The Hybrid Method for the PDF Equations of Turbulent Reactive Flows: Consistency Conditions and Correction Algorithms

The hybrid method solves the modeled transport equation for the joint PDF of velocity, turbulence frequency, and compositions for turbulent reactive flows. A finite-volume (FV) method is used to solve the mean conservation equations for mass, momentum, and energy and the mean equation of state; and a particle method is used to solve the modeled PDF equation. The method is completely consistent at the level of the governing equations solved by the FV and particle algorithms. In this work, the conditions to be fulfilled for full consistency at the numerical solution level are examined and the independent consistency conditions are identified. Then correction algorithms are developed to enforce these independent consistency conditions to achieve full consistency at the numerical solution level. In addition, a new formulation of the energy equation and the equation of state is developed which is both general and simple. The hybrid method is applied to a non-premixed piloted-jet flame. The numerical results show that the correction algorithms are completely successful in achieving consistency. The convergence of the method is demonstrated and, in particular, it is shown that the bias error is dramatically reduced (compared to that in previous PDF calculations). In addition, the results are shown to be in a good agreement with some earlier PDF calculations and also with the available experimental data. Because of the substantially reduced numerical error (for given grid size and number of particles), the present hybrid method represents a significant advance in the computational efficiency of particle/mesh method for the solution of PDF equations.