• No results found

6.2 Phase Optimized Skeletal Models

6.2.3 Investigation 1

115

Figure 6.3 POSM steps for the solver.

116

Table 6.2 Engine parameters and boundary conditions.

Bore/ Stroke/ Rod 85 / 88 / 135 mm Displaced Volume 500 cm3 Compression Ratio 14.5

IVC -137 CAD

EVO 137 CAD

Crankshaft rotational speed 2500 rev/min Fuel n-heptane 70% toluene 30

% Wall temperature 450 K

Table 6.3 Parameters specific to the mixture.

Mixture λ = 1.0

Timing of Ignition (CAD) -11.5 Combustion duration (CAD) 50

Wiebe – a / Wiebe – m 3.2 / 1

The Chemical Model

The chemical kinetic mechanism employed, both for the standard two-zone SRM calculations and as a base mechanism for creating the POSM, is a skeletal n-heptane / toluene mechanism.

This skeletal mechanism had already undergone the necessity analysis with respect to the entire calculation to form an optimally reduced mechanism. The toluene mechanism developed in our group is based on the original mechanism [89]. It is combined with the skeletal mechanism of n-heptane oxidation [80, 11]. The n-n-heptane / toluene mechanism contains 125 species and 1066 reactions.

The POSM Created

For this investigation a very conservative level of reduction was employed. Using the original skeletal mechanism, a set of zero-dimensional constant volume calculations were made at five different starting temperatures, ranging from 800 to 1600 degrees Kelvin. All the calculations were made for a starting pressure of 40 bars. This resulted in five different phases consisting of one phase optimized skeletal mechanism in each phase (Table 6.4). The phases represent a fur-ther reduction in size from the original already reduced skeletal mechanism.

117

Table 6.4 Numbers of species and reactions used by the different mechanisms.

Original mechanism 125 species / 1066 reactions Phase 1 79 species / 604 reactions Phase 2 89 species / 774 reactions Phase 3 92 species / 818 reactions Phase 4 110 species / 995 reactions Phase 5 72 species / 537 reactions

In the constant volume ignition calculations carried out the phases can be readily identified.

Phases 1 and 2 are basically initiation phases. Phase 1 is more important at low starting tempera-tures. Phase 3 is a pre-ignition phase for the initial buildup of radicals. Phase 4 is an ignition phase in which the upper boundary is essentially the auto-ignition point. Phase 5 is the phase following ignition, marked by the buildup of combustion products.

Figure 6.4 Representation of the basic idea of involving calculations using POSM. The species used by the different phases are shown in gray while the total num-ber of species in the standard mechanism is both gray and white. The calcu-lations start with phase 1, which has only a few species, and continue on through the phases with differing number of species.

118

The decision tree created uses mass fractions of only certain species for deciding which phase to employ. Essentially, the questions were whether the mass fraction values were very low or not.

Temperature and pressure could be considered at an intuitive level, in the questions. However, since the tabulations made involved constant volume calculations where the temperature and pressure do not go down after combustion, unlike an engine calculation with its expansion, these were consciously ruled out.

Results

The aim of this study was to compare the POSM approach with the standard mechanism in terms of accuracy and computational time. The case considered involved simulations of an SI engine under knocking conditions, using a mixture of n-heptane and toluene as fuel.

Calculation Accuracy

Pressure and temperature profiles, together with mass fractions over time for the species CO, OH and CH2O are presented. These three species were chosen since they are commonly meas-ured and for the highly reactive OH also could provide some differences [28].

Figure 6.5 Calculated temperatures as a function of time (left axis) and of absolute dif-ferences between the calculations (right axis).

 

0 500 1000 1500 2000 2500

-0.5 0 0.5 1 1.5 2

-40 -30 -20 -10 0 10 20 30 40 POSM

Standard Mechanism Difference

Temperature [K] Difference [K]

Time[CAD]

119

As can be seen in Figures 6.5-6.9, the differences between the calculations are small. For more precise comparison purposes, the absolute differences between the calculations are also given. For each figure, the thin line is for POSM calculations, the thick dots are for standard mechanism calculations and the thin dotted line shows the absolute differences between the two sets of cal-culations. The differences in temperature between the standard calculations and POSM, shown in Figure 6.5 are too small for it to be possible to distinguish between them. As the difference curve indicates, the differences are well below 0.1% or 2 K throughout the calculations. The maximum differences are found at the autoignition points or roughly at 16, 18 and 24 CAD.

The differences are so small that they can be neglected.

Figure 6.6 Calculated pressures as a function of time (left axis) and of absolute differ-ences between the calculations (right axis).

The pressure curves in Figure 6.6 show exactly the same type of behavior as that for the tempera-ture curves. The capabilities of the two-zone SRM are clearly demonstrated by the smoothly rounded pressure peak and the jagged edges of knock. Just as in Figure 6.5, the differences are very small, less than 0.1 % or 4000 N/m2, and they also peak at the same time as the tempera-ture curves in Figure 6.5 do.

