# Assessment of Two Streamline Curvature Correction Methods for an Elliptic Blending Turbulence Model
## 4 Conclusions  
A previously developed elliptic blending RANS model was improved by introducing streamline curvature correction. Two approaches were adopted, one of which involved modifying the dissipation term in the \(\omega\)-equation, while the other modified the turbulent kinetic energy production term based on [PERSON]'s explicit algebraic stress model [8]. The two proposed models were assessed using three flows with strongly curved surfaces: The 2D infinite serpentine passage flow, the 2D U-turn duct flow, and the 2D periodic hill flow. The predictions were compared with DNS, experimental, and LES results from the literature. The results computed using the original SST \(k\)-\(\omega\)-\(\varphi\)-\(\alpha\) model and the SST \(k\)-\(\omega\)-CC model were also provided as reference. The following conclusions were drawn:  
(1) In the 2D infinite serpentine passage flow, the two proposed models produced improved results in terms of the velocity, friction coefficient, and re-circulation length, while the results obtained by the SST \(k\)-\(\omega\)-\(\varphi\)-\(\alpha\)-CC1 model were the best. Notably, the SST \(k\)-\(\omega\)-CC model was not capable of obtaining correct results: its predictions were even worse than those of the original SST \(k\)-\(\omega\)-\(\varphi\)-\(\alpha\) model.  
(2) Compared to the original SST \(k\)-\(\omega\)-\(\varphi\)-\(\alpha\) model, the two proposed models and the SST \(k\)-\(\omega\)-CC model all had positive effects on the 2D U-turn duct flow. The velocity, turbulent kinetic energy, and friction were slightly improved.  
(3) In the 2D periodic hill flow, the two proposed models significantly improved upon the results of the original SST \(k\)-\(\omega\)-\(\varphi\)-\(\alpha\) model. They effectively shortened the re-circulation zone and predicted the velocity, friction coefficient, and re-circulation zone more accurately. Again, the predictions by the SST \(k\)-\(\omega\)-CC model were poor.  
All cases used to assess the performance of the proposed models in the present paper are 2D. Actually, the SST \(k\)-\(\omega\)-\(\varphi\)-\(\alpha\)-CC1 model can be used for 3D flows since the Richardson number is generally suited for arbitrary 3D flows. However, the situation is different for the SST \(k\)-\(\omega\)-\(\varphi\)-\(\alpha\)-CC2 model. The regularized anisotropy tensor used (Equation (7)) is only valid for 2D flows, which would cause the model to only work well with 2D flows. Fortunately, an anisotropy tensor suited for 3D flows had been derived [29]. Although this 3D anisotropy tensor is complex, extending the SST \(k\)-\(\omega\)-\(\varphi\)-\(\alpha\)-CC2 model to 3D flows becomes possible, which will be investigated in future work.  
Conceptualization, X.Y. and L.Y.; methodology, X.Y. and Z.L.; software, X.Y. and Z.L.; validation, L.Y. and Z.L.; writing--original draft preparation, X.Y.; writing--review and editing, L.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China (Grant No. 2018 YFB2100901) and the Natural Science Foundation of Shenzhen, China (Grant No. 20200814105851001).  
Not applicable.  
The authors declare no conflict of interest.