Thermal/Turbulence Time Scale Ratios in Low Exothermic Reacting and Non-reacting Flows

Abstract

The aim of this work is to contribute to the study of chemistry effects on the turbulent scalar field that is, here, the temperature, through a better knowledge of the ratio between the scalar time scale and the mechanical time scale (R t ) in the distributed reaction regime characterized by a Damkö hler number lower than unity. The numerical studies are performed by calculating the order of magnitude of R t in both low exothermic reacting and nonreacting case. Propane has been chosen as a typical hydrocarbon for this study. The molar fractions are computed by the IEM (Interaction Exchange with the Mean) model in which the probability density function is calculated from its transport equation. The models and the numerical simulations are used to describe a jet stirred reactor with subsonic jet injection. The predictions are validated by comparison with experimental data for temperature and concentrations fields. It is pointed that in the non-reacting case, R t parameter is around unity; the temporal scales dynamics and scalar are coupled. In this case, the transport of the passive scalar is ensured by the dynamic field. In the reactive case, however, this coupling is not assured any more. Indeed, the chemical reaction, characterized by a non-linear source term, affects the scalar field by decreasing its characteristic scales, which results in R t lower than unity. The CFD-PDF predictions were within engineering accuracy of experimental data. It can be summarized that the results of exercise are satisfactory, and the CPU-time and RAM memory savings encouraging. INTRODUCTIONTemporal and spatial macroscopic velocity inhomogeneities or fluctuations are ubiquitous in turbulent flows. Large time and length scales (also termed integral scales) are associated to the external (initial=boundary conditions) or internal (flow instabilities) turbulence-triggering mechanisms. At the other end, the Kolmogorov time and length microscales characterize the viscous dissipation of kinetic energy into heat. The transfer of energy between large and small structures or eddies takes place across a wide range of intermediate scales.Heterogeneities in scalar fields can also be induced by injection process (initial and boundary conditions) and=or by the driving fluctuating velocity field. Local chemical source terms can also contribute to generate scalar fluctuations. The ratio of integral length to the Kolmogorov microscale is proportional to the turbulence Reynolds number to the power three-fourths, while the integral time over the Kolmogorov one scales as the Reynolds number to one-half (Dopazo & O'Brien, 1987). In order to resolve the smallest features of fluctuating fields, while keeping integral length scale inside the domain. The required computer storage is thus proportional to the Reynolds number to the nine-fourths power and the computational time goes a power slightly larger than eleven-fourths. This approach to the solutions of turbulent flows is named direct numerical simulation (DNS), as the governing equations are numericall...

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