A numerical study of the interactions between viscous flow, transport and kinetics in fixed bed reactors

Almgren, 1998, A conservative adaptive projection method for variable density incompressible Navier–Stokes equations, Journal of Computational Physics, 142, 1, 10.1006/jcph.1998.5890 Amsden, 1970, A simplified MAC technique for incompressible fluid flow calculations, Journal of Computational Physics, 6, 322, 10.1016/0021-9991(70)90029-X Amsden, A. A. & Harlow, F. H. (1970b). The SMAC method: a numerical technique for calculating incompressible fluid flows. Los Alamos Scientific Lab., Report No. LA-4370. Anderson, 1984 Beam, 1978, n Implicit factored scheme for compressible Navier–Stokes equations, AIAA Journal, 16, 393, 10.2514/3.60901 Bell, 1992, A second-order projection method for variable-density flows, Journal of Computational Physics, 101, 334, 10.1016/0021-9991(92)90011-M Benenati, 1962, Void fraction distribution in beds of spheres, American Institute of Chemical Engineering Journal, 8, 359, 10.1002/aic.690080319 Berge, 1998, A regional scale multi-layer model for the calculation of long term transport and deposition of air pollution in Europe, Tellus, 50, 205, 10.1034/j.1600-0889.1998.t01-2-00001.x Bird, 1960 Braza, 1986, Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder, Journal of Fluid Mechanics, 165, 79, 10.1017/S0022112086003014 Chorin, 1968, Numerical solution of the Navier–Stokes equations, Mathematical Computation, 22, 745, 10.1090/S0025-5718-1968-0242392-2 Dabdub, 1995, Extrapolation techniques used in the solution of stiff ODEs associated with chemical kinetics of air quality models, Atmospheric Environment, 29, 403, 10.1016/1352-2310(94)00282-P De Groote, 1995, Reactor modeling and simulation in synthesis gas production, Reviews in Chemical Engineering, 11, 145, 10.1515/REVCE.1995.11.2.145 Delhaye, J. M. & Achard, J. L. (1976). On the use of averaging operators introduced in two-phase flow modeling. Proc. CSNI Specialists’ Meeting, Toronto, 3–4 August 1976. In: Banerjee, S. and Weaver, K. R. (Eds.) Transient two-phase flow (Vol. 1) (pp. 5–84) AECL, Canada. Delhaye, J. M. & Achard, J. L. (1977). On the use of averaging operators in two-phase flow modeling. In: O. C., Jr. & Bankoff, S. G. (Eds.) Thermal and hydraulic aspects of nuclear reactor safety, 1: light water reactors. ASME Winter Meeting, 1977. Erlebacher, 1992, Towards the large-eddy simulation of compressible turbulent flows, Journal of Fluid Mechanics, 238, 155, 10.1017/S0022112092001678 Faires, 1993 Ferziger, 1996 Froment, 1990 Godunov, 1959, A difference method for the numerical calculation of discontinuous solutions of hydrodynamic equations, Mat. Sbornik, 47, 271 Govindarao, 1986, Voidage profiles in packed beds of spheres, Chemical Engineering Science, 41, 533, 10.1016/0009-2509(86)87035-X Harlow, 1965, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, The Physics of Fluids, 8, 2182, 10.1063/1.1761178 Hundsdorfer, 1995, A note on splitting errors for advection-reaction equations, Applied Numerical Mathematics, 18, 191, 10.1016/0168-9274(95)00069-7 Hutchinson, 1986, A multigrid method based on the additive correction strategy, Numerical Heat. Transfer, 9, 511, 10.1080/10407788608913491 Hutchinson, 1988, Application of additive correction multi-grid to the coupled fluid flow equations, Journal of Numerical Heat. Transfer, 13, 133 Jacobson, 1996, Application of a sparse-matrix, vectorized gear-type code in a new air pollution modeling system, ZAMM Z. Angew. Mathematical Mechanics, 76, 333 Jacobson, 1996, Simulation equilibrium within aerosols and non-equilibrium between gases and aerosols, Journal of Geophysics Research, 101, 9079, 10.1029/96JD00348 Jonson, 1998, EMEP Eulerian model for atmospheric transport and deposition of nitrogen species over Europe, Environmental Pollution, 102, 289, 10.1016/S0269-7491(98)80046-8 Kelkar, 1989, Development of generalized block correction procedures for the solution of discretized Navier–Stokes equations, Computer Physics Communications, 53, 329, 10.1016/0010-4655(89)90170-7 Klemp, 1978, The simulation of three-dimensional convective storm dynamics, J. Atmos. Sci., 35, 1070, 10.1175/1520-0469(1978)035<1070:TSOTDC>2.0.CO;2 Kim, 1985, Application of a fractional-step method to incompressible Navier–Stokes equations, Journal of Computational Physics, 59, 308, 10.1016/0021-9991(85)90148-2 Knoth, 1995, Numerical methods for the solution of large kinetic systems, Applied Numerical Mathematics, 18, 211, 10.1016/0168-9274(95)00054-X Knoth, 1998, An explicit–implicit numerical approach for atmospheric chemistry—transport modeling, Atmospheric Environment, 32, 1785, 10.1016/S1352-2310(97)00476-7 Knio, 1999, A semi-implicit numerical scheme for reacting flow, Journal of Computational Physics, 154, 428, 10.1006/jcph.1999.6322 Kuo, 1986 Lahey, 1989, The three-dimensional time and volume averaged conservation equations of two-phase flow, Advances in Nuclear Science and Technology, 20, 1, 10.1007/978-1-4613-9925-4_1 Lanser, 1999, Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modeling, Journal of Computational and Applied Mathematics, 