Multi-timescale Modeling of Ignition and Flame Propagation of Diesel Surrogate Fuel Mixtures

Transcription

1 070LT th U. S. Natonal Combuston Meetng Organzed by the Western States Secton of the Combuston Insttute and hosted by the Unversty of Utah May 9-, 03 Mult-tmescale Modelng of Ignton and Flame Propagaton of Desel Surrogate Fuel Mxtures Weq Sun, Hossam A. El-Asrag and Yguang Ju Department of Mechancal and Aerospace Engneerng, Prnceton Unversty Ansys, Inc., 0 Cavendsh Court Lebanon, NH The 3 rd order Weghted Essentally Non-Oscllatory (WENO) scheme and a recently developed Dynamc Adaptve Chemstry (DAC) method are ntegrated wth the hybrd mult-tmescale (HMTS) method and an adaptve unstructured grd system for computatonally effcent and adaptve drect numercal smulaton. The results show that compared to the st order total varaton dmnshng (TVD) scheme, the 3 rd order WENO scheme dramatcally reduces the numercal dsspaton whle keepng good computatonal effcency. In the dynamc adaptve chemstry method, the knetc mechansm s dynamcally reduced by the Path Flux Analyss (PFA) method on each computatonal grd. A hybrd mult-tmescale method, whch combnes the mplct and explct Euler schemes, s used to solve the chemcal reactons based on the dynamcally reduced mechansm. The algorthm s valdated and appled for smulaton of gnton and unsteady flame propagaton of n-decane/,,4 trmethyl benzene (TMB) desel fuel surrogate mxtures. The results show the present algorthm s not only computatonally effcent but also robust and accurate. The DAC method ncreases the computaton effcency dramatcally. Moreover, the unsteady flame propagaton smulaton shows that the 3 rd order WENO scheme can sgnfcantly reduce the numercal dsspaton and predct a more accurate flame speed compared to the st order scheme.. Introducton Due to the energy securty, energy sustanablty and global warmng ssues, ncreasng the fuel effcency of nternal combuston engnes and reducng ther emssons are of global mportance. Recent years, there s ncreasng nterest to develop nternal combuston engnes workng at low temperature combuston regme, such as the homogeneous charge compresson gnton (HCCI) and the reactvty controlled compresson gnton (RCCI) engnes [, ], to mprove engne effcency and emssons. Detaled knetc modelng of these new knds of engnes s of great mportance to optmze the gnton and combuston process. However, combuston process s a mult-scale physcal and chemcal process and nvolves a large range of tme and length scales [3], especally when turbulent transport nvolved. As such, accurate modelng of gnton and combuston n a practcal engne wth a detaled chemcal knetcs remans extremely challengng. In turbulent combuston modelng, large numercal dsspaton may ntroduce a unphyscal numercal dffuson [4], whch can dmnsh the small eddes n the turbulent flow when a coarse grd system s used. Therefore, a hgh order accuracy scheme s needed n numercal modelng to capture the sharp feature and avod large numercal dsspaton. The hgh-order accurate weghted essentally non-oscllatory (WENO) scheme [5-9] has the advantage of hgh order accuracy and

