Modeling of Conditional Dissipation Rate for Flamelet Models With Application to Large Eddy Simulation of Fire Plumes

Abstract

Subgrid scale (SGS) combustion modeling using flamelet approximations require a model for the conditional dissipation rate. For high Reynolds number flow, statistical independence between the mixture fraction and dissipation is often invoked allowing the conditional dissipation to be expressed in terms of its mean filtered value. This assumption fails for application to pool fires because of the transitionally turbulent nature of this class of flows. In this study, an alternative closure for conditional dissipation rate is proposed based on a transport equation for the mixture fraction filtered probability density function. Application of this model for use in Large Eddy Simulation (LES) of a large, 1 m in diameter, methaneair fire plume results in greatly improved predictions over existing models that invoke the use of statistical independence when comparisons are made to experimental measurements.

Large Eddy Simulations of CH4 Fire Plumes

“…However, with increasing axial distance from the fire source, only the influence of the baroclinic torque remains significant. In comparison to previously studied iso-thermal helium plumes [8,9], the non-monotonic behavior of density in the reaction zone of these large-scale fire plumes is responsible for the creation of two counter-rotating vortices, enhancing the transport of fuel into the reaction zone [18]. There was, overall, good qualitative and quantitative agreement between the simulation results obtained with the two codes, but also with the experiments performed by Tieszen et al [12,13] and well-known correlations reported in literature.…”

“…In the former, density initially decreases with increasing radius from the centerline until the reaction zone where it starts increasing again moving towards the air side, resulting in a more localized vorticity distribution. This effect generates a set of counter-rotating vortices on either side of the flame zone, causing fuel and oxidizer to be brought into the reaction zone [18]. This is illustrated in Figure 3, where the baroclinic and gravitational torques with FireFOAM for Test #17 are presented at different heights.…”

“…These stages are then repeated in every puffing cycle [8,9,18]. The low inlet velocity and the strong deflection of the plume from the axial direction at the source edges, indicate that vorticity from the source is not responsible for the formation of turbulent structures at the plume-air interface.…”

“…For all the test cases considered in this study, the conditions at the source were laminar (inlet velocities of only a few cm/s), but very quickly buoyancy-generated turbulence makes the flow turbulent (within an inlet diameter distance). The triggering mechanism [8,9,18] is the generation of instabilities at the edges of the source due to baroclinic and gravitational torques. If coarse grids are used in the numerical simulations then small-scale mixing is not well captured and temperatures are typically under-predicted, resulting in smaller density gradients.…”

“…Black et al [17] performed RANS simulations with two different turbulence treatments, a steady RANS solution with a model for buoyancygenerated turbulence, and an unsteady solution with closure models based on a temporal filter width. DesJardin et al [18] used LES to apply flamelet modeling combined with an alternative closure for the conditional dissipation rate, based on a transport equation for the mixture fraction filtered probability density function. Xin et al [19] performed LES in order to validate an earlier version of the Fire Dynamics Simulator (FDS) while Pasdarshahri et al [20] applied LES with Open-FOAM using the one-equation turbulence model.…”