**1. Introduction**

The marine large scale two-stroke diesel engine is widely adopted as the prime mover for the large merchant ships mainly because of its high thermal efficiency, reliability as well as the ability of burning low grade fuel, i.e., heavy fuel oil (HFO). For complying with the stringent international environmental legislations and obtaining improved fuel efficiency, engine manufacturers have developed new versions of marine engines, mainly including marine electronically controlled diesel engines and marine dual-fuel engines [1–3].

In consideration of the large size and weight of marine large scale two-stroke diesel engines as well as the substantial manpower and financial power required for carrying out experimental studies, various engine simulation techniques have been widely adopted for investigating engine performance, designing and testing the fault diagnosis algorithm, as well as developing the engine control system. Among these simulation models, 0-D models and mean value engine model (MVEM) are widely adopted by researchers mainly because of their fast running speed and satisfactory simulation accuracy. The di fference between the 0-D model and MVEM lies in the modeling approach for the cylinder. For the 0-D model, the cylinder is assumed as an open thermodynamic system, where the working medium is uniformly distributed in it. By applying mass and energy conservation laws and incorporating several relevant sub-models, the in-cylinder pressure trace can be predicted. Furthermore, the 0-D model is also capable of predicting engine performance at varying settings (e.g., varying the start of injection timing, exhaust valve opening/closing timing, turbine area, etc.), which is a special advantage in comparison to the MVEM [1]. In the book published by Eriksson and Nielsen, the MVEM is defined as "Mean value engine models are models where the signals, parameters, and variables that are considered are averaged over one or several cycles" [4]. In this respect, the mass and energy flow through the cylinder is assumed continuous for the MVEM, and the engine average performance over one or several cycles can be obtained. Consequently, the MVEM is able to run much faster than the 0-D model, which is therefore very suitable for cases that require fast running speed, such as the simulation of engine transients for a long period. On the other hand, despite similar predictive accuracy can be achieved by the two models, the in-cylinder pressure trace cannot be predicted by the MVEM, which is its major limitation [1,5].

In the literature, researchers tried to improve the predictive ability of the MVEM and the running speed of the 0-D model by adopting a "hybrid" modeling approach, meaning that di fferent modeling approaches can be adopted for di fferent engine components or di fferent phases of the engine cycle. This approach can e ffectively overcome the limitation caused by using only a single modeling approach. In the study carried out by Altosole et al., for meeting the requirement of real-time ship maneuvering simulation, the cylinder simulation was entirely based on a set of five-dimensional numerical matrices, each of which was generated by a 0-D model [6]. It was revealed from the simulation results that this modeling approach can achieve similar transient response but reduce the simulation time of about 99%; however, the in-cylinder pressure trace cannot be predicted. Nikzadfar and Shamekhi developed an extended MVEM for control-oriented modeling of diesel engines transient performance and emissions by replacing the cylinder model with two artificial neural networks (ANN). One is for predicting aspirated air mass flow, torque and exhaust gas temperature and the other for predicting soot and NOx emission [7]. Despite the fact that satisfactory predictive accuracy and running speed can be achieved with this extended MVEM, it still cannot predict the in-cylinder pressure trace. Based on the modular MVEM developed by Theotokatos [8], Baldi et al. proposed a combined mean value-zero dimensional model for a large marine four-stroke diesel engine, where the closed part of the cycle was represented by the 0-D model and the open part by the MVEM. The combined model fully takes the respective advantage of the 0-D model (ability to predict in-cylinder pressure trace) and MVEM (fast running speed) [9]. Nevertheless, it was pointed out by Theotokatos et al. that the 0-D model still needed to be called at each calculation step for the combined mean value-zero dimensional model, which made its running speed still scant for cases where engine transient simulation for a long period was required [1]. In the study carried out by Tang et al., the hybrid modeling approach was further improved by simplifying the in-cylinder pressure calculation during the scavenging and exhausting phases with two linear functions and abandoning engine cycles at certain intervals [5]. It was revealed that the modified model was able to predict the in-cylinder pressure trace and run as fast as the MVEM at steady state condition; however, during the transient process, the improvement in running speed is at the expense of predictive precision.

For practical applications that have high requirement on both predictive accuracy and running speed, the MVEM seems to be the best choice. However, due to the absence of a detailed mathematical description of in-cylinder working process, the in-cylinder pressure trace cannot be predicted with MVEM, which limits its practical value to some extent. This is the reason why 0-D model was incorporated into the MVEM in several studies [5,9]. However, it should be noted that even limited 0-D modeling will increase the model complexity and thus a ffect the running speed of the MVEM obviously. To solve this problem, the cylinder pressure analytic model proposed by Eriksson and

Andersson for the four-stroke SI (spark ignition) engine was modified and adapted to the 7S80ME-C9.2 marine two-stroke diesel engine in this paper [10]. By coupling the cylinder pressure analytic model to the MVEM, the MVEM is able to estimate the in-cylinder pressure trace. Furthermore, as the running speed of the cylinder pressure analytic model is much faster than the 0-D model, the merit of the MVEM in running speed is not a ffected significantly.

In consideration of the significant influence of compressor model on the simulation accuracy of the whole engine model, a novel compressor mass flow rate and isentropic e fficiency model was proposed in this paper based on the research results of a previous paper published by the first author, which compared and analyzed the predictive and extrapolative ability of several classical and recent proposed compressor mass flow rate and isentropic e fficiency empirical models. The incorporation of the novel compressor model will be very helpful for the MVEM to achieve satisfactory predictive accuracy in the whole engine operating envelope under both steady and transient conditions.

The MVEM developed in this paper is very suitable for applications that require both fast running speed and in-cylinder pressure trace predictive capability, for example, this MVEM has been attempted to be used in a VLCC (Very Large Crude Carrier) marine engine room simulator [11].
