Biodiesel fuel droplets: transport and thermodynamic properties

ILASS – Europe 2013, 25th European Conference on Liquid Atomization and Spray Systems, Chania, Greece, 1-4 September 2013 Biodiesel fuel droplets: transport and thermodynamic properties Ruslana Kolodnytska1, Mansour Al Qubeissi2 and Sergei S Sazhin2 1: Department of Mechanical Engineering, Zhytomyr State Technological University, Chernyahovskogo, 103, Zhytomyr 10005, Ukraine, e-mail: [email protected] 2: Sir Harry Ricardo Laboratories, School of Computing, Engineering and Mathematics, University of Brighton, Brighton BN2 4GJ, UK Abstract A detailed comparative analysis of transport and thermodynamic properties of biodiesel fuels and components of these fuels is presented. Five types of biodiesel fuels are considered: Palm Methyl Ester, produced from palm oil; Hemp Methyl Esters, produced from hemp oil in the Ukraine and European Union; Rapeseed oil Methyl Ester, produced from rapeseed oil in the Ukraine; and Soybean oil Methyl Ester, produced from soybean oil. Up to 16 components (methyl esters in most cases) of these fuels are considered. The results are applied to the analysis of biodiesel fuel droplet heating and evaporation in conditions relevant to internal combustion engines, using the model described elsewhere. Introduction As an alternative to Diesel fuel biodiesel fuels have been developed (1). The dominant oils for production of these fuels are rapeseed oil in Europe, soybean oil in the USA, and palm oil in Asia (2). The ‘second-generation biodiesels’ have been produced from inedible oil or algae (3); hemp biodiesel has been produced from waste (4). Most studies of biodiesel fuels have focused on rapeseed, soybean and palm oil biodiesels (5). This paper concentrates upon the investigation of biodiesel transport and thermodynamic properties in view of the application of the results to the modelling of fuel droplet heating and evaporation. Biodiesel fuels Five types of biodiesel fuel are considered: Palm Methyl Ester (PME), produced from palm oil (6); Hemp Methyl Esters, produced from hemp oil in the Ukraine (HME1) (4) and European Union (HME2) (7); Rapeseed oil Methyl Ester (RME), produced from rapeseed oil in the Ukraine (5); and Soybean oil Methyl Ester (SME), produced from soybean oil (8). The Sauter Mean Diameters (SMD) of biodiesel and Diesel fuel droplets at temperature 80C, as reported in (9, 10), are shown in Table 1. Table 1. The Sauter Mean Diameters (SMD) of biodiesel and Diesel fuel droplets at temperature 80C. Reference PME HME1 (9) (10) 25.1 m - 23.55 m HME2 23.55 m RME SME 28.8 m 26.69 m 25.7 m 23.87 m Diesel 17.7 m 18.3 m The average values of SMD of biodiesel fuel droplets (25.32 μm) are larger than those of Diesel fuel droplets which can be attributed to the higher viscosity of biodiesel fuels (10). Chemical formulae and molar fractions of components of biodiesel fuels (methyl esters) are shown in Table 2. 1 25th ILASS – Europe 2013 Biodiesel fuel droplets, transport and thermodynamic properties Table 2. Molar fraction and chemical formulae of components (pure methyl esters) for 5 biodiesel fuels. Components Chem. form. PME HME1 HME2 RME SME С12:0 М C13H26O2 0.0026 0.0000 0.0000 0.0000 0.0000 С14:0 М C15H30O2 0.0129 0.0000 0.0000 0.0000 0.0000 С16:0 М C17H34O2 0.4513 0.0662 0.0651 0.0495 0.109 С17:0 М C18H36O2 0.0000 0.0021 0.0000 0.0000 0.0000 С18:0 М C19H38O2 0.0447 0.0206 0.0246 0.0167 0.044 C20:0 М C21H42O2 0.0035 0.0045 0.0090 0.0056 0.004 C22:0 М С24:0 М C23H46O2 0.0000 0.0025 0.0000 0.0000 0.0000 C25H50O2 0.0000 0.0023 0.0000 0.0000 0.0000 С16:1 М C17H32O2 0.0021 0.0033 0.0000 0.0000 0.0000 С18:1 М C19H3602 0.3839 0.1188 0.1188 0.2671 0.240 C20:1 М C21H40O2 0.0017 0.0027 0.0090 0.0000 0.0000 C22:1 М C23H44O2 0.0000 