About the Zero Mach Number Assumption in the Calculation of Thermoacoustic Instabilities

Nicoud, Franck; Wieczorek, Kerstin

doi:10.1260/175682709788083335

Cited by 93 publications

(71 citation statements)

References 56 publications

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“…(1.1) relies on the so-called zero-Mach-number assumption stating that the mean velocity is very small compared to the speed of sound. Nicoud & Wieczorek (2009) suggest that the domain of validity of the zero mean flow assumption might be rather small. One reason for this is that Eq.…”

Section: Introductionmentioning

confidence: 98%

Mixed acoustic–entropy combustion instabilities in gas turbines

2014

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A combustion instability in a combustor terminated by a nozzle is analysed and modelled based on a low order Helmholtz solver. A Large Eddy Simulation (LES) of the corresponding turbulent, compressible and reacting flow is first performed and analysed based on Dynamic Mode Decomposition (DMD). The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approx. 320 Hz) and shows the presence of large entropy spots generated within the combustion chamber and convected down to the exit nozzle. The lowest purely acoustic mode being in the range 700 − 750 Hz, it is postulated that the instability observed around 320 Hz stems from a mixed entropy/acoustic mode where the acoustic generation associated with entropy spots being convected throughout the choked nozzle plays a key role. The DMD analysis allows to extract from the LES results a low-order model that confirms that the mechanism of the low-frequency combustion instability indeed involves both acoustic and convected entropy waves. The Delayed Entropy Coupled Boundary Condition (Motheau et al. 2014) is implemented into a numerical Helmholtz solver where the baseline flow is assumed at rest. When fed with appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz/DECBC solver predicts the presence of an unstable mode around 320 Hz, in agreement with both LES and experiments.

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Section: Introductionmentioning

confidence: 98%

Mixed acoustic–entropy combustion instabilities in gas turbines

2014

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“…Of course, the square matrix A depends on the discretization technique, both in its size and structure. Typically, a modal expansion produces a dense matrix of small size, as the expansion requires usually only few basis functions 8 , whereas a finite volume approach produces a large, but sparse matrix 9 .…”

Section: Introductionmentioning

confidence: 99%

“…where H q (x) is the amplitude of the flame response and can be related to the parameter n of n − τ -models 9 , τ (x) is the time delay and n ref is a unit vector. Assuming timeharmonic perturbations of pulsation ω, one may write p (x, t) = p(x)e −iωt and q ( x, t) = q(x)e −iωt .…”

Section: Introductionmentioning

confidence: 99%

Assessing non-normal effects in thermoacoustic systems with mean flow

Wieczorek

Sensiau²,

Polifke

et al. 2011

Physics of Fluids

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1In this paper, non-normal interactions in a thermoacoustic system are studied, using a low-order expansion of the state variables in terms of eigenmodes. The thermoa- The expansion in terms of eigenmodes is computationally efficient, making the approach potentially applicable to complex, 3D configurations including non-trivial boundary conditions and spatio-temporal distributions of heat release fluctuations.In the present paper, the method is applied to a 1D configuration that consists of a duct including a 1D heat source, followed by a choked isentropic nozzle. It is shown that for such a case it is essential to include the contribution of entropy perturbations in the calculation of the optimal initial perturbation and the maximum transient energy growth. Subsequently, the impact of increasing mean flow Mach number and increasing strength of flame/acoustic interaction on non normal effects is assessed in a parameter study.

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“…Many strategies are available to devise lower-order methods by neglecting viscous terms and through linearisation or reduction to one dimension [11,12]. The Linearised Euler Equations (LEEs) approach gives an accurate representation of the physical thermoacoustic phenomena [13,14] at a reasonable computational cost. However, solving LEE requires numerical schemes that are subject to instability and nonphysical techniques must be used, such as the addition of artificial viscosity [15].…”

Section: Introductionmentioning

confidence: 99%

“…It has been demonstrated in a previous study [14] that the zero-Mach-number assumption can lead to significant errors for the prediction of both the frequency and the growth rate of combustion instabilities, suggesting that improvements are required for the two items cited above. Since accounting for the non zero-Mach-number terms in the equations leads to a drastic increase in the complexity of the problem [15], the aim of this paper is to propose models that account for these effects in a Helmholtz solver.…”

Section: Introductionmentioning

confidence: 99%

Accounting for convective effects in zero-Mach-number thermoacoustic models

Motheau

Selle

Nicoud

2014

Journal of Sound and Vibration

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a b s t r a c tThis paper presents a methodology to account for some mean-flow effects on thermoacoustic instabilities when using the zero-Mach-number assumption. It is shown that when a computational domain is represented under the M¼ 0 assumption, a nonzero-Machnumber element can simply be taken into account by imposing a proper acoustic impedance at the boundaries so as to mimic the mean flow effects in the outer, not computed flow domain. A model that accounts for the coupling between acoustic and entropy waves is presented. It relies on a "delayed entropy coupled boundary condition" (DECBC) for the Helmholtz equation satisfied by the acoustic pressure. The model proves able to capture low-frequency entropic modes even without mean-flow terms in the fluctuating-pressure equation.

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About the Zero Mach Number Assumption in the Calculation of Thermoacoustic Instabilities

Cited by 93 publications

References 56 publications

Mixed acoustic–entropy combustion instabilities in gas turbines

Mixed acoustic–entropy combustion instabilities in gas turbines

Assessing non-normal effects in thermoacoustic systems with mean flow

Accounting for convective effects in zero-Mach-number thermoacoustic models

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