森吉 泰生

LSPI is an important issue to enable and enhance the effect of downsizing in SI engines. Experimental work was carried out by using 4 cylinder turbocharged gasoline engine, attaching the extra supercharger to get a higher boost pressure. Many parameters of driving condition, engine specification and lubricants were studied and some of them were extracted as the major items which affect the possibility of LSPI. Coolant temperature and Calcium (Ca) additive to lubricant had strong effect on the frequency of LSPI. Combustion strategy of strong miller cycle and LPEGR were also studied and compared in very high BMEP condition. Finally IMEPg of 3MPa at 1500rpm was achieved by using a single cylinder test engine equipped with 2-stage mechanically supercharged intake system.

The authors investigated the reasons of how a preignition occurs in a highly boosted gasoline engine. Based on the authors' experimental results, theoretical investigations on the processes of how a particle of oil or solid comes out into the cylinder and how a preignition occurs from the particle. As a result, many factors, such as the in-cylinder temperature, the pressure, the equivalence ratio and the component of additives in the lubricating oil were found to affect the processes. Especially, CaCO included in an oil as an additive may be changed to CaO by heating during the expansion and exhaust strokes. Thereafter, CaO will be converted into CaCO again by absorbing CO during the intake and compression strokes. As this change is an exothermic reaction, the temperature of CaCO particle increases over 1000K of the chemical equilibrium temperature determined by the CO partial pressure. The possibility of a preignition due to particles including CaCO particles is numerically simulated comparing with the experimental results. 3 3 2 3 2 3

Highly efficient natural gas engines have been widely used in wide range of sectors from industry and transportation. However, because combustion process in gas engines with a pre-chamber is very complicated, it is difficult to experimentally investigate the combustion process including flame propagation from the pre-chamber. In this study, combustion characteristics in the gas engine with a pre-chamber were numerically investigated by using three-dimensional numerical simulation with detailed chemical reactions. Torch flame combustion brings about high temperature and strong turbulence to the main chamber. Combustion processes of the natural gas engine with pre-chamber can be categorized in three stages. The first stage is high speed flame propagation induced by flame torches from the pre-chamber. The second stage is simple flame propagation in the main-chamber. This flame propagation speed is relatively lower than the first stage combustion, because turbulence kinetic energy is lower than that during the first stage. The curvature of rate of heat release relates to the surface area of flame front and excess air ratio in the flame front. The third stage is autoignition of the unburned mixture in the end gas region. Autoignition in the main-chamber occurs between the torches. The intensity of pressure oscillation and rate of heat release depend on both the mass of the unburned mixture in the end gas region and the onset positions of autoignition.

The analysis of preignition in a boosted gasoline engine is an important issue to improve the engine power and thermal efficiency. One of the convincing mechanisms is an autoignition of oil-gasoline droplets. The oil-gasoline droplets formation process that are adhered to the piston top-land in film is simulated by giving the acceleration of the piston motion. Using VOF method, the effects of several physical parameters, such as oil film thickness, fuel dilution rate, and top-land length on the droplet formulation which disperses in a combustion chamber are investigated. As a result, it was found that droplets formation have three steps and the oil film thickness is the most effective factor. Next, the possibility of ignition of the oil droplet inside the cylinder was examined. However, it was found difficult to cause autoignition. Therefore, CaCO3 included in the oil as an additive may be changed to CaO by heating during expansion and exhaust strokes and then, CaO may be converted into CaCO3 again by absorbing CO2 during the intake and compression strokes. As this change is an exothermic reaction, the temperature of the particle increases determined by CO2 partial pressure. The CaO particle may be a cause of preignition.

Closed-loop control is vital for an application of HCCI engines in passenger cars. This paper introduces a simplified control-oriented model for control of combustion phasing and IMEP of a Blowdown Supercharge Engine (BDSC). Despite the complexity of this particular engine, the model has been found to match not only the steady state values in high load HCCI, but also to reproduce the transients. This model takes advantage of the knowledge of non-dynamic processes within the engine that can be derived from steady state values, while the main dynamics are achieved by dynamically modelling of cyclic coupling via in-cylinder temperature alone and mean exhaust pressure dynamics. Furthermore, a simplified combustion model has been found to be accurate enough for the region of interest. An automated tuning scheme helps to match the model to the respective target values. With this model and the tuning scheme, the model can be easily tuned for every possible case. A model-based MIMO state controller, based on Sliding-Mode Control theory has been designed and tested on a detailed 1-D simulation code.

HCCI combustion can realize low NOx and particulate emissions and high thermal efficiency. Therefore, HCCI combustion has a possibility of many kinds of applications, such as an automotive powertrain, general-purpose engine, motorcycle engine and electric generator. However, the operational range using HCCI combustion in terms of speed and load is restricted because the onset of ignition and the heat release rate cannot be controlled directly. For the extension of the operational range using either an external supercharger or a turbocharger is promising. The objective of this research is to investigate the effect of the intake pressure on the HCCI high load limit and HCCI combustion characteristics with blowdown supercharging (BDSC) system. The intake pressure (Pin) and temperature (Tin) were varied as experimental parameters. The intake pressure was swept from 100 kPa (naturally aspirated) to 200 kPa using an external mechanical supercharger. The experimental results showed that the maximum load successfully increased with increasing the intake pressure. The highest load in this study was 935kPa in IMEPg at the condition of 200 kPa in Pin and 32 ŶC in Tin. The maximum load of boosted BDSC-HCCI engine can be achieved comparable to the full load of naturally aspirated SI engine. In addition, for conditions with above 200 kPa in Tin, A/F and G/F could be almost the same. The comparison of heat release rate between with and without BDSC showed that the peak value of heat release rate decreased and the combustion duration was prolonged with BDSC by thermal stratification. Not only the pressure rise rate but also the peak cylinder pressure could be reduced by BDSC system. Moreover, the intake temperature was decreased while maintaining the conditions of G/F and intake pressure to investigate the intake temperature on heat release. The results showed that the dP/dθ max is reduced with Tin less than 50 ŶC. © 2013 SAE Japan and © 2013 SAE International.

