For the validation a variety of mixtures and experimental data [44–49] is used to verify the accuracy of the algorithms described above. In general, the SRK EoS shows good correla-tions for hydrocarbons. Significant discrepancies can be observed for highly polar substances (methanol-water mixture) and hydrocarbons with big size differences (methane-decane, methane-propylbenzene). Nevertheless, the calculation of an ethane-methylcyclohexane mix-ture provides satisfactory results.
Table 5 shows the correlation of calculations with experimental data [46] for propane-cyclohexane. The calculations performed for propane-toluene and propane-m-xylene mixtures [46] demonstrate the same conformity with the experimental data. For the calculations, the pressure and liquid phase composition are preset, equilibrium temperature and vapor phase composition are predicted. Mixing rules parameters kij are listed in Table 5 along with the results obtained using the REFPROP© code [50] provided by the National Institute of Standards and Technology (NIST). This code uses the Span-Wagner modification [31] of the BWR EoS (2.17). REFPROP© has an extensive but non-exhaustive list of species and
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 10
20 30 40 50 60 70
80 experiment, Laugier et al.
calculation, this work
P, atm
H2S mole fraction
Figure 2.7: Equilibrium pressure vs. H2S mole fraction in an H2S-C6H14-C15H32 mixture.
Comparison of the experiment of Laugier et al. [44] and calculation. k12=0.07, k13= k23 = 0.
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
0 100 200 300 400 500
40 50 60 70 80 90 100
Pcrit , atm
T crit, K
Butane mole fraction Tcrit, experiment, Olds et al.
Tcrit, calculation, this work
Pcrit, experiment, Olds et al.
Pcrit, calculation, this work
Figure 2.8: Calculated and experimental [45] dependencies of critical pressure and tempera-ture for n-C4H10-CO2 system. Mixing rule parameter k12 = 0.06.
0 20 40 60 80 100 460
480 500 520 540
C10(75%)-C14(25%) experiment, 83 kPa, Huber et al.
C10(75%)-C14(25%) calculation, 83 kPa, this work C10(50%)-C14(50%) experiment, 83 kPa Huber et al.
C10(50%)-C14(50%) calculation, 83 kPa this work C10(50%)-C14(50%) experiment, 70 kPa Huber et al.
C10(50%)-C14(50%) calculation, 70 kPa this work
Temperature, K
Distillate volume fraction, %
Figure 2.9: Experimental and calculated distillation curves for 75/25 and 50/50 mole fraction mixtures of C10H22-C14H30at P = 83kPa and P = 70 kPa. Experimental data and surrogate mixture are from Huber et al. [17].
Table 5: Equilibrium concentrations in the propane(1)-cyclohexane(2) mixture; experi-mental data are compared with calculations using the presented algorithm and the NIST REFPROP© [43] package. Mixing rule coefficients k12= k21= 0.016.
P(atm) Texp(K) Tcalc(K) TNIST(K) x1 exp y1 exp y1 calc y1 NIST 2.52
5.47 8.44 11.45 13.01 9.18 12.44 16.09 21.42 26.05 38.29 17.76 28.62 46.98 58.23
313 313 313 313 313 393 393 393 393 393 393 473 473 473 473
312.4 311.2 311.9 312.8 312.1 389.5 389.1 388.8 390.2 391.6 470.2 470.4 473.6 475.7
281 296 306 310.5
313 354 357 360.5
373 382 450 433 438 442
0.152 0.378 0.615 0.847 0.97 0.138 0.208 0.287 0.395 0.491 0.731 0.054 0.175 0.372 0.515
0.906 0.962 0.9813 0.9922 0.9983 0.68 0.757 0.812 0.855 0.881 0.908 0.232 0.49 0.619 0.608
0.8286 0.9427 0.9776 0.9934 0.9989 0.7016 0.7928 0.8538 0.932 0.975 0.349 0.671 0.852 0.913
0.96 0.97 0.98 0.99 0.999 0.805 0.84 0.886
0.88 0.91 0.3 0.58
-Table 6: Composition of 7 hydrocarbons mixture, experimental [49] and calculated critical temperature and pressure.
Composition Hydrocarbon Fraction
i–C5H12 0.1989 n–C5H12 0.1963 n–C6H14 0.1483 n–C7H16 0.1344 n–C8H18 0.1213 n–C9H20 0.1137 n–C10H22 0.1142
Critical Properties calculated experimental Tcrit, K 543.3 543.37 Pcrit, atm 32.68 35.04
Table 7: Composition of 5 hydrocarbons mixture, experimental [49] and calculated critical temperature and pressure.
