**2.6 Steady-state engine-model tuning example**

The procedure outlined above allows the 1-D model of a turbocharged engine to obtain a rather high degree of predictability, not only in a qualitative sense, but also from a quantitative point of view. It was followed almost exactly in this way in (Baratta et al, 2010), from which Fig. 5 is taken. The engine features are reported in Table 1.

As can be seen, the engine model is generally well calibrated in all the tested cases. With reference to the whole intake system, and the portion of the exhaust ports within the cylinder head, the wall temperatures at the fluid side were set to specific values, which were selected on the basis of the outcomes of the experimental tests. The wall temperature was evaluated taking account of the gas-wall heat transfer for the pipes downstream from the exhaust ports and the external temperature was set equal to the value in the cell cabinet. The intake and exhaust ports were modelled as straight pipes, and heat-transfer multipliers were thus introduced to account for the bends, roughness, the additional surface area and turbulence caused by the valves and stems (Gamma Technologies, 2009). There was no need to set heat-transfer multipliers elsewhere in the intake system or to add friction multipliers to the model because the pressures and temperatures in the engine manifolds and ports were well reproduced (Fig. 5a,c,d). The agreement between the simulated and experimental values of PFP (peak firing pressure, Fig. 5e) and engine brake torque (Fig. 5f) demonstrate the accuracy of the combustion and engine friction sub-models, respectively. The above

Numerical Simulation Techniques for the

*cmp*

**2.7 Transient engine simulation** 

evolution versus time.

Number of

the turbine and compressor cycle-averaged power:

*T T cycle cycle*

consistent with the uncertainty of the pressure measurements.

The following aspects should also be taken into account:

Prediction of Fluid-Dynamics, Combustion and Performance in IC Engines Fuelled by CNG 271

experimental pressure at the turbine inlet and the experimental shaft speed, and to balance

<sup>1</sup> <sup>1</sup> ' 1

*m c T PR dt m c T PR dt*

(11)

, , 0 0

*air p in cmp cmp exh trb p in trb*

cylinders 6 (in line) Displacement 7.78 dm3

Table 1. Characteristics of a 7.8 litre turbocharged CNG engine (Baratta et al., 2010).

In particular, it is worth referring to the WOT conditions in Fig. 5, in which the first three points (engine speeds between 0.35 and 0.5 on the normalized scale) were characterized by a closed waste-gate (WG) valve, whereas the WG was partially open for the remaining two points. In those cases, the EM was selected on the basis of both the shaft speed and the pressure at the turbine inlet. MFM was selected so as to match the experimental pin,trb in the closed-WG points, and was then kept constant in the open-WG ones. The combined effect of MFM, EM, and WG position resulted in a slight overestimation of the turbine backpressure compared to the experiments for the open-WG points (Fig. 5c), although the differences are

The simulation of the transient behaviour of an engine by means of a 1-D simulation code is more challenging than a steady-state modelling approach. In fact, in a steady-state simulation, only the 'converged' results are significant, and the code is run until the differences in the engine variables are negligible in two consecutive simulated cycles. In a transient simulation, in which the engine speed and/or load versus time change, the model should accurately reproduce not only the engine variable at the end of the transient, but also their

Engine models that have to be used for transient simulation need a more careful calibration. In particular, it is not sufficient to set the model parameters with reference to the steady-state full-load conditions. This holds for all submodels, and was demonstrated in (Lefebvre & Guilain, 2006) for the combustion model. In fact, by simulating load transients using constant full-load combustion parameters, the model results presented unacceptable deviations from the experimental ones, and did not allow transient behaviour to be predicted correctly, or different engine configurations to be compared. The model inaccuracy decreased when the combustion process was modelled as a function of the engine load and speed, and the maps were included in GT-Power, and it was further reduced when the same procedure was followed for the in-cylinder heattransfer coefficient (c0 in Eq. (8)). A similar procedure was followed in (Baratta et al., 2010).


Number of valves 4 (per cylinder) Compression ratio 11:1 Bore 115 mm Turbocharged Yes Stroke 125 mm Intercooler Yes

1 1 ' 0 0 '

 

> 

Fig. 5. Model results under steady-state working conditions, as functions of the engine speed. (a): Manifold Absolute Pressure; (b): air mass-flow rate; (c): Pressure at the turbine inlet (cylinder 1 side); (d): Temperature at the turbine inlet; (e): Peak Firing Pressure (cylinder 1); (f): Engine brake torque. Each quantity is normalized to a specific value (Baratta et al., 2010).

calibration was made with reference to the engine model without the turbocharger. Subsequently, turbocharger and intercooler (IC) were added and the pressure at the turbine outlet was tuned first, acting on the friction multipliers of the pipes located downstream from the turbine. Then, the turbine MFM and EM were adjusted so as to match both the experimental pressure at the turbine inlet and the experimental shaft speed, and to balance the turbine and compressor cycle-averaged power:


Table 1. Characteristics of a 7.8 litre turbocharged CNG engine (Baratta et al., 2010).

In particular, it is worth referring to the WOT conditions in Fig. 5, in which the first three points (engine speeds between 0.35 and 0.5 on the normalized scale) were characterized by a closed waste-gate (WG) valve, whereas the WG was partially open for the remaining two points. In those cases, the EM was selected on the basis of both the shaft speed and the pressure at the turbine inlet. MFM was selected so as to match the experimental pin,trb in the closed-WG points, and was then kept constant in the open-WG ones. The combined effect of MFM, EM, and WG position resulted in a slight overestimation of the turbine backpressure compared to the experiments for the open-WG points (Fig. 5c), although the differences are consistent with the uncertainty of the pressure measurements.
