1 Introduction
2 Experimental procedures
2.1 Wind-tunnel, model, and operating regimes
Propeller geometry | Operating regimes | ||
---|---|---|---|
Number of blades N
| 4 | Blade revolution frequency | 330–350 Hz |
Propeller radius R
| 118 mm | Rotational velocity at r/R = 0.75 | 189.1 m/s |
Assembling tolerance | 7.5 mm | Advance free-stream velocity | 47.8 m/s |
Blade maximum chord c | 19.4 mm | Relative Mach at r/R = 0.75 | 0.63 |
Blade chord at r/R = 0.75 | 17.9 mm | Chord Reynolds number | 310,000 |
Pitch angle at r/R = 0.75 | 15 deg | Advance ratio J
| 0.58–0.62 |
Solidity ratio cN/(πR) | 0.21 | Real pitch/Ideal pitch | 0.92 |
2.2 PIV measurement apparatus
Illumination | |
---|---|
Laser | Quantel CFR 200 Nd:Yag |
Pulse energy | 200 mJ |
Light sheet thickness | 2 mm |
Imaging | |
---|---|
Camera | 2 Imager Pro LX |
Sensor format | 4,872 × 3,248 px |
Pixel pitch | 7.40 μm |
Lenses focal length | 105 mm |
M | 0.148 |
Imaging resolution | 19–23 px/mm |
FOV | ~18 × 12 cm2
|
Spatial resolution | From 0.8 to 0.2 mm |
Acquisition | |
---|---|
Software | LaVision Davis 7.2 |
Frequency | 1.5–2.5 Hz |
Pulse separation | 15 μs |
Number of recordings | 150–200 |
Window size | From 16 × 16 to 4 × 4 px |
2.3 Computational fluid dynamics model
3 Data reduction
3.1 Frames of reference
3.2 Pressure computation
3.3 Force determination by momentum integral
4 Uncertainty analysis
4.1 PIV measurement uncertainties
Uncertainties | Error estimator | Typical value | Relative velocity uncertainty (%) | |
---|---|---|---|---|
Random components | Fluctuations on the average (cross-corr. and stat. convergence) |
\( \left[ {{\frac{{\sigma_{meas} = f\left( {\varepsilon ,\sigma_{u} } \right)}}{\sqrt N }}} \right] \)
|
ε = 0.1 pixel
σ
u
= 4% | 0.35 |
Systematic components | Spatial resolution |
\( \left[ {{{ws} \mathord{\left/ {\vphantom {{ws} \lambda }} \right. \kern-\nulldelimiterspace} \lambda }} \right] \)
|
λ ~ 2 mm (wake) | ≤15 |
Peak locking |
\( \left[ {{\frac{{d_{\tau } }}{{\Updelta_{pix} M\Updelta t}}}} \right] \)
| <0.03 pixels | <0.2 | |
Aero-optical aberration |
\( \left[ {\left( {\vec{V} \cdot \nabla } \right)\vec{\xi }} \right] \)
| ≤2 | ||
Particle slip |
\( \left[ {\tau \vec{V}\left( {\nabla \vec{V}} \right)} \right] \)
|
τ = 1 μs | ≤1.5 |
4.2 Pressure and integral loads uncertainty
a) Stationary frame formulation, μ ± σ | ||||
---|---|---|---|---|
f (Hz) | PIV | CFD | ||
330 | 350 | 330 | 350 | |
|C
y
|
| 0.260 ± 0.004 | 0.354 ± 0.019 | 0.250 ± 0.001 | 0.316 ± 0.002 |
|C
x
|
| 0.080 ± 0.001 | 0.076 ± 0.006 | 0.096 ± 0.002 | 0.091 ± 0.003 |
|C
l
|
| 0.275 ± 0.005 | 0.362 ± 0.017 | 0.263 ± 0.001 | 0.323 ± 0.002 |
|C
d
|
| 0.013 ± 0.001 | 0.008 ± 0.011 | 0.024 ± 0.002 | 0.014 ± 0.003 |
b) PIV Stationary frame formulation, μ ± σ | ||||
---|---|---|---|---|
f (Hz) | 330 | |||
α (deg) | −10 | −5 | 5 | 10 |
|C
y
|
| 0.269 ± 0.010 | 0.262 ± 0.010 | 0.263 ± 0.004 | 0.277 ± 0.006 |
|C
x
|
| 0.100 ± 0.003 | 0.094 ± 0.006 | 0.104 ± 0.005 | 0.105 ± 0.005 |
|C
l
|
| 0.287 ± 0.010 | 0.277 ± 0.011 | 0.283 ± 0.002 | 0.294 ± 0.007 |
|C
d
|
| 0.029 ± 0.001 | 0.025 ± 0.003 | 0.032 ± 0.003 | 0.029 ± 0.003 |
PIV Moving-frame formulation, μ ± σ | ||||
---|---|---|---|---|
f (Hz) | 330 | |||
α (deg) | −10 | −5 | 5 | 10 |
|C
l
|
| 0.243 ± 0.009 | 0.270 ± 0.012 | 0.330 ± 0.009 | 0.340 ± 0.015 |