Okay, get started. I'm gonna give sort of
a preamble, and I'll turn it over to the
to the real show in a minute. My name
is Dennis Grove and work here. Denktas. I
would ask if you wouldn't mind just to sign the
sign up sheet. Um, on your way out
, I guess, if you would, please welcome
to Kelly Hall. Um, we are his home
of Actos, the Institute for Critical Technology and Applied
Science. We're really happy to have you here.
Our vision for this institute is to facilitate interdisciplinary,
uh, collaboration, innovative, interdisciplinary collaboration for sustainable
Future. And our New Horizons Seminar series is one
of the ways that we do that We're really very
excited to co sponsor this seminar series with create center
, the Center for Renewable Energy. An aerodynamic testing
as well as the department. Um, just a
little bit about our speaker series we have. We
have speakers that cover all eight of our thrusts here
, Denktas. But I'm going to mention some of
our previous energy related speakers. We had Eric tune
here. There is the director of our body.
We had William William Brinkman, who's the director of
the U s office of Basic Science. And we
had four filter over summer who runs the Runs and
Rails National and Technology Center. And this Friday,
we are hosting Stephen choose former secretary of secretary of
energy in the United States. So we're very excited
to bring these energy related speakers today, and I'm
passing it off the week. All right. Good
afternoon, everybody. It's my pleasure to to an
honor to introduce this afternoon. Speaker, uh,
professor Luciano Castillo from Texas Tech University. Uh,
he's the Don k Clay Cash distinguished, uh,
engineering a chair in wind energy at Texas Tech.
And he's also executive director of the and president of
the National Wind Resource Center. He's been a taxes
tax since, uh, 2011, uh, following
his time at 11 years. Was it 11 years
at r P? I, uh he is a
expert in turbulence measurement of turbulence, using experimental techniques
in direct numerical simulations of turbulence and multi scale a
syntactic analysis, impressive skills that in recent years he's
put towards wind energy and looking at the performance of
wind turbines. His, uh, presentation this afternoon
is entitled wind plant aerodynamics. A spectral analysis,
uh, for energy and train mint. There will
be time for questions after seminar. And I'm hoping
there is also going to We have the room till
3. 30. So if you want to meet
Professor Castillo after the seminar, there will be plenty
of time and possibly even some additional refreshments at that
time. Thank you. Thank you. With him
. It's a great honor. It's a great yes
. I'm always very delighted to come here and see
the wonderful things that everybody is doing here. And
this is a beautiful facility. I would like to
thank the center it to, uh, the department
and create create the center for this kind invitation.
And today I'm gonna be talking about something that I'm
super passionate about. And you will understand why,
um and, uh, the topic, as you
see, it's the one planet aerodynamics and typically come
from the idea that we're not looking necessary. What
happened at the single blade effects, and normally,
what you see here, um, is that you
? You see the effects of the single blade?
Sorry. I can, uh, the single blade
. And normally you try to design what is the
optimum blade design for the performance of the single turbine
. What we're asking here is not that question.
We would like to know what could be the optimum
blade design that would be optimum for the entire wind
farm. And that's a very different, different question
because, uh, the type of scales that contains
it will will deal with a different aspect of the
design. But more importantly, it tells you that
perhaps the design will be completely different then, if
you consider single turbine now from the other perspective,
uh, one of the important aspect and this is
what we're here is turbulent. And we argued that
turbulence continues pregnancy of scales and that variety of scales
could be very important in the energy and training and
the performance of the turbines. More importantly, we
would like to know what are the critical lan skills
that could supply some of that energy into the array
. Now there are two things that you could answer
from that if you know that there's a variety of
spectrums of scales and you know that tourists could play
a very big role. What does that mean?
It means that maybe I can change the design of
the single played in a different way That enhances that
, uh, in treatment of the energy. And
this is one of the things that I'm going to
show you today. Now, the other part of
the of this question, which we can't quite answer
that today. But I'm hoping with one of the
collaboration with one of your colleagues we could do that
. And that is that if we know that,
for example, I'm going to show you I'm gonna
tell you one of the answers that we showed that
all of the energy that is in training to the
wind farm doesn't necessarily come from the horizontal flow,
but comes from the vertical, uh, rain of
stress from the turbulent flow from the adversary flow.
And that means that you could now redesign the plates
in a way that optimizes that energy and treatment.
That's one example. Okay, so that's the idea
that we want to use. We want to use
the knowledge of that. We learn from turbulence,
and and there's this interaction of the wind farm.
Now, the interaction of the single played but of
the wind farm to design a better blade. Uh
, and of course, this work I need to
tell you this This work I didn't do it by
myself. I mean, I had to acknowledge charge
, Minimal from Johns Hopkins. We've been working together
since 2006, Jose LeBron, which was one of
my former student. He said United Technology and my
for my actor post because, uh, Jensen Newman
, that it comes from math department in R.
P. So one of the overview that I would
like to discuss is the motivation. Obviously, we
have to focus very clearly. What is the motivation
and challenges of this problem of wind energy? And
, uh, after that, I'm going to talk
about the objective was specifically we're gonna be doing today
. And then one of the issues that I want
to address is the questions emotion. I really love
equations, and hopefully many of you do and the
whole idea. And this is one of the advantage
that we have in in, In in engineering is
that you have equations of motion. So we're gonna
use the questions of motion in this case, the
never circuit question, and then we're gonna use the
kinetic energy question. Now if you have a set
of very clear defining questions, Then we could design
a set of experiments that will allow you to measure
all of those quantities. Now, if you can
measure all of those quantities, then you could understand
better the physics of the interaction between what? The
atmospheric boundary layer with the entire wind farm. And
that's basically the kind of things that we would like
to do during this discussion. Now, these these
scale experiment anybody and I will show you some pictures
Anybody that when you see a wind farm, there's
a major problems, right? The topography is a
major challenge, right? But the wind direction is
shaking constantly. Also, you had a lot of
effects, like temperature variation. So one of the
things we would like to do is then to understand
all of those effects very carefully in what well controlled
experimental setup. Okay. And one of the things
we're gonna do is a scale down. So we're
not gonna do the measurements and the entire food scale
. Instead, we're going to use it in a
scale down wind farm. Okay, And then at
the end was one of the things we want to
do is to discuss the result particularly what I said
about W t B. I'm talking about wind turbine
boundary layer profile, and that is that as they
get bigger and bigger and bigger, you would like
to know what is the wake or the velocity profile
that describes that wind farm? And the reason is
because if you know that you will know how you
could place them, you will know how much power
that wind farm will produce. And then you could
do all the characterizations, such a place and then
in a different location. And then at the end
, I'm just going to focus on some of the
conclusions. So let's start the show. Please stop
me at any time. Okay, So you have
any questions? Just stop, okay? You don't
have to wait until the end. So this is
a very, very famous picture. Almost every meeting
that you go with energy, you would see it
. And I feel very bad for for him.