In this paper, the necessary in-cylinder conditions for the transition from spark ignion (SI) to homogeneous charge compression ignition (HCCI) are analyzed. The hereby important factors for ignition time are investigated analytically. A control oriented combustion model, that is validated by experimental data, is used for sensivity analysis and a Monte-Carlo approach is taken to identify the important factors for transient HCCI and combustion mode switch.As a result, it was shown that the in-cylinder temperature plays a major role, exceeding other factors, such as the air-fuel ratio. The analytical conclusions are illustrated by numerical simulations after which the feasibility for actuation will be discussed. Final goal is to ensure a stable combustion in each cycle without crossing unstable combustion conditions.

The objective of this study is to extend the HCCI operational range while maintaining high thermal efficiency of a HCCI engine using the blowdown supercharge (BDSC) system. Two different compression ratios of 11.7 and 14.1 were tested by replacing the piston. The effect of compression ratio on both the HCCI operational range and thermal efficiency were investigated. The experimental results showed that the HCCI operational limit and the fuel consumption at the low load operation were successfully improved by increasing compression ratio. On the other hand, high load operational limit was hardly affected by compression ratio. Also, it was found that the BDSC-HCCI engine with higher compression ratio improves thermal efficiency of the whole HCCI operation range. © 2013 The Japan Society of Mechanical Engineers.

The objective of this research is to investigate the effect of the EGR guide, employed to generate a strong in-cylinder thermal stratification, on the recharged EGR gas flow into the cylinder in a gasoline HCCI engine equipped with the blowdown supercharging (BDSC) system. The recharged EGR gas flow was visualized using an optical access engine. A steady gas flow and an unsteady gas flow in motoring from the exhaust port into the cylinder were visualized via PIV method. The effect of the pressure difference between the exhaust port and the cylinder and the geometry of the EGR guide on the recharged gas flow was investigated. The results indicate that the flow field pattern is largely affected by the EGR guide height, and that an increase in the EGR guide height is effective to generate a strong in-cylinder thermal stratification. And then, the reduction of maximum pressure rise rate (dp/dθ) was investigated with a larger EGR guide height. Also, the in-cylinder thermal stratification was investigated by numerical simulation. The results indicate that thermal stratification gets stronger by a higher EGR guide. However, it was found that the reduction of maximum pressure rise rate takes a peak at a height of EGR guide. ©2013 The Japan Society of Mechanical Engineers.

An improvement of thermal efficiency is strongly demanded for gasoline engines. In this study, experiments were earned out to investigate the effects of intake air temperature and coolant temperature on brake thermal efficiency, heat loss and friction loss in a spark ignition gasoline engine. Experimental results showed that, intake air temperature has a little effect on brake thermal efficiency during partical load operation. During high load operation, a decrease in intake air temperature improved brake thermal efficiency due to an improvement in indicated thermal efficiency and decrease in exhaust loss. It was also revealed that the combination of high temperature cooling water for the engine block and low temperature cooling water for the cylinder heat is effective for improving brake thermal efficiency.

In order to extend the operational range with a gasoline fueled multi-cylinder homogeneous charge compression ignition engine, a blowdown supercharge system and an exhaust gas recirculation guide was developed. The concept was to provide a large amount of diluted mixture and a strong in-cylinder thermal stratification for decreasing nitrogen oxide emissions and pressure rise rate during high-load homogeneous charge compression ignition operation. Secondary air injection was also proposed to reduce a cylinder-to-cylinder variation in ignition timing, which is one of the limiting factors of multi-cylinder homogeneous charge compression ignition operation. In advance of experimental works, the blowdown supercharge system and the exhaust gas recirculation guide were proved to be effective to reduce pressure rise rate for high-load operation using three-dimensional in-cylinder flow simulations and zero-dimensional multi-zone simulations with detailed chemical kinetics. Based on the simulation results, experiments were conducted using a slightly modified production four-cylinder gasoline engine. At first, the effects of the proposed techniques were experimentally investigated by focusing on one cylinder out of four. Then, a four-cylinder homogeneous charge compression ignition operation test using the new techniques was carried out. The one-cylinder measurements revealed that the blowdown supercharge system with an exhaust gas recirculation guide is capable of extending the homogeneous charge compression ignition operating range up to a net indicated mean effective pressure of 590 kPa for naturally aspirated conditions. In addition, secondary air injection was experimentally demonstrated as a technique for reducing a cylinder-to-cylinder variation in ignition timing. Reducing the cylinder-to-cylinder variation in ignition timing, four-cylinder homogeneous charge compression ignition operation with a net indicated mean effective pressure of 570 kPa was successfully achieved with the blowdown supercharge system and the exhaust gas recirculation guide. © IMechE 2012.

The objective of this study is to develop a practical technique to achieve homogeneous charge compression ignition operation with a wide operating range using a blowdown supercharge system, which has been previously demonstrated as an effective technique to extend the upper load limit of acceptable homogeneous charge compression ignition operation. The valve actuation strategy to attain acceptable homogeneous charge compression ignition operation in a wide operating range has been newly developed and experimentally examined. The proposed strategy provides high in-cylinder temperature and a relatively small amount of in-cylinder mixture during low-load operations to improve the combustion stability while providing a large amount of diluted mixture for high-load operations to keep the in-cylinder pressure rise rate and nitrogen oxide emissions low. In addition, thermal efficiency and exhaust emissions for various homogeneous charge compression ignition operating loads using the blowdown supercharge system were experimentally investigated. Experimental results showed that the proposed valve actuation strategy, in which early intake valve closing and relatively late exhaust gas recirculation valve opening occurred, was effective to increase combustion stability during low-load conditions, and a stable homogeneous charge compression ignition operation at a net indicated mean effective pressure of 140 kPa was achieved. Compared to conventional spark-ignition operation, 14% to 35% improvement in brake specific fuel consumption rate was attained with more than 99% reduction in nitrogen oxide emissions for homogeneous charge compression ignition operation using the blowdown supercharge system. © IMechE 2012.