111, 201, 10.1016/S0377-0427(99)00143-0 Leonard, 1994, Comparison of truncation error of finite-difference and finite-volume formulations of convection terms, Applied Mathematical Modelling, 18, 46, 10.1016/0307-904X(94)90182-1 Le Veque, 1990 Lydersen, 1979 MacCormack, R. W. (1969). The effect of viscosity in hypervelocity impact catering. AIAA -69-354, 1–7. MacCormack, R. W. (1976). An Efficient Numerical Method for Solving the Time-Dependent Compressible Navier-Stokes Equations at High-Reynolds number. NASA TM 73129, also in: Computing in applied mechanics, Applied Mech. Div., Vol. 18. Majda, 1985, The derivation and numerical solution of the equations for zero Mach number combustion, Combustion Science and Technology, 42, 185, 10.1080/00102208508960376 Marchuk, 1974 Najm, 1998, A semi-implicit numerical scheme for reacting flows I. Stiff chemistry, Journal of Computational Physics, 143, 381, 10.1006/jcph.1997.5856 Ogura, 1962, Scale analysis of deep and shallow convection in the atmosphere, Journal of Atmosphere Science, 19, 171, 10.1175/1520-0469(1962)019<0173:SAODAS>2.0.CO;2 Olendrzynski, 2000, EMEP Eulerian model for acid deposition over Europe, International Journal of Environment and Pollution, 14, 391, 10.1504/IJEP.2000.000561 Panton, 1996 Patankar, 1980 Peyret, 1983 Press, 1992, 1 Rehm, R. G. & Baum, H. R. (1978). The equations of motion for thermally driven, buoyant flows. Journal of Research of the National Bureau of Standards, 83 (3) 297–308. Reid, 1988 Ridgway, 1968, Voidage fluctuations in randomly packed beds of spheres adjacent to a containing wall, Chemical Engineering Science, 23, 1147, 10.1016/0009-2509(68)87099-X Roe, 1986, Characteristic-based schemes for the Euler equations, Annual Review of Fluid Mechanics, 18, 337, 10.1146/annurev.fl.18.010186.002005 Rosner, 1986 Sandler, 1999 Sandu, 1997, Benchmarking stiff ODE solvers for atmospheric chemistry problems II: implicit vs. explicit, Atmospheric Environment, 31, 3151, 10.1016/S1352-2310(97)00059-9 Sandu, 1997, Benchmarking stiff ODE solvers for atmospheric chemistry problems II: Rosenbrock solvers, Atmospheric Environment, 31, 3459, 10.1016/S1352-2310(97)83212-8 Sathyamurthy, 1994, Block-correction-based multigrid method for fluid flow problems, Num. Heat Transfer, Part B, 25, 375, 10.1080/10407799408955926 Saylor, 1995, On the comparison of numerical methods for the integration of kinetic equations in atmospheric chemistry and transport models, Atmospheric Environment, 29, 2585, 10.1016/1352-2310(95)00187-4 Schiesser, 1991 Settari, 1973, A generalization of the additive correction methods for the iterative solution of matrix equations, SIAM Journal of Numerical Analysis, 10, 506, 10.1137/0710046 Skaare, S.H. (1993) Reaction and heat transfer in a wall-cooled fixed bed reactor, Dr. ing. Thesis, The Norwegian Institute of Technology. Skamarock, 1992, The Stability of time-split numerical methods for the hydrostatic and the non-hydrostatic elastic equations, Monthly Weather Review, 120, 2109, 10.1175/1520-0493(1992)120<2109:TSOTSN>2.0.CO;2 Slattery, 1990 Sod, 1978, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, Journal of Computational Physics, 27, 1, 10.1016/0021-9991(78)90023-2 Steger, 1977, Implicit finite-difference procedures for the computation of vortex wakes, AIAA Journal, 15, 581, 10.2514/3.60663 Strang, 1968, On the construction and comparison of difference schemes, SIAM Journal of Numerical Analysis, 5, 506, 10.1137/0705041 Sweby, 1984, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM Journal of Numerical Analysis, 21, 995, 10.1137/0721062 Tapp, 1976, A non-hydrostatic mesoscale model, Quarterly Journal of Royal Met. Society, 102, 277, 10.1002/qj.49710243202 Thompson, 1972 Toro, 1999 van Leer, 1974, Towards the ultimate conservation difference scheme II. Monotonicity and conservation combined in a second order scheme, Journal of Computational Physics, 14, 361, 10.1016/0021-9991(74)90019-9 Vanden Bussche, 1996, A steady-state kinetic model for methanol synthesis and the water gas shift reaction on a commercial Cu/ZnO/Al2O3 catalyst, Journal of Catalysis, 161, 1, 10.1006/jcat.1996.0156 Versteeg, 1995 Verwer, 1995, Explicit methods for stiff ODEs from atmospheric chemistry, Applied Numerical Mathematics, 18, 413, 10.1016/0168-9274(95)00068-6 Verwer, 1996, An implicit–explicit approach for atmospheric transport—chemistry problems, Applied Numerical Mathematics, 20, 191, 10.1016/0168-9274(95)00126-3 Verwer, 1996, A comparison of stiff ODE solvers for atmospheric chemistry problems, Atmospheric Environment, 30, 49, 10.1016/1352-2310(95)00283-5 Verwer, 1999, A second-order Rosenbrock method applied to photochemical dispersion problems, SIAM Journal of Science Computers, 20, 1456, 10.1137/S1064827597326651 Xu, 1989, Methane steam reforming, methanation and water–gas shift: I. Intrinsic kinetics, American Institute of Chemical Engineering Journal, 35, 88, 10.1002/aic.690350109 Xu, 1989, Methane steam reforming, methanation and water–gas shift: II. Diffusional limitations and reactor simulations, American Institute of Chemical Engineering Journal, 35, 97, 10.1002/aic.690350110