Nonlinear mechanisms of sound generation in a perturbed parallel jet flow

Abstract

An initial value problem with relevance to jet noise is investigated. A plane parallel jet flow is subjected to a spatially localized initial disturbance and is then left to evolve according to the two-dimensional compressible Navier-Stokes equations. The hydrodynamic response is in the form of a convecting vortex packet. The Ffowcs WilliamsHawkings approach is formulated in the time domain and used to extrapolate from the simulated near field to the acoustic far field. The predominant downstream sound radiation comes from an early stage of nonlinear development of the vortex packet. Two simplified models to account for the radiation are introduced, based on nonlinear mode interactions on a prescribed base flow. The first uses two sets of linearized Euler equations, coupled via the inviscid Lilley-Goldstein acoustic analogy. This formulation separates the linear sound field from the sound field driven by nonlinear interactions; qualitative agreement of the latter with the Navier-Stokes computations demonstrates the importance of nonlinear interactions. The second model uses combinations of linear inviscid eigenmodes to drive the sound field, which allows extraction of the dominant mode interactions responsible for the observed radiation pattern. The results indicate that a difference-wavenumber nonlinear interaction mechanism dominates sound radiation from subsonic instability modes in shear flows.

Nonlinear interaction model of subsonic jet noise

“…The source terms in (1.1) are set to zero within the solution domain; thus the flow is only forced by the imposed boundary condition. Following from considerations of the jump conditions for the Lilley-Goldstein equation (see Sandham et al 2006a, appendix B), a pressure gradient boundary condition is appropriate and is applied at rZa by setting …”

“…Indeed, the present line of research (cf. Sandham et al 2006a) started when we tried to interpret results from a DNS of a subsonic jet. We then ran simplified simulations and theoretical models to try to understand the flow physics.…”

“…In this paper, we extend the method from Sandham et al (2006a) to spatially developing waves. Wavenumbers and growth factors of instability modes are obtained from the compressible parabolized stability equations (PSE) with viscous and non-parallel terms included.…”

Jet noise from instability mode interactions

“…Up until now all the PSE results have been based on the fixed base flow given by equations (11)(12)(13)(14). An alternative approach is possible in which nonlinear interactions of PSE modes are used to update the mean flow.…”

“…The present work is a continuation of a line of research into the relevance of nonlinear mode interactions to sound radiation that we have been pursuing recently. In Sandham et al (2006a) a model problem was used to show how products of linear instability modes could be used as source terms, leading to potentially useful predictions of the main characteristics of the sound field. Any quadratic mode interaction can be split into a term involving the sum of the wavenumbers (or frequencies in the spatial case) and a term involving the differences.…”