scholarly journals Non-normality in combustion–acoustic interaction in diffusion flames: a critical revision

2013 ◽  
Vol 733 ◽  
pp. 681-683 ◽  
Author(s):  
Luca Magri ◽  
K. Balasubramanian ◽  
R. I. Sujith ◽  
M. P. Juniper
Keyword(s):  
Diffusion Flames ◽  
Initial Energy ◽  
Normal System ◽  
Transient Growth ◽  
Aircraft Engines ◽  
Acoustic Oscillations ◽  
Persistent Problem ◽  
Acoustic Interaction ◽  
Sustained Oscillations ◽  
Critical Revision

AbstractPerturbations in a non-normal system can grow transiently even if the system is linearly stable. If this transient growth is sufficiently large, it can trigger self-sustained oscillations from small initial disturbances. This has important practical consequences for combustion–acoustic oscillations, which are a persistent problem in rocket and aircraft engines. Balasubramanian & Sujith (J. Fluid Mech., vol. 594, 2008, pp. 29–57) modelled an infinite-rate chemistry diffusion flame in an acoustic duct and found that the transient growth in this system can amplify the initial energy by a factor,${G}_{max} $, of the order of$1{0}^{5} $to$1{0}^{7} $. However, recent investigations by L. Magri and M. P. Juniper have brought to light certain errors in that paper. When the errors are corrected,${G}_{max} $is found to be of the order of 1 to 10, revealing that non-normality is not as influential as it was thought to be.

Non-normality and nonlinearity in combustion–acoustic interaction in diffusion flames

2007 ◽  
Vol 594 ◽  
pp. 29-57 ◽  
Author(s):  
KOUSHIK BALASUBRAMANIAN ◽  
R. I. SUJITH
Keyword(s):  
Acoustic Field ◽  
Diffusion Flames ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Normal System ◽  
Acoustic Interaction ◽  
The Stability ◽  
The One ◽  
The Time Domain ◽  
Necessary And Sufficient

The role of non-normality and nonlinearity in flame–acoustic interaction in a ducted diffusion flame is investigated in this paper. The infinite rate chemistry model is employed to study unsteady diffusion flames in a Burke–Schumann type geometry. It has been observed that even in this simplified case, the combustion response to perturbations of velocity is non-normal and nonlinear. This flame model is then coupled with a linear model of the duct acoustic field to study the temporal evolution of acoustic perturbations. The one-dimensional acoustic field is simulated in the time domain using the Galerkin technique, treating the fluctuating heat release from the combustion zone as a compact acoustic source. It is shown that the coupled combustion–acoustic system is non-normal and nonlinear. Further, calculations showed the occurrence of triggering; i.e. the thermoacoustic oscillations decay for some initial conditions whereas they grow for some other initial conditions. It is shown that triggering occurs because of the combined effect of non-normality and nonlinearity. For such a non-normal system, resonance or ‘pseudoresonance’ may occur at frequencies far from its natural frequencies. Non-normal systems can be studied using pseudospectra, as eigenvalues alone are not sufficient to predict the behaviour of the system. Further, both necessary and sufficient conditions for the stability of a thermoacoustic system are presented in this paper.

Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition

2010 ◽  
Vol 667 ◽  
pp. 272-308 ◽  
Author(s):  
MATTHEW P. JUNIPER
Keyword(s):  
Periodic Solution ◽  
Simple Model ◽  
Initial Energy ◽  
Bypass Transition ◽  
Transient Growth ◽  
Governing Equations ◽  
Initial State ◽  
Rijke Tube ◽  
Sustained Oscillations ◽  
Sequence Of Events

With a sufficiently large impulse, a thermoacoustic system can reach self-sustained oscillations even when it is linearly stable, a process known as triggering. In this paper, a procedure is developed to find the lowest initial energy that can trigger self-sustained oscillations, as well as the corresponding initial state. This is known as the ‘most dangerous’ initial state. The procedure is based on adjoint looping of the nonlinear governing equations, combined with an optimization routine. It is developed for a simple model of a thermoacoustic system, the horizontal Rijke tube, and can be extended to more sophisticated thermoacoustic models. It is observed that the most dangerous initial state grows transiently towards an unstable periodic solution before growing to a stable periodic solution. The initial energy required to trigger these self-sustained oscillations is much lower than the energy of the oscillations themselves and slightly lower than the lowest energy on the unstable periodic solution. It is shown that this transient growth arises due to non-normality of the governing equations. This is analogous to the sequence of events observed in bypass transition to turbulence in fluid mechanical systems and has the same underlying cause. The most dangerous initial state is calculated as a function of the heat-release parameter. It is found that self-sustained oscillations can be reached over approximately half the linearly stable domain. Transient growth in real thermoacoustic systems is 105–106 times greater than that in this simple model. One practical conclusion is that, even in the linearly stable regime, it may take very little initial energy for a real thermoacoustic system to trigger to high-amplitude self-sustained oscillations through the mechanism described in this paper.

