Sound radiation from exponentially growing and decaying surface waves

Morfey

2006

J. Fluid Mech.

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.

Section: Discussionmentioning

confidence: 99%

Nonlinear mechanisms of sound generation in a perturbed parallel jet flow

Morfey

2006

J. Fluid Mech.

“…Two spatially developing unstable waves inside the jet with different frequencies f 1 and f 2 may interact via the source term in (1.1) to give effective sound radiation with frequency f 1 Kf 2 . Sandham et al (2006b) showed that wave packets based on growing and decaying envelope functions are inefficient at radiating sound for low Mach numbers, slow saturation time-scales and low frequencies; hence interactions involving the summed frequencies will be less effective radiators than those involving difference frequencies.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear interaction model of subsonic jet noise

Phil. Trans. R. Soc. A.

Salgado

2008

Noise generation in a subsonic round jet is studied by a simplified model, in which nonlinear interactions of spatially evolving instability modes lead to the radiation of sound. The spatial mode evolution is computed using linear parabolized stability equations. Nonlinear interactions are found on a mode-by-mode basis and the sound radiation characteristics are determined by solution of the Lilley-Goldstein equation. Since mode interactions are computed explicitly, it is possible to find their relative importance for sound radiation. The method is applied to a single stream jet for which experimental data are available. The model gives Strouhal numbers of 0.45 for the most amplified waves in the jet and 0.19 for the dominant sound radiation. While in near field axisymmetric and the first azimuthal modes are both important, far-field sound is predominantly axisymmetric. These results are in close correspondence with experiment, suggesting that the simplified model is capturing at least some of the important mechanisms of subsonic jet noise.

“…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.…”

Section: Results For a Variable Base Flowmentioning

confidence: 99%

“…We employ a method in which the profiles defined by equations (11)(12)(13)(14) are used as a template for the flow. For each step downstream the boundary layer equations are solved to give a provisional updated streamwise velocity profile V * z (r).…”

Section: Results For a Variable Base Flowmentioning

confidence: 99%

“…An alternative method of solving equation (1) is possible, at least for the S zz source term, based on the jump relations for the Lilley-Goldstein equation. In this approach (see Appendix B of Sandham et al, 2006) equation (1) is integrated across a shear layer, leading to relations between the jumps in p and ∂p/∂y and the source terms f and q defined by equation (2). The jump relations are given by ∆p = ρf y (16) and…”

Section: Comparison With Lilley-goldstein Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Jet noise from instability mode interactions

14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference)

Salgado

Agarwal

2008

A nonlinear interaction model is used to study sources of sound in jets. The model uses quadratic interactions of instability modes, which are obtained by solving the linear parabolized stability equations. Source terms involving nonlinear interactions are evaluated and a linear wave equation is solved with direct injection of the source terms. Thus the complete method solves only linear partial differential equations, coupled by nonlinear source terms. It allows the contribution of each modal interaction to be studied separately, giving a breakdown of the radiation pattern of each interaction. The method is demonstrated using a fixed base flow matched to the experiment of Stromberg et al. (J. Fluid Mech. 72(2), 1980). The squared streamwise velocity quadrupole is the largest source term for axisymmetric mode interactions, while for helical-helical mode interactions both the squared radial and squared azimuthal velocities are the main contributing sources, despite a strong cancelation effect between them. Results are also presented for an alternative implementation, in which the base flow is allowed to vary according to the Reynolds stresses of the developing instability modes. This model demonstrates sound production during mode growth and subsequent saturation.