Moderate or Intense Low-oxygen Dilution (MILD) combustion has potential to achieve both high energy efficiency and ultra-low emissions. This analysis adopts the critical point theory to characterise the Flame-Self Interaction (FSI) events and flow topologies in turbulent, homogeneous mixture, n-Heptane MILD combustion using Direct Numerical Simulations (DNS) with reduced chemical mechanism. The local flame geometry has also been categorised using the mean and Gauss curvatures. It was found that the Tunnel Formation (TF) and Tunnel Closure (TC) topologies are the most probable FSI events at all values of the reaction progress variable c, while the Unburned Pocket (UP) and Burned Pocket (BP) topologies were mostly present towards the unburned and burned mixtures of the flame, respectively. Moreover, increasing the turbulence intensity did not result in any significant changes in the distribution of FSI events. Investigation of the flow topology distribution showed that the features associated with non-zero dilatation rate did not exist in the MILD cases considered. This is a consequence of the negligible thermal expansion effect due to the small temperature rise in MILD combustion cases. Increasing the dilution factor caused a reduction in the frequency of FSI events for all c levels. The distributions of flame self-interaction events in homogeneous mixture MILD combustion have been found to be significantly different from previously reported distributions for conventional turbulent premixed combustion.
A priori Direct Numerical Simulation (DNS) assessment of mean reaction rate closures for reaction progress variable in the context of Reynolds Averaged Navier–Stokes (RANS) simulations has been conducted for MILD combustion of homogeneous (i.e., constant equivalence ratio), methane-air mixtures. The reaction rate predictions according to statistical (e.g., presumed probability density function), phenomenological (e.g., eddy-break up (EBU), eddy dissipation concept (EDC) and the scalar dissipation rate (SDR) based approaches), and flame surface description (e.g., Flame Surface Density) based closures are compared. The performance of the various reaction rate closures has been assessed by comparing the models’ predictions to the corresponding quantities extracted from DNS data. It has been found that the usual presumed probability density function (PDF) approach using the beta-function predicts the PDF of the reaction progress variable in homogenous mixture MILD combustion throughout the flame brush for all cases considered here provided that the scalar variance is accurately predicted. The accurate estimation of scalar variance requires the solution of a modelled transport equation, which depends on the closure of Favre-averaged SDR. A linear relaxation based algebraic closure for the Favre-averaged SDR has been found to capture the behaviour of the Favre-averaged SDR in the current homogenous mixture MILD combustion setup. It has been found that the EBU, SDR and FSD-based mean reaction rate closures do not adequately predict the mean reaction rate of the reaction progress variable for the parameter range considered here. However, a variant of the EDC closure, with model coefficients expressed as functions of micro-scale Damköhler and turbulent Reynolds numbers, has been found to be more successful in predicting the mean reaction rate of reaction progress variable compared to other modelling methodologies for the range of turbulence intensities and dilution levels considered here.
The flow and heat transfer characteristics over a single dimple and an array of staggered dimples have been investigated using the Reynolds Averaged Navier-Stokes (RANS) approach. The objective is to determine how reliably RANS models can predict this type of complex cooling flows. Three classes of low-Reynolds number RANS models have been employed to represent the turbulence. These included a linear Eddy Viscosity Model (EVM), a Non-Linear Model (NLEVM) and a Reynolds Stress transport Model (RSM). Variants of the k-ε model have been used to represent the first two categories. Steady and time-dependent simulations have been carried out at a bulk Reynolds number of around 5,000 with dimple print diameter to channel height ratios of D/H = 1.0, 2.0 and ratios of dimple depth to channel height of δ/H = 0.2, 0.4. The linear EVM and the RSM tested both produce symmetric circulations in the dimples, while the NLEVM produces an asymmetric pattern. The mean velocity profiles predicted numerically are generally in good agreement with the data. The main flow characteristics are reproduced by the RANS models, but some predictive deviations from available data point to the need for further investigations. All models report an overall enhancement in heat transfer levels when using dimples in comparison to those of a plane channel.
The effects of the definition of the reaction progress variable and equivalence ratio on the validity of Damköhler's hypotheses for turbulent premixed flames belonging to the thin reaction zone regime have been studied using multi-step chemistry direct numerical simulations of statistically planar [Formula: see text]–air premixed flames with equivalence ratios of 0.8 and 1.0. Although [Formula: see text]–air premixed flames with equivalence ratios of 0.8 and 1.0 have effective Lewis numbers close to unity, local differential diffusion effects can play a non-negligible role in determining the turbulent burning velocity and flame surface area in all cases. However, the augmentations of burning rate and flame surface area under turbulence do not occur in equal proportion, but their ratio remains of the order of unity. This conclusion holds irrespective of the definition of the reaction progress variable for the cases considered here. Damköhler's second hypothesis, which relates the ratio of turbulent burning velocity and the unstretched laminar burning velocity to the ratio of turbulent diffusivity and molecular diffusivity, has been found not to hold in the sense of equality, but it is valid in an order of magnitude sense for all choices of reaction progress variable definition. The findings of the current analysis indicate that Damköhler's first and second hypotheses should only be interpreted in an order of magnitude sense in the thin reaction zone regime even when the effective Lewis number remains close to unity.
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