Non-orthogonality and Transient Growth Analysis of a Premixed Flame-Acoustic Interaction in a Choked Combustor

2014 ◽  
Author(s):  
Dan Zhao ◽  
Chenzhen Ji ◽  
Shihuai Li ◽  
Xinyan Li
Keyword(s):  
Growth Analysis ◽  
Premixed Flame ◽  
Transient Growth ◽  
Acoustic Interaction

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.

Transient growth analysis of flow through a sudden expansion in a circular pipe

2010 ◽  
Vol 22 (3) ◽  
pp. 034101 ◽  
Author(s):  
C. D. Cantwell ◽  
D. Barkley ◽  
H. M. Blackburn
Keyword(s):  
Growth Analysis ◽  
Circular Pipe ◽  
Sudden Expansion ◽  
Transient Growth ◽  
Flow Through

scholarly journals Transient growth analysis of oblique shock-wave/boundary-layer interactions at Mach 5.92

2020 ◽  
Vol 5 (6) ◽  
Author(s):  
Anubhav Dwivedi ◽  
Nathaniel Hildebrand ◽  
Joseph W. Nichols ◽  
Graham V. Candler ◽  
Mihailo R. Jovanović
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Growth Analysis ◽  
Oblique Shock ◽  
Oblique Shock Wave ◽  
Transient Growth ◽  
Wave Boundary Layer ◽  
Wave Boundary

Convective instability in steady stenotic flow: optimal transient growth and experimental observation

2010 ◽  
Vol 655 ◽  
pp. 504-514 ◽  
Author(s):  
M. D. GRIFFITH ◽  
M. C. THOMPSON ◽  
T. LEWEKE ◽  
K. HOURIGAN
Keyword(s):  
Experimental Observation ◽  
Convective Instability ◽  
Growth Analysis ◽  
Optimal Growth ◽  
Reynolds Numbers ◽  
Bypass Transition ◽  
Transient Growth ◽  
Shear Layer Instability ◽  
Chaotic Region ◽  
Flow Through

An optimal transient growth analysis is compared with experimental observation for the steady flow through an abrupt, axisymmetric stenosis of varying stenosis degree. Across the stenosis range, a localized sinuous convective shear-layer instability type is predicted to dominate. A comparison of the shape and development of the optimal modes is made with experimental dye visualizations. The presence of the same sinuous-type disturbance immediately upstream of the highly chaotic region observed in the experimental flow is consistent with the optimal growth predictions. This, together with the fact that the flow is unstable globally only at much higher Reynolds numbers, suggests bypass transition.

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.

Global Transient-Growth Analysis of Hypersonic Flow on the HIFiRE-5 Elliptic Cone Model

2019 ◽  
Author(s):  
Helio Ricardo Quintanilha Junior ◽  
Vassilis Theofilis ◽  
Ardeshir Hanifi
Keyword(s):  
Hypersonic Flow ◽  
Growth Analysis ◽  
Transient Growth ◽  
Cone Model ◽  
Elliptic Cone
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