Impact of fuel supply impedance and fuel staging on gas turbine ...

3 Acoustics
Before analyzing the acoustic behavior <strong>of</strong> a combustion system, the basic
theory <strong>of</strong> the propagation <strong>of</strong> sound in gaseous media has to be understood.
This section presents the main relevant mathematical equations <strong>and</strong> their
simplifications, as they are appropriate in the present context. The later
sub-chapters deal with the relations used in the acoustic network model. All
relations can be found in various books <strong>and</strong> publications about basic acoustics
<strong>and</strong> aeroacoustics, especially in Dowling <strong>and</strong> Ffowcs Williams [24], Morse
<strong>and</strong> Ingard [81], Pierce [93], Rienstra <strong>and</strong> Hirschberg [110], Goldstein [38] or
Munjal [82].
3.1 Basic acoustic equations
The basis for the following derivations are the conservation equations for
mass, momentum <strong>and</strong> energy. The conservation equation for momentum reduces
to the Euler equation in absence <strong>of</strong> body forces <strong>and</strong> neglecting viscosity:
conservation <strong>of</strong> mass:
Dρ
+ ρ(∇·u)=0, (3.1)
Dt
conservation <strong>of</strong> momentum:
ρ Du
Dt
+∇p = 0, (3.2)
conservation <strong>of</strong> energy:
ρ D Dt
(e+ 1 2 |u|2 )
=−∇q−∇·(pu)+ ˙Q V . (3.3)
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