# A Power Based Analysis for a Transonic Transport Aircraft Configuration through 3D RANS Simulations
## 3 Results and Discussion
### Power Conversion of Boundary Layer Ingestion Configuration
The downstream wake power was increased rather than decreased in this configuration. This was associated with the excessive high-momentum addition of the actuator disc: the thrust not only balanced the body drag but also overcame the wing drag. The top picture of Figure 16 illustrates the intensity of \(\Phi\) in the flow field. The high intensity of \(\Phi\) is highlighted around the airframe surface and in the aircraft's downstream  
Figure 14: Total pressure contours in the vicinity of the wake-filling actuator disc model. Figure 15: Contours of \(\dot{\mathrm{E}}\)w integrand around the BLI configuration. region. Once all of the power inputs and outputs terms in the flow field were calculated, they were normalized and plotted at the corresponding X coordinates, as shown in Figure 16. This figure illustrates the power conversion process of the BLI configuration with a propulsor. It shares a similar pattern to that of the wing body configuration. The bottom plot in Figure 16 illustrates the power conversion process of the BLI configuration. The shaft power, \(\mathrm{P_{s}}\), as the only power input in the flow field, was implanted in the flow field by the propulsor. \(\mathrm{P_{s}}\) was converted into viscous dissipation, \(\Phi\), and wake power at the outlet plane, \(\mathrm{E_{w,out}}\), as well as the net force power, \(\mathrm{NV_{\infty}}\). The viscous dissipation, \(\Phi\), increased along the stream and shared a similar pattern as in the wing body configuration. It increased quickly over the aircraft surface, taking about 28% of the total power input at the body tail. Then, \(\Phi\) increased by 5% in the downstream region. Besides the viscous dissipation of the aircraft wake, the increase in \(\Phi\) in the downstream region was associated with the dissipation of the jet behind the actuator disc model. The wake power, \(\mathrm{E_{w}}\), increases across the airframe and decreases in the downstream reflow. At the outlet, \(\mathrm{E_{w}}\) took 22% of the total input power. This indicated a notable amount of mechanical power in the downstream flow mixed with the jet and wake. This study shows the limitations of a single wake-filling actuator disc model: It can refill the body wake, but it is not able to reduce the wing wake. On the other hand, the momentum excess of the actuator disc model was required to balance the momentum deficit of the wing. Figure 16: The intensity of viscous dissipation and the power conversion process of the BLI configuration. Therefore, the actuator disc model in this BLI configuration was not capable of reducing the downstream mechanical power to zero. For the BLI configuration, the thrust power, \(\text{TV}_{\infty}\), and drag power, \(\text{DV}_{\infty}\), mutually cancelled each other, leaving a finite value (10% of the total input power) of the net force power, \(\text{NV}_{\infty}\), as a power output term. \(\text{NV}_{\infty}\) was used to accelerate the aircraft. This was different from the wing body configuration, in which \(\text{NV}_{\infty}\) was zero to maintain the thrust/drag equilibrium. In the plot of power conversion, the total power input, \(\text{P}_{\text{s}}\), was not identical to the summation of the outputs in the flow field. The difference was about 35%, denoting the power imbalance error for the BLI case. A subdomain error study was performed to process the simulation results of the BLI configuration, as presented in Figure 17. It was clear that the error associated with the wing was 19.3%, which was significantly higher than the errors from the other subdomains, while the error of the BLI propulsor was 8.2%. This study shows that the error associated with the wing as well as the propulsor was mainly responsible for the high values of power imbalance error. The error of the mechanical power imbalance was larger than the typical values of power saving due to BLI. So far, the precision of power-based analysis in 3D simulation is not adequate to analyze the power saving of BLI. This poses challenges for future work.