Lagrangian PDF Transport Method for Simulations of Axisymmetric Turbulent Reacting Flows

Abstract

The scalar probability density function (PDF) transport method is being increasingly used for simulations of turbulent reacting flows. The key feature of this method is that turbulence-chemistry interactions are more accurately modeled than in conventional methods, thus a better representation of turbulent reacting fields is achieved. In this paper, a new scalar PDF transport method is presented for 2D axisymmetric flows. In this method, Monte-Carlo particles required for the solution of the PDF transport equation are tracked in a cylindrical coordinate system as opposed to the traditional method of tracking particles in a Cartersian coordinate system and transforming particle positions into cylindrical coordinates at every time-step. Solving the PDF equation in the cylindrical coordinate system also ensures consistency with the flow-solver, in that the PDF equation and the flow equations are all solved in the same coordinate system. Consistency of the solutions from the PDF solver with those from an Eulerian finite-volume solver for nonreacting flows are presented followed by a discussion on reacting calculations of the Sydney bluff-body flame, designated HM1 (see www.mech.eng.usyd.edu.au/thermofluids). φ C = model constant in the IEM model T D = turbulent diffusivity f = joint scalar probability density function (PDF) F = mass density function α i J = Diffusional flux of species α in the i th -coordinate direction k = turbulent kinetic energy k N = number of particles in the k th cell r = radial coordinate in the cylindrical coordinate system n r = radial location of the n th particle α S = chemical source term of species α t Sc = turbulent Schmidt number t = time i u = instantaneous velocity in the i th -coordinate direction i u = fluctuating velocity in the i th -coordinate direction i U = Favre mean velocity in the i th -coordinate direction n w = weight of the n