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

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

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

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

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

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

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

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 190.8 Hz N. K. Mukherjee, Marie Curie ESR

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

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

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

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

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

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

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

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

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

Thank you for your attention!!