The Effect of Unsteady Stretch on Laminar Premixed Curved Flames

Laminar flamelets are often used to model premixed turbulent combustion. The libraries of rates of conversion from chemical to thermal enthalpies used for flamelets are typically based on counter-flow, strained laminar planar flames under steady conditions. The significance of transient strain has been discussed in the literature with most assertions being that their chemical time scales are sufficiently short compared to the turbulent time scales to treat them as quasi-steady. Less discussed is the unsteady motion of a curved flame front component of stretch rate. This thesis seeks further understanding of the effect of stretch rate on premixed flames by developing and validating a model for use with transient premixed laminar flame dynamics in a cylindrically-symmetric outward radial flow geometry (i.e., inwardly propagating flame). A FORTRAN code is developed and validated which models a laminar premixed flame exposed to an oscillating mass flowrate. This code solves transient equations of continuity, momentum, energy, and individual species in radial coordinates. In this model, flame response is studied when the flow and scalar fields remain aligned (i.e., no strain). The model is applied to conditions in which the flame expands (positive stretch) and contracts (negative stretch) radially by the addition of the externally-defined oscillating mass flow rate. The transient response of laminar premixed flames results in amplitude decrease and phase shift increase with increasing frequency. In order to implement the transient behaviour of flamelets in turbulent modelling more efficiently, a frequency response analysis is applied as a process characterization tool to simplify the complex non-linear behaviour using flame transfer functions. It is shown that with increasing frequency of the perturbation, when equivalence ratio is kept constant, or with decreasing equivalence ratio in the same frequency, non-linear behaviour of the flame becomes prominent. Therefore, linear models can only predict the flame behaviour with accuracy below the threshold of when the fluid and chemistry time scales are the same order of magnitude. Various nonlinear models are studied in order to find the most appropriate flame transfer function for higher frequencies to extend the predictive capabilities of these models.