Nozzle flow acoustics with wall-friction and entropy two-dimensionality*

The behavior of one-dimensional linear flow disturbances in an isentropic nozzle flow can be solved in the zero frequency limit using the Marble & Candel (1977) relations. Frequency dependence be incorporated by rearranging the governing linearized Euler equations in terms of the flow invariants i.e. the perturbation quantities that are matched across an area change in the zero frequency limit. Semi-analytical solution using the Magnus expansion then follows, with frequency as an expansion parameter (Duran & Moreau 2013). Last year, we presented the first inclusion of flow non-isentropicity as a further Magnus expansion parameter – accounting for mean heat transfer along the nozzle (Yeddula et al. 2022).  

The present work extends this to nozzle flows with wall friction and two-dimensionality in which entropy perturbations have both radial and axial dependence. The analytical framework is developed, with frequency, wall-friction coefficient and an entropy “two-dimensionality” coefficient all incorporated as Magnus expansion parameters. Resulting predictions of entropy noise are validated against numerical simulations. The agreement confirms that the Magnus expansion is a powerful semi-analytical tool suitable for replacing full numerical simulations across a broad range of nozzle acoustic problems.