Combustion modeling in two and three dimensions—Some numerical considerations

Abstract The wide disparity in claims for combusting flow prediction models which are based upon numerical solution of a set of governing partial differential equations is examined in the light of potential and observed problem areas encountered in the equation solving process. These numerical difficulties are attributed to such case dependent items as large flow gradients requiring dense meshes, the presence of singular points such as re-entrant corners, and equation stiffness. In simple flows where none of these difficulties is encountered or is mitigated, experience is good and an encouraging level of predictive agreement is observed. Thus there exists considerable motivation to continue to develop the equation solving process so that these difficulties are either minimized or eliminated when encountered in the more practical systems. Techniques which treat some of these problem areas are discussed and their current status reviewed.

[1]  R. B. Simpson,et al.  Centered differencing and the box scheme for diffusion convection problems , 1976 .

[2]  R. Kee,et al.  A split-operator, finite difference solution for axisymmetric laminar jet diffusion flames , 1977 .

[3]  T. Butler,et al.  Transient dynamics of chemically reactive gaseous mixtures with turbulence , 1974 .

[4]  Jr. Jim Douglas Alternating direction iteration for mildly nonlinear elliptic difference equations , 1961 .

[5]  F. G. Blottner,et al.  Nonequilibrium laminar boundary-layer flow of ionized air , 1964 .

[6]  C. W. Gear,et al.  Numerical initial value problem~ in ordinary differential eqttations , 1971 .

[7]  S. I. Cheng,et al.  Numerical Integration of Navier-Stokes Equations , 1970 .

[8]  Stephen B. Pope,et al.  The calculation of near-wake flows , 1976, Journal of Fluid Mechanics.

[9]  F. Durst,et al.  Theoretical and Experimental Investigations of Turbulent Flows with Separation , 1979 .

[10]  R. Schulz An investigation of ducted, two-stream, variable-density, turbulent jet mixing with recirculation , 1977 .

[11]  S. Yakowitz,et al.  The Numerical Solution of Ordinary Differential Equations , 1978 .

[12]  A. Hindmarsh,et al.  GEAR: ORDINARY DIFFERENTIAL EQUATION SYSTEM SOLVER. , 1971 .

[13]  J. H. Whitelaw,et al.  Laminar flow in a square duct of strong curvature , 1977, Journal of Fluid Mechanics.

[14]  W. Roger Briley,et al.  Numerical prediction of incompressible separation bubbles , 1975, Journal of Fluid Mechanics.

[15]  B. Launder,et al.  Mathematical Models of turbulence , 1972 .

[16]  A. R. Mitchell Computational methods in partial differential equations , 1969 .

[17]  Jay P. Boris,et al.  Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works , 1973 .

[18]  D. Spalding,et al.  Prediction of furnace heat transfer with a three-dimensional mathematical model , 1978 .

[19]  G. Habetler,et al.  An Alternating-Direction-Implicit Iteration Technique , 1960 .

[20]  S. Pruess Solving linear boundary value problems by approximating the coefficients , 1973 .

[21]  A. Il'in Differencing scheme for a differential equation with a small parameter affecting the highest derivative , 1969 .

[22]  Essam E. Khalil,et al.  Measurement and Calculation of Furnace-Flow Properties , 1977 .

[23]  E. P. Bartlett,et al.  An analysis of the coupled chemically reacting boundary layer and charring ablator. Part 3 - Nonsimilar solution of the multicomponent laminar boundary layer by an integral matrix method , 1968 .

[24]  K. J. Victoria,et al.  On the solution of the unsteady Navier- Stokes equations including multicomponent finite rate chemistry☆ , 1973 .

[25]  D. N. De G. Allen,et al.  RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDER , 1955 .

[26]  Harry A. Dwyer,et al.  Numerical modeling of unsteady flame propagation , 1978 .

[27]  Y. Timnat,et al.  On the numerical solution of flows with fast reactions , 1974 .

[28]  M. Ciment,et al.  Review. The Operator Compact Implicit Method for Parabolic Equations , 1978 .

[29]  J. Murphy An Efficient Solution Procedure for the Incompressible Navier-Stokes Equations , 1977 .

[30]  Essam E. Khalil,et al.  THE CALCULATION OF LOCAL FLOW PROPERTIES IN TWO-DIMENSIONAL FURNACES , 1975 .

[31]  N. N. Yanenko,et al.  The Method of Fractional Steps , 1971 .

[32]  R. Maccormack,et al.  A numerical method for solving the Navier-Stokes equations with application to shock-boundary layer interactions , 1975 .

[33]  David Young,et al.  Alternating Direction Implicit Methods , 1962, Adv. Comput..

[34]  Michael D. Griffin,et al.  Navier-Stokes Solutions of the Flowfield in an Internal Combustion Engine , 1976 .

[35]  A. D. Gosman,et al.  Heat and Mass Transfer in Recirculating Flows , 1969 .

[36]  F. G. Blottner,et al.  Investigation of some finite-difference techniques for solving the boundary layer equations☆ , 1975 .

[37]  I. Castro Numerical Difficulties in the Calculation of Complex Turbulent Flows , 1979 .

[38]  G. Moretti Complicated One-Dimensional Flows , 1971 .

[39]  K. W. Morton Stability and convergence in fluid flow problems , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[40]  F. Blottner,et al.  FINITE DIFFERENCE METHODS OF SOLUTION OF THE BOUNDARY-LAYER EQUATIONS , 1970 .

[41]  A. Gosman,et al.  A three-dimensional procedure for combustion chamber flows , 1977 .

[42]  Some experiments with singularities in linear elliptic partial differential equations , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[43]  A. A. Amsden,et al.  A numerical fluid dynamics calculation method for all flow speeds , 1971 .

[44]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

[45]  A. R. Gourlay Some recent methods for the numerical solution of time-dependent partial differential equations , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.