Performance Of Spark Ignition Engine Research Articles

Comprehensive Review on Technical Developments of Methanol-Fuel-Based Spark Ignition Engines to Improve the Performance, Combustion, and Emissions

Abstract Methanol (CH3OH) is emerging as a viable alternative to fossil-based fuels, addressing the increasing global energy demand while promoting sustainability. The spark ignition (SI) engines are widely used to run the automobile sector. Methanol as a widely available and cheap source of energy can be strongly replaced with expensive and limited fossil-based fuels to power the SI engines. The prime objective of this study is to evaluate the advancements made in improving the fuel blends, performance, combustion, and emission characteristics of methanol-fueled SI engines. The investigation commences by examining the various technical improvements implemented in methanol-fueled SI engines to optimize their overall performance. These developments include advancements in fuel blends, engine design, combustion strategies, fuel injection systems, ignition systems, engine load, etc. The impacts of these developments on the performance parameters including brake thermal efficiency, power output, torque, fuel efficiency, thermal efficiency, etc., combustion parameters including ignition delay, combustion duration, heat release rate, in-cylinder pressure and temperature, etc., emission parameters including hydrocarbon, carbon monoxide, nitrogen oxide, formaldehyde, unburned methanol, etc., is reviewed comprehensively. The effectiveness of emission control techniques and the potential for meeting stringent environmental regulations are explored. The review paper then considers the wider implications of methanol-fueled SI engines by examining their technical, environmental, economic, and renewable applications. The technical aspects cover the compatibility of methanol-fueled SI engines with existing infrastructure and the associated challenges and opportunities. The environmental considerations delve into the potential reduction of greenhouse gas emissions and the overall sustainability of methanol as a renewable fuel. Finally, the research direction of methanol SI engines is discussed, highlighting the emerging trends and prospects in this field. The review paper concludes with recommendations for further research and development, addressing the key areas that require attention to unlock the full potential of methanol as an efficient and sustainable fuel for SI engines.

A Review on Investigation of Petrol and Ethanol Blend as fuel on Performance of Spark Ignition Engine

Abstract: Finding substitute fuels has been more popular in recent years as a response to escalating pollution levels and fuel shortages. The goal of this research is to find the ideal gasoline to ethanol ratio that will maximize engine performance and reduce emissions in spark ignition engines. In order to analyse the performance of different blending ratios, the research looks at metrics such carbon monoxide (CO) emissions, brake power (BP), brake specific fuel consumption (BSFC), and brake thermal efficiency (BTE). Blends of gasoline and ethanol with a 15% ethanol content greatly increase engine thermal efficiency at higher engine speeds. E12 mixes of gasoline and ethanol boost engine braking power while lowering CO emissions and breakspecific fuel usage. Blends of gasoline with ten to fifteen percent ethanol present a possible substitute.

Investigations on a Spark Ignition Engine, Part I: Fuelled With Biogas Extracted From Sewage

In this study, experiments were conducted on a single-cylinder, four-stroke modified diesel engine into a spark ignition engine using biogas from sewage sludge as fuel. The engine was operated at 1500 revolutions per minute at a compression ratio of 13:1. The throttle was set to 25% and 100% to operate the engine at various equivalence ratios to study the combustion, performance, and emissions. At various equivalence ratios and throttle openings, the effects of cycle-by-cycle variation were studied and compared. The brake thermal efficiency and brake power reached their highest values at an equivalence ratio of 0.95 and 1.01 respectively. At these equivalence ratios, carbon monoxide and hydrocarbon emissions were minimal but nitric oxide levels were high. When the mixture becomes lean, the coefficient of variation of the mean effective pressure increases considerably on both throttles. When the engine is running in steady conditions far from the lean limit, the cycle-by-cycle variation is stochastic in nature. Prior cycle impacts and cycle-by-cycle variation occur when the engine is running lean, and they are deterministic. Part II of this study represents the effect of hydrogen addition and change in compression ratio in the performance of spark ignition engines fueled with biogas.