Gasoline direct injection (GDI) systems have higher power and fuel efficiency than multi-point injection (MPI) systems. The direct injection of fuel into the combustion chamber leads to improved fuel economy because intake air is cooled by fuel evaporation. Direct fuel injection also improves knock resistance and volume efficiency. Furthermore, spray-guided direct injection (DI) combustion systems allow stratified lean combustion operation due to their ability to eliminate wall-wetting and form ignitable stratified mixtures near spark plugs.In this research, a spray-guided combustion system with a piezo-type gasoline direct injector was investigated for its applicability to stratified lean combustion engines. Tests were conducted at constant engine speeds and load conditions (2000 rpm, IMEP 0.28 MPa) that reflect typical operating conditions for passenger vehicles. Fuel economy and combustion stability were evaluated for various injection pressures at each excess air ratio. It is possible to create a sufficiently rich mixture for ignition in the vicinity of the spark plug, even under overall ultra-lean mixture conditions (λ = 3.0). Exhaust gas recirculation (EGR) and retarded ignition timing were considered to achieve a reduction in nitrogen oxide (NO ) emissions. EGR with optimized ignition timing was most effective when a spray-guided combustion system was employed. © 2012 Elsevier Ltd. x

To extend the operating range of a gasoline HCCI engine, the blowdown supercharging (BDSC) system and the EGR guide were developed and experimentally examined. The concepts of these techniques are to obtain a large amount of dilution gas and to generate a strong in-cylinder thermal stratification without an external supercharger for extending the upper load limit of HCCI operation whilst keeping dP/dθ and NO emissions low. Also, to attain stable HCCI operation using the BDSC system with wide operating conditions, the valve actuation strategy in which the amount of dilution gas is smaller at lower load and larger at higher load was proposed. Additionally to achieve multi-cylinder HCCI operation with wide operating range, the secondary air injection system was developed to reduce cylinder-to-cylinder variation in ignition timing. As a result, the acceptable HCCI operation could be achieved with wide operating range, from IMEP of 135 kPa to 580 kPa. Compared to conventional SI operation, BSFC was improved by 14 % ~ 35 % with more than 99 % reduction in NO emissions. Copyright 2011 Society of Automotive Engineers of Japan, Inc. and SAE International. max x x

To clarify the mechanism of high brake thermal efficiency of HCCI combustion compared to SI combustion, the contributions of pumping loss, friction loss and gross indicated thermal efficiency were investigated. Also, independent effects of heat loss, specific heat ratio, heat release profile and combustion timing on gross indicated thermal efficiency in HCCI combustion were analyzed in detail. As a result, high gross indicated thermal efficiency is found to be the main contributors to improvement in brake thermal efficiency. Also, it is found that heat loss in HCCI combustion is lower than SI combustion leading to the increase in gross indicated thermal efficiency. The improvement in gross indicated thermal efficiency in HCCI operation is mainly caused by lower heat loss in HCCI compared to SI combustion.Copyright © 2012 by the Japan Society of Mechanical Engineers.

It is expected that liquid fossil fuels will be replaced by gaseous fuel within twenty years, and hydrogen may be of great importance by the mid-twenty-first century. However, recently, it has been difficult to secure a hydrogen economy, which starts from the establishment of a hydrogen infrastructure and leads to production, storage, and application. A transitional strategy should be prepared, and it is believed that a kind of partial application, such as reforming hydrocarbon fuel, could be a technical bridge to a hydrogen economy. Natural gas as an energy source for transportation has the advantage of emission at low levels. However, more technical researches should be carried out to hold a dominant position of clean fuel over well-developed diesel vehicles. Hydrogen/natural gas blends (HCNG) are promising fuels for solving the problems of present natural gas vehicles. It may possibly meet reinforced emission regulation, and North America and some European countries have already begun the development of an HCNG vehicle and the supply project of an HCNG station. The HCNG research project of Korea started in 2009 for developing an HCNG bus that meets the EURO-VI standard. In order to study the performance and emission characteristics of an HCNG engine, an 11-L, heavy duty, lean burn engine was used. The level of nitrogen oxides (NOx), the most important component of emissions, is closely related to operation strategy. Therefore, operating parameters, including excess air ratio and spark advance timing, were optimized, and other parameters for high thermal efficiency were also examined. Copyright © 2012 by the Japan Society of Mechanical Engineers.

To find an ignition and combustion control strategy in a gasoline fueled HCCI engine equipped with the BlowDown SuperCharging (BDSC) system which is previously proposed by the authors, a one-dimensional HCCI engine cycle simulator capable of predicting the ignition and heat release of HCCI combustion was developed. The ignition and the combustion models based on Livengood-Wu integral and Wiebe function were implemented in the simulator. The predictive accuracy of the developed simulator in the combustion timing, combustion duration and heat release rate were validated by comparing to experimental results. Using the developed simulator, the control strategy for the engine operating mode switching between HCCI and SI combustion was explored with focus attention on transient behaviors of air-fuel ratio, A/F, and gas-fuel ratio, G/F. The simulation result showed that the one-step variations in the amount of recharged EGR gas and G/F can be attained by activation or deactivation of the EGR valve lift with the BDSC system. It is considered that this one-step variation in G/F allows the one-step transition from the HCCI operation to the SI operation with small torque fluctuation. However, in the combustion mode transition from SI to HCCI, the combustion timing during the transient HCCI combustion was excessively advanced. The excessively advanced ignition timing leads to the increase in in-cylinder pressure rise rate, dP/dθ. In the strategies examined in the present study, only intake throttle valve, exhaust throttle valve and EGR valve lift switching were used to control mixture conditions in terms of A/F and G/F during combustion mode transition. The results obtained suggest that additional devises to control mixture conditions during the combustion mode transition is necessary to attain the smooth transition from SI to HCCI combustion. Copyright © 2012 SAE International.

Fuel economy can be significantly improved in a gasoline direct-injection (GDI) engine owing to the stratified mixture formation strategy which guarantees stable combustion under ultra-lean air fuel mixture conditions. In the GDI engine, it is widely accepted that the spray-guided direct-injection system, which is characterized by a close configuration between the centrally mounted injector and the spark plug, is regarded as a promising technology among the efforts to realize stratified lean combustion. With this configuration, the split injection can be an effective fuel injection scheme because of its potential to modulate the spray characteristics as well as to create a combustible mixture in the proximity of the spark plug. In this study, the split-injection strategy was assessed as a way to achieve ultra-lean operation in a GDI engine and the resulting lean-combustion characteristics were investigated in terms of the engine performance and emissions. The engine was tested at constant operating conditions (an engine speed of 3000 r/min and an indicated mean effective pressure of 0.4 MPa) with a change in the fuel injection pressure ranging from 10 MPa to 20MPa. The excess air ratio l varied from stoichiometry to the lean flammability limit, which turned out to be extended in the GDI approach. The engine test results show that the split injection of fuel allowed the formation of an adequately stratified mixture in lean-combustion conditions, and thus stable combustion was guaranteed. These results indicate that an excess air ratio was one of the important factors affecting the thermal efficiency and nitrogen oxide (NOx) emissions and was significantly extended to λ = 2.0 by the split-injection scheme. In addition, several fuel injection parameters such as the injection quantity, the split ratio, and the number of splits were examined with an emphasis on their impact on the fuel economy and emissions. The results demonstrate that there exists a trade-off between the NOx reduction and the efficiency, and therefore it is required to choose an appropriate injection strategy depending on the engine operating conditions in order to satisfy emission regulations. © 2011 Authors.

