# Mesh Twisting Technique for Swirl Induced Laminar Flow Used to Determine a Desired Blade Shape
## 4 Conclusions  
In this paper, the desired shape design of guidance blades in laminar flow has been sought. In order to produce flow across the guidance blades numerically, a new type of mesh technique was explored. Instead of manually adjusting the mesh to conform to the irregular shaped guidance blades and possibly causing the largest errors where the most accuracy is needed (in the boundary layer close to the blades), a high quality mesh was constructed with blades conforming to the \(x\)-, \(y\)-, \(z\)-axes and the mesh then twisted until the desired shape of the guidance blades was reached. This mesh twisting technique was at first tested on laminar axial flow and was shown to give minimal errors in the axial velocity of order \(10^{-3}\) m/s compared to a mean velocity of 1 m/s. This was considered acceptable. When deciding on a desired shape of the guidance blades, the deviation angle based on the theoretical optimal velocity profile was used. Three cases were explored all with four blades, swirl number 0.2 and Re 100. Case I is where the twist angle is a function of axial location. Case II is where the deviation angle changes along the pipe axis according to the theoretical value. Case III is like Case II with a hollow center in order to minimize pressure drop. Case II has a lower swirl decay than Cases I and III. The pressure drop for Case III is slightly lower than for Case II but significantly higher for Case I than the other two cases. All cases have a non-uniform axial velocity profile in the angular direction half a diameter downstream from the swirler exit, resulting from the four blade set up. Cases I and II have an axial velocity profile with a closer match to the theoretical axial velocity component for laminar swirl flow than Case III. Case III has a strong axial velocity component in the middle of the pipe due to the hollow center, therefore, deviating from the optimal axial velocity profile for laminar swirl flow. All cases have half a diameter downstream of the swirler a tangential velocity similar to the theoretical laminar swirl flow tangential velocity profile. By comparing the three cases with regard to velocity field, swirl decay and pressure drop, one can conclude that Case II outperforms the other two cases and is therefore the desired blade shape design for a guidance swirler. In a further study, the length of the swirler and the number of swirl blades can be explored, as well as desired blade shape for turbulent flow.  
Conceptualization, A.H., S.L., F.B. and H.P.; Methodology, A.H., S.L., F.B. and H.P.; Software, H.P.; Validation, A.H., S.L., F.B. and H.P.; Formal Analysis, A.H., S.L., F.B. and H.P.; Investigation, A.H., S.L., F.B. and H.P.; Resources, A.H., S.L., F.B. and H.P.; Data Curation, A.H., and H.P.; Writing--Original Draft Preparation, A.H. and H.P.; Writing--Review and Editing, A.H., S.L., F.B. and H.P.; Visualization, H.P.; Supervision, A.H., and H.P.; Project Administration, A.H. and H.P.; Funding Acquisition, A.H., S.L., F.B. and H.P.  
[PERSON], a masters student doing a preliminary study on the subject [26], received in 2018 a grant from Energy Research Fund of Landsvirkjun, National Power Company of Iceland. This research, however, received no external funding.  
[PERSON], a masters student at University of Iceland worked on a preliminary project linked to this study [26].  
The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.