## 1 Introduction
Alternating half of the cylinders' deactivation was experimentally realized in a 6-cylinder diesel engine [24]. The most fuel consumption reduction was achieved when alternating CDA was employed. Similarly, the BSFC reduction change with engine load growth is not monotonous at a constant speed. A simulation and experiments of CDA with disabled valves were implemented by [PERSON] et al. [24] in a high-speed diesel engine. The results demonstrate a 9% reduced BSFC at 10% full load and a 30% reduced BSFC at 20% full load for 1500 rpm. However, the same operation of CDA applied to different engines does not always achieve the BSFC reduction at a light load and when idle, since the indicated efficiency of active cylinders is associated with the conventional engine performance (the dependence of the indicated efficiency and load), which determines the available operation range of engine for CDA. The indicated diagram in deactivated cylinders depends on different strategies of valve operation. When the intake and exhaust valves are entirely closed in deactivated cylinders, combustion does not occur, and the charge in cylinders changes periodically with piston movement. Due to gas leakage into the crankcase, the maximum gas pressure in the combustion chamber changes until it reaches a stable value. This process lasts only about 1 s for a light-duty diesel engine at a speed of 800 rpm so that this period can be neglected compared with the reactivation duration for cylinder work [25]. However, the minimum speed of heavy-duty diesel engines is as low as 300 rpm when idle. The change in the maximum gas pressure in deactivated cylinders interacts with the heat transfer in the combustion chamber, affecting the indicated efficiency. Therefore,it is necessary to investigate the factors impacting gas or air state change in deactivated cylinders at low speeds. The results obtained can be used for further investigation of fuel consumption in transient processes with CDA operation. In addition to the indicated efficiency, the other factor influencing fuel consumption is mechanical losses. At a light load and when idle, more than 20% of fuel energy is expended on overcoming friction and mechanical actuation [26]. After some cylinders are deactivated, gas pressure and temperature play an opposite role in mechanical friction for the active and deactivated cylinders, considering their impact on lubricated oil thickness and oil viscosity. The inconsistent effect of CDA on overall frictional losses of compression rings and big-end bearings has been noted for engines with different configurations. [PERSON] et al. [27] found that the total frictional loss under CDA is 9.53% higher than that under normal operation. Similar results have been achieved in [28; 29; 30]. However, a decrease in the overall frictional loss under CDA operation has been reported in [31; 32]. These studies demonstrate the necessity of considering total system effects with the application of CDA. The CDA strategy with all valves closed in deactivated cylinders has a a greater advantage for large-scale diesel engines since they have large size components and high inertia force from the perspective of reducing mechanical losses for valve trains. The fuel consumption reduction caused by CDA implies emission reduction, especially CO\({}_{2}\) emissions that rely primarily on the amount of burnt fuel. NOx emissions are strongly dependent on combustion temperature, load, and oxygen concentration [9]. Under CDA operation, about the doubled mass of cycle fuel delivery for the normal operation is supplied to the active cylinder, enhancing the combustion temperature in the active cylinder and consequently increasing the formation of NOx emission. The increase in NOx emissions under CDA operation has been experimentally found for a 6-cylinder 11 L diesel engine with an asymmetric exhaust structure [33]. However, the reduction in NOx emission has also been reported for CI engines under CDA operation.