On molecular transport effects in real gas laminar diffusion flames at large pressure

Abstract

Direct numerical simulations are conducted of unsteady, exothermic and one-dimensional laminar diffusion flames at large pressures. The simulations are used to assess the impact of molecular diffusion and real gas effects under high pressure conditions with simplified chemical kinetics. The formulation includes the fully compressible form of the governing equations, real gas effects modeled by the cubic Peng-Robinson equation of state, and a generalized form of the Soret and Dufour mass and heat diffusion vectors derived from nonequilibrium thermodynamics and fluctuation theory. The cross diffusion fluxes are derived for a ternary species system and include the effects of both heat and mass diffusion in the presence of temperature, concentration and pressure gradients ͑i.e., Soret and Dufour diffusion͒. The ternary species formulation is applied to a simplified single step reaction elucidating molecular and thermodynamic effects apparent in general combustion. Realistic models for pressure, temperature and species dependent heat capacities, viscosities, thermal conductivities and mass diffusivities are also included. Three different model reactions are simulated both including and neglecting Soret and Dufour cross diffusion. The simulation results show that Soret and Dufour effects are negligible for reactions comprised of species with equal or near equal molecular weights. However, Soret diffusion effects are apparent when species with nonequal molecular weights are involved in the reaction and result in reductions of the peak flame temperature. In addition, it is shown that neglect of cross diffusion leads to deviations in the predicted flame thicknesses, with under predictions for a hydrogen-oxygen system and over predictions for a heavy hydrocarbon reaction. These effects are explained in detail through examinations of the individual heat and mass flux vectors as well as through associated thermodynamic properties. A parametric study addresses the effects of the ambient pressure, the initial "flame Reynolds number," the Damkohler number and the heat release parameter.

A priori analysis of subgrid mass diffusion vectors in high pressure turbulent hydrogen/oxygen reacting shear layer flames

“…41 Harstad and Bellan 42 first derived the form and have applied it to binary species mixing systems. Palle 7,8 extended the application to arbitrary numbers of species and reacting hydrogen, heptane, and methane flames. The full forms of the heat flux and molar flux vectors, including multi-component, differential, and cross diffusion effects, are represented by…”

“…Comparisons can now be made to other SGS terms appearing in the filtered species transport equation, Eq. (8). Figure 14 presents PDFs of the ratio of the SGS mass flux vector magnitude, SG S = |J α j |, to the turbulent species flux vector magnitude, γ SGS = | ρ (Y α u j ) SGS |, for the global, large filtered SGS scalar dissipation, and large temperature SGS variance regions at the largest filter width ( f /δ ω0 ≈ 5.7) for the Re δ0 = 850 flame.…”

“…Figure 16 examines these terms by presenting the PDFs of the ratio of the magnitudes of the last and the second to last term on the right hand side of Eq. (8) for Re δ0 = 850. The SGS mass and species flux divergence magnitudes are symbolically defined by…”

“…neglected diffusion phenomena are necessary to accurately capture the physics of the combustion process; particularly at high pressure. [6][7][8][9][10][11][12][13][14][15][16] Numerical techniques have proven themselves to be a useful tool in studying a large number of flows, including those involving combustion. If sufficient computational resources are available, all spatial and temporal scales of the desired flow can be directly calculated.…”

Large-Eddy Simulation of Flame-Turbulence Interactions in a Shear Coaxial Injector

“…Despite the elevated pressure inside the PSU rig, the conditions are far from being supercritical and these cross-diffusion terms are inherently small (less than 10% of the heat/ mass fluxes). While they could promote intermittency and flame extinction, resulting in a slight decrease of the flame temperature, even detailed direct numerical simulation studies of mixing layers have not reached a definitive conclusion on their importance [15,16]. The subgrid species diffusive flux sgs i;k g V i;k Y k Ṽ i;kỸk is usually neglected because it has been shown to have a small magnitude at high Reynolds numbers [17,18], such as the ones found in the main shear layers of the current injector flow.…”