Pitchwise distributions of ensemble average velocites
Pitchwise distributions of ensemble average velocites
Pitchwise distributions of ensemble average velocites
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FEM for Turbomachinery Flows<br />
Corsini and Rispoli Inoue and Kuroumaru free vortex rotor (1984)<br />
Navier-Stokes prediction obtained with XENIOS finite<br />
element code (1991) - grid 59 × 21 × 31<br />
tip clearance t = 1.8% lc<br />
PS<br />
Vp/Uc<br />
passage<br />
Trailing<br />
vortex<br />
vortex<br />
Va/Uc<br />
trailing vortex<br />
Vr/Uc<br />
wake<br />
SS<br />
tip clearance t = 1.2% lc<br />
<strong>Pitchwise</strong> <strong>distributions</strong> <strong>of</strong> <strong>ensemble</strong> <strong>average</strong> <strong>velocites</strong><br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
Corsini and Rispoli Inoue and Kuroumaru free vortex rotor (1984)<br />
Navier-Stokes prediction obtained with XENIOS finite<br />
element code (1991) - grid 59 × 21 × 31<br />
tip clearance t = 1.8% lc<br />
Vr/Uc<br />
Va/Uc<br />
Vp/Uc<br />
Leakage vortex<br />
wake<br />
PS SS<br />
tip clearance t = 1.2% lc<br />
<strong>Pitchwise</strong> <strong>distributions</strong> <strong>of</strong> <strong>ensemble</strong> <strong>average</strong> <strong>velocites</strong><br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
Corsini and Rispoli Storer and Cumpsty linear cascade (1991)<br />
Navier-Stokes prediction obtained with XENIOS finite<br />
element code - grid 59 × 21 × 31<br />
tip clearance t = 1.8% lc<br />
te le<br />
0.5<br />
0.3<br />
0.4<br />
Navier-Stokes prediction obtained with Dawes finite volume code<br />
(1987) - grid 61 × 25 × 33<br />
tip clearance t = 4% lc<br />
Blade surface static pressure distribution (Cp) - pressure side<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
Corsini and Rispoli Storer and Cumpsty linear cascade (1991)<br />
te<br />
Navier-Stokes prediction obtained with XENIOS finite<br />
element code - grid 59 × 21 × 31<br />
tip clearance t = 1.8% lc<br />
leakage flow influence<br />
-0.6<br />
le<br />
Navier-Stokes prediction obtained with Dawes finite volume code<br />
(1987) - grid 61 × 25 × 33<br />
tip clearance t = 4% lc<br />
Blade surface static pressure distribution (Cp) - suction side<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
Corsini and Rispoli Storer and Cumpsty linear cascade (1991)<br />
Navier-Stokes prediction obtained with XENIOS finite<br />
element code - grid 59 × 21 × 31<br />
tip clearance t = 1.8% lc<br />
Leakage velocity<br />
Navier-Stokes prediction obtained with Dawes finite volume code<br />
(1987) - grid 61 × 25 × 33<br />
tip clearance t = 2% lc<br />
Chordwise distribution <strong>of</strong> <strong>average</strong>d tip leakage flow velocity<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
Corsini and Rispoli Storer and Cumpsty linear cascade (1991)<br />
Navier-Stokes prediction obtained with XENIOS finite<br />
element code - grid 59 × 21 × 31<br />
tip clearance t = 1.8% lc<br />
0.5<br />
0.4<br />
0.3<br />
0<br />
Navier-Stokes prediction obtained with Dawes finite volume code<br />
(1987) - grid 61 × 25 × 33<br />
tip clearance t = 2% lc<br />
Blade surface static pressure distribution (Cp) - pressure side<br />
prediction measurement<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
CFD ORIENTED AXIAL FAN DESIGN IMPROVEMENT (1)<br />
• CFD INTER-BLADE FLOW PHYSICS PREDICTION<br />
R<br />
blade tip<br />
fraction <strong>of</strong> chord lenght<br />
Velocity field close to the blade suction side<br />
modeled streamtraces<br />
predicted streamtraces<br />
• Blade lift synthesized by use <strong>of</strong> “cone couple” model<br />
R<br />
blade tip<br />
fraction <strong>of</strong> chord lenght<br />
Velocity field close to the blade pressure side<br />
separate optimization <strong>of</strong> blade pressure and suction sides<br />
extend the validity <strong>of</strong> 2D cascade concept<br />
