LA-11560-MS KIVA-II: A Computer Program for Chemically Reactive Flows with Sprays Los Alamos N A T I O N A L L A B O R A T O R Y Los Alamos National Laboratory is operated by the University of California for the United States Department of Energy under contract W-7405-ENG-36. Prepared by Adrienne Rosen, Group T-3 This work was supported by the US Department of Energy, Division of Energy Conservation and Utilization Technologies. An Affirmative Action/Equal Opportunity Employer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither The Regents of the University of California, the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by The Regents of the University of California, the United States Government, or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of The Regents of the University of California, the United States Government, or any agency thereof. Los Alamos National Laboratory strongly supports academic freedom and a researcherÕs right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness. LA-11560-MS UC-96 Issued: May 1989 KIVA-II: A Computer Program for Chemically Reactive Flows with Sprays A. A. Amsden P. J. OÕRourke T. D. Butler Los Alamos N A T I O N A L L A B O R A T O R Y Los Alamos, New Mexico 87545 TABLE OF CONTENTS ABSTRACT . 1 I. INTRODUCTION AND BACKGROUND . 1 n. THEGOWRNINGE QUATIONS . 7 ~, Tk-e-~5.kic2Phase==..=, =. =. ==. ...=... .. T IL. ‘[email protected]@ets-:..=..=. ... ... ... ... 12- C.. Boundary-Conditions . ..... ........,.,.:.=.=.=........=.. 20. m. THEN~QT3mRIcALs+IwFim= . ~q= A. Telmporal”D”iffweneing . 24- B. Sp_atial Differencing . ~: .-.. -.. =–.,–..–. ...=.. ...’.. 24 StOc-ha-sti?Parti5ie’~e&nique . .. 32. D; State IReiations . 34 E. ~~~dII~fid~-~h”aS~ ~iI~erenCe ~qUatiOns ... ,. ... .. .... ... .. .. ... ... 34. Mass Density Equations . 34 ;: MomentumEquation . .. 36 3. C41Fa~h T-ormall#eloeities- . ...—...—,—,—,—,—=—=—3-7 4.. bterndfier~.Eq.ution .,..... ... ... ... 39- 5; T--ur*ulen~e-Equa~i~n~- . ...—.—,—,—,—,—,—:—41 6. VolumeChang&Equation and Equations ufState . .... .... .... .. 42. P ~tiopkt-~quatiims. 43. ~. $olutionP>oeAur~forbplieitPhase B-~@uatiom. 43- G. Phase C . 47 H. Accuracy Conditions and Automatic Timestep C&nt;~i . 52 12v-.. TEECICIWH!l/%31L~OGRAM . W- _A”.- (@nera~ S&ru@~re . .....—,—,.,.,.,.=.:............. ~&. B-. The Computing Mesh . ................................... ...... 60 L T-heFiv@&sh .T=y~*-*ailab}e. ~: .........–:–,—,—=.=.=....................... .. ~& 2-D “tO3-D(jjnv~r~ion .-.-..–-–-–=–~–=–=–.–=–.–.–.–.–.—.–.=.–==.=..=..=.. 53 c. The Indexing Notation . ..~-.l-..~”..~:.lL1 63 D. &orageolZel]”13ata . 64 ~. Me~hGene~+,ion . ~q= 1. T~e15stm-.Face . 08P. 2. The Cylinder Head . ::::::::: 74 -- J!. Celland Vertex Flags . 76 G. F-uelSprays . 77 Spray. Origjn, Profile, and Orientation .,, . .. s..=..,.. =..=....’ ....’. ~~ ;: Spray Flow Definition . ... ... ... =. =.. ... ‘?9 ~:3. Particle Radius . 81 stockiastiikjdjo~. S1 H; Spar!! Ignition=. 81 L. kitial.Be~elElmcti~ nSWirlProfiie . Om- J-. Fuel Library . --.-.-.-.,.,.=.=.=.=.=.=.-.---.-....=.,z= K: LaP.-ew.andGutfiow.Boundaities- . 85”- L. output . 87 M. ~WS~@tiV~-~~OtS....... ...... ........ ..... ..... ... ... .. ... .. .. 88 N. Chopper . .......–.–.—=—=—=—=—=–=–=—=—=—,.................. ... 94. 0. Ikq22m~Rf#x3r~. .. 94 ACKNOW-LEDG~NTS . 95 v A.PPENDIX A. DETERMJ.NATION OF THE PGS PARAMETER . 96 A.PPENDIX B. TURBULENT BOUNDARY LAYER TREATMENT . 98 APPENDIX C. NUMERICAL SOLUTION OF THE EQUATIONS GOVERNING SPRAY DYNAMICS . 107 APPENDIX D. PARTICLE RADIUS SELECTION AT INJECTION . 113 APPENDIX E. THE DROPLET COLLISION CALCULATION . 115 A.PPENDIX F. THE DROPLET OSCILLATION AND BREAKUP CALCULATION . 117 APPENDIX G. CALCULATION OF DROPLET TURBULENT DISPERSION 120 APPENDIX H. THE VARIABLE IMPLICITNESS PARAMETERS . 122 APPENDIX I. KINETIC CHEMICAL REACTIONS . 128 AJ?PENDIX J. EQUILIBRIUM CHEMICAL REACTIONS . 129 APPENDIX K. CALCULATION OF VELOCITY GRADIENTS AND VISCOUS STRESSES . 136 APPENDIX L. THE ALTERNATE NODE COUPLER . 137 APPENDIX M. QUASI-SECOND-ORDER UPWIND DIFFERENCING . 142 APPENDIX N. PARTIAL DONOR CELL DIFFERENCING . 149 APPENDIX O. ROBIN HOOD ALGORITHM . 151 APPENDIX P. ANGULAR MOMENTUM CONSERVATION LOGIC . 152 REFERENCES . 