PAPER NO.: 39 Modelling of the oxidation of fuel sulfur in low speed two-stroke Diesel engines

Transcription

1 CONSEIL INTERNATIONAL DES MACHINES A COMBUSTION INTERNATIONAL COUNCIL ON COMBUSTION ENGINES PAPER NO.: 39 Modelling of the oxidation of fuel sulfur in low speed two-stroke Diesel engines Anders Andreasen, MAN Diesel, Denmark Stefan Mayer, MAN Diesel, Denmark Abstract: In large marine two stroke Diesel engines during combustion of sulfur containing fuel, the sulfur is oxidised to SO 2, mainly, although substantial amounts of SO 3 and H 2 SO 4 will form as well. These latter species may cause corrosional wear of the cylinder liner if not neutralised by lube oil additives. Potential attacks is due to either condensation of sulfuric acid on the cylinder liner lube oil film or direct dissolution of oxidised sulfur species in the lube oil film in which reaction with dissolved water may be the source of acidic species. In order to evaluate and predict corrosional wear of the liner material, it is pivotal to have realistic estimates of the distribution/concentration of oxidised sulfur species as well as a reliable model of formation, transport and destruction of acidic species in the oil film. This paper addresses the former part by invoking a detailed reaction mechanism in order to simulate the oxidation of fuel bound sulfur and predicting the concentration of SO 2 as well as the conversion fraction into SO 3 and H 2 SO 4. The reaction mechanism is coupled to a realistic model of the combustion process in which the air entrainment into the combustion zone is accounted for. The results of the simulation are evaluated with respect to previously applied models as well as existing data on the conversion fraction of SO 2 to SO 3 and H 2 SO 4. The conversion fraction is found to be in a range of %. c CIMAC Congress 2010, Bergen

2 INTRODUCTION During the combustion of sulfur containing fuel, the sulfur will be oxidised mainly to SO 2 but significant fractions of SO 3 and H 2 SO 4 will also form [1]. While emissions of CO, HC and NO x to some extent can be controlled through the combustion conditions e.g. air excess ratio, combustion temperature etc. the total emission of sulfur can only be controlled through the sulfur content of the fuel [2] or by appropriate exhaust gas after treatment e.g. by scrubbing technologies [3]. From an environmental point of view SO x emissions are undesired, primarily due to the formation of atmospheric H 2 SO 4, which is the main source of acid rain. From a technical/engineering point of view the problems related to the sulfur content of the fuel are mainly corrosional wear due to sulfuric acid (produced from fuel sulfur, oxygen and moisture) attacking various parts of the engine and auxiliaries [4, 5, 6]. Especially the corrosional wear of the cylinder liner has received special attention in the past [7, 8, 9, 10, 11, 12, 13]. Sulfuric acid may potentially cause corrosion either by condensation, if the liner temperature drops below the dew point of the combustion gas [7, 12] or by direct transport of acidic gas phase species into the cylinder liner lube oil film [13]. The acidic species may diffuse through the cylinder lube oil and reach the metal surface eventually leading to corrosional wear. This can be avoided through neutralisation of sulfuric acid with alkaline lube oil additives. Further it has been proposed that SO 2 is absorbed in the lube oil film in which further reaction with water leads to acid formation [11]. Standard textbooks on the topic of internal combustion engines and combustion in general only surface the topic of sulfur oxide formation during combustion of sulfur containing fuels [2, 14, 15]. To the best of our knowledge no results on experimental measurements of SO x in the exhaust gas from large two-stroke diesel engines have been published in peer reviewed journals in the past. Engel et al. reported measurements of both SO 2 and SO 3 in the exhaust gas of a range of heavy duty four stroke diesel engines [4]. They found that approx. 