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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 47, 2004 - Issue 1
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Original Articles

THE NUMERICAL SIMULATION OF VARIABLE-PROPERTY REACTING-GAS DYNAMICS: NEW INSIGHTS AND VALIDATION

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Pages 27-56 | Received 10 Jun 2004, Accepted 05 Aug 2004, Published online: 24 Feb 2007

REFERENCES

  • C. Depcik , Modeling Reacting Gases and Aftertreatment Devices for Internal Combustion Engines, Ph.D. thesis , University of Michigan , Ann Arbor , MI , 2003 .
  • P. A. Gnoffo , Computational, Fluid Dynamics Technology for Hypersonic Applications, AIAA Paper 2003–3259 , 2003 .
  • P. A. Gnoffo , Planetary-Entry Gas Dynamics , Annu. Rev. Fluid Mech. , vol. 31 , no. 1 , pp. 459 – 494 , 1999
  • B. van Leer , Upwind-Difference Methods for Aerodynamic Problems Governed by the Euler Equations, Large-Scale Computations in Fluid Mechanics , Lect. Appl. Math. , vol. 22 , no. 2 , pp. 327 – 336 , 1985 .
  • A. Onorati , G. Ferrari , and G. D'Errico , Fluid Dynamic Modeling of the Gas Flow with Chemical Specie Transport through the Exhaust Manifold of a Four Cylinder SI Engine, SAE Paper 1999-01-0557 , 1999 .
  • A. Onorati , G. Ferrari , and G. D'Errico , 1D Unsteady Flows with Chemical Reactions in the Exhaust Duct-System of S.I. Engines: Predictions and Experiments, SAE Paper 2001-01-0939 , 2001 .
  • A. Onorati , G. Ferrari , G. D'Errico , and G. Montenegro , The Prediction of 1D Unsteady Flows in the Exhaust System of a S.I. Engine Including Chemical Reactions in the Gas and Solid Phase, SAE Paper 2002-01-0003 , 2002 .
  • A. Onorati , G. D'Errico , and G. Ferrari , 1D Fluid Dynamic Modeling of Unsteady Reacting Flows in the Exhaust System with Catalytic Converter for S.I. Engines, SAE Paper 2000-01-0210 , 2000 .
  • D. E. Winterbone and R. J. Pearson , Theory of Engine Manifold Design: Wave Action Methods for IC Engines , SAE Press , London , 2000 .
  • G. D. van Albada , B. van Leer , W. W. Roberts , A Comparative Study of Computational Methods in Cosmic Gas Dynamics , Astron. Astrophy. , vol. 108 , pp. 76 – 84 , 1982 .
  • P. L. Roe , Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , J. Comput. Phys. , vol. 43 , pp. 357 – 372 , 1981 . [CROSSREF] [CSA]
  • T. Morel , R. Keribar , and P. N. Blumberg , A New Approach to Integrating Engine Performance and Component Design Analysis through Simulation, SAE Paper 880131 , 1988 .
  • H. Zhang and S. K. Widener , An Integrated Engine Cycle Simulation Model with Species Tracking in Piping System, SAE Paper 960077 , 1996 .
  • B. Riemann , Uber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite , Gott. Abh , 8 (Math.) , pp. 43 – 65 , 1858 .
  • E. Jenny , Unidimensional Transient Flow with Consideration of Friction, Heat Transfer, and Change of Section , Brown Boveri Rev. , vol. 37 , pp. 447 – 461 , 1950 .
  • T. Bulaty and H. Niessner , Calculation of 1-D Unsteady Flows in Pipe Systems of I.C. Engines , J. Fluids Eng. , vol. 107 , pp. 407 – 412 , 1985 .
  • R. S. Benson , R. D. Garg , and D. Woollatt , A Numerical Solution of Unsteady Flow Problems , Int. J. Mech. Sci. , 6 , 117 – 144 , 1964 . [CROSSREF]
  • R. S. Benson , The Thermodynamics and Gas Dynamics of Internal-Combustion Engines , chap. 6–7 , Oxford University Press , New York , 1982 .
