scholarly journals Calculation of the Thermoacoustic Stability of a Main Stage Thrust Chamber Demonstrator

2020 ◽  
pp. 235-247
Author(s):  
Alexander Chemnitz ◽  
Thomas Sattelmayer
Keyword(s):  
Transfer Function ◽  
Injection Pressure ◽  
Scattering Matrix ◽  
Main Stage ◽  
Stability Prediction ◽  
Mean Flow ◽  
Linearized Euler Equations ◽  
Thrust Chamber ◽  
Flame Response ◽  
The Stability

Abstract The stability behavior of a virtual thrust chamber demonstrator with low injection pressure loss is studied numerically. The approach relies on an eigenvalue analysis of the Linearized Euler Equations. An updated form of the stability prediction procedure is outlined, addressing mean flow and flame response calculations. The acoustics of the isolated oxidizer dome are discussed as well as the complete system incorporating dome and combustion chamber. The coupling between both components is realized via a scattering matrix representing the injectors. A flame transfer function is applied to determine the damping rates. Thereby it is found that the procedure for the extraction of the flame transfer function from the CFD solution has a significant impact on the stability predictions.

Centre modes in inviscid swirling flows and their application to the stability of the Batchelor vortex

2007 ◽  
Vol 576 ◽  
pp. 325-348 ◽  
Author(s):  
C. J. HEATON
Keyword(s):  
Continuous Spectrum ◽  
Single Point ◽  
Stability Boundary ◽  
Infinite Family ◽  
Neutral Curve ◽  
Swirling Flows ◽  
Mean Flow ◽  
Linearized Euler Equations ◽  
Numerical Studies ◽  
The Stability

We identify a family of centre-mode disturbances to inviscid swirling flows such as jets, wakes and other vortices. The centre modes form an infinite family of modes, increasingly concentrated near to the symmetry axis of the mean flow, and whose frequencies accumulate to a single point in the complex plane. This asymptotic accumulation allows analytical progress to be made, including a theoretical stability boundary, inO(1) parameter regimes. The modes are located close to the continuous spectrum of the linearized Euler equations, and the theory is closely related to that of the continuous spectrum. We illustrate our analysis with the inviscid Batchelor vortex, defined by swirl parameterq. We show that the inviscid instabilities found in previous numerical studies are in fact the first members of an infinite set of centre modes of the type we describe. We investigate the inviscid neutral curve, and find good agreement of the neutral curve predicted by the analysis with the results of numerical computations. We find that the unstable region is larger than previously reported. In particular, the value ofqabove which the inviscid vortex stabilizes is significantly larger than previously reported and in agreement with a long-standing theoretical prediction.

Modeling the Response of Premixed Flames to Mixture Ratio Perturbations

2003 ◽  
Author(s):  
Ju Hyeong Cho ◽  
Tim C. Lieuwen
Keyword(s):  
Transfer Function ◽  
Equivalence Ratio ◽  
Flame Length ◽  
Flame Speed ◽  
Heat Of Reaction ◽  
Mean Flow ◽  
Mixture Ratio ◽  
Flame Response ◽  
The Mean ◽  
Flame Position

Combustion instabilities continue to cause significant reliability and availability problems in low emissions gas turbine combustors. It is known that these instabilities are often caused by a self-exciting feedback loop between unsteady heat release rate and reactive mixture equivalence ratio perturbations. We present an analysis of the flame’s response to equivalence ratio perturbations by considering the kinematic equations for the flame front. This response is controlled by three processes: heat of reaction, flame speed, and flame area. The first two are directly generated by equivalence ratio oscillations. The third is indirect, as it is generated by the flame speed fluctuations. The first process dominates the response of the flame at low Strouhal numbers, roughly defined as frequency times flame length divided by mean flow velocity. All three processes play equal roles at Strouhal numbers of O(1). The mean equivalence ratio exerts little effect upon this transfer function at low Strouhal numbers. At O(1) Strouhal numbers, the flame response increases with decreasing values of the mean equivalence ratio. Thus, these results are in partial agreement with heuristic arguments made in prior studies that the flame response to equivalence ratio oscillations increases as the fuel/air ratio becomes leaner. In addition, a result is derived for the sensitivity of this transfer function to uncertainties in mean flame position. For example, a sensitivity of 10 means that a 5% uncertainty in flame position translates into a 50% uncertainty in transfer function. This sensitivity is of O(1) for St<<1, but has very high values for St∼O(1).

