Response of Rod Stabilized Flames to Harmonic Excitation:

The objective of this research is to understand the dynamics of acoustically forced, bluff body flames. Particular attention is focused on the interaction of the flame with the separated shear layer of the bluff body. It is shown that the amplitude of flame front oscillations grows spatially downstream for approximately three convective wavelengths, λc (given by Uo/f, denoting the free stream velocity and forcing frequency, respectively), then reaches a maximum and decays. This flame response depends upon two key processes: the excitation of the flame by shear layer instabilities that are initiated by the acoustic forcing, and the kinematic response of the flame to this forcing. It is suggested that the flame excitation can be parametrized by Stθ, the Strouhal number based on the momentum thickness of the shear layer. In turn, kinematic processes are responsible for the basic shape of the flame response. In the bluff body nearfield, the flame response grows with downstream distance due to the flame anchoring “boundary condition”, which prevents significant flame movement near the flame base. Farther downstream, the flame response reaches a maximum and then decays due to the action of flame propagation normal to itself, which acts to smooth out the wrinkles generated by the harmonic flow forcing. Nomenclature d = Bluff body diameter f = Frequency of excitation fK = von-Karman shedding frequency fSL = Natural frequency of the shear layer instabilities G = a scalar denoting interface between reactants and products L ’ = Amplitude of flame front fluctuation at the frequency of excitation p = Pressure Red = Reynolds number based on bluff body diameter and mean velocity SL = laminar flame speed Std = Strouhal number based on bluff body diameter and mean velocity Stθ = Strouhal number based on the momentum thickness of the shear layer t = time u = velocity field Uo = Mean Velocity Us = Velocity at the point in the flow-field prior to rollu