Numerical Simulation of the Dynamics of Turbulent Swirling Flames

A.6 Derivation of the Linearized Acoustic Equations
Figure A.4: Power spectrum of DRBS Input signals with different frequency
limit.
Figure A.5: Autocorrelation matrix of DRBS Input signals with different frequency
limit.
A.6 Derivation of the Linearized Acoustic Equations
The 1D linearized acoustic equations are derived using the decomposition
presented in section 6.1:
u(x, t) = ū + u ′ (x, t),
p(x, t) = ¯p + p ′ (x, t),
ρ(x, t) = ¯ρ + ρ ′ (x, t).
(A.22)
(A.23)
(A.24)
Considering that:
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