A parallel solution - adaptive method for three-dimensional turbulent non-premixed combusting flows

A parallel adaptive mesh refinement (AMR) algorithm is proposed and applied to the prediction of steady turbulent non-premixed compressible combusting flows in three space dimensions. The parallel solution-adaptive algorithm solves the system of partial-differential equations governing turbulent compressible flows of reactive thermally perfect gaseous mixtures using a fully coupled finite-volume formulation on body-fitted multi-block hexahedral meshes. The compressible formulation adopted herein can readily accommodate large density variations and thermo-acoustic phenomena. A flexible block-based hierarchical data structure is used to maintain the connectivity of the solution blocks in the multi-block mesh and to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. For calculations of near-wall turbulence, an automatic near-wall treatment readily accommodates situations during adaptive mesh refinement where the mesh resolution may not be sufficient for directly calculating near-wall turbulence using the low-Reynolds-number formulation. Numerical results for turbulent diffusion flames, including cold- and hot-flow predictions for a bluff-body burner, are described and compared to available experimental data. The numerical results demonstrate the validity and potential of the parallel AMR approach for predicting fine-scale features of complex turbulent non-premixed flames.

[1]  J. Lepper,et al.  Parallelization of a simulation code for reactive flows on the intel paragon , 1998 .

[2]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[3]  H. Im,et al.  Direct numerical simulation of ignition front propagation in a constant volume with temperature inhomogeneities: I. Fundamental analysis and diagnostics , 2006 .

[4]  Beth Anne V. Bennett,et al.  Local Rectangular Refinement in Three Dimensions (LRR3D): Development of a Solution-Adaptive Gridding Technique with Application to Convection-Diffusion Problems , 2007 .

[5]  Marsha Berger,et al.  Three-Dimensional Adaptive Mesh Refinement for Hyperbolic Conservation Laws , 1994, SIAM J. Sci. Comput..

[6]  B. Hjertager,et al.  On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion , 1977 .

[7]  Timothy J. Barth,et al.  Recent developments in high order K-exact reconstruction on unstructured meshes , 1993 .

[8]  William D. Henshaw,et al.  Adaptive Mesh Refinement on Overlapping Grids , 2005 .

[9]  Clinton P. T. Groth,et al.  International Journal of Computational Fluid Dynamics a Parallel Adaptive Mesh Refinement Algorithm for Predicting Turbulent Non-premixed Combusting Flows a Parallel Adaptive Mesh Refinement Algorithm for Predicting Turbulent Non-premixed Combusting Flows , 2022 .

[10]  C. Wilke.  A Viscosity Equation for Gas Mixtures , 1950 .

[11]  S. Pope,et al.  Calculations of bluff-body stabilized flames using a joint probability density function model with detailed chemistry , 2005 .

[12]  Bassam B. Dally,et al.  Instantaneous and Mean Compositional Structure of Bluff-Body Stabilized Nonpremixed Flames , 1998 .

[13]  Marc Garbey,et al.  Numerical Simulation of a Combustion Problem on a Paragon Machine , 1995, Parallel Comput..

[14]  V. Gregory Weirs,et al.  Adaptive Mesh Refinement - Theory and Applications , 2008 .

[15]  P. Colella,et al.  A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier-Stokes Equations , 1998 .

[16]  Scott Northrup,et al.  Parallel Implicit Adaptive Mesh Refinement Scheme for Body-Fitted Multi-Block Mesh , 2005 .

[17]  Jacqueline H. Chen,et al.  Direct numerical simulation of autoignition in non- homogeneous hydrogen-air mixtures , 2003 .

[18]  Robert W. Dibble,et al.  The structure of turbulent nonpremixed flames of methanol over a range of mixing rates , 1992 .

[19]  D. L. De Zeeuw,et al.  Three-dimensional mhd simulation of coronal mass ejections , 2000 .

[20]  Fue-Sang Lien,et al.  A Cartesian Grid Method with Transient Anisotropic Adaptation , 2002 .

[21]  Vigor Yang,et al.  Large-Eddy Simulation of Combustion Dynamics of Lean-Premixed Swirl-Stabilized Combustor , 2003 .

[22]  Ke Chen.  Error Equidistribution and Mesh Adaptation , 1994, SIAM J. Sci. Comput..