0.0017 0.0000 0.2204 0.003 С24:1 М C25H48O2 0.0000 0.0015 0.0000 0.0077 0.0000 С18:2 М C19H34O2 0.0916 0.5671 0.5482 0.2484 0.528 С18:3 М C19H32O2 0.0019 0.2067 0.2007 0.0973 0.072 0.0246 0.0873 - Other 0.0038 - The numbers of carbons in fatty acids ( nacid ) and numbers of double bonds (DB) are shown by the numbers on the left and on the right of ‘:’ respectively in the expressions for the components. For example, C18:2 M has nacid = 18 and DB = 2. The total number of carbon atoms in methyl esters is equal to nacid +1. Transport and thermodynamic properties of liquid components The methyl ester density shown in Table 2 is estimated based on the following formula which is valid in the temperature range 288.15 T Tcr (11): (1) l  l 0 T (T  288.15) , where 250.718DB  280.899 7.536 , T  l 0  851.471   0.446 . 1.214  nacid ln( nacid )  3.584 The methyl esters’ kinematic viscosity in the temperature range T  0.7 Tcr in the case of saturated molecules (DB=0) is estimated as (12): 403.66 109.77nacid ln  l  106  2.177  0.202nacid   ; (2) T T in the case of unsaturated molecules (DB>0), it is estimated using the Orrick and Erbar method (13):   106 B (3) ln l l  Ak  k , l (20) M T   where l ( 20) is liquid density at T = 293.15 K. The molar latent heat of evaporation of components is estimated as (14): L  (aL  bL M ) L , where Tcr  acr  bcr M , Tb  ab  bb M ,  T T  L   cr  Tcr  Tb    (4) (5) 0.38 . (6) 2 25th ILASS – Europe 2013 Biodiesel fuel droplets, transport and thermodynamic properties Eq. (4) gives good agreement with experimental data (15) for saturated molecules as shown in Fig. 1. 160 L (kJ/mol) 140 120 100 80 L (modelling) 60 L (experiment) 40 12 14 16 18 20 Number of carbons 22 24 Figure 1. Latent heat of evaporation at 298.15 K for saturated methyl esters against experimental data (15). The liquid heat capacity and liquid thermal conductivity of components are estimated as (14,13): cl  (a pl  b plT  c plT 2 )103 , kl  A * Tb1.2 (1  Tr ) 0.38 , MTcr0.167 Tr 1/ 6 (7) (8) T . Tcr Eqs. (4), (7), (8) are used in our analysis for temperatures from 300 K up to the critical temperature. The coefficient A* in Eq. (8) was set at A*= 0.0713 which is different from A*= 0.0415 suggested by Latini (13). The values of coefficients in Eqs. (3), (4), (5), (6), (7) are given in Table 3 (16, 17). The values for C18:3M in Eqs. (4), (7) have been obtained via the linear extrapolation of the values of coefficients for C18:1M and C18:2 M. where Tr  Table 3. The values of coefficients used in Eqs. (3) - (7). Coefficients Ak C12:0 M – C24:0 M - C16:1 M – C24:1 M -10.83 C18:2 M -9.93 C18:3 M -9.03 Bk - 2099 1721 1343 ab bb 348.7 350.4 352.1 353.82 0.8478 0.8463 0.8463 0.8472 acr bcr 534.3 538.5 542.6 546.8 0.784 0.777 0.772 aL 7 1.506  10 bL 5 0.7711 7 1.389  10 1.270  10 1.154  107 1.814  10 5 1.822  10 1.834  10 1.843 105 (Tcr  Tb )0.38 7.027 7.047 7.067 7.087 a pl 1.816 1.915 2.018 2.115 b pl - 1.4 62 10-3 - 2.16310-3 - 2.87810-3 - 3.580 10-3 c pl 7.5110-6 8.2910-6 9.09 10-6 9.92 10-6 7 5 3 25th ILASS – Europe 2013 Biodiesel fuel droplets, transport and thermodynamic properties The liquid diffusivity of biodiesel Dl is estimated using the Wilke-Chang approximation (13) assuming that liquid diffusivity is the same for all components: 7.4  10 15 M v T , Dl  lVv0.6 (9) where M v is the average molar mass of components,  l is the liquid dynamic viscosity, kg m-1 s-1. Molar volume Vv at the normal boiling point and Lennard-Jones length  v for individual components is estimated as (18,19): Vv  v / 1.183 , (10) . v  1.486M The plots of liquid diffusivity for PME, SME and HME2 calculated based on Eq. (9) are shown in Fig. 2. 