Effect of Hydroxy Gas Addition in Gasoline-ethanol Fuel Mixture on Performance of Spark Ignition Engine

Fossil fuel continues as primary energy source for the transportation industry, particularly for the fuel used in spark ignition (SI) engines. The use of biofuels such as bioethanol is a solution to the reliance on fossil fuels to reduce green-house gas emissions in the atmosphere and improve environmental air quality. However, the use of bioethanol as a fuel for the SI engine has limitations, such as a reduction in power produced as compared to pure gasoline due to the low energy input contained by bioethanol compared to gasoline. The objective of this study is to improve the energy conversion efficiency of the SI engine by adding Hydroxy (HHO) from water electrolysis to the gasoline-bioethanol mixture, allowing for increasing application of bioethanol at higher concentrations as an additive in future. The test was performed on a 155 cc SI engine equipped with an Engine Control Unit (ECU) to control the fuel injection. The pressure, temperature, oxygen, and throttle position sensors located on the engine and connected to a NI-MyRIO microcontroller. The injection duration of HHO gas based on the duration of gasoline fuel injection, both of fuel are injected through each injector at the intake manifold. The result shows the characteristics of HHO gas improved the disadvantages of biofuels, which have a lower heating value and higher flame speed of bioethanol and gasoline fuel. The presence of HHO gas into the bioethanol-gasoline blend affected to increase the produced power, torque and thermal efficiency of the SI engine. An increase in thermal efficiency at 9.16% obtained at concentration of 20% bioethanol and HHO.

Experimental evaluation of gasoline-hexane fuel blends usage in a spark ignition engine

In the present study, the influences of hexane addition to gasoline were researched on performance and exhaust emissions in a SI engine. It was aimed to increase engine performance and thermal efficiency of spark ignition engine. So, a single cylinder, four stroke SI engine was operated with gasoline and gasoline/hexane fuel volumetric mixtures (H10, H20, H30 and H40) at wide opening throttle (WOT) and 4000, 3600, 3200, 2800 and 2400 rpm. It was seen that engine torque and power output decreased while SFC increased with the addition of hexane in the fuel blends. Engine torque decreased by 5.69%, 7.66%, 10.80%, 14.86% with H10, H20, H30 and H40 compared to gasoline at 2800 rpm grespectively. Thermal efficiency declined by 3.27%, 7.50%, 8.95% and 11.12% using H10, H20, H30 and H40 test fuels compared to gasoline at 2800 rpm respectively. Higher CO and HC were measured with fuel blends according to gasoline for all test fuels. CO reduced by 3.77% with H40 compared to H10 at 3200 rpm. On the contrary, CO2 increased by 16.49% with H40 compared to H10 at 3600 rpm. HC increased by about 21.26% H40 compared to H10 at 3200 rpm. Although there is no positive difference on exhaust emissions and thermal efficiency is reduced, gasoline/hexane fuel mixtures can be used without modifications in SI engines.

The effects of hydrogen peroxide-ethanol blend/gasoline on the combustion and emission performance of a combined injection spark ignition engine

Hydrous ethanol is a green fuel with great potential to deal with crises in the environment and energy. The study on the ethanol life cycle showed hydrous ethanol with 10%–20% water content had the best benefit, but the water content >10% would deteriorate engine power and emission performance. In this paper, the effects of the 30 vol% laboratory-grade H2O2 on the combustion performance and emission characteristics were explored in an ethanol/gasoline combined injection engine. At the engine operating condition of engine speed/manifold air pressure = 1500 rpm/49.5 kPa, the H2O2-ethanol blend direct injection (DI) and gasoline port injection were conducted. Results showed that H2O2 greatly improved the operating performance of the hydrous ethanol/gasoline engine. As the 30 vol%-H2O2 ratio in the H2O2-ethanol blend (H2O2r) increased, the Pmax and the Tmax first increased and then decreased. Both CA0-10 and CA10-90 were slightly extended. For the DI ratio = 10%–40%, the optimal IMEP was obtained at H2O2r = 15%, which was 0.09 bar–0.11 bar higher than H2O2r = 0%. The optimal BTE was 0.86%, 0.75%, 0.71% and 0.75% higher than H2O2r = 0%, respectively. As the H2O2r and DI ratio increased, HC and NOx emissions descended, and CO emissions decreased first and then ascended slightly with the critical H2O2r = 10%–15%. Optimal CO, HC and NOx emissions were 21.76%, 58.83% and 42.02% lower than gasoline, respectively. H2O2 could reduce particulate emissions, while the H2O2r < 15% at the DI ratio = 30%–40% should be adopted.