  • F. Payri , J. M. Corberán , and F. Boada , Modifications to the Method of Characteristics for the Analysis of the Gas Exchange Process in Internal Combustion Engines , Proc. Inst. Mech. Eng. , vol. 200 , no. D4 , pp. 259 – 266 , 1986 .
  • J.-T. Yang and G.-L. Tsai , The Simulation of Gas Exchange Process of the Multi-cylinder Internal Combustion Engines , J. Chinese Soc. Mech. Eng. , vol. 11 , no. 5 , pp. 455 – 463 , 1990 .
  • Y. Zhu and R. D. Reitz , A 1-D Gas Dynamics Code for Subsonic and Supersonic Flows Applied to Predict EGR Levels in a Heavy-Duty Diesel Engine, Int. J. Vehicle Design , vol. 22, no. 3/4, pp. 227–252, 1999. [CSA]
  • G. P. Blair , S. J. Kirkpatrick , D. O. Mackey , and R. Fleck , Experimental Validation of 1-D Modeling Codes for a Pipe System Containing Area Discontinuities, SAE Paper 950276 , 1995 .
  • G. P. Blair , S. J. Kirkpatrick , and R. Fleck , Experimental Validation of a 1-D Modeling Code for a Pipe Containing Gas of Varying Properties, SAE Paper 950275 , 1995 .
  • P. Lax and B. Wendroff , System of Conservation Laws , Commun. Pure Appl. Math. , vol. 13 , pp. 217 – 237 , 1960 .
  • J. P. Boris and D. L. Book , Flux Corrected Transport: I. SHASTA, A Fluid Transport Algorithm That Works , J. Comput. Phys. , vol. 55 , pp. 1 – 32 , 1973 . [CROSSREF] [CSA]
  • D. L. Book , J. P. Boris , and K. Hain , Flux-Corrected Transport: II. Generalizations of the Method , J. Comput. Phys. , vol. 18 , pp. 248 – 283 , 1975 . [CROSSREF] [CSA]
  • A. Harten , The Artificial Compression Method for Computation of Shocks and Contact Discontinuities: III. Self-adjusting Hybrid Schemes , Math. Comput. , vol. 32 , no. 142 , pp. 363 – 389 , 1978 . [CSA]
  • A. Harten and G. Zwas , Self-adjusting Hybrid Schemes for Shock Computations , J. Comput. Phys. , vol. 9 , pp. 568 – 583 , 1972 . [CROSSREF]
  • R. D. Richtmyer , A, Survey of Difference Methods for Nonsteady Fluid Dynamics, NCAR Tech. Note 63–2 , Boulder , CO , 1963 .
  • R. W. MacCormack , The, Effect of Viscosity in Hypervelocity Impact Cratering, AIAA Paper 69-354 , 1969 .
  • J. D. Hoffman , Numerical Methods for Engineers and Scientists , chap. 12 , McGraw-Hill , New York , 1992 .
  • C. Hirsch , Numerical Computation of Internal and External Flows , Wiley , New York , 1990 .
  • J. M. Corberán and L. Gascón , New Method to Calculate Unsteady 1-D Compressible Flow in Pipes with Variable Cross Section: Application to the Calculation of the Flow in Intake and Exhaust Pipes of I.C. Engines , Engine Model. , vol. 23 , pp. 77 – 87 , 1995 .