3 % (volumetric) of the SO 2 was converted to SO 3 on average. Previous modelling studies devoted to the prediction of diesel engine in-cylinder formation of sulfur oxides including sulfuric acid [7] has been based either on the assumption that i) SO 2, SO 3, and H 2 SO 4 are in equilibrium at temperatures above 1000 C, viz. the reactions responsible for their formation are much faster than the time scales being considered. Below 1000 C the reaction systems are considered frozen i.e. the amount of the species already formed will be constant, or ii) a fixed instantaneous conversion ratio of SO 2 to SO 3 of e.g. 5% [12, 13]. In order to provide a deeper understanding of corrosional wear of the cylinder liner through modelling studies it is pivotal to have reasonable concentrations of both SO 2, SO 3 and H 2 SO 4 as input. In contrast to diesel engines the published research on formation of SO x and H 2 SO 4 from aircraft turbines has been significantly more extensive both experimentally as well as theoretically [16, 17, 18, 19, 20] (and references therein). The modelling studies reported are based on large detailed reaction mechanisms describing the oxidation of fuel bound sulfur formation [18, 17, 19]. In this preliminary study it will be investigated how both chemical kinetics and thermodynamics influence the distribution of oxidised sulfur species during combustion of sulfur containing fuel in large two-stroke diesel engines. The main motivation for this study is the fact that the current knowledge about the in-cylinder formation of SO 3 and H 2 SO 4 in large two-stroke diesel engines is very limited. Improving the understanding in this field will indeed be helpful in evaluating potential in-cylinder corrosional wear both for engines in service, especially considering choice of lube oil type and lube oil consumption, but certainly also for engines in the design phase. Furthermore, exhaust gas recirculation (EGR) is becoming an emerging method for NO x reduction for large two-stroke marine diesel engines running on heavy fuel oil (sulfur content up to 4.5 w.w %) [21, 22]. A detailed knowledge of the composition of sulfur species in the EGR line will be helpful in the design and control of the EGR scrubber in order to control the level of sulfur species entering the cylinder through the scavenge ports potentially increasing the risk of cylinder liner corrosional wear if not neutralised. The basis of this study is real measured engine data from a large two-stroke diesel engine e.g. directly measured in-cylinder pressure as a function of degree crank angle as well as exhaust gas NO concentraion, derived fuel mass burned fraction and trapped air amount (air excess ratio). This is used as input for simulations invoking a detailed reaction mechanism describing the formation of oxidised sulfur species from fuel injection start to exhaust valve opening. CIMAC Congress 2010, Bergen Paper No. 39 2

3 METHODS Experimental The engine used to acquire input data to the kinetic model is the MAN Diesel custom built test engine located in Copenhagen. A summary of engine characteristics is given in Table 1. The engine is equipped for full electronic-hydraulic control of the fuel injection and the exhaust valve timing. A total of four engine tests have been conducted at the following loads: 100, 75, 50, and 25% (at 123, 112, 98 and 78 rpm, respectively) of the maximum continuous rating (MCR). The engine speed decrease as a function of load according to a simulated propeller curve [23]. The air excess ratio (trapped air only, scavenging air not included) for the four tests was 2.27, 2.43, 2.36, 2.74 for 100, 75, 50, and 25% load, respectively. The used fuel was diesel oil with the following atomic composition of C and H atoms: 86.8 w/w % and 13.2 w/w %. The sulfur content of the fuel was 0.05 w/w % and heating value of the fuel is kj/kg. All values determined from an analysis performed by an external laboratory. The exhaust gas concentration of NO has been measured in the exhaust duct between the turbine and the stack by the heated chemiluminescence technique (HCLD) according to ISO 8178 standards. Figure 1 Measured in-cylinder pressure averaged over 50 revolutions as a function of degree crank angle after top dead center (ATDC). Table 1 Test engine specifications Manufacturer MAN B&W Diesel Type 4T50ME-X Number of cylinders 4 Bore 500 mm Stroke 2200 mm Connecting rod length 2885 mm MCR speed 123 RPM MCR power 7050 kw