Transcript PowerPoint 프레젠테이션

ASME-JSME-KSME Joint Fluids Engineering Conference 2011
Numerical Study on Unsteadiness of Tip Clearance Flow and
Performance Prediction of Axial Compressor
Yoojun Hwang ∙ Shin-Hyoung Kang
July 26, 2011
Mechanical and Aerospace Engineering,
Seoul National University, Seoul, Korea
Contents
 Introduction
 Calculation Models and Methods
 Results
– Unsteady Feature of Tip Leakage Flow
– Mechanism of Unsteady Tip Leakage Flow
– Effect of Unsteady Tip Leakage Flow on Performance Prediction
 Conclusions
1
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Introduction (1/2)
 Previous Studies
– Unsteady Tip Clearance Flow in Axial Compressors near Stall
 Periodically fluctuating tip leakage vortex was investigated by Mailach et al.
(2001)1, Marz et al. (2002)2, Kielb et al. (2003)3, Bae et al. (2004)4, Hah et al.
(2008)5, etc.
 The origin or the role of the flow has been studied by Du et al. (2010)6,
Thomassin et al. (2009)7, Drolet et al. (2009)8, etc.
 The unsteady flow was referred to as rotating instability or self-induced
unsteadiness.
Mailach, R., Lehmann, I., and Vogeler, K., 2001, “Rotating Instabilities in an Axial Compressor Originating From the Fluctuating Blade Tip Vortex,” ASME Journal of Turbomachinery, Vol. 123,
pp. 453-463.
2 März, J., Hah, C., and Neise, W., 2002, “An Experimental and Numerical Investigating Into the Mechanisms of Rotating Instability,” ASME Journal of Turbomachinery, Vol. 124, pp. 367-375.
3 Kielb, R. E., Barter, J. W., Thomas, J. P., and Hall, K. C., 2003, “Blade Excitation by Aerodynamics Instatbilites — A Compressor Blade Study,” ASME Turbo Expo 2003, GT2003-38634.
4 Bae, J., Breuer, K. S., and Tan, C. S., 2004, “Periodic Unsteadiness of Compressor Tip Clearance Vortex,” ASME Turbo Expo 2004, GT2004-53015.
5 Hah, C., Bergner, J., and Schiffer, H.-P., 2008, “Tip Clearance Vortex Oscillation, Vortex Shedding and Rotating Instability in an Axial Transonic Compressor Rotor,” ASME Turbo Expo 2008,
GT2008-50105.
6 Du, J., Lin, F., Zhang, H., and Chen, J., 2010, “Numerical Investigation on the Self-Induced Unsteadiness in Tip Leakage Flow for a Transonic Fan Rotor,” ASME Journal of Turbomachinery, Vol.
132, pp. 021017.
7 Thomassin, J., Vo, H. D., and Mureithi, N. W., 2009, “Blade Tip Clearance Flow and Compressor Nonsynchronous Vibrations: The Jet Core Feedback Theory as the Coupling Mechanism,” ASME
Journal of Turbomachinery, Vol. 132, pp. 011013.
8 Drolet, M., Thomassin, J., Vo, H. D., and Mureithi, N. W., 2009, “Numerical Investigation into Non-Synchronous Vibrations of Axial Flow Compressors by the Resonant Tip Clearance Flow,”
ASME Turbo Expo 2009, GT2009-59074
2
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
1
Introduction (2/2)
 Motivation
– In the previous studies, the unsteady tip leakage flow has been found to be
inherent.
– The relation between the unsteady feature and the flow condition has not been
obvious.
 Objective
– Investigate characteristics of the unsteady tip leakage flow and mechanisms of
the unsteadiness varying with the flow coefficient.
– Examine changes in performance prediction due to the unsteadiness.
3
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Calculation Models and Methods (1/3)
 Compressor Model
–
–
–
–
–
Low speed research axial compressor (LSRC)
4 stages
Number of blades: IGV(53), Rotor(54), Stator(74)
Hub-to-tip ratio: 0.85
Tip clearance size to blade height: 2.8%
 Experimentally Measured Data
– Performance measured by Wisler (1981)1
 Numerically Calculated Data
– Code: ANSYS-CFX 11.0
– Standard k-ε model with the wall function
– Structured H-mesh with as a coarse grid as 40,000 cells/blade passage
1
Wisler, D. C., 1981, “Core Compressor Exit Stage Study Volume IV—Data and Performance Report
for the Best Stage Configuration,” NASA CR-165357.