  • J. M. Corberán and M. L. Gascón , TVD Schemes for the Calculation of Flow in Pipes of Variable Cross-Section , Math. Comput. Model. , vol. 21 , no. 3 , pp. 85 – 92 , 1995 . [CROSSREF]
  • C.-W. Hong and G.-H. Huang , Numerical Computation of Unsteady Gas Flow in the Ducts of Reciprocating Engines , Numer. Heat Transfer A , vol. 32 , pp. 769 – 785 , 1997 . [CSA]
  • M. Vandevoorde , R. Sierens , and E. Dick , Validation of a New TVD Scheme against Measured Pressure Waves in the Inlet and Exhaust System of a Single Cylinder Engine , J. Eng. Gas Turbines Power , vol. 122 , pp. 533 – 540 , October 2000 . [CROSSREF]
  • M. Vandevoorde , J. Vierendeels , R. Sierens , E. Dick , and R. Baert , Comparison of Algorithms for Unsteady Flow Calculations in Inlet and Exhaust Systems of IC Engines , J. Eng. Gas Turbines Power , vol. 122 , pp. 541 – 548 , October 2000 . [CROSSREF]
  • M. Poloni , D. E. Winterbone , and J. R. Nichols , Comparison of Unsteady Flow Calculations in a Pipe by the Method of Characteristics and the Two-Step Differential Lax-Wendroff Method , Int. J. Mech. Sci. , vol. 29 , no. 5 , pp. 367 – 378 , 1987 .
  • S. J. Kirkpatrick , G. P. Blair , R. Fleck , and R. K. McMullan , Experimental Evaluation of 1-D Computer Codes for the Simulation of Unsteady Gas Flow through Engines—A First Phase, SAE Paper 941685 , 1994 .
  • J. Liu , N. Schorn , C. Schernus , and L. Peng , Comparison Studies on the Method of Characteristics and Finite Difference Methods for One-Dimensional Gas Flow through IC Engine Manifold, SAE Paper 960078 , 1996 .
  • A. Onorati , Numerical, Simulation of Exhaust Flows and Tailpipe Noise of a Small Single Cylinder Diesel Engine, SAE Paper 951755 , 1995 .
  • A. Onorati , and G. Ferrari , Modeling of 1-D Unsteady Flows in I.C. Engine Pipe Systems: Numerical Methods and Transport of Chemical Species, SAE Paper 980782, 1998.
  • A. Onorati , M. Perotti , and S. Rebay , Modelling One-Dimensional Unsteady Flows in Ducts: Symmetric Finite Difference Schemes versus Galerkin Discontinuous Finite Element Methods , Int. J. Mech. Sci. , vol. 39 , pp. 1213 – 1236 , 1997 . [CROSSREF]
  • S. F. Davis , TVD Finite Difference Schemes and Artificial Viscosity, NASA CR-172373 , Hampton , VA , 1984 .
  • S. R. Chakravarthy , S. Osher , A New Class of High Accuracy TVD Schemes for Hyperbolic Conservation Laws, AIAA Paper 85-0363 , 1985 .
  • S. Osher and F. Solomon , Upwind Schemes for Hyperbolic Systems of Conservation Laws , Math. Comput. , vol. 38 , pp. 339 – 374 , 1982 . [CSA]
  • G. Zhang and D. N. Assanis , Manifold Gas Dynamics Modeling and Its Coupling with Single-Cylinder Engine Models Using Simulink , Trans. ASME J. Eng. Gas Turbines Power , vol. 125 , no. 2 , pp. 563 – 571 , 2003 . [CROSSREF] [CSA]
  • A. Harten , A High Resolution Scheme for the Computation of Weak Solutions of Hyperbolic Conservation Laws , J. Comput. Phys. , vol. 57 , pp. 357 – 393 , 1983 .
  • A. Harten , P. D. Lax , and B. van Leer , On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , SIAM Rev. , vol. 25 , no. 1 , pp. 35 – 61 , 1983 .
  • G. P. Blair , An, Alternative Method for the Prediction of Unsteady Gas Flow through the Internal Combustion Engine, SAE Paper 911850 , 1991 .
  • S. Godunov , Résolution, numérique des problèmes multidimenionnels de la dynamique des gaz , MIR , Moscow , 1979 .
  • S.-C. Chang , X.-Y. Wang , and C.-Y. Chow , The Space-Time Conservation Element and Solution Element Method—A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. I. The Two Dimensional Time Marching Schemes, NASA Tech. Memo. 1998-208843 , Cleveland , OH , 1998 .
