2. VELOCITY DIAGRAM AND CALCULATIONS FOR
IMPULSE TURBINES
• Velocity diagram gives an account of velocity of fluid entering
and leaving the turbine. Velocity diagrams for single stage of
simple impulse turbine and compound steam turbine are
described here. Simple impulse turbine: Single stage of simple
impulse turbine is shown in Fig. 14.14. It comprises of a row of
nozzle followed by moving blade row. Pressure and velocity
variations along the stage in nozzle ring and moving blade ring
are also shown. Subscript 0, 1 and 2 refer to nozzle inlet,
nozzle exit or moving blade inlet and moving blade exit
respectively.
3.
4. Figure 14.15 gives the inlet and outlet velocity diagrams at inlet edge and
outlet edge of moving blade along with the combined inlet and outlet
velocity diagram for a stage of simple impulse turbine.
The notations used for denoting velocity angles and other parameters
during calculations are explained as under, (SI system of units is used
here).
U = Linear velocity of blade = ∏d60/N , m/s where d = mean diameter of wheel
in ‘m’
N = Speed in rpm.
C1 = Absolute velocity of steam at inlet to moving blade or velocity of steam
leaving nozzle.(Absolute velocity is the velocity of an object relative to the earth)
C2 = Absolute velocity of steam at exit of moving bade.
5. C1w = Whirl velocity at inlet to moving blade or tangential component of absolute
velocity at inlet to moving blade.
C2w = Whirl velocity at exit of moving blade or tangential component of absolute
velocity at exit of moving blade.
C1a = Flow velocity at inlet to moving blade or axial component of absolute
velocity at inlet to moving blade.
C2a = Flow velocity at exit of moving blade or axial component of absolute velocity
at exit of moving blade.
V1 = Relative velocity of steam at inlet of moving blade (Blade velocity at inlet)
(Relative velocity is the absolute velocity of one moving object compared with
absolute velocity of other object.)
V2 = Relative velocity of steam at exit of moving blade (Blade velocity at exit).
m = Mass of steam flowing over blade
p = Ratio of linear velocity of blade and absolute velocity at inlet of moving blade
= U/C1
6. k = Blade velocity coefficient (Ratio of relative velocity at exit and inlet) =
Alpha ∂ = Angle of absolute velocity with respect to the direction of blade motion.
alpha ∂1 = Angle of absolute velocity at inlet to moving blade or nozzle angle.
alpha ∂2 = Angle of absolute velocity at exit of moving blade or inlet angle of fixed blade
in next stage.
BetaB= Angle of relative velocity with respect to the direction of blade motion.
Beta B1 = Angle of relative velocity at inlet or inlet angle of moving blade.
Beta B2 = Angle of relative velocity at exit or exit angle of moving blade.
7.
8. • Here steam enters the nozzle and leaves so as to smoothly glide
into the ring of moving blades. Steam leaves nozzle with absolute
velocity C1 and at an angle of 1. This steam stream will be delivered
to moving blade with velocity C1 and angle 1 but due to linear
velocity of moving blade the steam stream actually glides over the
moving blade with velocity V1 and blade angle at inlet 1. This
velocity V1 is actually the result of two velocity vectors C1 and U. V1
is called the relative velocity of steam at inlet of moving blade.
Steam stream leaves the moving blade with velocity V2 which is
relative velocity of steam at exit of moving blade. Thus relative
velocity is the actual velocity with which steam flows over the
moving blade. For a perfectly smooth and frictionless blade this
relative velocity should not change from inlet to exit as there is no
expansion of steam in moving blade (blades are symmetrical and
passage between two consecutive moving blades is of constant
area type from inlet to exit). Actually there always exist some
friction over the blade so the relative velocity at outlet will be
smaller than the relative velocity at inlet, i.e. V2 < V1. This reduction
in relative velocity is quantified by parameter called blade velocity
coefficient (K). Blade velocity coefficient (K) is defined as,
• K=V2/V1
9. • If we look at inlet section 1, then it is obvious that
for the maximum change in momentum steam
should be delivered to the moving blade
horizontally i.e. (alpha)∂1=0 and also leave
horizontally i.e. ∂2 = 0 with the semi-circular
shaped moving blade. This semi-circular moving
blade is not possible practically as the moving
blade wheel (ring) has series of blades and each
blade has to receive steam from series of nozzles
one after the other. This is the reason due to
which nozzles are placed at some angle to the
blade, say angle 1 in this case.
10. • Due to injection of steam at angle ∂1 with velocity C1
over the blade, steam shall have two components of
velocity i.e. one tangential component and other axial
component. Tangential component of velocity is
parallel to the direction of rotation of blades and is also
called as whirl velocity. Axial component of velocity is
perpendicular to the direction of rotation of blade and
is also called flow velocity. Axial component or flow
velocity is responsible for maintaining flow of steam
across the moving blade row. Volume flow rate of
steam across the moving blade ring can be given by the
product of flow velocity and effective passage area
available for flow. The magnitude of flow velocity
influences the size of wheel for given steam volume
flow rate.
11. • The whirl component of velocity is responsible for generation of thrust force
due to change in momentum. Both whirl velocity and flow velocity being the
two perpendicular components of absolute velocity depend largely upon the
angle of absolute velocity i.e, ∂. At inlet the angle ∂1 should be selected
depending upon the thrust requirement and maintenance of flow across the
blade row. With increase in angle 1 the whirl velocity, C1 cos ∂1, decreases
while the flow velocity, C1 sin∂ 1, increases. Thus the maximization of one
leads to minimization of the other and so the compromise should be had for
selecting the angle of absolute velocity. Similarly at exit of blade again there
shall be whirl velocity and flow velocity components. For absolute velocity at
exit being C2 and angle of absolute velocity at exit being ∂2 (this shall be the
inlet angle for subsequent nozzle if more than one similar stages are there),
the whirl velocity shall be C2 cos ∂2 and flow velocity as C2 sin ∂2. In the
simple impulse turbine stage this whirl velocity component at exit is a kind of
loss at exit. Therefore in order to minimize loss at exit this component should
be minimum. For minimizing the whirl velocity at exit i.e. C2 cos ∂2, the angle
∂2 should be made minimum. Minimum loss could be reduced to zero if
angle ∂2 is equal to 90. This becomes a typical case in which the turbine
discharges axially (at 90) and such turbines are also called axial discharge
turbine.
12. • Thus it is obvious that in case of impulse turbine stage the moving
blade merely deflects the steam and the change in direction of
steam from inlet to exit causes change of momentum and thus
thrust is generated. Moving blades being of symmetrical type offer
a constant cross-section area between two consecutive blades from
inlet to exit and so no expansion occurs in the moving blade. The
steam expansion only occurs in the nozzle. Also in the absence of
expansion across moving blade the pressure of steam remains
constant from inlet to exit under ideal conditions. For symmetrical
blades the inlet and exit angles of blade are same i.e. Beta1 =
Beta2.
• Velocity diagrams are separately drawn at inlet of moving blade and
at exit of moving blade as shown in Fig. 14.15. Combined velocity
diagram for the stage is also given here. Using the velocity diagram
various parameters can be estimated as discussed ahead.
