Page 99 - Fluid Mechanics and Thermodynamics of Turbomachinery

80 Fluid Mechanics, Thermodynamics of Turbomachinery
Fan blade design (McKenzie)

The cascade tests and design methods evolved by Howell, Carter and others,
which were described earlier, established the basis of British axial compressor
design. However, a number of empirical factors had to be introduced into the
methods in order to correlate actual compressor performance with the performance
predicted from cascade data. The system has been in use for many years and has
been gradually modified and improved during this time.
McKenzie (1980) has described work done at Rolls-Royce to further develop the
correlation of cascade and compressor performance. The work was done on a low-
speed four-stage compressor with 50 per cent reaction blading of constant section.
The compressor hub to tip radius ratio was 0.8 and a large number of combinations
of stagger and camber was tested.
McKenzie pointed out that the deviation rule originated by Howell (1945), i.e.
eqns. (3.39) and (3.40a) with n D 0.5, was developed from cascade tests performed
without sidewall suction. Earlier in this chapter it was explained that the consequent
thickening of the sidewall boundary layers caused a contraction of the main through-
flow (Figure 3.8), resulting in a reduced static pressure rise across the cascade and
an increased air deflection. Rolls-Royce conducted a series of tests on C5 profiles
with circular arc camber lines using a number of wall suction slots to control the
axial velocity ratio (AVR). The deviation angles at mid-span with an AVR of unity
were found to be significantly greater than those given by eqn. (3.39).
From cascade tests McKenzie derived the following rule for the deviation angle:
υ D .1.1 C 0.31 /.s/l/ 1/3 (3.41)

where υ and are in degrees. From the results a relationship between the blade
stagger angle and the vector mean flow angle ˛ m was obtained:
0.213, (3.42)
tan D tan ˛ m
where tan ˛ m is defined by eqn. (3.6). The significance of eqn. (3.42) is, that if the
air inlet and outlet angles (˛ 1 and ˛ 2 respectively) are specified, then the stagger
angle for maximum efficiency can be determined, assuming that a C5 profile (or a
similar profile such as C4) on a circular arc camber line is being considered. Of
course, the camber angle and the pitch/chord ratio s/l still need to be determined.
In a subsequent paper McKenzie (1988) gave a graph of efficiency in terms of
Cp i and s/l, which was an improved presentation of the correlation given in his
earlier paper. The ideal static pressure rise coefficient is defined as
2
Cp i D 1 .c 2 /c 1 / . (3.43)
McKenzie’s efficiency correlation is shown in Figure 3.23, where the ridge line of
optimum efficiency is given by
s/l D 9 ð .0.567 Cp i / (3.44)
EXAMPLE 3.3. At the midspan of a proposed fan stator blade the inlet and outlet
0
0
air angles are to be ˛ 1 D 58 and ˛ 2 D 44 . Using the data and correlation of
McKenzie, determine a suitable blade camber and space chord ratio.