2D flow visualization
The stereoscopic velocity fields, merged in a 3D volume of data, are visualized as different measurement planes perpendicular to the blade axis in Fig. 4. The 3D pressure as derived from integration of Eq. 2 has been projected back onto the original measurement planes, in order to be compared with the velocity information. The experimental 3D relative velocity and pressure contours are presented in Fig. 5 for different locations perpendicular to the blade axis, ranging from 90 to 102% of the blade radius. Due to the effect of the laser shadow, a narrow region upstream the blade is not measured. However, given the regularity of the flow in this small region, a quadratic interpolator closes the contours in the load analysis and in the data visualization (example in IR region in Fig. 5), primarily where the flow is not perturbed from its free-stream value. The measurement planes identify different profile sections along the blade shape, reflected in the evolution of the flow field along the blade span. The iso-contours of relative velocity and pressure in Fig. 4 show a net decrease in the blade angle of attack with the increase in the z position, reflected in the decrease in the profile suction in the same direction from r/R = 92 to 102%. The maximum velocity variations are contained within 1.2 times the relative free-stream of 223 m/s (at r/R = 92%), while the minimum variations are measured close to the tip of the blade (r/R = 100%), where both the relative velocity and pressure ratios are contained within 5% of their free-stream values. As can be already seen from the present qualitative analysis, the blade has been designed to have a suction profile that extinguishes at the tip location, the only region where a negligible pressure difference across the blade profile is found. In design conditions, at a revolution frequency of 330 Hz (with the wind-tunnel free-stream of 42.3 m/s), the flow angle of attack for the nonsymmetrical profile tip at r/R = 100% is close to 1 degree. Moreover, the relatively small chord thickness of about 1 mm contributes to the small extent of the pressure difference across the profile at this location. As will be discussed in the next section, the decreasing lifting distribution with increasing z is still beneficial to the blade thrust generation, as it determines a relatively weaker trailing vortex, in particular reducing the pressure drag and eventually the blade torque.
Surface pressure distribution
The evolution of the 3D flow field around the propeller blade determines the force distribution on the model, as explained in Sect. 4.2. In particular, the surface pressure distribution represents the main contribution to the blade loading. A quantitative study of the surface pressure coefficient is carried out by the extraction of the integrated 3D pressure along different airfoil profiles, defined as intersection of the measurement planes with the blade geometry (Ragni et al. 2009). Numerical data computed from the propeller simulation as explained in Sect. 2.3 have been used as a comparison to the experimental data. In Fig. 6, the experimental surface pressure coefficient distribution has been compared to the simulated data for 4 different locations between r/R = 92% and r/R = 100%. Due to the shadow region in some of the planes, the comparison has been restricted to the suction side of the propeller blade, region where the highest flow accelerations, therefore pressure variations, occur.
The pressure coefficient profiles, coherently with those presented in the previous sub-section, show a suction decrease toward the tip. Heavy separation and local sonic regions have not been encountered on the blade surface, due to the propeller operational regime close to optimum. From Fig. 6, it appears that the PIV profiles follow the numerical ones up to the highest flow accelerations, primarily identified on the A-B profiles (location r/R = 92–95%). The largest discrepancies with the numerical data occur primarily on pressure recover zone of the blade profiles. In these specific regions, the inexact representation of the experimentally tested blade by the reproduced mesh determines small variations in the blade curvature, affecting the slope of the pressure coefficient curves. Typical pressure coefficient differences of the order of ΔC
= 0.02 are appreciated in these zones, which are maintained at the blade trailing edge. At the blade-tip, the values of the pressure coefficient differences are relatively small compared to the value itself, and comparable to the measurement uncertainty of the order of 0.005–0.01. From a more careful investigation, it has been noted that the numerical data show a slightly more diffused vorticity content in the wake (see Sect. 5.3 as well), with a relatively thicker wake, determining a slower C
recover at the location r/R = 96–97%. For the present model, investigation on the numerical data has shown that changing the turbulence model from k-ε to Spalart-Allmaras causes pressure coefficient variations of ΔC
< 0.01 in the trailing edge. On the other side, the number of elements to represent the blade surface has been found to have a stronger impact on the pressure coefficient variations, especially close to the profiles trailing edge, where the small differences on the C
curvature are enhanced by the approximate CAD representation of the real blade curvature.
3D flow visualization
The stereoscopic velocity measurements acquired from several phase-locked planes are merged in a 3D volume and presented as 3D visualization of the flow in Fig. 7. The resulting investigated region of the propeller blade-tip extends over 60 × 40 × 12 mm3 (7 x-y planes with 2 mm spacing).
