Welcome to engineering with
Rosie and part three of my series: "How does a wind turbine
work?" In the first two videos we talked about wind turbine
aerodynamics, how much energy is available to the turbine and how
the wind turbine blades use that energy to turn. We also talked
about how to analyze a wind turbine to calculate the amount
of power it generates. In today's video, I'm going to talk
about how to use the aerodynamic theory we discussed last time to
design an efficient wind turbine rotor. We saw in the last video
the equation for lift, the lift force depends on the air density
the local airflow speed, chord and lift coefficient, which
itself depends on the shape of the airfoil and the local angle
of attack. The most efficient lift distribution occurs when
there's constant circulation along the span. If you want to
see the maths behind this, then I'll put a link in the
description to where you can find that. But basically, what
you need to know is that the lift divided by the relative
flow velocity should be constant along the span. Because the
local wind speed and angle vary along the length of the blade, a
straight rectangular blade will not give constant lift along its
length. So the geometry of a wind turbine blade needs to be
changed to achieve a more constant lift distribution. If
you assume a single aerofoil for the whole blade, then to get an
optimized blade, then you need to change the cord and twist
angle along the blade span so that the lift force will be
constant. The chord needs to decrease as the local wind speed
increases along the span and the twist angle needs to change so
that you keep the profiles operating at the most efficient
angle, which is the angle of maximum lift to drag ratio. This
image shows that theoretical optimal chord distribution in
green. It has a very large chord at the route due to the low
rotational velocity there. But you can imagine that if you
manufactured a blade like that, it would be very heavy because
of that huge chord at the blade route. Real wind turbine blades
generally don't look like that. Wind turbine blade designers
usually choose to make a simpler design like this red outline
which has a linear taper. This design takes a small hit to the
aerodynamic efficiency in order to make it easier to manufacture
and to make it lighter. The aerodynamic performance of the
inner blade section is not as important as the outer section
since locations close to the hub have low torque and therefore
they make a smaller contribution to the power output. So the loss
in aerodynamic efficiency is not large compared to the gains in
manufacturability. And weight and also cost savings from
reducing material. If you design a blade with a chord and twist
distribution changing like this, then you will end up with a
constant lift force on the blade length. But only at the specific
wind speed that the blade was designed for. If you change the
wind speed but leave the rotational speed the same, then
the chord and angle of the profiles along the span are no
longer optimal. If the wind speed is lower than the design
speed, then the local angle of attack will be lower than
optimal so you'll get worse performance. In the other
direction, if the wind speed is higher than the design wind
speed, then local angle of attacks are larger than optimal.
If the local angle of attack increases beyond a certain point
called the stall angle, then the flow over the profile will
separate and it will stall. This causes a sudden drop in lift
force and a sudden increase in drag. Operating a wind turbine
in wind speeds other than the speed it was designed for leads
to less efficient operation, if the rotational speed stays the
same. In the examples I just went through, we kept rotational
speed constant as we changed the wind speed, and we saw the local
speed and angle of the airflow change away from our design
conditions resulting in a less efficient operation. But if you
can change the rotational speeds as the wind speed changes, then
you can keep your optimal design over a range of wind speeds. You
can see from the equation that it's actually the ratio between
the rotational speed and the wind speed that matters. Wind
turbine designers use this ratio as an important design
parameter. They call it the tip speed ratio. That is the ratio
between the speed of the blade tip due to rotation and the wind
speed. Modern wind turbines are mostly able to rotate at
variable speeds so they can keep the tip speed ratio constant to
allow optimal performance over a large range of wind speeds. Okay, so now we've talked about
how the blade geometry changes along the span to keep lift
constant and how rotational speed and wind speed need to be
kept in proportion. We've seen how all these parameters need to
be adjusted if one of them has changed in order to keep
performance the same. There is one last important parameter
that we need to discuss, and that is blade solidity. That is
the proportion of the swept disc that is covered by blade. So
either one fat blade or several slimmer ones will give you the
same solidity. In the previous video, we talked about the Betz
Limit, which is the maximum amount of energy that can be
extracted by a wind turbine. Following the same conditions
that get you to the Betz limit, you can find the optimal design
of a wind turbine taking all of the parameters we've just
discussed into account. Again, I won't go into the derivation
because the maths is complicated, but I'll put a link
in the description where you can find it if you are interested to
find out. And I need to note that this equation is a slight
simplification, with the same limitations as the BEM theory
that I mentioned in the previous video. But again, it's accurate
enough to design these important blade geometry parameters. So we
can see from this equation that we can alter any of these
parameters and still maintain optimal aerodynamic performance
if you alter the other parameters accordingly. But this
doesn't give us a very neat design process. Because if
everything is flexible, then you don't really know where to
start, you need to be able to lock something in in order to be
able to start the design of the other parameters. So where do
wind energy engineers start? So far, in this video series, we've
been talking about optimal aerodynamic design. But now we
have reached the end of what we can achieve by considering only
the aerodynamics. To find a starting off point, we need to
step outside to a big, complicated and pretty messy
list of competing design requirements. I'll talk about
some of the major ones here. But remember that these will change
from application to application and any change can be
accommodated to make a turbine with good aerodynamic
performance if you adjust the other parameters. So first of
all, you've probably noticed that most wind turbines have
three blades, most wind turbine manufacturers are not
considering changing the number of blades for each new turbine
design they create. So that is typically one starting point:
three blades. Another aspect that is really important to
overall turbine design is blade solidity. One big design trend
is to move towards more slender blades. This is appealing to
designers because a slimmer blade rotating at a higher speed
can produce the same power with lower aerodynamic loads and
lower extreme loads when there are high wind speeds during a
storm. So that means that there's less force that has to
be carried by other turbine components and less force that
tries to push the turbine over. If you want to reduce the chord
and maintain performance, then you need to increase the tip
speed ratio and therefore the rotational speed. This is
typically limited by noise considerations. The amount of
noise that a blade makes depends on how fast the blade tip is
moving through the air. So especially for onshore turbines,
the rotational speeds tend to be limited due to noise. designers
of onshore turbines will use the maximum rotational speed that
allows the turbine to stay below a regulated or agreed noise
limit. And then one last remaining parameter that we
haven't discussed is the lift coefficient, which is a function
of the shape of the airfoil. The aerofoils of a wind turbine
blade commonly differ along the span. For aerodynamic and
structural reasons the outboard blades section experiences
higher relative wind speed, and contributes more torque than the
inboard section. This makes aerodynamic performance critical
at the tip and thin, high-lif aerofoils are typically used i
that region. On the other hand the inboard blade sections -
hose close to the root - ha e less effect on aero
ynamic performance but a large effect on the structural beha
ior of the blade. So in thi area, you'll use bigger aero
oils that have better struc ural characteris That is the basics of wind
turbine blade aerodynamic design, and there is a lot more
to the topic than I've mentioned here. But I'm going to leave
that for future videos. I'll also be making a video on blade
structural design so stay tuned for that in the future. And as
always, if you didn't understand something or want more detail on
a topic, then please let me know in the comment and I also love
to get ideas for new videos that way. If you want to see more
videos like this, then please like, subscribe and share with
your friends. I'll see you next time.
