# Large Eddy Interaction with Propagating Flames

## Abstract

In this report, we describe work in progress on a long-range project to model combustion within a moving piston. While the ultimate goal is a three-dimensional simulation of the interaction between vortex stretching, flame propagation and large-scale eddy formation, the current project is aimed at a 2-D calculation of the effect of varying fuel inlet placement and inclination angles on flame propagation in a swirling fluid. The equations of motion are the equations of zero Mach number combustion, which describe viscous, uniformly compressible flow. At the core of the hydrodynamic calculation is the random vortex method, originally designed for high Reynolds number turbulent flow. At the center of the flame algorithm has been a volume of fluid advection scheme to track the motion of the burning fluid. While this will probably remain the main ingredient on the combustion side, we are currently studying a new algorithm that is proving particularly useful for the analysis of specialized combustion phenomena requiring highly accurate schemes.

## Keywords

Flame Front Flame Propagation Flame Speed Vortex Method Recirculation Bubble## Preview

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## References

- 1).C. Anderson and C. Greengard,
*On vortex methods*, SIAM J. Numer. Anal.,**22**(1985), pp. 413–440.MathSciNetADSzbMATHCrossRefGoogle Scholar - 2).B.F. Armaly, F. Durst, J.C.F. Pereira and B. Schonung,
*Experimental and theoretical investigation of backward-facing step flow*, J. Fluid Mech.,**127**, (1983), pp.473–496.ADSCrossRefGoogle Scholar - 3).J.T. Beale and A. Majda,
*Vortex methods. I: Convergence in three dimensions*, Math. Comp.**39**(1982), pp. 1–27.MathSciNetADSzbMATHGoogle Scholar - 4).J.T. Beale and A. Majda,
*Vortex methods. II: Higher order accuracy in two and three dimensions*, Math. Comp.**39**(1982), pp. 29–52.MathSciNetzbMATHGoogle Scholar - 5).A.J. Chorin,
*Numerical study of slightly viscous flow*, J. Fluid Mech.,**57**(1973), pp. 785–796.MathSciNetADSCrossRefGoogle Scholar - 6).A.J. Chorin,
*Vortex sheet approximation of boundary layers*J. Comp. Phys.,**27**(1978), 428–442.ADSzbMATHCrossRefGoogle Scholar - 7).V.M. Del Prete and O.H. Hald,
*Convergence of vortex methods for Euler’s equations*, Math. Comp.,**32**(1978), pp 791–809.MathSciNetADSzbMATHGoogle Scholar - 8).F. Durst and C. Tropea,
*Flows over two-dimensional backward-facing steps*, Structure of Complex Turbulent Shear Flows (R. Dumas and L. Fulachier, Eds.), IUTAM Symposium, Springer-Verlag, Berlin, (1982).Google Scholar - 9).A.F. Ghoniem and J.A. Sethian,
*Dynamics of turbulent structure in a recirculating flow: a computational study*, AIAA 23rd Aerospace Sciences Meeting, (1985), AIAA-85-0146, to appear in AIAA Journal.Google Scholar - 10).O.H. Hald,
*Convergence of vortex methods for Euler’s equations, II*, SLAM J. Numer. Anal.,**16**(1979), pp. 726–755.MathSciNetADSzbMATHCrossRefGoogle Scholar - 11).O.H. Hald,
*The flowmap for Euler’s equations*, to be published.Google Scholar - 12).
- 13).A. Majda and J.A. Sethian,
*The derivation and numerical solution of the equations for zero mach number*combustion, Combust. Sci. Tech.,**42**, (1985), pp. 185–205.CrossRefGoogle Scholar - 14).S. Osher and J. Sethian,
*Numerical methods for calculating fronts propagating with curvature dependent speeds*, preprint, to be submitted for publication.Google Scholar - 15).J. Periaux, O. Pironneau, F. Thomasset,
*Computational results of the back step flow workshop*, Fifth International GAMM Conference on Numerical Methods in Fluid Mechanics, Springer-Verlag, 1983.**9**, (1976), pp.75–103.Google Scholar - 16).J.A. Sethian,
*Curvature and the Evolution of Fronts*, Comm. Math. Phys.,**101**(1985), pp.487–499.MathSciNetADSzbMATHCrossRefGoogle Scholar - 17).J.A. Sethian,
*Numerical simulation of flame propagation in a closed vessel*, Proc. Fifth Int. GAMM Conf. Numer. Meth. Fluid Mech., Rome, Italy, (1983)Google Scholar - 18).J.A. Sethian,
*Turbulent combustion in open and closed vessels*, J. Comp. Phys.,**55**, (1984), pp.425–456.ADSCrossRefGoogle Scholar - 19).J.A. Sethian and A.F. Ghoniem,
*Validation study for vortex methods*, submitted to J. Comp. Phys.,Google Scholar - 20).J.A. Sethian,
*Vortex methods and turbulent combustion*, Lectures in Applied Mathematics,**22**, (1985).Google Scholar - 21).J.A. Sethian,
*The wrinkling of a flame due to viscosity*, Fire Dynamics and Heat Transfer, (J. Quintiere, Ed.), Proc. 21st Nat. Heat. Transfer Conf., (1983), pp. 29.Google Scholar