An important issue for the aeronautical industry is the reduction of aircraft noise. The rotor–stator interaction is a predominant part of the noise emission. Presented are an introduction to these interaction theories, whose applications are numerous. For example, the conception of air-conditioning ventilators requires a full understanding of this interaction.
A rotor wake induces on the downstream stator blades a fluctuating vane loading, which is directly linked to the noise emission.
Consider a B blades rotor (at a rotation speed of
\Omega
B\Omega
mB\Omega
Fm
mB\Omega
Pm
Example
For an airplane air-conditioning ventilator, reasonable data are :
B=13
\Omega=12000
The blade passing frequency is 2600 Hz, so it is only necessary to include the first two multiples (2600 Hz and 5200 Hz), because of the human ear high-sensibility limit. The frequencies m=1 and m=2 must be studied.
As the source levels can't be easily modified, it is necessary to focus on the interaction between those levels and the noise levels .
The transfer function
{{Pm}\over{Fm}}
s=+infty | |
\sum\limits | |
s=-infty |
{e\over2}}JmB}(mBM)
Where M is the Mach number and
JmB
Back to the example :
For m=1, with a Mach number M=0.3, the argument of the Bessel function is about 4. Avoiding mB-sV less than 4 is required. If V=10, then 13-1x10=3, so there will be a noisy mode. If V=19, the minimum of mB-sV is 6, and the noise emission will be limited.
Remark :
The case that is to be strictly avoided is when mB-sV can be nul, which causes the order of the Bessel function to be 0. As a consequence, care must be taken regarding B and V as prime numbers.
The minimization of the transfer function
{{Fm}\over{Pm}}
Fm
All this study was made for a privileged direction : the axis of the rotor–stator. All the results are acceptable when the noise reduction is ought to be in this direction. In the case where the noise to reduce is perpendicular to the axis, the results are very different, as those figures shown :
For B=13 and V=13, which is the worst case, the sound level is very high on the axis (for
\theta=0
For B=13 and V=19, the sound level is very low on the axis but high perpendicularly to the axis (for
\theta=Pi/2