A numerical investigation of the influence of ozone on combustion to improve the performance of spark ignition engines

The aim of this work is to exploit the influence of using ozonized air to achieve stable and efficient combustion of lean mixtures in a gasoline-fuelled Spark-Ignition (SI) engine. The influence of ozone on the combustion of near-stoichiometric mixtures, which are typical of SI engines, has also been assessed. A Computational Fluid Dynamics (CFD) model has been employed to simulate compression, combustion, and expansion of a spark ignition, axisymmetric engine fuelled with iso-octane/air/ozone mixtures. The aim is to assess how ozone improves the engine performance under different engine speeds, ignition timings and equivalence ratios. The model has been validated against experimental data available in the literature. Parametric analyses have been carried out by considering three values of engine speeds (800, 1000 and 1200 rpm), three different ozone concentrations at Intake Valve Closure (IVC) (0, 100 and 200 ppm) and two equivalence ratios (0.9 and 0.7). The results show that ozone enables reactions in the Low Temperature Combustion (LTC) regime, modifies the mixture chemical composition and the auto-ignition tendency. Specifically, for all the cases under examination, the addition of ozone to the air/fuel mixture reduces the combustion duration, leading to an increase in terms of work output and a reduction of the specific fuel consumption. Moreover, the advantage of using ozone is greater for lean mixtures than for near-stoichiometric mixtures. Finally, for the near-stoichiometric cases, when the residence time of the mixture is high enough, auto-ignition occurs in the end gases.

Impact of Cylinder-to-Cylinder Dispersion of Exhaust Gas Recirculation on the Three-Way Catalyst Performance and Tailpipe Emissions of Spark-Ignition Engines

Abstract New generations of spark-ignition engines include exhaust gas recirculation (EGR) to improve the engine efficiency. Depending on the design of the EGR routing, some differences in the total amount of recirculated gases that reach each cylinder can be induced. This affects the air-to-fuel ratio on each cylinder due to the combination of the different temperature and composition of the gases at the intake valve closure. As a consequence, significant deviations in the combustion process and the subsequent composition upstream the three-way catalyst can be reached. This paper explores these effects on catalyst performance and tailpipe emissions, individualizing the behavior for each regulated species. The study was performed in a four-cylinder naturally aspirated engine with Atkinson cycle and a close-coupled three-way catalyst. The most significant deterioration in conversion efficiency appeared for the nitrogen oxides, directly linked to the EGR dispersion level. In the case of carbon monoxide (CO) emissions, no significant impact was observed except at high average EGR rates, where one or more of the cylinders exceeded the EGR tolerance for that speed and load. Based on these results, a strategy where the fuel injector command is adapted to correct the air-to-fuel ratio deviations induced by the EGR was developed and implemented.

Effect of gasoline-ethanol blends on the performance of a four stroke engine using Ricardo Wave software

Purpose The purpose of this study is to assess the performance of fuel blends containing ethanol and gasoline in spark ignition engines. The aim is to explore alternative fuels that can enhance performance while minimizing or eliminating adverse environmental impacts, particularly in the context of limited fossil fuel availability and the need for sustainable alternatives. Design/methodology/approach The authors used the Ricardo Wave software to evaluate the performance of fuel blends with varying ethanol content (represented as E0, E10, E25, E40, E55, E70, E85 and E100) in comparison to gasoline. The assessment involved different composition percentages and was conducted at various engine speeds (1,500, 3,000, 4,500 and 6,000 rpm). This methodology aims to provide a comprehensive understanding of how different ethanol-gasoline blends perform under different conditions. Findings The study found that, across all fuel blends, the highest brake power (BP) and the highest brake-specific fuel consumption (BSFC) were observed at 6,000 rpm. Additionally, it was noted that the presence of ethanol in gasoline fuel blends has the potential to increase both the BP and BSFC. These findings suggest that ethanol can positively impact the performance of spark-ignition engines, highlighting its potential as an alternative fuel. Originality/value This research contributes to the ongoing efforts in the automotive industry to find sustainable alternative fuels. The use of Ricardo Wave software for performance assessment and the comprehensive exploration of various ethanol-gasoline blends at different engine speeds add to the originality of the study. The emphasis on the potential of ethanol to enhance engine performance provides valuable insights for motor vehicle manufacturers and researchers working on alternative fuel solutions.

