## 3 Results and Discussion
### 3D Asymmetric Diffuser Flow  
To provide detailed and reliable data for the CFD model validation, [PERSON] et al. [19; 20] designed a fully 3D diffuser flow and measured the velocity field and pressure distribution in detail. Using the same geometry and boundary conditions, a DNS was performed by [PERSON] et al. [21]. The DNS results were in good agreement with the measurements. This case has been chosen to validate turbulence models by many researchers. For example, [PERSON] et al. [22] considered the performances of four RANS turbulence models (the SST \(k\)-\(\omega\) model of [PERSON] [23], the \(\mathrm{BL}-\overline{v^{2}}/k\) model of [PERSON] and [PERSON] [8], the Speziale-Sarkar-Gatski (SSG) model of [PERSON] et al. [24], and the elliptic blending Reynolds stress model (EBRSM) of [PERSON] and [PERSON] [25]) in this flow. It was found that only the EBRSM could predict reasonable results. [PERSON] and [PERSON] [26] simulated this case using a pure RANS model, a pure LES model, and a hybrid RANS-LES model. The same mesh with a moderate grid resolution was used for the three models. It was shown that the hybrid RANS-LES model yielded better results than the other models. The pure LES model failed because the grid resolution was insufficient. [PERSON] and [PERSON] [27] simulated the 3D diffuser flow using a RANS model and an SAS model. It was found that the results predicted by the SAS model were in good agreement with the experimental and DNS findings, but the results predicted by the RANS model were not. Figure 1 showed a schematic of the geometry and relevant boundary conditions of the 3D diffuser flow used in this study. Consistent with the experiment [19] and DNS [21], the Reynolds number (Re) based on the bulk velocity at the inlet (\(U_{b}\)) and the height of the inlet duct (\(H\)) was 10,000. The fully developed profiles, which were extracted from a precursor simulation in a long duct at the same Re and with relevant turbulence models, were used at the inlet. The number of computational meshes was 3.24 million, which was similar to that used by [PERSON] and [PERSON] [27]. The timestep size was 0.02 \(H/U_{b}\). The statistics began at 5000 steps and continued to 10,000 steps to ensure that the mean values of the variables remained unchanged with time. The DNS data of [PERSON] et al. [21] were used as references. A comparison of the contours of the mean stream-wise velocity \(\overline{u}\) at different cross-sections, which was normalized by \(U_{h}\), is shown in Figure 2. At \(x/H=2\), both the SST-\(k\)-\(\omega\)-\(\varphi\)-\(\alpha\)-SAS and the SST-SAS models predicted the flow separation at the top-right corner, where the two expanding walls intersect. However, the SST-SAS model incorrectly predicted a large separation at the top-left corner. The SST-\(k\)-\(\omega\)-\(\varphi\)-\(\alpha\) model also predicted the flow separation at the top-right corner, but the separation bubble was too large compared to that predicted by the DNS. Compared with the DNS, both the SST-\(k\)-\(\omega\)-\(\varphi\)-\(\alpha\)-SAS and the SST-SAS models predicted an earlier separation near the top-left corner (see the contours at \(x/H=5\)), but a delayed separation near the center of the top wall (see the contours at \(x/H=8\)). The proposed SAS model was better than the SST-SAS model in terms of predicting the location of the maximum velocity. At \(x/H=15\), the advantage of the SST-\(k\)-\(\omega\)-\(\varphi\)-\(\alpha\)-SAS model was even more pronounced. Compared to the SST-SAS model, the flow pattern predicted by the proposed SAS model showed better agreement with that obtained from the DNS. In the results of the SST-\(k\)-\(\omega\)-\(\varphi\)-\(\alpha\) model, the flow separation started at the top-right corner and then developed further downward along the side wall. The flow separated completely from the side wall quickly (at \(x/H=5\)). Obviously, this behavior did not correspond to that of the DNS results.