EFFECT OF CURVATURE ON DUAL SOLUTIONS OF FLOW-THROUGH A CURVED CIRCULAR TUBE

Dual solutions, i.e., two-vortex and four-vortex solutions, of the flo w through a curved circular tube are numerically obtained by the spect ral method for 0 less-than-or-equal-to delta less-than-or-equal-to 0.8 and 500 less-than-or-equal-to Dn less-than-or-equal-to 10000, where 5 is the non-dimensional curvature of the tube and Dn the Dean number. It is found that the critical Dean number above which the four-vortex solution exists takes the lowest value 956 at delta = 0 and increases with delta. In terms of the Reynolds number of the flow, however, the critical Reynolds number decreases from infinity as delta increases fr om zero, takes the minimum value of about 250 at delta almost-equal-to 0.52, and then increases again.