*3.3. Engine Transient Response*

For the purpose of investigating the transient response of the MVEM as well as the compressor model developed in this paper, two simulation experiments are carried out in this paper. In the first experiment, the engine setting speed steps down from 72 rpm to 66.8 rpm at 500 s, from 66.8 rpm to 60.7 rpm at 1000 s, from 60.7 rpm to 57.1 rpm at 1500 s, from 57.1 rpm to 50.7 rpm at 2000 s, from 57.1 rpm to 45.4 rpm at 3000 s, from 45.4 rpm to 38.3 rpm at 4000 s. These engine speeds correspond to 100%, 80%, 60%, 50%, 35%, 25% and 15% engine load, respectively, thus covering the whole engine operating envelope. As shown in Figure 12, the engine rotational speed, brake power and fuel index are able to stabilize in a short time, whereas it takes more time for the other engine performance parameters until stabilization. This phenomenon is caused mainly by the turbocharger inertia as well as the relatively large volume of the scavenging and exhaust manifolds. As shown in Figure 12b, with the decrease in engine setting speed, the turbocharger rotational speed gradually decreases. Starting from 4050 s, the turbocharger rotational speed becomes lower than 7200 rpm, which is the lowest speed available in the compressor performance map, and then enters into the LS o ff-design operating area, finally the turbocharger rotational speed stabilizes at 4990 rpm. As can be inferred from the trajectory of the compressor operating points as shown in Figure 12j, the compressor model developed in this paper is capable of interpolating within the design operating area and extrapolating to the LS off-design operating area reasonably and robustly.

**Figure 12.** Simulation results for the engine transient operation with setting speed changes: (**a**) engine rotational speed; (**b**) turbocharger rotational speed; (**c**) exhaust manifold and turbine outlet temperature; (**d**) scavenging manifold and compressor outlet temperature; (**e**) scavenging and exhaust manifold pressure; (**f**) fuel-air equivalence ratio; (**g**) brake power; (**h**) fuel index; (**i**) BSFC; (**j**) compressor operating points trajectory.

Figure 13 presents the engine transient response with a setting speed of 72 RPM when the resistant torque steps up at the 100th s. As can be observed from this figure, the engine rotational speed drops down quickly when the resistant torque increases. Then, under the control of engine governor, more fuel will be injected into the cylinders to balance the increased resistant torque for stabilizing the engine speed. Consequently, more thermal energy will be stored in the exhaust gas, which drives the turbocharger to work with higher rotational speed. Finally, the scavenging manifold pressure increases and more air flows into the engine cylinders. In addition, as can be inferred from the trajectory of the

compressor operating points as shown in Figure 13j, the compressor model is able to extrapolate to the HS o ff-design operating area reasonably and robustly.

**Figure 13.** Simulation results for the engine transient operation with resistant torque changes: (**a**) engine rotational speed; (**b**) turbocharger rotational speed; (**c**) exhaust manifold and turbine outlet temperature; (**d**) scavenging manifold and compressor outlet temperature; (**e**) scavenging and exhaust manifold pressure; (**f**) fuel-air equivalence ratio; (**g**) brake power; (**h**) fuel index; (**i**) BSFC; (**j**) compressor operating points trajectory.

### **4. Coupling of MVEM with Cylinder Pressure Analytic Model**

As discussed in the Introduction section, MVEM is unable to predict the in-cylinder pressure trace, which weakens MVEM's practical value to some extent. To solve this problem, the cylinder pressure analytic model proposed by Eriksson and Andersson for the four-stroke spark ignition (SI) engine was adapted to the 7S80ME-C9.2 marine two-stroke diesel engine and coupled to the MVEM developed in this paper [10]. The major merit of this analytic model is that the calculation of in-cylinder pressure is completely based on algebraic equations without needing to solve any differential equation as it is done in the 0-D model, thus greatly accelerating the model's simulating speed in predicting in-cylinder pressure trace.

In this section, the cylinder pressure analytic model is firstly adapted to the marine two-stroke diesel engine with its basic idea shown in Figure 14; then, the model parameter calibration procedure is discussed in detail; finally, the model is coupled to the MVEM and its in-cylinder pressure trace predictive ability is evaluated by comparing with the measured indicator diagram.

**Figure 14.** Basic idea of the cylinder pressure analytic model (SPC: Scavenging ports closing; SPO: Scavenging ports opening; EVC: Exhaust valve closing; EVO: Exhaust valve opening).
