Turbulent Combustion
Large-Eddy Simulation of a non-premixed turbulent flame
The activities on this topic were initiated within the framework of a research visit to the Center for Turbulence Research (CTR) at the Stanford University, USA. The direct numerical simulation (DNS) of turbulent flows at technically relevant Reynolds numbers will remain unfeasible due to its huge computational cost in the forseeable future. This is specially true for turbulent combustion, where the interactions between turbulence and chemistery add to the complexity of the flow problem. The method of Large Eddy Simulation (LES) offers here an attractive compromise. As shown in figure 1 the basic idea of LES is that it resolves numerically only the large structures of the turbulent motion, which are associated with small wave numbers range, while it models unresolved small so-called subgrid-scale (SGS) structures. The lower resolution requirements makes the LES approach applicable also to high Reynolds number flow, where it is capable to capture the large structures, which are typically determined by the actual flow geometry and boundary conditions. LES additionally benefits from the fact that the unresolved small structures tend to be more general and isotropic, and, hence, simplier to model.
Figure 1: Portion of the turbulent energy spectrum captured by DNS and LES, respectively.
The present project considers LES of a turbulent non-premixed jet flame, where fuel and oxidizer enter the combustion chamber separately, as schematically shown in figure 2. Since the reactants have to get mixed in the turbulent flow field before they can react the chemistry is mainly determined by the mixture fraction Z. The mixture fraction, which represents the local mixedness, is zero in the pure oxidizer feed and one in the fuel feed, respectively, and it adopts some value between in the mixing layer.
Figure 2: typical non-premixed jet flame configuration, yellow region denotes mixing layer
For the present LES a model based on the Conditional Moment Closure (CMC) method was developed to close the chemical source terms being unresolved on the coarse LES grid. Thereby, the proposed Conditional Source-term Estimation (CSE) model adopts the basic idea of CMC to solve for the chemistry in terms of ensemble averages conditioned on the mixture fraction. The solutions obtained in the mixture fraction space are then mapped into the physical space according to the local probability density of the mixture fraction as the random variable. The closure using CSE was tested in a predictive self-sustained LES of a piloted methane-air jet flame, which has been experimentally investigated in the SANDIA laboratories (Sandia D flame). The instantaneous temperature field obtained by the LES for this flame is shown in figure 3. The LES results agreed well with the experimental data.The CSE concept was also successfully applied in LES using unsteady laminar flamelet approches to model the chemistry.
Figure 3: Large-Eddy Simulation of the Sandia D flame, instantaneous temperature field non- dimensionalized with the reference temperature T0=293K
Related publications:- Steiner H., Bushe W. K. (1998) LES of non-premixed turbulent reacting flows with Conditional Source term Estimation, Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford University, 23 - 34.
- Bushe, W. K., Steiner, H. (1999) Conditional Moment Closure for Large Eddy Simulation of non-premixed turbulent reacting flows, Physics of Fluids 11, 1896 - 1906.
- Steiner H., Bushe W. K. (1999) Large Eddy Simulation of a turbulent diffusion flame with Conditional Source-term Estimation, Annual Research Briefs, Center for Turbulence Research, NASA Ames/Stanford University.
- Pitsch H., Steiner H. (2000) Large-eddy simulation of a turbulent piloted methane/air diffusion flame (Sandia flame D), Physics of Fluids 12, 2541 - 2554.
- Pitsch H., Steiner H. (2000) Scalar mixing and dissipation rate in large-eddy simulations of non-premixed turbulent combustion, Proceedings of the Combustion Institute 28, 41 - 49.
- Steiner H., Bushe W. K. (2001) Large Eddy Simulation of a turbulent reacting jet with Conditional Source-term Estimation, Physics of Fluids 13, 754 - 769.
- Bushe W. K., Steiner H. (2003) Laminar flamelet decomposition for Conditional Source-term Estimation, Physics of Fluids 15, 1564 - 1575.