WEBVTT
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Okay, get started. I'm gonna give sort of
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a preamble, and I'll turn it over to the
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to the real show in a minute. My name
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is Dennis Grove and work here. Denktas. I
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would ask if you wouldn't mind just to sign the
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sign up sheet. Um, on your way out
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, I guess, if you would, please welcome
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to Kelly Hall. Um, we are his home
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of Actos, the Institute for Critical Technology and Applied
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Science. We're really happy to have you here.
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Our vision for this institute is to facilitate interdisciplinary,
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uh, collaboration, innovative, interdisciplinary collaboration for sustainable
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Future. And our New Horizons Seminar series is one
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of the ways that we do that We're really very
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excited to co sponsor this seminar series with create center
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, the Center for Renewable Energy. An aerodynamic testing
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as well as the department. Um, just a
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little bit about our speaker series we have. We
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have speakers that cover all eight of our thrusts here
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, Denktas. But I'm going to mention some of
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our previous energy related speakers. We had Eric tune
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here. There is the director of our body.
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We had William William Brinkman, who's the director of
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the U s office of Basic Science. And we
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had four filter over summer who runs the Runs and
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Rails National and Technology Center. And this Friday,
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we are hosting Stephen choose former secretary of secretary of
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energy in the United States. So we're very excited
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to bring these energy related speakers today, and I'm
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passing it off the week. All right. Good
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afternoon, everybody. It's my pleasure to to an
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honor to introduce this afternoon. Speaker, uh,
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professor Luciano Castillo from Texas Tech University. Uh,
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he's the Don k Clay Cash distinguished, uh,
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engineering a chair in wind energy at Texas Tech.
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And he's also executive director of the and president of
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the National Wind Resource Center. He's been a taxes
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tax since, uh, 2011, uh, following
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his time at 11 years. Was it 11 years
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at r P? I, uh he is a
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expert in turbulence measurement of turbulence, using experimental techniques
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in direct numerical simulations of turbulence and multi scale a
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syntactic analysis, impressive skills that in recent years he's
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put towards wind energy and looking at the performance of
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wind turbines. His, uh, presentation this afternoon
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is entitled wind plant aerodynamics. A spectral analysis,
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uh, for energy and train mint. There will
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be time for questions after seminar. And I'm hoping
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there is also going to We have the room till
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3. 30. So if you want to meet
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Professor Castillo after the seminar, there will be plenty
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of time and possibly even some additional refreshments at that
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time. Thank you. Thank you. With him
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. It's a great honor. It's a great yes
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. I'm always very delighted to come here and see
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the wonderful things that everybody is doing here. And
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this is a beautiful facility. I would like to
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thank the center it to, uh, the department
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and create create the center for this kind invitation.
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And today I'm gonna be talking about something that I'm
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super passionate about. And you will understand why,
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um and, uh, the topic, as you
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see, it's the one planet aerodynamics and typically come
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from the idea that we're not looking necessary. What
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happened at the single blade effects, and normally,
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what you see here, um, is that you
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? You see the effects of the single blade?
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Sorry. I can, uh, the single blade
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. And normally you try to design what is the
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optimum blade design for the performance of the single turbine
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. What we're asking here is not that question.
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We would like to know what could be the optimum
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blade design that would be optimum for the entire wind
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farm. And that's a very different, different question
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because, uh, the type of scales that contains
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it will will deal with a different aspect of the
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design. But more importantly, it tells you that
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perhaps the design will be completely different then, if
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you consider single turbine now from the other perspective,
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uh, one of the important aspect and this is
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what we're here is turbulent. And we argued that
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turbulence continues pregnancy of scales and that variety of scales
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could be very important in the energy and training and
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the performance of the turbines. More importantly, we
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would like to know what are the critical lan skills
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that could supply some of that energy into the array
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. Now there are two things that you could answer
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from that if you know that there's a variety of
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spectrums of scales and you know that tourists could play
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a very big role. What does that mean?
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It means that maybe I can change the design of
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the single played in a different way That enhances that
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, uh, in treatment of the energy. And
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this is one of the things that I'm going to
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show you today. Now, the other part of
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the of this question, which we can't quite answer
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that today. But I'm hoping with one of the
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collaboration with one of your colleagues we could do that
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. And that is that if we know that,
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for example, I'm going to show you I'm gonna
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tell you one of the answers that we showed that
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all of the energy that is in training to the
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wind farm doesn't necessarily come from the horizontal flow,
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but comes from the vertical, uh, rain of
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stress from the turbulent flow from the adversary flow.
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And that means that you could now redesign the plates
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in a way that optimizes that energy and treatment.
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That's one example. Okay, so that's the idea
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that we want to use. We want to use
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the knowledge of that. We learn from turbulence,
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and and there's this interaction of the wind farm.
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Now, the interaction of the single played but of
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the wind farm to design a better blade. Uh
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, and of course, this work I need to
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tell you this This work I didn't do it by
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myself. I mean, I had to acknowledge charge
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, Minimal from Johns Hopkins. We've been working together
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since 2006, Jose LeBron, which was one of
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my former student. He said United Technology and my
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for my actor post because, uh, Jensen Newman
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, that it comes from math department in R.
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P. So one of the overview that I would
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like to discuss is the motivation. Obviously, we
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have to focus very clearly. What is the motivation
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and challenges of this problem of wind energy? And
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, uh, after that, I'm going to talk
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about the objective was specifically we're gonna be doing today
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. And then one of the issues that I want
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to address is the questions emotion. I really love
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equations, and hopefully many of you do and the
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whole idea. And this is one of the advantage
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that we have in in, In in engineering is
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that you have equations of motion. So we're gonna
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use the questions of motion in this case, the
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never circuit question, and then we're gonna use the
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kinetic energy question. Now if you have a set
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of very clear defining questions, Then we could design
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a set of experiments that will allow you to measure
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all of those quantities. Now, if you can
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measure all of those quantities, then you could understand
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better the physics of the interaction between what? The
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atmospheric boundary layer with the entire wind farm. And
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that's basically the kind of things that we would like
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to do during this discussion. Now, these these
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scale experiment anybody and I will show you some pictures
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Anybody that when you see a wind farm, there's
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a major problems, right? The topography is a
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major challenge, right? But the wind direction is
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shaking constantly. Also, you had a lot of
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effects, like temperature variation. So one of the
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things we would like to do is then to understand
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all of those effects very carefully in what well controlled
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experimental setup. Okay. And one of the things
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we're gonna do is a scale down. So we're
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not gonna do the measurements and the entire food scale
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. Instead, we're going to use it in a
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scale down wind farm. Okay, And then at
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the end was one of the things we want to
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do is to discuss the result particularly what I said
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about W t B. I'm talking about wind turbine
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boundary layer profile, and that is that as they
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get bigger and bigger and bigger, you would like
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to know what is the wake or the velocity profile
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that describes that wind farm? And the reason is
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because if you know that you will know how you
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could place them, you will know how much power
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that wind farm will produce. And then you could
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do all the characterizations, such a place and then
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in a different location. And then at the end
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, I'm just going to focus on some of the
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conclusions. So let's start the show. Please stop
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me at any time. Okay, So you have
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any questions? Just stop, okay? You don't
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have to wait until the end. So this is
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a very, very famous picture. Almost every meeting
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that you go with energy, you would see it
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. And I feel very bad for for him.
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But that was taken by Christians tennis. Because if
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you have patent that picture, he could have make
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some good money out of that. And I'm one
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of them that I used it a lot, but
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I give him credit And if you look at these
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pictures is a very, very important picture. This
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is an offshore wind farm in Denmark, and it's
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actually show you in real life what is really going
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on in that particular case. You take that picture
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from a helicopter and you have enough condensation that you
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could have a perfect flow visualization and what you can
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see from this picture if I'm sorry that do we
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have a Is there some Denise, do you have
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another point? That that's all right, But but
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you would have to take my word for it,
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okay? Or we have to. But But if
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you look at this picture one of the things that
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the flow comes from this from the front and it
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is expand through the back and what you actually see
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is that you see a lot of coherent structure.
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You see structures of turbulent flow that seems to be
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repeated themselves. So as you move downstream, you
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see that the floor is highly turbulent. We could
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see that because you see a lot of mixing.
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But you could also see that there is a boundary
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. This is the boundary is a region where physical
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effects see are important, but you could see a
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growth of the bounds of the velocity feel as you
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move downstream. In other words, if you go
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, you're moving X direction. You can see that
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growth in the vertical direction, and you could also
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see that spread. So this picture tells you the
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whole thing that I'm going to do today. And
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actually, one of the important aspect of this is
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this, for example, Uh, and this is
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one of the reasons why we want to do,
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um, winter and experiment, because in the field
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, what do you have with the incoming flow is
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changing drastically over time. Alright, every second is
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changing not only in terms of the magnitude velocity,
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but the direction. If you look at the temperature
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, the temperature also exchanging. So a lot of
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the inlet conditions is very, very important. And
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one of the important aspect of this is this.
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If the inlet flow is changing, one of the
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important question is how does the devolution of that flow
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affect the performance of the entire wind farm? So
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that's one of the questions we want to be able
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to address. But from the perspective of all of
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this discussion is what is the role of turbulence in
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all of this energy and treatment. Now, if
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you go if you go to this part, what
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do you have? Well, if you look carefully
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, you see that the first survivor experienced very little
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turbulence of none was the one in the back.
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What you see is a highly experienced high levels of
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turbulence, and this is what is called the way
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to wake effects. And this is one of the
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things that is the limiting causes for wind farm performance
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. And that's one of the questions we want to
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be addressed today. Now, if you look further
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from this, this is I don't know how many
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of you are. I'm assuming some of you took
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three dynamics. But if you look far downstream,
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there seems to be a region where the velocities they
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don't seem to be changing that much, and that
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region is called a fully developed. In fact,
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if you look at the flow when you took in
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fluid dynamics, Shannon flow in a pipe, you
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say Well, the flow becomes fully developed when the
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velocity profile no longer changes, right? So in
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this particular case. This is very, very important
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. So you can see that in the inlet you
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can see it developing region. You can see that
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the flow is changing a lot as you move.
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And then as you move far downstream, what do
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you see? Very little changes. And one of
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the question is, Is this Can we characterize this
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flow in a way that you could say is this
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is fully developed or not? And you know this
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. If it's fully developed, you will know what
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the weight profile will be. If you know what
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the work is, then you could use this in
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different set of equations, even to create cost of
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any cause of economic model costs. Okay, so
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this is one of the important issues we want to
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be able to address from this picture. Now the
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other one is this. These machines are massive.
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In fact, you could put a 7 47 inside
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of the rotors of these turbines. So now you
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worry about that you have a highly turbulent flow.
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You have to worry about that. These machines are
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massive, and then you have to worry about the
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interaction between the flow behind the turbines. Okay,
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And then at the end of this, this is
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the story. You have a turbine in a highly
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turban for us. So just imagine this. You're
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flying in an airplane, and at some point the
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pilot panics and say you have to put your seatbelt
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because we have a lot of trouble. And,
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Floyd, we're gonna be here for five minutes and
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everybody is panic. Right? Well, imagine these
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turbines 24 hours a day, seven days a week
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for the entire year, experiencing highly true in the
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flow. So So this is one of the important
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aspect. And in fact, I always say turbulence
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is the order of one problem on wind energy.