But that was taken by Christians tennis. Because if
you have patent that picture, he could have make
some good money out of that. And I'm one
of them that I used it a lot, but
I give him credit And if you look at these
pictures is a very, very important picture. This
is an offshore wind farm in Denmark, and it's
actually show you in real life what is really going
on in that particular case. You take that picture
from a helicopter and you have enough condensation that you
could have a perfect flow visualization and what you can
see from this picture if I'm sorry that do we
have a Is there some Denise, do you have
another point? That that's all right, But but
you would have to take my word for it,
okay? Or we have to. But But if
you look at this picture one of the things that
the flow comes from this from the front and it
is expand through the back and what you actually see
is that you see a lot of coherent structure.
You see structures of turbulent flow that seems to be
repeated themselves. So as you move downstream, you
see that the floor is highly turbulent. We could
see that because you see a lot of mixing.
But you could also see that there is a boundary
. This is the boundary is a region where physical
effects see are important, but you could see a
growth of the bounds of the velocity feel as you
move downstream. In other words, if you go
, you're moving X direction. You can see that
growth in the vertical direction, and you could also
see that spread. So this picture tells you the
whole thing that I'm going to do today. And
actually, one of the important aspect of this is
this, for example, Uh, and this is
one of the reasons why we want to do,
um, winter and experiment, because in the field
, what do you have with the incoming flow is
changing drastically over time. Alright, every second is
changing not only in terms of the magnitude velocity,
but the direction. If you look at the temperature
, the temperature also exchanging. So a lot of
the inlet conditions is very, very important. And
one of the important aspect of this is this.
If the inlet flow is changing, one of the
important question is how does the devolution of that flow
affect the performance of the entire wind farm? So
that's one of the questions we want to be able
to address. But from the perspective of all of
this discussion is what is the role of turbulence in
all of this energy and treatment. Now, if
you go if you go to this part, what
do you have? Well, if you look carefully
, you see that the first survivor experienced very little
turbulence of none was the one in the back.
What you see is a highly experienced high levels of
turbulence, and this is what is called the way
to wake effects. And this is one of the
things that is the limiting causes for wind farm performance
. And that's one of the questions we want to
be addressed today. Now, if you look further
from this, this is I don't know how many
of you are. I'm assuming some of you took
three dynamics. But if you look far downstream,
there seems to be a region where the velocities they
don't seem to be changing that much, and that
region is called a fully developed. In fact,
if you look at the flow when you took in
fluid dynamics, Shannon flow in a pipe, you
say Well, the flow becomes fully developed when the
velocity profile no longer changes, right? So in
this particular case. This is very, very important
. So you can see that in the inlet you
can see it developing region. You can see that
the flow is changing a lot as you move.
And then as you move far downstream, what do
you see? Very little changes. And one of
the question is, Is this Can we characterize this
flow in a way that you could say is this
is fully developed or not? And you know this
. If it's fully developed, you will know what
the weight profile will be. If you know what
the work is, then you could use this in
different set of equations, even to create cost of
any cause of economic model costs. Okay, so
this is one of the important issues we want to
be able to address from this picture. Now the
other one is this. These machines are massive.
In fact, you could put a 7 47 inside
of the rotors of these turbines. So now you
worry about that you have a highly turbulent flow.
You have to worry about that. These machines are
massive, and then you have to worry about the
interaction between the flow behind the turbines. Okay,
And then at the end of this, this is
the story. You have a turbine in a highly
turban for us. So just imagine this. You're
flying in an airplane, and at some point the
pilot panics and say you have to put your seatbelt
because we have a lot of trouble. And,
Floyd, we're gonna be here for five minutes and
everybody is panic. Right? Well, imagine these
turbines 24 hours a day, seven days a week
for the entire year, experiencing highly true in the
flow. So So this is one of the important
aspect. And in fact, I always say turbulence
is the order of one problem on wind energy.
And and there are many reasons for that. I'm
not biased about that. Okay, So one of
the things that we want to address today is the
following. Can we characterize the development of that boundary
layer? Can we do that? And And the
question is, what set of tools we have that
we could characterize that flow as you move downstream in
the floor. Okay. And as you characterise that
you say so what? Yes, That's not a
big deal. We could determine whether or not is
fully developed. But the mayor question we want to
be able to address is this. What is the
role of turbulence? Number two. What are these
scales that will be important to provide energy for that
array. And if I can know those skills,
I can do many things. I can redesign the
plates to impact those skills. And I could know
exactly how I can play those termites so I can
maximize that instrument of those claims skills in the floor
. All right, so we move forward, I'm
gonna use the same to talk about the challenges.
So this is what this story is so disturbance in
the front are basically designed to what? To experience
a very nice uniform flow. And, of course
, the turbines in the back. They experience a
highly turbulent flow. And then you begin to worry
that Hey, we have turbulent flow and there are
32 reasons. It is our friend, uh,
Ricardo. He would worry about what are the skills
that are going to be important for my noise generation
, Right. And then, if you have somebody
in material science, they may be worried about what
are dealing skills that are going to be important for
what? The external load that those plates are going
to experience. But if you talk to somebody like
me in turbulence will say how important is turbulence to
produce energy? So the good thing is that turbulence
could have a very good news. And it could
also have very bad news, depending on the question
you want to address and the one that I'm gonna
focuses on what? The energy, the life skills
that will be responsible for the energy. And so
if you look at this chart is a very,
very important chart, this is what's taken by Rebecca
Barthelemy from Indiana University and what you look here,
This is the normalized power. So what you have
taken is the the first turbine you put and and
then you take the power generated by any turbine around
any given role. And you normalize that power by
what the power produced by the first turbine. So
if you're in the first turbine, the power is
what is one is 100%. So So this is
what you see. Uh, in the 1st 3rd
1 here. Now this is plotted are different turbines
. 1234567 But it's plotted as a function of what
? The space in between turbines. In other words
, the further away you are from the turbines.
What happened? The less the drop you get.
Okay, So if you're 10, 10 diameters,
if you're 10 diameters from the 10 10.5 rotor diameter
, you have a drop about close to about 2022%
. And if you look at the green, which
is 99 rotor diameter, you get a power drop
energy loss due to the weight from the first round
to the second, about 30%. But if you
decided to play the storm and even closer to each
other about seven rotor diameter, you're talking about a
drop about 40%. That is bad news. And
in fact, depending on the wind direction, you
can see that this power seems to settle down over
the entire region. And the question you want to
say this is, where does the energy comes from
to feed this array? Okay, so the issue
here is this. If you rely only on the
mean velocity to provide some of the energy during bad
luck, you're out of commission. Uh, if
you look at the picture on the right hand side
, the difference is that you have a different wind
direction. So you can see from this picture very
clearly that not only the level of tourists is critical
, but the wind direction will also play a role
about the power that these turbines will produce. Now
, if you're in finances and this is what I
love about this this field, this is the the
best playground for everyone to play. If you have
friends in economics, guess what they could play here
. If you have friends in electrical engineering, they
could play because of the power transmission, right?
