Evolution of Surface Density Function in an Open Turbulent Jet Spray Flame

Abstract

A three-dimensional Direct Numerical Simulation of an open turbulent jet spray flame representing a laboratory-scale burner configuration has been used to analyse the statistical behaviours of the magnitude of reaction progress variable gradient $$\left| {\nabla c} \right|$$ ∇ c [alternatively known as the Surface Density Function (SDF)] and the strain rates, which affect its evolution. The flame has been found to exhibit fuel-lean combustion close to the jet exit, but fuel-rich conditions have been obtained further downstream due to the evaporation of fuel droplets, which leads to the reduction in the mean value of the SDF in the downstream direction. This change in mixture composition in the axial direction has implications on the statistical behaviours of the SDF and the strain rates affecting its evolution. The mean value of dilatation rate remains positive, whereas the mean normal strain rate assumes positive values where the effects of heat release are strong but becomes negative towards both unburned and burned gas sides. The mean values of dilatation rate, normal strain rate and tangential strain rate decrease downstream of the jet exit. However, the mean behaviours of displacement speed and its components do not change significantly away from the jet exit. The mean values of normal strain rate arising from flame propagation remain positive and thus act to thicken the flame. The mean tangential strain rate due to flame propagation (alternatively the curvature stretch rate) remains negative throughout the flame at all axial locations investigated. The mean effective normal strain rate assumes positive values throughout the flame and it increases in the downstream direction for the present case, which is consistent with the reduction in the peak mean value of the SDF in the axial direction. The mean effective tangential strain rate (alternatively stretch rate) assumes negative values throughout the flame at all axial locations.

Flame self-interactions in an open turbulent jet spray flame

“…The standard conservation equations for mass, momentum, energy and species for reacting flows are solved for the Eulerian gaseous phase. The standard transport equations of position, diameter, momentum, and energy are solved for individual liquid fuel droplets in a Lagrangian framework 22,23,[25][26][27]29,30 . Coupling between the Eulerian and Lagrangian phases is achieved by the Particle-Source-In-Cell approach 22,23,[25][26][27]29,30 where particles are modelled as spherical point masses.…”

“…The standard transport equations of position, diameter, momentum, and energy are solved for individual liquid fuel droplets in a Lagrangian framework 22,23,[25][26][27]29,30 . Coupling between the Eulerian and Lagrangian phases is achieved by the Particle-Source-In-Cell approach 22,23,[25][26][27]29,30 where particles are modelled as spherical point masses. A polydisperse spray with a diameter distribution matching that of the experiment is injected based on a log-normal distribution with diameters ranging from 1 to 80 (the most likely diameter is ~20 ).…”

“…To ensure an appropriate resolution of both the turbulence and the flame structure, the smallest cell size at the nozzle exit is taken to be ∆ = ∆ = ∆ = 150 . Further details on the boundary conditions and mesh can be found elsewhere 22,23,[25][26][27]29,30 34 . The turbulent Reynolds number is in the range of 50-100 in the high shear regions of the axial locations considered as discussed in detail in previous studies involving this simulation 23,27,30 .…”

“…where and are mass fraction and the molar mass of element , respectively 27,29,30 . A reaction progress variable based on the oxidiser mass fraction can be defined, as done so in several previous analyses 19, 29,30,[36][37][38][39][40][41][42][43][44] , in the following manner:…”

“…the magnitude of the gradient of the reaction progress variable |∇ |). The transport equation for the reaction progress variable can be written as 29,30,36,37 :…”