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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. Anderson and C. Greengard, On vortex methods, SIAM J. Numer. Anal., 22 (1985), pp. 413–440.
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.
J.T. Beale and A. Majda, Vortex methods. I: Convergence in three dimensions, Math. Comp. 39 (1982), pp. 1–27.
J.T. Beale and A. Majda, Vortex methods. II: Higher order accuracy in two and three dimensions, Math. Comp. 39 (1982), pp. 29–52.
A.J. Chorin, Numerical study of slightly viscous flow, J. Fluid Mech., 57 (1973), pp. 785–796.
A.J. Chorin, Vortex sheet approximation of boundary layers J. Comp. Phys., 27 (1978), 428–442.
V.M. Del Prete and O.H. Hald, Convergence of vortex methods for Euler’s equations, Math. Comp., 32 (1978), pp 791–809.
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).
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.
O.H. Hald, Convergence of vortex methods for Euler’s equations, II, SLAM J. Numer. Anal., 16 (1979), pp. 726–755.
O.H. Hald, The flowmap for Euler’s equations, to be published.
H. Honji, The starting flow down a step, J. Fluid Mech., 69, (1975), pp.229–210.
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.
S. Osher and J. Sethian, Numerical methods for calculating fronts propagating with curvature dependent speeds, preprint, to be submitted for publication.
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.
J.A. Sethian, Curvature and the Evolution of Fronts, Comm. Math. Phys., 101 (1985), pp.487–499.
J.A. Sethian, Numerical simulation of flame propagation in a closed vessel, Proc. Fifth Int. GAMM Conf. Numer. Meth. Fluid Mech., Rome, Italy, (1983)
J.A. Sethian, Turbulent combustion in open and closed vessels, J. Comp. Phys., 55, (1984), pp.425–456.
J.A. Sethian and A.F. Ghoniem, Validation study for vortex methods, submitted to J. Comp. Phys.,
J.A. Sethian, Vortex methods and turbulent combustion, Lectures in Applied Mathematics, 22, (1985).
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag New York Inc.
About this paper
Cite this paper
Sethian, J.A. (1988). Large Eddy Interaction with Propagating Flames. In: Engquist, B., Majda, A., Luskin, M. (eds) Computational Fluid Dynamics and Reacting Gas Flows. The IMA Volumes in Mathematics and Its Applications, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3882-9_16
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3882-9_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8388-1
Online ISBN: 978-1-4612-3882-9
eBook Packages: Springer Book Archive