Numerical Study of the Flow of a Viscous Fluid in a Curved Channel

Abstract

Steady flow of a viscous fluid in a channel with a corner was studied numerically. Three types of corners were investigated: (a) Both inner and outer corners are rectangular, (b) inner corner is rectangular but outer corner is circular, (c) both corners are circular. Main results obtained are as follows: (i) For the flow in a channel with a corner, conventional method of integration of Navier‐Stokes equation is effective for Reynolds number less than about 50. (ii) With Greenspan's method, convergent results are obtained for Reynolds number as large as 256. (iii) A standing vortex appears near the inner wall just downstream of the corner with Reynolds number about 30 for cases (a) and (b), but its appearance is postponed until the Reynolds number is increased to 128 for case (c). (iv) Pressure loss due to the existence of a corner is nearly proportional to Reynolds number.