0.297 Figure 2. The liquid diffusivity (11) Dl for PME, SME, and HME2 calculated based on Eq. (9). As one can see from Fig. 2 the highest liquid diffusivity is for PME, the diffusivities for SME and RME are close to each other, the liquid diffusivity for HME2 is very close to the diffusivity for HME1 (plots are not presented). An alternative approximation for liquid diffusivity of components was suggested by Hayduk and Minhas (13):  P 0.5  T 1.29 0 (12) DAB  15.5  1012  0B.42  0.23 0.92 ,  PA  VB  B where  B is the dynamic viscosity of solvent B, cP; PA and PB are Parahors (see (10,13) for the details) for the solute and solvent. The following approximation was derived for liquid diffusivity of saturated molecules (C12:0 M - C24:0 M) at the temperature 293.15K using Eqs. (12), (10) and (11): D 0AB  AD 108 e( 0.142nacid ) , (13) where AD =2 for methyl esters C12:0 M – C24:0 M. Transport and thermodynamic property of methyl esters vapour The saturated vapour pressure (in Pa) of pure liquid methyl esters is estimated based on the following general formula which is valid in the temperature range (260 K < T <610 K) (20): c   pv  103 aCN ,0 auc ( DB  1)  bUC  uc  exp (a CN ,1 nacid ) , (14) DB  1  where 4 25th ILASS – Europe 2013 Biodiesel fuel droplets, transport and thermodynamic properties aCN ,0  1.908 exp[0.01715T ]. aCN ,1  5.656  0.02649T  4.5417 105T 2  2.6571108T 3 , for DB  0 or T  323 K, auc  0 , buc  1 , cuc  0 , otherwise, auc  4.62  105 T 2  3.06  102 T  5.05 , buc  3.39  102 T  9.93 , cuc  2.97  102 T  9.62 . Using data provided in (21), the following approximation for the vapour heat capacities of the components of biodiesel fuels in the range of temperatures 300 K< T <1500 K has been derived: c pv  4184C pv,0C pv,1M 1 ( J kg1K 1 ) (15) where C pv ,0  (6.37561  n acid  6.6472) ln(T) - 31.361  n acid - 26.118 , C pv,1 = exp(0.01105ln( T )  0.0425)DB . Vapour diffusion coefficients were approximated as (17, 22): 2  10 10 T 1.75 , p where p is ambient pressure in bars. Dv  Transport and thermodynamic properties of biodiesel fuels Data presented earlier allow us to calculate average values of liquid density, specific heat capacity, dynamic viscosity and thermal conductivity for all 5 biodiesel fuels using the mixture rules (23, 24). Table 3 shows the values of calculated/estimated (27) density and viscosity for RME and calculated/estimated (28) values of thermal conductivity for RME. Table 4. The values of calculated liquid density and viscosity versus experimental data (27); and calculated/ estimated thermal conductivity (28) for RME. Temperature 293.15 K 303.15 K 313.15 K 323.15 K 333.15 K 343.15 K 353.15 K 363.15 K 373.15 K Dynamic viscosity Measured/Calculated 0.0063413/0.0058339 0.0048825/0.0046859 0.0038665/0.0038166 0.0031336/0.0031482 0.0025883/0.0026269 0.0021724/0.0022151 0.0018320/0.0018860 0.0015837/0.0016198 0.0013923/0.0014026 Density Measured/Calculated 879.6/878.823 872.9/871.729 865.7/864.634 858.3/857.540 851.0/850.445 843.7/843.350 836.4/836.256 829.1/829.161 821.7/822.066 Temperature 300 K 350 K 400 K 450 K 500 K 550 K 600 K Thermal conductivity Estimated/Calculated 0.17696/0.16423 0.16860/0.15349 0.15991/0.14320 0.15083/0.13306 0.14125/0.12280 0.13104/0.11415 0.11997/0.11317 As one can see from Table 4, the calculated and experimental data for density and dynamic viscosity are very close and the agreement between the predicted values of thermal conductivity for both approaches is reasonably good. The thermal conductivity of biodiesel is higher than that of Diesel fuel (25). Biodiesel produced from rapeseed oil has a thermal conductivity of 0.153 0.002 Wm-1K-1 (25) (or 0.17 W·m-1·K-1(26)) at 298 K compared to Diesel fuels, for which the respective value is 0.115 0.002 Wm-1K-1 (25). Biodiesel droplet evaporation modelling The above results were applied to the analysis of biodiesel fuel droplet heating and