Elucidating Optimal Exhaust Manifold Divergence and Temperature Distribution in Improving Low-End Engine Speed Performance

The exhaust manifold plays a crucial role in optimizing the performance of Spark-Ignition (SI) engines by effectively expelling combustion products. This study focuses on the optimization of the exhaust manifold design and temperature distribution in a 115-cc single-cylinder SI engine. The objective is to investigate the association between the design characteristics of the exhaust manifold, particularly its divergence, and the engine's performance in terms of brake power. Using computer-aided design (CAD), a three-dimensional model of the exhaust manifold with reduced diameter was developed. The optimized design aimed to enhance the engine's overall performance by achieving lower temperatures, particularly at low-end speeds. Subsequently, a 1D engine study was conducted to evaluate the performance of the engine with the optimized exhaust manifold design and validate the improved temperature distribution. The results demonstrate that the optimized exhaust manifold design leads to higher brake power while maintaining lower temperatures, especially at low-end speeds. This highlights the importance of exhaust manifold optimization and temperature distribution in maximizing the efficiency of the selected SI engine. To further enhance the engine's performance, future research should focus on identifying the most appropriate value for the exhaust manifold's divergence. This will contribute to the ongoing development of more efficient and high-performance SI engines. The findings of this study provide valuable insights into the optimization of exhaust manifold design and temperature distribution for improved engine performance in the context of the tested engine.

Performance and Emission Characteristics of Spark Ignition Engine Operating with Biogas at Graded Purity

Performance and Emission Characteristics of Spark Ignition Engine Operating with Biogas at Graded Purity

Numerical investigation on the combustion performance of ammonia-hydrogen spark-ignition engine under various high compression ratios and different spark-ignition timings

This paper aims to numerically investigate the effects of high compression ratio (CR) on the performance of ammonia-hydrogen engines. In this work, four CRs from 10.7 to 13.7 with scanning spark timing (ST) from 28°CA to 0°CA BTDC were analyzed. The main results are as follows: As the CR increases, there is a trade-off relationship between the dissipation rate of turbulence and the turbulent kinetic energy (TKE). Initially, the TKE rises as the CR increases. As the CR continues to rise, the tendency for an increase in TKE diminishes, while the turbulent dissipation rate consistently rises. Additionally, there is an escalation in heat transfer loss. Therefore, there is a trend of rising and then falling in the flow velocity and turbulence intensity with the increase of the CR. Ammonia-hydrogen flame propagation is susceptible to temperature and flow field, and a high CR can improve ignition stability, shorten combustion duration, minimize cooling loss, and enhance output power. Unfortunately, the emission of NOx gradually rises as the CR increases. At high CR, the combustion performance is optimized by adjusting ST, and the maximum IMEP and ITE are 4 bar and 38.3 %, respectively. The ST for maximum braking torque (MBT) should be gradually delayed toward TDC as the CR increases.

Analysing the effects of toluene percentages and exhaust gas re-circulation rates on spark-ignition engine performance and emissions

This study delves into the intricate dynamics of gaseous emissions in relation varying parameters in spark-ignition engines: gasoline-toluene blending ratios, exhaust gas re-circulation (EGR) rates, and spark timings. With increasing toluene concentrations, there was a consistent reduction in emissions, culminating in HC values of 67 ppm, CO at 0.6% volume, PM at 11 mg/m?, and NOx at 100 ppm for a 100% toluene blend. The implementation of EGR demonstrated its efficacy in mitigating NOx emissions, registering a decline to 60 ppm at a 30% EGR rate. However, the same augmentation in EGR rates witnessed an uptick in HC and CO emissions. Analysis of spark timings pinpointed an optimal advance of 30? CA bTDC at a 50% engine load, yielding minimized emissions. Conclusively, the research underscores the potential of fine-tuning engine parameters, such as fuel composition, EGR rates, and spark advance, to achieve a harmonious balance between engine efficiency and emission reductions. This study lays foundational data for further exploration and optimization in the realm of internal combustion engines.

