The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise

Cumpsty, N. A.; Marble, Frank E.

doi:10.1098/rspa.1977.0171

Cited by 138 publications

(86 citation statements)

References 4 publications

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“…There exist several methods to solve this system of equations. Here, a modification of the method proposed by Cumpsty & Marble (1977) to solve the propagation of acoustic and entropy waves through a two-dimensional compact stator vane is adapted to the one-dimensional non-compact nozzle. The matrix system of equation (5.4) can be rearranged to have the unknowns on one side of the equation and the forcing values of the waves on the other side.…”

Section: Subsonic Flowmentioning

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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Section: Subsonic Flowmentioning

confidence: 99%

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

2013

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“…It has been demonstrated that unsteady flames can generate entropy waves, which are advected downstream by the mean flow and may reach the exit nozzle of the combustor [3,5,6]. Due to the significant acceleration of the mean flow in the exit nozzle and the first stages of the high pressure turbine, entropy waves can be converted into acoustic waves [7,8]. This forms a source of noise in the gas turbine, which originates from the combustion process.…”

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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“…The compact approximation works well when the nozzle is much shorter than all the wavelengths. The compact nozzle theory of Marble & Candel [6] was extended by Cumpsty & Marble [19,20] and Cumpsty [21] to study entropy noise produced in a gas turbine at the combustor outlet and turbine blade stages. A significant increase of entropy noise generation was found with the increase of pressure drop over a turbine stage.…”

Section: Introductionmentioning

confidence: 99%

Acoustic and Entropy Waves in Nozzles in Combustion Noise Framework

2017

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A low-order model is presented to study the propagation and interaction of acoustic and entropic perturbations through a convergent-divergent nozzle. The calculations deal with choked, unchoked, as well as compact and non-compact nozzles. In the choked case, a normal shock exists in the divergent section of the nozzle. To validate the models developed, cylindrical configurations corresponding to Entropy-WaveGenerator (EWG) and Hot-Acoustic-Testrig (HAT) of DLR are studied. For the EWG, an entropy wave is generated upstream of a nozzle by an electrical heating device, and for the HAT a speaker is used to generate pressure waves. In these two configurations and for the choked case, the supersonic region between the nozzle throat and the normal shock is assumed to be acoustically compact. The results of the low-order model are found to give excellent agreement with the experimental results of the EWG and HAT rigs. To give insight into the physics, the model is used to undertake a parametric study for a range of nozzle lengths and shock strengths. The low order model is finally used to calculate the direct to indirect (entropy and vorticity) combustion noise ratio for an idealised thin-annular combustor. For this model combustor the direct acoustic noise is found to dominate within the combustor while, the entropy indirect noise is found to be the main source of noise downstream of the choked nozzle. The indirect vorticity noise has a negligible contribution.

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The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise

Cited by 138 publications

References 4 publications

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

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

Acoustic and Entropy Waves in Nozzles in Combustion Noise Framework

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