4
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Calculation Models and Methods (2/3)
 Pressure Rise Performance

– Averaging 4 stages
p s
1
2
U t2
, 
cx
Ut
 Pressure Rise at Design Point
0.7
• Similar trend around the design point
• The calculation underestimates the
0.6
pressure rise by 15%.
0.5
• Blade row interactions have beneficial
effects on rotor performance at least 3%
0.4

up to 10%: Valkov and Tan (1999)1, Sirakov
Design point
0.3
and Tan (2003)2, Graf et al. (1999)3
• More than 5% remains to be explained.
0.2
0.1
0
0.3
 At Low Flow Rates
Measured - Wisler (1981)
Calculated with mixing-plane
0.35
0.4
• The difference in pressure rise is larger.
0.5
0.45

 Unsteady calculation
Valkov, T. V. and Tan, C. S., 1999, “Effect of Upstream Rotor Vortical Disturbances on the Time-Averaged Performance of Axial Compressor Stators: Part 1—Framework of
Technical Approach and Wake-Stator Blade Interactions,” ASME Journal of Turbomachinery, Vol. 121, pp. 377-386.
2 Sirakov, B. T. and Tan, C. S., 2003, “Effect of Unsteady Stator Wake — Rotor Double-Leakage Tip Clearance Flow Interaction on Time-Average Compressor Performance,”
ASME Journal of Turbomachinery, 125, pp. 465-474.
3 Graf, M. B., Greitzer, E. M., Marble, F. E., and Sharma, O. P., 1999, “Effects of Stator Pressure Field on Upstream Rotor Performance,” ASME Turbo Expo 1999, 99-GT-99.
1
5
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Calculation Models and Methods (3/3)
 Unsteady Calculation Method
– Modified part-annulus of rotor
– Exclude the effect of stator
Numerical monitor
(near casing; rotating)
 Modification of the Number of Rotor Blade
• 54  56
 IGV + Additional Domain
• Single blade + Mixing-Plane
• Provide circumferentially uniform flow to the inlet of
the rotor row
• Exclude inlet wakes from IGV
 Boundary Conditions
• Inlet: Atmospheric conditions (pt, Tt) and flow angle
• Exit: Mass flow rate  Adjust operating conditions
IGV
Rotor
Additional domain
Configuration of 1/8 annulus of rotor
 Numerical Monitor
• Between rotor and stator in the rotating frame
• Record static pressure signal
 Calculation Process
• Reduce mass flow rate from the design point
• Until the pressure signal is stably periodic
6
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Unsteady Feature of Tip Leakage Flow (1/7)
 Results of Single Blade Passage Calculations
– Contours of axial velocity at the exit of the rotor
– Frequency spectrum of pressure signal from rotating monitoring point
 Axial Velocity Contours
• Low axial velocity means flow blockage.
1 blade pitch
rotation
• The flow in the tip region oscillates in
time.
• The period of the oscillation does not
correspond to the blade passing time.
1
Rotating monitoring point
Amplitude
0.8
 Frequency Analysis
350Hz
0.6
• The frequency of 350 Hz corresponds to
the unsteady tip leakage flow.
0.4
Harmonics
0.2
0
0
1000
2000
Frequency [Hz]
3000
7
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Unsteady Feature of Tip Leakage Flow (2/7)
 Frequencies
inlet
sta.1
sta.2
exit
– Rotating and fixed monitoring points
 The frequency is different depending on
whether the monitoring point rotates.
R
(1)
(1)
Rotating monitoring point
Fixed monitoring point
1
1
Rotating monitoring point
Fixed monitoring point
0.8
0.8
 TLF: Tip Leakage Frequency
350Hz: TLF
 BPF: Blade Passing Frequency
0.6
Amplitude
Amplitude
IGV
0.4
0.6
0.4
Harmonics
0.2
0
394Hz: TLF
0.2
0
1000
2000
0
3000
Frequency [Hz]
747Hz: BPF
0
1000
2000
3000
Frequency [Hz]
8
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Unsteady Feature of Tip Leakage Flow (3/7)
 Frequencies
 Vrel: Relative Phase Velocity
– Rotating and fixed monitoring points
 Vabs: Absolute Phase Velocity
Flow direction
Tangential
velocity: Ut
Rotor
 The tip leakage flow forms a
circumferential wave pattern.
Vrel
λ
Monitoring point rotating
with rotor blades
Vabs
λ
Fixed monitoring point
Ut
Vrel
 Each monitoring point observes
different frequencies.
 The frequency difference is
explained by Doppler Shift
Effect: Kielb et al. (2003)1
 The unsteadiness is a
circumferential feature.
