PhD-Dissertation-materials

Video 1: Vorticity contours for 0.16<t/T<0.3 at the 90 degree cross section of curved pipe with no torsion, case T-0.

Video 2: Vorticity contours for 0.16<t/T<0.3 at the 90 degree cross section of curved pipe with torsion for case T-1.

Video 3: Vorticity contours for 0.16<t/T<0.3 at the 90 degree cross section of curved pipe with torsion for case T-2.

Video 4: Negative regions of d2 contours for 0.16<t/T<0.3 at the 90 degree cross section of curved pipe with no torsion, case T-0.

Video 5: Negative regions of d2 contours for 0.16<t/T<0.3 at the 90 degree cross section of curved pipe with torsion for case T-1.

Video 6: Negative regions of d2 contours for 0.16<t/T<0.3 at the 90 degree cross section of curved pipe with torsion for case T-2.

Video 7: Vorticity component normal to each plane for Moderate-Step flow rate with no-slip wall condition. Four cross-sectional slices are shown at the 30, 45, 60, and 90 degree locations and the axial slice location is at the Z=-2.5 mm. The black line in the cross-sectional views shows the location of axial slice. Vorticity component along Z direction (shown in axial slice) forms a branch at t≈0.24 between 30 and 60 degree cross-sections closer to inner wall which this vorticity region is connected to the Lyne-type vortex region later in time.

Video 8: Vorticity component normal to each plane for Moderate-Step flow rate with idealized slip wall condition. Four cross-sectional slices are shown at the 30, 45, 60, and 90 locations and the axial slice location is at the Z=-2.5 mm. The black line in the cross-sectional views shows the location of axial slice. Vorticity component along Z direction (shown in axial slice) which is introduced by inlet velocity profile propagates through the curved pipe and forms the Lyne-type vortex region later in time.

Video 9: Iso-surface of λ₂=-90, colored by streamwise vorticity (ω_n) component for the Moderate-Step flow rate with no-slip wall condition at four instances in time. ω_n vorticity shown at the 90 degree cross-section and the shaded areas are corresponding to λ₂≤-90 locations identifying vortex core. This figure shows the formation phase of Lyne-Type vortex.

Video 10: Iso-surface of λ₂=-40, colored by streamwise vorticity (ω_n) component for the Moderate-Step flow rate with slip wall condition at four instances in time. ω_n vorticity shown at the 90 degree cross-section and the shaded areas are corresponding to λ₂≤-40 locations identifying vortex core.

Video 11: Contours of λ₂<0 at the 55 degree cross-section during the High-Step transient flow. This figure shows that only the deformed-Dean (DD) vortices existed at the beginning of the flow and later in time at t=0.135 s the Lyne-type (LT) vortex is forming, while at later times toward the steady state condition λ₂ shows a connected regions of three vortices (in dark blue).

Video 12: Streamwise vorticity (ω_n) contour and secondary velocity streamlines at the 90 degree cross-section of the pipe during pure oscillatory flow in Lyne problem with $\alpha=17$ and maximum Re=700. The axial (streamwise) velocity profile is plotted along the horizontal diameter (black) line in cross-section, and ω_n is plotted along the vertical radius (blue line). The labels DD and L denote the deformed-Dean and Lyne vortices, respectively.

Movie 13: Three-dimensional and side views of vortex regions identified by swirling strength (λ_ci>0) at the 90 degree cross-section during the oscillatory sinusodal flow rate. Plotted lines (ξ_n) are parallel to the vortex axis and show the rotation axis. The ξ_n lines are colored by ω_n and show that the Lyne vortex is mostly aligned with the streamwise direction. The lower half of pipes wall are shown to illustrate the angle of view.