Bambusa tulda: A potential feedstock for bioethanol and its blending effects on the performance of spark ignition engine

Alternatives to conventional fuel sources must be investigated due to strict regulatory requirements and the depletion of fossil fuel supplies. As a result, of better transportation and population growth, the requirement for energy is increasing daily. Bioethanol may be used successfully to replace both gasoline and spark ignition engine diesel. Most nations blend 10% bioethanol with gasoline in automobiles. Several nations, notably India, have announced that they will soon begin blending 20% bioethanol with gasoline. Bambusa Tulda is used as a raw material for the extraction of bioethanol, which is a type of Indian bamboo. This study covers both the ethanol extraction from bamboo and the effects of various mixtures on spark-ignited engine performance. Four separate blends were developed on a volumetric basis at varying engine speeds, and the wide-open throttle was utilized to evaluate the performance and emissions of each mix with a constant compression ratio of 10:1. When bioethanol was enhanced, combustion efficiency, indicated power, engine power, mechanical efficiency, and volumetric efficiency all increased. Hydrocarbon, carbon monoxide, and carbon dioxide emissions decreased, while nitrogen oxide emissions increased. The engine performance of BE 15 was found to be the greatest among all the gasoline blends tested. According to this study, when nitrogen oxide emission control methods are applied, bamboo may be used as a feedstock for the manufacture of second-generation bioethanol. This invention offers a bioethanol production process that is good for environmental sustainability.

Impacts of Injection Parameters on the Mixture Formation and Performance of Two-Stroke Spark-Ignition Direct-Injection Aviation Kerosene Engine

Abstract Two-stroke spark-ignition engines play a significant role in the field of power sources of small and medium unmanned aerial vehicles. There is a certain transition from burning gasoline to aviation kerosene (or heavy oil) and from carburetor or inlet injection system to direct-injection fuel system. However, the performance of two-stroke spark-ignition direct-injection engines fueled with aviation kerosene was not very ideal under heavy loads. Generally, the mixture formation is very important for engine combustion and performance, while injection parameters have great effects on mixture formation. Thus, various injection parameters of a two-stroke direct-injection kerosene engine were examined here. The results showed too early or too late injection timing (tinj) would deteriorate the mixture formation, resulting in lower brake power and brake thermal efficiency. Here the most suitable tinj was 150 deg CA BTDC. Too high or too low injection pressure (pinj) caused fuel short circuit loss and poor mixture quality, so the optimum pinj was 10 MPa. Too large injector installation angle (β) easily results in fuel spray impingement, and too small β causes fuel short circuit loss. Therefore, the best β was concluded to be 30 deg in this paper.

Experimental Investigation on the Effects of Direct Injection Timing on the Combustion, Performance and Emission Characteristics of Methanol/Gasoline Dual-Fuel Spark Turbocharged Ignition (DFSI) Engine with Different Injection Pressures under High Load

The exceptional properties of methanol, such as its high octane number and latent heat of evaporation, make it an advantageous fuel for efficient utilization in dual-fuel combustion techniques. The aim of this study is to investigate the effect of direct methanol injection timing on the combustion, performance and emission characteristics of a dual-fuel spark ignition engine at different injection pressures. We conducted four different direct injection pressure tests ranging from 360° ahead to 30° CA ahead at 30° CA intervals. The experimental results indicate that regardless of the injection pressure, altering the methanol injection timing from −360° to −30° CA ATDC leads to distinct combustion behavior and changes in the combustion phase. Initially, as the injection timing is delayed, the combustion process accelerates, which is followed by a slower combustion phase. Additionally, the combustion phase itself experiences a delay and then advances. Regarding performance characteristics, both the brake thermal efficiency (BTE) and exhaust gas temperature (EGT) exhibit a consistent pattern of first increasing and then decreasing as the injection timing is delayed. This suggests that there is an optimal injection timing window that can enhance both the engine’s efficiency and its ability to manage exhaust temperature. In terms of emissions, there are different trends in this process due to the different conditions under which the individual emissions are produced, with CO and HC showing a decreasing and then increasing trend, and NOx showing the opposite trend. In conclusion, regardless of the injection pressure employed, adopting a thoughtful and well-designed injection strategy can significantly improve the combustion performance and emission characteristics of the engine. The findings of this study shed light on the potential of methanol dual-fuel combustion and provide valuable insights for optimizing engine operation in terms of efficiency and emissions control.