  • S. C. Chang and W. M. To , A Brief Description of a New Numerical Framework for Solving Conservation Laws—The Method of Space-Time Conservation Element and Solution Element, NASA Tech. Memo. 105757 , Cleveland , OH , 1992 .
  • S.-C. Chang , The Method of Space-Time Conservation Element and Solution Element—A New Approach for Solving the Navier-Stokes and Euler Equations , J. Comput. Phys. , vol. 119 , pp. 295 – 324 , 1995 . [CROSSREF] [CSA]
  • B. Cockburn and C. W. Shu , TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. II: General Framework , Math. Comput. , vol. 52 , no. 186 , pp. 411 – 435 , 1989 .
  • F. Bassi and S. Rebay , Discontinuous Finite Element High Order Accurate Numerical Solution of the Compressible Navier-Stokes Equations , 4th Int. Conf. on Fluid Dynamics. , Clarendon Press , Oxford , 1995 .
  • P. Giannattasio and A. Dadone , Applications of a High Resolution Shock-Capturing Scheme to the Unsteady Flow Computation in Engine Ducts , IMeche Int. Conf. Comp. Eng. Tech. , 119 – 126 , 1991 .
  • P. Batten , C. Lambert , and D. M. Causon , Positively Conservative High-Resolution Convection Schemes for Unstructured Elements , Int. J. Numer.Meth. Eng. , vol. 39 , no. 11 , pp. 1821 – 1838 , 1996 . [CROSSREF]
  • M. Chapman , J. M. Novak , and R. A. Stein , Numerical Modeling of Inlet and Exhaust Flows in Multi-cylinder Internal Combustion Engines , Winter Annual Meeting of the American Society of Mechanical Engineers , Phoenix , AZ , 1982 .
  • M. Chapman , FRAM—Nonlinear Damping Algorithms for the Continuity Equation , J. Comput. Phys. , vol. 44 , no. 1 , pp. 84 – 103 , 1981 . [CROSSREF]
  • J. A. White and J. H. Morrison , A Pseudo-temporal Multi-grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations, AIAA Paper 99-3360 , 1999 .
  • S. Gordon and B. J. McBride , Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications , NASA Ref. Publ. 1311, Cleveland , OH , 1996.
  • B. McBride and S. Gordon , Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications: II. Users Manual and Program Description , NASA Ref. Publ. 1311 , Cleveland , OH , 1996 .
  • S. Gordon and B. McBride , Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications: I. Analysis , NASA Ref. Publ. 1311 , Cleveland , OH , 1994 .
  • B. van Leer , Towards the Ultimate Conservative Difference Scheme V. A Second Order Sequel to Godunov's Method , J. Comput. Phys. , vol. 32 , pp. 101 – 136 , 1979 . [CROSSREF] [CSA]
  • P. L. Roe , Discrete Models for the Numerical Analysis of Time-Dependent Multidimensional Gas Dynamics , J. Comput. Phys. , vol. 63 , pp. 458 – 476 , 1986 . [CROSSREF] [CSA]
  • J. R. Edwards , A Low-Diffusion Flux-Splitting Scheme for Navier-Stokes Calculations , Comput. Fluids , vol. 26 , no. 6 , pp. 635 – 659 , 1997 . [CROSSREF]
  • T. J. Barth , Numerical, Aspects of Computing High-Reynolds Number Flows on Unstructured Meshes, AIAA Paper 91-0721 , 1991 .
  • T. J. Barth , D. C. Jespersen , The Design and Application of Upwind Schemes on Unstructured Meshes, AIAA Paper 89-0366 , 1989 .
