# Study on Correction Method of Internal Joint Operation Curve Based on Unsteady Flow
## 3 Results
### Simultaneous Unsteady Correction at Compressor and Turbine  
Both the compressor and the turbine are at the unsteady flow boundary when the turbocharger matches the engine operation, and it is necessary to consider the unsteady flow coefficients at both ends of the turbocharger at the same time. The separate unsteady flow correction is carried out in the previous section to illustrate the effects of the compressor and turbine unsteady flow and the correction methods separately, which are the basis and reference for accounting for the unsteady coefficient correction at both ends simultaneously. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structure** & **Steady** & **Steady Power** & **Unsteady** & **Unsteady Power** & **Degree of** & **Power** \\
**Efficiency/\%** & **Consumption** & **Efficiency/\%** & **Consumption/\%** & **Deviation/\%** & **Consumption** \\ \hline Original & 64.38 & 3.87 & 67.40 & 4.08 & 5.4 & 1.054 \\ compressor & 65.10 & 3.75 & 68.25 & 4.04 & 7.7 & 1.077 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance comparison of different compressor structures at 150,000 rpm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structure** & **110,000 rpm** & **130,000 rpm** & **150,000 rpm** & **170,000 rpm** & **190,000 rpm** \\ \hline Original & 1.042 & 1.049 & 1.054 & 1.042 & 1.028 \\ Optimized & 1.047 & 1.063 & 1.077 & 1.068 & 1.058 \\ compressor & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Distribution of power consumption coefficients for the compressor unsteady flow. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structure** & **110,000 rpm** & **130,000 rpm** & **150,000 rpm** & **170,000 rpm** & **190,000 rpm** \\ \hline Original & 1.518 & 1.331 & 1.143 & 1.087 & 1.030 \\ Optimized & 1.790 & 1.563 & 1.335 & 1.284 & 1.232 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Distribution of turbine pulse energy utilization coefficients. Turbocharger performance at medium-low speeds is quantitatively evaluated by surge margin [39; 40]. In addition, the definition of the surge margin (SM) used in this paper is  
\[SM=\left(\frac{\frac{P_{s}}{m_{scor}}}{\frac{m_{scor}}{m_{scor}}}-1\right)\times 1 00\% \tag{2}\]  
where \(P_{s}\) is corrected power consumption at surge, \(m_{scor}\) is corrected flow rate at surge, \(P_{w}\) is corrected power consumption at operation point, \(m_{wcor}\) is corrected flow rate at operation point. The corrections of the unsteady coefficient at both ends of the turbocharger are carried out based on Tables 7 and 8. The compressor steady flow power consumption is corrected by the unsteady flow power consumption coefficient, as well as the turbine steady flow effective output power for the corresponding speed is corrected by the pulse energy utilization coefficient. Then, the corrected compressor power consumption curve and the corrected turbine effective output power curve are coupled to obtain the internal joint operating point for the unsteady coefficient correction at both ends simultaneously. The corrected joint point clearly shifts to the left and slightly up at 150,000 rpm, as shown in Figure 11.  
The compressor power consumption curves and turbine effective output power curves for all revolution speed steady flows are superimposed and coupled with unsteady flow corrections to obtain the corrected internal joint operation curves at both ends of the turbocharger, respectively. The curve based on the original turbocharger with unsteady flow correction at both ends is shown in Figure 12. The curve based on the optimized turbocharger with unsteady flow correction at both ends is shown in Figure 13. The compressor power consumption maps are corrected by the unsteady coefficient in Figures 12 and 13.