Bifurcation analysis of steady states and limit cycles in a thermal pulse combustor model

Abstract

Oscillatory behaviour of state variables is desirable in pulse combustors, as properly designed pulsations lead to improved performances, such as higher thermal efficiency and lower emissions compared to steady combustors. In the present work, we perform a systematic investigation of the stability of steady states and limit cycles of a pulse combustor model through numerical continuation. Different bifurcation parameters such as tailpipe friction factor, wall temperature, convective heat transfer coefficient, inlet temperature and inlet fuel mass fraction are varied to identify the complete ranges of those parameters at which limit cycles can be expected. This analysis identifies alternative stable periodic regimes in parameter space (e.g. friction factor). In addition, a few performance indicators such as amplitude of oscillations, cycle-averaged heat transfer and cycle-averaged specific thrust are compared between different ranges of friction factor yielding limit cycle oscillations. The comparison clearly shows that, depending upon the application, friction factor can be chosen from different regimes. The time-integration of the model is also performed to support the bifurcation results obtained from numerical continuation, wherever appropriate. The complete stability margin of limit cycle oscillations for those bifurcation parameters can be useful for improved design of the combustor and for determining the optimal operating conditions of pulse combustors.