Al Qubeissi, Mansour

Crua, C.

Heikal, M.R.

Sazhin, S.S.

This paper presents the application of the Discrete Component Model for heating and evaporation to multi-component biodiesel fuel droplets in direct injection internal combustion engines. This model takes into account the effects of temperature gradient, recirculation and species diffusion inside droplets. A distinctive feature of the model used in the analysis is that it is based on the analytical solutions to the temperature and species diffusion equations inside the droplets. Nineteen types of biodiesel fuels are considered. It is shown that a simplistic model, based on the approximation of biodiesel fuel by a single component or ignoring the diffusion of components of biodiesel fuel, leads to noticeable errors in predicted droplet evaporation time and time evolution of droplet surface temperature and radius

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Modelling of heating and evaporation of biodiesel fuel droplets Al Qubeissi, M. , Sazhin, S.S. , Crua, C. and Heikal, M.R. Author post-print (accepted) deposited in CURVE January 2016  Original citation & hyperlink:  Al Qubeissi, M. , Sazhin, S.S. , Crua, C. and Heikal, M.R. (2015) Modelling of heating and evaporation of biodiesel fuel droplets. International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, volume 9 (1): 46-49. http://waset.org/Publication/modelling-of-heating-and-evaporation-of-biodiesel-fuel-droplets/10000158    World Academy of Science, Engineering and Technology applies the Creative Commons Attribution (CC BY) license to works we publish. This license was developed to facilitate open access – namely, free immediate access to, and unrestricted reuse of, original works of all types. Under this license, authors agree to make articles legally available for reuse, without permission or fees, for virtually any purpose. Anyone may copy, distribute, or reuse these articles, as long as the author and original source are properly cited.       CURVE is the Institutional Repository for Coventry University http://curve.coventry.ac.uk/open  1 Abstract—This paper presents the application of the Discrete Component Model for heating and evaporation to multi-component biodiesel fuel droplets in direct injection internal combustion engines. This model takes into account the effects of temperature gradient, recirculation and species diffusion inside droplets. A distinctive feature of the model used in the analysis is that it is based on the analytical solutions to the temperature and species diffusion equations inside the droplets. Nineteen types of biodiesel fuels are considered. It is shown that a simplistic model, based on the approximation of biodiesel fuel by a single component or ignoring the diffusion of components of biodiesel fuel, leads to noticeable errors in predicted droplet evaporation time and time evolution of droplet surface temperature and radius.   Keywords—Heat/Mass Transfer, Biodiesel, Multi-component Fuel, Droplet, Evaporation.  I. INTRODUCTION IODIESEL fuel droplets heating and evaporation are crucial processes leading to fuel combustion in the internal combustion engines [1]. As such, the accuracy of modelling these processes is important for improving the design of these engines [1]–[3]. There have been several suggestions for accurate modelling of fuel droplet heating and evaporation (see [2], [4]–[10]).  