Core noise in aeroengines is due to two main mechanisms: direct combustion noise, which is generated by the unsteady expansion of burning gases, and indirect combustion noise, which is due to the acceleration of entropy waves (temperature fluctuations generated by unsteady combustion) within the turbine stages. This paper shows how a simple burner model (a flame in a combustion chamber terminated by a nozzle) can be used to scale direct and indirect noise. An analytical formulation is used for waves generated by combustion. The transmission and generation of waves through the nozzle is calculated using both the analytical results of Marble and Candel (Marble, F. E., and Candel, S., "Acoustic Disturbances from Gas Nonuniformities Convected Through a Nozzle," Journal of Sound and Vibration, Vol. 55, 1977, pp. 225-243.) and a numerical tool. Numerical results for the nozzle verify and extend the analytical approach. The analytical relations for the combustion and the nozzle provide simple scaling laws for direct and indirect noise ratio as a function of the Mach number in the combustion chamber and at the nozzle outlet. Nomenclature A = nozzle cross-sectional area, m 2 A c = throat nozzle cross-sectional area, m 2 A f = combustor cross-sectional area, m 2 c = speed of sound, m=s c p = massic heat capacity at constant pressure, J=K=kg c v = massic heat capacity at constant volume, J=K=kg ' f = flame length, m ' n = nozzle length, m M = Mach number _ m = mass flow rate, kg=s PWfg = spectral power density of computed with Welch's method p = thermodynamic pressure, Pa _ Q = heat release rate, W _ q = heat release rate per volume unit, W=m 3 r = massic ideal gas constant, J=K=kg s = massic entropy, J=K=kg T = temperature, K t = time, s u = gas velocity, m=s w S = dimensionless entropy wave w = dimensionless acoustic wave propagating downstream w= dimensionless acoustic wave propagating upstream x = x-axis value, m y = y-axis value, m z = z-axis value, m = specific heat capacities ratio = Dirac distribution = ratio between indirect and direct noise = mass density, kg=m 3 = temporal mean value of 0 = temporal fluctuation value of = reduced angular pulsation ! = angular pulsation, rad=s Subscripts AA = acoustic response of the nozzle to an acoustic perturbation CC = response of the combustion chamber to a heat release fluctuation SA = acoustic response of the nozzle to an entropy perturbation t = total quantity of 0 = quantity upstream from the combustor 1 = quantity downstream from the combustor and upstream from the nozzle 2 = quantity downstream from the nozzle

. Numerical and analytical modelling of entropy noise in a supersonic nozzle with a shock. Journal of Sound and Vibration, Elsevier, 2011, 330 (16) that the acoustic impedance downstream of the nozzle must be accounted for to properly recover the experimental pressure signal. The analytical method can also be used to optimize the experimental parameters and avoid the interaction between transmitted and reflected waves.

International audienceAnalytical and numerical assessments of the indirect noise generated through a nozzle are presented. The configuration corresponds to an experimental setup operated at DLR by Bake et al. (2008) where an entropy wave is generated upstream of the nozzle by means of an electrical heating device. Both 3-D and 2-D axisymmetric simulations are performed to demonstrate that the experiment is mostly driven by linear acoustic phenomena, including pressure wave reflection at the outlet and entropy-to-acoustic conversion in the accelerated regions. Results show that the acoustic impedance downstream of the nozzle must be accounted for appropriately in order to recover the experimental pressure signal. A good agreement is also obtained with a purely analytical assessment based on the Marble and Candel compact nozzle approximation

The combustion noise in aero-engines is known to have two different origins. First, the direct combustion noise is directly generated by the flame itself. Second, the indirect combustion noise is caused by the acceleration in the turbine stages, of entropy spots generated by the combustion. In both cases, the turbo-machinery is involved in the combustion-noise transmission and generation. Numerical simulations are performed in the present study to assess the global noise for a real aeronautical configuration. On the one hand, the acoustic and entropy transfer functions of an isolated blade row are obtained using two-dimensional unsteady simulations. The transfer functions of the blade row are compared with the model of Cumpsty and Marble that assumes an axially compact configuration. On the other hand, the acoustic and entropy sources coming from a combustion chamber are calculated from a threedimensional Large Eddy Simulation (LES). This allows an evaluation of the error introduced by the model for the present combustion chamber using the previous numerical simulations. A significant error is found for the indirect combustion noise, whereas it stays reasonable for the direct one.

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