This is the HTML version of a paper presented at:
The American Helicopter Society International Specialists' Meeting, Stratford, Connecticut, October 11-13, 1995.
Unsteady Pressures
The time-dependent pressures measured on the lifting surface showed more complex variations than were measured previously on the body surface (Ref. 18, 20). Also, it was not entirely possible to clearly classify the unsteady pressure signatures into categories that were related to the local flow physics as was done in Ref. 16. This was not unexpected, since the environment at the empennage location was much more three-dimensional due to the nature of the rotor wake and its roll-up as described previously, as well as the influence of the flow separation and wake system generated by the tail itself.
Like the time-averaged airloads, the general nature of the unsteady loads was found to be closely related to the proximity of the rotor tip vortices. For example, Fig. 17 shows representative time-dependent pressures measured at one location on the upper surface of the stabilizer for a range of advance ratios at a constant rotor thrust and shaft angle, and with the low tail position. The rotor wake has been shown previously by the flow visualization results to convect relatively far below the tail at low advance ratios ( µ < 0.15), and the unsteady loads were found to be negligible. However, as the advance ratio was increased, the unsteady loads were found to quickly build in intensity due to the closer proximity of the rotor wake boundary.
Figure 17: Variation of unsteady pressure coefficient with advance ratio at transducer number 5 (upper surface, retreating side, leading-edge) for alpha_s = -2° , BL = 0.075, and low tail position
For the test conditions in Fig. 17, the wake boundary was very close to the tail between µ = 0.20 and 0.25. This can be seen in Fig. 12, which represents nearly the same test conditions, but with a slightly higher blade loading. At this point, the unsteady loads reached their maximum value. For advance ratios above 0.25, the separation distance between the wake boundary and the horizontal stabilizer increased slightly, with a corresponding slight decrease in unsteady loading. It should be remembered that for high advance ratios, the position of the wake boundary remained relatively unaffected by changes in advance ratio (see Figs. 11), and the unsteady loads were nearly maintained at the same overall magnitude. However, since the convection velocity of the individual filaments increased with increasing advance ratio, a change in phase of the unsteady loads on the tail with respect to the rotor position was observed.
The effect of the horizontal tail position can be more clearly illustrated by examination of the one-sided autospectral density function. This function was obtained by computing the autocorrelation function of the time-history data, and subsequently performing an FFT analysis (see Ref. 29). Figure 18 shows the variation in the 4P and 8P loading with advance ratio for high and low tail configurations for blade loadings of BL = 0.075 and 0.085. These are measurements of the unsteady loads at the leading edge (x/c = 0.075) on the lower surface on the retreating side of the horizontal tail. The results correspond to the wake boundaries shown in Figs. 9, 10, and 12. The corresponding loads on the upper surface of the tail are shown in Fig. 19.
Figure 18: Variation of periodic pressures coefficient with advance ratio at transducer number 13 (lower surface, retreating side, leading-edge) for alpha_s = -2° , BL = 0.075, and low tail position
Figure 19: Variation of periodic pressures coefficient with advance ratio at transducer number 5 (upper surface, retreating side, leading-edge) for alpha_s = -2° , BL = 0.075, and low tail position
For the high tail configuration, the results showed a steady increase in unsteady loading for both the 4P and 8P components. The primary cause for this was the decreasing separation distance between the wake boundary and the horizontal stabilizer, and the secondary cause was the increase in non-circulatory loading (Ref. 10) due to the increase in streamwise wake convection velocity. These trends were also obtained in a full-scale test discussed in Refs. 6 and 7. It is noteworthy that while the 4P forcing was the most dominant, significant 8P loads were also present.
Below µ = 0.15, both the 4P and 8P unsteady loads were found to be quite small for both the low and high tail positions. This was expected since the wake boundary was relatively far from the tail at low advance ratios. Furthermore, the steady pressure measurements have shown that the flow over the stabilizer airfoil was stalled below µ = 0.15.
The variation in unsteady loading with the low tail configuration was found to be considerably different to that for the high tail configuration. The 4P forces began to increase at a lower advance ratio of µ = 0.10, which was due to the lower wake/tail separation distance. At an advance ratio of µ = 0.20, as the wake boundary started to encroach on the horizontal tail, the 4P forces reached approximately the same intensity as for the high tail configuration. However, a sharp increase in 8P forcing was noticed here. It is possible that some of the rotor wake vortices underwent large distortions and/or were perforated by the lifting surface via a cutting type of interaction (see Ref. 30), although this could not be confirmed here by the flow visualization.
