POWER April 2021 - 30

HYDROPOWER
(P / γ) + (α x V2 / 2 x g) + Z = system constant
where P is the pressure, γ is the specific
weight of water, α is the velocity
head or Coriolis correction factor, V is
the average or mean velocity, g is acceleration
of gravity, and Z is the piezometric
data elevation.
The small case Greek letter " α " is a
3. The runner shown here is from a Kaplan
turbine. Source: Creative Commons / Reinraum
countries
has been reported to leave
10% of the whirl component in the flow
discharged from the runner.
Earlier draft tubes were designed
with several internal flow-guidance features.
One of these was a Moody cone.
This is an inverted, reinforced concrete
cone, which extends from the bottom
of the draft tube elbow upward toward
the center of the bottom of the runner.
It was used for vertical-shafted turbines
having a large whirl component at the
exit of their runner and was intended
to reduce the whirling action of water.
It was reported to have an efficiency of
up to 85%.
Another flow-guidance structure was
installed on the first two turbines at the
original or first powerhouse at Bonneville
Dam on the Columbia river. These
were reinforced concrete,
horizontal
splitter vanes that were also intended
to remove any whirl component in the
flow being discharged from a runner.
An unwatered inspection after the first
couple of months of operation found
they had all been ripped out flush with
the draft tube wall.
Velocity Head
The discharge of water from the exit of
the draft tube is a necessary part of the
flow process. To be discharged, that water
necessarily contains kinetic energy
that could not be converted into shaft
mechanical energy. Therefore, even if
the fluid is inviscid (has no hydraulic
losses), a reaction turbine can never truly
be 100% efficient. However, any excess
kinetic energy that is also discharged is
simply wasted and results in a decrease
in generation efficiency.
The most common form of Bernoulli's
equation contains the sum of the three
forms of fluid energy at any point in the
flow process, including issuing from the
exit of a draft tube. The equation is:
30
coefficient of the velocity head term
composed of the square of the average
velocity and gravity over a given crosssection.
If the average velocity is not uniform
or constant over the cross-section,
the correction factor is greater than one
and the kinetic energy represented by
that surplus over one is wasted, decreasing
generation efficiency.
Test Codes
For more than seven decades, there
have been two test codes for hydraulic
turbines. These each have procedures
for measuring and calculating the performance
of prototype hydraulic turbines.
The first is the American Society
of Mechanical Engineers Performance
Test Code 18 (ASME PTC 18), " Hydraulic
Turbines and Pump-Turbines. " The
second is the International Electrotechnical
Commission (IEC) Publication 41,
" Field acceptance tests to determine
the hydraulic performance of hydraulic
turbines, storage pumps and pumpturbines, "
published in Geneva, Switzerland.
The ASME code also applies
to turbine model tests, while the IEC
has a separate publication for turbine
model tests.
Originally the two codes had two
significant differences. First, the IEC
code has sophisticated procedures to
calculate test uncertainties or test inaccuracies
and apply a band of those values
to the test results. The ASME code
had no provision for calculating any test
uncertainties. Today, both codes have
methods of applying test uncertainties
to the test results.
The second difference is the location
of the downstream energy station
for the calculation of the net head acting
on the turbine. Specific energy has
been adopted by both codes for the
term head. Originally, the ASME code
specified the downstream energy station
was to be the equivalent still water
surface one-unit monolith width, downstream
from the draft tube exit. However,
the IEC code specifies the location
as upstream of the draft tube exit so
that the sudden expansion losses of
the fluid exiting the draft tube can be
www.powermag.com
calculated as though the velocity head
correction factor is unity and any wasted
excess kinetic energy is not charged
against the turbine's performance.
Experiments conducted at a hydraulic
research laboratory found that for
both barrels, at two different flow rates,
on a large vertical-shafted Kaplan-model
turbine located on the Snake River in
eastern Washington, the velocity head
correction factor was twice that for a
uniform velocity profile. The velocity
profiles showed the flows for both barrels,
at both flow rates, were highest
in the barrel centers. In other words, in
all cases, twice as much kinetic energy
was being wasted by being discharged
than was required. Today, both codes
specify the prototype
downstream
energy station is to be inside and upstream
from the draft tube exit. In this
manner, this inefficiency is not being
measured nor charged to the turbine.
Head Augmentation
Utilizing a Draft Tube
Over the years, designs have been proposed,
developed, and tested for auxiliary
water passages to convey unused
forebay water directly into draft tubes.
The first such method was constructed
by Thomas Edison on the Fox River in
Appleton, Wisconsin. There, he built
the first hydropower plant in the U.S. to
power his light bulbs in a friend's home.
This was a low-head plant, reported to
be no more than 10 feet.
During floods or high water runoffs,
the tailwater would rise and there would
not be sufficient specific energy for
home lighting purposes. He therefore
designed a conveyance in the brickwork
of his powerhouse that routed some of
the surplus forebay water into a circular
expansion at the upstream beginning of
the draft tube. This accelerated the total
draft tube flow, decreasing the pressure
under the runner, and was reported to
have restored about 40% of the specific
energy lost due to high tailwater. ■
-Lee H. Sheldon, PE is a hydropower
engineer with 50 years of experience.
He has published 35 technical papers
and a college textbook on hydropower
engineering, and has worked on every
federal hydroelectric project in the
Pacific Northwest, among others. He is
presently a senior hydromechanical
engineer with KGS Group in Seattle,
Washington, and was formerly a
professor at the Oregon Institute of
Technology, where he taught hydropower
engineering and fluid mechanics.
POWER | April 2021
http://www.powermag.com

POWER April 2021

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