Introduction

More than 98% of today's transport vehicles are powered by internal combustion engines (ICE) (Perry 2013). Even in 2035, most cars and trucks are projected to still have ICE. However, due to their high consumption of fossil fuels and harmful effects on gas emissions, they are considered a public health issue. The fuel consumption to produce one kWh in internal combustion engines ranges from 217 to 272 g/kWh for diesel engines and 229 to 353 g/kWh for gasoline (Canada 2023). Increasing engine efficiency has been identified as one of the most effective ways to reduce fuel consumption (Suppes and Storvick 2016; Dincer and Zamfirescu 2018). Even with optimization, the need for further optimization will continue to exist (BMW Forschung und Technik 2011; Giorgio et al. 2018).

The greatest losses in internal combustion engines occur during the thermodynamic process of converting chemical energy into shaft work. However, improvements in other factors could reduce fuel consumption. In a gasoline engine, about 40% of the heat loss occurs during the exhaust stroke, while only 25% remains as useful energy output (Rai et al. 2018). Thus, engine efficiency can be increased by reducing heat loss through exhaust gases and converting it into useful energy. Water injection has been used in both reciprocating and turbine aircraft engines (Roux 2007; Xiao et al. 2018), as well as in automobile engines. BMW's M4 GTS was one of the first car engines to combine gas and water injection, along with providing intermediate cooling (BMW 2015). Moreover, there have been improvements in the injection of water and steam in the gas cycles to increase power in the Brayton or Joule cycles (Göke et al. 2012; Kayadelen and Ust 2018).

The concept of the six-stroke engine dates back to the nineteenth century, with the development of the Griffin six-stroke engine by Samuel Griffin in 1883 (Nimsiriwangso et al. 2019). This engine is based on the four-stroke engine, where the waste heat from the exhaust stroke in the four-stroke design is captured and used to make two additional strokes (Conklin and Szybist 2010). The Griffin six-stroke engine utilized a slide valve and a single-acting six-stroke design, allowing for more precise combustion control. The results showed that when the heat release from the first and second combustion stages was equivalent, the maximum gas temperature in the cylinder was lower than that of a four-stroke diesel engine. The Griffin engine found applications in electricity generation due to its ability to efficiently operate light loads and quickly respond to high power demands. However, its heavy construction limited its use in mobile applications.

Subsequently, other six-stroke engine designs were explored, such as Dyer, Bajulaz, Velozeta, NIYKADO, Crower, and various two-piston designs (Gupta et al. 2018; Nimsiriwangso et al. 2019). These designs aimed to improve fuel consumption, increase power output, reduce pollution, and offer fuel versatility. Technologies employed included water injection, preheating chambers, air injection, and innovative piston configurations. These advancements promised greater efficiency and environmental sustainability for internal combustion engines. However, the developments and designs of six-stroke engines in the twentieth century were mainly focused on patents (Dyer 1915; Tibbs 1976). It was not until 1994, with Arai M's work, that academic research on this technology began (Arai et al. 1994). Arai (1994) proposed a new six-stroke diesel engine and numerically and experimentally analyzed its thermodynamic performance. The results showed that when the heat release from the first and second combustion stages was equivalent, the maximum gas temperature in the cylinder was lower than that of a four-stroke diesel engine. This implied a reduction in excessive heat generation and, therefore, a lower thermal load on engine components. Additionally, having a lower maximum gas temperature suggested that a higher thermal load would be attained in a low-heat-rejection six-stroke engine.

From 2000 onwards, new patents for six-stroke engines, such as the Velozeta and NIYKADO engines developed in 2005, were proposed (Howard Kelem and Estelle Kelem 2010; Ei Tsukahara and Takurou Kamichika 2014). These advancements paved the way for further research on the thermodynamics of these engines. Multiple studies have demonstrated the advantages of a six-stroke engine over traditional four-stroke internal combustion engines (Conklin and Szybist 2010; Chen et al. 2015; Koksharov 2015; Arabaci and Kilic 2018; Nimsiriwangso et al. 2019; Selvakumar 2021). First, the problem of effective cooling of the internal walls of the combustion chamber is solved. While reducing the need for a unique cooling system that consumes power, increases weight, reduces overall efficiency, and demands more maintenance, the six-stroke engine presents better performance in comparison to four or two-stroke engines (Naresh and Hari Babu 2015; Selvakumar 2021). Moreover, the absence of a radiator allows designers to reduce the drag coefficient of the car body by eliminating air intake and a radiator grille (Selvakumar 2021). Secondly, internal cooling makes it possible to significantly boost engines in terms of compression ratio by 30–50% while avoiding detonation and increasing the compression ratio for gasoline to 14–16:1 and 25–35:1 for diesel (Koksharov 2015). This dramatically increases the combustion efficiency of the air–fuel mixture (by 40% compared to the Otto cycle), thereby improving the environmental performance of the engine (Conklin and Szybist 2010; Chen et al. 2015). Finally, while nitrogen dioxide filtration and neutralization systems in modern cars are very expensive, the relatively low-temperature regime in the combustion chamber dramatically reduces the formation of harmful nitrogen dioxide (Nimsiriwangso et al. 2019). Some studies also suggest that hot steam can prevent the formation of carbon deposits on the valves and walls of the combustion chamber, cleaning them during the “steam” or six-stroke, like a steam cleaner (Koksharov 2015). Yet, long-term testing of the prototype is required.

