# Dual-Fuel Combustion for Future Clean and Efficient Compression Ignition Engines
## Materials and Methods
### In-Cylinder Pressure Signal Analysis  
The combustion analysis was performed with an in-house developed one-zone model named CALMEC. This combustion diagnosis tool uses the in-cylinder pressure signal and the mean variables recorded during the experiments (engine speed, coolant, oil, inlet and exhaust temperatures, air, EGR, and fuel mass flow) as its main inputs. The full description of the model can be found in [29], and the main hypotheses are enumerated next:  
* The pressure is supposed homogeneous in the combustion chamber. This hypothesis is generally accepted since the fluid and the flame propagation velocity are lower than the speed of sound. * The fluid that evolves inside the combustion chamber is considered as a mixture of air, gaseous fuel, and burned products, which are considered to evaluate the thermodynamic conditions of the mass trapped in the cylinder. * An ideal gas behavior is assumed for the mixture that evolves in the combustion chamber. It is reasonable to accept this assumption for the air and burned products, however, it could seem inadequate for the gaseous fuel. In this sense, [PERSON] [30] compared the results from the combustion analysis model using different state equations for the gaseous fuel. The results confirmed that the differences in the mean temperature and Rate of Heat Release (RoHR) are small enough to accept the hypothesis. During the experiments, the in-cylinder pressure was measured with a resolution of 0.2 CAD using a Kistler 61215C pressure transducer coupled with a Kistler 5011B10 charge amplifier. The pressure traces from 150 consecutive engine cycles were recorded in order to compensate the cycle-to-cycle variation during engine operation. Then, the individual pressure data of each engine cycle was smoothed using a Fourier series low-pass filter. Once filtered, the collected cycles were ensemble averaged to yield a representative cylinder pressure trace, which was used to perform the analysis. The first law of thermodynamics was applied between intake valve closing (IVC) and exhaust valve opening (EVO), considering the combustion chamber as an open system because of the blow-by and fuel injection. The main result of the model used in this work was the Rate of Heat Release (RoHR), which is calculated as stated in Equation (1). \[RoHR=m_{cyl}\cdot\Delta u_{cyl}+\Delta Q_{W}+p\cdot\Delta V-\left(\overline{h} _{f,iny}-u_{f,g}\right)\cdot\Delta m_{f,eup}+R_{cyl}\cdot T_{cyl}\cdot\Delta m _{bb} \tag{1}\]  
The different terms found in the equation are explained below:  
* _RoHR_: This term corresponds to the thermal energy released by the fuel assuming a constant heat power along the combustion event. * \(m_{cyl}\cdot\Delta u_{cyl}\): This is the sensible internal energy variation of the gas trapped in the control volume. As detailed in [PERSON] [31], this term is calculated by means of a specific correlation for each specie. For each temporal step, these correlations are solved as a function of the mean temperature in the control volume while pondering by the mass fraction of each specie. * \(\Delta Q_{w}\): This terms accounts the heat transfer from the gas trapped in the control volume to the surrounding surfaces of the piston, liner, cylinder-head and valves. The model do not consider the possibility of fuel impinged in the wall. The instantaneous heat transfer coefficient between the gas and the different surfaces is based on Woschni [32] with some improvements detailed in [PERSON] et al. [33]. For the calculation of the different wall temperatures, a nodal heat transfer model was implemented [34]. * \(p\cdot\Delta V\): This term represents the total work made by the gas trapped in the control volume during the calculation period. For the instantaneous calculation of the combustion chamber volume, a mechanical deformations model is considered. This submodel takes into account both the pressure made by the gas on the piston head and the inertial forces generated by the alternative movement of the masses.