[23]  Michael Zingale,et al.  Adaptive low Mach number simulations of nuclear flame microphysics , 2004 .

[24]  Bernd Einfeld.  On Godunov-type methods for gas dynamics , 1988 .

[25]  D. Venditti,et al.  Adjoint error estimation and grid adaptation for functional outputs: application to quasi-one-dimensional flow , 2000 .

[26]  J. G. Verwer.  Reportrapport Vlugr3: a Vectorizable Adaptive Grid Solver for Pdes in 3d. I. Algorithmic Aspects and Applications Vlugr3: a Vectorizable Adaptive Grid Solver for Pdes in 3d I. Algorithmic Aspects and Applications , 1994 .

[27]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[28]  A. M. Eaton,et al.  Components, formulations, solutions, evaluation, and application of comprehensive combustion models , 1999 .

[29]  Fue-Sang Lien,et al.  Two‐dimensional anisotropic Cartesian mesh adaptation for the compressible Euler equations , 2004 .

[30]  Clinton P. T. Groth,et al.  3D multi‐fluid MHD studies of the solar wind interaction with Mars , 1999 .

[31]  Udo Ziegler,et al.  A three-dimensional Cartesian adaptive mesh code for compressible magnetohydrodynamics , 1999 .

[32]  Hong G. Im,et al.  Correlation of Flame Speed with Stretch in Turbulent Premixed Methane/Air Flames , 1997 .

[33]  M. Gonzalez,et al.  Modelling finite-rate chemistry effects in nonpremixed turbulent combustion: Test on the bluff-body stabilized flame , 1997 .

[34]  Scott B. Baden,et al.  Dynamic Partitioning of Non-Uniform Structured Workloads with Spacefilling Curves , 1996, IEEE Trans. Parallel Distributed Syst..

[35]  Alexandre Ern,et al.  An adaptive finite element method with crosswind diffusion for low Mach, steady, laminar combustion , 2003 .

[36]  Denis Veynante,et al.  Turbulent combustion modeling , 2002, VKI Lecture Series.

[37]  Rony Keppens,et al.  Hybrid block-AMR in cartesian and curvilinear coordinates: MHD applications , 2007, J. Comput. Phys..

[38]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[39]  J. Laufer,et al.  The Structure of Turbulence in Fully Developed Pipe Flow , 1953 .

[40]  Michael J. Aftosmis,et al.  Robust and efficient Cartesian mesh generation for component-based geometry , 1997 .

[41]  Robert W. Dibble,et al.  Raman-rayleigh measurements in bluff-body stabilised flames of hydrocarbon fuels , 1992 .

[42]  Jacqueline H. Chen,et al.  Direct numerical simulation of hydrogen-enriched lean premixed methane–air flames , 2004 .

[43]  M. D. Salas,et al.  Algorithmic Trends in Computational Fluid Dynamics , 1993 .

[44]  William D. Henshaw,et al.  A Fourth-Order Accurate Method for the Incompressible Navier-Stokes Equations on Overlapping Grids , 1994 .

[45]  C. Law,et al.  Direct Numerical Simulations of Turbulent Lean Premixed Combustion. , 2006 .

[46]  Bassam B. Dally,et al.  The structure of the recirculation zone of a bluff-body combustor , 1994 .

[47]  Edward A. Mason,et al.  Thermal Conductivity of Multicomponent Gas Mixtures. II , 1958 .

[48]  P. Colella,et al.  A Fast Adaptive Vortex Method in Three Dimensions , 1994 .

[49]  Bjarne Stroustrup,et al.  The C++ programming language (3. ed.) , 1997 .

[50]  Jaroslav Kautsky,et al.  Equidistributing Meshes with Constraints , 1980 .

[51]  M. Smooke,et al.  Adaptive continuation algorithms with application to combustion problems , 1989 .

[52]  D. D. Zeeuw,et al.  Global three‐dimensional MHD simulation of a space weather event: CME formation, interplanetary propagation, and interaction with the magnetosphere , 2000 .

[53]  William D. Henshaw,et al.  Applications Involving Moving Grids and Adaptive Mesh Refinement on Overlapping Grids , 2002 .

