A study is carried out for swirling¯ow of a¯uid containing dispersed micro-bubbles (nominal size 80 mm in diameter). From experimental results the location of the stagnation point is found to be a strong function of the swirl ratio, but independent of the aspect ratio of the rotating pipe section when the actual position is normalized to the length of the section. It is also found from experimental results, with an aid of a numerical simulation, that a parabolic surface is formed by some larger bubbles which are caught in orbits of the rotating¯ow ®eld. It is further veri®ed that smaller-sized bubbles pass along limited stream lines.

The¯ow characteristics and dynamic behaviour of micro-bubbles were investigated experimentally and numerically for swirling¯ow within rotating pipe sections. In the present investigation, three types of rotating pipe section were used in order to study the eVects of geometric con®guration upon the¯ow®eld. Experimental data were obtained for locations of the stagnation point and pro®les of the parabolic surface. The results obtained from experiments were examined and veri®ed with the aid of numerical analysis. It was found that the air pocket formed at the stagnation point was moved upstream by the eVect of the suddenly expanded part when pipe rotation was increased. The reattachment point did not shift downstream as a result of an increase in the Reynolds number. This is due to the fact that the vortex zone at the expanded corner expands or shrinks, depending on the speed of rotation. NOTATIONA aspect ratio C a virtual mass coe cient C D drag coe cient C L lift coe cient d bubble diameter (mm) d c critical bubble diameter (mm) d s simple mean bubble diameter (mm) D inner pipe diameter (D 1 and D 2 ) (mm) E expansion ratio g gravity acceleration (m/s 2 ) L ! length of the rotating pipe section (mm) L ¤ normalized length based on L ! L ¤ 0 normalized length from the stagnation point m b mass of the bubble (kg) m L liquid mass of the exclusion volume of the bubble (kg) N number density (1/m 3 ) p isotropic pressure (Pa) p ¤ dimensionless pressureˆp=…» L U 2 ave † r ¤ normalized length based on R R pipe radius (mm) Re axial Reynolds number Re b bubble Reynolds number Re ! rotational Reynolds number u liquid¯ow velocity vector (m/s) u b bubble velocity vector (m/s) U ave mean axial velocity (m/s) V b volume of bubble (m 3 )

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