# Study on Correction Method of Internal Joint Operation Curve Based on Unsteady Flow
## 4 Discussion  
The steady isentropic efficiency is one of the main performance parameters of compressors and turbines and is an indicator to evaluate the perfection of their structural design [41; 42; 43]. The steady isentropic efficiency is proposed based on steady flow and cannot fully reflect the energy utilization of the booster under unsteady flow conditions. Therefore, the concept of the turbocharger unsteady flow energy utilization factor is proposed to quantitatively assess the turbocharger energy utilization under actual operating conditions, which is the ratio of the turbine pulse energy utilization coefficient to the compressor unsteady flow power consumption coefficient. The unsteady flow energy utilization coefficient can be attained as per the following equation:  
\[\varepsilon=\frac{\varepsilon_{T}}{\varepsilon_{C}} \tag{3}\]  
where \(\varepsilon_{T}\) and \(\varepsilon_{C}\) are the turbine pulse energy utilization coefficient and the compressor unsteady flow power consumption coefficient, respectively. In Equation (3), each coefficient is 1 at the steady state. While the compressor's unsteady power consumption is more than that of the steady flow, \(\varepsilon_{C}\) is greater than 1, indicating that the compressor operating consumes extra energy due to the unsteady flow effect. When the turbine is under unsteady flow conditions, \(\varepsilon_{T}\) is greater than 1, indicating that the turbine's unsteady output power is greater than the corresponding steady output power, increasing the degree of turbocharger energy utilization, which is consistent with the  
Figure 14: Comparison of the corrected curves of two turbochargers. actual operating conditions. The turbocharger unsteady flow energy utilization coefficient needs to consider the unsteady flow effects at both the compressor and the turbine. A combined coefficient \(\varepsilon\) is formed through the unsteady coefficients of the compressor and turbine, quantifying the energy conversion under unsteady flow conditions. Figure 15 shows the trend of the unsteady flow energy utilization coefficients of the two turbochargers on the corrected internal joint operation curve. The unsteady flow energy utilization coefficient keeps decreasing with the speed and flow rate rise. The energy utilization coefficient is higher and the curve distribution is steeper at medium-low speeds because of the significant turbine unsteady flow effect. In the high-speed range at 170,000 rpm and beyond, the overall unsteady flow effect is weak for both the compressor and the turbine, and the compressor unsteady coefficient is close to 1, resulting in a flat distribution of unsteady flow energy utilization coefficients. The unsteady flow energy utilization coefficient of the optimized turbocharger is significantly higher than that of the original turbocharger, especially in the medium-low-speed range, which is more than 14.5% higher. The energy utilization advantage is obvious, which can effectively improve the admission performance of the engine in the medium-low-speed range. The design and performance studies of compressors and turbines are mostly independent of each other, which is different from the real conditions of turbochargers. The results of optimizing the compressor and turbine separately and optimizing both ends of the turbocharger simultaneously based on the joint operating curves show that optimizing one end of the turbocharger separately results in poorer engine performance than optimizing both ends of the turbocharger.