[54]  C. Westbrook,et al.  Simplified Reaction Mechanisms for the Oxidation of Hydrocarbon Fuels in Flames , 1981 .

[55]  R. Fox.  Computational Models for Turbulent Reacting Flows , 2003 .

[56]  B. Bennett,et al.  Local Rectangular Refinement with Application to Nonreacting and Reacting Fluid Flow Problems , 1999 .

[57]  William Leonard Kleb.  Matching Multistage Schemes to Viscous Flow , 2005 .

[58]  D. Venditti,et al.  Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows , 2003 .

[59]  de Hc Rick Lange,et al.  MODELING OF CONFINED AND UNCONFINED LAMINAR PREMIXED FLAMES ON SLIT AND TUBE BURNERS , 1995 .

[60]  John B. Bell,et al.  Cartesian grid method for unsteady compressible flow in irregular regions , 1995 .

[61]  Tianfeng Lu,et al.  Structure of a spatially developing turbulent lean methane–air Bunsen flame , 2007 .

[62]  T. Mexia,et al.  Author ' s personal copy , 2009 .

[63]  Philip L. Roe,et al.  Adaptive-mesh algorithms for computational fluid dynamics , 1993 .

[64]  D. Venditti,et al.  Grid adaptation for functional outputs: application to two-dimensional inviscid flows , 2002 .

[65]  R. LeVeque.  Approximate Riemann Solvers , 1992 .

[66]  D. Wilcox.  Turbulence modeling for CFD , 1993 .

[67]  Sanford Gordon,et al.  Computer program for calculation of complex chemical equilibrium compositions , 1972 .

[68]  John B. Bell,et al.  An Adaptive Projection Method for Unsteady, Low-Mach Number Combustion , 1998 .

[69]  W. Henshaw,et al.  Composite overlapping meshes for the solution of partial differential equations , 1990 .

[70]  W. Henshaw,et al.  An adaptive numerical scheme for high-speed reactive flow on overlapping grids , 2003 .

[71]  V. Guinot.  Approximate Riemann Solvers , 2010 .

[72]  T. Poinsot,et al.  Theoretical and numerical combustion , 2001 .

[73]  S. Cant.  High-performance computing in computational fluid dynamics: progress and challenges , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[74]  J. Sachdev,et al.  A parallel solution-adaptive scheme for multi-phase core flows in solid propellant rocket motors , 2005 .

[75]  de Hc Rick Lange,et al.  Numerical flow modelling in a locally refined grid , 1994 .

[76]  Robert K. Cheng,et al.  Numerical simulation of Lewis number effects on lean premixed turbulent flames , 2007 .

[77]  Phillip Colella,et al.  Numerical Solution of Plasma Fluid Equations Using Locally Refined Grids , 1997 .

[78]  J. Ferziger,et al.  An adaptive multigrid technique for the incompressible Navier-Stokes equations , 1989 .

[79]  Ann S. Almgren,et al.  A parallel adaptive projection method for low Mach number flows , 2002 .

[80]  Bassam B. Dally,et al.  The instantaneous spatial structure of the recirculation zone in bluff-body stabilized flames , 1998 .

[81]  D. D. Zeeuw,et al.  An adaptively refined Cartesian mesh solver for the Euler equations , 1993 .

[82]  Gediminas Adomavicius,et al.  A Parallel Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries , 2000 .

[83]  Quentin F. Stout,et al.  A parallel solution-adaptive scheme for ideal magnetohydrodynamics , 1999 .

[84]  Jacqueline H. Chen,et al.  Comparison of direct numerical simulation of lean premixed methane–air flames with strained laminar flame calculations , 2006 .

[85]  Clinton P. T. Groth,et al.  Parallel Adaptive Mesh Refinement Scheme for Turbulent Non-Premixed Combusting Flow Prediction , 2006 .

[86]  G. Turpin,et al.  Validation of a two-equation turbulence model for axisymmetric reacting and non-reacting flows , 2000 .

[87]  P. Lax,et al.  On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , 1983 .

[88]  H. Im,et al.  Stretch effects on the burning velocity of turbulent premixed hydrogen/air flames , 2000 .

[89]  Marshall B. Long,et al.  A comparison of the structures of lean and rich axisymmetric laminar Bunsen flames: application of local rectangular refinement solution-adaptive gridding , 1999 .

