Fig. 1 A schematic of the elbow-type draft tube More

Fig. 2 Photographs of the transparent Plexiglas cone ( a ) and index matching box ( b ) More

Fig. 3 Contours of time-dependent axial velocity field during transient operation from HL to BEP. The data are presented along Line 1 (see Fig. 1 ), the velocity field is nondimensionalized using the absolute velocity of flow. More

Fig. 4 Contours of time-dependent axial velocity field during transient operation from HL to BEP. The data are presented along Line 2 (see Fig. 1 ), the velocity field is nondimensionalized using the absolute velocity of flow. More

Fig. 5 Contours of time-dependent radial velocity ( u* ) field during transient operation from HL to BEP. The data are presented along Line 1 (see Fig. 1 ), the velocity field is nondimensionalized using the absolute velocity of flow. More

Fig. 6 Contours of time-dependent radial velocity ( u* ) field during transient operation from HL to BEP. The data are presented along Line 2 (see Fig. 1 ), the velocity field is nondimensionalized using the absolute velocity of flow. More

Fig. 7 Gradients of the axial velocity during transient operation from HL to BEP. The data are presented along Line 1 (see Fig. 1 ). More

Fig. 8 Streamlines of the averaged velocity field for 20 similar repetitions in the cone during transient from HL to BEP: ( a ) t  = 8.45 s, ( b ) t  = 8.70 s, ( c ) t  = 8.95 s, ( d ) t  = 9.2 s, ( e ) t  = 9.45 s, ( f ) t  = 9.70 s, ( g ) t  = 9.95 s, and ( h ) t  = 10.20 s More

Fig. 1 Sketch of the flow configuration More

Fig. 2 The x -component and y -component of the bubble centroid velocity versus time for different resolutions, R e b = 300 , M o = 5.76 × 10 − 12 , Eo = 0.130 , r b f = 0.1 , m = 0.1 More

Fig. 3 A bubble and its trajectory in a swirling pipe/channel flow in a rotating reference frame, at several times, for two different rotation rates More

Fig. 4 The trajectory of the bubble for two different rotation rates seen from two different angles: ( a ) R e b = 300 ( ω z = 1.0 ) and ( b ) R e b = 30 ( ω z = 0.1 ) More

Fig. 5 Position and velocity of the bubble centroid: ( a ) The radial distance between the bubble centroid and the channel centerline versus time and ( b ) The azimuthal, radial and axial centroid velocity of the bubble centroid versus time More

Fig. 6 Effect of the angular velocity on the motion of the bubbles More

Fig. 7 Effects of the physical properties on the motions of the bubbles, ρ b is the bubble density, μ b is the bubble viscosity, and σ is the surface tension between the bubble and ambient fluid More