Study of 2D slot stabilized flame for unperturbed and perturbed equivalence ratio

Flame speed is sensitive to both the strain rate and the curvature of the flame surface. Slot-stabilized flames have curvature and strain rate variation along the flame surface. Hence, we investigate the variation of the flame speed with these two parameters for a steady, unperturbed slot-stabilized flame.

Local quenching of reactions on the flame surface is a significant concern in lean combustion devices, directly related to the net heat release rate and the overall performance of the system. A steady flammability limit-based extinction criterion is more restrictive and demands an unnecessarily high equivalence ratio (Sankaran & Im, 2002). (Sankaran & Im, 2002) have suggested the concept of dynamic flammability limit, to include the effect of flow time scale(strain rate) and equivalence ratio perturbation on flammability limit.

(Bansal & Im, 2007) have extended the concept of dynamic flammability limit. They have studied counterflow premixed flame configuration subjected to various strain rates and have successfully incorporated various time scales in combustion to make extinction criteria more generalized. They also have proposed a Dynamic Flammability Limit Extension (DFLE) as a function of non-dimensional frequency ($\eta$). (Bansal & Im, 2007)’s work is mainly focused on counterflow configuration. Here, we study the applicability of this extinction criterion to a 2D slot-stabilized flame.

Case setup

The fluid domain configuration is illustrated in the following figure, along with the initial conditions for various flow variables.

The no-slip boundary condition is applied at the wall, and the non-reflecting boundary condition is applied at the outlet. The computational domain is decomposed onto a multiblock structured grid with 2.4 million grid points and 965 blocks.

Steady state

The steady-state solution is obtained for an equivalence ratio of $\phi=0.6$. Some of the steady-state flow variables are illustrated in the following figures.

The velocity field is overlaid on the temperature field.

Flame speed $S_L$ as a function of curvature $C$ and strain rate $\kappa$ over the flame.

Analyzed the flame speed $S_L$, flame curvature $C$, and strain rate $\kappa$ at 350 K contour for steady state, i.e., without equivalence ratio perturbation.

The sensitivity of flame speed to strain rate, i.e., the Markstein length $L_u$, is shown in the left figure. In the right figure, $L_u$ is marked with a red asterisk and is close to the linearly extrapolated Markstein length.

Furthermore, we found that Markstein’s length is in close agreement with the experimental study by (Varea et al., 2012), as shown in the above figure.

Perturbed Cases

We study the behaviour of the flame under the equivalence ratio perturbation and with three normalized perturbation amplitudes ϵ = 0.05, 0.2, 0.4.

(a)

(b)

(c)

(d)

Deviation of equivalance ratio $\phi$ from dynamic flammability limit $\phi_t$ i.e. ($\phi-\phi_t$), temperature(K), hear release rate contours and velocity vector field for different phase angles at inlet (a) $0^{\circ}$, (b) $90^{\circ}$, (c) $180^{\circ}$, (d) $270^{\circ}$ ($\bar{\phi}=0.6$, $\epsilon=0.4$, $f=60Hz$).

In the analysis for the perturbed case, each case is plotted with the normalized minimum equivalence ratio extension below the steady flammability limit and the normalized frequency to locate the case in either the flammable or non-flammable region. The case with ϵ = 0.05 lies in the flammable region, where ϵ = 0.2 and 0.4 lie in the non-flammable region. But no extinction is found in any of the cases. To understand this flame behavior, the combined effect of strain rate and curvature on the flammability limit needs to be considered, which can be explored as future work.

ME Thesis

References

2012

Measurement of laminar burning velocity and Markstein length relative to fresh gases using a new postprocessing procedure: Application to laminar spherical flames for methane, ethanol and isooctane/air mixtures

Emilien Varea, Vincent Modica, Alexis Vandel, and 1 more author

Combustion and Flame, 2012

Abs DOI

The purpose of this study is to present a new tool for extracting the laminar burning velocity in the case of spherically outward expanding flames. This new procedure makes it possible to determine the laminar burning velocity directly based on the flame displacement speed and the global fresh gas velocity near the preheat zone of the flame front. It therefore presents a very interesting alternative to the standard method (commonly used in the literature), which is based on the flame front displacement and the ratio of unburned and burned gas densities. The influence of external flame stretching on the burning velocity can be characterized and the Markstein length relative to the unburned gases (i.e., fresh gases) can be deduced by using this new tool. Contrary to the standard procedure, the unstretched laminar burning velocity is determined directly without using the fuel mixture properties. The temporal evolution of the flame front is visualized by high-speed laser tomography and the algorithm, based on a tomographic image correlation method, makes it possible to accurately measure the fresh gas velocity near the preheat zone of the flame front. The measurements of laminar flame speeds are carried out in a high-pressure and high-temperature constant-volume vessel over a wide range of equivalence ratios for methane, ethanol, and isooctane/air mixtures. To validate the experimental facility and the postprocessing of the flame images, fresh gas velocities and unstretched laminar burning velocities, as well as Markstein lengths relative to burned and unburned gases, are presented and compared with experimental and numerical results of the literature for methane/air flames. New results concerning ethanol/air and isooctane/air flames are presented for various experimental conditions (373K, equivalence ratios range 0.7–1.5, pressure range 0.1–5MPa).

2007

Time scales in unsteady premixed flame extinction with composition fluctuations

Gaurav Bansal and Hong G. Im

Combustion and Flame, 2007

DOI

2002

Dynamic flammability limits of methane/air premixed flames with mixture composition fluctuations

Ramanan Sankaran and Hong G. Im

Proceedings of the Combustion Institute, 2002

Proceedings of the Combustion Institute

Abs DOI

As a fundamental study in the application to direct-injection spark-ignition engines or gas turbines, in which mixture stratification and partial quenching are of serious concerns, unsteady premixed methane/ air flames subjected to time-varying composition fluctuations are investigated computationally. The code OPUS employs an unsteady opposed-flow combustion configuration, including detailed chemical kinetics, transport, and radiation models, using an adaptive time integration method for a stiff system of differential-algebraic equations with a high index. The primary issue of the study is to establish the concept of the dynamic flammability limit, defined as the minimum equivalence ratio above which the unsteady flame can sustain combustion. For the weak and strong strain rate cases studied, it is observed that the dynamic flammability limit depends on the mean and frequency of the composition fluctuation. The parametric study demonstrated that the flammability limit of an unsteady premixed flame is further extended to a leaner condition as the frequency or mean equivalence ratio fluctuation increases. It is also found that, under all conditions, the mean equivalence ratio and the minimum flame temperature must be higher than those at the steady flammability limit to sustain combustion. It is further shown that the dynamic flammability limit is primarily determined by the instantaneous, branching-termination balance at the reaction zone. The behavior of the flame response attenuation with increasing frequency is found to scale properly using the normalized frequency based on the imposed flow strain rate, which represents the characteristic time scale of the transport process within the flame.