The great integration, energy storage. But also in
this in this study by Elkington, Manuel and Mark
Goldman. In 2006, they showed that the biggest
uncertainty in the economic cost that exists is due to
the weight loss. In other words, the fact
that you do not quite well where the wake is
, you have a process minus 20% of uncertainty.
This is big. Okay, that's not a joke
. Um, so now if you continue with this
discussion about the challenges in terms of of the turbulence
. You can see that if one of the study
actually from charge, many of all for many of
all admires in 2011, they show that the optimum
spacing between turbines is not seven is not nine.
It's not 10 rotor diameters, but 15. Well
, that was good that he showed that the bad
news is that that would increase your cost of energy
. Because that means that you have to get more
, more land. All right, so you don't
want that? Um But if you continue through this
study, one of the major issues is that what
the load that or that unsteady flow that is acting
on the blade or on the tower will damage your
gearbox will damage your rotors, and it will damage
what your your tower. So the challenge here for
many of you is is many of these turbines what
they're designed to last for what, 20 years?
Yes. Is that in line? Turbines are there
for a strike yet? Not not for in line
. So in this case, yes, yes,
a very good question. In fact, one of
the one of the major issues I cannot just pointed
out here, but it is in this type of
rectangular arrangement. But one of the important findings that
the group from Minnesota Well, you tomorrow, That
is now Urbana Champagne. And there's a group in
Syracuse that we did something similar. We did an
optimization, and you could find that there's a different
configuration. Not this exactly. This arrangement where you
could actually even increase the performance. The the capacity
factor by 10 10% senses going to be time to
go on the jets in line. Yeah. Yes
, sir. Patient? Yeah, it was found
. Yeah, Yeah, yeah. Yeah. Staff
, Yes. That. Yeah, Yeah, sure
. And here, Yes. Yes. And that's
the case. I mean, you could see the
one and I will show you this. The one
that I prefer to use this arrangement is because you
reduce the number of variability. In other words,
we want to have enough as more controlled conditions as
possible to be able to understand the physics. But
if you do that, you would have a difference
. What you need to consider there is the the
great, the lines, the power lines. And
that's part of the issue. Um, but but
this is part of the issue. They're breaking down
in seven years. And the question again, my
argument is turbulence is the number one issue even on
this problem. So So let us now look at
the objective. Alright, so number one, what
I'm going to show you is that turbulence will play
a very key role. And not only that,
but you will look from the questions of motion that
I know if currency is very important, mainly in
a training energy from above, that means I can
redesign the plate, right. I can redesign the
place such that they attract more of the energy.
All right, so So I'm going to focus on
that, Then the other part that I'm gonna focus
is to characterize the development of this array. You
know the word. Remember the picture when you see
those those big race in the wind farm. The
question is, can you characterize that in a way
that you can determine whether or not they are fully
developed or not? And the question is, if
you know, that's fully developed. Guess what happened
. The boundary will not grow anymore, right?
The boundary. Basically, we settled down, so
if you know that there is a growth of the
boundary layer. That means you could change the altitude
in a way that you can optimize the energy even
further. All right, so there's a lot of
insight that we could use here to do these studies
. So one of the things that we're gonna look
is that the power measurements, we're gonna look at
the budget analysis, and then we're gonna look at
the main profiles, I mean, and rhinoceroses as
well. And finally, this is the question we
want to all of us want to look at today
. What is the role of the large skills of
turbulence in the in the performance of the wind farms
? All right, so So let us start with
the with the questions. All right, So So
let's suppose you have this very, very large array
, all right? And this typically is great.
And 10 boundary thickness of 10 Delta is typically the
boundary thickness of the atmosphere. Okay, what about
one kilometer? And the question is, as these
guys get bigger and bigger and bigger, you would
like to know what is this profile? Okay,
now that profile you saw from before what happened?
Well, the flow is what highly three dimensional right
? What's changing in space? And it's also changing
drastically in time. So when you perform average in
time and then you x subsea means that we have
performed an average in what in space. So if
you do all of that, then you could characterize
basically one profile that only varies on one variable.
And this is quite nice, because if you know
that this is the profile, this is what we
call the wind terrible and boundary profile. Then you
could characterize the the power produced by this array.
So this is one of the things that we want
to do today. What is a profile? And
then, um, this is the question. You
know that question already? First, we want to
characterize whether or not this is a fully developed number
two. We want to also understand what is that
wind turbine and boundary profile again? If I know
that I can work with somebody in design and those
people in design could say You know what, Luciano
? The best way to locate these turbines is not
this perfectly shape. Is this triangular shape? Why
? Because you already have the profile of that week
. Okay, so this is what, One of
the reasons why this is very important. And then
the last one is, uh what is the rate
at which all of your statistics? Because fully developed
. Okay, just remember this fully developments that the
profile no longer exchanges. So we're gonna perform that
analysis and and see what is really going on in
this entire ray. Okay, I didn't tell you
the whole story as to why winning such a big
deal, but normally, like I do that.
But if you look at this, for example,
this is the induction factor. And if you remember
, this is normally used to create a wake function
. So if you look at a is induction factor
, this is basically the ratio of the velocity,
the average velocity in the back in the back of
this disk, okay, and the average velocity in
the front. So if you take both races of
that velocity, that's what you call the induction factor
. Now you can use that induction factor and create
what awake model and that wake mother will represent what
the profile for that are typically is. All right
now, this is very important, because now you
could now understand how you can maximize the power.
And at the same time, you could know how
you could place these turbines. Okay, so there
are different types of wake model that exists. I'm
just going to present one here that tried to explain
why this is important. So if you look at
here, this is from Jensen 1983. Basically what
he said, you subzero represents what? The incoming
velocity. Uh, a is what? The induction
factor will depend on what develops it in the back
and develops it in the front and theta. Remember
that you suffer from this picture that this floor was
, what highly turbulent flow, Right? So we
don't forget that the argument is let's forget all of
that, and I'm gonna dump all of that effect
of turbulence in this parameter data. Okay, so
that's an empirical constant where we're gonna input all of
the variation due to turbulence. All right. Very
, very simplistic. And at the end of the
day, you can use this to describe how you're
gonna locate disturbance. In fact, their economic models
that rely also on this information as well So let's
do this. So if we have this, we
also learn the following from we learned that this velocity
is highly three dimensional, right? It depends on
what X, y and Z depends on space and
depends on time. So what I'm going to do
is that we're gonna perform an average in time,
and then we're gonna ended up and the average xz
, these are called special averages. So if we
perform both of those, you only ended up with
one with one function. That depends on what one
coordinate. Okay. And that's the whole story.
Because now I can represent how does the mean velocity
or render stresses various with the vertical distance. All
right. And so let us start with the average
stock in question. So if you look at this
, So So this is the X component. Um
, So if you remember, the meters Law Force
is equal to m A. This is what it
is if you put the density in the front of
the left hand side and I'm sorry, I cannot
see, uh, if you put the density in
the left hand side, these are basically what the
nurture terms those are the terms responsible for what?