MCR 20 bar Turbocharger MAN TCA55-VTA Model and calculational setup The starting point in the kinetic model is measured cylinder pressure as a function of crank angle. From the measured in-cylinder pressure the fuel mass burned fraction is derived from the integrated heat release rate as obtained from a single zone heat release analysis using an in-house code. The measured cylinder pressure as a function of degree crank angle for the four engine tests is depicted in Figure 1. The rate of heat release as determined from the in-cylinder measured pressure traces shown in Figure 1 is shown in Figure 2. Figure 2 Rate of heat release for the 4 load cases In order to model the kinetics of the formation of oxidised sulfur species i.e. SO 2, SO 3, and H 2 SO 4, a detailed reaction mechanism is called upon. For this purpose the Glarborg sulfur mechanism is used [24] which is a result of a continuous effort in literature data review, experimental laboratory reactor measurements as well as theoretical predictions [25, 26, 27, 28, 29]. Other sulfur oxidation mechanisms exists e.g. the Leeds sulfur mechanism [30], however a substantial part of the S subset is based on the work of Glarborg et al. anyway. The S subset in the Glarborg mechanism contains 96 elementary reactions. In addition to the S subset the mechanism contains an O/H subset describing the formation of O, OH, HO 2, H 2 O 2. A complete listing of all reactions along with rate coefficient and thermodynamic parameters will not be given. In order to describe the formation of CIMAC Congress 2010, Bergen Paper No. 39 3

4 sulfuric acid a single reaction has been added in which H 2 SO 4 is formed from SO 3 and H 2 O. The kinetic parameters for this reaction have been taken from [31]. In order to integrate the kinetic rate equations the Cantera open source software [32, 33] is used. The used mechanism include a thermodynamical description of all involved species expressed through 7 coefficient NASA polynomials [34]. In order to simulate the oxidation of fuel bound sulfur a multi-zone model is invoked and the details of the model will summarised in following. Up to the time of fuel ignition the fresh charge of the cylinder is considered as a single zone and the working gas is compressed isentropically. By the time of ignition and until the combustion has ended, for each crank angle degree a new zone is created by mixing the differential amount of fuel burned during this particular time step (one crank angle degree) stoichiometrically with fresh air and subsequently equilibrating [35] at the corresponding measured cylinder pressure. We will refer to such a unit as a parcel. After its creation and subsequent equilibration no more fuel is added to this particular parcel. Only fresh air is allowed to be added at a predefined mixing rate. The multi-zone approach taken here is in close analogy with that in [36]. In each parcel the rate equations describing O/H chemistry and sulfur oxidation are integrated up to the time of the exhaust valve opening. Some further assumptions of the model are: Sulfur contained in the fuel is modeled as elemental S in the fuel feed. The fuel is mimicked by a mixture of n- octane, benzene and ethanol. The exact composition is tuned in order to match the heating value of the real fuel as well as the elemental composition. The concentration of all gas phase species is isotropic i.e. mixing is fast and complete. For each time step it is assumed that temperature and pressure is constant at the starting value for that particular time step. In order for the flame temperatures calculated not being unrealistically high a temperature drop due to radiation losses is included [36] (1) in which T ad is the adiabatic flame temperature calculated by equilibrating fuel and air at λ=1, c p is the constant pressure heat capacity of the combustion products and C rad is a heat radiation constant with a value chosen to give a temperature drop of approx 100 K for the parcels created early. Throughout this paper we will refer to a so-called conversion fraction or conversion efficiency of sulfur into SO 3 and H 2 SO 4 which is denoted ε. The definition of ε is (2) where [SO x ] is the sum of the concentrations of all sulfur containing species i.e. (SO 