**2.5.1 Combustion and in-cylinder heat-transfer model calibration**

The accurate prediction of the in-cylinder pressure trace is mandatory for a good estimation of the engine indicated power, which in turn is fundamental to achieve the correct value of the brake power and torque. For this reason, the in-cylinder pressure is almost always acquired, on a crank angle basis, on engine test rigs. Experimental in-cylinder pressure is the main reference data for the calibration of combustion and in-cylinder heat transfer models. The xb profile versus crank angle can be extracted by means of a diagnostic analysis (also known as heat-release analysis), (Catania et al., 2003; Guezennec & Hamada, 1999; Heywood, 1988). Then, the 'experimental' xb profile can constitute the basis for the calibration of a predictive combustion model, can be used to set up specific lookup tables for the Wiebe parameters ('semi-predictive' approach), or it can be directly imposed in the model.

Some commercial codes, such as GT-Power, embed tools that are specifically developed for this purpose (Gamma Technologies, 2009). Using these embedded tools, most of the needed inputs for the burn rate calculation (such as trapped air-mass and residual fraction) can be worked out directly by running the simulation of the engine model. In addition, diagnostics is carried out with the same thermodynamics and chemistry as that used for the predictions. Sometimes, heat-release (HR) profiles from external diagnostic tools may be available. However, it should be pointed out that the different thermodynamic models between the diagnostic and the simulation codes can introduce additional uncertainties into the calculation of the gas thermodynamic properties as functions of temperature. For this reason, the tools provided by the adopted 1-D code for HR analysis should be used whenever possible.

As far as the calibration of the heat transfer within the cylinder is concerned, two alternatives are possible.

a. If the HR is worked out internally, the procedure allows the calibration of the heat transfer at the same time (Gamma Technologies, 2009). For example, the diagnostic tool embedded in GT-Power ('EngBurnRate' template) provides a few parameters that allow the heat-transfer calibration to be assessed. In particular, the heat transfer multiplier can be calibrated to minimize both the deviations of the so-called fuel 'lower heating value multiplier' (LHVM) from unity and the 'cumulative compression heat release'. The code determines LHVM on the basis of an energy balance, that is similar to the one proposed in (Baratta et al., 2005; Catania et al., 2003).

b. If the heat release has been determined previously and is directly imposed, the heat transfer can only be calibrated on the basis of the match between the experimental and numerical in-cylinder pressure. However, in this case, such a calibration is also affected by an additional uncertainty, due to the calculation of the gas thermodynamic properties with different sub-models. In some applications, it may be acceptable to keep the standard C0 coefficient, and to match the cylinder pressure by slightly shifting the HR profile. However, the alternative a) is preferable.

Once the heat transfer model has been calibrated at all the engine working points which have been investigated experimentally, the related heat-transfer multiplier values can be organized in lookup tables and then included in the engine model.
