A New Tip Correction Based on the Decambering Approach

A limitation of the standard Blade Element Momentum (BEM) technique is that it represents the surface loading by an averaged value determined by locally computed airfoil characteristics. Thus, it does not take into account the chord wise distribution of the induction. Likewise, lifting line methods suffer from the problem that the induction from the free wake vortices is only evaluated along a line representing the center of pressure.

Hence, the effect from the chord wise distribution of the induction is neglected. As a consequence, the loading in the proximity of the tip is generally found to be overestimated. To remedy this problem, a correction has been developed, which modifies the circulation by taking into account the additional influence of the induction of the free wake vortices.

This is done by correcting the circulation, using the so-called decambering effect and thin-airfoil theory. The correction is implemented as an additional correction to the Prandtl tip correction. Where the Prandtl tip correction serves to correct the axisymmetric momentum theory for a finite number of blades (see Goldstein, 1929), the new model further corrects the blade element model to represent the line distribution by a surface loading.

Comparing computations of the new model with results from a 'standard' BEM model and computations using a 3D panel code, show that the inclusion of the correction greatly improves the results. The new model also explains some of the discrepancies that earlier on have been observed when using a BEM technique based alone upon standard tip corrections (Shen et al., 2005).