2, SO 3, H 2 SO 4,...). RESULTS AND DISCUSSION Examination of the equilibrium An overall, yet simplified, description of the oxidation of fuel bound sulfur is outlined in the following reactions. S + ½O 2 = SO (3) SO + ½O 2 = SO 2 (4) SO 2 + ½O 2 = SO 3 (5) SO 3 + H 2 O = H 2 SO 4 (6) The enthalpy of formation, ΔH 298o, of the individual species are 6 kj/mol (gas), -297 kj/mol (gas), -396 kj/mol (gas), and -814 kj/mol (liquid) for SO, SO 2, SO 3, and H 2 SO 4, respectively [37]. To which degree the sulfur is oxidised or converted into H 2 SO 4 depends on both thermodynamics and reaction kinetics. The above reactions are listed in the order of increasing thermodynamic stability of the product. According to the principle of Le Chatelier this implies that the higher the temperature the less degree of oxidation i.e. SO is favored vice versa at lower temperatures SO 3 /H 2 SO 4 is favored. Also pressure is important; the higher the pressure, the higher degree of oxidation. To get a comprehension of the quantitative influence of temperature and pressure on the distribution of sulfur containing species the O 2 /SO 2 /SO 3 /H 2 SO 4 equilibrium composition is CIMAC Congress 2010, Bergen Paper No. 39 4

5 calculated. The results of the equilibrium calculations are shown in Figure 3. As seen from the figure the main transition from SO 3 to SO 2 takes place at around 1100 K at 10 bar and at approx K at a pressure of 100 bar. Thus, in the early phase of the combustion all sulfur will be in the form of SO 2. No significant amounts of SO were found unless above 2200 K. At the lowest temperatures sulfuric acid is favored. At a temperature of 1273 K the fraction of SO 3 relative to SO 2 +SO 3 equals 14 and 35 % at 10 and 100 bar, respectively. Upon cooling from high temperatures, the amount of SO 3 and H 2 SO 4 will increase from a thermodynamic point of view. However, due to potential kinetic limitations the SO 3 and H 2 SO 4 concentration may be frozen by quenching the gas. The exact concentration of sulfur containing species is thus a complex function of temperature, pressure, initial concentrations, cooling rate, and residence time. The effect of kinetics on the formation of SO 3 /H 2 SO 4 is investigated in the next section. Both limits are unrealistic for modelling real mixing controlled diesel spray combustion and emission formation. The former limit will result in too high parcel temperatures and too low oxygen concentration and for the latter limit the opposite is the case. In reality the mixing rate is somewhere in between the two. Thus the temperature (cooling by fresh gas) and oxygen concentration in each parcel is closely linked to the applied mixing rate. In order to investigate the effect of applied mixing rate on the calculated conversion fraction, ε, a number of simulations have been performed in which the mixing rate is varied. The results are depicted in Figure 4. Figure 4 Conversion fraction, ε, resulting air excess ratio in the burned zones at exhaust valve opening, and calculated NO concentration as a function of applied mixing rate. Results are calculated for the 75 % load case Figure 3 Concentration of SO 2, SO 3, and H 2 SO 4 as a function of temperature at (upper) a pressure of 10 bar and at (lower) a pressure of 100 bar. Initial concentration is x O2 = 0.15, x H2O = 0.05, x S = 0.01, no other components other than Argon present. Simulations of in cylinder formation of sulfur species Adjustment of mixing rate. The main tuneable parameter in the model applied in this study is the mixing rate at which fresh air is mixed into each parcel. The limits of the mixing rate is zero, at the low end, corresponding to fuel being burned at stoichiometric conditions i.e. λ = 1 and cooling is only due to the expansion of cylinder gas. The higher limit corresponds to an infinite mixing rate i.e air is mixed into each parcel increasing the local lambda from 1 towards the global lambda very fast. In addition to the calculated ε and the resulting average air excess ratio in the burned zones, the results of a NO model have been included as well. The NO model used is the extended Zeldovich mechanism [2, 14] N 2 + O = NO + N (7) N + O 2 = NO + O (8) N + OH = NO + H (9) The kinetic parameters are taken from [14]. Since NO has been measured for the tests investigated in the present study comparison between measured and calculated NO concentrations allows a tuning of the mixing ratio in order to give satisfactory agreement. As seen from the figure the conversion fraction, ε, increases due to increased mixing. The resulting average air excess ratio in the burned zones increase up to the global air excess ratio at a mixing rate of 10. Both the lowest and highest CIMAC Congress 2010, Bergen Paper No. 39 5

