Viscous eddies near a 90° and a 45° corner in flow through a curved tube of triangular cross-section

1976 ◽  
Vol 76 (03) ◽  
pp. 417 ◽  
Author(s):  
W. M. Collins ◽  
S. C. R. Dennis
Keyword(s):  
Cross Section ◽  
Triangular Cross Section ◽  
Curved Tube ◽  
Flow Through

Steady flow in a curved tube of triangular cross section

1976 ◽  
Vol 352 (1669) ◽  
pp. 189-211 ◽  
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Steady Flow ◽  
Cross Section ◽  
Numerical Solutions ◽  
Constant Pressure ◽  
Layer Structure ◽  
Asymptotic Model ◽  
Triangular Cross Section ◽  
Curved Tube

The steady flow of a viscous fluid moving under a constant pressure gradient in a curved tube with a uniform triangular cross section is investigated. Numerical solutions of the equations of motion have been found for the range 100-12 000 of the Dean number D = Ga 3 √(2a/ L )/ μv , where G is the constant pressure gradient, a is a dimension of the triangle, L the radius of the circle in which the tube is coiled, μ the viscosity and v the coefficient of kinematic viscosity of the fluid. The results for low D have been checked by an independent numerical method in which the stream function is expanded in a series of powers of D following the method of Dean (1928). All the results have been checked for accuracy by varying the grid size used in the numerical computations. The trend of the results as D increases is examined for evidence of the development of a boundary-layer structure as D → ∞. Some indication is found of the formation of a boundary layer of thickness proportional to D –1/3 near the side walls of the tube with an associated inviscid core region in the centre of the tube. In particular, comparison is made with details of an asymptotic model as D → ∞ proposed by Smith (1976). A measure of agreement with the general characteristics of this model is obtained, although there are some discrepancies in the precise details. It is possible that the range of D considered in the present work is not great enough to form any definite conclusions regarding the precise nature of the flow as D → ∞. A feature of the present results which develops for D > 3000 is that the maximum axial velocity in the tube ceases to occur on the axis of symmetry of the cross section. This feature appears to be generally consistent with numerical results obtained by Cheng & Akiyama (1970) and Hocking (unpublished) for a tube of rectangular cross section. The sequence of corner vortices of the type identified by Moffatt (1964) is found to occur in the numerical solutions. A detailed study of the vortices has already been published (Collins & Dennis 1976).

Analysis of Q-factors of structural imperfections in triangular cross-section nanobeam photonic crystal cavities

2015 ◽  
Vol 32 (9) ◽  
pp. 1792 ◽  
Author(s):  
Yuki Yamaguchi ◽  
Seung-Woo Jeon ◽  
Bong-Shik Song ◽  
Yoshinori Tanaka ◽  
Takashi Asano ◽  
...  
Keyword(s):  
Photonic Crystal ◽  
Cross Section ◽  
Photonic Crystal Cavities ◽  
Triangular Cross Section ◽  
Q Factors ◽  
Structural Imperfections

Electroosmotic flow of Maxwell fluid in a microchannel of isosceles right triangular cross section

2021 ◽  
Vol 33 (12) ◽  
pp. 123113
Author(s):  
Xu Yang ◽  
Shaowei Wang ◽  
Moli Zhao ◽  
Yue Xiao
Keyword(s):  
Cross Section ◽  
Electroosmotic Flow ◽  
Maxwell Fluid ◽  
Triangular Cross Section
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