2 070LT-065 robust, sharp, and essentally non-oscllatory shock resoluton [6]. However, most of the WENO schemes used n the lterature are based on the structured, unform grd system. Another dffculty n combuston modelng s the large and stff detaled chemcal mechansms. Recently, there have been many efforts n developng large detaled knetc mechansm for desel and jet fuels. However, a detaled knetc mechansm can contan hundreds of speces and thousands of speces. For example, a detaled n-heptane mechansm can have 034 speces and 436 reactons [0]. Even wth the avalablty of hgh performance supercomputng capablty at petascale and beyond, the numercal smulaton wth such a huge number of speces and reactons s stll too expensve. Therefore, the detaled mechansms need to be reduced n order to realze drect numercal smulaton (DNS). Many methods have been developed to do the chemcal reductons. For example, recently, the Drect Relaton Graph (DRG) [, ] method and mult-generaton Path Flux Analyss (PFA) [3] method show great effcency and accuracy n mechansm reductons. However, there s a drawback for the global, pre-reduced mechansms. In order to guarantee the accuracy of the reduced mechansms n dfferent condtons, they stll contan a large set of speces and reactons; even most of the speces are not actvated n a long tme regme. Fgure shows the actve speces profle durng the auto gnton process. In ths fgure, the homogeneous gnton of stochometrc Aachen desel surrogate fuel [4]/ar mxture at 0 atmospheres and 000K ntal temperature s studed. The number of actve speces vares wth tme. After gnton, only a few speces s actve. But n order to be applcable to the whole process, the pre-reduced mechansm must contan all the speces of whch most of them are actve n dfferent tme sequences. Therefore, the pre-reduced mechansms suffer from the loss of computatonal effcency to calculate all speces at all tme and space domans. In order to reduce mechansms locally and obtan more compact reduced mechansms, Gou et al. developed an error-controlled dynamc adaptve chemstry (EC- DAC) [5] method. It s based on the PFA method and does the chemcal reducton dynamcally at each grd pont to obtan the sub-mechansm based on the local condtons. The threshold value of EC-DAC method s determned by a progress varable [6] to satsfy the requred accuracy. However, n the prevous EC-DAC method, the VODE [7] solver s used to solve the chemcal reactons. The CPU tme cost by VODE solver, whch contans Jacoban matrx decomposton, s proportonal to the cube of the speces number. Thus, the computng tme wll ncrease rapdly when the sze of the mechansm gettng larger. In order to ncrease the effcency of computaton of chemcal reactons, a hybrd mult-tme scale (HMTS) [8] method s developed by Gou et al. n 00. HMTS solver combne mplct Euler method and explct Euler method together and solved the speces reacton based on ther own characterstc tme. HMTS method can dramatcally reduce the computng tme. The goal of ths paper s to develop a hgh order numercal scheme by usng dynamc adaptve chemstry (DAC) method based on HMTS method and extendng the 3 rd order WENO scheme to an adaptve non-unform grd system to acheve great computatonal effcency and accuracy for combuston modelng wth detaled chemcal knetcs. The Aachen desel fuel surrogate [4], whch conssts of 80% n-decane and 0%,,4-trmethylbenzene by weght (77% n-decane and 3%,,4- trmethylbenzene by volume) and contans 8 speces and 57 speces, s used to valdate the ntegrated WENO-DAC- HMTS approach. The hydrogen mechansm [9] wth 0 speces and 3 reactons s used to test and valdate the effect of WENO scheme on numercal dsspaton. Numercal smulatons of homogeneous gnton and unsteady flame propagaton of desel surrogate mxtures are carred out to demonstrate the accurate and robust of the proposed algorthm.

3 070LT-065 Fg.. Number of actve speces profle durng homogeneous gnton process wth stochometrc Aachen surrogate fuel/ar mxture at 0 atmospheres.. Numercal Methods The development of an ntegrated WENO scheme and DAC method wth HMTS solvers to smulate unsteady reactve flow wth an adaptve unstructured grd system s based on our prevous code, the adaptve smulaton of unsteady reactve flow (ASURF) code [0, ] developed at Prnceton. The orgnal scheme n ASURF, the st order total varaton dmnshng (TVD) scheme [], s replaced by the 3 rd order WENO scheme to mprove the numercal accuracy and the DAC method s mplemented at each grd pont to reduce mechansms locally... WENO scheme In order to mnmze numercal dsspaton whle keepng good computatonal effcency, the 3 rd order WENO scheme [9] s appled to dscretze the convectve terms based on an unstructured, nonunform grd system. Snce the grds are not unform, the WENO reconstructon fluxes and weght functons used here s derved from the orgnal form of WENO scheme ntroduced by Shu [9]. In the 3 rd order WENO scheme, a functon vx ( ) at the th cell center pont x can be reconstructed as:

