Blade Element Calculations - Small Wind Turbines: Analysis, Design, and Application - page 77

Chapter 5
Blade Element Calculations

5.1 Introduction

Equations 3.10 and 3.11 are the basic blade element equations and there probably
have been many programs written to implement them. Two important and pub-
lically-available examples are PROPID 1 written by Professor Michael Selig at the
University of Illinois, Urbana-Champaign and WT_Perf, written by Marshall Buhl
at NREL. 2
Over the years, a large number of modifications to the basic equations have been
proposed. The only one considered here is meant to account for the finite number of
blades (N \?) on any real turbine. The necessity of some correction for finite
N comes from realising that the streamtube analysis of Chaps. 2 and 3 assumed that
the velocities and pressures are uniform in the circumferential direction, whereas
non-uniformities must arise for a finite number of blades. In other words, the axial
velocity at the blade element may be different from U 1 which is the streamtube's
average velocity. A simple and commonly used correction for this effect is ''Pra-
ndtl's tip loss factor'', F, defined as the ratio of the average induction factor, a, to the
value at the blades, a b : F = a/a b . The implementation of the tip loss factor as
described here follows closely the work of Shen et al. [ 1 ], Xudong et al. [ 2 ] and
Clifton-Smith [ 3 ]. In its simplest form, the equation for F is:

e f = p F ¼ 2 cos 1

ð 5 : 1 Þ

where

f ¼ NR r ð Þ= 2 r sin / ð Þ ð 5 : 2 Þ

In practice, F, which is always less than unity, makes a difference of around
5-10% to the predicted turbine performance and is often neglected, especially

1

http://www.ae.illinois.edu/m-selig/propid.html (accessed 25 Sept 2010).

2

http://wind.nrel.gov/designcodes/simulators/wtperf/ (accessed 25 Sept 2010).