6 mixing rates applied may seem unrealistic, nevertheless they provide a rough range for ε of approx. 1-12%. The measured NO concentration is 1266 vol. ppm. In order for the calculated NO concentration to equal this, a mixing rate of 3.29 is required, as found by interpolation. The corresponding ε is 4.43 %. Using the same approach in order to match the experimental NO concentration for the remaining load cases of 1119, 1236, and 1320 vol ppm for 100, 50, and 25% load, respectively, the corresponding values of ε are 2.59, 4.25, and 6.72 %. Thus, for a wide range of engine loads ε apparently lies in a relatively narrow range of %. From these results as well as from Figure 4 it is interesting to note the similar effect of varying mixing rate on both NO and ε. Engel et al. measured the conversion of SO 2 to SO 3 on a number of heavy duty diesel engines operated at different load, different fuel quality, different sulfur content etc. In their study they found a conversion fraction ranging from 2 8%. Clearly our results agree very well with these findings. In the following the 75% load case with a mixing rate of 3.29 will be investigated in more detail. Crank angle resolved results Figure 5 shows selected results from the 75% load case with an applied mixing rate of The calculated NO concentration (B) is for the trapped cylinder gas only. Diluting with additional air, used in the scavenging process, results in a NO concentration of 1266 ppm which is equal to the measured value (after the exhaust gas turbine). As seen from Figure 5 (A) the SO 2 concentration increase rapidly around TDC and the increase follows the rate of combustion very closely. Both SO 3 and H 2 SO 4 are at very low levels during the combustion period. This is due to the fact that the equilibrium conversion of SO 2 (cf. Figure 5 (B)) is low at the very high temperatures (cf. Figure 5 (C)) as well as the time required for a significant conversion into SO 3 and H 2 SO 4 has not elapsed. The mean combustion temperature in the parcels in Figure 5 is a result of both the expansion of the cylinder content as well as the rate at which the much colder fresh air is mixed into the parcels. After the combustion has ended the temperature has dropped sufficiently in order to favour a significant conversion fraction of SO 2 into SO 3 and H 2 SO 4. As seen from Figure 5 (C) the reaction rates controlling the oxidation of SO 2 appear to be very fast at least until up to 80 CAD ATDC. From this point the temperature has dropped enough in order to cause a slow-down in the rate of SO 2 oxidation and the result is a deviation from equilibrium. It appears as though the oxidation of SO 2 is not frozen at the end of the simulation (corresponding to the opening of the exhaust valve). However during blow-down the hot combustion gases are expanded rapidly causing a further temperature drop, and once the scavenge ports are uncovered cold intake is mixed with the combustion gases causing a further cooling. Thus, it may seem reasonable to assume that the further oxidation of SO 2 will be on a much smaller scale. Comparison with equilibrium assumptions. In a previous study, related to cylinder liner corrosive wear due to sulfuric acid condensation, Teetz [7] applied the assumption that reactions responsible for SO 2 oxidation are very fast i.e. equilibrated above 1000 o C, while below this temperature the reactions become frozen i.e. no further reactions take place. This assumption is valid according to [1] and references within. In the following we will apply the above assumption from now on denoted the frozen equilibrium assumption. The assumption is applied assuming a single zone combustion i.e. combustion takes place in the same zone containing the entire amount of fresh air. This is in contrast to the previous multizone approach 1. The result is shown in Figure 6 (A) where a comparison with the equilibrium conversion fraction as found in the burned zones using the multi-zone approach is made. The temperature in the single burned zone is depicted in Figure 6 (B). The most important observation is the fact that the mean temperature using the single-zone approach is much lower than in the multi-zone approach, coupled with the high pressure near TDC, this results in a very high equilibrium conversion fraction. Furthermore the resulting ε is approx. 