126
3 Fans
dence. Figure 3.18 is a sketch of the velocity triangles at the rotor outlet (absolute
velocity v 2 ) and after the width leap (absolute velocity v’ 2 ). A tangential deflection
velocity is generated. We denote with subscript 2” the entrance flow of the volute
at radius r 2 after the tangential deflection by incidence. The incidence loss may be
calculated with a formula like Eq. (3.32). Enlarging the slope angle of the volute
implies that the volute is adapted to a lower flow rate than the design flow rate. The
rotor and the volute now become mismatched. The above demonstrates that some
degree of mismatch mostly is unavoidable.
The typical mismatch of the volute and the rotor, in the sense that the volute is
adapted to a lower flow rate, implies acceleration in the volute: 2
2
''
'
u
u
v
v
> . The spontaneous deceleration in the volute (Fig. 3.17, left) may completely be undone by it.
Another consequence of the mismatch is enforcement of a non-uniform pressure
distribution to the rotor, namely pressure decreasing in the flow sense. A pressure
leap at the tongue is generated thus. The non-uniform pressure distribution causes
increase of losses at the rotor outlet. In practice, it is not always obvious how to
determine the angle α s imposed by the volute. Generally [2, 6], the tangential velocity imposed by the volute to the rotor outlet v u
2
''
is calculated from the flow rate,
assuming equal angular momentum between the outlet of the volute and the rotor
outlet, ( )
''
rv
r v
C
u
3
2 2
= =
, so that
bdr
Q C r
= ∫ at the volute outlet (Fig. 3.17, left).
The loss associated to the velocity difference v
v
u
u
2
2
'
' '
−
is calculated as a deflection
loss.
3.4.7 Friction Loss Within the Volute
The friction loss may be estimated analogously to the friction loss in the rotor. The
entire friction surface must be determined.
3.4.8 Diffusion at the Rotor Inlet
The velocity within an air transporting duct in an industrial plant may be as high
as 20 m/s and even higher for short ducts (the economic velocity follows from a
Fig. 3.18 Top: velocity triangles at the rotor outlet before
and after slip ( dashed line
without slip); Bottom: velocity triangles at the volute inlet
after the width leap, before
and after tangential velocity
deflection due to incidence;
the radial velocity is drawn
exaggerated for clarity
3 Fans
dence. Figure 3.18 is a sketch of the velocity triangles at the rotor outlet (absolute
velocity v 2 ) and after the width leap (absolute velocity v’ 2 ). A tangential deflection
velocity is generated. We denote with subscript 2” the entrance flow of the volute
at radius r 2 after the tangential deflection by incidence. The incidence loss may be
calculated with a formula like Eq. (3.32). Enlarging the slope angle of the volute
implies that the volute is adapted to a lower flow rate than the design flow rate. The
rotor and the volute now become mismatched. The above demonstrates that some
degree of mismatch mostly is unavoidable.
The typical mismatch of the volute and the rotor, in the sense that the volute is
adapted to a lower flow rate, implies acceleration in the volute: 2
2
''
'
u
u
v
v
> . The spontaneous deceleration in the volute (Fig. 3.17, left) may completely be undone by it.
Another consequence of the mismatch is enforcement of a non-uniform pressure
distribution to the rotor, namely pressure decreasing in the flow sense. A pressure
leap at the tongue is generated thus. The non-uniform pressure distribution causes
increase of losses at the rotor outlet. In practice, it is not always obvious how to
determine the angle α s imposed by the volute. Generally [2, 6], the tangential velocity imposed by the volute to the rotor outlet v u
2
''
is calculated from the flow rate,
assuming equal angular momentum between the outlet of the volute and the rotor
outlet, ( )
''
rv
r v
C
u
3
2 2
= =
, so that
bdr
Q C r
= ∫ at the volute outlet (Fig. 3.17, left).
The loss associated to the velocity difference v
v
u
u
2
2
'
' '
−
is calculated as a deflection
loss.
3.4.7 Friction Loss Within the Volute
The friction loss may be estimated analogously to the friction loss in the rotor. The
entire friction surface must be determined.
3.4.8 Diffusion at the Rotor Inlet
The velocity within an air transporting duct in an industrial plant may be as high
as 20 m/s and even higher for short ducts (the economic velocity follows from a
Fig. 3.18 Top: velocity triangles at the rotor outlet before
and after slip ( dashed line
without slip); Bottom: velocity triangles at the volute inlet
after the width leap, before
and after tangential velocity
deflection due to incidence;
the radial velocity is drawn
exaggerated for clarity