155 vi KIVA-11: A COMPUTER PROGRAM FOR CHEMICALLY REACTIVE FLOWS WITH SPRAYS by A. A. A-msden; P; J. (3’Ruurke; and--T. II: i3utier ABSTRACT T.hi~rePor~- documents the-K! VA--11-computer-pro-gram for the numerical calculation of transient, two- and three-dimensional? chemically- reactive- tl-uid- fl-ows with sprays. K-IVA-H extendsand: enii~ the-earlier. KI..V..cde,e, impro%’-ing-~t%eomputatio nal -aam- racy and efficiency and its ease-of-use. The KIVA-11 .equatiuns.and- numerical solution procedure are very general and can be applied to. ia~ina~ oc tur-bulent- flow% subsonic-or supersonic- flows; anti- skgk-pka-o-r dkqxrrsed-- two-phase fio ws. A-rbitrary numbers of- speck and chemica.r.etikms .ars -ak-wda.. .A4KM4R3*% gm-%ie+e method is used to calculate evaporating.liquid sprays, includingthe- effects of-”di-oplet-collisions and aerodynamic breakups. Although the initial and boundary conditions and mesh generationhamxbeen- written for internal combustion engine calculations, the logic for tlmse- specificatio-ns- c-an- be easily modified: for a variety of- oth-er applications= Eolluwlng--an=o\’ecview of-ihe=pl+uci~l=tiiul-es-of=the KIVA-11 program, we describe. in-detail. the equations- solved$ t,h~ numer-ical solution- procedure, and- the- structure of the computer pr~gr-am, Six%een -appendices provide additional- cietails co.nccnm- ;ngthe -numetical :s0Iuti unqxa-ce-d ure. 1. INTRO DUC-1’IW.AND.BACK.GROUND- The in-cylinder dynmicsoftianc~d ~nternal.mbustion en@ne~j saeh as--the direct-injection stratified-ehargdDISC) engine, involve anumber&compkx, closely ~mupledphysic%l and-chemical processes These include &lietransiimt three-dimensional t @n=~m .u~-evapra%ifigf. e tiei’sprays i“nteractfng witii fIowing multicomponent gases undergoing inixing; ignition; chemical reactions, and “heat transfer.. ‘The KIYF.-codei ‘J“has k the ability to calculate such flows in engine cylinders with arbitrarily shaped piston L geometries, including.the.effeckcdkmhulence and wall heat transfer. In response to the L needs of a kirg~- user community and to reeentdeveloprnents imthefieids-of -numerical fluid dynamics -mdinternal combustion engjne mocieiing> we ‘kiave-irnpkmemted .many. E improvements to ‘KIVA- .since.ikpuhlk release in 1985. T-hethan ggs~e&cor~ratedin a ~ 1 new version of the code, called KIVA-11, that is documented in this report. KIVA-11 builds on the capabilities of I-UVA and is quite similar in structure. Current users of KIIVA will find the transition to KIVA-11 to be straightforward. An excerpt from Ref. 1 explains the basis under which IS(VA was written: ‘<Since KIVA was developed with applications to internal combustion engines in mind, it contains several features designed to facilitate such applications. However, the basic code structure is modular and quite general, and most of the major options (chemical reactions, sprays, etc.) can be individually activated or deactivated by setting appropriate values for the associated input switches. The code is therefore applicable to a wide variety of multi- dimensional problems in fluid dynamics, with or without chemical reactions or sprays.” Indeed, KIVA has been used for numerous studies besides internal combustion engines, including cold flow analyses in complicated geometries, continuous spray combustors, Bunsen burner flames, nonreacting sprays, and hydrogen-oxygen flames propagating in long tubes, to name just a few. It is impractical to cite all such studies here because of the widespread distribution and use of the code in industry and universities. For internal combustion engines, besides the studies of the DISC engine that have been carried on at General Motors Research Laboratories, Princeton University, and Los Alamos National Laboratory,4-7 it has been used as the basis for numerical investigations of diesel engines8-10 and of coal-fired dieselsl 1as well. From a historical perspective, KIVA-11 is the latest in a series of multidimensional codes that we have produced since we began work on numerical simulations of internal combustion engines 12 years ago, under the sponsorship of what has become the Department of Energy’s Energy Conversion and Utilization Technologies (ECUT) program. All of them are multidimensional finite-difference codes that solve the transient equations of motion. The first of these was the RICE code. 12 RICE was a two-dimensional Eulerian code that utilized rectangular computing zones for its mesh, eddy diffusivity to model the turbulence, Arrhenius kinetics with an arbitrary number of reactions and species to represent the chemical kinetics, and a partially implicit finite difference formu- lation