Impact of Shear Flow Instabilities on the Magnitude and Saturation of the Flame Response

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
Steffen Terhaar ◽  
Bernhard Ćosić ◽  
Christian Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Transfer Function ◽  
Shear Flow ◽  
High Speed ◽  
Transfer Functions ◽  
Flow Fields ◽  
Shear Layers ◽  
Flow Instabilities ◽  
Mean Flow ◽  
Swirl Number ◽  
Flame Response

Amplitude-dependent flame transfer functions, also denoted as flame describing functions, are valuable tools for the prediction of limit-cycle amplitudes of thermoacoustic instabilities. However, the effects that govern the transfer function magnitude at low and high amplitudes are not yet fully understood. It is shown in the present work that the flame response at perfectly premixed conditions is strongly influenced by the growth rate of vortical structures in the shear layers. An experimental study in a generic swirl-stabilized combustor was conducted in order to measure the amplitude-dependent flame transfer function and the corresponding flow fields subjected to acoustic forcing. The applied measurement techniques included the multi-microphone-method, high-speed OH*-chemiluminescence measurements, and high-speed particle image velocimetry. The flame response and the corresponding flow fields are assessed for three different swirl numbers at 196 Hz forcing frequency. The results show that forcing leads to significant changes in the time-averaged reacting flow fields and flame shapes. A triple decomposition is applied to the time-resolved data, which reveals that coherent velocity fluctuations at the forcing frequency are amplified considerably stronger in the shear layers at low forcing amplitudes than at high amplitudes, which is an indicator for a nonlinear saturation process. The strongest saturation is found for the lowest swirl number, where the forcing additionally detached the flame. For the highest swirl number, the saturation of the vortex amplitude is weaker. Overall, the amplitude-dependent vortex amplification resembles the characteristics of the flame response very well. An application of a linear stability analysis to the time-averaged flow fields at increasing forcing amplitudes yields the decreasing growth rates of shear flow instabilities at the forcing frequency. It therefore successfully predicts a saturation at high forcing amplitudes and demonstrates that the mean flow field and its modifications are of utmost importance for the growth of vortices in the shear layers. Moreover, the results clearly show that the amplification of vortices in the shear layers is an important driver for heat release fluctuations and their saturation.

Impact of Shear Flow Instabilities on the Magnitude and Saturation of the Flame Response

2013 ◽  
Author(s):  
Steffen Terhaar ◽  
Bernhard Ćosić ◽  
Christian Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Transfer Function ◽  
Shear Flow ◽  
High Speed ◽  
Transfer Functions ◽  
Flow Fields ◽  
Shear Layers ◽  
Flow Instabilities ◽  
Mean Flow ◽  
Swirl Number ◽  
Flame Response

Amplitude-dependent flame transfer functions, also denoted as flame describing functions, are valuable tools for the prediction of limit-cycle amplitudes of thermoacoustic instabilities. However, the effects that govern the transfer function magnitude at low and high amplitudes are not yet fully understood. It is shown in the present work that the flame response at perfectly premixed conditions is dominated by the growth rate of vortical structures in the shear layers. An experimental study in a generic swirl-stabilized combustor was conducted in order to measure the amplitude-dependent flame transfer function and the corresponding flow fields subjected to acoustic forcing. The applied measurement techniques included the Multi-Microphone-Method, high-speed OH*-chemiluminescence measurements, and high-speed Particle Image Velocimetry. The flame response and the corresponding flow fields are assessed for three different swirl numbers at 196 Hz forcing frequency. The results show that forcing leads to significant changes in the time-averaged reacting flow fields and flame shapes. A triple decomposition is applied to the time-resolved data, which reveals that coherent velocity fluctuations at the forcing frequency are amplified considerably stronger in the shear layers at low forcing amplitudes than at high amplitudes, an indicator for a nonlinear saturation process. The strongest saturation is found for the lowest swirl number, where the forcing additionally detached the flame. For the highest swirl number, the saturation of the vortex amplitude is weaker. Overall, the amplitude-dependent vortex amplification resembles the characteristics of the flame response very well. An application of linear stability analysis to the time-averaged flow fields at increasing forcing amplitudes yields decreasing growth rates of shear flow instabilities at the forcing frequency. It therefore successfully predicts a saturation at high forcing amplitudes and demonstrates that the mean flow field and its modifications are of utmost importance for the growth of vortices in the shear layers. Moreover, the results clearly show that the amplification of vortices in the shear layers is a dominant driver for heat release fluctuations and their saturation.

Broadband liner impedance eduction for multimodal acoustic propagation in the presence of a mean flow

2016 ◽  
Vol 11 (2) ◽  
pp. 150-155
Author(s):  
R. Troian ◽  
D. Dragna ◽  
C. Bailly ◽  
M.-A. Galland
Keyword(s):  
Numerical Model ◽  
Flow Characteristics ◽  
Acoustic Propagation ◽  
Rational Fraction ◽  
Physical Parameters ◽  
Mean Flow ◽  
Linearized Euler Equations ◽  
Grazing Flow ◽  
Propagation Medium ◽  
Difference Time

Modeling of acoustic propagation in a duct with absorbing treatment is considered. The surface impedance of the treatment is sought in the form of a rational fraction. The numerical model is based on a resolution of the linearized Euler equations by finite difference time domain for the calculation of the acoustic propagation under a grazing flow. Sensitivity analysis of the considered numerical model is performed. The uncertainty of the physical parameters is taken into account to determine the most influential input parameters. The robustness of the solution vis-a-vis changes of the flow characteristics and the propagation medium is studied.

