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, stained laminar planar flames under steady conditions. The current research seeks further understanding of the effect of stretch on premixed flames by considering laminar flame dynamics in a cylindrically-symmetric outward radial flow geometry (i.e., inwardly propagating flame). This numerical model was designed to study the flame response when the flow and scalar fields align (i.e., no tangential strain on the flame) while the flame either expands (positive stretch) or contracts (negative stretch, which is a case that has been seldom explored) radially. The transient response of a laminar premixed flame has been investigated by applying a sinusoidal variation of mass flow rate at the inlet boundary with different frequencies to compare key characteristics of a steady unstretched flame to the dynamics of an unsteady stretched flame. An energy index (EI), which is the integration of the source term in the energy equation over all control volumes in the computational domain, was selected for the comparison. The transient response of laminar premixed flames, when subjected to positive and negative stretch, results in amplitude decrease and phase shift increase with increasing frequency. Other characteristics, such as the deviation of the EI at the mean mass flow rate between when the flame is expanding and contracting, are nonmonotonic with frequency. Also, the response of fuel lean flames is more sensitive to the frequency of the periodic stretching compared to a stoichiometric flame. An analysis to seek universality of transient flame responses across lean methane-air flames of different equivalence ratios (i.e., 1.0 to 0.7) using Damköhler Numbers (i.e., the ratio of a flow to chemical time scales) had limited success.
The stretched laminar flame model provides a convenient approach to embed realistic chemical kinetics when simulating turbulent premixed flames. When positive-only periodic strain rates are applied to a laminar flame there is a notable phase lag and diminished amplitude in heat release rate. Similar results have being observed with respect to the other component of stretch rate, namely the unsteady motion of a curved flame when the stretch rates are periodic about zero. Both cases showed that the heat release rate or consumption speed of these laminar-premixed flames vary significantly from the quasi-steady flamelet model. Deviation from quasi-steady behaviour increases as the unsteady flow time scale approaches the chemical time scale that is set by the stoichiometry. A challenge remains in how to use such results predictively for local and instantaneous consumption speed for small segments of turbulent flames where their unsteady stretch history is not periodic. This paper uses a frequency response analysis as a characterization tool to simplify the complex nonlinear behaviour of premixed methane air flames for equivalence ratios from 1.0 down to 0.7, and frequencies from quasi-steady up to 2000 Hz using flame transfer functions. Various linear and nonlinear models were used to identify appropriate flame transfer functions for low and higher frequency regimes, as well as extend the predictive capabilities of these models. Linear models were only able to accurately predict the flame behaviour below a threshold of when the fluid and chemistry time scales are the same order of magnitude. Other proposed transfer functions were tested against arbitrary multi-frequency stretch inputs and were shown to be effective over the full range of frequencies.
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, stained laminar planar flames under steady conditions. The current research seeks further understanding of the effect of stretch on premixed flames by considering laminar flame dynamics in a cylindrically-symmetric outward radial flow geometry (i.e., inwardly propagating flame). This numerical model was designed to study the flame response when the flow and scalar fields align (i.e., no tangential strain on the flame) while the flame either expands (positive stretch) or contracts (negative stretch, which is a case that has been seldom explored) radially. The transient response of a laminar premixed flame has been investigated by applying a sinusoidal variation of mass flow rate at the inlet boundary with different frequencies to compare key characteristics of a steady unstretched flame to the dynamics of an unsteady stretched flame. An energy index (EI), which is the integration of the source term in the energy equation over all control volumes in the computational domain, was selected for the comparison. The transient response of laminar premixed flames, when subjected to positive and negative stretch, results in amplitude decrease and phase shift increase with increasing frequency. Other characteristics, such as the deviation of the EI at the mean mass flow rate between when the flame is expanding and contracting, are nonmonotonic with frequency. Also, the response of fuel lean flames is more sensitive to the frequency of the periodic stretching compared to a stoichiometric flame. An analysis to seek universality of transient flame responses across lean methane-air flames of different equivalence ratios (i.e., 1.0 to 0.7) using Damköhler Numbers (i.e., the ratio of a flow to chemical time scales) had limited success.
The stretched laminar flame model provides a convenient approach to embed realistic chemical kinetics when simulating turbulent premixed flames. When positiveonly periodic strain rates are applied to a laminar flame there is a notable phase lag and diminished amplitude in heat release rate. Similar results have been observed with respect to the other component of stretch rate, namely the unsteady motion of a curved flame front when the stretch rates are periodic about zero. Both cases showed that the heat release rate or consumption speed of these laminar premixed flames can vary significantly from the quasi-steady flamelet model. Deviation from quasi-steady behaviour increases for conditions further from stoichiometric such that unsteady time scales of the flow are of the same magnitude as the chemistry. A challenge remains in how to use such results predictively for local and instantaneous consumption speed for small segments of turbulent flames where their stretch history is not periodic. This paper uses a frequency response analysis as a characterization tool to simplify the complex non-linear behaviour of premixed methane air flames for equivalence ratios from 1.0 down to 0.7, and frequencies from quasi-steady up to 2000 Hz using flame transfer functions. Various linear and nonlinear models were studied to identify appropriate flame transfer functions for low and higher frequency regimes, as well as to extend the predictive capabilities of these models. Linear models were only able to accurately predict the flame behaviour below a threshold of when the fluid and chemistry time scales are the same order of magnitude.
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