An embedded upward flame spread model using 2D direct numerical simulations
A fully coupled 2D fluid-solid direct numerical simulation (DNS) approach is developed to simulate fluid-solid heat and mass transfer processes using Cartesian grids. The solid geometry is identified using level set based embedded interface method. The flow field is described by the 2D Navier Stokes equations using a vorticity-streamfunction approach. First a fluid-solid coupling formulation for the thermal and momentum fields is developed that is robust, computationally efficient and second-order accurate. Solutions for several example problems are presented for flow over stationary and moving cylinders to bench mark the current approach. Heat transfer for an isolated cylinder and two cylinders in series are then examined to explore the Nusselt number dependence on cylinder spacing and unsteady conjugate heat transfer processes. Secondly, the methodology is extended to simulate flame spread over poly(methyl methacrylate) (PMMA) at different angles of inclination. Comparison of simulations and experimental measurements are conducted for flame spread rates. Results show that the heat flux to the preheating region varies considerably in time - contradicting often employed assumptions used in established flame spread theories. Accounting for the time dependent behaviour is essential in accurate predictions of flame spread, however, a universal characterization in terms of easily defined parameters is not found. Alternatively, a reaction progress variable based embedded flame model is developed using mixture fraction, total enthalpy and surface temperature. State maps of the gas-phase properties and surface heat flux are constructed and stored in pre-computed lookup tables. The resulting model provides a computationally efficient and a local formulation to determine the flame heat flux to the surface resulting in excellent agreement to DNS and experiments for predictions of flame spread rate and position of the pyrolysis front.