  • V. Venkatakrishnan , Convergence to Steady-State Solutions of the Euler Equations on Unstructured Grids with Limiters , J. Comput. Phys. , vol. 118 , pp. 120 – 130 , 1995 . [CROSSREF] [CSA]
  • H. C. Yee , Construction of Explicit and Implicit Symmetric TVD Schemes and Their Applications , J. Comput. Phys. , vol. 68 , no. 1 , pp. 151 – 179 , 1987 . [CROSSREF] [CSA]
  • F. M. Cheatwood and P. A. Gnoffo , User's Manual for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA), NASA Tech. Memo. 4674 , Hampton , VA , 1996 .
  • et al. , Opportunities for Breakthroughs in Large-Scale Computational Simulation and Design, NASA TM-2002-211747 , Hampton , VA , 2002 .
  • P. A. Gnoffo , Hypersonic, Flows over Biconics Using a Variable-Effective-Gamma, Parabolized-Navier-Stokes Code, AIAA Paper 83-1666 , 1983 .
  • P. A. Gnoffo , K. J. Weilmuenster , R. D. Braun , and C. I. Cruz , Influence of Sonic-Line Location on Mars Pathfinder Probe Aerothermodynamics , J. Spacecraft Rockets , vol. 33 , no. 2 , pp. 169 – 177 , 1996 . [CSA]
  • E. L. Rubin and S. Z. Burstein , Difference Methods for the Inviscid and Viscous Equations of a Compressible Gas , J. Comput. Phys. , vol. 2 , pp. 178 – 196 , 1967 . [CROSSREF]
  • S. Song , R. K. Hanson , C. T. Bowman , and D. M. Golden , Shock Tube Determination of the Overall Rate of NH2 + NO ⇒ Products in the Thermal De–NOx Temperature Window , Int. J. Chem. Kinetics , vol. 33 , pp. 715 – 721 , 2001 . [CROSSREF]
  • M. Rohrig , E. L. Peterson , D. F. Davidson , and R. K. Hanson , A Shock Tube Study of the Pyrolysis of NO2 , Int. J. Chem. Kinetics , vol. 29 , pp. 483 – 493 , 1997 . [CROSSREF]
  • M. Rohrig , E. L. Peterson , D. F. Davidson , and R. K. Hanson , Measurement of the Rate Coefficient of the Reaction CH + O2 ⇒ Products in the Temperature Range 2200 to 2600 K , Int. J. Chem. Kinetics , vol. 29 , pp. 781 – 789 , 1997 . [CROSSREF]
  • D. A. Masten , R. K. Hanson , and C. T. Bowman , Shock-Tube Study of the Reaction H + O2 ⇒ OH + O Using Laser Absorption , J. Phys. Chem. , vol. 94 , no. 18 , pp. 7119 – 7128 , 1990 .
  • J. B. Goodman and R. J. LeVeque , On the Accuracy of Stable Schemes for 2D Scalar Conservation Law , Math. Comput. , vol. 45 , pp. 15 – 21 , 1985 . [CSA]
  • M.-S. Liou , B. van Leer , and J.-S. Shuen , Splitting of Inviscid Fluxes for Real Gases , J. Comput. Phys. , vol. 87 , no. 1 , pp. 1 – 24 , 1990 . [CROSSREF] [CSA]
  • J.-S. Shuen , M.-S. Liou , and B. van Leer , Inviscid Flux-Splitting Algorithms for Real Gases with Non-equilibrium Chemistry , J. Comput. Phys. , vol. 90 , pp. 371 – 395 , 1990 . [CROSSREF] [CSA]
  • S. Gordon and B. J. McBride , Computer Program for Computation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouguet Detonations, NASA SP-273, Cleveland , OH , 1976.
  • M. M. Felling , R. H. Page , H. H. Korst , and R. A. White , An Experimental Analysis and Demonstration of the Non-steady Flow in a Shock Tube , Int. J. Eng. Educ. , vol. 14 , no. 1 , pp. 59 – 66 , 1998 .
  • C. F. Colebrook , Turbulent Flow in Pipes, with Particular Reference to the Transition Region between the Smooth and Rough Pipe Laws , J. Inst. Civil Eng. , vol. 11 , pp. 133 – 156 , 1938–1939 .
