# Thermodynamic Analysis of In-Cylinder Steam Assist Technology within an Internal Combustion Engine
## 2 Methodology  
### Thermodynamic Model and Validation  
A schematic of the in-cylinder steam-assisted cycle and its thermodynamic process are shown in Figure 1. Some assumptions for the thermodynamic cycle process are given to simplify the computation. The compression and expansion strokes are assumed to be adiabatic processes. Compared to conventional gasoline engine, high-temperature and high-pressure water is directly injected into the combustion, which absorbs combustion heat and generates high-temperature and high-pressure steam instantly. This leads to an enhancement in in-cylinder pressure, which leads to higher compression work and thermal efficiency. As shown in previous study, injected steam evaporates immediately as it is injected into the combustion chamber at the end of compression [33]. Therefore, the effect of in-cylinder steam evaporation on the combustion process can be ignored for the theoretical thermodynamic analysis [26; 34]. The established theoretical in-cylinder steam-assisted cycle is a closed system [26; 28]. According to the first law of thermodynamics, its energy equation can be expressed as:  
\[\delta U=\delta Q+\delta W \tag{1}\]  
where \(U\) is internal energy, \(Q\) is thermal energy, and \(W\) is work. First, the thermal state for the Point \(1\) was calculated by the general gas equation:  
\[p_{1}V_{1}=mRT_{1} \tag{2}\]  
Then, assuming that the compression stroke of the proposed cycle is adiabatic in a closed system, the mixture is adiabatic compressed from Point \(1\) to Point \(2\) with a specific compression ratio:  
\[V_{2}=\frac{V_{1}}{\epsilon},\,s_{2}=s_{1} \tag{3}\]  
Figure 1: Schematic and \(P\)-\(V\) curve of the in-cylinder steam-assisted cycle. where \(\varepsilon\) is the compression ratio, and \(s\) is the specific entropy. Then, the energy equation for the compression stroke is:  
\[W_{12}=m\cdot\int_{T_{1}}^{T_{2}}c_{\text{\tiny{P}}}\cdot dT \tag{4}\]  
Here, \(W_{12}\) is the work in the compression stroke, \(m\) is the intake charge mass, \(T\) is temperature, and \(c_{\text{\tiny{P}}}\) is the specific heat at constant volume. Second, fuel burns within a constant volume, and its energy is released instantly, and the temperature after combustion \(T_{3}\) is calculated by the element potential method. Accompanied by the combustion process, high-temperature steam is introduced into the combustion chamber by an injector in the expansion stroke. The energy change during the steam injection process can be described as:  
\[m_{\text{w}}\cdot h_{\text{w}}=\int_{T_{4}}^{T_{4}}\left(m+m_{\text{w}}\right) \cdot c_{\text{\tiny{P}}}\cdot dT \tag{5}\]  
where \(m_{\text{w}}\) is the injected steam mass and \(h_{\text{w}}\) is its specific enthalpy. Except for the energy conversion, the working medium for the closed system increases after steam injection. Then, the expansion stroke of exhaust and high-temperature vapour is also assumed to be adiabatic in the closed system. The change in energy can be expressed as:  
\[W_{35}=\int_{T_{3}}^{T_{4}}m\cdot c_{\text{\tiny{P}}}\cdot dT+\int_{T_{4}}^{T _{4}}\left(m+m_{\text{w}}\right)\cdot c_{\text{\tiny{P}}}\cdot dT+\left(m+m_ {\text{w}}\right)\cdot\int_{T_{4}}^{T_{5}}c_{\text{\tiny{P}}}\cdot dT \tag{6}\]  
Here, \(W_{35}\) is the work in the expansion stroke. In order to maintain the steam in a fluid state, it is pressurized to >10 MPa before the heat exchanger. The energy of pump consumption can be written as:  
\[W_{\text{pump}}=m_{\text{w}}\cdot\int_{P_{\text{initial}}}^{P_{\text{ injection}}}v\cdot dp/\eta_{\text{pump}} \tag{7}\]  
where \(W_{\text{pump}}\) is the work consumed by the pump, \(v\) is specific volume, \(p\) is injection pressure, and \(\eta_{\text{pump}}\) is the pump's efficiency.