Improving FGM: multiple chemical time scales: Applied to predict the fate of NO and CO in Nozzle Guide Vanes

In this work, we propose an innovative approach intended to improve the general accuracy of the Flamelet Generated Manifolds chemistry reduction method. It is based on increasing the dimensionality of the FGM by allowing for an additional degree of freedom. This extra dimension of the manifold accounts for chemical kinetics, describing conversion of one species into others. We follow the ideas of ILDM to perform a time scale analysis of chemical source term. It is done locally in each grid point of the FGM, yielding the local chemical time scales and the directions in composition space of their corresponding reaction groups. The assumption is that the chemistry evolution quickly vanishes in the directions of the fast reaction groups. This means that the reaction process develops only along the few “slowest” directions. Then the FGM is extended locally by the directions of the slow chemistry. Still, the movement in the direction of the extension is bound to the narrow vicinity of the original manifold. An additional transport equation needs to be solved for the secondary reactive control variable used to parametrize the movement in the direction of the extension. The movement on the manifold along the 1D FGM is still parametrized by the reaction progress variable, which is the main reactive control variable. This approach is not restricted to just one additional dimension. On the contrary, an arbitrary number of chemically reactive dimensions can be included.
The performance of the new developed model is examined in one-dimensional test configurations, which simulate the process of expansion of a mixture of burnt gases. The purpose of this theoretical exercise is to obtain conditions severe enough for the thermochemistry to go off the FGM with one chemical degree of freedom, in the direction of the secondary reactive dimension. In the utilized test cases, this is achieved by the high rate at which the expansion happens. These fast time scales of the change of the thermodynamic variables can interact with the post flame chemistry, for example altering the concentration of the pollutants. The idea of expansion or compression of burnt gases can be related to several applications. Often, expansion of burnt gases is used to convert the released heat into work. Here, we adopt a somewhat idealized test case setup that resembles the idea of the gas turbine stators, also called the nozzle guide vanes (NGV). There, the burnt gases, formed in the combustor, are led through a decreasing area duct. Accompanied by the decrease of temperature and pressure, the velocity increases almost up to the speed of sound. Due to the high velocity, the residence time inside the NGV is small, resulting in a high rate of cooling and expansion.
The results of the test problems show that the FGM method with one additional reactive dimension yielded a better agreement with the detailed chemistry simulations. Improvements are observed for the source terms of the reactive control variables and for the species composition. Also, the accuracy of the CO and NOx predictions increased by an order of magnitude.