Instability in a thermoacoustic prime-mover: A numerical approach

Abstract

A numerical model aimed at investigating the development of instability in a thermoacoustic prime-mover is presented. It is based on a discretization of the two-dimensional compressible Navier–Stokes equations, and does not rest on the plane pressure wave assumption. The computational domain is made of a single stack interplate space extended up to both resonator ends. The working gas is assumed to be initially at rest, and a longitudinal temperature gradient is enforced. The linear instability properties of the system are then given by the eigenmodes of the discretized evolution operator linearized in the vicinity of the above basic state. Temporal growth-rate and oscillation frequency are thus obtained for all thermoacoustic modes, and the prime-mover instability onset is determined as a function of the various parameters (mainly temperature gradient magnitude and mean pressure). As far as linear instability is concerned, this formulation is attractive, since it avoids any direct numerical simulation and any problem involved by the presence of two very different time scales.