scholarly journals Non-normality and nonlinearity in combustion–acoustic interaction in diffusion flames – CORRIGENDUM

2013 ◽  
Vol 733 ◽  
pp. 680-680 ◽  
Author(s):  
K. Balasubramanian ◽  
R. I. Sujith
Keyword(s):  
Fluid Mechanics ◽  
Diffusion Flames ◽  
Transient Growth ◽  
Acoustic Interaction

Recent investigations by L. Magri and M. P. Juniper have brought to light certain errors in the paper by Balasubramanian and Sujith (Journal of Fluid Mechanics, vol. 594, 2008, pp. 29–57). The revision is available in a separate note (Journal of Fluid Mechanics, vol. 733, 2013, pp. 681–683), which shows that these ducted diffusion flames exhibit a transient growth of order 1 to 10. These results are in contrast to those presented by Balasubramanian & Sujith (2008), who found the transient growth to be of order $1{0}^{5} $ to $1{0}^{7} $.

On the secondary instabilities of transient growth in Couette flow

2017 ◽  
Vol 813 ◽  
pp. 528-557 ◽  
Author(s):  
Michael Karp ◽  
Jacob Cohen
Keyword(s):  
Couette Flow ◽  
Initial Energy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Transient Growth ◽  
Vortical Structures ◽  
Inflection Points ◽  
Theoretical Predictions ◽  
Secondary Instabilities ◽  
Good Agreement

The secondary instability of linear transient growth (TG) in Couette flow is explored theoretically, utilizing an analytical representation of the TG based on four modes and their nonlinear interactions. The evolution of the secondary disturbance is derived using the multiple time scales method. The theoretical predictions are compared with direct numerical simulations and very good agreement with respect to the growth of the disturbance energy and associated vortical structures is observed, up to the final stage just before the breakdown to turbulence. The theoretical model enables us to perform a full parametric study, including TG symmetry type, various wavenumbers, initial energy, TG nonlinearity and Reynolds number, to find all possible routes to transition and the optimal parameters for each type of the secondary disturbance. It is found that the most dangerous secondary disturbances are associated with spanwise wavenumbers which generate the strongest inflection points, i.e. those having maximal shear, rather than with those maximizing the energy gain during the TG phase.

High Performance Condition Monitoring of Aircraft Engines

2005 ◽  
Author(s):  
James P. Herzog ◽  
Jason Hanlin ◽  
Stephan W. Wegerich ◽  
Alan D. Wilks
Keyword(s):  
Real Time ◽  
Condition Monitoring ◽  
High Performance ◽  
Cost Savings ◽  
Aircraft Engine ◽  
Nonparametric Model ◽  
Normal System ◽  
High Fidelity ◽  
Aircraft Engines ◽  
Secondary Damage

A similarity-based modeling (SBM) technique is demonstrated that provides very early annunciation of the onset of gas path faults in aircraft engines. This powerful approach is shown to provide high fidelity estimates for real-time condition monitoring of aircraft engine signals. These estimates are used to detect the onset of changes in the inter-relationship between the various signals using a sophisticated set of built-in algorithms and tools. The ability of the SBM software to reliably detect subtle changes in signal behavior that are characteristic of a developing anomaly is coupled with a diagnostic rules engine to enable a rapid and robust fault recognition capability. The SBM software operates using a set of algorithms that construct a multivariate nonparametric model of the traditional monitoring sensors (pressure transducers, thermocouples, flow meters, etc.) present in the system. This model is used to generate real-time estimates of sensor values that represent normal system operation. A series of sophisticated tools compares these very high fidelity estimates to the actual sensor readings to detect discrepancies. Finally, a series of logic rules derived from a combination of engineering analysis and experience is applied to the output from the modeling engine in real-time to alert the user of developing serious conditions that need either immediate or planned maintenance attention. The software system provides a complete approach to asset monitoring that minimizes down time, maximizes availability, encodes (preserves) operator knowledge and lowers the overall costs associated with maintaining the assets. In this paper, we demonstrate the use of the similarity-based modeling approach for detecting faults in the gas path of aircraft engines. Some results from the monitoring of over 1,100 engines at a major commercial airline over a two-year period are described. Operationally, the early detection of developing engine faults has prevented delays and cancellations, and has contributed to a reduction in the airline’s in-flight shutdown rate. Financially, this approach has led to significant cost savings by the prevention of major secondary damage.

