Statistics and Modelling of Turbulent Kinetic Energy Transport in Different Regimes of Premixed Combustion

Abstract

The statistical behaviour of turbulent kinetic energy transport in turbulent premixed flames is analysed using data from three-dimensional Direct Numerical Simulation (DNS) of freely propagating turbulent premixed flames under decaying turbulence. For flames within the corrugated flamelets regime, it is observed that turbulent kinetic energy is generated within the flame brush. By contrast, for flames within the thin reaction zones regime it has been found that the turbulent kinetic energy decays monotonically through the flame brush. Similar trends are observed also for the dissipation rate of turbulent kinetic energy. Within the corrugated flamelets regime, it is demonstrated that the effects of the mean pressure gradient and pressure dilatation within the flame are sufficient to overcome the effects of viscous dissipation and are responsible for the observed augmentation of turbulent kinetic energy in the flame brush. In the thin reaction zones regime, the effects of the mean pressure gradient and pressure dilatation terms are relatively much weaker than those of viscous dissipation, resulting in a monotonic decay of turbulent kinetic energy across the flame brush. The modelling of the various unclosed terms of the turbulent kinetic energy transport equation has been analysed in detail. The predictions of existing models are compared with corresponding quantities extracted from DNS data. Based on this a-priori DNS assessment, either appropriate 206 Flow Turbulence Combust (2011) 87:205-235 models are identified or new models are proposed where necessary. It is shown that the turbulent flux of turbulent kinetic energy exhibits counter-gradient (gradient) transport wherever the turbulent scalar flux is counter-gradient (gradient) in nature. A new model has been proposed for the turbulent flux of turbulent kinetic energy, and is found to capture the qualitative and quantitative behaviour obtained from DNS data for both the corrugated flamelets and thin reaction zones regimes without the need to adjust any of the model constants.

Statistics of Conditional Fluid Velocity in the Corrugated Flamelets Regime of Turbulent Premixed Combustion: A Direct Numerical Simulation Study

“…The modelling of ρu i c has been discussed in [24,[27][28][29] and thus will not be further addressed in this paper for the sake of conciseness. It can be seen from Figure 2 The evolution of ρu 1 u 1 and ρu 2 u 2 within a statistically planar one-dimensional turbulent flame brush (that propagates from right to left) is affected by several physical mechanisms [30][31][32], which can be evident from the following transport equations:…”

“…The statistical behaviours of the various terms of (14a) and (14b) for this database have been discussed elsewhere [31,32] in detail and will be not be repeated here for the sake of brevity. The main behavioural trends will be summarised here.…”

Vorticity isotropy in high Karlovitz number premixed flames

“…A variety of configurations have been used in DNS of premixed flames such as V-flames, 41 slot Bunsen flames, 42,43 statistically planar flames with decaying turbulence, 18,44 and statistically planar flames with forced turbulence. 9,10,12,15 In order to isolate the effects of the flame on the turbulence and to reach high Karlovitz numbers, the DNSs analyzed here were statistically planar and used turbulence forcing to prevent the decay of turbulence.…”

“…[9][10][11][12][13] In premixed turbulent combustion, the coupling of the flame and turbulence has been observed to vary with the Karlovitz number. 2,9,[13][14][15][16][17][18] The Karlovitz number is defined as the ratio of the flame time scale (τ F ) to that of the smallest turbulent eddies (τ η ),…”

“…These goals are accomplished by analyzing a series of DNS with varying Karlovitz numbers, Reynolds numbers, and flame density ratios previously performed by Bobbitt et al 6 The simulations are of statistically one-dimensional, slightly lean n-heptane/air flames using either finite-rate chemistry or tabulated chemistry. Simplified chemical and transport models are often used in numerical simulations of premixed turbulent combustion to reduce the computation cost, 15,16,18,22,23,25 but their impact on vorticity isotropy is not known. By analyzing DNS with different models, their impact on vorticity may be tested.…”