Combustion and emission characteristics of CNG/gasoline DFSI engine with CNG direct injection

CNG was a low-carbon alternative fuel for engines, which also had the advantages of higher engine knock resistance and better fuel/air mixing. The CNG injection and ignition timing was of significant importance for the performance of Dual Fuel Spark Ignition (DFSI) engines. In this paper, the coordinated effects of CNG injection strategy and ignition timing on the combustion and emission characteristics of CNG/gasoline DFSI engines were investigated. The results showed that the CNG/gasoline engine can achieve a comparable level of BMEP to that of a pure gasoline engine by using the CNGDI plus GPI injection approach with an optimal combination of injection and igniting timing. The cyclic variations of CNG/gasoline engines were increased with the advancing of ignition timing, and these variations can be ceased by using proper CNG injection strategies (early or mild). The gaseous emissions (HC, CO, and NOx) of CNG/gasoline engines were equivalent to those of pure gasoline engines; but the PN emissions were lower than that of gasoline engines. The particle size distribution of CNG/gasoline DFSI engines followed a single peak nucleation pattern and most of the particles were in nucleation mode (d ≤ 50 nm) peaking at around 15 nm. This study would be beneficial for the application of CNG in gasoline engines, which was promising to alleviate the strong dependence of engines on petroleum energy and to reduce their greenhouse gas emission.

A novel differential thermodynamic model for simulating spark ignition engine performance

A novel differential thermodynamic model for simulating spark ignition engine performance

Experimental Investigations and Quasi Dimensional Modelling of Spark Ignition Engine Fuelled With Gasoline and Oxyhydrogen Gas Mixture

Oxy-hydrogen gas is a mixture of hydrogen and oxygen gas in 2:1 molar proportion. Oxy-hydrogen gas can be easily and economically produced from electrolysis of water by using dry cell electrolysers. Oxy-hydrogen gas is one of the alternative fuel options which can replace conventional fossil fuels like gasoline, diesel, etc., because of its high-octane number (&gt;130) and moderate calorific value (21.4 MJ/kg). Current research work consists of both experimental and simulation parts. Experiments focussed on studying the performance and emission characteristics of spark ignition engine fuelled with gasoline (petrol) and dual fuel (gasoline + Oxy-hydrogen) mixture at variable load and constant speed condition with three different oxy-hydrogen flow rates. Comparative findings suggest that NOx emission and brake thermal efficiency increased by 1.75% and 800 PPM, respectively, at full load and at a flow rate of 1.54 lit/min. Carbon monoxide emission dropped by 0.25% at full load and at a flow rate of 1.54 lit/min. A two-zonequasi dimensional modelling of spark ignition engine was carried out in order to understand the combustion process efficiently. The predicted values accord well with the experimental data, with just a small variance. Commercially available software MATLAB R2021a is used to develop code for the engine simulation.

Numerical investigation of performance, combustion, and emission characteristics of spark-ignition engine fuelled with compressed natural gas and hydrogen

The combustion of gasoline engines running on blends of compressed natural gas and hydrogen fuels was investigated using the quasi-dimensional and two-zone model. This model could investigate and predict the combustion characteristics, emissions, and performance parameters of petrol engines using MATLAB software. The impact of hydrogen inclusion to compressed natural gas on the cylinder temperature, pressure, cumulative work done, and heat transfer related to compressed natural gas was investigated. The engine’s thermal efficiency and output power were increased while specific fuel consumption was decreased when hydrogen was blended up to 20%. The highest decline in specific fuel consumption of 20% hydrogen was 25.1% for compressed natural gas. The torque values are 4.25, 4.34, 4.42, 4.51, and 4.60 N·m for compressed natural gas, hydrogen with compressed natural gas HCNG 5%, HCNG 10%, HCNG 15%, and HCNG 20%, respectively, at rated speed of 2500 r/min. The peak decreases in peak cylinder temperature and pressure for HCNG 20% compared to compressed natural gas are 5.9% and 5.2%, respectively. For HCNG 20%, the greatest cylinder pressure, temperature, and cumulative work done were 7.9 MPa, 2309.97 K, and 190.88 J, respectively. NO x emissions were increased for hydrogen-compressed natural gas blends but hydrocarbon emissions were decreased. In comparison to compressed natural gas, the highest hydrocarbon emission reduction is up to 2.64% for HCNG 20%. The model's validity was examined in comparison to the findings from the literature and the Diesel RK program. The results show that the MATLAB code is appropriate. Several alternative fuels can be used using this mathematical model.