Research on non-normality that could be ready for experiments... - Transient growth in thermoacoustics - Sensitivity analyses in hot jets and flames Matthew Juniper, Larry Li, Gary Chandler Department of Engineering

Triggering in the Rijke tube Transient growth in thermoacoustics

Non-normal triggering in thermoacoustics Model of the Rijke tube hot wire air flow unstable periodic solution stable periodic solution unstable periodic solution stable fixed point (non-dimensional wire temperature) Acoustic Energy Our model of a Rijke tube (from Heckl) has a subcritical bifurcation to a stable periodic solution

Acoustic energy Pressure We predict that low amplitude noise will be able to trigger high amplitude stable oscillations by first triggering low amplitude unstable oscillations.

There is some experimental evidence for this (but we would like more).

Sensitivity analysis in hot jets and flames... inspired by sensitivity analyses in uniform density wake flows

Low density jets are unstable (similar to uniform density wakes)

air helium air helium air The receptivity to external forcing* The sensitivity to internal feedback* Receptivity and sensitivity of a helium jet* * Chandler and Juniper (2010) We have mapped out the receptivity and sensitivity of model flows with non-uniform density Gary Chandler’s low Mach number code (planar or axisymmetric base flow, 2D perturbation)

We have mapped out the receptivity and sensitivity of a lifted flame sensitivity to internal feedback

H 2 /N 2 (30:70) in airCH4 flame in air The local stability properties of flames can be tuned by varying the position of the flame (density profile) relative to the shear layer. Forcing of self-excited round jet diffusion flames H 2 /N 2 (40:60) in airH 2 /N 2 (80:20) in air

Questions from Colm Caulfield Experiments have often identified the observed wavelength of a perturbation with ‘the most unstable mode of linear theory’. What about situations where there substantial transient growth is possible? Experiments often have an obvious finite residence time or dimension. Can flows be identified where this will make a non-trivial difference to the predicted perturbations that develop. Can measurements of ‘gain’ be made quantitatively? What are the best measurements to be made? In particular are there relatively low Re experiments where transient phenomena can be observed? What should the norm be in density-stratified flows?