A lattice Boltzmann algorithm for calculation of the laminar jet diffusion flame

A new two-distribution lattice Boltzmann equation (LBE) algorithm is presented to solve the laminar diffusion flames within the context of Burke-Schumann flame sheet model. One distribution models the transport of the Schvab-Zeldovich coupling function, or the mixture fraction to combine the energy and species equations. The other distribution models the quasi-incompressible Navier-Stokes equations with the low Mach number approximation. In the quasi-incompressible flows, the thermodynamics quantities depend on the coupling function but not on the hydrodynamic pressure, and the fluid components are assumed to be compressible only in the mixing/reaction region. A systematic and consistent approach to deriving LBEs for the general advection-diffusion equation and the quasi-incompressible Navier-Stokes equations are also presented. The streaming step of the LBEs are discretized by the total variation diminishing (TVD) Lax-Wendroff scheme. Numerical simulations are carried out to reproduce the low frequency flame oscillation (or flame flicker) of buoyant jet diffusion flame. Comparison between the quasi-incompressible model and the incompressible model is presented and the role of non-solenoidal velocity is examined.

[1]  W. M. Roquemore,et al.  Buoyant diffusion flames , 1989 .

[2]  Shiyi Chen,et al.  Lattice Boltzmann computations for reaction‐diffusion equations , 1993 .

[3]  Ching-Long Lin,et al.  Pressure evolution lattice-Boltzmann-equation method for two-phase flow with phase change. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  O. Filippova,et al.  A Novel Lattice BGK Approach for Low Mach Number Combustion , 2000 .

[5]  B. V. Leer,et al.  Towards the Ultimate Conservative Difference Scheme , 1997 .

[6]  Robert W. Bilger.  Turbulent jet diffusion flames , 1976 .

[7]  Philip L. Roe,et al.  Generalized formulation of TVD Lax-Wendroff schemes , 1984 .

[8]  W. M. Roquemore,et al.  Time evolution of a buoyant jet diffusion flame , 1992 .

[9]  J. Buckmaster,et al.  The infinite candle and its stability—A paradigm for flickering diffusion flames , 1988 .

[10]  R Zhang,et al.  Effective volumetric lattice Boltzmann scheme. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[12]  Kenji Amagai,et al.  Diffusion flames and their flickering motions related with Froude numbers under various gravity levels , 2000 .

[13]  Taehun Lee,et al.  An Eulerian description of the streaming process in the lattice Boltzmann equation , 2003 .

[14]  Sauro Succi,et al.  Lattice Kinetic Theory for Numerical Combustion , 1996, comp-gas/9609003.

[15]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme , 1974 .

[16]  George Granger. Brown,et al.  Combustion Symposium: Introduction , 1928 .

[17]  Shiyi Chen,et al.  Lattice-Boltzmann Simulations of Fluid Flows in MEMS , 1998, comp-gas/9806001.

[18]  K. Wohl,et al.  I. Diffusion Flames , 1956 .

[19]  Qisu Zou,et al.  A improved incompressible lattice Boltzmann model for time-independent flows , 1995 .

[20]  L. Luo,et al.  Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation , 1997 .

[21]  Kazuhiro Yamamoto,et al.  Simulation of Combustion Field with Lattice Boltzmann Method , 2002 .

[22]  Raoyang Zhang,et al.  A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh-Taylor Instability , 1998 .

[23]  G. Doolen,et al.  Discrete Boltzmann equation model for nonideal gases , 1998 .

[24]  V. Vilimpoc,et al.  VORTICITY GENERATION IN JET DIFFUSION FLAMES , 1991 .

[25]  Hirotada Ohashi,et al.  Lattice Boltzmann Simulation of Multiphase Fluid Flows through the Total Variation Diminishing with Artificial Compression Scheme , 2000 .

[26]  Ching-Long Lin,et al.  A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio , 2005 .

[27]  M S Day,et al.  Numerical simulation of laminar reacting flows with complex chemistry , 2000 .

[28]  Yue-Hong Qian,et al.  Dissipative and dispersive behaviors of lattice-based models for hydrodynamics , 2000 .

[29]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[30]  H. Saunders.  Book Reviews : The Finite Element Method (Revised): O.C. Zienkiewicz McGraw-Hill Book Co., New York, New York , 1980 .

[31]  D. Hänel,et al.  Lattice-BGK Model for Low Mach Number Combustion , 1998 .

[32]  Alejandro L. Garcia,et al.  Stabilization of thermal lattice Boltzmann models , 1995 .

[33]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[34]  R. F. Warming,et al.  Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows , 1976 .

[35]  J. Lowengrub,et al.  Quasi–incompressible Cahn–Hilliard fluids and topological transitions , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[36]  Lea-Der Chen,et al.  Higher-order numerical model for simulation of time-dependent variable-density flows , 1996 .

[37]  F. G. Roper.  The prediction of laminar jet diffusion flame sizes: Part I. Theoretical model , 1977 .

[38]  D. d'Humières,et al.  Multiple–relaxation–time lattice Boltzmann models in three dimensions , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[39]  D. Spalding,et al.  INTRODUCTION TO COMBUSTION , 1979 .