The acceleration of the flow. So it deploys fully
developed. Guess what? There is no such acceleration
. All right? And so you have all of
these terms that are responsible for the nursery terms this
dp infinity dx represent what? The pressure gradient and
, uh, guess what? You ve you prime
b prime bar represents what? This is the rain
of stresses. Remember this. You took the instantaneous
signal and you brought that into what and mean quantity
plus a fluctuation. And you ended up with what
? One of notes and that of noise called here
the Reynolds Shear stresses and X subsidies because you have
performed special averages and I would explain why this is
such a big deal. In other words, if
you have a complex terrain, you're gonna perform special
averages in the sea to remove many of those effects
. Or if you have turbines are took place to
each other, you will worry about what is called
here. The dispersants stresses. So you double prime
the prime are called, this person stresses. So
this is the difference between the time average quantity and
the special average. All right, so when you
perform a special average and this time average that difference
will ended up with what with what you call here
. We call here disperses, stresses, and this
was done by Europol in in 1991 and f the
last term in the right is what? The average
trust. So as the flow goes through the turbine
, that would create a trust trust force on the
blade. And that's what you call the F bar
. Okay, Now, look at this. If
you take the dot product of the force of this
component X with the U component, what did you
get? I mean, kinetic energy, right?
So you take the dot product of this X component
, and that's that's the rest of the story.
So So if you do this, you will end
it up with the main kinetic energy industry in west
direction. So you can do this. You can
write the vertical component of the universe socket question,
and then you do the product with the velocity,
the vertical component, and you get what you mean
kinetic energy for the normal component. In this case
, I'm only including the the X component. So
all of this term here represent what? The objection
term, Okay. And what is this? Here
is a correlation of the mean velocity with the pressure
gradient. And this is where the story is.
We're going to focus here, Okay? This year
is called the energy flux. Those are the flux
is due to what? To the reign of stresses
. So we could show from the main kinetic energy
question how important all of these terms are. So
if I can measure all of them number one,
I can determine whether or not in fact, if
you're close enough to the world what happened to the
infection terms, they go to zero. I don't
care about them. And then I can use this
equation as a measure of whether or not the flow
, because fully developed number one, I can do
that. But the most important issue this term here
represent the entrainment, the energy flux due to the
rain of stresses. This is the flux due to
this person stresses. And this is what typically,
this term is called what? Production term. But
because you're talking about for the term money, we're
going to call it, uh, terrible anticipation.
Okay, Because that energy is not going to determine
it is going to flow itself. And then the
double prime B prime that represent what this person is
dissipation. Okay. Again, when you perform an
average, the average quantity introduced a new unknown,
which is dispersing stresses those quantities with the ground with
y, with you cannot produce more energy. So
they become disperses, stresses and P is what the
dot product of what these three wives velocity with what
with the trust force. And guess what I can
. If I can measure all of these, I
can balance the budget. So not a big deal
. But this is what I want to know how
important these guys are. Okay, so we have
made the assumption that we're very close to the war
. Close enough, and we could drop all the
infection terms. All right, Now, what is
the goal here? Well, the goal here is
that if I can take advantage of the two questions
of motion that I have and continue to see,
I can use that information design a well controlled experiment
, okay, in which I can measure all of
this information. And from that I mean, I'm
talking about four centimetres turbines. I can use that
to understand the physics of the flow, and then
I can use that for modeling. Now, this
tells us that if you cannot use the ransom question
to solve this problem, you must account for this
term. If you're going to use in a complex
terrain Now say if you move forward, the the
this is basically the experimental setup. So this is
the winter Johns Hopkins. Uh, this is what
is called the course in winter now, and,
uh, if you can see here, this is
some streaks. So this this black line here,
basically what we have done is to create some streaks
in which there is a polynomial feet and at the
bottom, it has a gradual big changes. And
the idea is that you want to introduce one high
gradients of velocity very close to the wall, and
I will show you the winter in a prison.
But the inflow right here is described here. So
now guess what you know very precisely. What is
incoming? Flow number one and number two. You
have these turbines. These turbines are what 12 centimeters
in the in in rotor diameter. These 12 centimeters
in Hub High and the distant Here's what five diameter
. So this operation is quite shorter than what you
saw before. It's not seven, it's not nine
, it's not. 10 is five, and this
was done on purpose. And the reason was in
the early experiments that we did, I think,
actually show some of those experience. Last time when
disturbance were two separate too far, the role of
the disperses stresses were very, very minimum in the
entire energy budget. So what we decided to do
is to add two things. One, we added
this change. So this tried to represent some sort
of a complex topography. And to do these studies
are very, very difficult. We took this one
took about three or four years to complete. But
these are districts that I was telling you about.
You can see it right at the bottom. They
are very, um hi. Variation at the bottom
. So that produces what high share as the flow
enters the winner A. And then you have this
. This change and you have an array of three
by five. So again you can see that this
is very regular geometry. Nothing really crazy. Why
because I want to remove Remove the number of uncertainties
in this study. Okay. In other words,
I want to have a world control experiment. What
? I I know enough about the floor. So
So you can see here that this this change here
, that that I look at it here are about
1.5 centimeters in high. So this is 1.5 centimeters
in high. All of these turbines are rotating.
And now you know very well what the incoming flow
is. So now you're in very good positions.
If you would like to do some simulations, we
can do very nice comparison. A simulation with the
experiment. And the other thing is that we did
is that we did P i V. So we
have a 23 by 22 centimeter field of view so
you could get measurements at different points in a plane
. Okay, this is to D p I.
V Okay. And so if you look at this
from the other angle, So if you look at
the separation in X is five diameters so this this
distance I'm sorry. This system is X. This
is in Z, and this one is three diameter
in the X direction. The separation five and it
is P ratio is four. So from all of
this information, we basically have enough details. Now
there's one limitation. This place I mean, the
hope high is 12 centimeters. You're talking about very
, very small turbine and the problem that we're talking
about it today, this morning that why we want
to go to a bigger array is the following the
thickness of this place. They don't have a profile
. In other words, this is basically two dimensional
. It's like because they're very, very too small
to be able to create any profile on the play
themselves. Um, but if you look at the
the sample, we took 3000 samples at seven years
and the field of view of the P I v
. So in other words, so if you take
a snapshot in a plane around the center line,
you can see how some of these structures of the
flow are changing in the entire plane. So this
is one of the objectives of using this At the
same time, I can know what how the profile
changes in the entire acceleration. In other words,
you can see the entire evolution of the flow.
And this is part of the idea of what we
want to attack here. Yes. Did you you
mentioned the tip speed ratio was four. What does
that mean? In terms of the rpm, how
it scales to full scale. And uh huh.
Fork order. Yes, they do. They do
this disturbance, they do have a small motor,
and actually, you have a resistant on them.
So the rpm is about 1000. About 1000.
They're going very, very fast, super fast.