In this study, an experimental investigation on a naturally aspirated (NA), 8-L spark ignition engine fueled by biogas with various methane concentrations - which we called the N dilution test - was performed in terms of its thermal efficiency, combustion characteristics and emissions. The engine was operated at a constant engine rotational speed of 1800 rpm under a 60 kW power output condition and simulated biogas was employed to realize a wide range of changes in heating value and gas composition. The N dilution test results show that an increase of inert gas in biogas was beneficial to thermal efficiency enhancement and NO emission reduction, while exacerbating THC emissions and cyclic variations. Then, as a way to achieve stable combustion for the lowest quality biogas, H addition tests were carried out in various excess air ratios. H fractions ranging from 5 to 30% were blended to the biogas and the effects of hydrogen addition on engine behavior were evaluated. The engine test results indicated that the addition of hydrogen improved in-cylinder combustion characteristics, extending lean operating limit as well as reducing THC emissions while elevating NO generation. In terms of efficiency, however, a competition between enhanced combustion stability and increased cooling energy loss was observed with a rise in H concentration, maximizing engine efficiency at 5-10% H concentration. Moreover, based on the peak efficiency operating point, a set of optimum operating conditions for minimum emissions with the least amount of efficiency loss was suggested in terms of excess air ratio, spark ignition timing, and hydrogen addition rate as one of the main results. © 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. 2 2 x 2 2 x 2 2

The objective of this study is to develop a practical technique to achieve HCCI operation with wide operation range. To attain this objective, the authors previously proposed the blowdown supercharge (BDSC) system and demonstrated the potential of the BDSC system to extend the high load HCCI operational limit. In this study, experimental works were conducted with focusing on improvement of combustion stability at low load operation and the reduction in cylinder to cylinder variation in ignition timing of multi-cylinder HCCI operation using the BDSC system. The experiments were conducted using a slightly modified production four-cylinder gasoline engine with compression ratio of about 12 at constant engine speed of 1500 rpm. The test fuel used was commercial gasoline which has RON of 91. To improve combustion stability at low load operation, the valve actuation strategy for the BDSC system was newly proposed and experimentally examined. With the newly proposed valve actuation strategy, only intake valve lift was varied and EGR and exhaust valve lifts were fixed with variation in target load. Compared to the previously proposed valve actuation strategy for the BDSC system, relatively late EGR valve opening timing with early intake valve closing timing is applied at low load condition in the proposed strategy. This provides high in-cylinder temperature and relatively rich fuel concentration at low load operation while providing a large amount of diluted mixture at high load operation. Additionally, effect of coolant water temperature on combustion stability was experimentally investigated. Coolant water temperature was varied from 85°C to 105°C. Experimental result showed that for low load HCCI operation, the valve timing with early intake valve closing and relatively late EGR valve opening was effective to increase combustion stability due to increases in in-cylinder temperature and fuel concentration. With early intake valve closing and relatively late EGR valve opening, a stable HCCI operation at net IMEP of 200 kPa was achieved. However, brake thermal efficiency was slightly deteriorated due to increase in pumping work utilized to increase in in-cylinder temperature. The increase in coolant water temperature also improved combustion stability and extends the low load operational limit due to increase in in-cylinder temperature. With a cooling water temperature of 105°C, the low load HCCI with net IMEP of 134 kPa was attained. In addition, to reduce the cylinder to cylinder variation in ignition timing which restricts HCCI operating range with multi-cylinder operation, the secondary air injection system in which air is injected into an exhaust port of each cylinder to control recharged EGR gas temperature using gas fuel injector was proposed and examined to control ignition timing of each cylinder independently. As a result, the cylinder to cylinder variation in ignition timing was successfully reduced and the high load HCCI operational limit with four-cylinder operation was extended up to net IMEP of 570 kPa. Compared to conventional SI operation, brake thermal efficiency was improved by about 15 % using the newly proposed strategy with more than 99% reduction in NO emission. © 2011 SAE International. x

Because blending hydrogen with natural gas can allow the mixture to burn leaner, reducing the emission of nitrogen oxide (NO ), hydrogen blended with natural gas (HCNG) is a viable alternative to pure fossil fuels because of the effective reduction in total pollutant emissions and the increased engine efficiency. In this research, the performance and emission characteristics of an 11-L heavy duty lean burn engine using HCNG were examined, and an optimization strategy for the control of excess air ratio and of spark advance timing was assessed, in consideration of combustion stability. The thermal efficiency increased with the hydrogen addition, allowing stable combustion under leaner operating conditions. The efficiency of NO reduction is closely related to the excess air ratio of the mixture and to the spark advance timing. With the optimization of excess air ratio and spark advance timing, HCNG can effectively reduce NO as much as 80%. © 2010, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. x x x

To extend the operating range of a gasoline HCCI engine, the blowdown supercharging (BDSC) system and the EGR guide were developed and experimentally examined. The concepts of these techniques are to obtain a large amount of dilution gas and to generate a strong in-cylinder thermal stratification without an external supercharger for extending the upper load limit of HCCI operation whilst keeping dP/dθ and NO emissions low. Also, to attain stable HCCI operation using the BDSC system with wide operating conditions, the valve actuation strategy in which the amount of dilution gas is smaller at lower load and larger at higher load was proposed. Additionally to achieve multi-cylinder HCCI operation with wide operating range, the secondary air injection system was developed to reduce cylinder-to-cylinder variation in ignition timing. As a result, the acceptable HCCI operation could be achieved with wide operating range, from IMEP of 135 kPa to 580 kPa. Compared to conventional SI operation, BSFC was improved by 14 % ∼ 35 % with more than 99 % reduction in NO emissions. © Copyright 2011 Society of Automotive Engineers of Japan, Inc. and SAE International. max x x

