To increase the pulse combustor load, a higher amount of fuel-air mixture has to be supplied. This increases the flow rate or equivalently, the flow time is reduced. However, an increase in flow rate leads to an early extinction. This implies that obtaining pulsating combustion is difficult at higher loads. The objective of the present work is to explore the possibility of extending the regime of pulsating combustion at higher flow rates by preheating and diluting the reactants. In this work, the effects of preheating and dilution are examined by varying the inlet temperature and inlet fuel mass fraction. Varying these parameters, a map, presenting regime of pulsating combustion from steady combustion to extinction for each value of flow time considered, has been made. Lastly, Hopf bifurcation points of the system have been investigated by determining the eigenvalues of Jacobian matrix of the coupled non-linear system at the fixed point using a specialised package for bifurcation analysis, MATCONT. It has been found that at higher load, pulsating combustion can be achieved at higher inlet temperature and lower inlet fuel mass fraction. Comparing the Hopf points with mapping, it is found that existence of Hopf bifurcation agrees with the birth and death of pulsating combustion. The results indicate that altering the mixture condition at the inlet can be used for controlling chaos and stabilising periodic solutions in thermal pulse combustors and thus increase the range of pulsating combustion to higher power regimes.
Nomenclature
ACombustor surface area (m 2 ) A e Combustor cross-sectional area (m 2 ) BPre-exponential factor (s −1 ) C p Specific heat at constant pressure (J/kgK)1 First characteristic length (V/A) L c,2 Second characteristic length (V/A e ) L TP Length of tailpipe (m) m i Mass flow rate at combustor inlet (kg/s) * Downloaded by [University of Tennessee, Knoxville] at 08:55 22 December 2014 60 S. Mondal et al. m e Mass flow rate at combustor exit (kg/s) PPressure (Pa) P 0 Ambient pressure (Pa) P p/p 0 (dimensionless) p e Pressure in tailpipe (bar) P e p e /p 0 (dimensionless) T Temperature (K) T a Activation temperature (K)Fuel mass fraction (dimensionless) y fi Inlet fuel mass fraction (dimensionless)Ratio of specific heats (dimensionless) κ P Planck mean absorption coefficient ρ 0 Ambient density (kg/m 3 ) σStefan-Boltzmann constant (W/m 2 K 4 ) τ c Characteristic flow time (s) τ f Characteristic heat transfer time (s) τ h Characteristic chemical reaction time (s) ω f Fuel consumption rate (kg/m 3 s)
IntroductionPulse combustors are known to have high thermal efficiency, high heat transfer rates and lower pollutant emission than steady flow combustors. These differences from steady state combustors are generally attributed to the self-sustained oscillations, which are caused by the strong coupling between the combustor dynamics and the flow in the tailpipe (cf. Figure 1). Keller and Hongo [1] showed that lower NO x production was due to reduced residence time at peak temperature, caused by mixing ...