While water injection has been studied for four-stroke ICE (Hoppe et al. 2016; Zhu et al. 2019; Fratita et al. 2021), few refer to a six-stroke redesign. Several authors have verified the increase in the efficiency of the ignition times for four-stroke engines with water injection, thanks to the reduction of sensitivity to knock, and the decrease in temperature and pressure in the cylinder (Hoppe et al. 2016). Moreover, with water injection implementation, the level of carbon monoxide (CO) emissions has been shown to decrease, with an increase in carbon dioxide (CO2) produced, as a result of better combustion (Fratita et al. 2021). Yang et al. (2023) revealed that the use of water injection for cylinder wall cooling presents difficulties in maintaining stable combustion and water evaporation, emphasizing the criticality of engine temperature control. Overcoming these challenges is essential for the successful realization of a practical and efficient six-stroke engine using water injection.

In consequence, there is a need for a comprehensive study of the thermodynamic operation of this type of technology that allows for an increase in efficiency while reducing the negative effects of IC engines. This review intends to provide an inclusive understanding of six-stroke engines together with a thermodynamics model that governs six-stroke Otto and Diesel engine motors. A literature review for Otto and Diesel engines seen from the thermodynamic field is shown, centered on the last two strokes. Finally, this study presents a comprehensive literature overview of the topic of water injection in hot gas environments within the engine cylinder.

Functioning

The six-stroke engine has the same power transmission mechanism as the traditional internal combustion engine. Work is obtained with the translation of the axial to the rotatory movement of the piston to the crankshaft. Moreover, the first four-strokes of 6-stroke engines use conventional fossil fuels such as gasoline or diesel.

Thus, with the conventional four-stroke, two extra strokes are added with an alternative working fluid as fuel (i.e., water, or air). In the case of air, the compressed fluid is supplied through the inlet valve to the cylinder. As the cylinder temperature remains high towards the end of the expansion stroke, air comes into the chamber, absorbs this heat, and expands rapidly. Thus, pushing the piston head down to deliver an additional second stroke of power. As a result, it produces more energy per cycle and increases engine torque by 35% depending on the type of fuel used (Nimsiriwangso et al. 2019). In the case of water, the fluid is atomized in the piston chamber so that it turns into steam when it comes into contact with the hot gases remaining in the cylinder, pushing the piston down in a similar way to the previous case. Likewise, alternative fuels such as hydrogen, brown gas, and a mixture of alcohols have been studied to increase the efficiency and performance of the six-stroke engine. (Mohandas and Desai-Patil 2015).

Figure 1a shows the moment when the difference between conventional four-stroke engines and six-stroke engines materializes. At the end of the fourth stroke the exhaust valves open and the gases are about to leave the chamber. However, after a Δθ the valves closes again with hot pressurized gases inside. Then the water is injected near the top dead center of the cylinder at 720 °CA, increasing the in-cylinder pressure, see Figs. 1b and c. In addition, the injection of water in the cylinder has a cooling effect since the water can store thermal energy in the form of sensible and latent heat that is released during its evaporation and expansion as shaft work.

Fig. 1
figure 1

Six stroke engines. a Initial phase for water stroke with partial exhaust of combustion gases b in-cylinder conditions of water droplets expansion process, c in-cylinder pressure as function of crank angle for the two additional strokes

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Six stroke engine research

A literature review was carried out, limiting the search to articles that met the following criteria:

  1. 1.

    Due to the little literature found on academic research on six-stroke engines, the publication date criterion was defined from the first academic research records found in 1994 to 2023.

  2. 2.

    Written in Spanish, English, or French.

  3. 3.

    Thermodynamics related topics.

