**5. Results**

### *5.1. Average Mass Flow Rate and Discharge Coe*ffi*cient*

The discharge coefficient was used to correct the difference between the 1D gas flow analysis and the measurement results. The reason is to use the gas flow analysis results to predict the performance of the experimental apparatus.

Figure 5 and Table 4 show the average mass flow rate and the discharge coefficient of the intake air according to the engine speed.

**Figure 5.** Average mass flow rate and discharge coefficient of intake air.

**Table 4.** Comparison of the average mass flow rate and the discharge coefficient according to the engine speed.


The experimental results refer to the average mass flow rate measured using a laminar flowmeter. In order to compare the average mass flow rate, the mass flow rate calculation results of the 1D gas flow rate analysis were converted to the average mass flow rate [26].

The volumetric efficiency associated with the average mass flow rate did not continue to increase in proportion to the engine speed due to valve overlap, the influence of the reflected waves, etc. However, in terms of the engine of this study, it was confirmed through a previous study that the volumetric efficiency increases in proportion to the engine speed up to 1700 rpm [22]. As the engine

speed increased to 1500 rpm, the average mass flow rate increased, and the di fference between the experiment and the 1D flow analysis results also increased. The reason for the di fference in the average mass flow rate is the di fference between the actual physical phenomena and the theoretical calculations [27,28]. The higher engine speed is the larger flow rate into the cylinder, so the di fference is thought to have occurred because of this. In order to correct the di fferences in the results of the 1D gas flow analysis, the discharge coe fficient was calculated using Equation (10). The discharge coe fficient obtained in this way is a correction method for the di fference between the experiment and 1D gas flow analysis. Therefore, it can be used to predict the performance of the experimental apparatus through the results of 1D gas flow analysis in the future.

### *5.2. Mass Flow Rate in One-dimensional Gas Flow Analysis*

One-dimensional gas flow analysis can calculate the mass flow rate over time [18]. Figure 6 shows the intake air mass flow rate during the intake period compared to the case where the discharge coe fficient was applied.

**Figure 6.** One-dimensional analysis results of the mass flow rate. AVC, air–intake valve closes; AVO, air–intake valve opens; BDC, bottom dead center; EVC, exhaust valve closes; TDC, top dead center.

The mass flow rate does not increase as soon as the intake valve was opened [29]. This is because, during the valve overlap period (342~378 CA◦), the outflow from the cylinder exits through the exhaust port. The higher engine speed is the larger gas exchange flow rate, so the timing at which the mass flow rate increases is delayed. The mass flow rate increases after the top dead center (TDC; 360 CA◦), and the intake air enters the cylinder until the bottom dead center (BDC; 540 CA◦). If the mass flow rate is large, the corrected value due to the application of the discharge coe fficient also increases. Therefore, the correction of the result through the application of the discharge coe fficient has more influence on the results of the gas exchange process in the valve open state than in the valve closed state.