18% at the end of simulation, which is almost four times larger than that found in Figure 5 with a mixing rate of 3.3 and more than twice than assuming full equilibrium in the parcels. Although we have found evidence supporting the use of the frozen equilibrium assumption for premixed combustion 2, it is clearly insufficient for modelling emission formation during the mixing controlled combustion in diesel engines. 1 No parcels in the multi-zone approach are cooled below 1000 o C, thus the result would not differ from the equilibrium in Figure 5 2 Unpublished. A. Andreasen, S. Mayer CIMAC Congress 2010, Bergen Paper No. 39 6

7 (A) (B) (C) (D) Figure 5 Results from multi-zone approach for the 75% load case. (A) Calculated concentrations of SO 2, SO 3, and H 2 SO 4 (B) Calculated NO concentration (C) Conversion fraction of SO 2, equilibrium conversion fraction of SO 2, and oxygen concentration in the burned zones (D) Temperature of the fresh cylinder air and the average temperature in the burned zones. CIMAC Congress 2010, Bergen Paper No. 39 7

8 (A) (B) Figure 6 (A) ε calculated with the frozen equilibrium assumption using a single zone approach compared with the equilibrium ε from the multi-zone parcel model. (B) Temperature in the single zone model (dashed line). Effect of sulfur content In order to investigate the effect of the fuel sulfur content on the resulting conversion fraction, a number of simulations with different sulfur content has been conducted. The results from the 75% load case are depicted in Figure 7. The simulations have been conducted with all other parameters including the applied mixing rate fixed for all sulfur contents. As seen from Figure 7 the conversion fraction decreases with increasing sulfur content. Taking the relatively large range in sulfur content into account the decrease in ε is modest. Nevertheless, the result is in qualitative agreement with the literature [1, 4]. Figure 7 Conversion fraction, ε, as a function of fuel sulfur content. Results from simulations of the 75% load case Reactions controlling conversion fraction The reaction mechanism applied in the present work has provided valuable insight as already discussed. Nevertheless the models investigated are still coarse with many simplifying assumption. In order to take the analysis to the next level it would be desirable to use the applied reaction mechanism coupled to a full CFD code. However due to the high number of reaction steps this approach will be expensive in terms of the time required for simulating a single combustion cycle. This cost can be significantly reduced if a reduced mechanism, still capturing the most important reaction paths, can be formulated. In fact it often turns out that even large reaction mechanisms contain a few steps which govern the overall rate [38, 39]. It is not the purpose of the present paper to propose a reduced mechanism. Nevertheless, some hints and guidelines can be found in the literature pin pointing the most important reactions. These will be briefly summarized below. Previous studies by Cerru et al. [40, 41] have been devoted to the formulation of a reduced mechanism for sulfur oxidation. Although a two step mechanism is formulated for SO 2 oxidation a number of reaction rates (used in linear combinations) are required. Tremmel and Schumann [18] conducted a sensitivity analysis study, and concluded that the rate constant of the reaction SO 2 + OH(+M) = HOSO 2 (+M) (10) CIMAC Congress 2010, Bergen Paper No. 39 9

