IC Engine Flow Simulation using KIVA code and A Modified Reynolds Stress Turbulence Model

Transcription

1 IC Engne Flow Smulaton usng KIVA code and A Modfed Reynolds Stress Turbulence Model Satpreet Nanda and S.L. Yang Mechancal Engneerng-Engneerng Mechancs Department Mchgan Technologcal Unversty Houghton, Mchgan 4991 Abstract The flow processes nsde an engne are very complex and to smulate the hghly ansotropc turbulent engne flows, second moment models (Reynolds stress models) are used. The KIVA code has been modfed to nclude the Reynolds stress turbulence model (RSTM) for ths purpose. In ths study the exstng RSTM n the KIVA code [1] has been modfed to resolve the flow better n the engne. The flow nsde the engne has hgh bul veloctes n the vertcal plane and the flow n the horzontal plane s slow and nfluenced by shear and pressure effects. In the modfed RSTM the dsspaton equaton has been modfed to be more senstve to shear effects and rrotatonal strans. The modfed RSTM s used to smulate the flow nsde a four-valve engne cylnder and the results are compared wth the Standard - model, the orgnal RSTM n the KIVA code and the expermental results. The comparsons are made for the ntae and compresson stroes. The modfed RSTM shows better results and s able to resolve the flow characterstcs better than the orgnal RSTM n the KIVA code. Introducton The n-cylnder flud dynamcs n engnes has been shown to play an mportant role durng the combuston process. In partcular, n-cylnder flud flows contrbute to fuel ar mxng whch s mportant to the fuel-burnng rate. Turbulence generated n an I.C. engne s ansotropc. Durng the Intae process, the flow passng the valve separates and results n a hghly unsteady moton. Ths flow contans both large-scale and small-scale turbulence. Snce turbulence has a major effect on combuston, flow-mxng and on heat-transfer n an engne, to model the flow nsde an engne a proper turbulence model should be used. Most ndustral computatons of engne flows use the two-equaton models based on the Boussnesq approxmaton. Usng ths assumpton the Reynolds stress tensor s drectly proportonal to the stran rate, whch mples that the Reynolds stress s drectly n phase wth the stran rate, whch s not the case n real complex flows. The second moment model (from now on referred as Reynolds stress turbulence model, RSTM) has the potental to resolve complex flow-felds and t has been shown that t s able to resolve engne flow better than other models [ & ]. The models based on the Boussnesq approxmaton suffer from many shortcomngs, whch are overcome n the RSTM. A modfed model of the RSTM has been developed to mprove the dsspaton equaton and better resolve the flow n the engne. Frst, the orgnal RSTM n the KIVA code s To whom the correspondence should be made 1

2 shown followed by the modfcatons and there effects on the model. In the end the results obtaned from dfferent models are compared wth expermental results. Modfcatons to orgnal RSTM The orgnal RSTM was modfed by addng three extra terms to the dsspaton rate equaton and modfyng a term n the Reynolds stress transport equatons The modfcaton n the Reynolds stress transport equaton s n the dsspaton term that has been taen to be ansotropc. Generally for hgh Reynolds number models the dsspaton expresson used n the Reynolds transport equaton s modeled as j = ρδ j, here the vscous effects are neglected. As the flud approaches a sold wall the energy contanng and dsspaton range of motons overlap and the dsspaton uu j rate s then commonly expressed [] as j = ρ (1 fs ) δ j + fs. The dsspaton equaton used n ths research wth the modfcatons s as follows: ρ ( U ) ρ U µ t + = C + 1 C ρ t x x x σ x + ρ ( C1 P) + ρ ( C ) + S + S l + SG (1) The last three terms are the ones that are added to the orgnal dsspaton equaton. S s the vortcty term, ths term may be nterpreted as emphaszng the role of rrotatonal deformatons n promotng energy transfer across the spectrum or, equvalently, of augmentng the nfluence of normal strans. S = C f ρ () where C = 0. 1 and U j = j s the mean vortcty vector, x S senstzes the producton of (n fact, the spectral energy transfer) to both the sgn and ntensty of the rrotatonal stranng and s benefcal for modelng the evoluton of n flows wth strong acceleraton and deceleraton (compresson and expanson as n engne flows). S l s added to compensate for excessve growth of the length scale l, ths was orgnally ntroduced by Hanjalc and Jarlc [4] nto the transport equaton for. Ths term ncreases locally n the zone where the turbulence length scale becomes excessve.