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And and there are many reasons for that. I'm
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not biased about that. Okay, So one of
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the things that we want to address today is the
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following. Can we characterize the development of that boundary
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layer? Can we do that? And And the
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question is, what set of tools we have that
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we could characterize that flow as you move downstream in
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the floor. Okay. And as you characterise that
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you say so what? Yes, That's not a
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big deal. We could determine whether or not is
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fully developed. But the mayor question we want to
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be able to address is this. What is the
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role of turbulence? Number two. What are these
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scales that will be important to provide energy for that
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array. And if I can know those skills,
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I can do many things. I can redesign the
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plates to impact those skills. And I could know
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exactly how I can play those termites so I can
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maximize that instrument of those claims skills in the floor
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. All right, so we move forward, I'm
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gonna use the same to talk about the challenges.
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So this is what this story is so disturbance in
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the front are basically designed to what? To experience
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a very nice uniform flow. And, of course
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, the turbines in the back. They experience a
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highly turbulent flow. And then you begin to worry
311
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that Hey, we have turbulent flow and there are
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32 reasons. It is our friend, uh,
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Ricardo. He would worry about what are the skills
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that are going to be important for my noise generation
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, Right. And then, if you have somebody
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in material science, they may be worried about what
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are dealing skills that are going to be important for
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what? The external load that those plates are going
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to experience. But if you talk to somebody like
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me in turbulence will say how important is turbulence to
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produce energy? So the good thing is that turbulence
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could have a very good news. And it could
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also have very bad news, depending on the question
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you want to address and the one that I'm gonna
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focuses on what? The energy, the life skills
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that will be responsible for the energy. And so
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if you look at this chart is a very,
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very important chart, this is what's taken by Rebecca
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Barthelemy from Indiana University and what you look here,
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This is the normalized power. So what you have
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taken is the the first turbine you put and and
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then you take the power generated by any turbine around
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any given role. And you normalize that power by
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what the power produced by the first turbine. So
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if you're in the first turbine, the power is
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what is one is 100%. So So this is
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what you see. Uh, in the 1st 3rd
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1 here. Now this is plotted are different turbines
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. 1234567 But it's plotted as a function of what
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? The space in between turbines. In other words
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, the further away you are from the turbines.
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What happened? The less the drop you get.
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Okay, So if you're 10, 10 diameters,
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if you're 10 diameters from the 10 10.5 rotor diameter
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, you have a drop about close to about 2022%
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. And if you look at the green, which
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is 99 rotor diameter, you get a power drop
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energy loss due to the weight from the first round
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to the second, about 30%. But if you
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decided to play the storm and even closer to each
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other about seven rotor diameter, you're talking about a
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drop about 40%. That is bad news. And
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in fact, depending on the wind direction, you
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can see that this power seems to settle down over
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the entire region. And the question you want to
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say this is, where does the energy comes from
357
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to feed this array? Okay, so the issue
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here is this. If you rely only on the
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mean velocity to provide some of the energy during bad
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luck, you're out of commission. Uh, if
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you look at the picture on the right hand side
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, the difference is that you have a different wind
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direction. So you can see from this picture very
364
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clearly that not only the level of tourists is critical
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, but the wind direction will also play a role
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about the power that these turbines will produce. Now
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, if you're in finances and this is what I
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love about this this field, this is the the
369
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best playground for everyone to play. If you have
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friends in economics, guess what they could play here
371
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. If you have friends in electrical engineering, they
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could play because of the power transmission, right?
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The great integration, energy storage. But also in
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this in this study by Elkington, Manuel and Mark
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Goldman. In 2006, they showed that the biggest
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uncertainty in the economic cost that exists is due to
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the weight loss. In other words, the fact
378
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that you do not quite well where the wake is
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00:17:29.539 --> 00:17:33.910 A:middle L:90%
, you have a process minus 20% of uncertainty.
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This is big. Okay, that's not a joke
381
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. Um, so now if you continue with this
382
00:17:38.970 --> 00:17:42.289 A:middle L:90%
discussion about the challenges in terms of of the turbulence
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00:17:42.299 --> 00:17:45.029 A:middle L:90%
. You can see that if one of the study
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actually from charge, many of all for many of
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all admires in 2011, they show that the optimum
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spacing between turbines is not seven is not nine.
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It's not 10 rotor diameters, but 15. Well
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, that was good that he showed that the bad
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news is that that would increase your cost of energy
390
00:18:06.140 --> 00:18:07.099 A:middle L:90%
. Because that means that you have to get more
391
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, more land. All right, so you don't
392
00:18:10.819 --> 00:18:12.789 A:middle L:90%
want that? Um But if you continue through this
393
00:18:12.789 --> 00:18:17.220 A:middle L:90%
study, one of the major issues is that what
394
00:18:17.230 --> 00:18:21.180 A:middle L:90%
the load that or that unsteady flow that is acting
395
00:18:21.180 --> 00:18:23.160 A:middle L:90%
on the blade or on the tower will damage your
396
00:18:23.160 --> 00:18:26.869 A:middle L:90%
gearbox will damage your rotors, and it will damage
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00:18:26.869 --> 00:18:30.779 A:middle L:90%
what your your tower. So the challenge here for
398
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many of you is is many of these turbines what
399
00:18:33.529 --> 00:18:37.269 A:middle L:90%
they're designed to last for what, 20 years?
400
00:18:37.940 --> 00:18:41.720 A:middle L:90%
Yes. Is that in line? Turbines are there
401
00:18:41.720 --> 00:18:45.289 A:middle L:90%
for a strike yet? Not not for in line
402
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. So in this case, yes, yes,
403
00:18:48.349 --> 00:18:49.509 A:middle L:90%
a very good question. In fact, one of
404
00:18:49.509 --> 00:18:52.789 A:middle L:90%
the one of the major issues I cannot just pointed
405
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out here, but it is in this type of
406
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rectangular arrangement. But one of the important findings that
407
00:18:57.339 --> 00:19:00.660 A:middle L:90%
the group from Minnesota Well, you tomorrow, That
408
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is now Urbana Champagne. And there's a group in
409
00:19:03.039 --> 00:19:06.829 A:middle L:90%
Syracuse that we did something similar. We did an
410
00:19:06.839 --> 00:19:08.680 A:middle L:90%
optimization, and you could find that there's a different
411
00:19:08.690 --> 00:19:11.509 A:middle L:90%
configuration. Not this exactly. This arrangement where you
412
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could actually even increase the performance. The the capacity
413
00:19:15.599 --> 00:19:22.029 A:middle L:90%
factor by 10 10% senses going to be time to
414
00:19:22.029 --> 00:19:29.289 A:middle L:90%
go on the jets in line. Yeah. Yes
415
00:19:29.289 --> 00:19:34.559 A:middle L:90%
, sir. Patient? Yeah, it was found
416
00:19:37.140 --> 00:19:38.460 A:middle L:90%
. Yeah, Yeah, yeah. Yeah. Staff
417
00:19:40.640 --> 00:19:47.049 A:middle L:90%
, Yes. That. Yeah, Yeah, sure
418
00:19:47.539 --> 00:19:48.970 A:middle L:90%
. And here, Yes. Yes. And that's
419
00:19:48.970 --> 00:19:49.750 A:middle L:90%
the case. I mean, you could see the
420
00:19:49.759 --> 00:19:52.319 A:middle L:90%
one and I will show you this. The one
421
00:19:52.319 --> 00:19:55.220 A:middle L:90%
that I prefer to use this arrangement is because you
422
00:19:55.220 --> 00:19:56.819 A:middle L:90%
reduce the number of variability. In other words,
423
00:19:56.819 --> 00:20:00.380 A:middle L:90%
we want to have enough as more controlled conditions as
424
00:20:00.380 --> 00:20:03.190 A:middle L:90%
possible to be able to understand the physics. But
425
00:20:03.190 --> 00:20:04.079 A:middle L:90%
if you do that, you would have a difference
426
00:20:04.089 --> 00:20:07.900 A:middle L:90%
. What you need to consider there is the the
427
00:20:07.910 --> 00:20:10.720 A:middle L:90%
great, the lines, the power lines. And
428
00:20:10.720 --> 00:20:14.170 A:middle L:90%
that's part of the issue. Um, but but
429
00:20:14.180 --> 00:20:15.210 A:middle L:90%
this is part of the issue. They're breaking down
430
00:20:15.210 --> 00:20:21.500 A:middle L:90%
in seven years. And the question again, my
431
00:20:21.500 --> 00:20:23.210 A:middle L:90%
argument is turbulence is the number one issue even on
432
00:20:23.210 --> 00:20:26.210 A:middle L:90%
this problem. So So let us now look at
433
00:20:26.210 --> 00:20:30.440 A:middle L:90%
the objective. Alright, so number one, what
434
00:20:30.440 --> 00:20:32.529 A:middle L:90%
I'm going to show you is that turbulence will play
435
00:20:32.529 --> 00:20:33.529 A:middle L:90%
a very key role. And not only that,
436
00:20:33.529 --> 00:20:36.750 A:middle L:90%
but you will look from the questions of motion that
437
00:20:36.750 --> 00:20:38.450 A:middle L:90%
I know if currency is very important, mainly in
438
00:20:38.450 --> 00:20:41.990 A:middle L:90%
a training energy from above, that means I can
439
00:20:41.990 --> 00:20:45.349 A:middle L:90%
redesign the plate, right. I can redesign the
440
00:20:45.349 --> 00:20:48.759 A:middle L:90%
place such that they attract more of the energy.
441
00:20:48.769 --> 00:20:49.410 A:middle L:90%
All right, so So I'm going to focus on
442
00:20:49.410 --> 00:20:52.039 A:middle L:90%
that, Then the other part that I'm gonna focus
443
00:20:52.049 --> 00:20:56.160 A:middle L:90%
is to characterize the development of this array. You
444
00:20:56.160 --> 00:20:57.200 A:middle L:90%
know the word. Remember the picture when you see
445
00:20:57.200 --> 00:21:00.089 A:middle L:90%
those those big race in the wind farm. The
446
00:21:00.089 --> 00:21:03.430 A:middle L:90%
question is, can you characterize that in a way
447
00:21:03.440 --> 00:21:04.809 A:middle L:90%
that you can determine whether or not they are fully
448
00:21:04.809 --> 00:21:07.380 A:middle L:90%
developed or not? And the question is, if
449
00:21:07.380 --> 00:21:10.670 A:middle L:90%
you know, that's fully developed. Guess what happened
450
00:21:11.039 --> 00:21:12.180 A:middle L:90%
. The boundary will not grow anymore, right?
451
00:21:12.240 --> 00:21:15.880 A:middle L:90%
The boundary. Basically, we settled down, so
452
00:21:15.880 --> 00:21:17.720 A:middle L:90%
if you know that there is a growth of the
453
00:21:17.720 --> 00:21:19.289 A:middle L:90%
boundary layer. That means you could change the altitude
454
00:21:19.299 --> 00:21:22.559 A:middle L:90%
in a way that you can optimize the energy even
455
00:21:22.559 --> 00:21:23.859 A:middle L:90%
further. All right, so there's a lot of
456
00:21:23.859 --> 00:21:26.529 A:middle L:90%
insight that we could use here to do these studies
457
00:21:26.539 --> 00:21:29.109 A:middle L:90%
. So one of the things that we're gonna look
458
00:21:29.109 --> 00:21:30.130 A:middle L:90%
is that the power measurements, we're gonna look at
459
00:21:30.130 --> 00:21:33.599 A:middle L:90%
the budget analysis, and then we're gonna look at
460
00:21:33.599 --> 00:21:36.960 A:middle L:90%
the main profiles, I mean, and rhinoceroses as
461
00:21:36.960 --> 00:21:40.220 A:middle L:90%
well. And finally, this is the question we
462
00:21:40.220 --> 00:21:41.609 A:middle L:90%
want to all of us want to look at today
463
00:21:41.619 --> 00:21:44.619 A:middle L:90%
. What is the role of the large skills of
464
00:21:44.630 --> 00:21:47.970 A:middle L:90%
turbulence in the in the performance of the wind farms
465
00:21:47.980 --> 00:21:49.160 A:middle L:90%
? All right, so So let us start with
466
00:21:49.160 --> 00:21:52.859 A:middle L:90%
the with the questions. All right, So So
467
00:21:52.869 --> 00:21:55.359 A:middle L:90%
let's suppose you have this very, very large array
468
00:21:55.839 --> 00:21:57.049 A:middle L:90%
, all right? And this typically is great.