Articles that did not meet the established criteria but were relevant to the study were manually added to the analysis. Figure 2 shows an alluvial diagram to represent the changes in the studies found over time. From the analysis, articles were divided according to the variables of interest (i.e., type of model developed, thermodynamic cycle, working fluid, and idealization of heat transfer).

Fig. 2
figure 2

Alluvial diagram for literature review results of Six stroke IC engines

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A total of 18 articles were obtained, most of them published between 2015 and 2019 and only one article published in each of the following years. Interestingly, half of articles use analytical models (Conklin and Szybist 2010; Chen et al. 2015; Arabaci and Kilic 2018; Owunna and Ikpe 2021). However, five represent heat transfer losses as they are experimental models (Arai et al. 1994; Arabaci and İçingür, 2016; Arabaci 2021), however only (Arai et al. 1994; Arabaci 2021) present thermodynamic equations and models to model certain heat losses. Arabaci and İçingür (2016) is the only one to model both convection and radiation losses, however many constants were assumed and the change in properties with crankshaft movement was not considered. Similarly, all the analytical models implemented equations independent of the angle of the crankshaft, however the pressure, temperature and other thermodynamic properties vary as the piston travels 360 °CA (Mohammed et al. 2019). Furthermore, few articles deal with Six-stroke engines with charged fluids other than water, Owunna and Ikpe (2021) found that the IC 6-stroke engine efficiency was higher when water is used as the working fluid compared to air, however, experimental tests are needed to corroborate such results. Gupta et al. (2018) made an experimental setup using gasoline and acetylene as fuel with water injection at the end of the recompression stroke for a gasoline engine modified from four to six strokes. They obtained an increase of 5.18 and 1.55% for brake power and thermal efficiency respectively, using acetylene compared to gasoline in the six-stroke engine. In addition, 13.33 and 0.67% of CO and HC reduction were observed with acetylene compared to gasoline due to better combustion of acetylene. However, recent articles such as (Yang et al. 2023) have managed to implement multiple approaches, from analytical modeling, simulation, and experimentation, concluding that the central mechanism of the six-stroke engine cannot function properly unless it is not possible to bring heat from anywhere other than the mixture in the cylinder, for example, from the wall or from the outside of the cylinder. The ideal condition to satisfy these requirements is the injection of steam, achieving an indicated mean effective pressure IMEP increase from 5.89 to 6.21 bar with respect to the four-stroke engine when 97.81 mg of steam were injected at 20 bar of pressure.

In conclusion, there is a significant deficit in studies regarding six-stroke engines that work with non-idealized or experimental models. In addition, the effects of different charged fluids on engine performance should be explored with their variation with respect to Otto and Diesel cycles.

Six stroke engine research

There are currently two trends in six-stroke engine designs. The first consists of the addition of two additional strokes on the main piston. The engine captures the heat lost from the fourth stroke of the Otto or Diesel cycle and uses it to generate additional power from the injection of a working fluid. In this concept, several designs are distinguished (i.e., Bajulaz engine, Crower six-stroke, Niykado six-stroke engine, Velozeta engine) (Lukman Nul-Hakem 2012; Mohandas and Desai-Patil 2015). See Fig. 3.

Fig. 3
figure 3

Six-stroke engines and designs. a Bajulaz engine (Roger Bajulaz 2008) b Crower engine (Crower 2007) c Patent for the control device for injection in a Six-stroke engine (Ei Tsukahara and Takurou Kamichika 2014)

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The second concept uses a second opposing piston that moves at half the cyclic speed of the main one, giving six piston movements per cycle. Thus, it increases the compression ratio and replaces the traditional engine valve mechanism. Designs in this class include the Beare Head engine, M4 + 2 and the German charge pump.

Most researchers have focused on the first concept of the main piston since it is easier to model for thermodynamic analysis. Allowing experimental data to be extracted from conventional four-stroke engines and be used for six-stroke IC engine models (Howard Kelem and Estelle Kelem 2010; Lukman Nul-Hakem 2012; Ei Tsukahara and Takurou Kamichika 2014; Mohandas and Desai-Patil 2015).

Environmental impact

The level of air pollution is measured by the atmospheric emissions per unit of work produced by the engine (Mustafa Moraes et al. 2016; Gilbert et al. 2018). Any substance that, due to its concentration, can become harmful to health is considered a contaminant. In general, the group of pollutants that serve as universal indicators of air quality are sulfur dioxide (SO2), suspended particles, carbon monoxide (CO), ozone (O3), nitrogen oxide (NOx), and hydrocarbons (HC), and carbon dioxide (CO2).

