*3.2. Engine Steady State Performance*

In order to validate the MVEM developed in this paper, the engine steady state operation was simulated at 15%, 25%, 50%, 75%, 80% and 100% of the engine MCR point. The predicted engine performance parameters were compared to the respective measured values provided in the engine shop trial report, whereas their relative errors are presented in Table 3. To assess the prediction accuracy of the MVEM developed in this paper, the simulation results shown in the paper published by Tang et al. from the same research group is also presented in Table 3 for comparison [5]. The same engine was adopted as the simulation object in Tang et al. but the engine model was developed by using the 0-D modeling approach [5].


**Table 3.** Relative error of the engine performance parameters.

As can be observed from Table 3, satisfactory predictive accuracy was obtained at each investigated engine loading condition with all the relative errors of brake power and BSFC (Brake Specific Fuel Consumption) less than 1%, whereas most of the relative errors of the other engine performance parameters are less than 4%. The measured turbocharger rotational speed is 4981 rpm at 15% engine load, which is lower than the lowest speed available in the compressor performance map. On the other hand, the predicted turbocharger rotational speed is 4979 rpm at this load condition with an extreme low relative error of only −0.043%, indicating the fidelity of the novel compressor model when extrapolating to the LS area. In addition, except for the 50% engine load, the relative errors of the compressor outlet temperature are all around 1%, indicating the satisfactory predictive accuracy of the zonal compressor isentropic efficiency model.

In the research carried out by Tang et al., only the relative errors of brake power, BSFC, scavenging manifold pressure, exhaust manifold temperature and turbocharger speed are presented; in addition, the relative errors at 15% engine load are not provided, perhaps it is because unsatisfactory simulation accuracy was achieved at this load condition [5]. For brake power, BSFC and turbocharger rotational speed, better simulation accuracy is generally obtained with the MVEM. The compressor model developed in this paper contributes to the better simulation accuracy of the MVEM in turbocharger rotational speed with respect to the 0-D model developed by Tang et al. where the compressor is modeled by using look-up table method [5]. Although better simulation accuracy is achieved with the 0-D model for scavenging manifold pressure and exhaust manifold temperature, the difference is not significant and they all meet the requirement on simulation accuracy; on the other hand, it should be noted that the MVEM runs much faster than the 0-D model.

As the model calibration procedure was carried out based on the measured engine performance parameters provided by the engine shop trial report and the model validation was also implemented by comparing the predicted results to these measured ones, therefore, in order to further validate the fidelity of the MVEM, the Computerized Engine Application System-Engine Room Dimensioning tool provided in the official website of MAN Diesel & Turbo is used to generate engine performance parameters within the engine load region from 15% to 100%. However, it should be noted that the engine performance parameters generated by using CEAS (Computerized Engine Application System) tool is for 7S80ME-C9.5 engine and the respective LHV (Lower Heating Value) of fuel is 42700 kJ/kg, whereas the investigated engine in this paper is 7S80ME-C9.2 and the LHV is 42151 kJ/kg, which will inevitably cause deviations on the engine performance parameters between the engine shop trial report and the CEAS. Despite these limitations, the results generated by CEAS is very valuable for reference in investigating the qualitative changing trend of engine performance parameters with engine load condition.

Figure 11 presents the engine performance parameters predicted by the MVEM and calculated by the CEAS within the load region from 15% to 100%. In addition, the measured values obtained from the engine shop trial report are also plotted in Figure 11 for reference. As can be observed from Figure 11, despite the existing of deviations, the simulation results for brake power, SFOC, scavenging manifold pressure and temperature and the turbine outlet temperature all agree well with the results obtained from the CEAS qualitatively. In addition, the other engine performance parameters also vary reasonably with the engine load.

At 65% engine load, the BSFC and turbine outlet temperature predicted by the MVEM reaches the minimum, indicating that the engine and turbocharger achieves the optimal operating state, which is consistent with the fitted BSFC curve based on the measured data as shown in Figure 11b. It should be noted that this optimal load is obviously lower than that of marine two-stroke diesel engines designed in earlier years. One reason of this relatively low optimal engine load is that low steaming is taken into account during the ship design phase in recent years. Noticeable discontinuity is observed at 35% engine load and this is because that below this load, the auxiliary blower is activated, which results in a larger amount of scavenging air supplied to the cylinder and thus lowers the fuel-air equivalence ratio as shown in Figure 11j. Consequently, with respect to 35% engine load, the fuel-air equivalence ratio at 30% load decreases from 0.3182 to 0.2872, the exhaust gas manifold temperature decreases from 573.3 K to 542.2 K and the turbine outlet temperature decreases form 515 K to 492.5 K; in addition, the scavenging manifold temperature increases from 299.2 K to 304.8 K mainly owing to the compression effect by the auxiliary blower. When the engine load decreases from 25% to 20%, the exhaust outlet temperature increases slightly from 486.9 K to 488.4 K, whereas it decreases from 488.4 K to 486 K when the engine load decreases from 20% to 15%. The opposite phenomenon in the two engine load interval (25%–20% and 20%–15%) is caused probably by the different changing rate of fuel injection rate and air mass flow rate with engine load, which is represented by the changing trend of fuel-air equivalence ratio as shown in Figure 11j.

**Figure 11.** *Cont*.

**Figure 11.** Steady state simulation results and comparison with engine shop trial report and CEAS (Computerized Engine Application System): (**a**) brake power; (**b**) brake specific fuel consumption (BSFC); (**c**) exhaust manifold pressure; (**d**) exhaust manifold temperature; (**e**) scavenging manifold pressure; (**f**) scavenging manifold temperature; (**g**) compressor outlet temperature; (**h**) turbine outlet temperature; (**i**) turbocharger rotational speed; (**j**) fuel-air equivalence ratio.
