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112 Chapter 6: Boundary conditions for low Mach number acoustic codes
6.6 Transmitted and Reflected Waves through an ideal Compressor: the enthalpy
jump case
In the previous two sections, the focus was on the acoustic response of ducts due to:
• a change in the mean flow due to variations of section area: the nozzle case.
• a change in the mean flow due to an entropy jump : the 1D flame case.
The purpose of this section is to focus on the acoustic response of a system when the changes in
the mean flow are due to enthalpy jumps. The case to study here is then an ideal compressor.
The first step when modeling a compressor is to consider it as an isentropic element that creates
a difference in both the total pressure and the kinetic energy in the flow, i.e., an element that
exerts a work on the flow by changing its total enthalpy. The case considers a constant section
duct (as in the 1D flame case) with a jump of total enthalpy at the middle. This is represented
in Fig. (6.10)
Compressor
Impossed
Atmosphere
p’=0
M 1 M 2
w 2
+
w 2
-
Figure 6.10: compressor
In this configuration an upstream travelling acoustic wave w − 2
is imposed at the outlet while a
Dirichlet acoustic condition is imposed at the inlet (p ′ = 0). This analytical/numerical setup is
a simplified representation of the inlet air circuit and compressor of an aeronautical engine. The
acoustic waves, produced in the combustion chamber, travel upstream through the compressor
until reaching the atmosphere which is considered as a totally reflecting acoustic condition (
p ′ = 0 → R = 1 with a phase φ = π). As done before, this study is carried out both analytically
and numerically (SNozzle).
6.6.1 Building the linear system of equations for the analytical solution
Equation (6.22) is the momentum equation of the 1D LEE for compact systems. The influence
of the compressor into the system is accounted for by the term F. ˆ Nevertheless, the most
practical characterization of a compressor in a 1D system is simply by its total pressure ratio