scholarly journals The Concepts of Well-Posedness and Stability in Different Function Spaces for the 1D Linearized Euler Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Stefan Balint ◽  
Agneta M. Balint
Keyword(s):  
Euler Equation ◽  
Function Space ◽  
Euler Equations ◽  
Small Perturbation ◽  
Function Spaces ◽  
Well Posedness ◽  
Small Solution ◽  
Null Solution ◽  
Linearized Euler Equations ◽  
The Stability

This paper considers the stability of constant solutions to the 1D Euler equation. The idea is to investigate the effect of different function spaces on the well-posedness and stability of the null solution of the 1D linearized Euler equations. It is shown that the mathematical tools and results depend on the meaning of the concepts “perturbation,” “small perturbation,” “solution of the propagation problem,” and “small solution, that is, solution close to zero,” which are specific for each function space.

Random filters which preserve the stability of random inputs

1988 ◽  
Vol 20 (2) ◽  
pp. 275-294 ◽  
Author(s):  
Stamatis Cambanis
Keyword(s):  
Transfer Function ◽  
Moving Average ◽  
Random Processes ◽  
Time Shift ◽  
Linear Filter ◽  
Random Inputs ◽  
The Stability ◽  
Non Gaussian ◽  
Random Gain

A stationary stable random processes goes through an independently distributed random linear filter. It is shown that when the input is Gaussian or harmonizable stable, then the output is also stable provided the filter&s transfer function has non-random gain. In contrast, when the input is a non-Gaussian stable moving average, then the output is stable provided the filter&s randomness is due only to a random global sign and time shift.

Effects of finite-rate chemistry and detailed transport on the instability of jet diffusion flames

2014 ◽  
Vol 745 ◽  
pp. 647-681 ◽  
Author(s):  
Yee Chee See ◽  
Matthias Ihme
Keyword(s):  
Transport Properties ◽  
Diffusion Flames ◽  
Diffusive Transport ◽  
Mean Flow ◽  
Stability Behaviour ◽  
Jet Diffusion Flames ◽  
One Step ◽  
The Mean ◽  
Modelling Assumptions ◽  
The Stability

AbstractLocal linear stability analysis has been shown to provide valuable information about the response of jet diffusion flames to flow-field perturbations. However, this analysis commonly relies on several modelling assumptions about the mean flow prescription, the thermo-viscous-diffusive transport properties, and the complexity and representation of the chemical reaction mechanisms. In this work, the effects of these modelling assumptions on the stability behaviour of a jet diffusion flame are systematically investigated. A flamelet formulation is combined with linear stability theory to fully account for the effects of complex transport properties and the detailed reaction chemistry on the perturbation dynamics. The model is applied to a methane–air jet diffusion flame that was experimentally investigated by Füriet al.(Proc. Combust. Inst., vol. 29, 2002, pp. 1653–1661). Detailed simulations are performed to obtain mean flow quantities, about which the stability analysis is performed. Simulation results show that the growth rate of the inviscid instability mode is insensitive to the representation of the transport properties at low frequencies, and exhibits a stronger dependence on the mean flow representation. The effects of the complexity of the reaction chemistry on the stability behaviour are investigated in the context of an adiabatic jet flame configuration. Comparisons with a detailed chemical-kinetics model show that the use of a one-step chemistry representation in combination with a simplified viscous-diffusive transport model can affect the mean flow representation and heat release location, thereby modifying the instability behaviour. This is attributed to the shift in the flame structure predicted by the one-step chemistry model, and is further exacerbated by the representation of the transport properties. A pinch-point analysis is performed to investigate the stability behaviour; it is shown that the shear-layer instability is convectively unstable, while the outer buoyancy-driven instability mode transitions from absolutely to convectively unstable in the nozzle near field, and this transition point is dependent on the Froude number.

Dynamic analysis and control of an active engine mount system

2002 ◽  
Vol 216 (11) ◽  
pp. 921-931 ◽  
Author(s):  
Y-W Lee ◽  
C-W Lee
Keyword(s):  
Transfer Function ◽  
Dynamic Characteristics ◽  
Performance Test ◽  
Adaptive Controller ◽  
Lms Algorithm ◽  
Equivalent Mass ◽  
Engine Mount ◽  
Active Engine ◽  
The Stability ◽  
Mass Spring

Dynamic characteristics of a prototype active engine mount (AEM), designed on the basis of a hydraulic engine mount, have been investigated and an adaptive controller for the AEM has been designed. An equivalent mass-spring-damper AEM model is proposed, and the transfer function that describes the dynamic characteristics of the AEM is deduced from mathematical analysis of the model. The damping coefficient of the model is derived by considering the non-linear flow effect in the inertia track. Experiments confirmed that the model precisely describes the dynamic characteristics of the AEM. An adaptive controller using the filtered-X LMS algorithm is designed to cancel the force transmitted through the AEM. The stability of the LMS algorithm is guaranteed by using the secondary path transfer function derived on the basis of the dynamic model of the AEM. The performance test in the laboratory shows that the AEM system is capable of significantly reducing the force transmitted through the AEM.

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

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