## 2 Numerical Models
### Engine Model  
A simulation model for the investigated engine was developed with GT-SUITE to study the influence of CDA on mechanical losses and fuel consumption. The developed engine model combines a thermodynamic system (combustion and gas exchange) and a dynamic mechanical system (piston-connecting rod-crankshaft mechanism) and is shown in Figure 1. The working parameters of the combustion process (pressure, temperature, etc.) as boundary conditions affect the calculation of mechanical losses in each cylinder; the mass flow rate in the thermodynamic system is determined by crankshaft speed calculated by the conservation of angular momentum in the dynamic system. Based on this model, the overall impact of CDA on the BSFC and engine performance can be analyzed, as well as the specific parameters between the active and deactivated cylinders. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Engine type & V16 \\ Rated power & 2250 kW \\ Rated speed & 1000 rpm \\ Stoke/Bore & 260 mm/260 mm \\ Compression ratio & 13.5 \\ Total displacement & 220.8 L \\ Valve train & Four valves per cylinder (two intake; two exhaust) \\ Fuel supply system & Direct-acting plunger pump \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of the investigated diesel engine D-49. The predictive diesel combustion model 'EngCylCombDIJet' was chosen to include the effect of fuel injection and atomization on the combustion process [45]. In this model, the fuel spray is divided into hundreds of zones to calculate its development and the evaporation rate of fuel droplets based on momentum conservation. Given the specifics of the fuel injection system of the diesel engine D-49, increasing injection mass means higher injection pressure at low loads, accurate injection profiles for different cycle deliveries are settled to guarantee the accuracy of calculation results. The combustion process is calculated in the block 'EngCylinder', and the simulated gas pressure is transmitted as an input force to the 'Piston' model. The mechanical model consists of several parts, including the crankshaft, reciprocating components, valvetrain, and accessories. Therein, mechanical losses from valvetrain friction and accessories friction are calculated using semi-empirical formulas [46]. There are three compression rings and one oil ring between the piston and the cylinder wall (Figure 2). The piston-connecting rod-crankshaft model allows a convenient investigation for analyzing friction losses in the active and deactivated cylinders with CDA operation. The gas pressure on the top and radial outer surfaces of the piston ring is considered as the pressure acting on the top surface [47]. The pressure applying on the bottom surface is calculated using a blow-by model proposed in [48]. Hydrodynamic friction is modeled using the Reynolds hydraulic equation, and the contact friction between mental surfaces is calculated using the Greenwood-Tripp model [49]. The result analysis is conducted on steady state conditions. Therefore, the mechanical system is set to 'Rigid' in the block 'Cranktrain Analysis', not considering the fluctuation of crankshaft speed resulting from torsional deformation. The 'Rigid Engine Block' has defined space coordinates of the crankshaft support. The physical interaction between the supports and ground is described by the relationship between damping and resilience. The prototype engine D-49 has a V-shaped arrangement of cylinders with two camshafts; therefore, it is most convenient to deactivate one side of eight cylinders from the point of view of practical implementation. Fuel supply is cut off to deactivate cylinders in all cases of the CDA modes studied in this work. In order to control air/gas mass left in deactivated cylinders after the closure of the intake and exhaust valves, the valve closing timing needs to be adjusted with the crankshaft position signal. Figure 1: Constructed engine model of the diesel engine D-49.