# Study on Correction Method of Internal Joint Operation Curve Based on Unsteady Flow
## 3 Results  
### Concept and Calculation Method of Unsteady Correction for Compressor  
The unsteady flow pressure ratio curve of the compressor forms a circle, which is formed during a fluctuation cycle of the compressor, and the unsteady flow pressure ratio characteristic circle is distributed counterclockwise according to the sequence of time, as shown in Figure 10. At the same flow rate, the pressure ratio of the rising section before the peak is smaller than that of the lower stage after the peak, and the pressure ratio difference between them is about 3.3%. The average value of the pressure ratio characteristic circle is higher than the corresponding steady flow pressure ratio, and the difference between them is 4.4%, as shown in Table 5. This indicates that the average value of the unsteady flow pressure ratio of the compressor cycle is clearly different from the steady flow pressure ratio. In the pressure ratio characteristic circle of the compressor, the maximum flow rate is not in the minimum pressure ratio position, which is at the end of the rising section before the peak, and a hysteresis effect appears in the pressure ratio curve. In the case of steady  
Figure 9: (**a**) The joint operating point when the bypass valve is open; (**b**) the internal joint operating curve when the bypass valve is open. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Pressure Ratio** & **Efficiency/\%** &
\begin{tabular}{c} **Power** \\ **Consumption/kW** \\ \end{tabular} \\ \hline Steady flow & 1.83 & 64.38 & 3.87 \\ Unsteady flow & 1.91 & 67.40 & 4.08 \\ Degree of & 4.4 & 4.7 & 5.4 \\ deviation/\% & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the unsteady flow energy of the original compressor at the joint point with the steady flow value at 150,000 rpm. flow, the higher the flow rate, the smaller the pressure ratio, and the flow rate and pressure ratio are in correspondence. It shows that the distribution of the pressure ratio of unsteady flow and steady flow is different. The average values of compressor performance based on two unsteady flow cycles are presented, as shown in Table 5. The average values of unsteady flow performance are higher than the corresponding steady flow performance, with a difference of 4.4% to 5.4%. All the compressor unsteady flow performance deviates significantly from the steady flow condition. The premise of the unsteady flow correction for the compressor is to calculate the degree of deviation of the unsteady flow performance. The ratio of the unsteady flow performance to the corresponding steady flow performance is the compressor unsteady flow correction coefficient. The variation of the compressor power consumption affects the power balance between the compressor and the turbine according to the turbocharger internal match. Therefore, the average ratio of the compressor's unsteady flow power consumption and the corresponding steady flow power consumption is defined as the compressor unsteady flow power consumption coefficient, which is used to indicate the degree of deviation of the compressor unsteady flow power consumption from the corresponding steady flow power consumption, and the formula for calculating the compressor unsteady flow power consumption coefficient is shown in Equation (1). The unsteady flow power consumption coefficient is the compressor unsteady correction coefficient. \[\varepsilon_{C}=\frac{P_{unsteady}}{P_{steady}}, \tag{1}\]  
where \(P_{unsteady}\) is the average value of compressor power consumption for unsteady flow and \(P_{steady}\) is the corresponding compressor steady flow power consumption value. According to Table 5, the joint point of the original compressor unsteady flow power consumption coefficient is 1.055 at 150,000 rpm, which is the unsteady correction coefficient at this point. The correction factor is used to indicate the deviation of the compressor unsteady flow power consumption from that of the corresponding steady flow.