4 070LT-065 v v v (0) () 0 (0) () where v and v are two mplementatons of vx ( ) and 0, are there weghts. The expressons (0) of () v and v are: where x x v v v (0) x x x x x x x v v v () x x x x x j s the jth grd sze and v j s the value of functon vx ( ) at jth grd pont. () (.a) (.b) (0) () The weghts 0 and depend on the smoothness of the mplementatons v and v. r r, r s0 s d r r, r 0, (3) where s a small, postve real number to avod the denomnator beng zero. Here we choose 0-6. d r s the coeffcent and r s the measurement of smoothness. They are functons of grd sze: x x d0 (4.a) x x x x d (4.b) x x x x ( v v ) o x x x ( v v ) x x If the grds are unform, the reconstructon decays to the normal 3 rd order WENO scheme [6], whch people always use: (0) () 3 v v v, v v v (6) d0, d (7) Dynamc Adaptve Chemstry v v, v v 0 In ths paper, both HMTS and VODE solvers are used to solve the stff ODEs of detaled chemstry and ther computaton effcences are compared. In order to obtan the adaptve submechansm based on the local, the PFA method s appled to each grd pont. The Aachen surrogate fuel [4] wth 8 speces and 57 reactons s used here to valdate the present algorthm. (5.a) (5.b) (8)

5 070LT-065 The PFA method can dentfy and keep mportant speces and reacton pathways based on the producton and consumpton fluxes, and remove trval speces and reactons. For smplcty, all the studes n ths paper only contan the frst generaton flux although the method can nclude multgeneraton path flux analyss. For speces A, the overall producton and consumpton fluxes, P A and C A can be expressed [5] as: P max( v,0), CA max( va,,0) A A,, I where v A, s the stochometrc coeffcent of speces A n the th reacton, s the net reacton rate. I s the number of reacton order. Whle the producton and consumpton fluxes between speces A and speces B, P AB, C AB, are: P AB A, B, I, I max( v,0), CAB max( va, B,0) where B s unty f speces B s nvolved n th reacton and 0 otherwse. Then we use the maxmal producton or consumpton flux to normalze P AB and C AB and obtan the flux ratos for producton and consumpton of speces A va speces B: prost PAB const CAB rab, rab () max( P, C ) max( P, C ) A A The PFA calculaton starts from a preselect lst of mportant speces and flags all the speces prost const related to the preselect speces. If ther flux ratos r AB or r AB great than the threshold value, they wll be add to the select lst. Then, the program wll start from the select lst and do the teraton agan and agan, untl there s no new speces added nto the select lst. Fnally, the local reduced mechansm can be constructed by the speces contaned n the select lst. A threshold value s used n ths paper. In the dynamc adaptve chemstry (DAC) process, the PFA reducton s appled at each grd pont every 0 or 00 tme steps. Ths process s very effcent because only reacton rates need to be calculated. The tme consumng of PFA s proportonal to the total number of speces. 3. Results and dscusson In order to valdate the algorthm and test ts performance, a smple hydrogen mechansm wth 0 speces and 3 reactons and a detaled Aachen desel fuel surrogate (a mxture of 80% n-decane and 0%,,4-trmethylbenzene by weght and 77% n-decane and 3%,,4-trmethylbenzene by volume) mechansm wth 8 speces and 57 speces are used n the smulatons. The premxed hydrogen flame propagaton process wth stochometrc H /ar mxture s calculated by both the 3 rd order WENO scheme and the st order total varaton dmnshng (TVD) scheme to show the dramatc decrease of numercal dsspaton n the hgher order scheme. The homogeneous gnton of Aachen desel surrogate at dfferent ntal temperatures and equvalent ratos are modeled by the VODE and HMTS solver wth and wthout dynamc adaptve chemstry. The results demonstrate the great effcency and accuracy of DAC method. Also, a study of an outwardly propagatng premxed sphercal flame of stochometrc Aachen surrogate fuel/ar mxture wth and wthout DAC s carred out to valdate the DAC method n unsteady flame propagaton process., I A A (9) (0)