And, uh but then you put some resistant,
and actually, this is how we measure the power
. So the more of themselves have a little current
from which we could measure the voltage and we will
get the current. And that's how we get the
power on this. So they have some resistance in
all of them and actually, from the entire distance
from all of them, we could actually get the
power for the entire way. Yeah, so the
the So there's some limitations and actually the scaling This
is some of the issue. One of the issues
that we cannot scale the Reynolds number. The rain
is somebody is completely out of the question. But
the the rest of the information is comparable for the
most part. Mhm, Yes. So the this
is the curve for the power. So basically,
what you have this is the angular velocity. And
I basically this is the curve from kind of meh
novo. And the idea is that you could get
this relationship and t is basically the torque. And
you can see that this expression in terms of the
current if you know what the current is through the
resistance of the motors, you could basically back up
what the power is that they produce. And if
you look at this curve, this is the power
curve. This is the vertical. This is the
powering each of the roses. 123 So this is
looking at determined 123 so and so forth. And
if you look at the center, this is the
power of the center of the turbine. This is
at the edge. This is the other one,
and you can see the power from the first one
to the second one drastically dropped about 40%. Oh
, thank you. Thank you. Uh huh.
Thank you Okay? Okay. Now we're in business
, so you can look at the power drop from
the first one to the second one, which is
about 40%. If you remember, that was exactly
what you saw in the sharp from the field of
in Barthelemy. Now, the question is this.
If you look at this curve, basically the power
settles down. And if you're very naive, many
of these studies in the past have been shown that
if the power drop reaches a constant value, this
race are called fully developed. What I wanted to
argue today is that that that observation of using only
mean values to represent whether or not this is fully
developed is quite is inconsistent. Actually, you cannot
use that to represent this as a fully developed.
This is the last turbine. And what you show
here is that the power here is about 0.23.
What now? So now you have a means by
which one can make arguments whether or not this is
fully developed from the power measurements themselves. Of course
, we're not saying that this is the way you
should do this. Now the question we would like
to do If you know what this information is.
Can I use other set of information? In other
words, can I use the data from the from
the From the velocity field measurements and the mean Kennedy
Kennedy question to make the assessment whether or not these
are actually really becomes fully developed. And if you
look at that, for example, this is the
profile. So what we're gonna look now is the
rain of shear stresses. Now again, to be
able to get all of that information need to know
what are different stresses what is the mean velocity.
And I need to get the revelations and put that
into the kinetic energy question. Once I do that
, then I can make that assessment. So why
basically represent the vertical axis? And you basically represents
what this right here is the Reynolds Shear stresses you
ve and you double prime is what Remember this.
This is personal stresses, and in the past,
what we show actually was that those his personal stresses
were very, very small. Actually, when we
when we first did these studies in 2000, the
top paper that we published in 2010, we showed
that those his personal stresses were very insignificant. But
what we show here is quite the opposite. That
that when you have some sort of a complex terrain
or when determines, are too close to each other
. The role of this, this person stresses,
are very high. And actually, you begin to
be to be suspicious. Here. You can see
that as they these turbines are rotating. They seem
to be producing what high levels of turbulence. And
so this is the tip. The top line here
represent the tip. The top tip. This one
is the lower part. And guess what? If
you put the duck product of these Reynaud stresses with
the mean those are what the flux is right,
the energy flux due to the rain of stresses.
And we could do this. Actually, if you
look at this chart, this is represented vertical axis
. And here you have what the stresses in this
case is what you ve the Reynolds Shear stresses with
what with the U bar. So it's the mean
flow, right? So this is the energy flux
is and guess what? If you take the area
underneath this curve, what? This represents the energy
flux due to the rain of stresses. And so
this is very nice, because now you can use
what the questions of motion you could use The lost
the field measurements to make assessment as to how important
those terms are. So if you look at this
is the area, this is the density. Here
you have the area, and here's the Renaissance stresses
. This is the correlation with the mean flow.
And if you subtract the lower point, all of
this area here will basically give you what the energy
flux due to the rain of stresses. Okay,
Now let us remember this. This gives up a
0.62. What does that mean? Well, look
at this. We measure about 0.23 right in that
fourth turbine. That means that the energy flux and
produced by the Rennes stresses is of the same order
magnitude as the power measured by the turbines. This
is a big deal. It tells you now that
the role of these Reynaud stresses are going to be
very, very important. In other words, you
don't have to worry about only about the stream wise
energy, but the vertical entrainment of the energy,
And that's a big deal now, because now I
can say, Look, if this radio stresses the
flux of energy due to the registries are very important
, I can then redesign the blade in such a
way that maximize that vertical entrainment of the energy.
Okay, And I'm gonna show you some more pictures
that I'm going to illustrate that point. Now,
if you look at the disperses stresses, which is
this component with the main flow, you could do
exactly the same. So you can look at the
energy flux is due to the, uh, disperses
stresses. And this again, this is this person
stresses, is the main flow. You can take
the top value minus the lower value. And that
difference basically will give you what the total value of
the energy. So the energy produced by the disperses
stresses is about 0.13. What, which is close
to what you measure before. And that tells us
that now, when you have some sort of a
complex train, you do have to worry about modeling
. This disperses stresses, and this is part of
the the idea here. Now you can do this
for the energy flux is you could. I mean
, I'm not going to show you here because I'm
going to focus more on the part of this story
. But if you look at the pressure and you
can get the pressure gradient and the correlation with the
mean velocity, you can get the pressure drop here
, and then you could measure How much is the
power or the energy produced by the pressure drop across
the entire ray? And from this, you could
now make estimate of what? Remember this the entire
energy budget so you could get the power that you
measure. Um, and then you could you could
get the The flux is due to the radio stresses
. Then you could get the flux is due to
what this person stresses. And then you could get
what the losses due to what the Reynosa stresses,
this is the true anticipation. This is the participation
. And here what do you have? The correlation
due to the pressure gradient. And if you add
all of these terms, you're gonna tell me Luciano
, this is not equal to zero, right?
And that tells us something. Remember what we did
. We make the assumption that in the case of
the fully developed, the infection terms are going to
be zero. So they tell the two things first
, that this array is way too small to be
fully developed. In other words, you need a
way, way longer array to perhaps begin to see
that this assumption that dropping the infection term in the
case of fully developed is actually valid. The second
important point is that this contribution of the infection terms
should be important in the consideration. So now we
know demonstrated two things. First, when you get
the power measurements, our conclusion was that perhaps this
array is fully developed. When you look at them
in kinetic energy and you perform the energy budget based
on the assumption that if this is fully developed,
those terms in the infection terms will be zero.
You basically we conclude that this is completely inconsistent to
what you see before. Now, what option do
we have? Well, we could try to look
at the profiles, right? We could characterize the
entire profile and see how do they change in X
? That's probably one hope and try to see How
does that compare to all of this? But to
summarize. What I wanted to point out is this
This is very critical. So from this, besides
the fact that this is not fully developed, what
we demonstrated here was that this reign of stresses are
the first order term. This is what I was
telling at the beginning that the major important issues on
on wind energy or the other one problem is turbulence
. And and this is evidence of that. So
the fact that this term is that the same order
magnitude as a power that you measure tell us this
that a lot of the energy is going to be
fed from the array above. Okay. And that's
actually before you could take advantage of that information of
that knowledge to redesign the plate. So we go
back to what we were talking this afternoon. Can
we go back and redesign this plate? That is
optimal for the array. And this is on the
idea now that we learned that the registrations are important
, that all of the energy is coming from the
atmospheric boundary layer above. So what I would like
to do is I'm gonna press some some points here
, but let's look at this This is the this
is, uh this is a fairly new result.