469
00:21:57.049 --> 00:22:00.599 A:middle L:90%
And 10 boundary thickness of 10 Delta is typically the
470
00:22:00.599 --> 00:22:03.809 A:middle L:90%
boundary thickness of the atmosphere. Okay, what about
471
00:22:03.809 --> 00:22:06.769 A:middle L:90%
one kilometer? And the question is, as these
472
00:22:06.769 --> 00:22:08.220 A:middle L:90%
guys get bigger and bigger and bigger, you would
473
00:22:08.220 --> 00:22:11.339 A:middle L:90%
like to know what is this profile? Okay,
474
00:22:11.349 --> 00:22:15.869 A:middle L:90%
now that profile you saw from before what happened?
475
00:22:15.880 --> 00:22:18.220 A:middle L:90%
Well, the flow is what highly three dimensional right
476
00:22:18.220 --> 00:22:21.430 A:middle L:90%
? What's changing in space? And it's also changing
477
00:22:21.430 --> 00:22:25.049 A:middle L:90%
drastically in time. So when you perform average in
478
00:22:25.049 --> 00:22:27.740 A:middle L:90%
time and then you x subsea means that we have
479
00:22:27.740 --> 00:22:30.960 A:middle L:90%
performed an average in what in space. So if
480
00:22:30.960 --> 00:22:33.559 A:middle L:90%
you do all of that, then you could characterize
481
00:22:33.559 --> 00:22:37.960 A:middle L:90%
basically one profile that only varies on one variable.
482
00:22:38.440 --> 00:22:41.150 A:middle L:90%
And this is quite nice, because if you know
483
00:22:41.150 --> 00:22:42.369 A:middle L:90%
that this is the profile, this is what we
484
00:22:42.369 --> 00:22:45.859 A:middle L:90%
call the wind terrible and boundary profile. Then you
485
00:22:45.859 --> 00:22:49.450 A:middle L:90%
could characterize the the power produced by this array.
486
00:22:51.440 --> 00:22:52.009 A:middle L:90%
So this is one of the things that we want
487
00:22:52.009 --> 00:22:55.759 A:middle L:90%
to do today. What is a profile? And
488
00:22:55.759 --> 00:22:56.559 A:middle L:90%
then, um, this is the question. You
489
00:22:56.559 --> 00:23:00.410 A:middle L:90%
know that question already? First, we want to
490
00:23:00.410 --> 00:23:03.380 A:middle L:90%
characterize whether or not this is a fully developed number
491
00:23:03.380 --> 00:23:06.839 A:middle L:90%
two. We want to also understand what is that
492
00:23:06.839 --> 00:23:10.180 A:middle L:90%
wind turbine and boundary profile again? If I know
493
00:23:10.180 --> 00:23:11.920 A:middle L:90%
that I can work with somebody in design and those
494
00:23:11.920 --> 00:23:14.960 A:middle L:90%
people in design could say You know what, Luciano
495
00:23:14.970 --> 00:23:17.319 A:middle L:90%
? The best way to locate these turbines is not
496
00:23:17.319 --> 00:23:19.960 A:middle L:90%
this perfectly shape. Is this triangular shape? Why
497
00:23:19.970 --> 00:23:23.059 A:middle L:90%
? Because you already have the profile of that week
498
00:23:23.339 --> 00:23:25.880 A:middle L:90%
. Okay, so this is what, One of
499
00:23:25.880 --> 00:23:27.660 A:middle L:90%
the reasons why this is very important. And then
500
00:23:27.660 --> 00:23:32.509 A:middle L:90%
the last one is, uh what is the rate
501
00:23:32.519 --> 00:23:34.839 A:middle L:90%
at which all of your statistics? Because fully developed
502
00:23:34.849 --> 00:23:37.369 A:middle L:90%
. Okay, just remember this fully developments that the
503
00:23:37.369 --> 00:23:41.009 A:middle L:90%
profile no longer exchanges. So we're gonna perform that
504
00:23:41.009 --> 00:23:44.539 A:middle L:90%
analysis and and see what is really going on in
505
00:23:44.539 --> 00:23:45.819 A:middle L:90%
this entire ray. Okay, I didn't tell you
506
00:23:45.819 --> 00:23:49.220 A:middle L:90%
the whole story as to why winning such a big
507
00:23:49.220 --> 00:23:52.109 A:middle L:90%
deal, but normally, like I do that.
508
00:23:52.119 --> 00:23:55.589 A:middle L:90%
But if you look at this, for example,
509
00:23:55.589 --> 00:23:57.349 A:middle L:90%
this is the induction factor. And if you remember
510
00:23:59.140 --> 00:24:00.940 A:middle L:90%
, this is normally used to create a wake function
511
00:24:00.940 --> 00:24:03.160 A:middle L:90%
. So if you look at a is induction factor
512
00:24:03.160 --> 00:24:06.900 A:middle L:90%
, this is basically the ratio of the velocity,
513
00:24:06.900 --> 00:24:10.349 A:middle L:90%
the average velocity in the back in the back of
514
00:24:10.359 --> 00:24:11.759 A:middle L:90%
this disk, okay, and the average velocity in
515
00:24:11.759 --> 00:24:15.099 A:middle L:90%
the front. So if you take both races of
516
00:24:15.109 --> 00:24:18.519 A:middle L:90%
that velocity, that's what you call the induction factor
517
00:24:18.529 --> 00:24:21.509 A:middle L:90%
. Now you can use that induction factor and create
518
00:24:21.509 --> 00:24:25.609 A:middle L:90%
what awake model and that wake mother will represent what
519
00:24:25.609 --> 00:24:27.980 A:middle L:90%
the profile for that are typically is. All right
520
00:24:27.990 --> 00:24:30.599 A:middle L:90%
now, this is very important, because now you
521
00:24:30.599 --> 00:24:33.170 A:middle L:90%
could now understand how you can maximize the power.
522
00:24:33.539 --> 00:24:37.359 A:middle L:90%
And at the same time, you could know how
523
00:24:37.359 --> 00:24:40.380 A:middle L:90%
you could place these turbines. Okay, so there
524
00:24:40.380 --> 00:24:42.299 A:middle L:90%
are different types of wake model that exists. I'm
525
00:24:42.299 --> 00:24:45.480 A:middle L:90%
just going to present one here that tried to explain
526
00:24:45.490 --> 00:24:48.660 A:middle L:90%
why this is important. So if you look at
527
00:24:48.660 --> 00:24:52.019 A:middle L:90%
here, this is from Jensen 1983. Basically what
528
00:24:52.019 --> 00:24:55.380 A:middle L:90%
he said, you subzero represents what? The incoming
529
00:24:55.380 --> 00:24:57.220 A:middle L:90%
velocity. Uh, a is what? The induction
530
00:24:57.220 --> 00:25:00.369 A:middle L:90%
factor will depend on what develops it in the back
531
00:25:00.380 --> 00:25:03.099 A:middle L:90%
and develops it in the front and theta. Remember
532
00:25:03.099 --> 00:25:06.549 A:middle L:90%
that you suffer from this picture that this floor was
533
00:25:06.549 --> 00:25:08.730 A:middle L:90%
, what highly turbulent flow, Right? So we
534
00:25:08.730 --> 00:25:11.519 A:middle L:90%
don't forget that the argument is let's forget all of
535
00:25:11.519 --> 00:25:14.680 A:middle L:90%
that, and I'm gonna dump all of that effect
536
00:25:14.680 --> 00:25:17.799 A:middle L:90%
of turbulence in this parameter data. Okay, so
537
00:25:17.799 --> 00:25:19.539 A:middle L:90%
that's an empirical constant where we're gonna input all of
538
00:25:19.539 --> 00:25:22.369 A:middle L:90%
the variation due to turbulence. All right. Very
539
00:25:22.369 --> 00:25:25.410 A:middle L:90%
, very simplistic. And at the end of the
540
00:25:25.410 --> 00:25:29.009 A:middle L:90%
day, you can use this to describe how you're
541
00:25:29.009 --> 00:25:30.940 A:middle L:90%
gonna locate disturbance. In fact, their economic models
542
00:25:30.950 --> 00:25:34.529 A:middle L:90%
that rely also on this information as well So let's
543
00:25:34.529 --> 00:25:37.589 A:middle L:90%
do this. So if we have this, we
544
00:25:37.589 --> 00:25:41.200 A:middle L:90%
also learn the following from we learned that this velocity
545
00:25:41.210 --> 00:25:44.430 A:middle L:90%
is highly three dimensional, right? It depends on
546
00:25:44.430 --> 00:25:47.220 A:middle L:90%
what X, y and Z depends on space and
547
00:25:47.220 --> 00:25:48.339 A:middle L:90%
depends on time. So what I'm going to do
548
00:25:48.339 --> 00:25:51.269 A:middle L:90%
is that we're gonna perform an average in time,
549
00:25:51.839 --> 00:25:53.930 A:middle L:90%
and then we're gonna ended up and the average xz
550
00:25:53.940 --> 00:25:56.910 A:middle L:90%
, these are called special averages. So if we
551
00:25:56.910 --> 00:26:00.269 A:middle L:90%
perform both of those, you only ended up with
552
00:26:00.269 --> 00:26:03.440 A:middle L:90%
one with one function. That depends on what one
553
00:26:03.440 --> 00:26:06.000 A:middle L:90%
coordinate. Okay. And that's the whole story.
554
00:26:06.000 --> 00:26:08.000 A:middle L:90%
Because now I can represent how does the mean velocity
555
00:26:08.009 --> 00:26:11.890 A:middle L:90%
or render stresses various with the vertical distance. All
556
00:26:11.890 --> 00:26:15.480 A:middle L:90%
right. And so let us start with the average
557
00:26:15.480 --> 00:26:18.559 A:middle L:90%
stock in question. So if you look at this
558
00:26:18.039 --> 00:26:21.960 A:middle L:90%
, So So this is the X component. Um
559
00:26:22.839 --> 00:26:26.180 A:middle L:90%
, So if you remember, the meters Law Force
560
00:26:26.180 --> 00:26:26.809 A:middle L:90%
is equal to m A. This is what it
561
00:26:26.809 --> 00:26:29.910 A:middle L:90%
is if you put the density in the front of
562
00:26:29.910 --> 00:26:30.819 A:middle L:90%
the left hand side and I'm sorry, I cannot
563
00:26:30.819 --> 00:26:33.940 A:middle L:90%
see, uh, if you put the density in
564
00:26:33.940 --> 00:26:36.529 A:middle L:90%
the left hand side, these are basically what the
565
00:26:36.529 --> 00:26:38.930 A:middle L:90%
nurture terms those are the terms responsible for what?