9 showed the highest impact on the conversion fraction for conditions relevant for aviation turbine conditions. At some conditions the rate constant of the following reaction was found to also control the conversion fraction SO 2 + O(+M) = SO 3 (+M) (11) Reaction Eq. 11 is highlighted to be of major importance by Glarborg [28], especially at high temperatures. Reaction Eq. 10 in combination with the reaction HOSO 2 + O 2 = SO 3 + HO 2 (12) is proposed to be important mainly at lower temperatures i.e. when the burned gases are cooled. In another study Glarborg and co-workers [24] also point out the importance of the reactions SO 2 + OH = SO 3 + H (13) and SO 2 + HO 2 = SO 3 + OH (14) through a rate of production and sensitivity analysis. Since the importance of the above reactions has been proven at conditions not exactly matching those in a large two-stroke diesel engines a future sensitivity study should be devoted to the formulation of a reduced mechanism. CONCLUSIONS In this paper the in-cylinder formation of SO 3 and H 2 SO 4 of a large two-stroke diesel engine has been studied. A detailed kinetic mechanism has been used in combination with measured incylinder pressure in order to calculate the concentration of sulfur containing species using a multi zone approach with the rate of mixing of fresh gas into the burned parcels as the main adjustable parameter. By combining the multizone model with a NO formation model (Zeldovich) the mixing rate has been adjusted in order for the calculated NO to match the measured value. Applying the fitted mixing rates values of ε lying in a range from 2.6 to 6.7% is found. The results are comparable with previous measurements of the SO 2 conversion fraction in heavy duty diesel engines [4]. and H 2 SO 4 on a qualitative scale. Nevertheless, in order to improve the predictive reliability of the model on a more quantitative scale, a number of recommended actions remain to be taken. 1. Real experimental evidence of the conversion fraction in large two-stroke diesel engines is severely lacking. In order to improve the confidence in the model the conversion fraction must be measured and compared with model predictions. 2. In this study we have relied on the kinetic parameters for conversion of SO 3 to H 2 SO 4 as reported by Reiner and Arnold [31]. Several other studies exists e.g. [42, 43, 44, 45] signalling both the complexity of the reaction as well as its importance in relation to acid rain. Unfortunately the studies are limited to low pressure and close to ambient temperature. Thus reliable kinetic parameters at elevated temperature and pressure are needed. 3. Until now only the time until exhaust valve opening has been considered. It should also be investigated further what happens after the exhaust valve opens (decrease in temperature and pressure), during the scavenging process and in the exhaust receiver. It should be expected that significantly more SO 3 is converted to H 2 SO 4 during these processes. 4. It is well known that vanadium oxide catalyse the oxidation of SO 2 to SO 3 [46, 47]. Since the fuel used for large twostroke engines may contain significant levels of vanadium, the catalysed oxidation may contribute significantly to the overall conversion fraction. Future analysis should take this possibility into account. NOMENCLATURE c p Specific heat capacity at constant pressure, J/(mol K) C rad Heat radiation constant, J/(mol K 4 ) Conversion fraction of S to SO 3 and H 2 SO 4 The presented model gives valuable information about the process of in-cylinder formation of SO 3 ΔH 298 Standard formation enthalpy at 298 K CIMAC Congress 2010, Bergen Paper No

10 λ MCR MEP T ad T rad w/w Air excess ratio Maximum continous rating Mean effective pressure, bar Adiabatic flame temperature, K Temperature drop due to radiation Weight fraction ACKNOWLEDGEMENTS We would like to thank our colleagues Mrs. Charlotte B. Røjgaard, Mr. Kjeld Aabo, Mr. Michael F. Pedersen, and Mr. Svend Eskildsen for invaluable discussions during the making of this manuscript. Further we would like to express our deepest gratitude to Prof. Peter Glarborg, Department of Chemical and Biochemical Engineering, CHEC Research Centre, Technical University of Denmark, for many enlightening discussions and, in particular, for commenting on the manuscript. REFERENCES [1] Cullis, C. F., and Mulcahy, M. F. R., The kinetics of combustion of gaseous