Abstract
In this paper, we develop a method of prescribing time dependent boundary conditions for reacting flows. The method builds on earlier results, and derives from a linearization of the flow field around a base state. The base state is specified in terms of the flow dilatation, and we establish a general expression for the dilatation in reacting flows at low Mach number. This expression is then used to derive acoustically transparent boundary conditions. The utility of the approach is demonstrated via a number of laminar flame calculations, ranging in complexity from single step chemistry to a multi-step methane mechanism. The accuracy of the resulting solutions is found to be superior to those obtained using other means.
Similar content being viewed by others
References
Strikwerda, J.: Initial boundary value problems for incompletely parabolic systems. Commun. Pure Appl. Math. 30, 797–822 (1977)
Gustafsson, B., Sundström, A.: Incompletely parabolic problems in fluid dynamics. SIAM J. Appl. Math. 35, 343–357 (1978)
Dutt, P.: Stable boundary conditions and difference schemes for Navier-Stokes equations. SIAM J. Numer. Anal. 25, 245–267 (1988)
Tsynkov, S.: Numerical solution of problems on unbounded domains. A review. Appl. Numer. Math. 27, 465–532 (1998)
Ryaben‘kii, V., Tsynkov, S.: An application of the difference potentials method to solving external problems in CFD. Tech. Rep. 110338, NASA Technical Memorandum
Thompson, K.: Time dependent boundary conditions for hyperbolic systems. J. Comput. Phys. 68, 1–24 (1987)
Rudy, D., Strikwerda, J.: A nonreflecting outflow boundary condition for subsonic Navier-Stokes calculations. J. Comput. Phys. 36, 55–70 (1980)
Hedstrom, G.: Nonreflecting boundary conditions for nonlinear hyperbolic systems. J. Comput. Phys. 30, 222–237 (1979)
Prosser, R.: Improved boundary conditions for the direct numerical simulation of turbulent subsonic flows I: inviscid flows. J. Comput. Phys. 207, 736–768 (2005)
Grinstein, F.: Open boundary conditions in the simulation of subsonic turbulent shear flows. J. Comput. Phys. 115, 43–55 (1994)
Colonius, T., Lele, S., Moin, P.: Boundary conditions for direct computation of aerodynamic sound generation. AIAA J. 31, 1574–1582 (1993)
Hu, F.: On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer. J. Comput. Phys. 129, 201–219 (1996)
Hu, F.: A stable, perfectly matched layer for linearized Euler equations in unsplit physical variables. J. Comput. Phys. 173, 455–480 (2001)
Baum, M., Poinsot, T., Thévenin, D.: Accurate boundary conditions for multicomponent reactive flows. J. Comput. Phys. 116, 247–261 (1994)
Thevénin, D., Baum, M., Poinsot, T. (eds.): Direct Numerical Simulation for Turbulent Reacting Flows. Editions Technip, Paris (1996)
Sutherland, J., Kennedy, C.: Improved boundary conditions for viscous, reacting, compressible flows. J. Comput. Phys. 191, 502–524 (2003)
Yoo, C., Wang, Y., Trouvé, A., Im, H.: Characteristic boundary conditions for direct simulations of turbulent counterflow flames. Combust. Theory Model. 9, 617–646 (2005)
Prosser, R.: Towards improved boundary conditions for the DNS and LES of turbulent subsonic flows. J. Comput. Phys. 222, 469–474 (2007)
Poinsot, T., Lele, S.: Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys 101, 104–129 (1992)
Klein, R.: Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics I: one dimensional flow. J. Comput. Phys. 121, 213–237 (1995)
Polifke, W., Wall, C., Moin, P.: Partially reflecting and non-reflecting boundary conditions for simulation of compressible viscous flow. J. Comput. Phys. 213, 437–449 (2006)
McMurtry, P., Jou, W., Riley, J., Metcalfe, R.: Direct numerical simulations of a reacting mixing layer with chemical heat release. AIAA 24, 962–970 (1986)
Williams, F.: Combustion Theory, 2nd ed. Addison Wesley, Menlo Park, California (1985)
Echekki, T., Chen, J.: Unsteady strain rate and curvature effects in turbulent premixed methane-air flames. Combust. Flame 106, 184–202 (1996)
Asato, K., Nagata, H., Kawamura, T.: Extinction of premixed curved flames stabilized in a stagnation flow. In: Kuhl, A., Leyer, J., Borisov, A., Sirignano, W. (eds.) Dynamics of Deflagrations and Reactive Systems: Flames, pp. 161–175. AIAA (1989)
Kee, R., Rupley, F.: Chemkin II: a FORTRAN chemical kinetics package for the analysis of gas-phase chemical kinetics. Tech. Rep. SAND89-8009, Sandia National Laboratories, Livermore, CA 94551 (1989)
Prosser, R.: Assessment of numerical methods used in computational combustion. (2005, unpublished)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Prosser, R. Improved Boundary Conditions for the DNS of Reacting Subsonic Flows. Flow Turbulence Combust 87, 351–376 (2011). https://doi.org/10.1007/s10494-010-9307-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10494-010-9307-y