Fan sound laws
Not withstanding the analysis of sound sources, in Section 14.3, and how they vary with rotational speed and diameter, it is felt that a simplified approach may prove useful when carrying out predictive calculations.
Just as we can calculate the air performance of a given size of fan at a given speed, from tests on another size at another speed, in a range of similar units, so it is desirable to be able to establish similar scaling laws for the acoustic performance. It is understood that such laws would be subject to the same limitations as those for air flow, i. e. strict geometric proportionality with respect to all air passages and impellers, applicable only to corresponding points of operation (equal fan efficiencies) and valid only for a specified range of fan Reynolds numbers.
The great majority of fans operate in the turbulent gas flow regime and thus generate fluctuating forces which are received by the ear as noise. If the fluctuation is regular, a fixed pitch “note” is produced, but if the process is random, then broad band noise results.
As the noise output of a fan dBW is expressed in watts, i. e. a power, it can be expected that the noise will bear some fixed re-
THIRD OCTAVE BAND FREQUENCY (Hz) FAN SPEEDS 1110 rpm. AIR SPEEDS 14-9m/sec.
X………. X GRID ONLY
O———- O FOAM BALL
X———- x NOSECONE
+ • • + TURBULENCE SCREEN
Figure 14.21 Variations in measured sound power levels for a mixed flow fan according to microphone shield used
Lationship to the impeller power. There will also probably be Mach number and Reynolds number effects.
We therefore say that the fan sound power level dBW cc fan impeller power x U (Ma) x f2 (Re).
Now for standard air conditions:
Impeller power cc N3D5
Mach number oc Tip speed <x ND
Reynolds number oc Tip speed x diameter oc ND2
Therefore in the general case:
Fan SWL ocN3D5 x(ND)a x(ND2)b Equ 14.27
Whilst we may call this a “fan sound law” it must be appreciated that it can vary widely and is not nearly so accurate as the fan aerodynamic laws given in Chapter 4.
Considering firstly Mach number effects, the noise produced will increase with the velocities involved and according to the source of noise:
TOC o "1-5" h z For a monopole source a = 1
For a dipole source a = 3
For a quadrupole source a = 5
Reynolds number effects are more difficult to identify but for straightforward boundary layer separation one would expect a negative and fractional index, i. e. 0 > b > -1.
Such effects will depend on absolute velocities through the impeller, thicknesses, clearances, number of blades, blade angle, etc. It seems reasonable to suggest therefore that there will be
Some interdependence with fan specific speed Ns = 075 and that the lower Ns the nearer b will approach -1
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