Conventional internal combustion engines produce about 10% of the world's greenhouse gas emissions (Reitz et al. 2020). Moreover, in 2019 about 58% of transportation emissions are come from exhaust gases from IC engines in cars and light-duty trucks. (Reitz et al. 2020).

Past studies have proposed environmental impact analysis for modified six-stroke diesel engines. Hayasaki & Arai Confirmed by numerical and experimental methods that the dual-fuel six-stroke engine was superior to the four-stroke engine with a 90% decrease in NOx concentration and partial removal of soot by adding a small amount of methanol in the second combustion process (Arai et al. 1994; Hayasaki et al. 1999).

More recent studies proposed an experimental analysis, Arabaci et al. (2015) varied the mass injection and entry duration in the fifth stroke. Due to the reduction in the temperature of the combustion gases, the HC and CO emissions decreased by 18.23% and 21.97% at a speed of 3000 rpm. Thus, agreeing with results obtained by (Gupta et al. 2018), in addition to a reduction of NOx emissions by 5.65% with acetylene due to the lower maximum temperature due to water injection.

However, from a thermodynamic simulation of an Otto cycle engine, (Nimsiriwangso et al. 2019) found an 85% increase in hydrocarbon (HC) emission compared to the 4-stroke engine, while NOx emission was reduced by 80%.

Although the six-stroke engine has shown a considerable reduction in pollution gases compared to its four-stroke counterpart. The fact that the humidified exhaust gas combined with the fresh intake mixture may be beneficial in terms of emissions needs to be evaluated (Arabaci and Kilic 2018). Likewise, there's a need for more experimental and numerical analysis of the different design concepts of six-stroke engines. Nonetheless, there's an agreement on the general reduction in NOx emissions, and a potential reduction of other pollutants is yet to be studied. Moreover, it is usual to find NOx and SO2 traces in the exhaust gases after a conventional ICE operation (Ferguson and Kirkpatric 2016), in fact, the SO2 emissions are the main cause of producing sulphuric acid in the atmosphere, due to the presence of condensate water in clouds, with the risk of formation of nitric acids due to the NO traces. (Ferguson and Kirkpatric 2016; Ghojel 2020).

Consequently, there is a need to evaluate the risk of the formation of such substances for six-stroke engines working with water injection. Analysis of their impact on the environment and implications in public health problems thanks to its corrosive nature.

CFD and simulation

Several software have been used for the six-stroke IC engines (P&M 1980; Los Alamos National 1985). Gupta et al. (2018) used an internal version of KIVA for a CFD model of the multicomponent fuel in a six-stroke diesel engine. It was possible to characterize the behavior of the fuel according to variables such as its evaporation, droplet breakup and collision with the cylinder. Thus, Rajput et al. (2018) obtained an energy distribution of the total fuel energy in the form of work energy, wall heat loss, exhaust energy and unburned fuel concluding that the operation of the six-stroke cycle successfully recovers the thermal energy that would be wasted in the operation of the corresponding four-stroke cycle engine. Similarly, Nimsiriwangso et al. (2019) obtained an increase in efficiency for a modified six stroke motor with the use of AVL-BOOST software, simulating various speeds and water injection rates to finally obtain the optimal operating parameters (Nimsiriwangso et al. 2019).

The CONVERGE v2.4 software proved to be an important tool for analyzing the droplet evaporation conditions in the pistons (Yang et al. 2023). Yang et al. (2023) validated the simulation models through experimental results. Using simulations with various injection times, water masses, and temperatures, it was concluded that achieving a six-stroke engine using water injection was difficult unless a significant amount of thermal energy for evaporation was obtained from sources external to the cylinder mixture. Moreover, it was found that the cylinder wall cooled due to continuous water injection, leading to unstable evaporation, and requiring wall temperature control for a successful six-stroke engine using water injection. Similar results were obtained analytically by Arabaci (2021), it was concluded that engine performance alone is not enough while exhaust heat recovery is investigated. Thus, the best indication of exhaust heat recovery under the same test conditions is the irreversibility variation.

Furthermore Yang et al. (2023) found that with the addition of more additional strokes and a constant wall temperature, the IMEP decreased by approximately 0.4 bar compared to the four-stroke engine, but around 40% of this loss could be recovered through water injection.

As a result, numerical modeling represents an opportunity to characterize both the engine and the fluids that interact in the system. Avoiding costly experimental setups and allowing the parametrization for a wide range of variables.

Machine learning and new technologies

Machine learning is both a technology and a science that allows a machine to realize some action without programming it for doing this. The main objective of machine learning is to predict some parameters of a model starting with a large statistical database. Nevertheless, any of the studies from the literature review reported machine learning techniques implemented in their models.

