**5. Conclusion**

The lean premixed combustion allows for reducing the production of thermal NOx, therefore it is largely used in stationary gas turbines and for other industrial combustion. Lean premixed combustors are, however, prone to combustion instabilities with both low and high frequencies. For the prediction of the stability of technical combustion systems the knowledge of the periodic-non-stationary mixing and reacting behaviour of the applied flame type and a quantitative description of the resonance characteristics of the gas volumes in the combustion chamber is conclusively needed.

200 Advanced Fluid Dynamics

external excitation e.g. compressor or other incoming disturbances from ambient or even periodic flow instabilities depending on the design of the burner. Thus the flame is also pulsating. The amplitude of this pulsation will be amplified to the limit cycle if the time lag of the flame changed so that the pressure fluctuation and the heat release fluctuation meet

Fig. 13. Frequency spectrum of the outlet mass flow rate of the coupled resonators

latter calculation can provide the damping ratio for the analytical model.

investigation of combustion instabilities is essential.

in the combustion chamber is conclusively needed.

The results of the earlier investigations show that the pulsation and the high shear in the resonator neck produce highly anisotropic swirled flow. Therefore it is unlikely that a URANS simulation can render such flow reliably. Furthermore if the turbulence is modelled statistically, it cannot excite the flow in the combustion chamber. The use of LES for the

For the analytical model the eigenfrequency of the system is an important input parameter. If the geometry is rather simple the undamped Helmholtz resonator model can be used. Further important achievement of the present computations is that the eigenfrequency of the system with geometry of high complexity can be predicted without an additional modal analysis. The calculation with constant mass flow rate is a preparation for the investigation with excitation at the inlet. As the amplitude of the excitation is not well defined in the former case only the

The lean premixed combustion allows for reducing the production of thermal NOx, therefore it is largely used in stationary gas turbines and for other industrial combustion. Lean premixed combustors are, however, prone to combustion instabilities with both low and high frequencies. For the prediction of the stability of technical combustion systems the knowledge of the periodic-non-stationary mixing and reacting behaviour of the applied flame type and a quantitative description of the resonance characteristics of the gas volumes

the Rayleigh criterion.

**5. Conclusion** 

In this chapter the numerical investigation of the non-reacting flow in a Helmholtz resonator-type model combustion chamber and in a coupled system of burner and combustion chamber is presented briefly. The work was a part of series of investigations to determine the stability limits of combustion systems. The resonance characteristics of the combustion systems were calculated using Large Eddy Simulation. The results are in good agreement with the experimental data and a reduced physical model, which was developed to describe the resonant behaviour of a damped Helmholtz resonator-type combustion chamber (Büchner, 2001).

The solution of the fully compressible Navier-Stokes equations was essential to capture the physical response of the pulsation amplification, which is mainly the compressibility of the gas volume in the chamber. Viscous effects play a crucial role in the oscillating boundary layer in the neck of the Helmholtz resonator and, hereby, in the damping of the pulsation. The pulsation and the high shear in the resonator neck produce highly anisotropic turbulent flow. Therefore it is improbable that an URANS simulation can render such flow reliably.

The investigation of the case without external excitation showed that the frequency spectrum of the mass flow rate signal at the outlet of the exhaust gas pipe provides a peak at the eigenfrequency of the combustion chamber. The only possible forcing of this pulsation was the turbulent fluctuations generated by the jet in the combustion chamber. The broadband excitation of the turbulent flow can be amplified by the flame and can produce a broadband background heat release rate oscillation as detected also in (Yi & Gutmark, 2008). If the eigenfrequency of the combustion chamber or other vibratory component is in the range of the frequencies of the energetic turbulent eddies a dominant pulsation can occur. The amplitude of this pulsation will be amplified to the limit cycle if the time lag of the flame changed so that the pressure fluctuation and the heat release fluctuation meet the Rayleigh criterion. If the turbulence is modelled statistically (URANS), it cannot excite the flow in the combustion chamber. The use of LES for the investigation of combustion instabilities is essential.
