Numerical study of eigenmode forcing effects on jet flow development and noise generation mechanisms

Abstract

The effect of nonlinear interaction of instability eigenmodes on jet flow transition and its near acoustic field for a high-subsonic round jet at a Reynolds number of Re= 4.5ϫ 10 5 and a Mach number of Ma= 0.9 is investigated using large-eddy simulations. At the inflow, helical perturbations of azimuthal wavenumbers ͉n͉ = 4 , . . . , 8 determined from linear stability theory are superimposed on a laminar base flow in order to trigger transition to turbulence. The disturbance amplitude is varied parametrically in the range from 1.5% to 4.5% of the jet exit velocity U j . Thereby we aim to characterize sources of noise generation and, in particular, underlying mode interactions. With increasing forcing amplitude, the transitional behavior of the jet changes which affects the mean flow and also the acoustic near-field, which are both analyzed in detail. As the forcing amplitude is increased, the axial root-mean-square peak levels along the jet centerline are reduced by approximately 7%. Simultaneously, pronounced dual-peak distributions are generated along the jet lip line which are related to the localization of vortex pairings of the jet column mode. For low-amplitude excitation the azimuthal turbulent kinetic energy spectra show that the unexcited, naturally least stable axisymmetric mode n = 0 and the helical mode n = 1 dominate the early nonlinear regimes between z Ϸ 6r 0 and 9r 0 where r 0 is the jet radius. An analysis of the Fourier mode amplitude clarifies that this energy rise is linked to the helical mode n = 1. For higher forcing amplitudes, in addition to the varicose mode n = 0 interactions between the excited even mode n = 4 and higher azimuthal harmonics thereof dominate the azimuthal energy spectra. These differences in the early nonlinear development of the eigenmodes are found to alter the acoustic near-field. At small angles from the downstream jet axis, the peak acoustic frequency occurs at a Strouhal number based on the angular frequency and the jet diameter D j of St= D j / ͑2U j ͒ Ϸ 0.4. For low-amplitude forcing sound pressure levels are slightly enhanced which can be linked to the dominant low azimuthal wavenumbers identified in the transitional region. In the sideline direction, regardless of the excitation level, broadbanded spectra with maxima in the band 0.7 Յ StՅ 0.8 are found which is maintained at intermediate observer angles. For high forcing amplitude, however, a tonal component outside the initially excited frequency range is observed. This peak at StϷ 0.88 can be explained by weakly nonlinear interactions of initially forced eigenmodes n = 4 and n = 8 together with the jet column mode.

Finite differences for coarse azimuthal discretization and for reduction of effective resolution near origin of cylindrical flow equations

“…In the present finite-difference-based method, the effective resolution is consequently reduced near the origin, in the same way as in the classical approach consisting in removing the highest Fourier modes when using spectral methods [11,[15][16][17][18][19]. Note that the azimuthal derivatives must still be estimated at all points.…”

“…This limitation can be alleviated by an appropriate rearrangement of the grid points to relieve the mesh density near the origin [12], or by the application of implicit differentiation schemes in the azimuthal direction [13,14]. When spectral methods are implemented in the azimuthal direction, it appeared also natural in many simulations [11,[15][16][17][18][19] to reduce the effective resolution in the azimuth by artificially removing the highest Fourier modes. Finally, it can be noted that using finite-difference schemes for cylindrical coordinate system, energy conservation might not be strictly satisfied [20].…”

Impact of rotating and fixed nozzles on vortex breakdown in compressible swirling jet flows

“…A fourth-order Runge-Kutta scheme [33] is employed for time integration. The numerical code has been validated extensively in previous investigations [18,34,25,22,24]. A nozzle is included in the computational domain which is modelled as an isothermal, no-slip wall to study the effects of the upstream flow on vortex breakdown and to allow for an interaction of the nozzle and the jet flow.…”

Inflow Treatment for the Simulation of Subsonic Jets with Turbulent Nozzle Boundary Layers

“…The strong resolution requirements restrict such simulations to low Reynolds numbers. The numerical framework to perform such simulations has been described extensively in [6,7]. Further information about the specific treatment of the nozzle boundary and the parallelization can be found in [10,11], respectively.…”