Vabs
 Need to examine the
circumferential length scale
1
Kielb, R. E., Barter, J. W., Thomas, J. P., and Hall, K. C., 2003, “Blade Excitation by Aerodynamics Instabilities — A Compressor Blade Study,” ASME Turbo
Expo 2003, GT2003-38634.
9
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Unsteady Feature of Tip Leakage Flow (4/7)
 Effect of Calculation Domain Size on Flow Structure Near Casing
– Single blade passage
– 1/8 annulus passage (7 blades)
– 1/4 annulus passage (14 blades)
1
Rotating monitoring point
Amplitude
0.8
278Hz: TLF
0.6
1/8 Annulus
1/4 Annulus
0.4
0.2
1/8 Annulus
0
Single Blade
0
1000
2000
3000
Frequency [Hz]
 Longer Calculation Domains
• The length scale is 1.4 times
longer than the blade pitch.
• The corresponding frequency
changed to 278 Hz.
1/4 Annulus
 1/8 annulus is selected
10
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Unsteady Feature of Tip Leakage Flow (5/7)
 Frequency Spectrums of the Signal from Rotating Monitoring Points
– Decreasing flow rate
1
1
 = 0.407
278Hz: TLF
0.6
0.4
248 Hz: TLF
0.6
 A lower frequency is
observed at low flow rate
points, which does not vary
with the flow rate.
0.4
0.2
0.2
0
 The tip leakage frequency
decreases as the flow
coefficient decreases.
 = 0.387
0.8
Amplitude
Amplitude
0.8
0
1000
2000
0
3000
Frequency [Hz]
10
0
500
1000
1500
2000
Frequency [Hz]
3
 = 0.358
 = 0.366
8
6
215 Hz: TLF
4
109 Hz: low frequency
2
Amplitude
Amplitude
109 Hz: low frequency
204 Hz: TLF
1
2
0
0
500
1000
Frequency [Hz]
1500
2000
0
0
500
1000
1500
2000
Frequency [Hz]
11
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Unsteady Feature of Tip Leakage Flow (6/7)
 Flow Structure at Low Flow Rate
τ: 1 pitch time
– Axial velocity contour at the exit of the rotor
– Rotating frame
 = 0.366
Induced rotating disturbance causes
more blockage in the tip region.
 The incoming flow near the casing is
turned toward the hub, and the axial
t0
velocity of the main flow increases.
 The length scale of the disturbance is
corresponding to 1/8 of the
t0 + 1 τ
circumference.
 The low frequency does not vary with
the flow rate since the disturbance is
t0 + 2 τ
induced by the rotating distribution of
pressure.
 Associated with rotating stall
t0 + 3 τ
inception.
12
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Unsteady Feature of Tip Leakage Flow (7/7)
 Effect of Flow Coefficient
 w θ decreases as the flow coefficient
– At the exit of the rotor row
– Time-averaged; pitch-averaged
decreases in the tip region.
 Linear relation between Vrel and wθ
 The frequency is changed by
the flow coefficient.
0.6
1
Relative phase velocity
of the tip leakage flow
pattern
0.9
0.8
0.5
0.7
V rel / U t
Span
0.6
0.5
0.4
0.4
0.3
 = 0.407
0.2
 = 0.366
 = 0.387
0.3
 = 0.358
Averaged relative tangential
velocity at 90% span
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.2
0.2
1
w / U t
0.3
0.4
0.5
0.6
w / U t
13
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Mechanism of Unsteady Tip Leakage Flow (1/3)
 Entropy Contours
– At the design mass flow rate
– At the 95% span
τ: 1 pitch time
L.E.
 = 0.407
T.E.
t0
 High entropy region: tip leakage
flow
t0 + 1 τ
The leakage flow periodically
impinges on the pressure side of
the adjacent blade at 30 – 70%
t0 + 2 τ
chord.
 Flow pattern from the steadystate calculation impinges at
t0 + 3 τ
40% chord.
Steady
14
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Mechanism of Unsteady Tip Leakage Flow (2/3)
 Entropy Contours
– At the low flow rate
– At the 95% span
τ: 1 pitch time
L.E.
 = 0.358
T.E.
t0
 The tip leakage flow periodically
spills over the leading edge.
t0 + 1 τ
The spilled flow divides into two
flows.
t0 + 2 τ
 From steady-state calculation,
the interface forms at upstream
of the leading edge.
t0 + 3 τ
Steady
15
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Mechanism of Unsteady Tip Leakage Flow (3/3)
 Pressure Contours
 = 0.358
– At the low flow rate
– At the 95% span
high p
low p
low p
high p
 Tip leakage flow from the
L.E.
previous time step induces
pressure distribution.
T.E.
