THESE de DOCTORAT - cerfacs

6
Boundary conditions for low Mach number
acoustic codes
Contents
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2 The quasi 1D Linearized Euler Equations - SNozzle . . . . . . . . . . . . . . . 97
6.3 The 1D linearized Euler equations for compact systems . . . . . . . . . . . . . 98
6.3.1 The transmitted and reflected waves . . . . . . . . . . . . . . . . . . . . . 100
6.4 Transmitted and reflected acoustic waves in isentropic nozzles . . . . . . . . . 103
6.4.1 Acoustic Response of Chocked and Unchocked Nozzles . . . . . . . . . 104
6.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.5 When entropy does not remain constant through a duct . . . . . . . . . . . . . 106
6.5.1 Analytic Solution : Building the linear system of equations . . . . . . . . 108
6.5.2 The mean flow in SNozzle . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.6 Transmitted and Reflected Waves through an ideal Compressor: the enthalpy
jump case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.6.1 Building the linear system of equations for the analytical solution . . . 112
6.6.2 The mean flow in SNozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.6.3 Introducing π c in the momentum equation . . . . . . . . . . . . . . . . . 114
6.6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
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