evaporation in conditions relevant to Diesel engines, using the Effective Thermal Conductivity/Effective Diffusivity (ETC/ED) model (23, 24). Our analysis is focused on the following values of parameters (assuming that the ideal gas law is valid):  a = 11.9 kg/m3, Ta= 880K, pa = 30 bar and assuming that droplets have a velocity of 10 m/s. Fig. 3 shows the results of calculations using the multi-component evaporation model taking into account the contribution of some or all of the 16 components shown in Table A2 for SME and HME1. Our results show that HME1 droplets take slightly longer to evaporate than SME droplets and the surface temperatures of HME1 droplets at the final stage of droplet evaporation are slightly higher than the ones predicted for the SME droplets or HME2 droplets (plots for HME2 are very close to SME and are not presented in Fig. 3). The difference in evaporation between HME1 and HME2 can be attributed to the presence or absence of the heaviest components (C22:1 and C24:1 M) in HME2 and HME1 (see Table 2). A more detailed analysis of biodiesel fuel droplet heating and evaporation is presented in our parallel paper (29). 5 25th ILASS – Europe 2013 Biodiesel fuel droplets, transport and thermodynamic properties Conclusion A detailed comparative analysis of transport and thermodynamic properties of biodiesel fuels and components of these fuels (methyl esters) is presented. The analysis has been focused on five types of biodiesel fuels: Palm Methyl Ester (PME); Hemp Methyl Esters, produced from hempseed oil in the Ukraine (HME1) and European Union (HME2); Rapeseed oil Methyl Ester (RME), produced from rapeseed oil in the Ukraine; and Soybean oil Methyl Ester (SME), produced from soybean oil. Up to 16 components of these fuels are considered. The results are applied to the analysis of biodiesel fuel droplet heating and evaporation in Diesel engine-like conditions using the previously suggested model that takes into account temperature gradient and recirculation inside droplets and species diffusion within them. Our results show that the evaporation time for Hemp Methyl Esters is very close to that of Soybean oil Methyl Esters. Figure 3. The plots of SME and HME1 droplet surface temperatures (Ts) and radii (Rd) versus time predicted by the multi-component model. Gas temperature and pressure are assumed to be equal to 880 K and 30 bar respectively. The initial droplet radius is assumed to be equal to 12.66 μm. The droplet is assumed to be moving with a constant velocity equal to 10 m/s. Acknowledgements The authors are grateful to the Ministry of Education of the Ukraine, Zhytomyr State Technological University (Ukraine) and INTERREG IVa (Project E3C3, Reference 4274) for their financial support. Nomenclature Symbol c D DB k L M nacid p T V    v Description specific heat capacity diffusion coefficient number of double bonds thermal conductivity latent heat of evaporation molar mass number of carbon atoms in acid pressure temperature molar volume at boiling temperature kinematic viscosity density dynamic viscosity Lennard-Jones length Unit J·kg-1·K-1 m2·s-1 - W·m-1·K-1 J·kmol-1 kg kmol-1 Pa/bar K sm3mol-1 m2·s-1 kg·m-3 kg m-1 s-1/ cP  A 6 Subscripts A a B cr b l p r v 0 Description Solute air solvent critical boiling liquid constant pressure reduced vapour initial 25th ILASS – Europe 2013 Biodiesel fuel droplets, transport and thermodynamic properties References 1. M. Lapuerta, O. Armas, Effect of biodiesel fuels on diesel engine emissions. Progress in Energy and Combustion Science 34, 198-223 (2008). 2. S.K. Hoekman, A. Broch, Review of biodiesel composition, properties, and specifications. Renewable and Sustainable Energy Reviews 16, 143-169 (2012). 3. G. 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