566
00:26:38.940 --> 00:26:41.839 A:middle L:90%
The acceleration of the flow. So it deploys fully
567
00:26:41.839 --> 00:26:45.670 A:middle L:90%
developed. Guess what? There is no such acceleration
568
00:26:45.680 --> 00:26:48.089 A:middle L:90%
. All right? And so you have all of
569
00:26:48.089 --> 00:26:51.519 A:middle L:90%
these terms that are responsible for the nursery terms this
570
00:26:51.529 --> 00:26:56.039 A:middle L:90%
dp infinity dx represent what? The pressure gradient and
571
00:26:56.049 --> 00:26:59.299 A:middle L:90%
, uh, guess what? You ve you prime
572
00:26:59.299 --> 00:27:02.519 A:middle L:90%
b prime bar represents what? This is the rain
573
00:27:02.519 --> 00:27:04.470 A:middle L:90%
of stresses. Remember this. You took the instantaneous
574
00:27:04.470 --> 00:27:07.779 A:middle L:90%
signal and you brought that into what and mean quantity
575
00:27:07.779 --> 00:27:11.289 A:middle L:90%
plus a fluctuation. And you ended up with what
576
00:27:11.299 --> 00:27:12.849 A:middle L:90%
? One of notes and that of noise called here
577
00:27:12.859 --> 00:27:17.509 A:middle L:90%
the Reynolds Shear stresses and X subsidies because you have
578
00:27:17.789 --> 00:27:21.460 A:middle L:90%
performed special averages and I would explain why this is
579
00:27:21.460 --> 00:27:22.690 A:middle L:90%
such a big deal. In other words, if
580
00:27:22.690 --> 00:27:26.079 A:middle L:90%
you have a complex terrain, you're gonna perform special
581
00:27:26.089 --> 00:27:29.579 A:middle L:90%
averages in the sea to remove many of those effects
582
00:27:29.589 --> 00:27:30.589 A:middle L:90%
. Or if you have turbines are took place to
583
00:27:30.589 --> 00:27:33.259 A:middle L:90%
each other, you will worry about what is called
584
00:27:33.259 --> 00:27:37.880 A:middle L:90%
here. The dispersants stresses. So you double prime
585
00:27:37.880 --> 00:27:41.210 A:middle L:90%
the prime are called, this person stresses. So
586
00:27:41.210 --> 00:27:45.099 A:middle L:90%
this is the difference between the time average quantity and
587
00:27:45.099 --> 00:27:48.440 A:middle L:90%
the special average. All right, so when you
588
00:27:48.440 --> 00:27:51.079 A:middle L:90%
perform a special average and this time average that difference
589
00:27:51.089 --> 00:27:52.809 A:middle L:90%
will ended up with what with what you call here
590
00:27:52.819 --> 00:27:55.950 A:middle L:90%
. We call here disperses, stresses, and this
591
00:27:55.950 --> 00:28:00.789 A:middle L:90%
was done by Europol in in 1991 and f the
592
00:28:00.789 --> 00:28:03.289 A:middle L:90%
last term in the right is what? The average
593
00:28:03.289 --> 00:28:06.970 A:middle L:90%
trust. So as the flow goes through the turbine
594
00:28:06.980 --> 00:28:08.619 A:middle L:90%
, that would create a trust trust force on the
595
00:28:08.619 --> 00:28:11.259 A:middle L:90%
blade. And that's what you call the F bar
596
00:28:11.839 --> 00:28:14.309 A:middle L:90%
. Okay, Now, look at this. If
597
00:28:14.309 --> 00:28:15.490 A:middle L:90%
you take the dot product of the force of this
598
00:28:15.490 --> 00:28:18.579 A:middle L:90%
component X with the U component, what did you
599
00:28:18.579 --> 00:28:22.509 A:middle L:90%
get? I mean, kinetic energy, right?
600
00:28:22.519 --> 00:28:26.799 A:middle L:90%
So you take the dot product of this X component
601
00:28:26.809 --> 00:28:29.039 A:middle L:90%
, and that's that's the rest of the story.
602
00:28:29.049 --> 00:28:30.539 A:middle L:90%
So So if you do this, you will end
603
00:28:30.539 --> 00:28:33.059 A:middle L:90%
it up with the main kinetic energy industry in west
604
00:28:33.059 --> 00:28:34.799 A:middle L:90%
direction. So you can do this. You can
605
00:28:34.799 --> 00:28:37.559 A:middle L:90%
write the vertical component of the universe socket question,
606
00:28:38.039 --> 00:28:41.190 A:middle L:90%
and then you do the product with the velocity,
607
00:28:41.190 --> 00:28:42.430 A:middle L:90%
the vertical component, and you get what you mean
608
00:28:42.430 --> 00:28:47.099 A:middle L:90%
kinetic energy for the normal component. In this case
609
00:28:47.109 --> 00:28:48.460 A:middle L:90%
, I'm only including the the X component. So
610
00:28:48.470 --> 00:28:52.640 A:middle L:90%
all of this term here represent what? The objection
611
00:28:52.640 --> 00:28:55.809 A:middle L:90%
term, Okay. And what is this? Here
612
00:28:55.819 --> 00:28:57.640 A:middle L:90%
is a correlation of the mean velocity with the pressure
613
00:28:57.640 --> 00:29:02.269 A:middle L:90%
gradient. And this is where the story is.
614
00:29:02.740 --> 00:29:04.660 A:middle L:90%
We're going to focus here, Okay? This year
615
00:29:04.670 --> 00:29:07.789 A:middle L:90%
is called the energy flux. Those are the flux
616
00:29:07.789 --> 00:29:08.960 A:middle L:90%
is due to what? To the reign of stresses
617
00:29:10.339 --> 00:29:11.420 A:middle L:90%
. So we could show from the main kinetic energy
618
00:29:11.420 --> 00:29:15.579 A:middle L:90%
question how important all of these terms are. So
619
00:29:15.579 --> 00:29:18.359 A:middle L:90%
if I can measure all of them number one,
620
00:29:19.039 --> 00:29:22.500 A:middle L:90%
I can determine whether or not in fact, if
621
00:29:22.500 --> 00:29:23.579 A:middle L:90%
you're close enough to the world what happened to the
622
00:29:23.579 --> 00:29:27.730 A:middle L:90%
infection terms, they go to zero. I don't
623
00:29:27.730 --> 00:29:30.920 A:middle L:90%
care about them. And then I can use this
624
00:29:30.920 --> 00:29:33.970 A:middle L:90%
equation as a measure of whether or not the flow
625
00:29:33.970 --> 00:29:37.079 A:middle L:90%
, because fully developed number one, I can do
626
00:29:37.079 --> 00:29:40.670 A:middle L:90%
that. But the most important issue this term here
627
00:29:41.039 --> 00:29:42.640 A:middle L:90%
represent the entrainment, the energy flux due to the
628
00:29:42.640 --> 00:29:45.009 A:middle L:90%
rain of stresses. This is the flux due to
629
00:29:45.009 --> 00:29:49.109 A:middle L:90%
this person stresses. And this is what typically,
630
00:29:49.259 --> 00:29:52.400 A:middle L:90%
this term is called what? Production term. But
631
00:29:52.400 --> 00:29:55.619 A:middle L:90%
because you're talking about for the term money, we're
632
00:29:55.619 --> 00:29:57.650 A:middle L:90%
going to call it, uh, terrible anticipation.
633
00:29:57.660 --> 00:30:00.579 A:middle L:90%
Okay, Because that energy is not going to determine
634
00:30:00.589 --> 00:30:03.789 A:middle L:90%
it is going to flow itself. And then the
635
00:30:03.799 --> 00:30:07.779 A:middle L:90%
double prime B prime that represent what this person is
636
00:30:07.779 --> 00:30:11.119 A:middle L:90%
dissipation. Okay. Again, when you perform an
637
00:30:11.119 --> 00:30:15.809 A:middle L:90%
average, the average quantity introduced a new unknown,
638
00:30:15.809 --> 00:30:18.589 A:middle L:90%
which is dispersing stresses those quantities with the ground with
639
00:30:18.589 --> 00:30:22.910 A:middle L:90%
y, with you cannot produce more energy. So
640
00:30:22.910 --> 00:30:26.210 A:middle L:90%
they become disperses, stresses and P is what the
641
00:30:26.210 --> 00:30:29.180 A:middle L:90%
dot product of what these three wives velocity with what
642
00:30:29.420 --> 00:30:32.500 A:middle L:90%
with the trust force. And guess what I can
643
00:30:32.509 --> 00:30:33.190 A:middle L:90%
. If I can measure all of these, I
644
00:30:33.190 --> 00:30:37.980 A:middle L:90%
can balance the budget. So not a big deal
645
00:30:37.019 --> 00:30:40.569 A:middle L:90%
. But this is what I want to know how
646
00:30:40.569 --> 00:30:42.940 A:middle L:90%
important these guys are. Okay, so we have
647
00:30:42.940 --> 00:30:45.829 A:middle L:90%
made the assumption that we're very close to the war
648
00:30:45.839 --> 00:30:47.849 A:middle L:90%
. Close enough, and we could drop all the
649
00:30:47.849 --> 00:30:49.490 A:middle L:90%
infection terms. All right, Now, what is
650
00:30:49.490 --> 00:30:52.799 A:middle L:90%
the goal here? Well, the goal here is
651
00:30:52.799 --> 00:30:55.519 A:middle L:90%
that if I can take advantage of the two questions
652
00:30:55.519 --> 00:30:56.359 A:middle L:90%
of motion that I have and continue to see,
653
00:30:56.369 --> 00:31:00.329 A:middle L:90%
I can use that information design a well controlled experiment
654
00:31:00.339 --> 00:31:03.460 A:middle L:90%
, okay, in which I can measure all of
655
00:31:03.460 --> 00:31:07.099 A:middle L:90%
this information. And from that I mean, I'm
656
00:31:07.099 --> 00:31:08.740 A:middle L:90%
talking about four centimetres turbines. I can use that
657
00:31:08.740 --> 00:31:11.859 A:middle L:90%
to understand the physics of the flow, and then
658
00:31:11.859 --> 00:31:14.369 A:middle L:90%
I can use that for modeling. Now, this
659
00:31:14.369 --> 00:31:15.349 A:middle L:90%
tells us that if you cannot use the ransom question
660
00:31:15.349 --> 00:31:18.519 A:middle L:90%
to solve this problem, you must account for this
661
00:31:18.519 --> 00:31:21.609 A:middle L:90%
term. If you're going to use in a complex
662
00:31:21.609 --> 00:31:26.200 A:middle L:90%
terrain Now say if you move forward, the the
663
00:31:26.210 --> 00:31:27.750 A:middle L:90%
this is basically the experimental setup. So this is
664
00:31:27.750 --> 00:31:30.299 A:middle L:90%
the winter Johns Hopkins. Uh, this is what
665
00:31:30.299 --> 00:31:33.529 A:middle L:90%
is called the course in winter now, and,
666
00:31:33.539 --> 00:31:34.180 A:middle L:90%
uh, if you can see here, this is
667
00:31:34.180 --> 00:31:37.779 A:middle L:90%
some streaks. So this this black line here,
668
00:31:37.789 --> 00:31:40.329 A:middle L:90%
basically what we have done is to create some streaks
669
00:31:40.339 --> 00:31:42.140 A:middle L:90%
in which there is a polynomial feet and at the
670
00:31:42.140 --> 00:31:45.910 A:middle L:90%
bottom, it has a gradual big changes. And
671
00:31:45.910 --> 00:31:48.299 A:middle L:90%
the idea is that you want to introduce one high
672
00:31:48.299 --> 00:31:51.119 A:middle L:90%
gradients of velocity very close to the wall, and
673
00:31:51.119 --> 00:31:52.670 A:middle L:90%
I will show you the winter in a prison.
