# 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  
Various sources in the previous study on BLI showed that the value of power saving due to BLI is in the range of 3-10%. On the other hand, the error of mechanical power imbalance is about 30%. The precision of power-based analysis in 3D simulation is not adequate to study the power saving of BLI. This section limits the discussion to the aspect of the power conversion process of the aircraft using BLI. The BLI configuration combines the wing body configuration with a BLI propulsor. This study employed a wake-filling actuator disc model with a nonuniform pressure jump to mimic an ideal BLI propulsor [13; 31]. This model re-energized the ingested boundary layer flow into the state of free stream so that the mechanical energy of the downstream wake and jet was minimized. The actuator disc model utilized a UDF function, which increased the total pressure of the ingested flow into a constant total pressure, \(\mathrm{P_{tconst}}\). In this case the \(\mathrm{P_{tconst}}\) value was 46,000 Pascal, higher than the free stream total pressure. In this manner, the thrust, T, generated by the actuator disc model was higher than the airframe drag, D. The UDF function enabled a nonuniform pressure jump \(\Delta\mathrm{P}\), which was simply equal to \(\mathrm{P_{tconst}}\)-\(\mathrm{P_{tupstream}}\). \(\mathrm{P_{tupstream}}\) refers to the total pressure of the upstream flow. The thrust of this actuator disc model, T, was obtained as the surface integral of \(\Delta\mathrm{P}\) over the disc plane, as given in Equation (16). The T value was 116 N, so the \(\mathrm{TV_{\infty}}\) value of 30,232 watts was obtained. It was noted that \(\mathrm{TV_{\infty}}\) was considered a power output term, while the actual power input of the propulsor was shaft power, \(\mathrm{P_{s}}\), which was evaluated using Equation (7). In this BLI case, the \(\mathrm{P_{s}}\) value was 54,793 watts and was used as the reference value for normalizing the power terms. \[\mathrm{T}=\oint_{\mathrm{prop}}\Delta\mathrm{PdS}=\oint_{\mathrm{prop}}\bigl{(} \mathrm{P_{tconst}}-\mathrm{P_{tupstream}}\bigr{)}\mathrm{dS} \tag{16}\]  
Figure 14 shows the total pressure distribution at the symmetry plane in the vicinity of the actuator disc model. The boundary layer of the body is denoted by the contours of low-valued total pressure over the body surface. It was noted that the boundary layer over the bottom surface was thicker than that over the top surface. This was attributed to the non-axisymmetric pressure diffusion of the aft body shape. The total pressure was not uniform in the region behind the actuator disc model. Therefore, the actuator disc model was not capable of refilling the total pressure in an ideal manner. This could be attributed to the highly distorted flow ingested by the actuator disc. This study suggests that the aft body should be axisymmetric to best utilize the BLI benefit. Aircraft drag, D, is the drag force imposed on the wing and body surface. The drag coefficient was 0.03290 in the BLI configuration. That was about 8% higher than the value in the wing body configuration. The increase in drag was due to the suction of the actuator disc model imposed on the aft body. The drag power, \(\mathrm{DV_{\infty}}\), is obtained by multiplying D by \(\mathrm{V_{\infty}}\) as a power input of the flow field. As discussed, the wake energy flow, \(\dot{\mathrm{E}}_{\mathrm{w}}\), was assessed as the surface integral over the survey planes and the outlet plane. The integrand of \(\dot{\mathrm{E}}_{\mathrm{w}}\) is illustrated in Figure 15. Compared with the pattern in the case of the wing body configuration. The pattern in the BLI case is similar: the wake power accumulated as the flow passed through the aircraft and gradually reduced in the downstream region. Compared with the wing body configuration, a notable difference for the BLI configuration was the high intensity of \(\dot{\mathrm{E}}_{\mathrm{w}}\) in the downstream flow of the actuator disc.