Composition Hydrocarbon Fraction
n–C5H12 0.2465 n–C6H14 0.2176 n–C7H16 0.1925 n–C8H18 0.1779 n–C9H20 0.1656
Critical Properties calculated experimental Tcrit, K 541.14 541.26 Pcrit, atm 30.49 30.6
can have problems with convergence near critical points, which cannot be evaluated with this tool. Model validation for the 9 – species mixture [48], H2S-CO2-N2-CH4-C2H6-C3H8-nC4H10 -isoC4H10-C5H12, is presented in Fig. 2.6. The calculation is made both by using the developed code and REFPROP©. A comparison of calculated evaporation line with experimental data for a three component mixture of H2S-C6H14-C15H32 at constant temperature 424.5 K [44] is shown in Fig. 2.7.
The results of the model validation on experimental data for critical point can be seen in Tables 6 and 7 and Fig. 2.8. Figure 2.9 shows the comparison of the calculated and experimental distillation curves. Due to the size of the condenser, the evaporated liquid arrives in the collecting vessel with the time delay. This causes a horizontal offset on the volume fraction axis, so the experimental points, except for the point corresponding to the initial boiling temperature, are subject to an adjustment of several percent, depending on the experimental apparatus and on the operating conditions. The calculations for a fuel surrogate suggested in [20] S-8 as well as for a C10H22-C14H30 mixture show a very good correlation with the experimental data.
The results of the model validation presented above prove that the selected algorithms describe thermodynamic phase equilibrium of multi-component mixtures reasonably well and can be used successfully to evaluate evaporation characteristics of surrogate blends.
The tools developed for two-phase equilibrium, critical points, and distillation curve cal-culations are first applied to examine the predictive capabilities of the surrogate models presented in literature, Table 8, to reflect the phase equilibrium. Only in [13] and [51] did the authors include the distillation curve for the determination of the chemical composition of
500 525 550 575 600 625 650 675 700 5
10 15 20 25 30
P, atm
T, K
PD., Schulz et al.
CP., Schulz et al.
PD., Linstedt et al.
CP., Linstedt et al.
PD., Violi et al.
CP., Violi et al.
experiment. PD, Edwards et al.
experimant. CP, Edwards et al.
PD., Malwid et al.
CP., Malwid et al.
PD., Dagaut et al.
CP., Dagaut et al.
Figure 2.10: Phase diagrams calculated using developed algorithm for fuel surrogates pro-posed in [6, 7, 13, 51, 52] compared to experimental data for Jet-A kerosene cited in [11]. CP – critical point, PD – phase diagram.
the surrogate model. Other proposed fuel models are tested only for the modeling of chemical properties. All suggested surrogates show good results in modeling concentration profiles and ignition delays of real fuels [6, 7, 13, 51, 52], but they do not describe the two-phase diagram.
In Fig. 2.10 the comparisons of phase diagrams calculated for mixtures from [6, 7, 13, 51, 52]
and experimental data cited in [11] are shown. While the critical pressure is described rather satisfactory, the discrepancies in critical temperatures are remarkably severe.
It is possible to reproduce the heat release characteristics of a fuel with a model that does not reflect the evaporation properties of the fuel at all. For example, in Figs. 2.11 and 2.12 the distillation curve and the two-phase diagram for gasoline RD387 and its reference model - a blend of 63%n-C7H16+ 17%i-C8H18 + 20%C7H8 proposed by Gauthier et al. [53] are shown.
This mixture does not describe the evaporation characteristic of the fuel. However, the ignition delay times modeled with this surrogate show good conformity with the experimental data [54]. The explanation for that lies in the different nature of modeled processes and in the difference between the methods applied in chemical and physical modeling.
The chemical models of hydrocarbon combustion have a hierarchical structure. Hydro-carbon molecules and radicals that have similar functional groups have similar reaction rates, which determines the rate of combustion. While the behavior of functional groups is the key for chemical time scales, physical properties depend more upon intermolecular forces and molecular weight. Therefore, hydrocarbons with similar functional groups may differ strongly in physical properties. Also the temperatures of the processes, for which the blends are being analyzed, differ.
Chemical combustion modeling deals mostly with temperatures above 800 K, while the
0 20 40 60 80 100 300
320 340 360 380 400 420 440 460 480 500
T boil
,K
Distillate volume fraction, % 63% C
7 H
16
+17% C 8
H 18
+20% C 7
H 8
, Gauthier et al.
Pure gasoline + 21% ethanol, de Oliveira et al.