674
00:31:52.039 --> 00:31:55.769 A:middle L:90%
But the inflow right here is described here. So
675
00:31:55.769 --> 00:31:59.210 A:middle L:90%
now guess what you know very precisely. What is
676
00:31:59.210 --> 00:32:01.490 A:middle L:90%
incoming? Flow number one and number two. You
677
00:32:01.490 --> 00:32:05.200 A:middle L:90%
have these turbines. These turbines are what 12 centimeters
678
00:32:05.200 --> 00:32:07.390 A:middle L:90%
in the in in rotor diameter. These 12 centimeters
679
00:32:07.390 --> 00:32:12.170 A:middle L:90%
in Hub High and the distant Here's what five diameter
680
00:32:12.440 --> 00:32:15.049 A:middle L:90%
. So this operation is quite shorter than what you
681
00:32:15.049 --> 00:32:16.190 A:middle L:90%
saw before. It's not seven, it's not nine
682
00:32:16.190 --> 00:32:20.059 A:middle L:90%
, it's not. 10 is five, and this
683
00:32:20.059 --> 00:32:22.299 A:middle L:90%
was done on purpose. And the reason was in
684
00:32:22.299 --> 00:32:23.049 A:middle L:90%
the early experiments that we did, I think,
685
00:32:23.049 --> 00:32:27.079 A:middle L:90%
actually show some of those experience. Last time when
686
00:32:27.079 --> 00:32:29.750 A:middle L:90%
disturbance were two separate too far, the role of
687
00:32:29.750 --> 00:32:31.819 A:middle L:90%
the disperses stresses were very, very minimum in the
688
00:32:31.819 --> 00:32:35.490 A:middle L:90%
entire energy budget. So what we decided to do
689
00:32:35.490 --> 00:32:38.000 A:middle L:90%
is to add two things. One, we added
690
00:32:38.000 --> 00:32:42.349 A:middle L:90%
this change. So this tried to represent some sort
691
00:32:42.349 --> 00:32:45.140 A:middle L:90%
of a complex topography. And to do these studies
692
00:32:45.140 --> 00:32:47.190 A:middle L:90%
are very, very difficult. We took this one
693
00:32:47.200 --> 00:32:51.309 A:middle L:90%
took about three or four years to complete. But
694
00:32:51.319 --> 00:32:52.049 A:middle L:90%
these are districts that I was telling you about.
695
00:32:52.440 --> 00:32:54.630 A:middle L:90%
You can see it right at the bottom. They
696
00:32:54.630 --> 00:32:58.750 A:middle L:90%
are very, um hi. Variation at the bottom
697
00:32:58.759 --> 00:33:01.230 A:middle L:90%
. So that produces what high share as the flow
698
00:33:01.240 --> 00:33:05.250 A:middle L:90%
enters the winner A. And then you have this
699
00:33:05.259 --> 00:33:07.269 A:middle L:90%
. This change and you have an array of three
700
00:33:07.269 --> 00:33:08.589 A:middle L:90%
by five. So again you can see that this
701
00:33:08.589 --> 00:33:14.039 A:middle L:90%
is very regular geometry. Nothing really crazy. Why
702
00:33:14.049 --> 00:33:16.769 A:middle L:90%
because I want to remove Remove the number of uncertainties
703
00:33:16.779 --> 00:33:20.029 A:middle L:90%
in this study. Okay. In other words,
704
00:33:20.029 --> 00:33:22.309 A:middle L:90%
I want to have a world control experiment. What
705
00:33:22.309 --> 00:33:24.359 A:middle L:90%
? I I know enough about the floor. So
706
00:33:24.359 --> 00:33:27.859 A:middle L:90%
So you can see here that this this change here
707
00:33:28.839 --> 00:33:30.980 A:middle L:90%
, that that I look at it here are about
708
00:33:30.980 --> 00:33:35.170 A:middle L:90%
1.5 centimeters in high. So this is 1.5 centimeters
709
00:33:35.170 --> 00:33:37.660 A:middle L:90%
in high. All of these turbines are rotating.
710
00:33:37.039 --> 00:33:39.950 A:middle L:90%
And now you know very well what the incoming flow
711
00:33:39.950 --> 00:33:43.119 A:middle L:90%
is. So now you're in very good positions.
712
00:33:43.119 --> 00:33:45.069 A:middle L:90%
If you would like to do some simulations, we
713
00:33:45.069 --> 00:33:46.230 A:middle L:90%
can do very nice comparison. A simulation with the
714
00:33:46.230 --> 00:33:51.329 A:middle L:90%
experiment. And the other thing is that we did
715
00:33:51.339 --> 00:33:52.210 A:middle L:90%
is that we did P i V. So we
716
00:33:52.210 --> 00:33:55.259 A:middle L:90%
have a 23 by 22 centimeter field of view so
717
00:33:55.259 --> 00:33:59.259 A:middle L:90%
you could get measurements at different points in a plane
718
00:33:59.740 --> 00:34:00.099 A:middle L:90%
. Okay, this is to D p I.
719
00:34:00.099 --> 00:34:04.019 A:middle L:90%
V Okay. And so if you look at this
720
00:34:04.029 --> 00:34:07.349 A:middle L:90%
from the other angle, So if you look at
721
00:34:07.349 --> 00:34:09.769 A:middle L:90%
the separation in X is five diameters so this this
722
00:34:09.769 --> 00:34:13.610 A:middle L:90%
distance I'm sorry. This system is X. This
723
00:34:13.610 --> 00:34:15.050 A:middle L:90%
is in Z, and this one is three diameter
724
00:34:16.139 --> 00:34:20.139 A:middle L:90%
in the X direction. The separation five and it
725
00:34:20.139 --> 00:34:22.170 A:middle L:90%
is P ratio is four. So from all of
726
00:34:22.170 --> 00:34:25.480 A:middle L:90%
this information, we basically have enough details. Now
727
00:34:25.480 --> 00:34:30.219 A:middle L:90%
there's one limitation. This place I mean, the
728
00:34:30.219 --> 00:34:31.420 A:middle L:90%
hope high is 12 centimeters. You're talking about very
729
00:34:31.420 --> 00:34:36.039 A:middle L:90%
, very small turbine and the problem that we're talking
730
00:34:36.039 --> 00:34:37.190 A:middle L:90%
about it today, this morning that why we want
731
00:34:37.190 --> 00:34:42.090 A:middle L:90%
to go to a bigger array is the following the
732
00:34:42.099 --> 00:34:44.650 A:middle L:90%
thickness of this place. They don't have a profile
733
00:34:44.650 --> 00:34:46.039 A:middle L:90%
. In other words, this is basically two dimensional
734
00:34:46.050 --> 00:34:49.989 A:middle L:90%
. It's like because they're very, very too small
735
00:34:50.000 --> 00:34:52.179 A:middle L:90%
to be able to create any profile on the play
736
00:34:52.179 --> 00:34:55.050 A:middle L:90%
themselves. Um, but if you look at the
737
00:34:55.440 --> 00:34:59.179 A:middle L:90%
the sample, we took 3000 samples at seven years
738
00:34:59.190 --> 00:35:00.659 A:middle L:90%
and the field of view of the P I v
739
00:35:00.659 --> 00:35:02.269 A:middle L:90%
. So in other words, so if you take
740
00:35:02.269 --> 00:35:06.429 A:middle L:90%
a snapshot in a plane around the center line,
741
00:35:06.440 --> 00:35:07.480 A:middle L:90%
you can see how some of these structures of the
742
00:35:07.480 --> 00:35:12.190 A:middle L:90%
flow are changing in the entire plane. So this
743
00:35:12.190 --> 00:35:14.539 A:middle L:90%
is one of the objectives of using this At the
744
00:35:14.539 --> 00:35:16.719 A:middle L:90%
same time, I can know what how the profile
745
00:35:16.719 --> 00:35:20.130 A:middle L:90%
changes in the entire acceleration. In other words,
746
00:35:20.130 --> 00:35:22.860 A:middle L:90%
you can see the entire evolution of the flow.
747
00:35:22.440 --> 00:35:24.460 A:middle L:90%
And this is part of the idea of what we
748
00:35:24.460 --> 00:35:31.860 A:middle L:90%
want to attack here. Yes. Did you you
749
00:35:31.860 --> 00:35:35.929 A:middle L:90%
mentioned the tip speed ratio was four. What does
750
00:35:35.929 --> 00:35:37.420 A:middle L:90%
that mean? In terms of the rpm, how
751
00:35:37.420 --> 00:35:39.840 A:middle L:90%
it scales to full scale. And uh huh.
752
00:35:40.440 --> 00:35:45.719 A:middle L:90%
Fork order. Yes, they do. They do
753
00:35:45.719 --> 00:35:47.889 A:middle L:90%
this disturbance, they do have a small motor,
754
00:35:47.900 --> 00:35:51.630 A:middle L:90%
and actually, you have a resistant on them.
755
00:35:51.639 --> 00:35:53.460 A:middle L:90%
So the rpm is about 1000. About 1000.
756
00:35:53.460 --> 00:35:57.090 A:middle L:90%
They're going very, very fast, super fast.
757
00:35:57.099 --> 00:35:59.579 A:middle L:90%
And, uh but then you put some resistant,
758
00:35:59.579 --> 00:36:00.469 A:middle L:90%
and actually, this is how we measure the power
759
00:36:00.480 --> 00:36:02.480 A:middle L:90%
. So the more of themselves have a little current
760
00:36:02.480 --> 00:36:06.119 A:middle L:90%
from which we could measure the voltage and we will
761
00:36:06.119 --> 00:36:07.719 A:middle L:90%
get the current. And that's how we get the
762
00:36:07.719 --> 00:36:10.210 A:middle L:90%
power on this. So they have some resistance in
763
00:36:10.210 --> 00:36:13.849 A:middle L:90%
all of them and actually, from the entire distance
764
00:36:14.530 --> 00:36:15.679 A:middle L:90%
from all of them, we could actually get the
765
00:36:15.679 --> 00:36:21.519 A:middle L:90%
power for the entire way. Yeah, so the
766
00:36:21.530 --> 00:36:24.150 A:middle L:90%
the So there's some limitations and actually the scaling This
767
00:36:24.150 --> 00:36:27.119 A:middle L:90%
is some of the issue. One of the issues
768
00:36:27.119 --> 00:36:29.690 A:middle L:90%
that we cannot scale the Reynolds number. The rain
769
00:36:29.690 --> 00:36:31.489 A:middle L:90%
is somebody is completely out of the question. But
770
00:36:31.500 --> 00:36:38.170 A:middle L:90%
the the rest of the information is comparable for the
771
00:36:38.170 --> 00:36:42.909 A:middle L:90%
most part. Mhm, Yes. So the this
772
00:36:42.909 --> 00:36:45.159 A:middle L:90%
is the curve for the power. So basically,
773
00:36:45.159 --> 00:36:46.690 A:middle L:90%
what you have this is the angular velocity. And
774
00:36:46.699 --> 00:36:49.679 A:middle L:90%
I basically this is the curve from kind of meh
775
00:36:49.679 --> 00:36:51.949 A:middle L:90%
novo. And the idea is that you could get
776
00:36:51.949 --> 00:36:53.769 A:middle L:90%
this relationship and t is basically the torque. And
777
00:36:53.769 --> 00:36:55.860 A:middle L:90%
you can see that this expression in terms of the
778
00:36:55.860 --> 00:36:58.989 A:middle L:90%
current if you know what the current is through the
779
00:36:58.989 --> 00:37:00.429 A:middle L:90%
resistance of the motors, you could basically back up
780
00:37:00.429 --> 00:37:04.239 A:middle L:90%
what the power is that they produce. And if
781
00:37:04.239 --> 00:37:06.389 A:middle L:90%
you look at this curve, this is the power
782
00:37:06.389 --> 00:37:07.869 A:middle L:90%
curve. This is the vertical. This is the
783
00:37:07.869 --> 00:37:10.769 A:middle L:90%
powering each of the roses. 123 So this is
784
00:37:10.769 --> 00:37:15.460 A:middle L:90%
looking at determined 123 so and so forth. And
785
00:37:15.469 --> 00:37:16.239 A:middle L:90%
if you look at the center, this is the
786
00:37:16.250 --> 00:37:19.300 A:middle L:90%
power of the center of the turbine. This is
787
00:37:19.300 --> 00:37:21.280 A:middle L:90%
at the edge. This is the other one,
788
00:37:21.289 --> 00:37:22.769 A:middle L:90%
and you can see the power from the first one
789
00:37:22.780 --> 00:37:29.780 A:middle L:90%
to the second one drastically dropped about 40%. Oh
790
00:37:29.789 --> 00:37:32.130 A:middle L:90%
, thank you. Thank you. Uh huh.
