This article revisits the problem of indirect combustion noise in nozzles of finite length. The analytical model proposed by Moase for indirect combustion noise is rederived and applied to subcritical nozzles having shapes of increasing complexity. This model is based on the equations formulated by Marble and Candel for which an explicit solution is obtained in the subsonic framework. The discretization of the nozzle into n elementary units of finite length implies the determination of 2n integration constants for which a set of linear equations is provided in this article. The analytical method is applied to configurations of increasing complexity. Analytical solutions are compared to numerical results obtained using SUNDAY (a 1D nonlinear Euler solver in temporal space) and CEDRE (3D Navier-Stokes flow solver). Excellent agreement is found for all configurations thereby showing that acceleration discontinuities at the boundaries between adjacent elements do not influence the actual acoustic transfer functions. The issue of nozzle compactness is addressed. It is found that in the subcritical domain, spectral results should be nondimensionalized using the flow-through-time of the entire nozzle. Doing so, transfer functions of nozzles of different lengths are successfully compared and a compactness criterion is proposed that writes x à РL 0 df=uðfÞ < 1 where L is the axial length of the nozzle. Finally, the entropy wave generator (EWG) experimental setup is considered. Analytical results are compared to the results reported by Howe. Both models give similar trends and show the important role of the rising time of the fluctuating temperature front on the amplitude of the indirect acoustic emission. The experimental temperature profile and the impedance coefficients at the inlet and outlet are introduced into the analytical formulation. Results show that the indirect combustion noise mechanism is not alone responsible for the acoustic emission in the subcritical case.

In the framework of jet noise computation, a numerical simulation of a subsonic turbulent hot jet is performed using large-eddy simulation. A geometrical tripping is used in order to trigger the turbulence at the nozzle exit. In a first part, the validity of the simulation is assessed by comparison with experimental measurements. The mean and rms velocity fields show good agreement, so do the azimuthal composition of the near pressure field and the far field spectra. Discrepancies remain close to the nozzle exit which lead to a limited overestimation of the pressure levels in both near and far fields, especially near the 90∘ angular sector. Two point correlation analyses are then applied to the data obtained from the simulation. These enable to link the downstream acoustic radiation, which is the main direction of radiation, to pressure waves developing in the shear layer and propagating toward the potential core end. The intermittency of the downstream acoustic radiation is evidenced and related to the coherent structures developing in the shear layer.

This article revisits the problem of indirect combustion noise in nozzles of finite length. The analytical model proposed by Moase et al. (JFM 2007) for indirect combustion noise is red-erived and applied to subcritical nozzles having shapes of increasing complexity. This model is based on the equations formulated by Marble & Candel (JSV 1977) for which an explicit solution is obtained in the subsonic framework. The discretization of the nozzle into n elementary units of finite length implies the determination of 2n integration constants for which a set of linear equations is provided in this article. The analytical method is applied to configurations of increasing complexity. Analytical solutions are compared to numerical results obtained using SUNDAY (a 1D non linear Euler solver in temporal space) and CEDRE (3D Navier-Stokes flow solver). An excellent agreement is found for all configurations thereby showing that acceleration discontinuities at the boundaries between adjacent elements do not influence the actual acoustic transfer functions. The issue of nozzle compactness is addressed. It is found that in the subcritical domain, spectral results should be nondimensionalized using the flow-through-time of the entire nozzle. Doing so, transfer functions of nozzles of different lengths are successfully compared and a compactness criterion is proposed that writes ω*∫0Ldζ/uζ<1 where L is the axial length of the nozzle. Finally, the EWG experimental setup of Bake et al. (JSV 2009) is considered. Analytical results are compared to the results reported by Howe (JFM 2010). Both models give similar trends and show the important role of the rising time of the fluctuating temperature front on the amplitude of the indirect acoustic emission. The experimental temperature profile and the impedance coefficients at the inlet and outlet provided by Bake et al. (JSV 2009) and Leyko et al. (JSV 2011) are introduced into the analytical formulation. Results show that the indirect combustion noise mechanism cannot be held responsible alone for the acoustic emission in the subcritical case.

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This paper is the first part of a series of papers on results obtained in the EXEJET project. EXEJET was a French government-funded program started in 2008 and concluded in 2013, involving 3 partners: Airbus, Onera, Snecma. The project aimed at improving understanding and tools to assess and reduce installed jet noise for modern airliners. Project highlights are the following: Airbus designed and manufactured a swept wing model specifically for wind-tunnel tests at the anechoic facility CEPRA19 -Snecma conceived a large BPR-9 scaled nozzle model with a range of chevron shapes and validated the design methodology -A high-quality experimental flow and noise database was acquired in wind tunnel -Different simulation methods were benchmarked upon this new data. The installation effects of the nozzle under wing are then subject of focus. Significant aeroacoustic installation effect were measured by wing-mounted unsteady pressure sensors, far-field microphones and by Onera three-dimensional source localization array. In the far field, the new wing generated significantly lower levels of background noise in the tunnel compared to previous experience. The installation effects were typically dominant in the low frequency range of jet noise and in the forward arc. Phased array techniques were able to characterize the acoustic installation effects in two dimensions, and quantify them by projection to the far field. In the near field of the powerplant, the unsteady pressure measurements on the wing under-side surface revealed large-scale fluctuations imposed by the jet and spatially coherent. In spite of the presence of pylon and wing, these wavepacket signatures were found qualitatively similar to previous measurements made on coaxial jets from simpler axi-symmetric nozzle. Thanks to the high degree of collaboration between the three partners, EXEJET represents a step beyond the previous common VITAL WP7.2 investigations. The EXEJET database provides a foundation for analysis and validation of future modeling and numerical simulation aiming at quantifying installed jets aeroacoustics. Nomenclature BP RBy-Pass Ratio of an Engine or Nozzle: mass flow ratio between secondary (fan) over primary (core) D mixMixed (or Equivalent) jet diameter (m) JF I Jet-Flap Interaction JW I Jet-Wing Interaction M a Mach number of the flight stream N P R Nozzle Pressure Ratio: total pressure at exhaust over ambient pressure OASP L Overall Sound Pressure Level (dB) OP Operating Point in the test matrix P IV Particle Image Velocimetry SP L Sound Pressure Level (dB) SN R Signal-to-Noise Ratio St Strouhal number T KE Turbulent Kinetic Energy V mix Mixed jet velocity (m/s)Flight stream velocity V P Primary jet exhaust velocity V S Secondary jet exhaust velocity Ψ Polar angle relative to inlet axis Θ Azimuthal angle relative to pylon (180 deg is flyover direction, opposite to the pylon and toward the ground) Dissipation rateThe data analysis presents characteristic distances and velocities in terms of the equivalent mixed jet to allow a better compar...