The objective of this study is to develop a practical technique to achieve HCCI operation with wide operation range. To attain this objective, the authors previously proposed the blowdown supercharge (BDSC) system and demonstrated the potential of the BDSC system to extend the high load HCCI operational limit. In this study, experimental works were conducted with focusing on improvement of combustion stability at low load operation and the reduction in cylinder to cylinder variation in ignition timing of multi-cylinder HCCI operation using the BDSC system. The experiments were conducted using a slightly modified production four-cylinder gasoline engine with compression ratio of about 12 at constant engine speed of 1500 rpm. The test fuel used was commercial gasoline which has RON of 91. To improve combustion stability at low load operation, the valve actuation strategy for the BDSC system was newly proposed and experimentally examined. With the newly proposed valve actuation strategy, only intake valve lift was varied and EGR and exhaust valve lifts were fixed with variation in target load. Compared to the previously proposed valve actuation strategy for the BDSC system, relatively late EGR valve opening timing with early intake valve closing timing is applied at low load condition in the proposed strategy. This provides high in-cylinder temperature and relatively rich fuel concentration at low load operation while providing a large amount of diluted mixture at high load operation. Additionally, effect of coolant water temperature on combustion stability was experimentally investigated. Coolant water temperature was varied from 85 °C to 105 °C. Experimental result showed that for low load HCCI operation, the valve timing with early intake valve closing and relatively late EGR valve opening was effective to increase combustion stability due to increases in in-cylinder temperature and fuel concentration. With early intake valve closing and relatively late EGR valve opening, a stable HCCI operation at net IMEP of 200 kPa was achieved. However, brake thermal efficiency was slightly deteriorated due to increase in pumping work utilized to increase in in-cylinder temperature. The increase in coolant water temperature also improved combustion stability and extends the low load operational limit due to increase in in-cylinder temperature. With a cooling water temperature of 105 °C, the low load HCCI with net IMEP of 134 kPa was attained. In addition, to reduce the cylinder to cylinder variation in ignition timing which restricts HCCI operating range with multi-cylinder operation, the secondary air injection system in which air is injected into an exhaust port of each cylinder to control recharged EGR gas temperature using gas fuel injector was proposed and examined to control ignition timing of each cylinder independently. As a result, the cylinder to cylinder variation in ignition timing was successfully reduced and the high load HCCI operational limit with four-cylinder operation was extended up to net IMEP of 570 kPa. Compared to conventional SI operation, brake thermal efficiency was improved by about 15 % using the newly proposed strategy with more than 99% reduction in NO emission. © 2011 SAE International. x

To improve thermal efficiency of gasoline engines, the effect of coolant system on fuel consumption rate is studied in this report. The authors tried to control the flow of cooling water to find an optimized flow system to improve thermal efficiency, especially for the cold start condition. Experiments were carried out using a four-cylinder SI engine. Three test conditions of i) normal cold start, ii) cold start without operating the water pump and iii) cold start but with heated engine oil were measured. Temperatures of cooling water at some positions were measured during the warming-up time. Secondly, the effect of cooling water temperature on thermal efficiency at a steady state condition was examined. As a result, a higher temperature causes an improvement of thermal efficiency due to a reduction in mechanical friction. © 2011 SICE.

To avoid knocking phenomena, a special crank mechanism for gasoline engine that allowed the piston to move rapidly near TDC (Top Dead Center) was developed and experimentally demonstrated in the previous study. As a result, knocking was successfully mitigated and indicated thermal efficiency was improved [1],[2],[3],[4]. However, performance of the proposed system was evaluated at only limited operating conditions. In the present study, to investigate the effect of piston movement near TDC on combustion characteristics and indicated thermal efficiency and to clarify the knock mitigation mechanism of the proposed method, experimental studies were carried out using a single cylinder engine with a compression ratio of 13.7 at various engine speeds and loads. The special crank mechanism, which allows piston to move rapidly near TDC developed in the previous study, was applied to the test engine with some modification of tooling accuracy. Experimental result showed that indicated thermal efficiency as improved at 1000 r/min from low to high load, and at 1600, 2000 r/min high load by Leaf-shape mechanism. Improvement of indicated thermal efficiency at 1000 r/min was due to the reduction of cooling loss and at 1600, 2000r/min high load due to the recovery of the degree of constant volume. Also it was found that high load operation with compression ratio of 13.7 without knocking was realized using the proposed piston movement mechanism. Auto-ignition occurred at high load conditions even though the proposed piston movement was applied, but auto-ignition was not followed by high frequent in-cylinder pressure oscillation shown in the case of knocking. © Copyright 2011 Society of Automotive Engineers of Japan, Inc. and SAE International.

Direct-injection diesel engines have become prime candidates for future transportation needs owing to their high thermal efficiency. However, the increase in nitrogen oxides (NO ) within local high-temperature regions and the increase in particulate matter within the diffusion flame region during diesel combustion are problematic and must be resolved. The utilization of NO -absorbing catalysts, based on the concept of NO storage and release, is one of the most promising techniques able to reduce NO emissions within net oxidizing gas conditions. This type of NO removal system, called the lean NO trap (LNT) catalyst, absorbs NO under lean exhaust gas conditions and releases NO under rich conditions. This technology provides the advantage of high NO conversion efficiency; however, the correct amount of reducing agent must be supplied within the catalytic converter under appropriate conditions in order to guarantee a high NO reduction efficiency. In this research, the performance characteristics of an LNT, using a hydrogen-enriched gas as a reductant, were examined via various injection strategies and rich exhaust gas conditions. Although the hydrogen concentration of hydrogen-enriched gas also affects the LNT performance, the composition of hydrogen-enriched gas was fixed as a similar composition to that for the ideal re-forming of diesel fuel. The NO reduction efficiency is closely connected to the injection timing and duration of reductant flow. When the injection was introduced 1.5s after throttling, the LNT NO conversion was maximized. However, the LNT NO conversion decreased when the injection timing was earlier or later than 1.5s. Because the actual rich duration of the exhaust gas is limited at a specific point during the rich operation for 3s, the LNT NO conversion was maximized when the hydrogen-enriched gas was injected at the minimum air-to-fuel ratio observed at the LNT inlet. By optimizing the control of this flow, the system encounters only a 1.9 per cent fuel penalty while maintaining a 90 per cent NO reduction efficiency. x x x x x x x x x x x x x x x

