Effect of Hub-Tip Ratio

The effect of hub-tip ratio on the unsteady lift coefficient and acoustic coef­ficients is studied for hub-tip ratios of 0.6, 0.6667, 0.7391, 0.8182, and 0.9048. We consider rotor/stator interaction with B = 16 and V = 24 and a mean ft>w of Mo = 0.3536, Mq = 0.1, Mr = 0.1. The c/rm ratio at the mean radius is 0.3491, C = 3n, and a grid of {nx x ng x nr} = {161 x 21 x 21} is used.

Figure (1) compares the absolute value of the unsteady lift coefficient along the span for the different hub-tip ratios. The figure shows significant effect of the hub-tip ratio. For the largest two ratios, variations in the lift coefficient along the span is small. These variations become significant as the ratio de­creases. For rh/rt = 0.6 and 0.6667, two propagating acoustic modes exist. For the other three values of rh /rt only one mode propagates. This explains the difference in the trend of the results between the two cases of rh /rt = 0.6 and 0.6667 and the other cases.

The magnitude of the upstream and downstream acoustic coefficients for the different hub-tip ratios are compared in Fig. (2). The downstream acoustic co­efficient of the first radial mode (n = 0) increases as the hub-tip ratio decreases until the second mode cuts on where it starts to decrease. Both downstream and upstream coefficients of the second acoustic mode increase as the hub-tip ratio decreases. These results show that change in the number of cut-on modes has strong influence on the aerodynamic and acoustic coefficients.