0 1 106 2 106 3 106 4 106 5 106

-1000 0 1000 2000 3000 4000

-40 -30 -20 -10 0 10 20 30 40

Pressure (N/m¨2) Difference (N/m¨2)

Time[CAD]

120

Figure 6.7 Calculated mass fractions of CO as a function of time (left axis) and of abso-lute differences between the calculations (right axis).

Regarding the mass fractions calculated for the species CO, OH and CH2O (Figures 6.7-6.9) one can note the same very small differences. In terms of accuracy, it is obvious that the POSM performs almost as well as the standard mechanism. For CO the largest difference, in the order of 1 %, occurs at 24 CAD.

The largest deviation in the calculations occurs for CH2O at 24 CAD and is in the order of 7 %.

However this happens at a point at which nearly all of the CH2O is already consumed and thus not of any significance. Most of the time, the difference is well below 0.1 %. Finally for OH which was suspected to be hard to match, actually shows a very good agreement for the calcula-tions. The largest difference is less than 0.1 %.

-0.005 0 0.005 0.01 0.015 0.02

-5 10-5 0 5 10-5 0.0001 0.00015

-40 -30 -20 -10 0 10 20 30 40

CO (massfraction) Difference

Time[CAD]

121

Figure 6.8 Calculated mass fractions of CH2O as a function of time (left axis) and of absolute differences between the calculations (right axis).

Figure 6.9 Calculated mass fractions of OH as a function of time (left axis) and of abso-lute differences between the calculations (right axis).

 

-0.0005 0 0.0005 0.001 0.0015 0.002

-2 10-5 -1.5 10-5 -1 10-5 -5 10-6 0 5 10-6

-40 -30 -20 -10 0 10 20 30 40

CH 2O (massfraction) Difference

Time[CAD]

-0.0005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003

-8 10-7 -6 10-7 -4 10-7 -2 10-7 0 2 10-7 4 10-7 6 10-7 8 10-7

-40 -30 -20 -10 0 10 20 30 40

OH (massfraction) Difference

Time[CAD]

122

Reduction in calculation time

As been shown, POSM shows excellent agreement with the standard mechanism, at the same time as it is roughly three times as fast. On a laptop having a 3.2 GHz Pentium processor the calculations using the standard mechanism required 318 s to be completed, while the POSM calculations were completed in 114 s. This translates to a factor of about 3 in terms of computa-tional savings.

Discussion

This part of the work shows that the POSM technique meets the major objectives for calcula-tions making us of a two-zone SRM code, namely retention of accuracy together with improved calculation efficiency. The current investigation showed good results. No extra effort was made to optimize the phase mechanisms, through the elimination of further species. A conservative necessity cutoff was chosen to ensure accuracy. In view of the level of accuracy achieved, the computational efficiency could be expected to improve significantly with optimization.

There appears to be considerable potential for much faster calculations being achieved with retention of accuracy, through further development of the POSM generation technique and greater emphasis being placed on reduction. Further computational efficiency can be gained through the accuracy criteria being relaxed in comparison with the stringent results currently being obtained. Examination of Figures 6.5-6.9 shows there to be distinct deviations at 16, 18 and 24 CAD coinciding with the auto-ignition events. These deviations are so small, however, that they can be neglected.

In the present study, the POSM phases were based on zero-dimensional constant-volume calcu-lations at given pressures and temperatures. It is likely that using calcucalcu-lations closer to engine conditions would improve POSM, such a through using a set of points obtained from actual SRM engine calculations. Even when using data that was not tuned to engine calculations, a speed-up was achieved, however. With use of more realistic starting data, more realistic phases can be expected to be found and still greater speed-up to be obtained. Finally, just as POSM can be used to improve the calculation speed it can also be used to improve the accuracy of the cal-culations. In that case the approach would be to have a number of optimized yet not reduced mechanisms for each phase. For numerical reasons, it would still be faster than a single mechan-ism would be.

Conclusions

An already reduced skeletal standard mechanism was divided into five sub mechanisms, each representing a phase in the combustion events. These Phase Optimized Skeletal Mechanisms, POSM, together with the establishing of the phases, were achieved by use of an automated tool employing machine-learning, clustering and decision tree algorithms. The phases were estab-lished on the basis of constant-volume calculations. The POSM model created was implemented

123

in the two-zone SRM code, comparative calculations being made for the standard mechanism and for the POSM, respectively, with the aim of determining the accuracy and the calculation speed of this novel technique. POSM shows excellent agreement with the standard mechanism, in terms of pressure, temperature and species mass fractions. The deviations are generally less than 0.1 %. POSM is three times as fast as the standard mechanism.