Actually, all of this is in the, uh
, forgot to put it. This is the paper
that we show in the physics of fluids that just
came out last month. But this is, for
example, as the floor comes from left to the
right, you can see that the flow, uh
, accelerate. In other words, the floor knows
, Hey, I have a structure. They are
better slow down, so you can see how it
slows down at the beginning. But this is what
I want you to pay attention. I want you
to look very carefully. How do you read?
Is high speed okay, so you can see above
the tip of the array high speed flow. In
other words, what you see is that there is
a complex interaction you have outside the atmospheric boundary layer
. And inside of the array, you have what
boundary airflow inside of the array. But at the
interface at the interface, you have a regional high
speed flow, and this is very, very important
because this could tell us that a lot of the
energy is coming from what the interaction of the flow
above with the array. Okay, this in blue
is obvious because if you have a wake, if
you have a structure that structure is going to produce
What awake? And that's what he slowed down here
. So you see, this week is quite far
and you can see this below, and then you
can see the high speed above the array. Now
, if you look at the vertical velocity and this
is quite interesting if we look at that, that
component this is again the flow comes from left,
right? This is the mean velocity again, okay
. And what you see here is the flow because
its direction he knows that there is a turbine.
The flow goes above. So it's positive velocity and
here goes below. So a lot of the velocity
goes above the turbine. Okay, not a big
deal, But you can see positive velocity here,
positive And as you move downstream, the structure seems
to be highly elongated. In other words, the
large skills downstream seems to be even more pronounced than
what you saw initially. The other important issue that
I want you to know there's a turbine here.
Just look at this. There's a turbine here,
Another turbine here, Another one here. And there's
one here. Now look at this. This velocity
in the top here is what is a positive vertical
velocity. And this one is what negative. What
it's telling you is that there is, as the
turbines are rotating the determine themselves or the voters are
producing What a rotation on the floor as well.
Okay, and and, uh, that's very evident
here. So from the vertical velocity, there are
two things. The flow goes around the turbines not
a big deal, but that this shows you evidence
that there's a week rotation as well. Now the
other important issue. Remember what I told you.
What was super important. The rhino stresses the correlation
of the U and V. So if you look
at this, this is very important. What do
you see here? What? We see the rain
of stresses at the beginning. As the flow comes
into the array, they're very, very small.
What that tells you that a lot of the as
the turbines rotate, they're going to produce what a
lot of the turbulence. I mean, you just
makes it more not a big deal. Nothing,
really. But look at this. Positive, remember
, was very important. Very positive was important.
Look at this. At the edge of the turbine
, a lot of the Iranian stresses is produced.
Okay? And again, this is consistent. What
? That is what this is telling us that a
lot of that interface between the atmospheric boundary layer and
the winter by an array is very critical. Okay
. And that interface is the one that we need
to take advantage to do other stuff. So outside
of the array, what you see, what low
values of Reno stress is very low values of Raina
stresses, but very high behind the turbine. Exactly
what you saw in the picture from the from Denmark
, remember? Now what I would like to show
you is that the following model based on this this
is telling us that it's very clear that there is
a boundless growing above the ray, right? It's
very clear we saw that. Right. So we
propose that there is a three layer one that is
above the turbine. So this is gonna be called
above the rotor. We're gonna call one in between
. That is going to call the swept and then
one below that, We're going to court below the
rotor. Now what we want to do is the
following. Remember that you could make the assessment whether
this this characterization of the winter been or it could
be done by what? Performing a velocity profile.
You can measure the power, or you can make
sure what you mean kinetic energy. And we saw
from the from the latest one that this is not
fully developed. Now, do you think this is
possible? Guys, if this is growing that now
, I can use this physical knowledge to redesign the
way the servants are developed. Phenomenal. The correct
the boundary will grow in this direction. What can
you do with the hope to hear? You could
increase it, right? These guys could be increased
. And that tells you that this fundamental knowledge of
understanding turbulence could help us redesign better, better performance
of wind farms. Okay, Um, so let's
look at this. I'm going to just switch this
, okay? So, again, this is the
mean velocity. This is the mean velocity, and
this is what we're going to do. Okay,
We're going to look a dash line. We're going
to have already velocity at the tip here over the
entire X direction. Remember that. If I know
that the X profiles are not changing too much,
that give us a sense of what whether or not
the flock will be fully developed. And then I'm
going to evaluate the velocity profile at the rotor swept
at the center of this the rotor. And we're
gonna see how those that profile changes with eggs and
then we're gonna do the same at the below the
rotor. You fix it? Why? And you
see how the exchanges and this is the first,
the first round. This is right here the second
, the third and the fourth. So it's moving
in this direction. And you could say from this
picture, Well, that profile above the rotor doesn't
quite seem to be fully developed. It seems to
start changing. It seems to change, but this
is the one that I love the most places.
So if you look at this picture, remember,
I mean, I don't know. Many of you
may be willing could recognize this, but many of
the profiles in a boundary layer looks like this.
This list, this profile in the rotor swept looks
very similar to what we know in boundary layers,
and in fact, the variation here doesn't seem to
be as much as what you see in the in
the above the water. But if you look at
below the rotor below the rotor, you see a
significant variation in you. So it's very confusing,
probably for you to look at all of this picture
. But what the most important one that you want
to see is that the the the the Rotor Swept
seems to be more in what, in an equilibrium
than above the rotor and below the rotor. So
the reason why I'm putting this up is because France
and in 1992 proposed that there's a two layers where
the layer below the hub high and there's another layer
above the hob high where those two layers are in
equilibrium. And in fact, he proposed that the
velocity profile in both of these letters could be longer
. It me are logarithmic. This one could be
, but there's no way that this profile is going
to look great in any way in any way.
And if you look at the V component, okay
, This is the same velocity. So what we
did here is that this is the same you velocity
. We took this average velocity at the top tip
, okay, for the entire region, the rotor
swept up. And then this one represents below the
rotor. And what this represents the maximum variation and
the minimum variation over those profiles. What you can
see here very clearly is that the maximum variation you
can see a large variation above the tip. But
look at this point. Oh, nine. That's
the difference. This telling us the variation in the
rotor swept along the entire X direction is what very
, very small compared to what? Below the rotor
and above the rotor. This is important. The
rotor swept seemed to be more equilibrium than everything else
. Okay? And so let's look at the V
component. And if you look at the V,
I'm gonna switch it because this is some interpretations that
we have to do. But if you look at
the V over the entire race, so this is
the first profile is right here, and then you
can see that all they are all scholars everywhere.
And part of the reason is because the velocity here
seems to be lower. So this is positive.