6 070LT-065 Fg.. Dependence of flame propagaton speed versus grd sze wth stochometrc H/ar mxture at atmosphere and 300K. Fgure shows the hydrogen flame propagaton speed as a functon of grd sze. In ths smulaton, a D flat flame of premxed stochometrc hydrogen/ar mxture at 300 K and atm s ntated by a hot spot of 600 K wth a length of mm at the end of the left hand sde boundary. The reflectve and transmssve boundary condtons are mposed, respectvely, on the left and rght boundares. Note that the speed here s not the flame speed but the flame propagaton speed relatve to the statonary coordnate. Due to the transmssve boundary condton on the rght-hand sde, the unburned gas moves to the rght, leadng a hgher flame propagaton speed than the flame speed. Moreover, t s seen that at a coarse grd, the numercal dsspaton ntroduces addtonal numercal dffuson flux to the transport process, whch leads to the larger numercal flame propagaton speed compared to the real propagaton speed. Wth decrease of the grd sze, the numercal dsspaton decreases and the predcted propagaton speeds also decrease. Fgure clearly shows that the 3 rd order WENO scheme gves smaller propagaton speed, whch mples less numercal dsspaton. Thus, the hgh-order WENO scheme can reduce the numercal dsspaton sgnfcantly. When grd sze gettng smaller, the propagaton speeds calculated from the st order TVD scheme and the 3 rd order WENO scheme approach to the physcal flame propagaton speed. Fgure 3 shows the gnton delay tme of Aachen surrogate/ar mxture as a functon of ntal temperature at 0 atmospheres, 0.6,.0 and.6 equvalent ratos, wth and wthout DAC. The

7 070LT-065 maxmal error n the results s 0.5%. The excellent agreement between the results wth DAC and wthout DAC valdates that the accuracy of DAC method s good enough to provde local reduced mechansm wthn a large range of temperature and equvalent rato. Fg. 3. Comparson of gnton delay tme between modelng wth and wthout DAC, wth Aachen surrogate fuel/ar mxture at P=0atm. Fgure 4 and Fgure 5 show the homogeneous gnton process s CPU tme comparson of VODE solver wth and wthout DAC and HMTS solver wth and wthout DAC, respectvely. They gve the dependence of CPU tme on dfferent ntal temperature at 0 atmospheres, 0.6,.0 and.6 equvalence ratos. The CPU tme s normalzed by the CPU tme wthout DAC. It s seen that for VODE solver, DAC method can ncrease the computatonal effcency by 40 to 60 percent n a broad temperature and equvalence rato range. For HMTS solver, the DAC method can ncrease the computatonal effcency by about 5 to 30 percent, especally when fuel s rch. However, ths s just for homogeneous gnton process. For most of the stuatons that DNS appled, chemcal reactons just happen n a very narrow tme and spatal regme. In the other nonreactve regmes, there wll be only a few of actve speces gven by DAC. Thus, n a long tme regme and large spatal area, the ode solvers just need to solve these a few actve speces. That wll cause computatonal effcency ncrease a lot. Fgure 6 shows the CPU tme comparson between VODE and HMTS solvers wth and wthout DAC at 0 atmospheres and stochometrc condton. All the CPU tme s normalzed

8 070LT-065 by the CPU tme of VODE solver wthout PFA. It clearly demonstrates that HMTS solver s much more effcent than the VODE solver. Fg.4. CPU tme comparson between VODE solver wth and wthout DAC for Aachen surrogate fuel/ar mxture gnton at 0 atmosphere.

9 070LT-065 Fg.5. CPU tme comparson between HMTS solver wth and wthout DAC for Aachen surrogate fuel/ar mxture gnton at 0 atmosphere.

10 070LT-065 Fg. 6. CPU tme comparson between VODE solver and HMTS solver wth and wthout DAC at 0 atmospheres and stochometrc condton. Fgure 7 shows the premxed sphercal flame trajectores wth and wthout DAC. The mxture s Aachen surrogate fuel and ar at stochometrc condton and 300 K, atmosphere. They are gnted at the center by a hot spot of 600 K wth a radus of mm. The chemcal reactons are solved by HMTS solver. It s seen that the flame trajectores are almost the same, the largest error s less than %, whch can demonstrate the accuracy of DAC method n unsteady flame propagaton process.