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

[91]  Scott M. Murman,et al.  Applications of Space-Filling-Curves to Cartesian Methods for CFD , 2004 .

[92]  Marsha Berger,et al.  Data structures for adaptive grid generation , 1986 .

[93]  Murat Bulgök,et al.  A QUADTREE-BASED ADAPTIVELY-REFINED CARTESIAN- GRID ALGORITHM FOR SOLUTION OF THE EULER EQUATIONS A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY , 2005 .

[94]  R. LeVeque,et al.  An Adaptive Cartesian Mesh Algorithm for the Euler Equations in Arbitrary Geometries , 1989 .

[95]  H. Pitsch.  LARGE-EDDY SIMULATION OF TURBULENT COMBUSTION , 2006 .

[96]  J. Blom,et al.  VLUGR3: A vectorizable adaptive grid solver for PDEs in 3D. II. Code description , 1994 .

[97]  Alexandre Ern,et al.  Detailed Chemistry Modeling of Laminar Diffusion Flames On Parallel Computers , 1995, Int. J. High Perform. Comput. Appl..

[98]  J. Janicka,et al.  ON THE FOURTH INTERNATIONAL WORKSHOP ON MEASUREMENT AND COMPUTATION OF TURBULENT NONPREMIXED FLAMES , 1999 .

[99]  Luc Vervisch,et al.  Three facets of turbulent combustion modelling: DNS of premixed V-flame, LES of lifted nonpremixed flame and RANS of jet-flame , 2004 .

[100]  T. Zacharia,et al.  Distributed Implementation of KIVA-3 on the Intel Paragon , 1996 .

[101]  Stephen B. Pope,et al.  PDF calculations of turbulent nonpremixed flames with local extinction , 2000 .

[102]  K. Powell,et al.  Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows , 1996 .

[103]  de Lph Philip Goey,et al.  A Numerical Study of a Premixed Flame on a Slit Burner , 1995 .

[104]  B. Bennett,et al.  Local rectangular refinement with application to axisymmetric laminar flames , 1998 .

[105]  V. Venkatakrishnan.  On the accuracy of limiters and convergence to steady state solutions , 1993 .

[106]  Jan Vierendeels,et al.  Application of a New Cubic Turbulence Model to Piloted and Bluff-Body Diffusion Flames , 2001 .

[107]  C. P. T. Groth,et al.  A Parallel Adaptive 3D MHD Scheme for Modeling Coronal and Solar Wind Plasma Flows , 1999 .

[108]  Darren L. de Zeeuw.  A quadtree-based adaptively-refined Cartesian-grid algorithm for solution of the Euler equations , 1993 .

[109]  P. Roe,et al.  A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics , 1999 .

[110]  Bassam B. Dally,et al.  Flow and mixing fields of turbulent bluff-body jets and flames , 1998 .

[111]  Marsha J. Berger,et al.  AMR on the CM-2 , 1994 .

[112]  M. Carbonaro,et al.  von Karman Institute for Fluid Dynamics , 2004 .

[113]  Edward A. Mason,et al.  Approximate Formula for the Thermal Conductivity of Gas Mixtures , 1958 .

[114]  James F. Driscoll,et al.  Numerical simulation of a laboratory-scale turbulent slot flame , 2007 .

[115]  J. Murthy,et al.  A PRESSURE-BASED METHOD FOR UNSTRUCTURED MESHES , 1997 .

[116]  Pedro J. Coelho,et al.  Calculation of a Confined Axisymmetric Laminar Diffusion Flame Using a Local Grid Refinement Technique , 1993 .

[117]  James J. Quirk,et al.  A Parallel Adaptive Mesh Refinement Algorithm , 1993 .

[118]  M. Berger,et al.  Robust and efficient Cartesian mesh generation for component-based geometry , 1998 .

[119]  Kenneth G. Powell,et al.  Three‐dimensional multiscale MHD model of cometary plasma environments , 1996 .

[120]  Quentin F. Stout,et al.  Adaptive Blocks: A High Performance Data Structure , 1997, SC.

[121]  Bram van Leer,et al.  Design of Optimally Smoothing Multi-Stage Schemes for the Euler Equations , 1989 .