You have positive velocity, you have negative. But
if you look at the sweat region, the profile
seems to be covered up, which is consistent to
wait to this. So this means that in the
in the region, in the boundary, a lot
of the energy is going what from the floor of
and indeed, when we do the energy budget and
we didn't show you here a lot of the energies
coming vertical, but a lot of the energy,
but the main vertical velocity is coming from the bottom
up. And And if you look at the the
below the rotor, you can see that this profile
is gonna cover up and everything else needs to be
not changing so much. I did not. Today
, with all of this, is very hard for
you to make a distinction whether or not all of
these profiles are fully developed or not, or characterize
this array. So if you take the average,
so if you take the average, which is the
solid line and this is the maximum, this is
the minimum. The difference between this is a point
Oh, nine. If you look at the rotor
swept this point Serial 67 and then below the rotor
is 670.15 The message here is that the rotor swept
seems to be in a more equilibrium than everything else
in terms of the main flow. Now what we
want to do is to have Can we characterize this
in a more rigorous way than what I show you
here? And we can do that. I'm sure
I'm going to show you hit this. We could
do that by taking what we call the heroin.
Or, in other words, you can look at
the profile over the X, the vertical direction and
horizontal direction in all of this plane and take the
difference in the second velocity. So if you look
at the profile in front and behind the 1st and
2nd turbine, if you look at that difference,
if this is very small, you could begin to
make assessment whether this is fully developed, so were
normalized. If we integrate the entire region here,
we integrate the entire region in the second one,
and we normalized by what the incoming flow. This
could give you an assessment as to how small or
how much the norm be, how much this flow
will become fully developed. So what we did is
that we did that for the mean velocity for the
world number, velocity, reign of stresses and even
the energy flux is, and this basically gives you
a more complete picture. So let me let me
explain you because I think I have dropped so much
information. All right? What we have done is
is we have performed well, control experiment right where
we know there's not so many variables in the floor
. Then we tie those want to what? The
questions of motion simply to make assessment as to how
much important turbulence could be in the floor and in
the energy budget. And then I also took the
same data and the what averages To understand what whether
or not the profile becomes what fully developed. Okay
, so is this in the same information in a
different way. If you do this, this a
r is Meanwhile, above the rotor r s is
the rotor sweat and below the rotor. And this
is the mean velocity war normal mean velocity. And
this is the Rennes Uh normal citywide stresses. Reynolds
stresses war, normal stresses and this is the energy
flux. But let's pay attention to this as you
go from the first turbine. In other words,
if you go from here to this is the 1st
and 2nd turbine sick 3rd and 4th and fourth and
five. If you look at this, this is
what you have the arrow nor in the first from
the first turbine as you move in the X direction
. Guess what happened? The flow as it gets
bigger and bigger in X becomes what, more fully
developed? Okay, so from the main perspective in
the above the ray, this vital 0.3 is the
norm. It goes down as you go from the
rotor swept. You can see the rotors. It
is about the same valley. It's a little bit
smaller, but if you go below below the turbine
, these points or nineties points or six, it
tells you what very close to the wall. The
main flow in the X direction is less in equilibrium
than above, so above the array, these proteins
to become more what in equilibrium and as you go
downstream, it more evident that this becomes what more
of a fully developed. But if you look at
the V component, if you look at the B
what you make, the first thing is that above
the road and you see what the paranormal is a
lot higher than in the main flow. So that
immediately telling you tells you what the world number component
is in less equilibrium, that the extreme wise component
and also you can see that this one look at
this this is 0.9 to 7.5 point 85 Guess what
happened. The vertical velocity becomes worse as you move
down. Three. Why? Because there is a
bound layer growing a boundary for a boundary to grow
. What happened to the vertical velocity has to be
important. The velocity has to be critical. And
if you look at the rotor swept, these values
are higher, so closer to the wall, closer
to the world, the violence becomes seems to be
more or less the same. So very close to
the world. The V velocity seems to be what
morning equilibrium than the U. And if you look
at the rain of stresses, look at this.
The reign of stress is the norm is what a
lot higher than the V. A lot higher than
you. So that tells you what If you go
from the first two first 22 wine to the three
and four. What happened to the euro? Norm
gets smaller. So as you move above the array
, the air norms becomes smaller in X because the
flow becomes more fully developed. But the other important
issue is a very close to the world. What
happened to the paranormal is a lot smaller than in
the mean velocity. Why the rhino stresses, even
though you have very close to the world, are
reducing the magnitude. But more importantly, the smaller
scale seems to be what more homogeneous so that very
close to the world they tend to be what,
more in a fully developed than when you look at
the V component or the U component. So with
all of this picture, basically, we have make
some assessment that clearly this boundary layer is not what
fully developed Number two, that there is a boundary
layer growing above theory is that we make the hypothesis
and we still don't know yet. I still have
not shown you What happened to the large scale?
So what is the first part? The first part
is that the Rennes Shear stresses is a very,
very critical component. Remember that All of that energy
that isn't training to the array is coming from the
above array and that this is not fully developed.
But we still need to find when you look at
the second statistics, what happened to them? Those
second statics is telling you that they have more.
They need more developing region to become what fully developed
. But I'm still have not answered one question to
you. Remember about the land skills. So I'm
gonna go briefly over that. Okay, so this
is what I'm gonna do. Okay, I see
that time, right? Well, do we have
time? Okay, so if you look at this
this line scale So what we're gonna do is to
look at the p. O. D. Analysis
. We're gonna do a low dimension analysis of this
data, and then we're gonna try to analyze the
kinetic energy question. Remember the kinetic energy question?
Those the energy flux is worthy one critical for the
internment of the energy and what we're gonna do there
is to find a characteristic length scale from that model
, the composition. And then then after that,
find what is the contribution of the large scales.
And I will go very quickly on this because I'm
not gonna bother you with this, but this is
the energy flux. Is that we can remember Dominican
Eric Energy. This is the index notation. This
is the terms that were very responsible for a lot
of the energy and training. So what we're going
to do is to use that one the mobile expansion
of this term. This is the three wise component
. This is a very emotional stresses. And this
one r D v. Okay, so this is
the second order term. We're only gonna worry about
the the the energy flux is that we saw before
. And what we're going to do is to do
this rendered decomposition. I'm sorry. We're going to
use the rest of the composition of the Rada stresses
in a mobile expansion. So these are the iron
functions that we could get from the data. So
we will expand the range of stresses in a model
expansion. Okay. And then from that, we're
going to determine which are the moat that are gonna
contribute to most of the energy that is entrained.
And if you do this, um, this is
the rain of stresses. This is only 100 times
steps, and you can see that a lot of
the energy in the food fields capture above the array
. If you take the 1st 30 mode, you
can see regions of high range of stresses. That's
what you saw before. And if you look at
the first mode, you can see, uh,
concentration behind the second turbine. Now, the question
is what are dealing skills that could contribute to a
lot of the energy and what I'm going to show
you. Uh, this is the key component.