Database such as Scopus, and IEEE Xplore shows a big increase in papers on machine learning around 2013, passing from 2000 to an average of 30,000 articles per year. Furthermore, six-stroke engines have in general a low investigation rate of only 1–2 papers per year, both indicators together can be seen as a possible cause for not machine learning implementation in six-stroke engine studies. In addition to the lack of experimental data needed to train the machine learning algorithms.

Thermodynamic models

The six-stroke cycle consists of a standard four-stroke Otto or diesel cycle followed by a heat recovery vapor expansion cycle considering constant volume and pressure respectively.

There are currently several thermodynamic models (i.e., computational (Kuo 1996; Rajput et al. 2018; Nimsiriwangso et al. 2019), experimental (Arai et al. 1994; Lukman Nul-Hakem 2012) and analytical (Hayasaki et al. 1999; Conklin and Szybist 2010; Arabaci and Kilic 2018)). While the latter presents two analysis methods, an idealized one with piecewise functions, while the other is based on correlations and differential equations to approximate the real situation as closely as possible. Both differ as the latter includes in its modeling the concepts of friction, volume, pressure, and temperature losses depending on the angle and speed of the piston, in addition to including the heat transfer between the piston, the combustion gases and the surrounding. In addition, two possibilities are presented in the fourth stroke, with a partial release of gases or without mass exit, that is, open or closed system, respectively.

Figure 4 shows the three important stages recognized to fully describe the behavior of the engine as: inputs, simulation and analysis, and outputs.

Fig. 4
figure 4

Flow chart of the six stroke engine model description

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Independently of the model type, it is required to know the engine geometry, and its functional parameters, such as RPM, valve timing, and ignition. The properties of the fuel (lower heating value, chemical composition, density, viscosity). And the standard atmospheric conditions, to determine all the thermophysical properties of the fluids that interact.

Independently of the model type, it is required to know the engine geometry, and its functional parameters, such as RPM, valve timing, and ignition. The properties of the fuel (lower heating value, chemical composition, density, viscosity). And the standard atmospheric conditions, to determine all the thermophysical properties of the fluids that interact.

Subsequently, a model should be determined, analytical, experimental, or numerical, using the properties indicated above. The present study focuses on analytical modeling, therefore it requires the use of differential equations to determine the variables of interest of pressure, temperature, and energy release as a function of the crankshaft angle. In addition, the component of the water droplet is added, modeling its interaction with the hot gases and its evaporation as a function of time.

Finally, the set of equations must be solved and a characterization of the behavior of the motor must be obtained. In this way, the pressure and temperature inside the chamber are known throughout the power cycle, the rate of heat released from the cylinder, the fraction of mass burned, the thermal efficiency, and, during the last two strokes, it is possible to know the coefficient of convection h that characterizes the droplets injection into de cylinder. This last parameter will affect the performance of the engine in the additional strokes and can be incorporated to refine the heat transfer model for the combustion gases.

Otto engine

The Otto cycle considers the idealized case of an internal combustion engine whose combustion is so fast that the piston does not move during the combustion process, thus it is assumed to take place at constant volume (Ferguson and Kirkpatric 2016). For the 6-stroke engine, the addition of the two new strokes is modeled in an analogous way to the compression and expansion for the 4-stroke cycle, replacing the combustion with gasoline by an injection of water. However, combustion in a spark ignition engine is not necessarily at constant volume and the actual engine temperature and pressure profile data do not match the idealized Otto models, thus requiring more realistic models (Ferguson and Kirkpatric 2016; Heywood 2018). Including vaporization delay for the specific engine condition to validate the approach.

The present study uses the finite energy release model of an engine cycle in which the heat addition is specified as a function of the crank angle. These energy release models can address issues that simple gas cycle models cannot (Ferguson and Kirkpatric 2016; Mohammed et al. 2019). (i.e., the effect of spark timing or heat and mass transfer on engine work and efficiency). Figure 5a compares the idealized Otto cycle for a 4-stroke engine and the energy release model as a function of angle. Clear differences are seen between the two, while the first one presents piecewise functions, the release of energy model allows a continuous function, better coupled to the experimental data.