As the advance ratio was increased to 0.25, the tip vortices passed over the horizontal stabilizer (see Fig. 12), and a very slight drop in 4P forcing was observed on the lower surface. More noticeable was the sharp decrease in 8P forcing when the wake boundary no longer impinged on the leading edge of the tail surface. This suggested that the 8P forcing was likely, in part, due to a cutting type of wake interaction. Further increases of the advance ratio resulted in increases of both 4P and 8P forcing, which was primarily due to the increase in the rotor wake convection velocity. Figure 19 illustrates the development of the 4P and 8P airloads on the upper surface of the horizontal stabilizer. These airloads were measured at the leading edge (x/c = 0.075) on the retreating side of the tail.
For the high tail position, the 4P and 8P components were negligible below µ = 0.15. However, as the advance ratio was increased, the unsteady loads were found to increase steadily, as had been observed on the lower surface of the tail. However, the magnitude of the unsteady pressures was nearly 40% smaller than on the lower surface. The primary cause for this difference was separation from the wake. At the high tail position, the wake passed below the tail for all test conditions. Therefore, it was expected that the unsteady pressure response on the upper surface would be substantially lower than on the lower surface.
When the tail position was lowered, the unsteady pressures were found to increase sharply. As was observed on the lower surface, there was a significant increase in 8P loading when the wake impinged on the tail, while the 4P loading increased slightly. As the advance ratio was increased further, and the vortices were convected further away from the tail, both the 4P and 8P forcing dropped. The maximum unsteady loading occurred at a slightly higher advance ratio than on the lower surface, since the wake impinged on the upper surface at a slightly higher wake skew angle.
It should be noted that the quantative behavior of the 4P and 8P airloads did not substantially change with blade loading. The increase in blade loading from BL = 0.075 to 0.085 produced higher inflow velocities, resulting in a slightly lower wake skew angle. This meant that the wake impinged on the tail at a higher advance ratio, which was shown by a corresponding shift in the 8P pressure peak. Furthermore, the increased blade loading produced slightly higher tip vortex strengths, also resulting in a higher 4P and 8P loading.
Note that the time-varying induced velocity field produced by the convecting tip vortices resulted in local time-varying angles of attack at a fairly high reduced frequency. This can be established by computing the reduced frequency at the tail from:
The ratio c/R is about 0.25 for the present configuration, so the reduced frequency of the flow at the tail for an advance ratio of 0.2 would be of order 2.5, which is a very high value indeed. Clearly, this requires the mathematical modeling of the problem to be considered fully-unsteady. Also, if and when stall occurs locally on the wing, the high effective reduced frequency of the flow means that separation and stall may be more dynamic in nature. This adds an additional level of complexity to the mathematical modeling of the rotor/empennage interaction problem.
Figure 20 shows measured time-dependent pressures at different chordwise positions on the upper surface of the retreating side the tail. Moving chordwise, the magnitude of the unsteady loads was found to diminish quickly. This is analogous to the steady state pressure distribution on a lifting surface, where the largest variations in pressure are observed near the leading-edge. Furthermore, the interaction with the lifting surface itself may alter the strengths and/or structure of the tip vortices in the wake, also resulting in a reduced magnitude of unsteady loading.
Figure 20: Variation of unsteady pressure coefficient with chordwise position on the upper surface, retreating side, for µ = 0.25, alpha_s = -2° , BL = 0.075, and low tail position
From Fig. 20, it is evident that the unsteady loading consisted of a superposition of two events. This is analogous to observations by Kitaplioglu and Caradonna (Ref. 31), who performed a series of experiments on the blade/vortex interactions (BVI). In these experiments, a vortex was generated from a fixed wing, and the interaction of this vortex with a rotor was studied. It should be kept in mind that the reduced frequency during these experiments was approximately 0.07, which was considerably less than in the present experiment, where it was on the order of 2.5.
The first event was evidenced by a large increase in suction pressure observed near the leading-edge (x/c = 0.075) at psi = 71° . The magnitude of this change in pressure decreased quickly along the chord, and it was barely visible at psi = 73° at x/c = 0.263. Only a slight change in phase was observed between different chordwise measurement points, suggesting that the pressure disturbance is due to lift generation on the wing due to the induced velocity field. The second event was much more consistent in magnitude, and is visible at psi = 86° at x/c = 0.263, at psi = 93° at x/c = 0.494, and at psi = 104° at x/c = 0.725. This event was characterized by a very sharp decrease in pressure, followed by a sharp increase. There was a significant chordwise phase lag in the measurements of this event, suggesting that the disturbance was being convected past the tail at the local flow velocity. The general overall pressure signature due to the second event was typical of vortex passage, and corresponded well with the signature of close vortex/surface interactions observed by Bi and Leishman (Ref.16).
The measured time-dependent pressures at different locations on the upper and lower surface showed the same overall types of signatures, but they were quite varied in magnitude and phase. In general, the observed sensitivity of the pressure loads at different points on the wing will make the theoretical prediction of these effects a significant challenge to the analyst.
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