We present a thermo-acoustic model on a cylindrical, or annular, domain capable of modeling instabilities of tangential acoustic modes. The model accounts for nonuniform density, damping, rotational flow, and heat-release coupling. It is shown that deliberately introducing spatial variations in some quantities has a similar effect to adding damping to the system. The effects of these symmetry-breaking conceptes are evaluated on the model through linear analysis and the net amount of additional damping is computed. We show how various symmetry-breaking concepts are robust with respect to the uncertainty in the model parameters and we examine propagation of uncertainty with respect to a recently defined measure of uncertainty.
NOMENCLATUREA = state space matrix a = speed of sound e = internal energy per unit volume K = heat-release gains p = pressure q = volumetric heat-release r, θ = radial, tangential (space) variables R = mean radius t = time u = velocity vector u r , u θ = radial, tangential velocities υ 2 ( ) = uncertainty metric x = state vector in Galerkin truncated model Y = acoustic boundary admittance γ = ratio of specific heats (= 1.4) ρ = density φ = tangential (Fourier) basis function ψ = radial basis function ξ = damping constant (·), (·) = mean, perturbation quantities (·) = normalized quantities (·) 0 , (·) m = spatially mean and m-periodic quantities