# A Power Based Analysis for a Transonic Transport Aircraft Configuration through 3D RANS Simulations
## 3 Results and Discussion
### The Analysis of Power Imbalance Error
#### 3.1.2 Impact Factors of Power Imbalance Error  
This section presents possible impact factors to reduce \(e_{domain}\). The influences of the mesh type, discretization scheme, and turbulence model are examined. Considering that the error associated with the wing, \(e_{wing}\), makes the major contribution to \(e_{domain}\), the subdomain of the wing is highlighted. As introduced in Section 2.3, both structured mesh and unstructured mesh were generated. The mesh sizes of the two were close: 4.1 million for the unstructured medium mesh and 5.1 million for the structured medium mesh. It was straightforward to perform the subdomain error study with their simulation results, as presented in Figure 11. It showed the same error contributions for the two types of mesh: high-value error existed in the subdomain of the wing, which was mainly responsible for the high values of \(e_{domain}\). The structured mesh indeed reduced the error in the wake region (less than 1%). Nevertheless, the error associated with the wing, \(e_{wing}\) (35.4%), was higher than that of the unstructured mesh (26.8%). The errors of \(e_{domain}\) and \(e_{wing}\) are summarized in Table 6. Even if the structured mesh obtained relatively low values of \(e_{domain}\), it did not offer a better result in terms of \(e_{wing}\), the major error source. This study adopts the unstructured medium mesh as the reference mesh in the following discussions. Figure 11: Subdomain error study for unstructured mesh (red lines) and multiblock structured mesh (blue lines). Figure 10: Subdomain error study of wing body configuration (unstructured medium mesh). In CFD simulations, discretization methods interpolate conservative independent variables. On the other hand, interpolation causes discretization error as an important source of numerical errors. This study tested two methods for comparison: the second-order upwind and the third-order MUSCL methods. The former method is widely used, and the latter method provides higher-order precision. A first-order discretization method is not discussed due to the low order precision. A subdomain error study was performed to check the impact of the discretization methods on the reference mesh. The results are listed in Table 7. The results showed that the reduction in \(e_{wing}\) due to the third-order MUSCL method was about 4.5%. Furthermore, the high-order discretization method reduced \(e_{wing}\) without increasing the error of other subdomains. Therefore, the high-order discretization method is suggested for power-based analysis. A turbulent model introduces complexity to simulations, and the impact of turbulent models was examined. This study examined three typical models: the S-A model, the standard k-\(\epsilon\) model, and the k-\(\omega\) SST model. The simulations employed the same reference mesh (unstructured medium mesh) and third-order MUSCL method discretization to eliminate the effects of the other impact factors. The results of the subdomain error study are listed in Table 8. It showed that the absolute value of \(e_{domain}\) ranged from 38.5% to 40.9%. The two-equation k-\(\omega\) SST model led to the minimum level of power imbalance error. As discussed in Section 3.1.1, the mesh size study showed that an increase in mesh size tended to decrease \(e_{domain}\). It might be beneficial to increase the mesh density in the subdomain of the wing. Based on the reference mesh (Unstructured medium mesh), the mesh density was increased universally over the wing surface. The total mesh size was increased accordingly from 4.1 million to about 8.0 million. This refinement of the mesh led to the reduction in \(e_{domain}\) from 38.5% to 36.6%, while \(e_{wing}\) was reduced from 22.3% to 22.0%. The increase in the mesh density of the wing reduced the power imbalance error by 2% at the cost of the doubled mesh size. Compared with the results of the unstructured fine mesh (8.2 million), the universal increase in mesh density over the wing surface did not provide an extra benefit.