## 2 Test of the EMVT and Valve Strategy
### Valve Strategy  
The charge trapped in the inactive cylinder of the CDA operation usually includes fresh air, low-pressure charge (deactivation of a cylinder after its exhaust event), and exhaust gas. Based on EMIV without any modification to the exhaust valves, three valve strategies based on fresh air trapping, low-pressure charge, and exhaust gas trapping are proposed. The schematic of the valve strategy for fresh air trapped during one active cycle and one inactive cycle is shown in Figure 2. The fresh air is first sucked into the inactive cylinder during the intake stroke of the inactive cycle. At the end of the inactive cycle, the exhaust valve event occurs normally, and thus the fresh air is released into the exhaust manifold. The schematic of the in-cylinder pressure during the inactive cycle is shown in Figure 3. The red line and blue line represent the in-cylinder pressure of different IVCs. The red line indicates that the intake valve closes before 540 CA, while the blue line demonstrates that the intake valve closes at about 540 CA. The advantage is that fewer pumping losses can be achieved if IVC closes to 540 CA. However, the fresh air trapped in the inactive cycle is exhausted into the exhaust pipe because of the normal exhaust valve event, which would cause decreased efficiency of the three-way catalytic converter. For this situation, [PERSON] et al. [5] proposed a novel strategy by connecting a branch pipe to the exhaust split pipe of inactive cylinders so as to guide the fresh air to flow from the inactive cylinders into the downstream of the catalyst convertor, which is suitable for the fixed CDA operation. However, this strategy is not applicable to the VCD operation, because all cylinders switch between deactivation and reactivation continuously. For the valve strategy of low-pressure charge, the intake valves are deactivated during the inactive cycle, as shown in Figure 4. Only the residual exhaust gas is trapped in the cylinder. The trapped residual exhaust gas expands to a lower pressure when the piston moves towards the bottom dead center (BDC), which may result in an undesired entry of lubricant into the combustion chamber of the inactive cycle. Moreover, when the exhaust valve opens normally in the exhaust stroke of the inactive cycle, the exhaust gases of the exhaust manifold would flow back to the inactive cylinder due to the  
Figure 1: Test bench of engine cylinder head with EMVT. The valve strategy of fresh air trapping involves fewer pumping losses, but may cause high exhaust oxygen because the exhaust valve opens normally in the exhaust stroke of the inactive cycle. If the fresh air is replaced with exhaust gas, high exhaust oxygen would be avoided and less pumping losses can be achieved. Meanwhile, the shortcomings of the low-pressure charge can also be overcome. The valve strategy of exhaust gas trapping is proposed based on EMIV, as shown in Figure 6. The intake valve opens from the exhaust stroke of the last active cycle to the intake stroke of the inactive cycle. Therefore, a part of the exhaust gas is first pressed into the intake manifold, and then sucked into the cylinder, mixing with a small amount of fresh air. At the end of the inactive cycle, the trapped gas is discharged into the exhaust pipe. In this process, the key is to reduce the amount of oxygen sucked into the inactive cycle. In the paper, the mass fraction of oxygen in the exhaust pipe is recommended to be less than 1% in order to avoid the reduction in efficiency of the three-way catalytic converter. In addition, for the gas trapped in the inactive cycle, the in-cylinder pressure should be guaranteed to be greater than the minimum in-cylinder pressure limit, which is set at 0.02 MPa, according to [PERSON]'s investigation [19]. The VCD valve strategy based on EMIV allows each cylinder to switch between deactivation and reactivation with the firing density varying from 50 to 100% continuously, which is different from the fixed CDA mode when the inactive cylinders always never work.