AI 91 gasoline, de Oliveira et al.
Pure gasoline, Smith et al.
RD 387, Gauthier et al.
Figure 2.11: Experimental distillation curves for gasoline [15,16] and calculated boiling points curve for RD 387 and its surrogate fuel [53]. The near to constant boiling temperature of the surrogate of Gauthier et al. [53] is caused by almost equal boiling temperatures of the surrogate components.
Table 8: Compositions of tested mixtures.
Authors Ref. Composition
Lindstedt, Maurice [7] n-decane 89%, toluene 11%
Mawid, Sekar [8]
MCH 5%, toluene 20%, n-decane 25%, iso-octane 5%, n-dodecane 25%, n-tetradecane
20%
Dagaut, Cathonnet [6] n-decane 74%, n-propylbenzene 15%, n-propylcyclohexane 11%
Violi et al., mix #2 [13] xylenes 8.5%, tetraline 8%, n-octane 3.5%, decalin 35%, n-dodecane 40%, n-hexadecane 5%
Schulz [51]
iso-octane 5.7%, MCH 5.1%, m-xylene 4.5%, cyclo-octane 4.7%, decane 16.2%, butyl benzene 4.6%, 1,2,4,5-tetramethyl benzene 4.4%, tetralin 4.1%, dodecane 21%, 1-methylnaphthalene 3.95%
300 350 400 450 500 550 0
10 20 30 40 50
P, atm
T, K
Surrogate 63% n-C7H16+17% i-C8H18+20% C7H8, Gauthier et al.
RD 387 fuel components, Gauthier et al.
Figure 2.12: Calculated two-phase diagram for RD 387 and its reference fuel [53]. Dew-point curve and bubble-Dew-point curve for surrogate are indistinguishable, because of very close properties of the surrogate components.
0 20 40 60 80 100
420 440 460 480 500 520 540 560 580 600 620
Jet-A, experiment, Smith et al.
Jet-A, experiment, Violi et al.
Jet-A #1, experiment, Rachner et al.
Jet-A #6, experiment, Rachner et al.
Jet-A #7, experiment, Rachner et al.
Jet-A #8, experiment, Rachner et al.
Jet-A #11, experiment, Rachner et al.
Jet-A, Suggested reference fuel, this work
T boil, K
Distillate Volume Fraction, %
Figure 2.13: Experimental distillation curves for kerosene samples from the works of Violi et al. [13], Rachner [21], Smith et al. [20] and calculated fuel boiling points curve for the proposed fuel surrogate.
400 450 500 550 600 650 700 0
5 10 15 20 25
P, atm
T, K
calculation with presented model experiment cited by Edwards et al.
Figure 2.14: Calculated phase diagram for the proposed fuel surrogate, Table 9, compared to experimental data cited by Edwards et al. [11] for Jet-A.
temperature range of the two-phase diagram is below 700 K. It means that the reference fuel model applied for CFD modeling of a practical combustion chamber must represent different properties of the fuel, which poorly correlate with each other. We can conclude that, for the reference model construction, the evaporation properties of the reference fuel must be tested first. Using the developed tools the reference mixture with 12 components proposed in [51], Table 8, is optimized to reproduce the phase equilibrium phenomena. The surrogate blend [51]
is selected as a starting point because its phase diagram matches the experimental data better than all other suggested models, Fig. 2.10. At first step the most complicated components, for which little or no information on kinetics is availiable, are deleted. Then components with similar structure are gradually deleted. During the whole process the fraction of other components are fitted so, that physical properties as well as distrubition between the molecule Table 9: Composition of the proposed blend for kerosene combustion and its basic properties.
11% - C9H18
propylcyclohexane Combustion enthalpy 4cHf 45.5 MJ/kg 14% - i-C8H18
iso-octane Formation enthalpy 4Hf -260 kJ/mol 22% - C12H26
dodecane Molar weight 163 g/mol
28% - C11H10
1-methylnaphtalene Approximate formula C11.8H21.4 25% - C16H34
hexadecane Sooting Tendency Index 27.8
classes stays in the allowed range. Finally the number of components in the initial formula of surrogate [51] is reduced to 5 components, which represent the paraffins, naphthenes and aromatics in the mixture, Table 9. This mixture reproduces the evaporation properties of kerosene: Figures 2.13 and 2.14 show a good correlation between experimental data and the calculated distillation curve and phase diagram. Some essential physical properties are easily calculated as linear combination of corresponding properties of pure components and presented in Table 9. They are in accordance with those of real kerosene. Chemical properties of this mixture will be discussed later.