# Thermodynamic Analysis of In-Cylinder Steam Assist Technology within an Internal Combustion Engine
## 2 Methodology
### Thermodynamic Model and Validation
Therefore, the indicated work output and thermal efficiency for each cycle would be:  
\[W_{\text{indicated}}=W_{12}+W_{35}-W_{\text{pump}} \tag{8}\]  
And  
\[\delta U=\delta Q+\delta W \tag{1}\]0  
where \(\eta_{\text{indicated}}\) is the indicated thermal efficiency, \(LHV_{\text{fuel}}\) is the low heating value of the fuel, which is assumed as 47.67 kJ/kg for the calculation, and \(m_{\text{fuel}}\) is the mass of fuel consumed per cycle. Based on this thermodynamic model, the thermodynamic state parameters of the constant-volume heating and adiabatic processes are acquired using the STANJAN software of Reynolds, which is an interactive computer program for chemical equilibrium analysis using the element potential method. Then, the thermodynamic state parameters after steam injection are acquired by a self-established MATLAB program. In addition to the thermodynamic model and its assumptions, the initial conditions and constraints are also critical parameters affecting the cycle's thermal efficiency and are listed in \[\delta U=\delta Q+\delta W \tag{1}\]1 The engine utilized in this theoretical model is a spark-ignition engine fuelled with iso-octane (i-C\({}_{8}\)H\({}_{18}\)) at the stoichiometric ratio (i.e., a conventional gasoline engine). The calculation is an ideal theoretical model, and the heat transfer through cylinders was not included for a maximum thermal efficiency of steam assist cycle. To be specific, the model simplifies the cycle as an adiabatic process with ideal heat release, and steam is introduced into the combustion chambers at TDC and evaporates instantaneously. The assumption of the instantaneous injection, vaporization, and mixing process are not physically realistic,but it is valid to estimate the upper bound on both the potential work output and thermal efficiency of this engine cycle. The combustion process focuses on the thermodynamic heat release, completed at the TDC combustion instantaneously. Thus, the combustion duration is negligible. The engine geometry, intake composition and initial temperature are set based on the parameters of the original spark-ignition engine, shown in \[\delta U=\delta Q+\delta W \tag{1}\]2 The initial cylinder pressure is set at the end of the intake stroke (0.1-0.3 MPa), which includes the load range of normally aspirated and turbocharged engines at various speeds. To investigate the gains of the compression ratio under different steam injection strategies, the compression ratio is varied from 10 to 16. To reveal the impacts of in-cylinder steam injection strategies on the thermal efficiency, the steam injection temperature range is 300-600 K. The steam injection pressure also varies from 20 to 50 MPa at a steam injection mass of 0-0.4 g. Finally, the thermodynamic model validates with the experimental pressure traces, as shown in \[\delta U=\delta Q+\delta W \tag{1}\]3 In the validated experiment, steam was injected into the cylinder at 473 K and 15 MPa, and the coolant temperature is 85 \({}^{\circ}\)C. The ideal heat release case considered the heat transfer loss and its heat transfer coefficient through cylinders was calculated based on the Woschni model. \begin{table}
\begin{tabular}{l c} \hline
**Item** & **Value** \\ \hline
**Initial conditions** & \\ \hline Fuel & Iso-octane \\ Ignition mode & Spark ignition \\ Low Heat value (kJ/kg) & 47.67 \\ Air-fuel ratio (-) & 14.7 \\ Initial temperature (K) & 298 \\ \hline
**Assumptions** & \\ \hline Heat transfer & Adiabatic \\ Steam injection timing & Instantaneous at TDC \\ Steam and air mixing & Instantaneous at TDC \\ \hline
**Boundaries** & \\ \hline Intake pressure (MPa) & 0.1–0.3 \\ Compression ratio (-) & 10–16 \\ Steam injection temperature (K) & 300–600 \\ Steam injection pressure (MPa) & 20–50 \\ Steam injection mass (g/cycle) & 0–0.4 \\ \hline \end{tabular}
\end{table} 
Table 1: Initial conditions, assumptions, and boundaries.