Further Comparisons of BEMT with Experiment

Results showing predictions made by the complete BEMT with measured thrust and power data for a hovering rotor are given in Fig. 3.23 for a four-bladed rotor of solidity

0. 1 and with — 13 degrees of linear blade twist. Compared to the modified momentum theory, now only a model for the profile drag losses must be assumed; all the induced losses resulting from nonuniform inflow and Prandtl tip losses are now calculated directly from the more complete BEMT method. Figure 3.23 shows that with the assumption that Cd — constant, the more complete BEMT underpredicts the power, and consequently it will

Figure 3.23 Comparison of the BEMT with and without higher-order profile drag terms versus measured thrust and power data (performance polar) for a four-bladed hovering rotor. Data source: Bagai & Leishman (1992).

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Power coefficient, Ср

tend to overpredict the figure of merit. The addition of the higher-order drag terms using Eq. 3.115 rectifies this, and the agreement with the measured data is much better.

Figure 3.24 shows a comparison of the complete BEMT with the measurements of thrust and power for a hovering rotor made by Knight & Hefner (1937). Again, the higher – order drag curve using Eq. 3.115 gives good agreement with the measurements. The only discrepancy is at higher values of Cj (> 0.005) where the rotor begins to stall and Eq. 3.115 is insufficient to model the drag behavior. There are also some additional effects of elastic blade twist here, which tend to twist the blade nose-down at the higher blade pitch angles and so aerodynamically offload the tip region.

Measurements of thrust and power in the axial climb condition are relatively rare. Flight test results have been given by Gustafson & Gessow (1945) and others, although it is difficult to estimate fuselage vertical drag and also to separate wake distortion effects resulting from the fuselage from the measured rotor thrust and shaft power in flight tests. These factors make comparisons of flight test results with the BEMT relatively difficult. Such issues are reviewed by Harris (1987), but as Prouty (1986) and others have shown, reasonable climb performance estimation can be expected from the momentum theory if appropriate empirical corrections are taken into account.

Felker & McKillip (1994) have measured isolated rotor performance on subscale rotors tested on a track facility. The thrusting rotor was mounted horizontally on a carriage and moved at constant velocity in still air, thereby simulating a steady climb. The thrust and power were measured with a balance system for constant collective pitch at several axial climb velocities. The measured thrust and power coefficient as a function of climb velocity, kc/Xh or Vc/Vh, are shown in Fig. 3.25 and are compared with results obtained using the BEMT. Because data were acquired at a constant collective pitch, increasing climb velocity reduces the blade element angles of attack resulting in a decrease in rotor thrust. Notice that although the BEMT predicts the thrust behavior well, it tends to underpredict the thrust somewhat at the higher climb velocities. For the lower collective pitch, the maximum underprediction is about 7%; and at the higher collective pitch it is about 4%. Because estimated uncertainties in the measurements are about 5%, the agreement of the BEMT with the measurements can be considered good. The corresponding predictions of power

are shown in Fig. 3.25(b), where the climbing work done by the rotor, CtK, has been added to the measurements. Again the agreement between the BEMT and experiment is good, except at the higher climb velocities where there is a maximum underprediction of no more than 10%.