This paper presents a comparison between the results, referring to fuel droplet evaporation times and time evolution of droplet surface temperatures and radii, predicted by the previously suggested simplified models (see [11], [12]) and the recently developed version of the Discrete Component (DC) model ([9], [13], [10]). The latter takes into account the recirculation, temperature gradient, and diffusion of species inside the droplets, based on the Effective Thermal Conductivity and Effective Diffusivity (ETC/ED) models. This approach is performed in contrast with the previously suggested models that ignore temperature gradients and diffusion of species by assuming Infinite Thermal Conductivity and Infinitely fast Diffusivity (ITC/ID) of species inside the droplets. The model originally described in [9], [13], [14] is used in the analysis. However, this model is applied to a considerably larger number of biodiesel fuels (19 types). These are: Tallow                                                             Al Qubeissi is with the Centre for Automotive Engineering (CAE), School of Computing, Engineering and Mathematics (CEM), University of Brighton (UoB), Brighton BN2 4GJ, UK (e-mail: m.alqubeissi@brighton.ac.uk). S.S. Sazhin is with the CAE, CEM, UoB, Brighton BN2 4GJ, UK (corresponding author, Tel: 0044 (0)1273 642677; e-mail: S.Sazhin@brighton.ac.uk). C. Crua and M.R. Heikal are with the CAE, CEM, UoB, Brighton BN2 4GJ, UK (e-mail: C.Crua@brighton.ac.uk, M.R.Heikal@brighton.ac.uk). Methyl Ester (TME), Lard Methyl Ester (LME), Butter Methyl Ester (BME), Coconut Methyl Ester (CME), Palm Kernel Methyl Ester (PMK), Palm Methyl Ester (PME), Safflower Methyl Ester (SFE), Peanut Methyl Ester (PTE), Cottonseed Methyl Ester (CSE), Corn Methyl Ester (CNE), Sunflower Methyl Ester (SNE), Soybean Methyl Ester (SME), Rapeseed Methyl Ester (RME), Linseed Methyl Ester (LNE), Tung Methyl Ester (TGE), Hemp-oil Methyl Ester, produced from Hemp seed oil in Ukraine (HME1), Hemp-oil Methyl Ester, produced in European Union (HME2), Canola seed methyl ester (CAN) and Waste cooking-oil Methyl Ester (WME). The molar fractions of the pure fatty acids contributing in these methyl esters are inferred from averaging data reported in [14]–[20]. These are shown in Table I. The thermodynamic and transport properties, inferred from [9], [15], are used in the analysis.  II. RESULTS AND DISCUSSION The time evolutions of droplet surface temperatures (Ts) and radii (Rd) for the abovementioned 19 types of biodiesel fuels have been studied. It is assumed that droplets with initial temperatures and radii 350 K and 12.66 μm, respectively, are moving through air at Ud= 35 m/s at temperature and pressure equal to 880 K and 30 bar respectively.  Two examples of the time evolutions of droplet surface temperatures and radii of Rapeseed Methyl Ester (RME) and Waste oil Methyl Ester (WME) droplets are shown in Figs. 1 and 2. The following models are used in our analysis: 1) the ETC/ED model taking into account the contributions of multiple components (ME); 2) a combination of ITC and single-component models, in which all species are treated as one-component (SI); and 3) a combination of ITC and one dominant component models, in which biodiesel fuel is approximated by a single dominant component (DI). As mentioned in Section I, the second and third models are commonly used in the analysis of heating and evaporation of biodiesel fuel droplets.  Modelling of Heating and Evaporation of Biodiesel Fuel Droplets Mansour Al Qubeissi, Sergei S. Sazhin, Cyril Crua, Morgan R. Heikal B World Academy of Science, Engineering and TechnologyInternational Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering Vol:9, No:1, 2015 46International Scholarly and Scientific Research & Innovation 9(1) 2015 scholar.waset.org/1999.8/10000158International Science Index, Mechanical and Mechatronics Engineering Vol:9, No:1, 2015 waset.org/Publication/10000158PCCtiofMethyl Esters AbiatTallow TMLard LMButter BMCoconut CMalm Kernel PMPalm PMSafflower SPeanut Pottonseed CCorn CSunflower SNTung THemp1 HMSoybean SMLinseed LHemp2 HManola seed CWaste oil WRapeseed RM Fig. 1 The dropme predicted b Fig. 2 Th As one can s the droplet sTYbrevions C8:0 C1E 0 0E 0 0E 5.19 2.8E 6.00 8.0K 2.60 4.0E 0 0FE 0 0TE 0 0SE 0 0NE 0 0E 0 0GE 0 0E1 0 0E 0 0NE 0 0E2 0 0AN 0 0ME 0 0E 0 0let surface temy the ME, SI ane same as Fig. ee from Figsurface temperPES OF BIODIESE0:0 C12:0 C14: 0.20 2.50 0 1.000 3.40 10.90 50.00 15.00 50.00 17.0 0.26 1.29 0 0  0 0.50 0 2.00 0 1.00 0 0  0 0  0 0  0 0.30 