791
00:37:32.139 --> 00:37:37.659 A:middle L:90%
Thank you Okay? Okay. Now we're in business
792
00:37:37.670 --> 00:37:38.480 A:middle L:90%
, so you can look at the power drop from
793
00:37:38.480 --> 00:37:40.460 A:middle L:90%
the first one to the second one, which is
794
00:37:40.460 --> 00:37:44.130 A:middle L:90%
about 40%. If you remember, that was exactly
795
00:37:44.130 --> 00:37:45.559 A:middle L:90%
what you saw in the sharp from the field of
796
00:37:45.570 --> 00:37:49.440 A:middle L:90%
in Barthelemy. Now, the question is this.
797
00:37:49.449 --> 00:37:52.960 A:middle L:90%
If you look at this curve, basically the power
798
00:37:52.960 --> 00:37:55.840 A:middle L:90%
settles down. And if you're very naive, many
799
00:37:55.840 --> 00:37:58.960 A:middle L:90%
of these studies in the past have been shown that
800
00:37:58.989 --> 00:38:01.679 A:middle L:90%
if the power drop reaches a constant value, this
801
00:38:01.679 --> 00:38:05.940 A:middle L:90%
race are called fully developed. What I wanted to
802
00:38:05.940 --> 00:38:09.780 A:middle L:90%
argue today is that that that observation of using only
803
00:38:09.789 --> 00:38:13.710 A:middle L:90%
mean values to represent whether or not this is fully
804
00:38:13.710 --> 00:38:16.059 A:middle L:90%
developed is quite is inconsistent. Actually, you cannot
805
00:38:16.059 --> 00:38:19.730 A:middle L:90%
use that to represent this as a fully developed.
806
00:38:19.739 --> 00:38:21.849 A:middle L:90%
This is the last turbine. And what you show
807
00:38:21.849 --> 00:38:23.579 A:middle L:90%
here is that the power here is about 0.23.
808
00:38:23.590 --> 00:38:28.530 A:middle L:90%
What now? So now you have a means by
809
00:38:28.530 --> 00:38:30.219 A:middle L:90%
which one can make arguments whether or not this is
810
00:38:30.219 --> 00:38:35.340 A:middle L:90%
fully developed from the power measurements themselves. Of course
811
00:38:35.340 --> 00:38:37.119 A:middle L:90%
, we're not saying that this is the way you
812
00:38:37.119 --> 00:38:38.440 A:middle L:90%
should do this. Now the question we would like
813
00:38:38.440 --> 00:38:40.590 A:middle L:90%
to do If you know what this information is.
814
00:38:40.599 --> 00:38:43.809 A:middle L:90%
Can I use other set of information? In other
815
00:38:43.809 --> 00:38:45.590 A:middle L:90%
words, can I use the data from the from
816
00:38:45.590 --> 00:38:51.059 A:middle L:90%
the From the velocity field measurements and the mean Kennedy
817
00:38:51.059 --> 00:38:53.320 A:middle L:90%
Kennedy question to make the assessment whether or not these
818
00:38:53.320 --> 00:38:57.480 A:middle L:90%
are actually really becomes fully developed. And if you
819
00:38:57.480 --> 00:38:59.360 A:middle L:90%
look at that, for example, this is the
820
00:38:59.360 --> 00:39:00.349 A:middle L:90%
profile. So what we're gonna look now is the
821
00:39:00.349 --> 00:39:05.159 A:middle L:90%
rain of shear stresses. Now again, to be
822
00:39:05.159 --> 00:39:07.210 A:middle L:90%
able to get all of that information need to know
823
00:39:07.210 --> 00:39:09.679 A:middle L:90%
what are different stresses what is the mean velocity.
824
00:39:09.690 --> 00:39:13.110 A:middle L:90%
And I need to get the revelations and put that
825
00:39:13.110 --> 00:39:15.809 A:middle L:90%
into the kinetic energy question. Once I do that
826
00:39:15.809 --> 00:39:17.960 A:middle L:90%
, then I can make that assessment. So why
827
00:39:17.960 --> 00:39:22.469 A:middle L:90%
basically represent the vertical axis? And you basically represents
828
00:39:22.469 --> 00:39:24.780 A:middle L:90%
what this right here is the Reynolds Shear stresses you
829
00:39:24.780 --> 00:39:29.409 A:middle L:90%
ve and you double prime is what Remember this.
830
00:39:29.420 --> 00:39:31.329 A:middle L:90%
This is personal stresses, and in the past,
831
00:39:31.329 --> 00:39:35.510 A:middle L:90%
what we show actually was that those his personal stresses
832
00:39:35.519 --> 00:39:37.550 A:middle L:90%
were very, very small. Actually, when we
833
00:39:37.550 --> 00:39:39.869 A:middle L:90%
when we first did these studies in 2000, the
834
00:39:39.880 --> 00:39:43.719 A:middle L:90%
top paper that we published in 2010, we showed
835
00:39:43.719 --> 00:39:46.480 A:middle L:90%
that those his personal stresses were very insignificant. But
836
00:39:46.480 --> 00:39:50.329 A:middle L:90%
what we show here is quite the opposite. That
837
00:39:50.340 --> 00:39:52.559 A:middle L:90%
that when you have some sort of a complex terrain
838
00:39:52.570 --> 00:39:53.909 A:middle L:90%
or when determines, are too close to each other
839
00:39:53.920 --> 00:39:55.710 A:middle L:90%
. The role of this, this person stresses,
840
00:39:55.710 --> 00:39:59.190 A:middle L:90%
are very high. And actually, you begin to
841
00:39:59.190 --> 00:40:00.250 A:middle L:90%
be to be suspicious. Here. You can see
842
00:40:00.260 --> 00:40:04.150 A:middle L:90%
that as they these turbines are rotating. They seem
843
00:40:04.150 --> 00:40:07.070 A:middle L:90%
to be producing what high levels of turbulence. And
844
00:40:07.079 --> 00:40:10.340 A:middle L:90%
so this is the tip. The top line here
845
00:40:10.340 --> 00:40:14.150 A:middle L:90%
represent the tip. The top tip. This one
846
00:40:14.150 --> 00:40:15.329 A:middle L:90%
is the lower part. And guess what? If
847
00:40:15.329 --> 00:40:19.230 A:middle L:90%
you put the duck product of these Reynaud stresses with
848
00:40:19.230 --> 00:40:22.550 A:middle L:90%
the mean those are what the flux is right,
849
00:40:22.550 --> 00:40:23.519 A:middle L:90%
the energy flux due to the rain of stresses.
850
00:40:24.510 --> 00:40:27.489 A:middle L:90%
And we could do this. Actually, if you
851
00:40:27.489 --> 00:40:30.989 A:middle L:90%
look at this chart, this is represented vertical axis
852
00:40:30.000 --> 00:40:34.309 A:middle L:90%
. And here you have what the stresses in this
853
00:40:34.309 --> 00:40:37.380 A:middle L:90%
case is what you ve the Reynolds Shear stresses with
854
00:40:37.380 --> 00:40:39.050 A:middle L:90%
what with the U bar. So it's the mean
855
00:40:39.050 --> 00:40:42.019 A:middle L:90%
flow, right? So this is the energy flux
856
00:40:42.019 --> 00:40:44.570 A:middle L:90%
is and guess what? If you take the area
857
00:40:44.570 --> 00:40:47.480 A:middle L:90%
underneath this curve, what? This represents the energy
858
00:40:47.480 --> 00:40:51.440 A:middle L:90%
flux due to the rain of stresses. And so
859
00:40:51.440 --> 00:40:52.690 A:middle L:90%
this is very nice, because now you can use
860
00:40:52.690 --> 00:40:55.789 A:middle L:90%
what the questions of motion you could use The lost
861
00:40:55.789 --> 00:41:00.199 A:middle L:90%
the field measurements to make assessment as to how important
862
00:41:00.210 --> 00:41:02.090 A:middle L:90%
those terms are. So if you look at this
863
00:41:02.090 --> 00:41:05.639 A:middle L:90%
is the area, this is the density. Here
864
00:41:05.639 --> 00:41:08.039 A:middle L:90%
you have the area, and here's the Renaissance stresses
865
00:41:08.050 --> 00:41:10.070 A:middle L:90%
. This is the correlation with the mean flow.
866
00:41:10.079 --> 00:41:13.380 A:middle L:90%
And if you subtract the lower point, all of
867
00:41:13.380 --> 00:41:17.000 A:middle L:90%
this area here will basically give you what the energy
868
00:41:17.000 --> 00:41:21.400 A:middle L:90%
flux due to the rain of stresses. Okay,
869
00:41:21.610 --> 00:41:24.010 A:middle L:90%
Now let us remember this. This gives up a
870
00:41:24.010 --> 00:41:28.639 A:middle L:90%
0.62. What does that mean? Well, look
871
00:41:28.639 --> 00:41:31.730 A:middle L:90%
at this. We measure about 0.23 right in that
872
00:41:31.730 --> 00:41:37.119 A:middle L:90%
fourth turbine. That means that the energy flux and
873
00:41:37.119 --> 00:41:39.530 A:middle L:90%
produced by the Rennes stresses is of the same order
874
00:41:39.530 --> 00:41:43.900 A:middle L:90%
magnitude as the power measured by the turbines. This
875
00:41:43.900 --> 00:41:45.570 A:middle L:90%
is a big deal. It tells you now that
876
00:41:45.579 --> 00:41:49.159 A:middle L:90%
the role of these Reynaud stresses are going to be
877
00:41:49.170 --> 00:41:52.099 A:middle L:90%
very, very important. In other words, you
878
00:41:52.099 --> 00:41:53.039 A:middle L:90%
don't have to worry about only about the stream wise
879
00:41:53.050 --> 00:41:57.630 A:middle L:90%
energy, but the vertical entrainment of the energy,
880
00:41:58.010 --> 00:41:59.599 A:middle L:90%
And that's a big deal now, because now I
881
00:41:59.599 --> 00:42:01.480 A:middle L:90%
can say, Look, if this radio stresses the
882
00:42:01.480 --> 00:42:05.699 A:middle L:90%
flux of energy due to the registries are very important
883
00:42:05.710 --> 00:42:08.139 A:middle L:90%
, I can then redesign the blade in such a
884
00:42:08.139 --> 00:42:12.320 A:middle L:90%
way that maximize that vertical entrainment of the energy.
