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2.3 Channels
2.3.2 Bends
Flow in a bend changes pressure and velocity distributions, generates adverse pressure gradients and secondary flows and the curvature affects the turbulence.
Figure 2.18 sketches the velocity distribution with an ideal fluid (frictionless).
The centrifugal force due to flow curvature generates a static pressure increase at
the bend outer part. Velocity is lower at the outer than at the inner part. There is an
adverse pressure gradient at the entrance of the outer part and at the exit of the inner part of the bend. The effect of friction causes the velocity to be higher within
the flow core than at the walls. The consequence is that the centrifugal force due
to bend curvature is higher within the flow core. The difference generates two vortex flows as sketched in Fig. 2.19. This transverse flow is termed secondary flow.
Low-energy fluid migrates from the outer part of the bend to the inner part. With
45° bends, with ratios of the radius of curvature of the bend to the diameter of
1–3, which are common values, it comes out that low-energy fluid arrives in the
adverse pressure gradient zone at the bend exit. There is then a separation risk. With
larger bend angles, core fluid arrives in the adverse pressure gradient zone at the
bend exit. There is thus a far lower separation risk with a 90° degree bend, which
is a surprising observation. Bends further affect the turbulence. Higher and lower
velocity turbulent eddies occur simultaneously at a certain place. Eddies with high
instantaneous velocity are subjected to high centrifugal force. These eddies migrate
to the bend outer part. They create vortex motions in the boundary layer that break
down into turbulence. The consequence is that turbulence at the outer part of the
bend increases. Inversely, eddies with low instantaneous velocity migrate to the inner part and damp the turbulence there. This phenomenon of turbulence migration
is clearly observed [6], but is not fully understood yet. We will describe it with the
term turbulence segregation. A consequence of the segregation is weakening of the
boundary layer at the inner part. This further increases the boundary layer separation risk at the bend inner part in the exit region.
Bend phenomena occur intensively in centrifugal rotor channels. At the
inlet, flow is deflected from the axial into the radial direction. Deflection
also occurs within the rotor channels, and the Coriolis force generates a
similar segregation effect as the centrifugal force. A bend represents a supplementary loss, on the one hand because of increased friction within the
bend, on the other by flow homogenisation downstream of the bend. By
homogenisation we mean here the recovery process of the velocity profile
towards an equilibrium profile adapted to the downstream channel. Velocity rearrangement of the fluid layers produces vortices that break down into
turbulent eddies. These eddies interact and further break down to smaller
size. The smaller the turbulent motion, the greater the impact of viscosity
forces onto the motion and the greater the fraction of the energy dissipated
in heat during the breakdown from larger to smaller structures. This process, causing energy dissipation, is termed the energy cascade. Figure 2.20
illustrates the dissipation process associated to velocity profile recovery
2.3 Channels
2.3.2 Bends
Flow in a bend changes pressure and velocity distributions, generates adverse pressure gradients and secondary flows and the curvature affects the turbulence.
Figure 2.18 sketches the velocity distribution with an ideal fluid (frictionless).
The centrifugal force due to flow curvature generates a static pressure increase at
the bend outer part. Velocity is lower at the outer than at the inner part. There is an
adverse pressure gradient at the entrance of the outer part and at the exit of the inner part of the bend. The effect of friction causes the velocity to be higher within
the flow core than at the walls. The consequence is that the centrifugal force due
to bend curvature is higher within the flow core. The difference generates two vortex flows as sketched in Fig. 2.19. This transverse flow is termed secondary flow.
Low-energy fluid migrates from the outer part of the bend to the inner part. With
45° bends, with ratios of the radius of curvature of the bend to the diameter of
1–3, which are common values, it comes out that low-energy fluid arrives in the
adverse pressure gradient zone at the bend exit. There is then a separation risk. With
larger bend angles, core fluid arrives in the adverse pressure gradient zone at the
bend exit. There is thus a far lower separation risk with a 90° degree bend, which
is a surprising observation. Bends further affect the turbulence. Higher and lower
velocity turbulent eddies occur simultaneously at a certain place. Eddies with high
instantaneous velocity are subjected to high centrifugal force. These eddies migrate
to the bend outer part. They create vortex motions in the boundary layer that break
down into turbulence. The consequence is that turbulence at the outer part of the
bend increases. Inversely, eddies with low instantaneous velocity migrate to the inner part and damp the turbulence there. This phenomenon of turbulence migration
is clearly observed [6], but is not fully understood yet. We will describe it with the
term turbulence segregation. A consequence of the segregation is weakening of the
boundary layer at the inner part. This further increases the boundary layer separation risk at the bend inner part in the exit region.
Bend phenomena occur intensively in centrifugal rotor channels. At the
inlet, flow is deflected from the axial into the radial direction. Deflection
also occurs within the rotor channels, and the Coriolis force generates a
similar segregation effect as the centrifugal force. A bend represents a supplementary loss, on the one hand because of increased friction within the
bend, on the other by flow homogenisation downstream of the bend. By
homogenisation we mean here the recovery process of the velocity profile
towards an equilibrium profile adapted to the downstream channel. Velocity rearrangement of the fluid layers produces vortices that break down into
turbulent eddies. These eddies interact and further break down to smaller
size. The smaller the turbulent motion, the greater the impact of viscosity
forces onto the motion and the greater the fraction of the energy dissipated
in heat during the breakdown from larger to smaller structures. This process, causing energy dissipation, is termed the energy cascade. Figure 2.20
illustrates the dissipation process associated to velocity profile recovery