233
6.9 Blade Shaping
has to be adapted for this higher load. In principle, a somewhat larger chord is necessary, but change of the profile shape is also possible. A second net effect is that
some mass flow is displaced from the end wall boundary layer towards the centre of
the vane channel. By this shift, the intensity of the passage vortex diminishes and it
spreads over a larger spanwise distance. So, the non-homogeneity of the outlet flow
is lower and mixing losses downstream of the vane row decrease. From the foregoing arguments one understands that bowing may be beneficial, but it should not be
too strong as by bowing, the flowed surface (so-called wetted area) increases and
by the spanwise load variation vortices are formed in the wake of a vane (trailing
vortices). It means that the actual optimisation of the bowing is quite delicate. Also,
introducing bowing on a vane row changes the inflow conditions of the downstream
blade row. So, the optimisation of a complete stage or even a number of stages has
to be considered. Concave bending at the suction side is advantageous with rotor
blades as well, for the same reasons as for stator vanes. For a discussion on the
different loss mechanisms, we refer to the overview paper by Denton [2]. A recent
experimental analysis of the effects of bowing in low aspect ratio turbine stages is
by Rosic and Xu [8]. An example of the optimisation of a steam turbine HP stage is
by Lampart and Hirt [5]. This last study shows that 3D shaping of HP and IP stages
may lead to an efficiency gain, but the possible gain is rather limited, typically 0.5
percentage points with respect to the straight stacked blades and vanes. With the
three-dimensional vane and blade shaping, the efficiency in steam turbine HP and
IP parts reaches about 94 % and 96 %. Better efficiency is achieved within IP parts
because of the lower effect of secondary losses.
6.9.2 LP Blades
The LP section of a large steam turbine is provided with long blades. Secondary
losses therefore do not play an important role. The problem with LP blades is the
large variation of the degree of reaction as a function of the blade height. Flow is
very tangential at the stator outlet. This induces a strong centrifugal force in the
space between stator and rotor, causing an important pressure gradient with high
pressure at the casing and a low pressure at the hub. Flow is almost axial at the
stator inlet and at the rotor outlet and there is no radial pressure gradient. The pressure gradient in between the stator and the rotor necessarily causes a high degree
of reaction at the casing and a low one at the hub. The enthalpy drop over the stage
should be approximately the same at all radii and thus the speed ratio increases
from the hub to the casing. The consequence is a natural correspondence between
the variation of the speed ratio and the variation of the degree of reaction, in the
sense that the speed ratio does not differ much from the optimal value appropriate
for the degree of reaction, as shown in Fig. 6.18. So, Fig. 6.18 represents the variation tendency of the velocity triangles from hub to casing, where typically R s ≈ 0.15
at the hub, and the degree of reaction increases with the radius. The longest blades
nowadays achieve R s ≈ 0.85 at the casing. The maximum blade length amounts to
about 1.20 m with a 2.00 m hub diameter (turbines at 3000 rpm: coal-fired) and
6.9 Blade Shaping
has to be adapted for this higher load. In principle, a somewhat larger chord is necessary, but change of the profile shape is also possible. A second net effect is that
some mass flow is displaced from the end wall boundary layer towards the centre of
the vane channel. By this shift, the intensity of the passage vortex diminishes and it
spreads over a larger spanwise distance. So, the non-homogeneity of the outlet flow
is lower and mixing losses downstream of the vane row decrease. From the foregoing arguments one understands that bowing may be beneficial, but it should not be
too strong as by bowing, the flowed surface (so-called wetted area) increases and
by the spanwise load variation vortices are formed in the wake of a vane (trailing
vortices). It means that the actual optimisation of the bowing is quite delicate. Also,
introducing bowing on a vane row changes the inflow conditions of the downstream
blade row. So, the optimisation of a complete stage or even a number of stages has
to be considered. Concave bending at the suction side is advantageous with rotor
blades as well, for the same reasons as for stator vanes. For a discussion on the
different loss mechanisms, we refer to the overview paper by Denton [2]. A recent
experimental analysis of the effects of bowing in low aspect ratio turbine stages is
by Rosic and Xu [8]. An example of the optimisation of a steam turbine HP stage is
by Lampart and Hirt [5]. This last study shows that 3D shaping of HP and IP stages
may lead to an efficiency gain, but the possible gain is rather limited, typically 0.5
percentage points with respect to the straight stacked blades and vanes. With the
three-dimensional vane and blade shaping, the efficiency in steam turbine HP and
IP parts reaches about 94 % and 96 %. Better efficiency is achieved within IP parts
because of the lower effect of secondary losses.
6.9.2 LP Blades
The LP section of a large steam turbine is provided with long blades. Secondary
losses therefore do not play an important role. The problem with LP blades is the
large variation of the degree of reaction as a function of the blade height. Flow is
very tangential at the stator outlet. This induces a strong centrifugal force in the
space between stator and rotor, causing an important pressure gradient with high
pressure at the casing and a low pressure at the hub. Flow is almost axial at the
stator inlet and at the rotor outlet and there is no radial pressure gradient. The pressure gradient in between the stator and the rotor necessarily causes a high degree
of reaction at the casing and a low one at the hub. The enthalpy drop over the stage
should be approximately the same at all radii and thus the speed ratio increases
from the hub to the casing. The consequence is a natural correspondence between
the variation of the speed ratio and the variation of the degree of reaction, in the
sense that the speed ratio does not differ much from the optimal value appropriate
for the degree of reaction, as shown in Fig. 6.18. So, Fig. 6.18 represents the variation tendency of the velocity triangles from hub to casing, where typically R s ≈ 0.15
at the hub, and the degree of reaction increases with the radius. The longest blades
nowadays achieve R s ≈ 0.85 at the casing. The maximum blade length amounts to
about 1.20 m with a 2.00 m hub diameter (turbines at 3000 rpm: coal-fired) and