Fig. 1 Schematic showing: ( a ) separated flow regions and ( b ) the secondary flow development in the pipe bend [ 2 ] More

Fig. 2 The computational domain topology for the simulations of the straight pipe More

Fig. 3 The computational domain topology for the pipe bend simulations More

Fig. 4 Location of the origin of the coordinate system and definition of planes A and B used in the results and discussion part More

Fig. 5 The radial profile of the normalized axial velocity in the straight pipe at Re = 60,000 compared with the experimental data reported by Benjamin et al. [ 27 ] at Re = 60,000 and Laufer [ 28 ] at Re = 50,000 More

Fig. 6 An overview of the computational mesh M3: ( a ) plan view of the surface mesh in the bend section and ( b ) cross-sectional view of the mesh More

Fig. 7 The normalized axial velocity at bend α = 0 deg in plane A for Re = 60,000 and R c / D = 2 for the investigated mesh density variants: dotted: M1; solid: M2; dashed: M3; dashed-dotted: M4 More

Fig. 8 The normalized axial velocity at bend α = 45 deg in plane A for Re = 60,000 and R c / D = 2 for the investigated mesh density variants: dotted: M1; solid: M2; dashed: M3; dashed-dotted: M4 More

Fig. 9 The normalized axial velocity at bend α = 90 deg in plane A for Re = 60,000 and R c / D = 2 for the investigated mesh density variants: dotted: M1; solid: M2; dashed: M3; dashed-dotted: M4 More

Fig. 10 The normalized axial velocity at locations: ( a ) y / D = 2 and ( b ) y / D = 3 behind the bend in plane A for Re = 60,000 and R c / D = 2 for the investigated mesh density variants: dotted: M1; solid: M2; dashed: M3; dashed-dotted: M4 More

Fig. 11 The normalized axial velocity in ( a ) plane A and ( b ) plane B at α = 0 deg , 45 deg , and 90 deg for Re = 60,000 and R c / D = 2 compared with the experimental data reported by Sudo et al. [ 11 ] and the numerical simulation by Tanaka et al. [ 20 ] and Kim et a... More

Fig. 12 The normalized axial velocity at ( a ) α = 0 deg , ( b ) α = 45 deg , ( c ) α = 90 deg , and ( d ) the distance of 1 D downstream of the bend for Re = 60,000 in plane A for different values of the curvature ratio, R c / D More

Fig. 13 The non-dimensional physical properties: the magnitude of the velocity perturbation, the pressure, and the axial vorticity (from the leftmost, respectively) visualized at α = 0 deg for ( a ) R c / D = 1, ( b ) R c / D = 2, ( c ) R c / D = 3, and ( d ) R c / D =... More

Fig. 14 Secondary flow and non-dimensional physical properties: the magnitude of the velocity perturbation, the pressure, and the axial vorticity (from the leftmost, respectively) visualized at α = 45 deg for ( a ) R c / D = 1, ( b ) R c / D = 2, ( c ) R c / D = 3, and ( d ... More

Fig. 15 Secondary flow and non-dimensional physical properties: the magnitude of the velocity perturbation, the pressure, and the axial vorticity (from the leftmost, respectively) visualized at α = 90 deg for ( a ) R c / D = 1, ( b ) R c / D = 2, ( c ) R c / D = 3, and ( d ... More

Fig. 16 The iso-surfaces of the Q -criterion for Q = 1: ( a ) R c / D = 1, ( b ) R c / D = 2, ( c ) R c / D = 3, and ( d ) R c / D = 4 at Re = 60,000 More

Fig. 17 Contours of the Q criterion plotted on pipe cross sections for ( a ) R c / D = 1, ( b ) R c / D = 2, ( c ) R c / D = 3, and ( d ) R c / D = 4 at Re = 60,000 More

Fig. 18 The normalized axial velocity for ( a ) R c / D = 1, ( b ) R c / D = 2, and ( c ) R c / D = 4 at α = 0 deg , 45 deg , and 90 deg in plane A for different Reynolds numbers More

Fig. 19 Secondary flow and non-dimensional physical properties: the magnitude of the velocity perturbation, the pressure, and the axial vorticity (from the leftmost, respectively) visualized at α = 45 deg for ( a ) Re = 10,000, ( b ) Re = 20,000, ( c ) Re = 40,000, and ( d ) Re = 60,000 f... More