Fig. 5
figure 5

ICE models. Idealized in-cylinder pressure vs release energy model for a 4th-stroke Otto engine, b for 4th-stroke Diesel, c Six stroke engine with a partial opening of exhaust valves, d Six stroke engine with total opening of exhaust valves

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For the present study, the Wiebe function is used to model the release of energy, such that it can be used in a wide variety of combustion systems (Ferguson and Kirkpatric 2016; Mohammed et al. 2019). The fraction of fuel burned is defined as (Ferguson and Kirkpatric 2016; Heywood 2018):

$$X_{b,O} = 1 - \exp \left[ { - a\left( {\frac{{\theta - \theta_{s} }}{{\theta_{d} }}} \right)^{n} } \right]$$
(1)

Depending on the crank angle, starting and duration of combustion \(\theta ,\theta_{s} , \theta_{d}\) respectively, and the values \(a,n\), which depend on the type of motor. However, values of fit the experimental data well (Heywood 2018).

$$v\left( \theta \right) = v_{c} + \frac{{v_{d} }}{2}\left[ {\sqrt {\varepsilon^{2} - \sin^{2} \theta } + 1 - \varepsilon - \cos \theta } \right]$$
(2)

The cylinder pressure as a function of °CA is obtained using the first law of thermodynamics, where P is the cylinder pressure, γ is specific heat ratio, \(v\left( \theta \right)\) is cylinder volume, and Q is the net heat input.

$$\frac{\text{d}P}{{\text{d}\theta }} = - \frac{\gamma P}{v}\frac{\text{d}v}{{\text{d}\theta }} + \frac{\gamma - 1}{v}\frac{\text{d}Q}{{\text{d}\theta }}$$
(3)

The differential of the heat release from the engine combustion can be obtained with the accumulative heat \(Q_{acc}\) and considering the convective heat transfer where h, the convective heat-transfer coefficient, can be estimated from a typical Nusselt correlation. (i.e., Hohenberg Woschni or Annand’s correlation) (Annand 1963; Woschni 1967; Hohenberg 1979; Dabbaghi et al. 2021).

$$\frac{\text{d}Q}{{\text{d}\theta }} = \frac{{hA\left( \theta \right)\left( {T_{w} - T\left( \theta \right)} \right)}}{\text{d}\theta /\text{d}t} + \frac{{\text{d}Q_{acc} }}{\text{d}\theta }$$
(4)

Finally, the temperature can be derived from the ideal gas equation in terms of the differential pressure and volume defined ahead.

$$\frac{\text{d}T}{{\text{d}\theta }} = \frac{1}{{m_{a} R_{a} }}\left[ {\frac{V\text{d}P}{{\text{d}\theta }} + \frac{P\text{d}V}{{\text{d}\theta }}} \right]$$
(5)

There is not a consensus on the fifth stroke initial conditions. Thus, at the final of the fourth stroke three set of conditions can be considered:

  1. 1.

    There is a partial exit of exhaust gases and a decrease in in-cylinder gas mass. By closing the valves, the pressure in the cylinder will be greater than atmospheric pressure but less than at the end of the fourth stroke (Fig 5c).

  2. 2.

    There is a total opening of the valves that allows the pressure of the cylinder to be equal to the atmospheric pressure, and a fraction of exhaust gases can escape (Fig 5d).

  3. 3.

    There is no exit of Combustion gases. The total gases are recompressed, and the initial pressure will be the final pressure of the expansion stroke.

As a result, (3) presents a problem due to the recompression process. Since the system will be doing more work by compressing all the hot gases, thus the work gained by the water injection vaporization may not be enough to compensate for the gas compression on the 5th stroke. However, (3) has the advantage of having a higher internal energy (pressure and temperature) at the beginning of the fifth stroke, which allows an increase in pressure at the stroke (time) of steam and gas expansion.

On the other hand, alternatives (1) and (2) present a reduction in pressure and combustion gases. Therefore, less work is done in the compression of the gases compared with (3). Still, the temperature and pressure at the beginning of the sixth race will be lower.

From the literature, most analytical articles work with conditions (2) and (3), due to the complexity that condition (1) represents. However, studies that implement simulation techniques or experimental analysis work with (1) as the closest condition to reality. Likewise, Yang et al. (2023) was able to optimize the IMEP depending on the point of closure of the spatial valves, such that the IMEP was the highest under the condition that the duration of the partial escape was CA 180°.

In consequence, defining the pressure and amount of mass for the start of the two additional strokes is essential for the characterization of the system, the injection timing of droplets, their size, and their mass flow to reduce the negative compression work. There is a need for a thermodynamic and heat transfer model that allows comparison between each set of conditions.