  • R. J. Kee , F. M. Rupley , E. Meeks , and J. A. Miller , Chemkin-III: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical and Plasma KineticsSandia Nat. Lab. Rep. 96-8216 , Albuquerque , NM , 1996 .
  • A. C. Hindmarsh , Serial, Fortran Solvers for ODE Initial Value Problems, Lawrence Livermore Nat. Lab., www.llnl.gov/CASC/odepack, August 8 , 2003 .
  • A. Seiff and D. B. Kirk , Structure of the Atmosphere of Mars in Summer at Mid-Latitudes , J. Geophys. Res. , vol. 82 , no. 28 , pp. 4364 – 4378 , 1977 . [CSA]
  • H. T. Woodward , Predictions, of Shock Layer Radiation from Molecular Band Systems in Proposed Planetary Atmospheres, NASA TN D-3850 , 1967 .
  • R. K. Hanson , Shock-Tube Study of Carbon Monoxide Dissociation Kinetics , J. Chem. Phys. , vol. 60 , no. 12 , pp. 4970 – 4976 , 1973 . [CROSSREF]
  • J. P. Appleton , M. Steinberg , and D. J. Liquornik , Shock-Tube Study of Carbon Monoxide Dissociation Using Vacuum-Ultraviolet Absorption , J. Chem. Phys. , vol. 52 , no. 3 , pp. 2205 – 2221 , 1970 .
  • C. Park , Review of Chemical-Kinetic Problems of Future NASA Missions, I: Earth Entries , J. Thermophys. Heat Transfer , vol. 7 , no. 3 , pp. 385 – 398 , 1993 . [CSA]
  • C. Park , J. T. Howe , R. L. Jaffe , and G. V. Candler , Review of Chemical-Kinetic Problems of Future NASA Missions, II: Mars Entries , J. Thermophys. Heat Transfer , vol. 8 , no. 1 , pp. 9 – 23 , 1994 . [CSA]
  • R. J. Pearson and D. E. Winterbone , The Simulation of Gas Dynamics in Engine Manifolds Using Non-linear Symmetric Difference Schemes , Proc. Inst. Mech. Eng. , vol. 211(C) , pp. 601 – 616 , 1997 .
  • R. H. Ni , A Multiple Grid Scheme for Solving the Euler Equations , AIAA J. , vol. 20 , pp. 1565 – 1571 , 1982 .
  • E. Dick , Multigrid Formulation of Polynomial Flux-Difference Splitting for Steady Euler Equations , J. Comput. Phys. , vol. 91 , pp. 161 – 173 , 1990 . [CROSSREF] [CSA]
  • E. Dick , A Flux Difference Splitting Method for the Steady Euler Equations , J. Comput. Phys. , vol. 43 , pp. 357 – 372 , 1988 . [CROSSREF] [CSA]
  • D. S. Park , J. U. Kim , and E. S. Kim , A Burner Type Trap for Particulate Matter from a Diesel Engine , Combustion and Flame , vol. 114 , pp. 585 – 590 , 1998 . [CROSSREF] [CSA]
  • C. Chen , A. Veshagh , and F. J. Wallace , A Comparison between Alternative Methods for Gas Flow and Performance Prediction of Internal Combustion Engines, SAE Paper 921734 , 1992 .
  • M. Vandevoorde , J. Vierendeels , E. Dick , and R. Sierens , A New Total Variation Diminishing Scheme for the Calculation of One-Dimensional Flow in Inlet and Exhaust Pipes of Internal Combustion Engines , Proc. Ins. Mech. Eng. , vol. 212 , no. D , pp. 437 – 448 , 1998 .
  • A. Harten and S. Osher , Uniformly High-Order Accurate Nonoscillatory Schemes. I. , SIAM J. Numer. Anal. , vol. 24 , no. 2 , pp. 279 – 309 , 1987 .

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