Numerical and analytical modelling of entropy noise in a supersonic nozzle with a shock

Leyko, Matthieu; Moreau, Stéphane; Nicoud, Franck; Poinsot, Thiérry

doi:10.1016/j.jsv.2011.01.025

Cited by 73 publications

(82 citation statements)

References 29 publications

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“…The area ratio are chosen in such a way that the outlet Mach numbers do not change in a constant heat transfer condition for the selected inlet Mach numbers [20], as Table 1 shows. …”

Section: Validationmentioning

confidence: 99%

Investigation of the transmitted noise of a combustor exit nozzle caused by burned hydrogen-hydrocarbon gases

Hosseinalipour

Fattahi

Karimi

2016

International Journal of Hydrogen Energy

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Transmitted noise is a major problem in industrial and aero-engine gas turbines. One of a noise generating part in the preceding systems is exit nozzle which can play as encouraging or discouraging sound waves. The generated noise may arise from an incident acoustic wave or entropy wave. In this paper, the effect of heat transfer and inlet Mach number of the exit nozzle as well as replacing the traditional hydrocarbon fuels with hydrogen and composite of hydrogen-hydrocarbon on noise generation is studied. Further, the influence of the hydrodynamic decaying mechanisms in a nozzle on the noise generated by entropy waves is investigated. It is found that hydrogen can reduce transmitted noise in a subcritical nozzle with an acoustic incident wave or in a supercritical nozzle with an incident entropic wave.

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“…The area ratio are chosen in such a way that the outlet Mach numbers do not change in a constant heat transfer condition for the selected inlet Mach numbers [20], as Table 1 shows. …”

Section: Validationmentioning

confidence: 99%

Investigation of the transmitted noise of a combustor exit nozzle caused by burned hydrogen-hydrocarbon gases

Hosseinalipour

Fattahi

Karimi

2016

International Journal of Hydrogen Energy

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“…The shock wave acts as an interface between the two regions. The response of the shock wave to acoustic and entropy perturbations has been studied in depth (Marble & Candel 1977;Kuo & Dowling 1996;Stow et al 2002;Moase et al 2007;Goh & Morgans 2011a;Leyko et al 2011). The main steps of the method are summarized here, the reader is referred to Moase et al (2007) and Goh & Morgans (2011a) for more details.…”

Section: Supersonic Flow With a Shock Wavementioning

confidence: 99%

Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion

2013

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The acoustic and entropy transfer functions of quasi-one-dimensional nozzles are studied analytically for both subsonic and choked flows with and without shock waves. The present analytical study extends both the compact nozzle solution obtained by Marble & Candel (1977) and the effective nozzle length proposed by Stow et al. (2002) and by Goh & Morgans (2011a) to non-zero frequencies for both modulus and phase through an asymptotic expansion of the linearized Euler equations. It also extends the piecewiselinear approximation of the velocity profile in the nozzle proposed by Moase et al. (2007) to any arbitrary profile or equivalently any nozzle geometry. The equations are written as a function of three variables, namely the dimensionless mass, total temperature and entropy fluctuations, yielding a first order linear system of differential equations with varying coefficients, which is solved using the Magnus expansion. The solution shows that both the modulus and the phase of the transfer functions of the nozzle have a strong dependence on the frequency. This holds for both choked flows and subsonic converging diverging nozzles. The method is used to compare two different nozzle geometries with the same inlet and outlet Mach numbers showing that, even if the compact solution predicts no differences between the transfer functions of the two nozzles, significant differences are found at non-zero frequencies. A parametric study is finally performed to calculate the indirect to direct noise ratio for a model combustor, showing that this ratio decreases at higher frequencies.

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“…For instance, the results of wellcontrolled experiments of Bake et al [19,20] in an entropy wave generator were initially in fair agreement with the classical prediction of Marble and Candel [12]. The causes of disagreement were explained and mostly resolved in the recent refinements of the original theory [15,11]. Despite these theoretical developments, most acoustic models still assume entropy waves to be one-dimensional and preserved during advection in the upstream channel, while the validity of these assumptions is unclear.…”

Section: Introductionmentioning

confidence: 99%

“…For more than three decades the formulations of Marble and Candel [12] were the main tools for modeling of acoustic effects of entropy waves in combustion dynamics. Over the last ten years, a number of attempts were made to release the assumptions made by Marble and Candel [12] about the linearity of the system and compactness of the nozzle [13,14,15,16,17,18]. These resulted in improving the predictability of the acoustic conversion of entropy waves.…”

Section: Introductionmentioning

confidence: 99%

On the dissipation and dispersion of entropy waves in heat transferring channel flows

2017

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This paper investigates the hydrodynamic and heat transfer effects upon the dissipation and dispersion of entropy waves in non-reactive flows. These waves, as advected density inhomogeneities downstream of unsteady flames, may decay partially or totally before reaching the exit nozzle, where they are converted into sound. Attenuation of entropy waves dominates the significance of the subsequent acoustic noise generation.Yet, the extent of this decay process is currently a matter of contention and the pertinent mechanisms are still largely unexplored. To resolve this issue, a numerical study is carried out by compressible large eddy simulation (LES) of the wave advection in a channel subject to convective and adiabatic thermal boundary conditions. The dispersion, dissipation and spatial correlation of the wave are evaluated by post-processing of the numerical results. This includes application of the classical coherence function as well as development of nonlinear quantitative measures of wave dissipation and dispersion. The analyses reveal that the high frequency components of the entropy wave are always strongly damped. The survival of the low frequency components heavily depends upon the turbulence intensity and thermal boundary conditions of the channel. In general, high turbulence intensities and particularly heat transfer intensify the decay and destruction of the spatial coherence of entropy waves. In some cases, they can even result in the complete annihilation of the wave. The current work can therefore resolve the controversies arising over the previous studies of entropy waves with different thermal boundary conditions.

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Numerical and analytical modelling of entropy noise in a supersonic nozzle with a shock

Cited by 73 publications

References 29 publications

Investigation of the transmitted noise of a combustor exit nozzle caused by burned hydrogen-hydrocarbon gases

Investigation of the transmitted noise of a combustor exit nozzle caused by burned hydrogen-hydrocarbon gases

Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion

On the dissipation and dispersion of entropy waves in heat transferring channel flows

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