Modern diesel engines have improved engine fuel economy and significantly reduced nitrogen oxides (NO ) and particulate matter (PM) emissions achieved by advances in both combustion and exhaust aftertreatment technologies. Recently, it has been shown that the vehicle emissions can be further improved by several catalytic systems including fuel reformers and aftertreatment systems, such as the Lean NO Trap (LNT). This NO removal system, called LNT, absorbs NO under lean exhaust gas conditions and releases NO under rich conditions. This technology can provide high NO conversion efficiency, but the right amount of reducing agent should be supplied into the catalytic converter under appropriate conditions. In this work, plasma reformer was used to supply a hydrogen-enriched gas as a NO reductant. The plasma reforming is one of the most promising on-board reforming technologies, which allows reformates containing H and CO to feed for LNT catalyst efficiently. Partial oxidation is induced by plasma in the fuel reformer and diesel fuel is converted into a hydrogen-enriched gas. The supplying strategy was focused on the maximization of NO reduction efficiency varying both the total amount of hydrogen-enriched reformate and the ratio of oxygen molecules to in the reformer air-fuel mixture prior to processing at a fixed engine operating condition. The effect of exhaust gas temperature was also studied. The NO reduction efficiency is closely connected to the amount of supplied fuel to the plasma reformer and the ratio of fuel/air feed rate. The LNT can reduce NO efficiently with only a 2.6% fuel penalty. Crown Copyright © 2009. x x x x x x x 2 x x x

In a motorcycle gasoline engine, the port fuel injection system is rapidly spread. Compared to an automotive engine, the injected fuel does not impinge on the intake valve due to space restriction to install the injector. In addition, as the air flow inside the intake pipe may become very fast and has large cycle-to-cycle variation, it is not well found how the injector should be installed in the intake pipe to prepare "good" fuel-air mixture inside the intake pipe. In this study, the formation process of the fuel-air mixture is measured by using ILIDS system that is a 2-D droplets' size and velocity measurement system with high spatial resolution. Experiments with changing conditions such as flow speed and injection direction are carried out. As a result, the effects of injection direction, ambient flow speed and wall roughness on the fuel-air mixture formation process was examined, considering the three conditions of cold start, light to medium load operation and high load operation. Copyright © 2010 SAE International and Copyright © 2010 SAE Japan.

Since ethanol is a renewable source of energy and has lower carbon dioxide (CO ) emissions than gasoline, ethanol produced from biomass is expected to be used more frequently as an alternative fuel. It is recognized that for spark ignition (SI) engines, ethanol has the advantages of high octane and high combustion speed and the disadvantage of ignition difficulties at low temperatures. An additional disadvantage is that ethanol may cause extra wear and corrosion of electric fuel pumps. On-board hydrogen production out of ethanol is an alternative plan. Ethanol has been used in Brazil as a passenger vehicle fuel since 1979, and more than six million vehicles on US highways are flexible fuel vehicles (FFVs). These vehicles can operate on E85 - a blend of 85% ethanol and 15% gasoline. This paper investigates the influence of ethanol fuel on SI engine performance, thermal efficiency and emissions. The combustion characteristics of hydrogen enriched gaseous fuel made from ethanol are also examined. Ethanol has excellent anti-knock qualities due to its high octane number and a high latent heat of evaporation, which makes the temperature of the intake manifold lower. In addition to the effect of latent heat of evaporation, the difference in combustion products compared with gasoline further decreases combustion temperature, thereby reducing cooling heat loss. Reductions in CO , nitrogen oxide (NOx), and total hydrocarbons (THC) combustion products for ethanol vs. gasoline are described. © 2010 Elsevier Ltd. All rights reserved. 2 2

A newly developed small-sized IES (inductive energy storage) circuit with a semiconductor switch at turn-off action was successfully applied to an ignition system. This IES circuit can generate repetitive nanosecond pulse discharges. An ignition system using repetitive nanosecond pulse discharges was investigated as an alternative to conventional spark ignition systems in the previous papers [ 1 ][ 2 ]. Experiments were conducted using constant volume chamber for CH and C H -air mixtures. The ignition system using repetitive nanosecond pulse discharges was found to improve the inflammability of lean combustible mixtures, such as extended flammability limits, shorted ignition delay time, with increasing the number of pulses for CH and C H -air mixtures under various conditions [ 1 ]. The mechanisms for improving the inflammability were discussed and the effectiveness of IES circuit under EGR condition was also verified [ 2 ]. Moreover, an application of this ignition system to a SI engine was conducted preliminarily and the effectiveness of IES circuit for the real engine was also confirmed [ 2 ]. Following previous studies, the present study moves to more realistic development stage using two experimental configurations same as former studies; a constant volume chamber and single cylinder SI engine. With a constant volume chamber, the effectiveness of IES circuit for Iso-octane (C H ) and conventional ignition plug is investigated, and the flame kernel formation process was observed using schlieren photography with a high speed camera to make the difference of the ignition mechanism between IES circuit and conventional ignition circuit clear. With a single cylinder SI engine, two experiments are carried out to qualify the difference of the inflammability between IES circuit and conventional ignition circuit. The operational limit of lean combustion is investigated. The result shows that the lean limit is extended from 20 to 23 in A/F at IMEP 440 kPa by replacing the ignition system from a conventional one. Also, the diluted limit is investigated. The result shows that the diluted limit is extended from 17.5 % to 22.5 % in EGR ratio at IMEP 630 kPa and that thermal efficiency is improved by 5%. The ignition delay and the combustion duration are decreased and the cycle-to-cycle variation of the ignition timing and IMEP are decreased. Copyright © 2010 SAE International. 4 3 8 4 3 8 8 18

