Unsteady Strained Premixed Laminar Flames

Abstract

The transient response of laminar flames to strain is studied numerically using a simplifying transformation not previously applied to these problems. Two time scales were found to characterize the flame response during straining. For slow strain. a slow time scale associated with the preheat zone dominates. For high strain. a fast time scale related to the reaction zone is important. The cross-over between these time scales is a function of the activation energy and occurs when the reaction zone thickness is a significant fraction of the total flame thickness. The overall time constant of the flame varies with the Darnkohler number to the 0.7 power. During relaxation from the strained state, the flame responds in a more self-similar manner and a single time constant suffices to describe its behaviour. The implications of these results for flarnelet models based on the local strain rate are that flame response time and history effects should be included. A, jJ. c p Pre-exponential factor, viscosity, specific heat at constant pressure (dimensional) B Metric in first transformation c Passive scalar c Ration of strain rates in the plane of the flame Da Damk6hler number SL Laminar flame speed (dimensional) SSTRAIN Strained flame speed Sa' s, Exponential fits to SSTRAIN S. r; Applied strain rate tensor and components t, Xi Time and space variables .t' Time and space variable in first transformation I, t1

A computational study of Saffman-Taylor instability in premixed flames

“…Calculations for a range of wave numbers, for both the constant and variable viscosity models, have been compiled to yield the growth rate versus wave number plot as shown in figures 5(a) and (b). The earlier results by Rutland et al [21] are also plotted for comparison and show good agreement with the constant viscosity model used in this paper. In figure 5(a), the two viscosity models result in a qualitatively similar trend, in that the destabilizing (positive growth rate) effect at low wave numbers due to the D-L mechanism is suppressed by the stabilizing effect of the D-T mode (negative growth rate) at higher wave numbers.…”

“…The length and timescales are normalized by the reference values shown in table 1. The constant viscosity model (µ = µ 0 ), as was given by Rutland et al [21], is plotted as a comparison. With the variable viscosity model, the actual flame thickness based on the temperature gradient is found to be larger than that with constant viscosity at the upstream temperature.…”

“…Rutland et al [21] applied this approach to reproduce the growth rate versus wave number curves to validate the linear analysis results in a more realistic situation. Kadowaki [22] also investigated the lateral movements of cellular flames with gravity effects using direct simulations.…”

A Semi-implicit Numerical Scheme for Reacting Flow

“…The projection scheme was originally developed by Chorin [65] for the incompressible NavierStokes equations. Recently, several variants have been proposed for variable-density (e.g., [66,67] and reacting flows (e.g., [68][69][70][71]). The present formulation is adapted from our previous effort in [4].…”

“…We consider the interaction of the above premixed methane-air flame with a counter-rotating 2D vortex pair. This is a typical flow that has been investigated both numerically [77,69,78,79,73,80] and experimentally [81][82][83][84][85][86], and serves as a useful test problem.…”