The following subsections describe the measurements required to implement the laser sensors in the VT SWT, from temperature compensation to position/orientation calibration. The end of the section details measurements the rotation and displacement measurements made with the DU96-W-180 model.
3.1. Sensitivity to Temperature
During the initial use of these lasers in the Stability Wind Tunnel [
12], the wind tunnel operators noted that the distance readings from the laser would change slightly with temperature. The wind tunnel is subject to atmospheric conditions, so the air temperature in the wind tunnel is correlated to the outside air temperature. Additionally, as the wind tunnel is operated for long stretches of time, the air temperature will rise due to convective heating from the wind tunnel motor. Because small changes in distance correspond to significant changes in model angle of attack, the distance output from the lasers needed to be verified for varying temperatures, independent of model deflections and aerodynamic loading.
The results from an in-situ temperature calibration are shown in
Figure 4. Static targets were placed in front of each laser inside of the test section. The laser distances and temperature were recorded every 25 s overnight, while the air temperature dropped from
C to
C. As the temperature dropped through the night, the distance readings from the laser changed. The exact cause of this temperature drift is unknown, but may be caused by thermal expansion of lenses and other mechanical components in the laser sensors. The temperature drift is large enough to cause a significant change in angle of attack. (A 0.8 mm change in Laser 2 would cause a ∼
shift in the calculated angle of attack.)
The temperature drift was accounted for by applying a linear regression to the results shown in
Figure 4. The temperature shift data were offset such that the average shift at
C was zero;
C was chosen as the calibration temperature because the laser position calibration (described in the following subsection) was performed at this temperature. The parameters for the regression fits are shown in
Table 1, while the regression is shown in
Figure 4. The regression lines do not track the temperature drift across the entire temperature range, so there is added uncertainty in the measurement after considering the temperature drift. The maximum difference between the data points shown in
Figure 1 and the regression line is shown in
Table 1; this value is added to the uncertainty based on the resolution of the measurement when considering the total uncertainty in the measured distance for the remaining calculations in this paper.
3.2. Laser Position Calibration
Before the lasers can be used in a wind tunnel experiment, the position (and orientation) of the laser sensors needs to be determined. Once the orientation and position of the lasers is known, the laser readings can be used to track the location of the model within the test section. With the wind tunnel turned off (no air flow), the model was rotated between
and
angle of attack in
increments. At each angle, the angle of attack (as measured by the encoder) and the laser distances are recorded. A simplex optimization routine was then used to calculate the laser positions/orientations (
,
,
, and
, as shown in
Figure 3) that reproduce the encoder angle of attack for all of the measurements, assuming that the model’s rotation point is fixed in space.
Results from this calibration are shown in
Figure 5. The calculated laser positions/orientations (shown in
Table 2) are consistent with the positions/orientations of the lasers in the wind tunnel. The top plot in
Figure 5 shows the measured laser distance for all four lasers as a function of angle of attack, while the remaining four plots show the calibration residuals (the difference between encoder angle of attack and the reconstructed laser angle of attack, using the recorded distance and the calibration constants.)
The error bars represent the maximum uncertainty in the angle of attack. This uncertainty was calculated by first considering the uncertainty in the measured laser distance, which was calculated by combining the uncertainty due to the measurement resolution and the uncertainty due to the temperature correction, shown in the last column of
Table 1. The maximum uncertainty in the angle of attack was then calculated by adding (or subtracting) the cumulative uncertainty in the distance to the measured distance reading, and calculating the associated change in angle of attack. Both the positive and negative uncertainty were calculated individually for each measurement point.
For the model geometry and laser locations used in this work, the relationship between laser distance and angle of attack was nearly linear for all four lasers in this angle of attack range. Laser 1 is the least sensitive to changes in angle of attack, because this laser is closer to the model rotation point than the other three lasers. The angle of attack uncertainty is nearly symmetric about the measured value and only varies weakly with the measured distance, because the relationship between laser distance and angle of attack is nearly linear. The largest uncertainties in the angle of attack results are ±0.042, ±0.027, ±0.020, and ±0.011 degrees for Lasers 1–4, respectively. Over 80% of the residuals are zero within the uncertainty of the angle of attack measurement, with the largest residuals being 0.044, 0.027, 0.020, and 0.011 for Lasers 1–4, respectively.
3.3. Rotation and Deflection Analysis
Once the laser positions/orientations were calculated, the sensors were used to track model angle of attack during a wind-on measurement, as described in
Section 2.2. For this analysis, the center of rotation was assumed to not move during the test, but the model could rotate/twist under aerodynamic load. The difference between the encoder angle of attack and the calculated angle of attack from the lasers is shown in
Figure 6. Lasers 2–4 (which are downstream of the model rotation point) show a difference in angle of attack that becomes more negative as the lift is increased. In contrast, Laser 1 (which is closer to and upstream of the model rotation point) shows the opposite trend. The discrepancy between Laser 1 and Lasers 2–4 is an order of magnitude larger than the uncertainty in the measurement, and indicates that the model is not uniformly rotating, but deforming in a more complex way. The model could be shifting or bending, which would move the model rotation point as a function along the span.
Lasers 1 and 2 were placed at the same spanwise location to address the discrepancy shown in
Figure 6 and separate deflection/bending from rotation.
Figure 7 shows the concept behind this calculation. In this analysis, the model rotation is allowed to move in the wall-normal direction. The distance output from the two lasers (two inputs) is used to solve a system of non-linear equations for two outputs: the rotation and the translation. By convention, a positive translation is movement towards the starboard wall, and a positive rotation is an increase in the angle of attack.
