.- Numerical Results 3D PASSAGE-AVERAGED FLOW ADIM. TANGENTIAL VELOCITY “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 37/64 37/64
38. 38. 4.- Numerical Results 3DPASSAGE-AVERAGED FLOW ADIM. AXIAL VELOCITY “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 38/64 38/64
39. 39. 4.- Numerical Results 3D PASSAGE-AVERAGED FLOW AZIMUT ANGLE “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 39/64 39/64
40. 40. 4.- Numerical Results 3D PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 40/64 40/64
41. 41. 4.- Numerical Results 3D PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 41/64 41/64
42. 42. 4.- Numerical Results 3D PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 42/64 42/64
43. 43. 4.- Numerical Results 3D PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 43/64 43/64
44. 44. 4.- Numerical Results 2D PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 44/64 44/64
45. 45. 4.- Numerical Results 2D PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 45/64 45/64
46. 46. 4.- Numerical Results 2D PHASE-AVERAGED FLOW “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 46/64 46/64
47. 47. 4.- Numerical Results 2D UNSTEADY FORCES “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 47/64 47/64
48. 48. 4.- Numerical Results 3D OUTLET PLANE PERTURBATIONS INLET PLANE PROPAGATION Tyler and Sofrin Rule Axial Velocity at Inlet/Outlet planes “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 48/64 48/64
49. 49. 4.- Numerical Results 3DPERTURBATIONS PROPAGATION (FIXED) (MOVING) “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 49/64 49/64
50. 50. 5.- Deterministic Analysis TURBO NAVIER-STOKES GENERALMACHINERY 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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 50/64 50/64
51. 51. 5.- Deterministic Analysis • 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 eui 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       “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 51/64 51/64
52. 52. 5.- Deterministic Analysis – Exp. DETERMINISTIC STRESS TENSOR Fixed Frame Tax-ax “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 52/64 52/64
53. 53. 5.- Deterministic Analysis – Exp. DETERMINISTIC STRESS TENSOR Fixed Frame Tcirc-circ “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 53/64 53/64
54. 54. 5.- Deterministic Analysis – Exp. DETERMINISTIC STRESS TENSOR Fixed Frame Tax-circ “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 54/64 54/64
55. 55. 5.- Deterministic Analysis – Num. DETERMINISTIC STRESS TENSOR Fixed Frame Tax-ax “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 55/64 55/64
56. 56. 5.- Deterministic Analysis – Num. DETERMINISTIC STRESS TENSOR Fixed Frame Tcirc-circ “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 56/64 56/64
57. 57. 5.- Deterministic Analysis – Num. DETERMINISTIC STRESS TENSOR Fixed Frame Tax-circ “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 57/64 57/64
58. 58. 5.- Deterministic Analysis – Num. DETERMINISTIC STRESS TENSOR Blade-to-blade 2DTax-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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 58/64 58/64
59. 59. 5.- Deterministic Analysis 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) “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 59/64 59/64
60. 60. 5.- Deterministic Analysis Numerical WAKE RECOVERY “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 60/64 60/64
61. 61. 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. “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 61/64 61/64
62. 62. 6.- Conclusions & Future Work 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. “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 62/64 62/64
63. 63. 6.- Conclusions & Future Work 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. “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 63/64 63/64
64. 64. 6.- Conclusions & Future Work 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 “Unsteady Rotor-Stator Interaction in an Axial Turbomachine”. Rotor- Turbomachine” Doctoral Thesis - Gijón. April, 7th, 2005. University of Oviedo. Gijó April, 64/64 64/64
65. 65. Doctoral Thesis “UNSTEADY ROTOR-STATOR INTERACTION IN AN AXIAL TURBOMACHINE” D. Jesús Manuel Fernández Oro Prof. Carlos Santolaria Morros23/11/2011