CIVIL WORKS GUIDELINES FOR MICRO-HYDROPOWER IN NEPAL
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limiting diameters beyond a certain range which could affect
the optimisation process. An example of Penstock
Optimisation is shown in Example 6.2
6.5 Surge calculation
6.5.1 GENERAL
The thickness of the penstock pipe is determined by the gross
and surge heads of the scheme. It is therefore important to
have some understanding of the concept of surge before
calculating the pipe wall thickness.
A sudden blockage of water or rapid change in velocity in the
penstock (or any pipe that has pressure flow) results in very
high instantaneous pressure. This high pressure is known as
‘surge’ pressure or often referred to as “waterhammer”. Surge
pressure travels as positive and negative waves throughout
the length of the penstock pipe.
Water hammer occurs as the surge wave travels from the source
or the origin of the disturbance, along the pipeline until it
strikes some boundary condition (such as a valve or other
obstruction) and is then reflected or refracted. If the pipe is
strong enough to withstand the initial surge effect, the
pressure will ultimately dissipate through friction losses in
the water and pipe wall as well as through the forebay. The
speed of the surge wave (wave velocity) is dependent on such
factors as the bulk modulus of water, flexibility of the pipe
and the ratio of pipe diameter to wall thickness.
In hydropower schemes, positive surge characteristics are
different for different types of turbines. Surge head calcula-
tions for the two most common turbines used in micro-hydro
schemes are discussed here. Note that these calculations are
based on the initial (i.e. undampened) positive surge head.
In practice there will be some damping of the surge pressure
as the wave travels along the pipe, and whilst the pressure
fluctuation is uniform in the lower portion it diminishes
gradually to zero at the forebay, as shown in Figure 6.3.
However, the pipe is normally designed for static head plus
constant positive surge over the full penstock length.
Note that the negative surge can produce dangerous negative
(sub-atmospheric) pressure in a penstock if the profile is as in
Figure 6.3. Once the negative pressure reaches 10 metres the
water column separates, and subsequent rejoining will cause
high positive surge pressure sufficient to burst the penstock.
Sub-atmospheric pressures less than 10 metres can cause
inward collapse of the pipe wall, so should also be avoided. If
there is any possibility of negative pressure the pipe wall
thickness must be checked for buckling (see Section 6.6.2).
To avoid negative pressure, move the forebay to Point A in
Figure 6.3. Alternatively take measures to reduce the surge
pressure.
Figure 6.3 Surge pressures
“Bursting disc” technology could provide a reliable means of
safely releasing excess head in case of surge pressure without
increasing the pipe thickness (which is the convention). This
is discussed in Chapter 10.
6.5.2 PELTON TURBINE
For a Pelton turbine use the following method to calculate the
surge head:
1. First calculate the pressure wave velocity ‘a’ using the
equation below.
a = 1440 / 1+(2150 x d/E x t) m/s
where:
E is Young’s modulus in N/mm2. The value of Young’s modulus
for mild steel, PVC and HDPE can be seen in Table 6.2.
d is the pipe diameter (mm) t is the nominal wall thickness
(mm), not teffective
2. Then calculate the surge head (hsurge), using the following
equation: hsurge = av/g x 1/n where: n is the total no. of
nozzles in the turbine(s).
Note that in a Pelton turbine it is highly unlikely for more
than one nozzle to be blocked instantaneously. Therefore, the
surge head is divided by the number of nozzles (n). For example
if a penstock empties into two Pelton turbines with two nozzles
on each turbine, n = 4
The
velocity
in
the
penstock
(V)
is:
V
=
4Q
πd2
3. Now calculate the total head: htotal = hgross + hsurge
4. As a precaution, calculate the critical time, Tc, from the
following equation: Tc = (2L)/a
where:
Tc is the critical time in seconds,
L is the length of penstock in m,
‘a’ is the wave velocity calculated earlier.