Development of a Log-Time Integration Method for Reactive Flows

In reactive flow simulations integration of the stiff species transport equations consumes most of the computational time. Another important aspect of combustion simulation is the need to simulate at least tens of species in order to accurately predict emissions and the related combustion dynamics. Small time scales and systems with tens of species lead to very high computational costs. Classic integration methods such as Euler method are restricted by the smallest characteristic time scale, and explicit Runge-Kutta methods require intermediate predictor corrector steps which make the problem computationally expensive. On the other hand, implicit methods are also computationally expensive due the calculation of the Jacobian. This work presents a strategy to significantly reduce computational time for integration of species transport equations using a new explicit integration scheme called Log-Time Integration Method (LTIM). LTIM is fairly robust and can compete with methods such as the 5th order Runge-Kutta method. Results showed that LTIM applied to the solution of a zero dimensional reactive system which consists of 4 chemical species obtains the solution around 4 times faster than 5th order Runge-Kutta method. LTIM was also applied to the solution of a one dimensional methane-air flame. The chemical reactions were modeled using a reduced chemical mechanism ARM9 that consists of 9 chemical species and 5 global reactions. The solution was carried out for 9 species transport equations along with the energy equation. Governing equations were decoupled into flow and chemical parts and were solved separately using a split formulation. Thermodynamic properties were obtained using NASA format polynomials and transport properties using kinetic-theory formulation. It is shown that the new one dimensional flame code is able to calculate the adiabatic flame temperature of the system and corresponding flame speed for the methane-air flame thus validating its robustness and accuracy.