In order to extend the HCCI high load operational limit, the effects of the distributions of temperature and fuel concentration on pressure rise rate (dP/dθ) were investigated through theoretical and experimental methods. The Blow-Down Super Charge (BDSC) and the EGR guide parts are employed simultaneously to enhance thermal stratification inside the cylinder. And also, to control the distribution of fuel concentration, direct fuel injection system was used. As a first step, the effect of spatial temperature distribution on maximum pressure rise rate(dP/dθmax) was investigated. The influence of the EGR guide parts on the temperature distribution was investigated using 3-D numerical simulation. Simulation results showed that the temperature difference between high temperature zone and low temperature zone increased by using EGR guide parts together with the BDSC system. Experiments were conducted by using a four-cylinder gasoline engine equipped with the BDSC with EGR guide system to investigate the effect of the EGR guide on the heat release rate and the in-cylinder pressure rise rate. Experimental results showed that 50% and 90 % mass fraction burned timing (CA50 and CA90) were delayed and combustion duration became longer when the EGR guide was used to enhance thermal stratification. As a result, the maximum pressure rise rate could be decreased and the HCCI high load limit successfully extended. Meanwhile10 % mass fraction burned timing (CA10) was not affected by the thermal stratification generated by the EGR guide. This is probably because the fuel is also spatially stratified such that the fuel concentration becomes lean in the high temperature zone. Next, the effect of the fuel distribution on high load HCCI operation was investigated. Numerical analysis using a multi-zone combustion model considering detailed chemical reactions was carried out. The simulation results showed that the maximum pressure rise rate was decreased by 27 % when the fuel distribution was uniform with temperature distribution generated by the BDSC with EGR guide system. Then, to obtain a uniform fuel distribution while keeping the temperature distribution generated by the BDSC with EGR guide system, a direct injection system was employed and the effect of fuel direct injection on maximum pressure rise rate was experimentally investigated. As a result, if 20 % of the total fuel was injected directly into the cylinder during the exhaust stroke, the spatial distribution of the fuel concentration (G/F; fuel mass ratio to the total mass of in-cylinder mixture) became more homogeneous and maximum pressure rise rate was decreased by 10%. And also, 20 % of the total fuel directly injected during the compression stroke, maximum pressure rise rate was decreased by 20 %. Finally, a simple method to predict the ignition timing using Livengood-Wu integral and 1-D numerical simulation code was examined. It was found that the proposed method can predict the ignition timing with small deviation around ±2 degrees. Copyright © 2010 SAE International.

A newly developed small-sized IES (inductive energy storage) circuit with semiconductor switch at turn-off action is successfully applied to an ignition system of a small gasoline internal combustion engine. This IES circuit can generate repetitive nanosecond pulse discharges. An ignition system using repetitive nanosecond pulse discharges is investigated as an alternative to a conventional spark ignition system. The present study focuses on the extension of the operational limits for lean and diluted combustion using the repetitive nanosecond pulse discharges. First, in order to investigate the flame kernel formation process when the repetitive nanosecond pulse discharges are used, the initial flame kernel is observed using Schlieren photography with a high speed camera. As a result, the flame kernel generated by repetitive pulse discharges is larger than by a conventional ignition system. Then, an application of repetitive nanosecond pulse discharges to a single cylinder SI engine is conducted and the operational limit of lean combustion is investigated. The result shows that the lean limit is extended from 20 to 23 in A/F at IMEP 440 kPa by replacing the ignition system from a conventional one. Also, the diluted limit is investigated. The result shows that the diluted limit is extended from 17.5% to 22.5% in EGR ratio at IMEP 630 kPa and that thermal efficiency is improved by 5%. The ignition delay and the combustion duration are decreased and the cycle-to-cycle variation of the ignition timing and IMEP are decreased. © 2009 SAE International.

A newly developed small-sized inductive energy storage (IES) circuit that uses a semiconductor switch for the turn-off action is successfully applied to an ignition system in spark ignition engines operating under lean fuel-air ratios. This IES circuit can generate repetitive nanosecond pulse discharges. Experiments are conducted by means of a spherically expanding flame configuration for C H -air mixtures under various conditions. Findings show the investigated ignition system improves the inflammability of lean combustible mixtures in terms of extended flammability limits, shorted ignition delay time, and extended dilution limits, compared with conventional spark ignition systems. © IMechE 2009. 3 8

本研究では，新たに開発した小型の誘導エネルギー蓄積式パルス電源により生成される，繰り返しパルスを用いることで，効率的に生成した活性化学種雰囲気下の混合気に対して，短パルスアーク放電することにより，希薄燃焼時の着火特性の改善を図る．本論文は第二報であり，点火機構の解明と実機への応用を試みた．

A newly developed small-sized IES (inductive energy storage) circuit with semiconductor switch at turn-off action is successfully applied to an ignition system of a small gasoline internal combustion engine. This IES circuit can generate repetitive nanosecond pulse discharges. An ignition system using repetitive nanosecond pulse discharges is investigated as an alternative to a conventional spark ignition system. The present study focuses on the extension of the operational limits for lean and diluted combustion using the repetitive nanosecond pulse discharges. First, in order to investigate the flame kernel formation process when the repetitive nanosecond pulse discharges are used, the initial flame kernel is observed using Schlieren photography with a high speed camera. As a result, the flame kernel generated by repetitive pulse discharges is larger than by a conventional ignition system. Then, an application of repetitive nanosecond pulse discharges to a single cylinder SI engine is conducted and the operational limit of lean combustion is investigated. The result shows that the lean limit is extended from 20 to 23 in A/F at IMEP 440 kPa by replacing the ignition system from a conventional one. Also, the diluted limit is investigated. The result shows that the diluted limit is extended from 17.5 % to 22.5 % in EGR ratio at IMEP 630 kPa and that thermal efficiency is improved by 5%. The ignition delay and the combustion duration are decreased and the cycle-to-cycle variation of the ignition timing and IMEP are decreased. Copyright © 2009 SAE International.

Direct fuel injection system is getting popular in internal combustion engines due to the superior performance in fuel economy and power. To optimize the fuel-air mixture distribution inside the cylinder, the geometry of nozzle and the mixture formation process must be well designed. To attain this, the numerical simulation will be a good tool, but the prediction ability is not enough for the practical design. In this study, a two-phase flow of fuel and gas including cavitation inside an axi-symmetrical nozzle was evaluated to improve the prediction ability. Two kinds of cavitaion model (quasi-steady dynamic bubble model and discrete bubble tracking model) are proposed and implemented into a commercial code FLUENT 6.4. As a result, the discrete bubble tracking model could obtain converged solutions even for a high differential pressure conditions between the nozzle entrance and the exit up to 100 MPa and predict the cavitaion phenomenon qualitatively.

