3.4 WHL Model Tail Rotor
3.4.3 Predicted and Measured Vortex Locations (Zero Twist)
When the later model tail rotor tests were originally reported, it was shown that the measured vortex tra- jectories fell between the prescribed displacements and contraction given by Landgrebe174 and Kokurek and
Tangler,166 although there was some doubt about the thrust coefficient which was used for the original com- parisons (due to scatter of the test data, and the fact that the theory used at the time tended to over-predict the thrust). However, in the present work, the CFD has been set up to replicate the pitch and coning of the experiment (and from the above comparisons, the thrust is in good agreement with the trends of the test data). Since it is generally accepted that the Kocurek and Tangler prescribed-wake provides a superior formulation to the earlier work of Landgrebe, especially for high solidity rotors, the vortex positions have been re-computed to provide a comparison at the same CT as predicted by the CFD.
Since much of the model tail rotor vortex position data was obtained on video, only a few still photographs of relatively poor-quality were taken during the tests, Figure 152. Better photographs were later obtained for a sequence of vortex ages from a model main rotor, as presented by Brocklehurst,56 and an example is included
here to illustrate the quality of wake visualisation that was achieved, Figure 153.
The vertical displacement, Figure 154, and contraction, Figure 155, together with the wake overall trajectory plot in Figure 156, show excellent agreement between the measured vortex locations and those extracted from the CFD results. In general there is better agreement between the (Euler) CFD results and the test measurements, than between the test data and the Kocurek and Tangler prescribed wake, and the latter appears to under-predict the wake displacements at low pitch and over-predict at high pitch (although the primary descent rate at low pitch and secondary descent rate at high pitch are in good agreement). Apart from instances of vortex ’pairing’, or ’gearing’ which is evident in the wake contraction plotted from test data at the highest and lowest pitch angles in the far-wake, the agreement between test, prescribed wake and CFD
3.4 WHL Model Tail Rotor 3 VALIDATION
Figure 150: Comparison of Euler CFD Torque-Thrust Predictions with Measurements from 1984 Model Tail Rotor Tests at a Tip Mach Number of 0.263, 0.361 and 0.492
Figure 151: Comparison of Euler CFD Corrected Predictions for Figure of Merit with Measurements from 1984 Model Tail Rotor Tests at a Tip Mach Number of 0.263, 0.361 and 0.492
3.4 WHL Model Tail Rotor 3 VALIDATION
Figure 152: Early Flow Visualisation Photograph of Wake of the Model Tail Rotor, Taken Prior to Employing New Strobes and Improved Video Techniques to Extract Vortex Locations
is good. The CFD results, however, shows some ’lobing’ between each blade passing (every 90 degrees), and although it is difficult to be sure, a similar effect is perhaps just discernable in the test data.
Looking again at Figure 155, at 5 degrees pitch the CFD and prescribed wake show similar contraction, while the test data shows a lack of contraction. For the 15 degree case, the test data and prescribed wake show slightly more contraction than predicted by the CFD, but overall, and at 8 and 10 degrees in particular, the wake positions are in excellent agreement.
Despite viscous effects being missing from the Euler solutions, the vortices were found to be well formed and closely follow the expected trajectories, giving confidence in the capability of an Euler CFD method to correctly predict the overall induced flow field and give good predictions of the thrust and induced power in attached flow conditions.
The Euler computations discussed above were carried out at an early stage in this research, and later the 8 degree impressed pitch case was repeated using Navier-Stokes as it was of interest as a baseline for the unsteady isolated rotor (no fin-blockage) case of Chapter 8. This allows a direct comparison to be made between Euler and Navier-Stokes, and between Navier-Stokes and test data for this particular model rotor case. As before, the actual blade angle for the datum rectangular blade, TRB-000v, allowing for pitch-flap coupling and 0.402 degrees of coning was 7.598 degrees. In the tests, the flow visualisation was carried out at a reduced rotational speed of 1600rpm, giving a tip Mach number of 0.2625 and a tip Reynolds number of only 510,000. The modified k-ω turbulence model based on Wilcox321was used in the computations. For this low tipspeed cases,
90,000 iterations were needed (at CFL=1.0) for the solution to completely settle. Even so, the wake did not completely connect to the Froude outlet at the far field, although judging by the vortex trajectories, this may not be very significant as most of the contraction has already taken place by the time the wake has descended 0.4R and the wake does not spread until about 1.5R beneath the rotor plane.