Diesel engine

The difference between the Diesel and Otto cycles is that the Diesel cycle considers the idealized case in which energy is added at a constant pressure. However, the combustion model for the gases in a fuel injection engine does not necessarily happen under constant pressure and the temperature and pressure of the ideal Diesel model may not agree with experimental data. Moreover, modeling the six-stroke cycle with piecewise functions does not correctly describe the interaction of the gases in the piston. Therefore, models that describe the properties of like pressure or temperature as a function of crankshaft angle would allow better coupling with experimental models, see Fig. 4b

The pressure and temperature expressions (3) and (5) used for the Otto engine can be used for the Diesel, considering a different expression for the fraction of gases burned. However, studies have also shown the importance of radiation heat transfer in diesel engines (Treiber 1928; Hohenberg 1979; Yoshikawa and Reitz 2009).

There are two models that can be used to model the fraction of fuel burned, the one proposed by Wiebe and the one proposed by Heywood (2018), Watson and Janota (1982).

A modification of the Wiebe function is used to model the release of energy, the double Double-Wiebe is defined as (Yasar et al. 2008):

$$X_{b,D} = \left( {1 - \alpha_{wall} } \right)\left( {1 - \exp \left( { - a\left( {\frac{{\theta - \theta_{s} }}{{\theta_{b} }}} \right)^{n + 1} } \right)} \right) + \alpha_{wall} \left( {1 - \exp \left( { - a\left( {\frac{{\theta - \theta_{s} }}{{\theta_{b} }}} \right)^{n + 1} } \right)} \right)$$
(6)

where \(\alpha_{wall}\) is the fraction of the mixture burned in the slow combustion region and \(K_{wall}\) is the ratio of the Diesel burn duration and Otto burn duration. Equation (6) is valid until the start of the fourth stroke.

For the six-stroke Diesel engine, the first part of thermodynamic modeling is, in fact, the same as a conventional four-stroke Diesel engine. However, for the two additional strokes, the model is based on the Otto cycle with isochoric injection.

In addition, the start of the fourth stroke can be modeled according to the three alternatives described above. For the present study, the equations for alternative (2) are presented as a partial release of exhaust gases with the valves closing at a specific crank angle. The gases are then compressed until a jet of water is immediately injected into the cylinder. Vaporizing is fast enough that the piston does not move during injection and an isochoric ideal process modelling is acceptable. Therefore, the last two strokes with water-steam can be modeled as Otto combustion and expansion, regardless of the engine system (Conklin and Szybist 2010).

The equations used for the ideal Otto and Diesel cycle are summarized in Table 1, according to equations developed by Kolchin and Demidov (1984), İÇİNGÜR et al. (2013), Ferguson and Kirkpatric (2016), Arabaci and Kilic (2018), Cengel et al. (2014) for each process. The water injection process is defined from thermodynamic states. Since there is no ignition from fuel burning, simple control volume analysis reduces to a fixed volume at TDC with a mass of incoming water at a given enthalpy or temperature (Cengel et al. 2014; Chen et al. 2015). Where the internal energy change in the combustion gases from state 6 to 7 is equal to the enthalpy variation of the water injected. Assuming adiabatic conditions and instant water injection, the energy conservation equation reduces to the equation at the top dead center TDC at 720 °CA. The specific internal energy of state 7 can then be found, to fully define the state.

Table 1 Thermodynamics cycle processes
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Water droplet

In order to improve the understanding of the six-stroke engine, it is essential to conduct research on the evaporation of water droplets in high-temperature and high-pressure environments. This research is crucial to comprehend the behavior of water inside the cylinder during the fifth stroke when water is injected. However, none of the reviewed articles have addressed the evaporation of water droplets at the ignition time. The existing literature commonly assumes that water injection and vaporization are instantaneously homogeneous (Yuen and Chen 1978; Conklin and Szybist 2010; Owunna and Ikpe 2021). Nonetheless, in real engine systems, the interaction between water and combustion gases remains challenging due to the finite duration of this process.

Models that explain the evaporation of water droplets in environments similar to the piston can be utilized by incorporating their results into the equations of the Otto or diesel cycle to account for heat transfer. Additionally, Volkov et al. (2017) employed an experimental approach to study the evaporation of a single water droplet within a high-temperature environment. They utilized a planar laser-induced fluorescence (PLIF) technique with five different schemes. The fifth scheme is of interest to this article as it simulates the free fall of a water droplet in a high-temperature muffle. It is important to note that in the engine, the droplets do not fall freely but are expelled at a high initial velocity, which is relevant for determining the instantaneous Nusselt and h values.