Large pressure difference at
Weak tip
leakage
the leading edge generates
Strong tip
leakage
strong tip leakage flow.
L.E.
T.E.
 The unsteady leakage flow
interacts with the blade
loading.
16
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Performance Prediction (1/3)
 Pressure Rise Performance
– Modified 1/8 annulus of the rotor
0.4
unsteady (1/8 annulus)
unsteady (single blade)
steady-state (mixing-plane)

0.3
Design point
(=0.407)
Pressure rise
coefficient (ψ)
Unsteady
(1/8 annulus)
0.2690
Unsteady
(single blade)
0.2652
- 1.4 %
Steady-state
(mixing-plane)
0.2502
- 7.0 %
Remarks
 Calculating the unsteady flow
structure increases the
performance prediction.
0.2
Design point
0.1
 Compensate for the
underestimation from the
0
0.32
steady-state calculation.
0.36
0.4
0.44

17
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Performance Prediction (2/3)
 Unsteady feature induces less
blockage in the tip region.
 Velocity Distributions
– At the exit of the rotor row
– At design mass flow rate  = 0.407
– Pitch averaged; time averaged
 Flow turning by the unsteady
calculation is slightly greater than by
the steady-state calculation.
Less blockage in the tip region
1
1
unsteady (1/8 annulus)
0.9
steady (mixing-plane)
0.8
0.8
0.7
0.7
0.6
0.6
Span
Span
0.9
unsteady (single blade)
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
1
cx / U t
unsteady (1/8 annulus)
unsteady (single blade)
steady (mixing-plane)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
c / U t
Tangential velocity
Axial velocity
18
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Performance Prediction (3/3)
 At the low flow rate, the decrease in
blockage and the increase in flow
turning are greater.
 Velocity Distributions
– At the exit of the rotor row
– At the low flow rate  = 0.358
– Pitch averaged; time averaged
 The difference in the predicted
performance becomes larger.
1
1
0.9
steady (mixing-plane)
0.8
0.8
0.7
0.7
0.6
0.6
Span
Span
0.9
unsteady (1/8 annulus)
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
1
unsteady (1/8 annulus)
steady (mixing-plane)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
c / U t
cx / U t
Axial velocity
Tangential velocity
19
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Conclusions
 The behavior of the tip leakage flow was investigated through numerical
calculations on one-eighth of the annulus of the rotor.
 The unsteady feature of the tip leakage flow varied with the operating points
since the flow velocity in the rotor passage changed.
 Changes in blade loading induced by the tip leakage flow were responsible for
the unsteady feature of the tip leakage flow.
 Calculating the unsteady feature compensated for underestimation of the
performance of the compressor by steady-state calculations.
20
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Thank you for your attention
21
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Appendix
22
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Blade Row Interaction Effects
 Effect of Upstream Stator Wake
– Wake recovery makes 1-3% pressure rise benefit: Valkov and Tan (1999)1
– Reduction of tip clearance fluid double-leakage due to Pressure pulses enhance pressure rise
by 2%: Sirakov and Tan (2003)2
 Effect of Downstream Stator Row
– Potential effect on upstream rotor tip leakage is up to 5% pressure rise benefit: Graf et al.
(1999)3
Wake stretching
No wake
Wake
Tan (2005)
Sirakov and Tan (2003)
Valkov, T. V. and Tan, C. S., 1999, “Effect of Upstream Rotor Vortical Disturbances on the Time-Averaged Performance of Axial Compressor Stators: Part 1—Framework of
Technical Approach and Wake-Stator Blade Interactions,” ASME Journal of Turbomachinery, Vol. 121, pp. 377-386.
2 Sirakov, B. T. and Tan, C. S., 2003, “Effect of Unsteady Stator Wake — Rotor Double-Leakage Tip Clearance Flow Interaction on Time-Average Compressor Performance,”
ASME Journal of Turbomachinery, 125, pp. 465-474.
3 Graf, M. B., Greitzer, E. M., Marble, F. E., and Sharma, O. P., 1999, “Effects of Stator Pressure Field on Upstream Rotor Performance,” ASME Turbo Expo 1999, 99-GT-99.
1
23
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Calculation Models and Methods for Unsteadiness
 Domain modification
– Blade number was changed to calculate part of the annulus: solidity was changed 1.20  1.24
– Little change in pressure rise due to the solidity change
– The solidity change had little effect on the pattern of the tip leakage flow.
•
Inoue, M. and Kuroumaru, M. (1989)1
 Monitoring point location
– The frequency of the unsteady tip leakage flow remains constant regardless of the location
where the signal is measured along the blade chord.
