The subject of the Desire project is the combustion chamber, as depicted in figure 1.2. One of the combustion chamber designs currently used in gas turbines is the so-called annular combustor (figure 1.3). In this design the combustion chamber is shaped as an annulus in which multiple burners (for instance 24) cause multiple swirling flames. It is very expensive to build a full annulus as a test rig, and therefore one section, containing one burner, is taken from the annulus. The interaction between flames from different burners is
Combustion, acoustics and vibrationThis section introduces the basic phenomenology, which is schematically depicted in figure 1.4, starting with the flame. The most characteristic influence of the flame is that it generates a temperature field (1), which strongly influences the acoustics of the system. This is mostly a static influence. The steady state temperature field created by the flame determines the steady state temperature field for the acoustics of the system. Unsteady combustion can give time-dependent temperature differences. When the flame moves, the local temperature field in the flame zone changes, but these perturbations have no global influence. When the amount of fuel that comes to the flame changes, the temperature of the total flame changes. These perturbations propagate through the combustion chamber with the flow velocity and are called entropy waves [78]. These are not taken into account in this thesis. Besides the steady influence, the flame also has unsteady components. Because the combustion is turbulent, the combustion speed constantly changes around the mean value. These changes generate an acoustic volume source (2), which gives an acoustic field in the combustor (this is commonly called combustion roar ). This acoustic field in turn generates perturbations in the fuel and air flow to the burner and to the mixture coming to the flame (3), which again generates perturbations in the speed of combustion. This loop can become unstable, which is known as a combustion instability. This behavior is studied extensively in the literature [23,62,69]. Another well-known example of an unstable feedback loop between heat and acoustics is the so-called Rijke tube [82].Vibration of the structure is influenced directly by the flame through the temperature field (1). This is again a steady phenomenon, the steady flame determines the temperature of the liner and therefore its material properties. Changes in operating conditions cause changes in thermal expansion of components and therefore cyclic thermal stresses, which can directly lead to relatively low cycle fatigue [95]. The interaction between acoustics and vibration is similar to that between combustion and acoustics. The acoustic field acts as a pressure load on the structure (4), which vibrates in response. This vibration imposes a velocity boundary condition on the acoustic domain (5), which generates an acoustic field. This loop does not become unstable, because there Table A.1: Coefficients of the c p polynomial, g...