885
00:42:12.699 --> 00:42:14.920 A:middle L:90%
Okay, And I'm gonna show you some more pictures
886
00:42:14.920 --> 00:42:16.369 A:middle L:90%
that I'm going to illustrate that point. Now,
887
00:42:16.369 --> 00:42:19.510 A:middle L:90%
if you look at the disperses stresses, which is
888
00:42:19.510 --> 00:42:22.449 A:middle L:90%
this component with the main flow, you could do
889
00:42:22.449 --> 00:42:23.539 A:middle L:90%
exactly the same. So you can look at the
890
00:42:23.539 --> 00:42:27.559 A:middle L:90%
energy flux is due to the, uh, disperses
891
00:42:27.559 --> 00:42:30.139 A:middle L:90%
stresses. And this again, this is this person
892
00:42:30.139 --> 00:42:31.139 A:middle L:90%
stresses, is the main flow. You can take
893
00:42:31.139 --> 00:42:35.710 A:middle L:90%
the top value minus the lower value. And that
894
00:42:35.710 --> 00:42:40.070 A:middle L:90%
difference basically will give you what the total value of
895
00:42:40.070 --> 00:42:44.440 A:middle L:90%
the energy. So the energy produced by the disperses
896
00:42:44.440 --> 00:42:46.800 A:middle L:90%
stresses is about 0.13. What, which is close
897
00:42:46.809 --> 00:42:50.530 A:middle L:90%
to what you measure before. And that tells us
898
00:42:50.530 --> 00:42:52.480 A:middle L:90%
that now, when you have some sort of a
899
00:42:52.480 --> 00:42:54.690 A:middle L:90%
complex train, you do have to worry about modeling
900
00:42:54.699 --> 00:42:58.800 A:middle L:90%
. This disperses stresses, and this is part of
901
00:42:58.800 --> 00:43:00.239 A:middle L:90%
the the idea here. Now you can do this
902
00:43:00.239 --> 00:43:04.230 A:middle L:90%
for the energy flux is you could. I mean
903
00:43:04.230 --> 00:43:06.099 A:middle L:90%
, I'm not going to show you here because I'm
904
00:43:06.099 --> 00:43:07.619 A:middle L:90%
going to focus more on the part of this story
905
00:43:07.630 --> 00:43:09.679 A:middle L:90%
. But if you look at the pressure and you
906
00:43:09.679 --> 00:43:13.199 A:middle L:90%
can get the pressure gradient and the correlation with the
907
00:43:13.199 --> 00:43:15.929 A:middle L:90%
mean velocity, you can get the pressure drop here
908
00:43:15.940 --> 00:43:17.400 A:middle L:90%
, and then you could measure How much is the
909
00:43:17.409 --> 00:43:21.900 A:middle L:90%
power or the energy produced by the pressure drop across
910
00:43:21.900 --> 00:43:22.980 A:middle L:90%
the entire ray? And from this, you could
911
00:43:22.980 --> 00:43:28.820 A:middle L:90%
now make estimate of what? Remember this the entire
912
00:43:28.829 --> 00:43:31.210 A:middle L:90%
energy budget so you could get the power that you
913
00:43:31.210 --> 00:43:34.610 A:middle L:90%
measure. Um, and then you could you could
914
00:43:34.610 --> 00:43:37.599 A:middle L:90%
get the The flux is due to the radio stresses
915
00:43:37.610 --> 00:43:39.239 A:middle L:90%
. Then you could get the flux is due to
916
00:43:39.239 --> 00:43:43.179 A:middle L:90%
what this person stresses. And then you could get
917
00:43:43.179 --> 00:43:45.949 A:middle L:90%
what the losses due to what the Reynosa stresses,
918
00:43:45.949 --> 00:43:50.639 A:middle L:90%
this is the true anticipation. This is the participation
919
00:43:50.650 --> 00:43:52.210 A:middle L:90%
. And here what do you have? The correlation
920
00:43:52.210 --> 00:43:54.579 A:middle L:90%
due to the pressure gradient. And if you add
921
00:43:54.590 --> 00:43:57.730 A:middle L:90%
all of these terms, you're gonna tell me Luciano
922
00:43:58.400 --> 00:44:00.409 A:middle L:90%
, this is not equal to zero, right?
923
00:44:00.989 --> 00:44:05.070 A:middle L:90%
And that tells us something. Remember what we did
924
00:44:05.079 --> 00:44:07.820 A:middle L:90%
. We make the assumption that in the case of
925
00:44:07.820 --> 00:44:08.619 A:middle L:90%
the fully developed, the infection terms are going to
926
00:44:08.619 --> 00:44:12.599 A:middle L:90%
be zero. So they tell the two things first
927
00:44:13.489 --> 00:44:15.010 A:middle L:90%
, that this array is way too small to be
928
00:44:15.010 --> 00:44:17.239 A:middle L:90%
fully developed. In other words, you need a
929
00:44:17.239 --> 00:44:22.280 A:middle L:90%
way, way longer array to perhaps begin to see
930
00:44:22.289 --> 00:44:24.440 A:middle L:90%
that this assumption that dropping the infection term in the
931
00:44:24.440 --> 00:44:28.519 A:middle L:90%
case of fully developed is actually valid. The second
932
00:44:28.519 --> 00:44:30.949 A:middle L:90%
important point is that this contribution of the infection terms
933
00:44:30.960 --> 00:44:36.360 A:middle L:90%
should be important in the consideration. So now we
934
00:44:36.360 --> 00:44:37.739 A:middle L:90%
know demonstrated two things. First, when you get
935
00:44:37.739 --> 00:44:42.369 A:middle L:90%
the power measurements, our conclusion was that perhaps this
936
00:44:42.369 --> 00:44:44.889 A:middle L:90%
array is fully developed. When you look at them
937
00:44:44.889 --> 00:44:47.340 A:middle L:90%
in kinetic energy and you perform the energy budget based
938
00:44:47.340 --> 00:44:50.480 A:middle L:90%
on the assumption that if this is fully developed,
939
00:44:50.489 --> 00:44:52.130 A:middle L:90%
those terms in the infection terms will be zero.
940
00:44:52.139 --> 00:44:55.929 A:middle L:90%
You basically we conclude that this is completely inconsistent to
941
00:44:55.929 --> 00:44:59.420 A:middle L:90%
what you see before. Now, what option do
942
00:44:59.420 --> 00:45:05.250 A:middle L:90%
we have? Well, we could try to look
943
00:45:05.250 --> 00:45:07.590 A:middle L:90%
at the profiles, right? We could characterize the
944
00:45:07.590 --> 00:45:09.000 A:middle L:90%
entire profile and see how do they change in X
945
00:45:09.489 --> 00:45:12.730 A:middle L:90%
? That's probably one hope and try to see How
946
00:45:12.730 --> 00:45:14.880 A:middle L:90%
does that compare to all of this? But to
947
00:45:14.880 --> 00:45:16.360 A:middle L:90%
summarize. What I wanted to point out is this
948
00:45:16.440 --> 00:45:20.719 A:middle L:90%
This is very critical. So from this, besides
949
00:45:20.719 --> 00:45:22.949 A:middle L:90%
the fact that this is not fully developed, what
950
00:45:22.949 --> 00:45:25.809 A:middle L:90%
we demonstrated here was that this reign of stresses are
951
00:45:27.190 --> 00:45:29.360 A:middle L:90%
the first order term. This is what I was
952
00:45:29.360 --> 00:45:31.340 A:middle L:90%
telling at the beginning that the major important issues on
953
00:45:31.349 --> 00:45:36.059 A:middle L:90%
on wind energy or the other one problem is turbulence
954
00:45:36.070 --> 00:45:37.960 A:middle L:90%
. And and this is evidence of that. So
955
00:45:37.960 --> 00:45:39.389 A:middle L:90%
the fact that this term is that the same order
956
00:45:39.389 --> 00:45:44.400 A:middle L:90%
magnitude as a power that you measure tell us this
957
00:45:44.409 --> 00:45:45.760 A:middle L:90%
that a lot of the energy is going to be
958
00:45:45.760 --> 00:45:49.690 A:middle L:90%
fed from the array above. Okay. And that's
959
00:45:49.690 --> 00:45:52.750 A:middle L:90%
actually before you could take advantage of that information of
960
00:45:52.750 --> 00:45:54.730 A:middle L:90%
that knowledge to redesign the plate. So we go
961
00:45:54.730 --> 00:45:57.809 A:middle L:90%
back to what we were talking this afternoon. Can
962
00:45:57.809 --> 00:46:00.059 A:middle L:90%
we go back and redesign this plate? That is
963
00:46:00.070 --> 00:46:01.789 A:middle L:90%
optimal for the array. And this is on the
964
00:46:01.789 --> 00:46:06.190 A:middle L:90%
idea now that we learned that the registrations are important
965
00:46:06.199 --> 00:46:07.440 A:middle L:90%
, that all of the energy is coming from the
966
00:46:07.449 --> 00:46:12.079 A:middle L:90%
atmospheric boundary layer above. So what I would like
967
00:46:12.079 --> 00:46:14.690 A:middle L:90%
to do is I'm gonna press some some points here
968
00:46:14.699 --> 00:46:15.989 A:middle L:90%
, but let's look at this This is the this
969
00:46:15.989 --> 00:46:19.309 A:middle L:90%
is, uh this is a fairly new result.
970
00:46:19.309 --> 00:46:21.349 A:middle L:90%
Actually, all of this is in the, uh
971
00:46:21.360 --> 00:46:22.269 A:middle L:90%
, forgot to put it. This is the paper
972
00:46:22.280 --> 00:46:23.989 A:middle L:90%
that we show in the physics of fluids that just
973
00:46:23.989 --> 00:46:25.800 A:middle L:90%
came out last month. But this is, for
974
00:46:25.800 --> 00:46:29.659 A:middle L:90%
example, as the floor comes from left to the
975
00:46:29.659 --> 00:46:31.750 A:middle L:90%
right, you can see that the flow, uh
976
00:46:31.760 --> 00:46:34.869 A:middle L:90%
, accelerate. In other words, the floor knows
977
00:46:34.869 --> 00:46:36.369 A:middle L:90%
, Hey, I have a structure. They are
978
00:46:36.369 --> 00:46:37.989 A:middle L:90%
better slow down, so you can see how it
979
00:46:37.989 --> 00:46:39.909 A:middle L:90%
slows down at the beginning. But this is what
980
00:46:39.909 --> 00:46:42.800 A:middle L:90%
I want you to pay attention. I want you
981
00:46:42.800 --> 00:46:45.449 A:middle L:90%
to look very carefully. How do you read?