• Du, J. et al. (2010)2
Inoue, M. and Kuroumaru, M., 1989, “Structure of Tip Clearance Flow in an Isolated Axial Compressor Rotor,” ASME Journal of Turbomachinery, Vol. 111,
pp. 250-256.
2 Du, J. Lin, F., Zhang, H., and Chen, J., 2010, “Numerical Investigation on the Self-Induced Unsteadiness in Tip Leakage Flow for a Transonic Fan Rotor,”
ASME Journal of Turbomachinery, Vol. 132, 021017.
1
24
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Direction of Unsteady Feature
 Feature of Fluctuation
inlet
sta.1
sta.2
exit
– Circumferential wave pattern (NOT axial)
Vrel: Relative Phase Velocity
Vabs: Absolute Phase Velocity
Flow direction
Tangential
velocity
Rotor
IGV
R
(1)
(1)
monitoring point (rotating)
monitoring point (fixed)
Ut = 41.89 m/s
Vrel
Tip leakage flow pattern (relative)
λ
frel = 350Hz @ monitoring point
Rotating monitoring point
λ = 0.0561 m (wave length)
 Vrel = λfrel = 19.63 m/s
Vabs
Ut
Tip leakage flow pattern (fixed)
λ
Fixed monitoring point
Vrel
Vabs
λ=0.0561 m (wave length)
Vabs= Ut-Vrel = 22.26 m/s
Doppler Shift
1
Kielb et al. (2003)1
 fabs= Vabs /λ = 397Hz
Kielb, R. E., Barter, J. W., Thomas, J. P., and Hall, K. C., 2003, “Blade Excitation by Aerodynamics Instabilities — A Compressor Blade Study,” ASME Turbo
Expo 2003, GT2003-38634.
25
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Mechanism of Unsteadiness of Tip Leakage Flow
 Cause of the Periodic Feature
– Circumferential velocity in the flow field near the rotor tip determines phase velocity of the tip
leakage flow.
– Mode number of the wave pattern of the tip leakage flow is close to half of the blade number.
– Frequency of the tip leakage flow is decided by the phase velocity and the mode number.
Bae et al. (2004)
Mailach et al. (2001)
Graf (1996)
 Reduced frequency
– Tip leakage flow frequency (f) is
normalized by blade chord (C), flow velocity (U)
 F+ = fC/U
between 0.6 and 0.9
– F+ = 0.5 in this study
26
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Mechanism of Unsteadiness of Tip Leakage Flow
 Self-Induced Unsteadiness
– Du et al. (2010)1
– Unsteady calculation
– 1 Rotor blade passage (NASA Rotor 67; transonic fan)
• Assumption: Same flow patterns in every blade passage
– Operating point studied: 92% of the chocking mass flow rate
 Rotating Instabilities
– Mailach et al. (2001)2
– Experimental measurement
– Flow pattern repeats at every second blade passage.
• Dominating cell number ~ half of the blade number
• Rotating speed ~ 50-60% of the rotor speed
• The result of our study is similar to this.
1
Du, J., Lin, F., Zhang, H., and Chen, J., 2010, “Numerical Investigation on the Self-Induced Unsteadiness in
Tip Leakage Flow for a Transonic Fan Rotor,” ASME Journal of Turbomachinery, Vol. 132, 021017.
2
Mailach, R., Lehmann, I., and Vogeler, K., 2001, “Rotating Instabilities in an Axial Compressor Originating
From the Fluctuating Blade Tip Vortex,” ASME Journal of Turbomachinery, Vol. 123, pp. 453-463.
27
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024
Relation to Rotating Stall
 Phenomena in Our Study
– Low frequency feature was observed at low flow rates, especially less than 90% of the design
mass flow rate.
– Periodic spillage of the flow at the leading edge
– Back flows of the tip leakage flow at the rotor exit plane
– Development of pressure disturbance in the circumferential direction
 Rotating stall inception with tip leakage flow
– Vo et al. (2008)1
– Spike rotating stall inception criteria
• Leading edge spillage
• Tip clearance backflow at trailing edge
– The two criteria and circumferential disturbance were satisfied in the result of our study.
• The rotating speed in our study (about 100% of the rotor speed) is somewhat faster than that of the
rotating stall inception in reference (about 70% of the rotor speed).
• This discrepancy is expected to be corrected by calculating the full annulus of the rotor.
1
Vo, H. D., Tan, C. S., and Greitzer, E. M., 2008, “Criteria for Spike Initiated Rotating Stall,” ASME Journal of Turbomachinery,
Vol. 130, 011023.
28
AJK Joint Fluids Engineering Conference 2011 / AJK2011-22024