11 070LT-065 Fg.7. Plame poston versus tme wth stochometrc Aachen surrogate fuel/ar mxture at atmosphere and 300K. 4. Concluson The 3 rd order WENO scheme based on an unstructured grd system and the dynamc adaptve chemstry (DAC) method combned wth HMTS solver and VODE solver are developed and ntegrated nto the adaptve smulaton of unsteady reactve flow (ASURF) code. The results show that the 3 rd order WENO scheme can sgnfcantly reduce the numercal smulaton, and the DAC method can ncrease the computatonal effcency a lot whle keepng excellent accuracy. The smulaton of homogeneous gnton of Aachen surrogate fuel/ar mxture at 0 atmospheres, wth dfferent ntal temperature and equvalent ratos show that the DAC method can mprove VODE solver s effcency by 40 to 60 percent and ncrease HMTS solver s effcency by about 5 to 30 percent, wth s much faster than the VODE solver. Moreover, the study of unsteady flame propagaton demonstrates the DAC method wth HMTS s not only computatonally effcent but also accurate and robust even when transport s ncluded. Therefore, the HMTS solver coupled wth DAC method has a great potental to be used n the DNS area.

12 070LT-065 Acknowledgements The authors would lke to thank the grant support from the Army Research Offce and the help from Dr. Xaolong Gou at Chongqng Unversty. Reference [] F Zhao, TW Asmus, DN Assans, JE Dec, JA Eng, PM. Najt. Homogeneous Charge Compresson Ignton (HCCI) Engnes, SAE Internatonal, 003. [] DS Km, CS Lee, Fuel, 85 (006) [3] E.A. Carter, J.H. Chen, F.L. Dryer, F.N. Egolfopoulos, W.H. Green, N. Hansen, R.K. Hanson, Y. Ju,.K. Law, J.A. Mller, S.B. Pope, C.J. Sung, D.G. Truhlar, H. Wang, Energy Fronter Research Center for Combuston Scence: From Fundamentals to Mult-scale Predctve Models For st Century Transportaton Fuels, 009. [4] JD Anderson, Computatonal flud dynamcs, Sprnger, 995. [5] X.D. Lu, S. Osher and T. Chan, J. Comput. Phys, 5 (994) 00-. [6] G.S. Jang and C.W. Shu, J. Comput. Phys, 6 (996) 0-8. [7] D.S. Balsara and C.W. Shu, J. Comput. Phys, 60 (000) [8] C.W. Shu, SIAM Revew 5 () (009) 8-6 [9] C.W. Shu, Hgh Order ENO and WENO Schemes for Computatonal Flud Dynamcs, Sprnger, 999. [0] H.J. Curran, P. Gaffur, W.J. Ptz, C.K. Westbrook, Combust. Flame 9 (3) (00) [] T.F. Lu, C.K. Law, Proc. Combust. Inst. 30 (005) [] P. Pepot-Desjardns, H. Ptsch, Combust. Flame 54 ( ) (008) [3] W.T. Sun, Z. Chen, X.L. Gou, Y.G. Ju, Combust. Flame 57 (7) (00) [4] S Honnet, K Seshadr, U Nemann, N Peters, Combust. Inst. 3 (009) [5] X.L. Gou, Z. Chen, W.T. Sun, Y.G. Ju, Combust. Flame, 60 (03) 5-3. [6] J.A. Van Ojen, F.A. Lammers, L.P.H. De Goey, Combust. Flame 7 (3) (00) [7] P.N. Brown, G.D. Byrne, A.C. Hndmarsh, Sam J. Sc. Stat. Comput. 0 (5) (989) [8] X.L. Gou, W.T. Sun, Z. Chen, Y.G. Ju, Combust. Flame 57 (6) (00). [9] L, J., Zhao, Z., Kazakov, A., and Dryer, F. L., Int. J. Chem. Knet. 36, 565 (004). [0] Z. Chen, M. P. Burke, Y.G. Ju, Combust. Inst. 3 (009) [] Z. Chen, Studes on the Intaton, Propagaton, and Extncton of Premxed Flames, Prnceton Unversty, 009. [] P Batten, MA Leschzner, UC Goldberg, J. Comput. Phys, 37 () (997)