**5. Conclusions**

In this article, a marine two stroke diesel engine MVEM with in-cylinder pressure trace predictive capability and a novel compressor model was developed.

A previous study carried out by the first author indicated that none of the compressor empirical mass flow rate models existing in the literature appears to achieve satisfactory predictive accuracy in the whole operating area. To solve this problem, the compressor whole operating area was divided into design, LS, HS and LPR operating areas by defining zonal division standard with appropriate functions, and then the compressor mass flow rate model that achieved the best predictive accuracy was selected for each operating area. In addition, an appropriate blending function was applied when the operating point enters into the LRP area from other areas to avoid the possible discontinuity.

The zonal compressor isentropic e fficiency model proposed in this paper was based on the Hadef model. By dividing the whole "Mass flow rate—actual specific enthalpy change" plane into several zones by using the iso-speed curves available in the performance map, the working characteristics of compressor within di fferent speed range can be captured much more accurately. It was revealed from the simulation results that with respect to the original Hadef model, the predictive accuracy of the zonal isentropic e fficiency model was e ffectively improved. In addition, satisfactory extrapolation accuracy was obtained with this zonal compressor isentropic e fficiency model.

As can be found from the trajectory of the compressor operating points during the transient process, the compressor model proposed in this paper is able to extrapolate to the LS and HS o ff-design operating areas reasonably and robustly; in addition, by comparing with the measured data provided in the engine shop trial report, the predictive accuracy of the engine performance parameters relevant to the turbocharger were all satisfactory at each steady state loading condition. Based on these simulation results, the fidelity of the proposed compressor model was validated. Due to the significant influence of the compressor on the engine steady state performance and transient response, the compressor model proposed in this paper is very helpful for improving the MVEM's predictive accuracy in the whole engine operating envelope.

By adapting the cylinder pressure analytic model to the 7S80ME-C9.2 marine two-stroke diesel engine, the MVEM is able to predict the in-cylinder pressure trace without impairing its merit in running speed. For achieving satisfactory predictive accuracy, the model parameters of the analytic model were finely calibrated by using the measured data and a 0-D engine model. At steady state condition, the extended MVEM runs as fast as the MVEM. During the transient process, the extended MVEM is able to achieve the running speed as similar as the MG model (0D + MVEM) proposed by Tang et al. [5] but captures the transient response of the in-cylinder pressure trace more accurately.

Although some sub-models of the MVEM are needed to be re-calibrated if another engine is to be modeled, they can be calibrated readily by only using the engine shop trial report and relevant performance maps. As a result of the lack of su fficient engine measured data, 2-D look-up tables were developed to calculate Wiebe function model parameters as well as the compression and expansion polytropic index. Although rapid calculation speed and satisfactory interpolation accuracy can be achieved with the 2-D look-up table, its extrapolative ability is big issue. In the future study, more measured engine data will be gathered to develop correlations between the model parameters and the engine performance parameters to enhance their extrapolative ability.

**Author Contributions:** H.S. contributed to the development of mathematical models, analysis of simulation results and the writing of the manuscript. J.Z. provided research conditions, team support and financial support. B.Y. and B.J. gave some useful suggestions. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China, gran<sup>t</sup> number 51479017, and the Fundamental Research Funds for the Central Universities, gran<sup>t</sup> number 3132019315.

**Acknowledgments:** The authors are especially grateful to Tang, who provided important technical support.

**Conflicts of Interest:** The authors declare no conflict of interest.