sulphur compounds. Combust. Flame, Vol. 18, 1972, pp [2] Turns, S. R., An Introduction to Combustion. McGraw-Hill, [3] Andreasen, A., and Mayer, S., Use of seawater scrubbing for SO 2 removal from marine engine exhaust gas. Energy Fuels, Vol. 21(6), 1996, pp [4] Engel, P. K., Thompson, R. E., and Silvestrini, R., Corrosion and fouling potential in diesel exhausts. Trans. ASME Journal of Engineering for Power, Vol. 101, 1979, pp [5] McKinley, T. L., Modeling sulfuric acid condensation in diesel engine EGR coolers. Engine modelling, Vol. 1255, 1997, pp [6] Huijbregts, W. M. M., and Leferink, R. G. I., Latest advances in the understanding of acid dewpoint corrosion: corrosion and stress corrosion cracking in combustion gas condensates. Anti-Corrosion Methods and Materials, Vol. 51, 2004, pp [7] Teetz, C., Beitrag zur Verminderung der Naßkorrosion im Dieselmotor. VDI Forschungsheft, Vol. 626, 1984, pp [8] Behrens, R., and Groth, K., Problems caused by burning heavy fuels in diesel engines (paper 3). Diesel Engine Combustion Chamber Materials for Heavy Fuel Operation, 1990, pp [9] Behrens, R., Brennstoffbedingte korrosion im dieselmotor. Motortechnische Zeitschrift, Vol. 49, 1988, pp [10] Behrens, R., Fuel-related wear mechanisms in heavy oil-fuelled diesel engines, as exemplified by first piston ring (paper 8). Maritime Systems Integrity, 1988, pp [11] Nagaki, H., and Korematsu, K., Relation between diffusion process of sulphur oxides in exhaust gas oil film and wear of cylinder liner and piston rings in diesel engines. SAE paper, , [12] Schramm, J., Henningsen, S., and Sorensen, S. C., Modelling of corrosion of cylinder liner in diesel engines caused by sulphur in the diesel fuel. SAE paper, , [13] van Helden, A. K., Valentijn, M. C., and van Doorn, H. M. J., Corrosive wear in crosshead diesel engines. Tribology International, Vol. 22, 1989, pp [14] Heywood, J. B., Internal Combustion Engine Fundamentals, McGraw-Hill, [15] Stone, R., Introduction to Internal Combustion Engines, 3rd ed. MacMillan Press Ltd, [16] Sorokin, A., Katragkou, E., Arnold, F., Busen, R., and Schumann, U., Gaseous SO 3 and H 2 SO 4 in the exhaust of an aircraft gas turbine engine: measurements by cims and implications for fuel sulfur conversion to sulfur (VI) and conversion of SO 3 to H 2 SO 4. Atmospheric Environment, Vol. 38, 2004, pp [17] Starik, A. M., Savel ev, A. M., Titova, N. S., and Schumann, U., Modeling of sulfur gases and chemiions in aircraft engines. Aerospace Science and Technology, Vol. 6, 2002, pp [18] Tremmel, H. G., and Schumann, U., Model simulations of fuel sulfur conversion efficiencies in an aircraft engine: Dependence on reaction rate constants and CIMAC Congress 2010, Bergen Paper No

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12 Combust. Inst., Vol. 30, 2005, pp [41] Cerru, F., Kronenburg, A., and Lindstedt, R., Systematically reduced chemical mechanisms for sulfur oxidation and pyrolysis. Combust. Flame, Vol. 146, 2006, pp [42] Wang, X., Jin, Y. G., Suto, M., and Lee, L. C., Rate constants of the gas phase reaction of SO 3 with H 2 O. J. Chem. Phys., Vol. 89, 1988, pp [43] Hofmann, M., and von Ragué Schleyer, P., Acid rain: Ab Initio investigation of the H 2 O SO 3 complex and its conversion into H 2 SO 4. J. Am. Chem. Soc., Vol. 116, 1994, pp [44] Lovejoy, E. R., Hanson, D. R., and Gregory Huey, L., Kinetics and production of the gas-phase reaction of SO 3 with water. J. Phys. Chem., Vol. 100, 1996, pp [45] Jayne, J. T., Pöschl, U., Chen, Y.-M., Dai, D., Molina, L. T., Worsnop, D. R., Kolb, C. E., and Molina, M. T., Pressure and temperature dependency of the gas phase reaction of SO 3 with H 2 O and the heterogeneous reaction of SO 3 with H 2 O/H 2 SO 4 surfaces. J. Phys. Chem. A., Vol. 101, 1997, pp [46] Livbjerg, H., and Villadsen, J., Kinetics and effectiveness factor for SO 2 oxidation on an industrial vanadium catalyst. Chemical Engineering Science, Vol. 27(1), 1972, pp [47] Froment, G. F., and Bischoff, K. B., Chemical Reactor Analysis and Design, 2 nd ed. John Wiley & Sons, Inc., Anders Andreasen and Stefan Mayer Basic Research, Process Development Reasearch & Development, Marine Low-speed MAN Diesel Teglholmsgade 41 DK-2450 Copenhagen SV Denmark CIMAC Congress 2010, Bergen Paper No