This analysis provides the rotation and deflection at a single spanwise location. Lasers 3 and 4 can then be used to gain information about the model’s position at different spanwise locations. Because there is only one laser at these spanwise locations, the displacement and rotation cannot be determined independently. For this analysis, we assumed that the airfoil model is rotating but not twisting, or that the angle of attack does not vary across the span. (This assumption is based on the shape and construction of the model.) If this assumption is true, than the distances from Lasers 3 and 4 can be used to determine the model deflection at each spanwise location.
This deflection/rotation analysis was applied to the calibration data shown in
Figure 5 to quantify the uncertainty associated with this technique. Because there was no aerodynamic loading during the calibration, the rotation and deflection should be identically zero. The results from this analysis are shown in
Figure 8. The error bars represent the maximum uncertainty in the rotation/deflection, which is calculated independently for each measurement point. For the rotation/deflection, the uncertainty was calculated by finding the worst-case scenario from different combinations of adding/subtracting the cumulative distance uncertainty to the measured distances from Lasers 1 and 2. The deflection uncertainty for Lasers 3 and 4 was calculated in a similar manner, while also incorporating the uncertainty in the rotation calculation. As noted in
Section 3.2, the error bars are nearly symmetrical and only vary weakly with angle of attack, because the relationships between laser distance and angle of attack for zero deflection are nearly linear (
Figure 5).
As expected, the rotation and deflections were zero within the uncertainty of the calculation. The uncertainty in the rotation was degrees, and the uncertainty in the deflection calculated by Lasers 1 and 2 was mm. The uncertainty associated with the deflection measured by Lasers 3 and 4 was mm; the uncertainty for these calculations is larger because of the added uncertainty in calculating the model rotation (which is then used to calculate the deflections measured by Lasers 3 and 4.)
3.4. Model Deflections/Rotations under Aerodynamic Loading
The rotation/deflection analysis described in
Section 3.3 was applied to 13 sets of DU96-W-180 aerodynamic measurements (8 clean and 5 tripped) in the VT SWT, taken over a two-week period. All of these runs were performed at a chord Reynolds number of 3.0 million. The air temperature varied from run to run, between
C and
C; the flow speed was adjusted to maintain a Reynolds number of 3.0 million, leading to flow speeds between 62.7 m/s and 66.7 m/s.
Figure 9 shows the deflection calculated using the distances calculated from Lasers 1 and 2.
Figure 2 shows that there is zero lift force on the model near
angle of attack; however, Lasers 1 and 2 showed a wide range of deflections at this angle, from −0.65 mm to 0.73 mm. This suggests that there might be some small shifts in model position over time. For this plot, the zero lift deflection was subtracted out to show the deflection relative to the zero lift deflection. At this spanwise location (660 mm above the floor), the model deflects up to 1.5 mm in the direction of the applied lift. The deflection is a linear function of the load in the linear region of the lift curve, from
to
. This deflection explains why
Figure 6 shows discrepancies between the laser outputs; the model rotation point is not fixed in space, and multiple lasers need to be used to calculate the model angle of attack.
Figure 10 shows the rotation calculated by Lasers 1 and 2, as a function of the the encoder angle of attack and the applied torque on the model shaft. The model rotation is approximately 0
at the most negative angle of attack, when the shaft torque is near-zero or slightly positive. As the angle of attack is increased, to
, there is a large shift in shaft torque to approximately −250 Nm, and the model undergoes a slight negative rotation. As the angle of attack is increased further, the magnitude of the negative rotation increases, to approximately
at the largest angles of attack. The relationship between the shaft torque and rotation shown in
Figure 10 was not anticipated; the expectation was that more negative shaft torques would create larger negative rotations. The torque/rotation points show the opposite trend, but it should be noted that the uncertainty in the rotation is
.
The deflections calculated from Lasers 3 and 4 provide evidence that the model is bending under load.
Figure 11 and
Figure 12 show the calculated deflections from Lasers 3 and 4, respectively. As with
Figure 9, the deflection at zero lift was subtracted out to show the relative deflection at these spanwise locations. Both Lasers 3 and 4 show deflections of
mm, which is larger than the uncertainty in the calculated deflection (
mm). The model is deflecting in the direction of the applied lift, which is consistent with the deflection calculated using Lasers 1 and 2. Under maximum loading, the model is deflecting ∼1.5 mm near mid-span and ∼0.8 mm close to the floor and ceiling; this deflection is consistent with model bending, with the model fixed at the floor and ceiling.
Finally,
Figure 13 shows the rotation/deflection analysis for the same dataset shown in
Figure 6. The figure shows the difference between the angle of attack measured by the encoder and two methods discussed in this paper: using a single laser while assuming that the center of rotation is fixed, and using multiple lasers at the same span location to account for model bending/translation. The multiple-laser technique shows that the model rotates slightly under loading, creating an approximately
offset in the angle of attack. This technique also showed a small amount of model bending (<2 mm). Previous studies with this model [
12,
13] have shown that boundary layer transition and other aerodynamic qualities do not vary in the span (z) direction, which suggests that this model bending does not affect the model aerodynamics. However, the bending is enough to bias the single laser angle of attack measurement. For example: at
encoder angle of attack, using only Laser 2 to calculate the angle of attack (while assuming that the center of rotation point is fixed) leads to an angle of attack measurement of
. When Lasers 1 and 2 are used simultaneously to remove bending effects, the angle of attack measurement is
. This shows that the bias caused by model bending can be even larger than the measured rotation, and multiple lasers should be used to accurately measure the angle of attack.