Linear response analysis and hydrodynamic transfer function of a reacting swirling jet

This presentation explores the linear hydrodynamic response of reacting swirling jets.  The framework for this study is an analysis of the linearized reacting Navier-Stokes equations. The base flow for this analysis is a single modeled swirling jet.  The homogeneous solution is calculated to explore the intrinsic instability characteristics, and then a linear response analysis algorithm is built to approximate the response to the additional non-linear terms of the inhomogeneous form. The numerical methods of this paper focus on discretization of the Navier-Stokes equations and applying boundary conditions for a specified geometry to obtain a weak variational form that can be solved using Taylor-Hood finite elements.  The result of the analysis is a transfer function for the hydrodynamic amplification of external excitations.  Together with this transfer function, the analysis elucidates the spatial structure of the flow’s externally excited coherent structures.