The mechanism of flame propagation in fuel beds of wildland fires is important to understand and quantify fire spread rates. Fires spread by radiative and convective heating and often require direct flame contact to achieve ignition. The flame interface in an advancing fire is unsteady and turbulent, making study of intermittent flames in complex fuels difficult. This thesis applies the one-dimensional turbulence (ODT) model to a study of flame propagation by simulating a lab-scale fire representative of the flame interface in a fuel bed and incorporating solid fuel particles into the ODT code. The ODT model is able to resolve individual flames (a unique property of this model) and provide realistic turbulent statistics. ODT solves diffusion-reaction equations on a line-of-sight that is advanced either in time or in one spatial direction (perpendicular to the line-of-sight). Turbulent advection is modeled through stochastic domain mapping processes. A vertical wall fire, in which ethylene fuel is slowly fed through a porous ceramic, is modeled to investigate an unsteady turbulent flame front in a controlled environment. Simulations of this configuration are performed using a spatial formulation of the ODT model, where the ODT line is perpendicular to the wall and is advanced up the wall. Simulations include radiation and soot effects and are compared to experimental temperature data taken over a range of fuel flow rates. Flame structure, velocities, and temperature statistics are reported. The ODT model is shown to capture the evolution of the flame and describe the intermittent properties at the flame edge, though temperature fluctuations are somewhat over predicted. A solid particle devolatilization model was included in the ODT code to study the convective heating of unburnt solid fuels through direct flame contact. Here the particles are treated as sweet gum hardwood and a single-reaction, first order decomposition model is used to simulate the devolatilization rates. Only preliminary results were presented for a simple case, but this extension of the ODT model presents new opportunities for future research.