Figure 157 shows the vortex trajectories, vertical displacement and contraction for Euler and Navier-Stokes predictions compared to the test data and the prescribed wake of Kocurek and Tangler.166 The vortex locations
were obtained from the vorticity computed in Tecplot, by taking planes at 5 (or 10) degree intervals and using the probe tool to obtain the required co-ordinates of the centre of the vortices. As mentioned previously, some of the vortices appear non-circular in shape due to proximity to the blade and the inboard vortex sheet breaking away from the tip vortex. The trajectory from the Navier-Stokes predictions lies outside that obtained from the Euler solution. It can be seen from the separate contraction and vertical displacement plots that the Navier-Stokes results show a reduced contraction, while the vertical displacement is initially almost identical
3.4 WHL Model Tail Rotor 3 VALIDATION
Figure 153: Illustration of Better Quality Flow Visualisation Photography on a Rectangular 2-blade Model Main Rotor Showing Improved Clarity of Vortex Trajectories, Similar to that Achieved on Model Tail Rotor Using Video Techniques
3.4 WHL Model Tail Rotor 3 VALIDATION
Figure 154: Comparison of Euler CFD Vortex Displacement with the Prescribed Wake of Kocurek and Tangler, and Measurements from 1980 Model Tail Rotor Tests at a Tip Mach Number of 0.263
Figure 155: Comparison of Euler CFD Wake Contraction with the Prescribed Wake of Kocurek and Tangler, and Measurements from 1980 Model Tail Rotor Tests at a Tip Mach Number of 0.263
3.4 WHL Model Tail Rotor 3 VALIDATION
Figure 156: Comparison of Euler CFD Vortex Trajectories with the Prescribed Wake of Kocurek and Tangler, and Measurements from Model Tail Rotor Tests at a Tip Mach Number of 0.263
up to about 180 degrees, except for a slight inflexion just after the first blade passage. Further down in the wake, the descent rate of the viscous solution continues to match that of the test data, while the Euler points suggested a steeper descent. For the Navier-Stokes results, the computed solutions better reflect the distortions of the trailed vortices as they leave the blade than was able to be measured in the experiment, and these details (which might be crucial to the performance) are also ignored by the prescribed wake model.
Most of the vortex locations in the wake were obtained as described above by using Tecplot to compute the vorticity in a post-processing operation, and the majority of the wake trajectory information presented in this thesis were formed using this technique. However, late in this research program the λ2 vortex identification
parameter was also computed using a Tecplot add-on, following the work of Jeong and Hussain.154 This
parameter takes into account the pressure and density field of the vortex as well as the velocities, and so should provide a better indication of the centre of the vortex.
Vortex trajectories, vertical displacement and contraction obtained from λ2 are compared to those from
vorticity in Figure 158. The differences in the initial part of the wake, close to the rotor, are surprisingly small, while after about 180 degrees age, the λ2 results show a greater contraction and fall closer to the prescribed
wake trend. The two methods of determining the vortex locations fall either side of the test data in this last half-turn of the wake for which vortex locations were extracted. The vertical displacement graph shows close agreement between the two sets of results, with perhaps slightly less inflexion after the first blade passing for theλ2 case. After about 180 degrees of vortex age theλ2 results fall slightly above the vorticity results, but
rejoin after 270 degrees. The agreement between the two methods is good, particularly prior to the vortex interacting with the blade atψ=90 degrees.
In summary, there appears to be little difference between the vorticity andλ2methods when used to simply
extract the centres of the vortices, except in the second half-turn of the wake development, towards the end of which the vortices are starting to decay. Both approaches show the vortices to contract less than the prescribed exponential and lie above the expected descent path. While care was taken to align the test measurements to the rotor centre, it may be possible that part of the discrepancy in vertical displacement might be a shift due to coning, or measurement datum error. However, the predictions have an initially flatter trend compared to the simplistic linear descent rate of the prescribed wake. Also, the predictions show a slower initial contraction which would appear to originate in the vortex formation process.
3.4 WHL Model Tail Rotor 3 VALIDATION
Figure 157: Vortex Trajectories from Euler and Navier-Stokes Predictions (using Vorticity) for the Datum Blade, TRB-000 (Mtip=0.26), compared to WHL Model Tail Rotor Measurements and the Prescribed Wake of Kocurek and Tangler.166
3.4 WHL Model Tail Rotor 3 VALIDATION
Figure 158: Vortex Trajectories from Navier-Stokes Predictions (using Vorticity andλ2) for the Datum Blade,
TRB-000 (Mtip=0.26), compared to WHL Model Tail Rotor Measurements and the Prescribed Wake of Kocurek and Tangler.166
3.4 WHL Model Tail Rotor 3 VALIDATION
Figure 159: Comparison of Thrust-Pitch Characteristics from HMB and WHL Hover Program with Test Data for the Rectangular Model Tail Rotor Blades with 0, 8 and 16 Degrees Twist