Research on non-normality that could be ready for experiments... - Transient growth in...
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![Page 1: Research on non-normality that could be ready for experiments... - Transient growth in thermoacoustics - Sensitivity analyses in hot jets and flames Matthew.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649d4e5503460f94a2dc8e/html5/thumbnails/1.jpg)
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
![Page 2: Research on non-normality that could be ready for experiments... - Transient growth in thermoacoustics - Sensitivity analyses in hot jets and flames Matthew.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649d4e5503460f94a2dc8e/html5/thumbnails/2.jpg)
Triggering in the Rijke tube
Transient growth in thermoacoustics
![Page 3: Research on non-normality that could be ready for experiments... - Transient growth in thermoacoustics - Sensitivity analyses in hot jets and flames Matthew.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649d4e5503460f94a2dc8e/html5/thumbnails/3.jpg)
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
![Page 4: Research on non-normality that could be ready for experiments... - Transient growth in thermoacoustics - Sensitivity analyses in hot jets and flames Matthew.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649d4e5503460f94a2dc8e/html5/thumbnails/4.jpg)
Acousticenergy
Pressure
We predict that low amplitude noise will be able to trigger high amplitude stable oscillations by first triggering low amplitude unstable oscillations.
![Page 5: Research on non-normality that could be ready for experiments... - Transient growth in thermoacoustics - Sensitivity analyses in hot jets and flames Matthew.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649d4e5503460f94a2dc8e/html5/thumbnails/5.jpg)
There is some experimental evidence for this (but we would like more).
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Sensitivity analysis in hot jets and flames
... inspired by sensitivity analyses in uniform density wake flows
![Page 7: Research on non-normality that could be ready for experiments... - Transient growth in thermoacoustics - Sensitivity analyses in hot jets and flames Matthew.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649d4e5503460f94a2dc8e/html5/thumbnails/7.jpg)
Low density jets are unstable (similar to uniform density wakes)
![Page 8: Research on non-normality that could be ready for experiments... - Transient growth in thermoacoustics - Sensitivity analyses in hot jets and flames Matthew.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649d4e5503460f94a2dc8e/html5/thumbnails/8.jpg)
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)
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We have mapped out the receptivity and sensitivity of a lifted flame
sensitivity to internal feedback
![Page 10: Research on non-normality that could be ready for experiments... - Transient growth in thermoacoustics - Sensitivity analyses in hot jets and flames Matthew.](https://reader036.fdocuments.in/reader036/viewer/2022062516/56649d4e5503460f94a2dc8e/html5/thumbnails/10.jpg)
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
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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?