Research on non-normality that could beready 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

airflow

unstable periodic solution

stable periodic solution

stable periodic solution

unstable periodic solutionstable fixed point

(non-dimensional wire temperature)

AcousticEnergy

Our model of a Rijke tube (from Heckl) has a subcritical bifurcation to a stable periodic solution

Acousticenergy

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

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

H2/N2 (30:70) in air CH4 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

H2/N2 (40:60) in air H2/N2 (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 theresubstantial 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 predictedperturbations that develop.

Can measurements of ‘gain’ be made quantitatively?

What are the best measurements to be made? In particular are there relatively lowRe experiments where transient phenomena can be observed?

What should the norm be in density-stratified flows?