What? I'm we're going to show you. I'm
sorry. What we're going to show you is that
you can decompose all of the reign of stresses.
These are all the rain of stresses in the model
expansion, and you could sum all of the energy
. In other words, you could represent a fraction
of the energy for every mode over the entire field
. And from that, you get what the fractional
contribution of energy for every mode. Okay, And
if you do this, what you show is following
. This is a fraction of energy due to the
Reno stresses that the first mode contains about 13% of
the energy. And if you look at the the
the DK, this DK is a rapid decay.
But what you can see the first night mode contained
54% of the energy. Okay, so from that
perspective, this is a very, very valuable information
, and you could actually use this to get what
a characteristic length scale. So you could say that
the highest space here we represent a characteristic landscape for
mode one for more than 20. You could do
the same. And this space here is what a
characteristic landscape for that mode. So I can represent
for every single mode what is the characteristic length scale
. And from that rations of skills over the entire
domain, I can have what, the variation of
the energy and that's that's the end of this.
Okay, and this is what you have. This
is all over the the line scale over the rotor
ratio, and what you see here is the first
nine mode contain about 50% of the energy. And
this is what we call what? Adjusting chromatic mode
. This is basically the large skills of energy.
In fact, the argument here is that the large
skills are in homogeneous and they contain most of the
energy in the entire flow. The decay here for
the smaller scales dedicated for your modes. And that
tells you that the smaller skills and that's the case
, like one over N that the smaller skills are
what homogeneous in annex. So this homogeneity, the
case, have won over end, and they contribute
to what? Very little portion of the energy of
the entire Ray. And this is indeed the most
important part of this discussion here. And this was
consistent to watch uh um, Ron, Adrian Beltre
show for, uh, internal flow. So with
this, I would like to conclude. Guys,
I'm very sorry. What we found here is the
first nine modes produce the land skills about what,
13 rotor diameter, and they produce 54% of the
energy and we're done. Thank you. I'm sorry
that if I went too fast in all of this
, Okay. What? Yes, if we had
servings differently. Damages. So I one roll 100
m play and the other 1 50. What is
the effect of that? Because getting back to the
blinds induced laws that regulate problem flows if we have
jets are different strengths. The entrainment Yes, yes
. Example. The weaker guy will try to go
and merge with the stronger guy. So yes,
six of them. He had the the for example
, the the we took. Not this data and
other data that we took in a winter now,
uh, many years ago. And we share that
with the group in Syracuse, and what they show
is that they did optimization design, and what they
were able to show is that by doing exactly taking
care of the different jets are placed that you could
, actually, if you the idea is that if
you have different altitude, different rotor diameters, different
hope, high and different locations, that is the
best way to do it from the perspective of the
power generation. But perhaps it's not economically survival right
, because it would have to deploy different grid line
, location and the construction. So in many cases
, that may not be the most viable from the
economic standpoint, but it is indeed the best way
. I mean, you would for no, there's
no There's no doubt that they would produce about 10%
more, uh, performance capacity, factor in the
performance. Really interested in knowing the work that we
do here? Or does that come work that has
been done in classical jet floor? Yeah. Yeah
. I haven't looked at that from that perspective.
To be honest with you, I have not think
about the looking at the jet studies. And,
yes, build a model. Yes. And you're
correct. And that's probably actually from this. You
can see that you saw it, right? A
lot of the growth of the entrainment comes from across
the radius, right? And, for example,
to just me, what is the pressure that was
, and how does that mean? And and actually
, it shouldn't be that bad. Because if we
borrow a lot of that knowledge and and look at
the V component because I mean, I'm sure it
will be quite easy to show in the vertical direction
that yes, yes, models exist. Interesting to
compare. Never have somebody tell me about the jet
comparison. Actually never thought about it, to be
honest with you, but it's a very good point
. Very good. Yes, We had a second
question. Yes, yes. Why? It could
be nice, but I'm not familiar. Oh,
why is it that they are always placed in a
regular, you know, really, like, especially
? Why can't we just explore more random arrangement?
See if that the second question is I'm not sure
if they take into consideration in dynamic orientation of the
rotor blades and things like what? Um, yeah
, so the okay. The first question the example
that I show you here are the exception. Actually
, if you go to any wind farm, if
you I wish you could do that sometime, fly
to Dallas and drive from Dallas to Lubbock is the
most fascinating trade. And and the reason is because
what you get is an ocean of turbines. Everywhere
is an ocean literally notion. And if you if
you look at them, actually, if you look
very carefully, they're not placed like this. Actually
, the best scientific way to have done this correctly
is to use proper optimization designed to place them.
Many of them are placed randomly. Many of them
are placed simply because of the I mean you have
a 57 diameters rotor distance. That's standard, but
they're placed in the way of degree more than anything
else. Okay, the so there's not reason behind
. This one is because it's offshore, and sometimes
you see them in a line in Denmark. But
when you look at them in United States are not
necessarily like this, and most of them are not
, Um so the second question was the effects of
what? The dynamics control. Yeah, so right
now the turbines have those controls embedded where and and
they're working. Okay, What? The future is
moving. I don't know if you're in control.
What the future is isn't predicting what the velocity is
going to be 23 minutes for now and then do
all the control strategies not only in the in this
direction but also in in inside of the air force
themselves, similar to what we have in the airplanes
with flaps and everything. This is if it's predicting
what the flow will be 23 minutes and do the
controls that that's because at that time it's not.
It's not late, right? And the question right
when you are reacting to what happened right now is
is a bit late and and that's what it is
. But more than that is can you develop contract
strategies like where you're discussing not just for one turbine
, but will be optimal for the entire A.
So when you're looking at the end, you're asking
me about the location. For example, when we
show the the importance of the reign of stresses that
tells you Look, I can change the the the
geometry To maximize this, I can also, from
the growth of the boundary layer away from the first
few turbines, I can gradually change the altitude or
change the rotor such that I'm always attracted more energy
from the floor above. So So there are many
parameters. Actually, this is a very complex brand
. This is why we like the winter because you
have less variability than what you would normally we have
in the field. And I didn't even talk about
. And you're working on that with this certification.
Eric graduate, you have the simulations with the stratification
and the effects on the wig. So So this
is something I didn't even touch it. Thanks.
Long time ago. You know Robert Taylor have a
junior at Cornell. He was looking at the effect
of turbulence on the corn. The growth of one
. Suppose you had the corn? I'm in the
Midwest, You know, fields of suppose you place
these wind tunnels there. What is the effect of
this draft on the growth of corn? Oh,
mhm. You're a tough guy. Um, actually
, actually, and I had to be honest with
you, we were discussing a proposal to see because
again, you have this This jet, these waves
propagate several kilometers downstream. And we were discussing about
a proposal to see the agricultural impact, the micro
climate and and those expressions. But But that will
definitely change the micro climate. I know for sure
, but we don't know exactly what are the benefit
? Uh, 1990 changes here. Ricardo, you
had another. Quick, You had a question there
. Let's thank Oh, thank you. Mhm. 1527 01:14:12.449 --> A:middle L:90% I