3 Another term S = C U ρ x x j U x x l, modelng the gradent of producton of dsspaton s added, ths term was ntroduced frst by Jones and Launder [5], and s desgned to resolve the producton of dsspaton n vscous regons. Expermental Set-up and Grd Generaton The expermental results were obtaned from Mchgan State Unversty s [MSU] Engne Research Laboratory. The expermental measurements were made usng Molecular Taggng Velocmetry (MTV) [6], a method developed at MSU s Engne Research Laboratory to study the engne n-cylnder processes. Two planes were chosen for collecton of MTV data. The frst one s the vertcal plane between the two ntae valves, n the center of the cylnder, whch wll be referred to as the tumble plane. Due to the lmted access, approxmately only the top half of ths plane s measured. The second plane of data was taen at a horzontal slce.4 cm below head face. The computatonal grd for the engne geometry was made usng GRIDGEN [7] and a modfed verson of the Kprep. A three dmensonal mult-bloc mesh was constructed usng GRIDGEN, where t frst reads the engne geometry (wre-frame) n PLOT-D format. To ensure the smulaton result s convergent, a grd dependency study was performed. The medum grd, whch s used to show the results, has around one hundred and thrty thousand cells and one forty three thousand vertces when the pston s at the bottom dead centre, the top vew s shown n Fgure 1 and the front vew s shown n Fgure. The test was only performed n non-reactng flow condtons for the ntae and compresson stroes. The terms added were frst lnearzed and then added to the respectve dfferental equaton. The terms added to the dsspaton equaton were lnearzed usng Taylor seres and the term added to the Reynolds stress transport equaton was lnearzed usng max and mn functons [8]. The dfferental expressons ntroduced n the equatons are then dscretzed usng the fnte-volume approach. The dfferental expressons wthn the volume ntegral were approxmated usng fnte-dfference approxmatons. Usng the relaton between physcal and computatonal space relatons was obtaned to approxmate the expressons. The detals of the method can be found n Nanda [9]. Results and Conclusons The velocty contour and vector plots for dfferent models have been compared wth the expermental result. Comparson of results are presented n both XY and XZ planes,.e., at Z=8.85 cm (horzontal plane) and Y=0.0 cm (plane between the two ntae valves, ths plane wll be referred to as the tumble plane) as shown n Fgure (a) & (b). Snce the engne geometry s symmetrc along the Y=0.0 cm axs, the flow should be symmetrc, whch can be seen n the numercal results, but the results from the MTV data are not symmetrc. Ths could be due to the hand-bult nlet manfolds (mght have some mnor mperfectons) used n the experment [10].

4 It can be seen from the results that the modfed model s able to resolve the flow better than the orgnal RSTM. Ths s because the modfed model s more senstve to rrotatonal/normal strans whch are qute domnant n engne flows. Also the modfed model s able to predct the ntensty better than the other models. A better result for recrculaton zones, velocty magntude and vectors s shown by the modfed RSTM. Acnowledgements The author would le to than Professor H. J. Schoc and Mr. Mar Nova of Mchgan State Unversty, Automotve Research Experment Staton, for provdng us wth the expermental data and nformaton about the expermental setup. The author wll also le to than the MEEM department at Mchgan Technologcal Unversty for provdng fnancal assstance durng ths research. References: 1. Yang, S. L., Pesche, B. D. and Hanjalc, K. Second-Moment Closure Model for IC Engne Flow Smulaton Usng KIVA code. J. Engneerng for Gas and Turbne Power, vol. 1, Aprl Yang, S. L. Sow, Y. K. and Pesche, B. D. Numercal study of non-reactng gas turbne combustor swrl flow usng Reynolds Stress Model. J. Engneerng for Gas and Turbne Power, vol. 5, October 00 (To be publshed).. Yang, S. L. Sow, Y. K., Teo, C. Y. Numercal Study of LDI Combustor wth Dscrete jet swrlers usng Reynolds stress Model. J. Engneerng for Gas and Turbne Power, July Hanjalc, K. and Launder, B. E. Contrbuton towards a Reynolds-Stress closure for low-reynolds-number turbulence. J. Flud Mechancs, vol. 74, pp59-610, Hanjalc, K. and Jarlc, S. Contrbuton towards the second moment closure modelng of separatng turbulent flow. Computers & Fluds, vol. 7, No., pp , Jones, W. P. and Launder, B. E. The predctons of Lamnarsaton wth a twoequaton model of turbulence. Int. J. Heat and Mass Transfer, vol 15, 01, Gendrch, C. P., Koochesfahan, M. M. and Nocera, D. G. Molecular Taggng Velocmetry and Other Novel Applcatons of a New Phosphorescent Supramolecule. Experments n Fluds (5) 61-7, GRIDGEN, Grd Generaton and Pre-Processng for CFD, V.14.1, Pontwse Inc., 1 S. Jennngs Ave., Fort Worth, TX , USA, Nanda, S. I.C. Engne Flow Smulaton Usng KIVA Code and a Modfed Reynolds Stress Turbulence Model. Masters Thess, Mchgan Technologcal Unversty, Fedewa, A. M. Prvate Conversaton, Graduate Student at Mchgan State Unversty, Engne Research Laboratory, 00. 4

5 Z Y X Z X Y Fgure 1 Bottom Vew Fgure Isometrc Vew Z=8.85 cm 11.5 cm.4 cm Inlet Runner Y= 0.0 cm Exhaust Runner Fgure (a) Front vew of engne wre-frame Fgure (b) Top vew of engne wre-frame 5

6 (a) Standard -H model (b) orgnal RSTM (c) modfed RSTM (d) MTV data Fgure 4 X component velocty contour and UV vector plots at Z=8.85 cm plane for C.A (a) Standard -H model (b) orgnal RSTM (c) modfed RSTM (d) MTV data Fgure 5 Z component velocty contour and UW vector plots at Y=0.0 cm plane for C.A (a) Standard -H model (b) orgnal RSTM (c) modfed RSTM (d) MTV data Fgure 6 X component velocty contour and UV vector plots at Z=8.85 cm plane for C.A (a) Standard -H model (b) orgnal RSTM (c) modfed RSTM (d) MTV data Fgure 7 Y component velocty contour and UV vector plots at Z=8.85 cm plane for C.A. 6