Abstract
Visualization studies of flow in vertically standing 180° bend rectangular section with strong curvature for Reynolds numbers (simplified Re) from 700 to 1500 reveal two regions of secondary flow. The secondary flow in such a strongly curved bends as curvature ratio 0.6 and 1.5 can be considered to have a forced vortex and a free vortex regions.
When fluid particles exist in the former region, then fluid motion is rotational so that the dye-streak developes into a fine spiral line by the centrifugal force and primary flow, and besides dye-particles exist in the latter region, then fluid motion is irrotational, so that the streak developes into circular wavy thin belt by shear deformation and primary flow.
A streak line which injecting dye to the center nozzle of the riser cross-section splits into two at θ=about 30° and secondary flow develop into rotation at θ=about 60° (θ=angular distance from the bend-starting point).
Thus, twin counterrotating vortices come into the bend flow. The radius of gyration of a fluid particle in the barrier circle between forced and free vortex increases or decreases according to the strength of the free vortex.
In this test, modiried Fround number exceeds far less than unity, the gravitation force will dominate than centrifugal force by bending. Further, the Coriolis force give rise to an additional acceleration to the centrifugal force.
By this study was found that the secondary flow constitute a pair of counter-rotating streamwise vortices which is combined free vortex with forced vortex for Re from 800 to 1300. But above Re of 1300, the forced vortex strengthen than the free vortex as Re increase. Downward to Re of 800, the forced vortex weaken than the free vortex as the Reynolds number decrease.
Numerical expressions for three typesof secondary flow patterns are given such as Vθ=αr +l, Vθ= αr1/2 and Vθ=αr-1 for the forced vortex, barrier and free vortex respectively, where Ve is peripheral velocity, r the radius of revolution and a constant.