0 0.20 0 0  0 0  0.20 0.67 0 0 perature (Ts) ad DI models, f1, but for a WM. 1 and 2, the atures, radii aL FUELS AND TH0 C16:0 C17:0 27.90 0  26.00 0 9 31.66 0 0 9.00 0 0 8.00 0  45.13 0 5.20 0  8.00 0  19.00 0  9.00 0 5.92 0 3.64 0 6.62 0.21 10.90 0  6.20 0 6.51 0 4.48 0.14 15.69 0.204.93 0 nd radius (Rd) vor a RME fuel E fuel dropleterrors in prednd evaporatioTABLE IEIR COMPOSITIOC18:0 C20:023.00 0.40 14.00 0 10.79 0.40 3.00 0 1.70 1.50 4.47 0.35 2.20 0 4.00 7.00 2.00 0 2.50 0 4.15 1.38 2.55 0 2.06 0.45 4.40 0.40 0.60 0 2.46 0.90 1.99 0.62 6.14 0.39 1.66 0.56  ersus droplet   ictions n time usicoMEprapretheinsthetheforAlthehasimcoFigareerrSI spemovearebe(e.thesamcotheC1moNS (MOLAR FRACFatty Acids C22:0 C24:0 C0.40 0 20 0 20.40 0 20 0 1.50 0 00.17 0 00 0 7.00 0 10 0 0 0 11.38 0 13.14 0 0.25 0.23 00 0 0 0 0 0 0.35 0.16 00.44 0.30 00 0 ng the convmponent DI)  model, arectical enginedictions of t importance ide droplets am. These err SI model co RME and Wso, the errors SI model cove been showThese errors ilar to those mpared to Ms. 1 and 2). T reasonably cors in evaporand DI modcies in the dels.  The plots ofrsus time for  shown in FigAs one can secome the domg. C24:1 M, fir contributioe time, thntributing oneir initial con8:2 and C18lar fractions TIONS OF FATTY16:1 C18:1 C20.50 40.00 0.3.80 44.00 2.0.40 26.37 1.00 7.00 0.40 12.00 0.21 38.39 00 76.38 0.50 49.00 00 31.00 2.5.50 40.00 1.00 18.46 00 10.10 0.8.33 11.88 0.20 24.00 00 18.00 00 11.88 0.9.36 59.66 1.4.73 42.84 0.50 26.61 0entional (sinmodels, com noticeable ering applicathese two moof taking intolongside the ors in dropletmpared to theME to be up in droplet sumpared to then to be up to in evaporatiinferred fromE model for bhe trends oflose to the onation times anels are relatdroplets are  surface maRME and WMs. 3 and 4 rese from Figs. inant ones or RME, andns at the inie lightest cs at the late tributions ar:3, for RMEof intermedia ACIDS) :1 C22:1 C24:0 0.30 0 0 2.00 0 0 1.00 0  0 0  0 0  0 0  0 0  0 0 0 2.50 0 0 1.00 0  0 0 1 0 0 7 0.17 0.15 0 0  0 0 0 0 0 9 0.42 0 6 0.15 0  22.32 0.77gle-componenpared with thand should ions. The devdels and the  account the effects of tem evaporation  ME model, h to 9.4% andrface temper ME model, 10.6% and 10on times an the applicatoth types of  the plots shoes reported ind temperatured to the facnot taken intss fractions E, predictedpectively.  3 and 4, the hat the late st C24:0 M, fortial stage areomponents stages of evape relatively l, and C16:0Mte componen1 C18:2 C18:32.00 0 8.00 0 3.00 0.602.00 0 1.30 0 9.16 0.1916.22 0 23.00 0 41.00 0 44.00 0 68.41 0.3013.75 51.64 56.71 20.6752.80 7.2016.00 59.0054.82 20.0720.89 9.4429.36 2.03 24.75 9.70t SI or dome predictions not be ignoiations betweME model indiffusion of sperature gradtimes, predicave been est 5.9%, respecatures, predicfor RME and.5%, respectivd temperaturion of the DIbiodiesel fuewn in Figs. 1 [9], [12], [14es, predicted t that diffuso account inof selected s by the ME eaviest compage of evapo WME), even very small. become theoration, evenarge (e.g. C1, for WMEts initially inOthers0.50 0.20 0 0 0 0.38 0 0 0 0 0 4.37 0 0 0 2.46 0 0.30 8.70 inant-of the red in en the dicate pecies ient in ted by imated tively. ted by  WME ely.  es are model ls (see  and 2 ]. The by the ion of  these pecies model, onents ration  when At the  least  when 6:0M, ). The crease World Academy of Science, Engineering and TechnologyInternational Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering Vol:9, No:1, 2015 47International Scholarly and Scientific Research & Innovation 9(1) 2015 scholar.waset.org/1999.8/10000158International Science Index, Mechanical and Mechatronics Engineering Vol:9, No:1, 2015 waset.org/Publication/10000158wenneCith time, but d of evapgligible.  Fig. 3 The plC16:0M, C18:RME droplFig. 