544
15 Axial and Radial Turbines for Gases
within the separated boundary layer with turbulent reattachment and formation of
a separation bubble. Driving the laminar separated boundary layer into turbulence
is often realised by appropriate impact of passing wake zones of an upstream blade
row (relative motion between stator and rotor). Tuning the impact is difficult. So,
optimising a turbine cascade is mainly a matter of boundary layer control. Optimum
profiles are therefore termed controlled boundary layer (CBL) profiles.
Within a turbine, the turbulence level in the core flow is very high. The degree of
turbulence, i.e. the magnitude of the fluctuating velocity compared to the average
velocity, typically exceeds 5 %. Transition in an attached boundary layer is then
directly induced by fluctuations of the main flow, without necessity for instability of the boundary layer flow, as with a very quiet main flow (natural transition
by Tollmien-Schlichting waves). Transition is then termed bypass transition,
meaning that the instability is bypassed (see discussion in Sect. 13.4.1). With impact of a wake zone of a preceding blade, transition is very quick in an attached
boundary layer due to the kinematic impact together with a high turbulence level
within the wake. The boundary layer may become laminar again after the wake
has passed. With wake impact onto a separated boundary layer, the separated shear
layer quickly becomes turbulent due to instability (Kelvin-Helmholtz instability),
strongly increasing the potential for reattachment. With a low Reynolds number, the
momentum loss thickness at the end of the suction side is mainly determined by the
size of the separation bubble. It is then favourable to choose a profile shape with
the velocity peak rather far forward and a high wake impact frequency. The separation bubble decreases by that. The turbulent part of the boundary layer increases,
causing friction loss increase in that part, but this increase does not counterbalance the strong decrease of the mixing loss behind the separation bubble. With a
higher Reynolds number the bubble size is already small spontaneously. It is then
favourable that the velocity peak lies rather far backward and that the frequency of
the wake impact is lower. So the optimum profile shape depends strongly on the
Reynolds number [3].
Adaptation to supercritical conditions is done the same way as with an aerofoil.
The Mach number distribution of Fig. 15.5 does not change essentially. The flow
becomes locally supersonic at the suction side and the supersonic zone ends with
a normal shock. The suction side shape must be such that the Mach number just
upstream of the normal shock is as low as possible.
Optimisation of a stator cascade does not principally differ from that of a rotor
cascade, but the general acceleration with a stator cascade is larger for a low degree
of reaction of the stage. With a limitation on the maximum Mach number at the suction side, the decelerating zone in Fig. 15.5, left, becomes weaker. This is beneficial
for the loss coefficient, but the level of outlet kinetic energy is higher.
Transonic Cascades
A transonic cascade means subsonic inlet and supersonic outlet. These cascades
occur in both rotors and stators. Figure 15.6, left, sketches the shock waves within a
15 Axial and Radial Turbines for Gases
within the separated boundary layer with turbulent reattachment and formation of
a separation bubble. Driving the laminar separated boundary layer into turbulence
is often realised by appropriate impact of passing wake zones of an upstream blade
row (relative motion between stator and rotor). Tuning the impact is difficult. So,
optimising a turbine cascade is mainly a matter of boundary layer control. Optimum
profiles are therefore termed controlled boundary layer (CBL) profiles.
Within a turbine, the turbulence level in the core flow is very high. The degree of
turbulence, i.e. the magnitude of the fluctuating velocity compared to the average
velocity, typically exceeds 5 %. Transition in an attached boundary layer is then
directly induced by fluctuations of the main flow, without necessity for instability of the boundary layer flow, as with a very quiet main flow (natural transition
by Tollmien-Schlichting waves). Transition is then termed bypass transition,
meaning that the instability is bypassed (see discussion in Sect. 13.4.1). With impact of a wake zone of a preceding blade, transition is very quick in an attached
boundary layer due to the kinematic impact together with a high turbulence level
within the wake. The boundary layer may become laminar again after the wake
has passed. With wake impact onto a separated boundary layer, the separated shear
layer quickly becomes turbulent due to instability (Kelvin-Helmholtz instability),
strongly increasing the potential for reattachment. With a low Reynolds number, the
momentum loss thickness at the end of the suction side is mainly determined by the
size of the separation bubble. It is then favourable to choose a profile shape with
the velocity peak rather far forward and a high wake impact frequency. The separation bubble decreases by that. The turbulent part of the boundary layer increases,
causing friction loss increase in that part, but this increase does not counterbalance the strong decrease of the mixing loss behind the separation bubble. With a
higher Reynolds number the bubble size is already small spontaneously. It is then
favourable that the velocity peak lies rather far backward and that the frequency of
the wake impact is lower. So the optimum profile shape depends strongly on the
Reynolds number [3].
Adaptation to supercritical conditions is done the same way as with an aerofoil.
The Mach number distribution of Fig. 15.5 does not change essentially. The flow
becomes locally supersonic at the suction side and the supersonic zone ends with
a normal shock. The suction side shape must be such that the Mach number just
upstream of the normal shock is as low as possible.
Optimisation of a stator cascade does not principally differ from that of a rotor
cascade, but the general acceleration with a stator cascade is larger for a low degree
of reaction of the stage. With a limitation on the maximum Mach number at the suction side, the decelerating zone in Fig. 15.5, left, becomes weaker. This is beneficial
for the loss coefficient, but the level of outlet kinetic energy is higher.
Transonic Cascades
A transonic cascade means subsonic inlet and supersonic outlet. These cascades
occur in both rotors and stators. Figure 15.6, left, sketches the shock waves within a