From Kuznetsov et al. (2020) can be highlighted the analytical expressions for the heating rate \(W_{h}\), the evaporation rate \(W_{e}\) and the correlations of the form Nu = f(Re), as functions of the environment temperature where the water droplet is released, its geometrical parameters and its thermophysical properties.

$$w_{h} = \Delta T_{d} /\Delta t_{h} = \left( {T_{d}^{*} - T_{d}^{0} } \right)/\Delta t_{h}$$
(7)
$$w_{e} = \rho_{d} \left( {R_{d}^{0} - R_{d}^{*} } \right)/\Delta t_{d}$$
(8)
$$w_{e} = Nu\lambda_{a} \left( {T_{a} - T_{s} } \right)/\left( {2R_{d} Q_{e} } \right)$$
(9)
$$w_{e} = \Delta m_{d} /\left( {S_{d}^{*} \Delta t_{d} } \right)$$
(10)

where

$$\Delta m_{d} = \rho_{d} 4/3\pi (R_{d\left( n \right)}^{*3} - R_{{d\left( {n - 1} \right)}}^{*3} )$$
(11)
$$S_{d}^{*} = 2\pi (R_{d\left( n \right)}^{*2} - R_{{d\left( {n - 1} \right)}}^{*2} ) - \pi (R_{d\left( n \right)}^{*} + R_{{d\left( {n - 1} \right)}}^{*} )d_{h}^{0}$$
(12)

Another thing that must be important to bring in this review is the update that they’ve made about the equation proposed by Yuen and Chen (1978) and Renksizbulut and Yuen (1983a, 1983b) which is of the form:

$$\text{Nu} = \left( {2 + 0.6\text{Re}^{\frac{1}{2}} \text{Pr}^{\frac{1}{3}} } \right)/\left( {1 + B} \right)^{1.4}$$
(13)

where B is a mass-transfer coefficient depending on the environment temperature given by Yuen and Chen (1978). The denominator of such equation, that needs a B coefficient from tables developed experimentally, is replaced by Kuznetsov et al. (2020), who gives an equation in the form:

$$\text{Nu} = \left( {2 + 0.6\text{Re}^{\frac{1}{2}} \text{Pr}^{\frac{1}{3}} } \right)/\left( {1 - \frac{{T_{s} }}{{T_{a} }}} \right)^{{T_{s} /T_{b} }}$$
(14)

Consequently, (14) presents an analytical expression for the Nusselt, depending on the surface temperature, the temperature of the air, and boiling temperature, thus avoiding the use of tables and experimental analysis.

Conclusion

In conclusion, this study provides a comprehensive understanding of six-stroke engines and presents a thermodynamics model governing six-stroke Otto and Diesel engines. Additionally, a thorough literature review on water injection in hot gas environments within the engine cylinder is described to enhance the understanding of the evaporation process. The main findings can be summarized as follows:

  1. 1.

    Limited investigations have focused on numerically and experimentally studying the advantages of six-stroke engines compared to four-stroke engines, particularly when operating with different fluids during the additional strokes, such as air or alcohol.

  2. 2.

    The concept of a six-stroke engine with a steam duty cycle can be further refined by an in-depth study of its thermodynamics. This involves developing a comprehensive model that accurately explains thermodynamic cycles as a function of crankshaft motion, incorporating factors such as heat transfer, water droplet vaporization, and friction losses. Addressing these aspects will lead to a more accurate understanding of engine performance.

  3. 3.

    The emission-reduction potential of six-stroke engines is substantiated by cases showcasing substantial reductions, including a 90% decrease in NOx concentration and significant drops in HC. Nevertheless, it is crucial to acknowledge the complexity of emissions control, as indicated by scenarios in which HC emissions increased by 85%, while NOx emissions were reduced by 80%. A comprehensive approach to emissions management is imperative to maximize their environmental benefits.

  4. 4.

    It is necessary to conduct a study that analytically, experimentally, or numerically compares the closing conditions in the fifth stroke of six-stroke engines. The role of numerical modeling: numerical modeling and computational fluid dynamics (CFD) simulations have proven valuable in understanding energy distribution and the potential for emissions reduction in six-stroke engines. These models provide insights into engine behavior, with up to 40% of the IMEP loss in six-stroke engines recoverable through water injection, highlighting the promise of this technology.

There is significant potential for implementing various technologies to enhance IC engine performance, including advanced engine combustion modes, novel and cost-effective engine architectures, and the utilization of renewable fuels. The unique characteristics of the six-stroke engine offer promise in advancing current engine technologies.

In conclusion, this study emphasizes the need for further research on fuel modeling, comprehensive thermodynamic analysis, and the exploration of innovative technologies to enhance IC engine performance. By delving into these areas, we can fully unlock the potential of the six-stroke engine and contribute to the development of more efficient and sustainable engines for the future.