4 The pl16:0M, C18:0Mfor a WME d Fig. 5 The plotnormalised diinstants 0.02 mlater their cooration timeots of time evo0M, C22:1M, Cet under the samots of time evo, C22:0M, C2roplet under ths of mass fractistance from thes, 0.3 ms and 0same conditintributions de these conlution of surfac24:1M, C18:2e conditions a lution of surfac4:0M, C20:1Me same conditions of C18:2M centre of the d.5 ms for a RMons as in Figs.  crease and ntributions be mass fractionM and C18:3Ms in Figs. 1 ande mass fraction, C18:2M and Cons as in Figs.  and C22:1M vroplet at three E droplet und1-4 ear the ecome  s of  for a  2  s of 18:3M 1-3  ersus time er the noinsrescanC1thadevictheforFiFicenWthe0.5hea rto The plots of rmalised disttants, for RMpectively.  In agreement see from F8:2M, for RMn the heaviecrease in mainity of the sse figures thmed inside dr ig. 6 The plotsnormalised disnstants 0.02 mg. 7 The plots tre of droplet ams for a RME  The plots of ME biodiesel centre of the ms and 0.8 msAs one can seating and evapather large grdroplet surfacmass fractionance from thE and WM with the resuigs. 5 and 6E, and C12:0r componentsss fractions ourface of the at the gradoplets increa of mass fractiotance from thes, 0.3 ms and 0same conditioof temperature t four time insdroplet under ttemperatures fuel droplets droplet at fo) are shown ie in Figs. 7 anoration (0.03adient of teme is formed. s of selectede droplet cenE, are shownlts shown inthat the lightM, for WME (e.g. C22:1f the lighter droplet. Also,ients of specse with time. ns of C12:0M centre of the d.5 ms for a WMns as in Figs. 1 versus normalitants 0.03 ms, 0he same condit inside the d versus normaur time instan Figs. 7 and d 8, at the in ms after the perature insiIn contrast to components tre at variou in Figs. 5  Figs. 3 and er component) evaporate qM), which lecomponents  it can be seeies mass fra and C22:1M vroplet at three tE droplet unde-5. sed distance fro.3 ms, 0.5 ms ions as in Figsroplet of RMlised distancnts (0.03 ms, 8, respectivelitial stage of dstart of the prde the drople the case of sversus s time and 6, 4, one s (e.g. uicker ads to in the n from ctions  ersus ime r the  m the and 0.8 . 1-6 E and e from 0.3 ms, y.  roplet ocess) t close pecies World Academy of Science, Engineering and TechnologyInternational Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering Vol:9, No:1, 2015 48International Scholarly and Scientific Research & Innovation 9(1) 2015 scholar.waset.org/1999.8/10000158International Science Index, Mechanical and Mechatronics Engineering Vol:9, No:1, 2015 waset.org/Publication/10000158mdrsmthanbeis FcegrthcoanapdrreCinthdi42th[1][2][3][4][5]ass fractions,oplets decreaall at 0.8 mse Infinite Thealysis of dropginning of thnot required. ig. 8 The plotsntre of droplet ms for a WMEIgnoring theadient and rese species mponent, whd evaporationplications, caoplet surfacecommended onductivity/Eto account difese processesThe authorsscussions and74) and Unive project.  S. S. Sazhin, D B. Abramzondroplet with t46, Jan. 2006 W. A. SirignaCambridge, U B. Abramzonof thermal rad1873, Apr. 20 A. E. Elwardheating and evol. 97, pp. 68 however, thse with time after the starmal Conduclet heating ane process, wh  of temperatureat four time ins droplet underIII. CO effects of ecirculation ican be reich are comm of biodiesel n lead to noti temperaturethat ffective Diffufusion of all . ACKNOW are grateful to INTERREersity of BrigREFroplets and Spr and S. S. Sazhermal radiation. no, Fluid Dynam.K: Cambridge U and S. Sazhin, ‘Diation’, Int. J. H05. any and S. S. Savaporation: Appl5–694, Jul. 2012e gradients o. These gradrt of the proctivity model cd evaporatioen high accu  versus normaltants 0.03 ms,  the same condNCLUSION species difnside dropletplaced by on practices fuel droplets ceable errors s and evapothe Effsivity (ETCspecies, is useLEDGMENTS to Mr JackG IVa (Projhton for theirERENCES  ays. 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Modelling of heating and evaporation of biodiesel fuel droplets

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Modelling of heating and evaporation of biodiesel fuel droplets

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