The analysis of spray characteristics is important to examine the combustion characteristics of DI (Direct Injection) gasoline engines because the fuel-air mixture formation is controlled by spray characteristics and in-cylinder gas motion. However, the mixture formation process has not been well clarified yet. In this study, the characteristics of a fan-shaped spray caused from a slit-type injector, such as the droplet size, its velocity and the droplet distribution were simultaneously measured on a 2D plane by using improved ILIDS (Interferometric Laser Imaging for Droplet Sizing) method. ILIDS method is an optical measurement technique using interference fringes by illuminating a transparent spherical particles with a coherent laser light. In the measurement of the wall-impinging spray, effects of the distance to the wall and the wall temperature on the spray characteristics were investigated. As a result, it was found that the SMD (Sauter Mean Diameter) near the wall surface increased with smaller distance. Meanwhile, in the measurement of spray under a crosswind, the relative velocity of between the droplet and the ambient gas was found influential on the atomization. Additionally, numerical simulation of the spray with a crosswind was examined. The in-nozzle two phase flow was calculated using VOF (Volume of Fluid) model and also the spray formation process was calculated using DDM (Discrete Droplet Model) with mathematical sub-models. As a result, the effects of boundary conditions at nozzle exit, breakup model and drag force model were evaluated comparing with experimental results. Copyright © 2009 SAE International.

A newly developed small-sized IES (inductive energy storage) circuit with semiconductor switch at turn-off action was successfully applied to an ignition system. This IES circuit can generate repetitive nanosecond pulse discharges. An ignition system using repetitive nanosecond pulse discharges was investigated as an alternative to conventional spark ignition systems. Experiments were conducted using spherically expanding flame configuration for CH and C H -air mixtures under various conditions. The ignition system using repetitive nanosecond pulse discharges was found to improve inflammability of lean combustible mixtures, such as extended flammability limits, shorted ignition delay time, with increasing the number of pulses. The authors seek for the mechanisms for improving the inflammability in more detail to optimize ignition system, and verify the effectiveness of IES circuit in EGR condition, for real engine use. Moreover, an application of this ignition system to a SI engine was conducted. As a result, the lean limit was extended from 20 to 23 in A/F at IMEP 440 kPa by replacing the ignition system from a conventional one, and indicated thermal efficiency was improved by 11%. Copyright © 2009 SAE International. 4 3 8

The objective of this study is to extend the high load operation limit of a gasoline HCCI engine. A new system extending the high load HCCI operation limit was proposed, and the performance of the system was experimentally demonstrated. The proposed system consists of two new techniques. The first one is the "Blow-down super charging (BDSC) system", in which, EGR gas can be super charged into a cylinder during the early stage of compression stroke by using the exhaust blow-down pressure wave from another cylinder phased 360 degrees later/earlier in the firing order. The other one is "EGR guide" for generating a large thermal stratification inside the cylinder to reduce the rate of in-cylinder pressure rise (dP/dθ) at high load HCCI operation. The EGR guides consist of a half-circular part attached on the edge of the exhaust ports and the piston head which has a protuberant surface to control the mixing between hot EGR gas and intake air-fuel mixture. The experiments were carried out using a 4-cylinder port fuel injection engine with a compression ratio of 12. As a result, HCCI operation at high loads, up to an IMEP of 650 kPa at an engine speed of 1500 rpm, was achieved. Copyright © 2009 SAE International.

DDM (Discrete Droplet Model) is widely used for the numerical analysis of a fuel spray. In order to achieve highly accurate calculations using DDM, many mathematical sub-models such as breakup, drag force and collision are employed with DDM. In the conventional DDM, an isolated droplet (parcel) is assumed and the influence of surrounding droplets is not directly considered. However, it is well known that the state of the wake flow of droplet or the vortex behind droplet changes by the distance between droplets, and the drag coefficient is influenced. Especially, this effect is important in a dense spray. In this study, a newly developed drag force model, containing the drag reduction effect with the droplet spacing as a parameter is adopted and also, the effect on the spray tip penetration and the spray volume is examined. As a result, the spray shape and Sauter mean diameter were found to depend on the mesh size that defines the droplet spacing. The drag force reduction by the droplet number density tends to increase the spray volume. The calculation of a diesel spray at the injection pressure of 133 and 55MPa indicated better agreements with experiments compared to the result using a conventional model.

本研究では、新たに開発した小型の誘導エネルギー蓄積式パルス電源を用いて生成した非平衡プラズマを利用して、予混合気の着火特性を調べる。本研究は、繰り返しパルスを用いることで、効率的に生成した活性化学種雰囲気下の混合気に対して、短パルスアーク放電することにより、希薄燃焼時の着火特性の改善を図る。

A newly developed small-sized IES (inductive energy storage) circuit with semiconductor switch at turn-off action was successfully applied to an ignition system. This IEC circuit can generate repetitive nanosecond pulse discharges. In this paper, the ignition system using repetitive nanosecond pulse discharges was investigated as an alternative to conventional spark ignition systems. The experiments were conducted using spherically expanding flame configuration for C H -air mixtures under various conditions. In conclusions, the ignition system using repetitive nanosecond pulse discharges was found to improve inflammability of lean combustible mixtures, such as extended flammability limits, shorted ignition delay time and extended dilution limits, compared with conventional spark ignition systems. Copyright © 2008 by the Japan Society of Mechanical Engineers. 3 8

A new gasoline combustion engine system with high compression ratio was studied and proposed in order to achieve higher thermal efficiency than that of a conventional SI engine. A special cranking mechanism was adopted which allowed the piston to move rapidly near TDC. Some mechanisms were proposed and two of them were designed and built for the testing. The experimental results showed that knocking was avoided and better indicated thermal efficiency was obtained. An inconstant speed gear mechanism with compression ratio of 14 could be operated up to 2500 r/min and thermal efficiency was improved by 18% compared to a conventional engine with compression ration of 10. Also, a cam mechanism driven by a planetary gear was tested to achieve higher engine speed up to 4000 r/min, but the improvement of thermal efficiency was not so large as much as of the inconstant speed gear mechanism. Copyright © 2008 by the Japan Society of Mechanical Engineers.

Thermocouples are widely used to measure the local gas temperature due to its accuracy and convenience. However, it is difficult to use thermocouples in a transient phenomenon such as reacting fields. In this study, the unsteady gas temperature inside a combustion chamber was measured by using an improved two-wire thermocouple technique. Based on previous two-wire methods, some modifications were examined. Firstly, numerical analysis of heat transfer between transient flow and thermocouple was performed to see what kind of modification was required. Secondly, a correction term was added to the basic equation, which was validated by experiments using a Rapid Compression and Expansion Machine. Finally, an improved two-wire thermocouple technique was evaluated by measuring the transient gas temperature inside a combustion chamber and compared to the estimated temperature using measured pressure data and assumptions of chemical equilibrium.