Computational multiscale methods for turbulent combustion in complex geometries
Final Report Abstract
As a result of all activities during the report period, various new methods could be developed and transferred into a new comprehensive computational framework. Computational approaches to five different problems are available, all of them particularly aiming at flow problems in the turbulent regime: non-reactive variable-density flow at low Mach number, two-phase flow as well as premixed combustion via a level-set/G-equation approach, premixed combustion via a progressvariable approach, and a mixture-fraction approach to be used for partially premixed combustion. All methods are theoretically covered within the framework of extended variational multiscale methods, bringing together the concepts of the variational multiscale method and the extended finite element method. Moreover, the concept of multifractal subgrid-scale modeling could be successfully integrated. The two main contributions by the Emmy Noether research group will be addressed in more detail in the following. The first main contribution is the development of a novel approach to large-eddy simulation of both turbulent incompressible flow and variable-density flow at low Mach number. For this method, ideas from three concepts could be beneficially brought together: variational multiscale methods (for the basic computational method), algebraic multigrid methods (for the scale separation), and multifractal subrid-scale modeling (for improved modeling of the effect of the unresolved scales). As an initial step, in the first research period, a method incorporating the first two concepts but relying on a small-scale subgrid-viscosity term based on a rather simple Smagorinsky model was generated; it already provided notably improved results compared to other state-of-the-art methods, but the advancement using multifractal subrid-scale modeling even elevated the quality of the results. Stability, remarkable robustness, also for complex geometries, and good computational efficiency could be demonstrated for the method, aside from accuracy. Based on all aforementioned attributes, the method appears to be one of the most powerful computational approaches to large-eddy simulation of turbulent flow currently available. The development of this first main contribution proceeded exceptionally smoothly, despite the fact that a multitude of new approaches were combined to obtain a comprehensive novel method. Hence, all goals originally aimed at could be achieved in time, and even some further minor contributions in this context could be made. The second main contribution is the development of an extended finite element method for the challenging problem of turbulent premixed combustion for the first time. Based on a level-set/G-equation approach, it is accounted for the flame front by extending the basic finite element functions via additional functions which are able to represent the discontinuities at the flame front. Promising results could be achieved with the initial version of the method, for which the jump conditions at the flame front were imposed via a distributed Lagrange multiplier approach for various two-dimensional flame configurations. While developing and testing the method, several challenges could be discerned during the first research period. Addressing these challenges in the last two years of the project resulted in a new semi-Lagrangean scheme for time integration in the context of extended finite element methods and a new, substantially more versatile approach for imposing jump conditions at the flame front based on Nitsche’s method, among others. The novel version of the method could already be validated for a two- and a three-dimensional test example. However, the application to the ORACLES test rig still exhibits stability problems, which origin could not be traced back so far. In general, challenges related to the development of this second main contribution turned out more severe than expected at the time of writing the proposal, which postponed the related time schedule. Nonetheless, the method could already be successully extended for and applied to laminar and turbulent two-phase flow, for which different types of conditions have to be enforced at the interface.
Publications
- Numerical simulation of premixed combustion using an enriched finite element method, J. Comput. Phys. 228 (2009) 3605–3624
F. van der Bos, V. Gravemeier
- An algebraic variational multiscale-multigrid method for large-eddy simulation of turbulent variable-density flow at low Mach number, J. Comput. Phys. 229 (2010) 6047–6070
V. Gravemeier, W.A. Wall
- An algebraic variational multiscalemultigrid method for large eddy simulation of turbulent flow, Comput. Methods Appl. Mech. Engrg. 199 (2010) 853–864
V. Gravemeier, M.W. Gee, M. Kronbichler, W.A. Wall
- Towards an extended algebraic variational multiscale-multigrid method for turbulent premixed combustion based on a combined G-equation/progress-variable approach, in: Annual Research Briefs - 2010, Center for Turbulence Research, Stanford University and NASA Ames Research Center, 2010, 185–196
V. Gravemeier
- An algebraic variational multiscalemultigrid method for large eddy simulation: generalized-α time integration, Fourier analysis and application to turbulent flow past a square-section cylinder, Comput. Mech. 47 (2011) 217–233
V. Gravemeier, M. Kronbichler, M.W. Gee, W.A. Wall
- An extended variational multiscale method for two-phase flow including surface tension, Comput. Methods Appl. Mech. Engrg. 200 (2011) 1866-1876
U. Rasthofer, F. Henke, W.A. Wall, V. Gravemeier
- Residual-based variational multiscale methods for laminar, transitional and turbulent variable-density flow at low Mach number, Int. J. Numer. Meth. Fluids 65 (2011) 1260–1278
V. Gravemeier, W.A. Wall
- Variational multiscale methods for premixed combustion based on a progress-variable approach, Combust. Flame 158 (2011) 1160–1170
V. Gravemeier, W.A. Wall
