1. Nalini Kanta Mukherjee Keele University
Analysis of instability frequencies
in laminar combustors
Nalini Kanta Mukherjee Keele University
TANGO project meeting at Ansaldo Energia, Genova, Italy
14-18 Sep 2015

2. Outline of presentation
Experimental observation of instability frequencies
1-D Mathematical model
Bifurcation diagrams
N. K. Mukherjee, Marie Curie ESR

3. Objective of current work
Schematic of the
experimental setup
N. K. Mukherjee, Marie Curie ESR

4. Experimental observation: Instability frequency vs. flame location
Instability frequency decreases as the flame moves down
N. K. Mukherjee, Marie Curie ESR

5. 1-D acoustic model of combustor
Temperature jump takes place
across this plane
N. K. Mukherjee, Marie Curie ESR

6. Instability frequency vs
Instability frequency vs. flame location (prediction by mathematical model)
Predicted frequencies are much higher than experimental observation
This trend is exactly opposite to experimental observation
N. K. Mukherjee, Marie Curie ESR

7. Inclusion of heat release in mathematical model
Heat release rate
is introduced at 𝒙= 𝒙 𝟏
𝑸 is predicted by linear 𝒏−𝝉 law
N. K. Mukherjee, Marie Curie ESR

8. Instability frequency calculation
Pressure balance at 𝒙= 𝒙 𝟏
𝑝 1 𝑥 = 𝑝 2 𝑥 = 𝑝 3 𝑥
Acoustic mass velocity balance at 𝒙= 𝒙 𝟏
𝜌 1 𝑆 1 𝑢 1 𝑥 + 𝛾−1 𝑐 2 𝑄= 𝜌 2 𝑆 2 𝑢 2 𝑥 + 𝜌 3 𝑆 3 𝑢 3 𝑥
Case Study:
The calculated modal frequency at 𝑥 𝑓 =52cm is 190 Hz
The experimentally measured instability frequency was Hz
N. K. Mukherjee, Marie Curie ESR

9. Contd..
Inclusion of heat release in 1-D model improves the accuracy of prediction of instability frequency
Can heat release rate explain the decreasing trend of frequency?
N. K. Mukherjee, Marie Curie ESR

10. Simplified 1-D acoustic model
𝑯𝒆𝒂𝒕 𝒓𝒆𝒍𝒆𝒂𝒔𝒆 𝒓𝒂𝒕𝒆, 𝑸=𝒏𝒖(𝒕−𝝉
𝒏=interaction index,
𝝉=time lag
N. K. Mukherjee, Marie Curie ESR

11. Bifurcation diagram (modal frequency vs. time lag)
4 modes
11 modes
N. K. Mukherjee, Marie Curie ESR

12. Bifurcation diagram (modal frequency vs. interaction index)
mode 2
mode 1
N. K. Mukherjee, Marie Curie ESR

13. Parametric study Identify the effect of Boundary condition Area jump
N. K. Mukherjee, Marie Curie ESR

14. Bifurcation diagram (for open-open boundary condition)
5 modes
13 modes
N. K. Mukherjee, Marie Curie ESR

15. Bifurcation diagram (modal frequency vs. area jump)
8 modes
6 modes
N. K. Mukherjee, Marie Curie ESR

16. Conclusions Heat release rate can alter modal frequencies
Heat release rate can introduce new modes
This effect can be accentuated by area contraction and change of boundary conditions
N. K. Mukherjee, Marie Curie ESR

17. Scope of future work Understanding modal stability
Heat transfer analysis of the setup
N. K. Mukherjee, Marie Curie ESR

18. Thank you for your attention!!