In Fig. 7, left one of the propeller blades is imaged together with the experimental 3D relative velocity field, with the relative inflow coming from the left as explained in Fig. 3. The propeller blade is mounted with a blade pitch angle α
(3/4R) = 15º in the propeller hub, with respect to the z-x plane, perpendicular to the free-stream wind-tunnel velocity directed along -y. In the prescribed conditions, with the wind-tunnel free-stream velocity of 42.3 m/s (see scheme in Fig. 4) and at 19,800 rpm, the aerodynamic angle of attack as computed with the tangential velocity ranges from α(r/R = 92%) 1.5º to 1.1º at the tip. The contour plot and iso-surfaces in Fig. 7 show the typical features of a 3D wing moving in the flow. In particular, it can be seen how the high relative velocity on the suction side seen in Fig. 7 left corresponds to the suction peak in the pressure in Fig. 7 right, while close to the leading and trailing edge of the blade, the regions of reduction in relative velocity correspond to the pressure recovery observed in the visualization in Fig. 7 right. A qualitative analysis shows how the difference in size between the pressure recovery at the trailing edge gives a visual representation of the pressure blade drag, while the relatively lower C
regions starting approximately from x = 20 mm, localizes the trailing vortex development, discussed in more details in the last part of this section. The experimental 3D surface pressure distribution is compared to the numerical one in Fig. 8. In this representation, the iso-surfaces of constant C
are super-imposed on the pressure coefficient contour at the volume boundary surface for both numerical and experimental data. The PIV contours (Fig. 8 left) show comparable magnitude to the numerical ones; in particular, they provide information on the extension of the maximum suction region, quantified to be about 20% of the measured blade surface and localized at about 30% of the r/R = 92% chord.
As already seen from both experimental and numerical data, the 3D suction distribution is reducing to 0 as the z location reaches the blade radius, where the pressure jump across the blade is almost negligible. This low-pressure difference contributes to weaken the vortex formation. In this respect, the flow visualization has been extended to the blade wake, in particular, focusing on the relatively low-pressure region formation from about x = 20 mm (Fig. 7 right) localizing the tip vortex. The vortex visualization is carried out by use of the 3D C
for both PIV and CFD data. Apart from a fair qualitative agreement in the flow field structure, a difference between the two results is observed as the pressure field is concerned, with a maximum experimental C
of −0.04 against the numerical −0.03, the first one corresponding to about 1,300 Pa pressure difference with respect to the free-stream pressure. However, the minimum pressure values in the vortex core have been found comparable to the ones computed from a simple analysis obtained by fitting a Lamb-Oseen laminar vortex model (Saffman et al. 1992) at the locations d
= 15 mm to 25 mm, assuming at this stage a negligible helicoidal curvature of the vortex. The discrepancy between the numerical and the experimental data is attributed to the relatively limited grid resolution in the computation. Indicating the distance along the x axis from the trailing edge at r/R = 92% as d
(orientation shown in Fig. 9), it is estimated that the unstructured mesh ensured an average amount of 4 grid-points per mm2 in the z-y planes up to d
= 15 mm, decreasing to 2 grid-points per mm2 at d
= 30 mm. Notwithstanding the remarkable size of the grids, both the numerical and experimental data are on the limit of their resolution to capture the inner vortex core dynamics. The 3D representation in Fig. 9 presents the vortex development at different distances from the blade trailing edge. In the limits of resolution, the iso-contours of out-of-plane vorticity ω
obtained by slicing the volume at different d
locations (Fig. 9) show the moderate curvature of the vortex shape, estimated to be of about 5 mm per 30 mm of elongation. The present shape is in agreement with its helicoidal motion, resulting by the combination of the blade rotational motion with the wind-tunnel free-stream. The imperfect misalignment of the experimental vortex distribution compared to the numerical one is within the uncertainty of the measurement. From the experimental data, the vortex peak-to-peak size is contained in a region of the z-y plane of about 3 × 3 mm2, while the numerical data confine the high vorticity in a region of about 30% higher.
The derived pressure fields together with the 3D velocity data are used to infer the main force components along the blade span by the surface-boundary contour-approach as explained in Sect. 4.2. The integration procedure, based on the one by van Oudheusden et al. 2007, has been adapted in the present investigation to retrieve the sectional forces in propeller aerodynamics. The blade itself is considered as a 3D wing, envelope of different profiles twisted along the radius, as already seen from the planar visualization in Fig. 5. Each profile contributes to the integral blade resultant load R with the local lift and drag function of the location z. In propeller aerodynamics, the numerical and experimental cross-sectional lift, drag and pitching moment of the single blade profiles are projected onto the orthogonal x-y-z frame as horizontal, tangential and torsional components, building up the blade sectional torque force Q′, thrust T′, and blade torsion M′
, in Fig. 9. This procedure for the loads estimation was also applied to the numerical flow simulation. In order to give an estimation on the uncertainty on the values of the sectional forces, the standard deviations on the different values obtained by integration over different contours were calculated and are shown as error bars for both the PIV and CFD data (Ragni et al. 2009).
The experimental cross-sectional thrust in Fig. 10a shows a decrease down to a negligible force to the tip, as already seen in the 2D and in the 3D visualization, again illustrating how the blade profile at r/R = 100% is meant to reduce the blade-tip vortex strength. The experimental results for the blade torque force, Fig. 10b, show a comparable decay toward the tip. The numerical prediction, on the other hand, due to the considerable but limited size of the mesh, displays a more diffused vorticity compared to the experimental data, which confirms the low finite drag coefficient values observed near the tip. Further analysis on those values, showed that the numerical grid resolution (mainly close to the tip where the minimum chord is identified) together with the experimental inaccuracy on the pressure values, contributes to the disagreement between the experimental and the numerical results at this particular scale, whereas the viscous and Reynolds stresses play a relatively lower role. The experimental and numerical results for the sectional torsion moment calculated at the mean-quarter-chord in Fig. 10c were found to be negligible within the measurement uncertainty.