Mesh Twisting Technique for Swirl Induced Laminar Flow Used to Determine a Desired Blade Shape
Abstract
:1. Introduction
2. Materials and Methods
2.1. Governing Equations
 Inlet:
 Velocity is purely axial, with a velocity profile specified in accordance with Equation (4) with an average velocity of 1 m/s (corresponding to Re $=100$). The normal gradient of pressure is set to zero, thus $\frac{\partial p}{\partial n}=0$.
 Outlet:
 The normal gradient of all velocity components is set to zero. Pressure normal gradient is still zero, but with a fixed average value of 0 which sets a reference pressure for the whole system.
 Walls:
 No slip is allowed for the velocity, effectively setting $\mathbf{V}=\mathbf{0}$, and the normal gradient of pressure is zero.
2.2. Swirling Flow
2.3. Numerical Approach
2.4. Mesh Morphing
2.5. Constructing Guidance Blades
 Blades where $tan(\varphi )$ changes linearly from the center of the pipe to the outer wall, assuming that $\varphi $ is the deviation angle. This is equivalent to constructing a single shape of blade, defined by a twist angle $\theta $ as a function of axial location z but not affected by radial location r.
 Blades where the deviation angle changes along the pipe axis, but also follows at the exit the angle defined in Figure 2, in the radial direction.
 Same blade setup as in Case II, but where 20% of the inner core is removed, thus reducing the flow restriction because of the blade connections in the center.
 The curvature at the inlet and exit is zero.
 The twist angle is zero at the inlet ($\eta =1$) and ${\theta}_{0}$ at the exit ($\eta =1$).
 The slope with respect to $\eta $ (deviation) is zero at the inlet, but is controlled by a at the exit.
 The deviation grows monotonically from the inlet to the exit, regardless of the selection of a.
Algorithm 1: Mesh morphing process. 

3. Results and Discussion
3.1. Mesh Size and Twisting Sensitivity
3.2. Guidance Blade Design
3.3. Case Comparison
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Case:  I  II  III 

Added pressure drop [diameters]  $11.47$  $10.44$  $10.25$ 
Twist angle at swirler exit ${[}^{\circ}]$  $108.9$  $74.5$  $84.8$ 
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Helgadóttir, Á.; Lalot, S.; Beaubert, F.; Pálsson, H. Mesh Twisting Technique for Swirl Induced Laminar Flow Used to Determine a Desired Blade Shape. Appl. Sci. 2018, 8, 1865. https://doi.org/10.3390/app8101865
Helgadóttir Á, Lalot S, Beaubert F, Pálsson H. Mesh Twisting Technique for Swirl Induced Laminar Flow Used to Determine a Desired Blade Shape. Applied Sciences. 2018; 8(10):1865. https://doi.org/10.3390/app8101865
Chicago/Turabian StyleHelgadóttir, Ásdís, Sylvain Lalot, Francois Beaubert, and Halldór Pálsson. 2018. "Mesh Twisting Technique for Swirl Induced Laminar Flow Used to Determine a Desired Blade Shape" Applied Sciences 8, no. 10: 1865. https://doi.org/10.3390/app8101865