modeled streamtraces<br />
predicted streamtraces<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
CFD ORIENTED AXIAL FAN DESIGN IMPROVEMENT (2)<br />
• on the basis <strong>of</strong> computed pitch-<strong>average</strong>d flow<br />
force factor is evaluated ( l t)<br />
cl<br />
optimum c l * is defined (Howell, 1942) ⇒ optimum solidity values ( l t)<br />
*<br />
c l * ( l ) cl<br />
t ( t)<br />
l *<br />
SS cone 0.893 1.004 1.124<br />
PS cone 0.591 0.859 1.453<br />
• optimized axial fan rotor geometry with FORWARD SWEPT blades<br />
casing<br />
midspan<br />
hub<br />
L<br />
ps<br />
T<br />
ps<br />
*<br />
ps<br />
=<br />
l > L T = l<br />
ss<br />
ss<br />
*<br />
ss<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
• NON FREE VORTEX DESIGN<br />
• CIRCULAR ARC CAMBERED<br />
PLATE<br />
SWEPT AXIAL FAN ROTOR<br />
Unswept bladed<br />
rotor<br />
Swept bladed rotor<br />
blade number 12 12<br />
hub-to-casing diameter ratio 0.676 0.676<br />
tip clearance (percent span) 2 % 2 %<br />
flow coefficient Φ 0.50 0.50<br />
Ideal total head rise<br />
coefficient Ψ<br />
0.70 0.70<br />
hub mid tip hub mid tip<br />
blade solidity l / t 1.53 1.24 1.05 1.79 1.23 1.13<br />
forward sweep angle, deg 0 0 0 30 30 30<br />
stagger angle, deg 47.9 42.2 38.3 56.3 43.1 37.4<br />
camber angle, deg 27.4 23.1 19.9 35.4 25.4 20.3<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
ϕ3a<br />
SWEPT AXIAL FAN ROTOR FLOW SURVEY (1)<br />
ϕ1a<br />
R<br />
ψ3<br />
a) b)<br />
ψth,FSW<br />
<strong>Pitchwise</strong>-<strong>average</strong>d flow data for FSW and USW rotors<br />
(circles: FSW; squares: USW)<br />
ψth,USW<br />
R<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
SWEPT AXIAL FAN ROTOR FLOW SURVEY (2)<br />
R<br />
R<br />
0.25<br />
USW<br />
FSW<br />
0.2<br />
PS<br />
PS<br />
0.3<br />
Uc<br />
0.3<br />
0.6<br />
0.6<br />
C<br />
C<br />
0.2<br />
SS<br />
[deg]<br />
SS<br />
[deg]<br />
ST<br />
ST<br />
W<br />
W<br />
Axial flow coefficient behind the rotor<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
SWEPT AXIAL FAN ROTOR FLOW SURVEY (3)<br />
R<br />
R<br />
USW<br />
FSW<br />
PS<br />
PS<br />
Uc<br />
0.55<br />
0.55<br />
1.25<br />
0.8<br />
C<br />
C<br />
1.2<br />
0.8<br />
Fig. 5: Local ideal total head rise coefficient<br />
behind the rotor<br />
SS<br />
[deg]<br />
SS<br />
[deg]<br />
W<br />
ST<br />
W<br />
ST<br />
Ideal total head rise coefficient<br />
behind the rotor<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
SWEPT AXIAL FAN ROTOR FLOW SURVEY (4)<br />
R<br />
R<br />
USW<br />
FSW<br />
PS<br />
PS<br />
Uc<br />
-0.08<br />
Uc<br />
-0.05<br />
C<br />
C<br />
0.0<br />
radial flow coefficient<br />
behind the rotor<br />
W<br />
SS<br />
ST<br />
W<br />
SS<br />
[deg]<br />
ST<br />
[deg]<br />
0.06<br />
0.08<br />
0.05<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
DF<br />
SWEPT AXIAL FAN ROTOR LOADING<br />
Diffusion factor pr<strong>of</strong>ile along the span<br />
(circles: FSW; squares: USW)<br />
DF( R ) =<br />
1 − w w + Δw / 2σ<br />
w<br />
out<br />
in<br />
p<br />
in<br />
R<br />
Alessandro Corsini, BUTE - 28 November 2000
FEM for Turbomachinery Flows<br />
R<br />
R<br />
SWEPT AXIAL FAN ROTOR LOSS BEHAVIOR<br />
USW<br />
PS<br />
FSW<br />
PS<br />
0.7<br />
Uc<br />
0.1<br />
0.1<br />
0.6<br />
0.6<br />
SS<br />
[deg]<br />
SS<br />
[deg]<br />
Loss coefficient distribution<br />
at 98% blade chord<br />
ω =<br />
0in<br />
Δω<br />
p −<br />
p 0.<br />
5ρV<br />
0out<br />
2<br />
in<br />
Δω(R) = ω FSW − ω USW | R<br />
Loss improvement factor<br />
Alessandro Corsini, BUTE - 28 November 2000<br />
R
FEM for Turbomachinery Flows<br />
SWEPT AXIAL FAN ROTOR FLOW SURVEY (5)<br />
streamlines on blade suction side streamlines on blade pressure side<br />
8% pitch from blade pressure side<br />
Alessandro Corsini, BUTE - 28 November 2000
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