Optimal energy density growth in Hagen–Poiseuille flow

1994 ◽  
Vol 277 ◽  
pp. 197-225 ◽  
Author(s):  
Peter J. Schmid ◽  
Dan S. Henningson
Keyword(s):  
Energy Density ◽  
Linear Stability ◽  
Growth Mechanism ◽  
Transient Stability ◽  
Numerical Range ◽  
Finite Amplitude ◽  
Initial Energy ◽  
Transient Growth ◽  
Time Optimal ◽  
Optimal Disturbances

Linear stability of incompressible flow in a circular pipe is considered. Use is made of a vector function formulation involving the radial velocity and radial vorticity only. Asymptotic as well as transient stability are investigated using eigenvalues and ε-pseudoeigenvalues, respectively. Energy stability is probed by establishing a link to the numerical range of the linear stability operator. Substantial transient growth followed by exponential decay has been found and parameter studies revealed that the maximum amplification of initial energy density is experienced by disturbances with no streamwise dependence and azimuthal wavenumber n = 1. It has also been found that the maximum in energy scales with the Reynolds number squared, as for other shear flows. The flow field of the optimal disturbance, exploiting the transient growth mechanism maximally, has been determined and followed in time. Optimal disturbances are in general characterized by a strong shear layer in the centre of the pipe and their overall structure has been found not to change significantly as time evolves. The presented linear transient growth mechanism which has its origin in the non-normality of the linearized Navier–Stokes operator, may provide a viable process for triggering finite-amplitude effects.

Non-normality and internal flame dynamics in premixed flame–acoustic interaction

2011 ◽  
Vol 679 ◽  
pp. 315-342 ◽  
Author(s):  
PRIYA SUBRAMANIAN ◽  
R. I. SUJITH
Keyword(s):  
State Space ◽  
Flame Front ◽  
The State ◽  
Acoustic Energy ◽  
Premixed Flame ◽  
Linear Stability Theory ◽  
Transient Growth ◽  
Acoustic Interaction ◽  
Evolving System ◽  
Linearized Operator

This paper investigates the non-normal nature of premixed flame–acoustic interaction. The thermoacoustic system is modelled using the acoustic equations for momentum and energy, together with the equation for the evolution of the flame front obtained from the kinematicG-equation. As the unsteady heat addition acts as a volumetric source, the flame front is modelled as a distribution of monopole sources. Evolutions of the system are characterized with a measure of energy due to fluctuations. In addition to the acoustic energy, the energy due to fluctuations considered in the present paper accounts for the energy of the monopole sources. The linearized operator for this thermoacoustic system is non-normal, leading to non-orthogonality of its eigenvectors. Non-orthogonal eigenvectors can cause transient growth even when all the eigenvectors are decaying. Therefore, classical linear stability theory cannot predict the finite-time transient growth observed in non-normal systems. In the present model, the state space variables include the monopole source strengths in addition to the acoustic variables. Inclusion of these variables in the state space is essential to account for the transient growth due to non-normality. A parametric study of the variation in transient growth due to change in parameters such as flame location and flame angle is performed. In addition to projections along the acoustic variables of velocity and pressure, the optimal initial condition for the self-evolving system has significant projections along the strength of the monopole distribution. Comparison of linear and corresponding nonlinear evolutions highlights the role of transient growth in subcritical transition to instability. The notion of phase between acoustic pressure and heat release rate as an indicator of stability is examined.

scholarly journals Effects of aromatic on soot characteristics of aviation fuel surrogates in diffusion flames

2015 ◽  
Vol 18 (4) ◽  
pp. 55-64
Author(s):  
Thong Duc Hong ◽  
Osamu Fujita
Keyword(s):  
Diffusion Flames ◽  
Soot Formation ◽  
Linear Functions ◽  
Aviation Fuel ◽  
Light Extinction ◽  
Flame Height ◽  
Aircraft Engines ◽  
Mass Consumption ◽  
Function Of Two Variables ◽  
Fuel Surrogates

Co-annular smoke-free laminar diffusion wick-fed flames of dodecane and its blended with various amounts of propylbenzene of 10, 20, 25 vol.% have been used to study soot formation characteristics. Dodecane and propylbenzene are selected as the surrogates for paraffin class and aromatic class of aviation fuel. A light extinction method is adopted to determine the total soot volume (TSV) as a function of flame height (Hf) and fuel mass consumption rate (FMCR). An empirical model has been built to predict soot formation of dodecane and propylbenzene (Do/PB) mixtures as the function of two variables of FMCR and concentration of propylbenzenet (%PB). TSVs of Do/PB mixtures increase with increasing Hf, FMCR and %PB. The effect of Hf, FMCR and %PB on soot formation are respectively expressed as the quadratic, power law and linear functions. The result of current work creates a database for optimizing the trade-off impacts of aromatic in aviation fuel. This information is of high importance when blending aromatic to bioparaffins, which is produced from triglycerides and fatty acids in the vegetable by hydrotreating process, for using as a fuel in aircraft engines.

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