## 2 Methodologies
### Measurement of in-Cylinder Pressure Diagrams and Calculation of Rate of Heat Release  
In-cylinder pressure diagrams were measured through a dedicated system, sampling four signals at a frequency rate selected according to the engine rotational speed in order to obtain a time period corresponding to a 0.1 crank angle rotation (i.e., 90 kHz for n = 1500 rpm, 120 kHz for n = 2000 rpm and 150 kHz for n = 2500 rpm). An uncooled piezoelectric transducer (Kistler 6125B, Kistler, Winterthur, Switzerland) was fitted in the glow plug seat of a cylinder for pressure measurements, while fuel pressure upstream of the injector and injector energising current of the same cylinder were also acquired, by means of a piezo-resistive transducer (Kistler 4067A2000, Kistler, Winterthur, Switzerland) and a current sensor, respectively. Crank angle was measured with a photoelectric incremental encoder.  
The measuring chains were completed by signal amplifiers (Kiag Swiss 5001 and Kistler 4618A2, Kistler, Winterthur, Switzerland) and a high frequency sampling device (NI PCI-6123, National Instruments, Austin, TX, USA). Data were processed by dedicated virtual instruments developed in a LabVIEW(r) environment, to evaluate the absolute pressure levels, to filter in-cylinder pressure signal and to calculate the average pressure diagram, peak pressure and the relevant crank angle.  
The calculation of the experimental rate of heat release for each tested engine operating condition was based on Equation (7):  
\[(\Delta Q/\Delta\theta)=[k/(k-1)]\times p\times(\Delta V/\Delta\theta)+[1/(k- 1)]\times(\Delta p/\Delta\theta)+(\Delta Q_{\rm coolant}/\Delta\theta). \tag{7}\]  
Equation (7) was implemented in a Fortran code developed by the author. \(\Delta Q\) is the heat released during a crankshaft rotation \(\Delta\theta\). The application of the first thermodynamics law to the cylinder gas, assuming complete combustion and neglecting the variation of mass due to fuel injection [25; 26], allows us to identify the three terms of Equation (7). The first is related to the measured level of in-cylinder pressure, multiplied for the corresponding variation of instantaneous cylinder volume (computed from the measured crank angle and engine geometry characteristics). The second is related to the pressure gradient between two subsequent samples, while the third represents heat transferred to the coolant, estimated using the Hohenberg correlation [27].  
The composition of intake charge and components inside the cylinder during combustion were considered for the evaluation of specific heats and their ratio, as well as their temperature, applying thermodynamic property functions of different gases listed in Reference [28].  
The injected fuel mass flow rate in each calculation step was derived from experimental data of injected quantities. Actual values of the pilot, pre and main injections start and their duration were estimated by adding proper delays at the start and end of the current signal, according to Reference [29]. All the numerical values of the start of injections and timings presented in Tables 3-8 and Figures 2-6 were obtained through this approach.