982
00:46:45.449 --> 00:46:46.949 A:middle L:90%
Is high speed okay, so you can see above
983
00:46:46.949 --> 00:46:51.090 A:middle L:90%
the tip of the array high speed flow. In
984
00:46:51.090 --> 00:46:52.800 A:middle L:90%
other words, what you see is that there is
985
00:46:52.800 --> 00:46:55.260 A:middle L:90%
a complex interaction you have outside the atmospheric boundary layer
986
00:46:55.269 --> 00:46:58.570 A:middle L:90%
. And inside of the array, you have what
987
00:46:58.579 --> 00:47:00.940 A:middle L:90%
boundary airflow inside of the array. But at the
988
00:47:00.949 --> 00:47:05.500 A:middle L:90%
interface at the interface, you have a regional high
989
00:47:05.500 --> 00:47:07.170 A:middle L:90%
speed flow, and this is very, very important
990
00:47:07.170 --> 00:47:09.750 A:middle L:90%
because this could tell us that a lot of the
991
00:47:09.750 --> 00:47:13.829 A:middle L:90%
energy is coming from what the interaction of the flow
992
00:47:13.840 --> 00:47:17.820 A:middle L:90%
above with the array. Okay, this in blue
993
00:47:17.829 --> 00:47:21.219 A:middle L:90%
is obvious because if you have a wake, if
994
00:47:21.219 --> 00:47:22.730 A:middle L:90%
you have a structure that structure is going to produce
995
00:47:22.730 --> 00:47:27.500 A:middle L:90%
What awake? And that's what he slowed down here
996
00:47:27.880 --> 00:47:30.179 A:middle L:90%
. So you see, this week is quite far
997
00:47:30.190 --> 00:47:31.079 A:middle L:90%
and you can see this below, and then you
998
00:47:31.079 --> 00:47:35.269 A:middle L:90%
can see the high speed above the array. Now
999
00:47:35.280 --> 00:47:37.099 A:middle L:90%
, if you look at the vertical velocity and this
1000
00:47:37.099 --> 00:47:37.900 A:middle L:90%
is quite interesting if we look at that, that
1001
00:47:37.900 --> 00:47:43.670 A:middle L:90%
component this is again the flow comes from left,
1002
00:47:43.670 --> 00:47:45.070 A:middle L:90%
right? This is the mean velocity again, okay
1003
00:47:45.079 --> 00:47:46.769 A:middle L:90%
. And what you see here is the flow because
1004
00:47:46.769 --> 00:47:50.219 A:middle L:90%
its direction he knows that there is a turbine.
1005
00:47:50.230 --> 00:47:52.489 A:middle L:90%
The flow goes above. So it's positive velocity and
1006
00:47:52.489 --> 00:47:54.650 A:middle L:90%
here goes below. So a lot of the velocity
1007
00:47:54.650 --> 00:47:58.409 A:middle L:90%
goes above the turbine. Okay, not a big
1008
00:47:58.409 --> 00:48:00.500 A:middle L:90%
deal, But you can see positive velocity here,
1009
00:48:00.869 --> 00:48:06.110 A:middle L:90%
positive And as you move downstream, the structure seems
1010
00:48:06.110 --> 00:48:08.690 A:middle L:90%
to be highly elongated. In other words, the
1011
00:48:08.699 --> 00:48:14.480 A:middle L:90%
large skills downstream seems to be even more pronounced than
1012
00:48:14.480 --> 00:48:16.380 A:middle L:90%
what you saw initially. The other important issue that
1013
00:48:16.380 --> 00:48:19.219 A:middle L:90%
I want you to know there's a turbine here.
1014
00:48:19.230 --> 00:48:21.119 A:middle L:90%
Just look at this. There's a turbine here,
1015
00:48:21.130 --> 00:48:22.929 A:middle L:90%
Another turbine here, Another one here. And there's
1016
00:48:22.929 --> 00:48:25.960 A:middle L:90%
one here. Now look at this. This velocity
1017
00:48:25.960 --> 00:48:29.940 A:middle L:90%
in the top here is what is a positive vertical
1018
00:48:29.940 --> 00:48:32.880 A:middle L:90%
velocity. And this one is what negative. What
1019
00:48:32.880 --> 00:48:35.989 A:middle L:90%
it's telling you is that there is, as the
1020
00:48:35.989 --> 00:48:39.619 A:middle L:90%
turbines are rotating the determine themselves or the voters are
1021
00:48:39.619 --> 00:48:43.389 A:middle L:90%
producing What a rotation on the floor as well.
1022
00:48:43.769 --> 00:48:46.070 A:middle L:90%
Okay, and and, uh, that's very evident
1023
00:48:46.070 --> 00:48:49.269 A:middle L:90%
here. So from the vertical velocity, there are
1024
00:48:49.269 --> 00:48:51.590 A:middle L:90%
two things. The flow goes around the turbines not
1025
00:48:51.590 --> 00:48:53.610 A:middle L:90%
a big deal, but that this shows you evidence
1026
00:48:53.619 --> 00:48:58.530 A:middle L:90%
that there's a week rotation as well. Now the
1027
00:48:58.530 --> 00:49:00.889 A:middle L:90%
other important issue. Remember what I told you.
1028
00:49:00.889 --> 00:49:04.300 A:middle L:90%
What was super important. The rhino stresses the correlation
1029
00:49:04.300 --> 00:49:06.550 A:middle L:90%
of the U and V. So if you look
1030
00:49:06.550 --> 00:49:08.710 A:middle L:90%
at this, this is very important. What do
1031
00:49:08.710 --> 00:49:10.400 A:middle L:90%
you see here? What? We see the rain
1032
00:49:10.400 --> 00:49:14.989 A:middle L:90%
of stresses at the beginning. As the flow comes
1033
00:49:15.000 --> 00:49:16.199 A:middle L:90%
into the array, they're very, very small.
1034
00:49:16.869 --> 00:49:20.510 A:middle L:90%
What that tells you that a lot of the as
1035
00:49:20.510 --> 00:49:22.500 A:middle L:90%
the turbines rotate, they're going to produce what a
1036
00:49:22.500 --> 00:49:25.230 A:middle L:90%
lot of the turbulence. I mean, you just
1037
00:49:25.230 --> 00:49:28.250 A:middle L:90%
makes it more not a big deal. Nothing,
1038
00:49:28.250 --> 00:49:30.150 A:middle L:90%
really. But look at this. Positive, remember
1039
00:49:30.150 --> 00:49:34.750 A:middle L:90%
, was very important. Very positive was important.
1040
00:49:34.750 --> 00:49:37.210 A:middle L:90%
Look at this. At the edge of the turbine
1041
00:49:37.219 --> 00:49:38.900 A:middle L:90%
, a lot of the Iranian stresses is produced.
1042
00:49:39.369 --> 00:49:43.230 A:middle L:90%
Okay? And again, this is consistent. What
1043
00:49:43.230 --> 00:49:45.340 A:middle L:90%
? That is what this is telling us that a
1044
00:49:45.340 --> 00:49:49.150 A:middle L:90%
lot of that interface between the atmospheric boundary layer and
1045
00:49:49.150 --> 00:49:52.949 A:middle L:90%
the winter by an array is very critical. Okay
1046
00:49:52.139 --> 00:49:53.840 A:middle L:90%
. And that interface is the one that we need
1047
00:49:53.840 --> 00:49:57.869 A:middle L:90%
to take advantage to do other stuff. So outside
1048
00:49:57.869 --> 00:50:00.539 A:middle L:90%
of the array, what you see, what low
1049
00:50:00.539 --> 00:50:02.659 A:middle L:90%
values of Reno stress is very low values of Raina
1050
00:50:02.659 --> 00:50:07.110 A:middle L:90%
stresses, but very high behind the turbine. Exactly
1051
00:50:07.110 --> 00:50:09.250 A:middle L:90%
what you saw in the picture from the from Denmark
1052
00:50:09.260 --> 00:50:13.260 A:middle L:90%
, remember? Now what I would like to show
1053
00:50:13.260 --> 00:50:17.239 A:middle L:90%
you is that the following model based on this this
1054
00:50:17.239 --> 00:50:21.429 A:middle L:90%
is telling us that it's very clear that there is
1055
00:50:21.429 --> 00:50:24.420 A:middle L:90%
a boundless growing above the ray, right? It's
1056
00:50:24.420 --> 00:50:28.079 A:middle L:90%
very clear we saw that. Right. So we
1057
00:50:28.079 --> 00:50:30.679 A:middle L:90%
propose that there is a three layer one that is
1058
00:50:30.679 --> 00:50:34.510 A:middle L:90%
above the turbine. So this is gonna be called
1059
00:50:34.519 --> 00:50:37.059 A:middle L:90%
above the rotor. We're gonna call one in between
1060
00:50:37.070 --> 00:50:40.070 A:middle L:90%
. That is going to call the swept and then
1061
00:50:40.139 --> 00:50:44.059 A:middle L:90%
one below that, We're going to court below the
1062
00:50:44.059 --> 00:50:45.480 A:middle L:90%
rotor. Now what we want to do is the
1063
00:50:45.480 --> 00:50:49.539 A:middle L:90%
following. Remember that you could make the assessment whether
1064
00:50:49.539 --> 00:50:52.110 A:middle L:90%
this this characterization of the winter been or it could
1065
00:50:52.110 --> 00:50:55.929 A:middle L:90%
be done by what? Performing a velocity profile.
1066
00:50:55.940 --> 00:50:59.409 A:middle L:90%
You can measure the power, or you can make
1067
00:50:59.409 --> 00:51:01.130 A:middle L:90%
sure what you mean kinetic energy. And we saw
1068
00:51:01.130 --> 00:51:05.460 A:middle L:90%
from the from the latest one that this is not
1069
00:51:05.469 --> 00:51:08.829 A:middle L:90%
fully developed. Now, do you think this is
1070
00:51:08.829 --> 00:51:13.380 A:middle L:90%
possible? Guys, if this is growing that now
1071
00:51:13.420 --> 00:51:16.570 A:middle L:90%
, I can use this physical knowledge to redesign the
1072
00:51:16.570 --> 00:51:21.280 A:middle L:90%
way the servants are developed. Phenomenal. The correct
1073
00:51:21.289 --> 00:51:22.909 A:middle L:90%
the boundary will grow in this direction. What can
1074
00:51:22.909 --> 00:51:25.530 A:middle L:90%
you do with the hope to hear? You could
1075
00:51:25.530 --> 00:51:29.079 A:middle L:90%
increase it, right? These guys could be increased
1076
00:51:29.090 --> 00:51:30.780 A:middle L:90%
. And that tells you that this fundamental knowledge of
1077
00:51:30.780 --> 00:51:36.940 A:middle L:90%
understanding turbulence could help us redesign better, better performance
1078
00:51:36.949 --> 00:51:39.519 A:middle L:90%
of wind farms. Okay, Um, so let's
1079
00:51:39.519 --> 00:51:43.030 A:middle L:90%
look at this. I'm going to just switch this
1080
00:51:43.030 --> 00:51:44.329 A:middle L:90%
, okay? So, again, this is the
1081
00:51:44.329 --> 00:51:46.010 A:middle L:90%
mean velocity. This is the mean velocity, and
1082
00:51:46.010 --> 00:51:47.320 A:middle L:90%
this is what we're going to do. Okay,
1083
00:51:47.329 --> 00:51:50.389 A:middle L:90%
We're going to look a dash line. We're going
1084
00:51:50.389 --> 00:51:54.630 A:middle L:90%
to have already velocity at the tip here over the
1085
00:51:54.630 --> 00:51:58.119 A:middle L:90%
entire X direction. Remember that. If I know
1086
00:51:58.119 --> 00:52:00.260 A:middle L:90%
that the X profiles are not changing too much,
1087
00:52:00.750 --> 00:52:04.840 A:middle L:90%
that give us a sense of what whether or not
1088
00:52:04.840 --> 00:52:07.119 A:middle L:90%
the flock will be fully developed. And then I'm
1089
00:52:07.119 --> 00:52:09.869 A:middle L:90%
going to evaluate the velocity profile at the rotor swept
1090
00:52:09.940 --> 00:52:14.000 A:middle L:90%
at the center of this the rotor. And we're
1091
00:52:14.000 --> 00:52:16.039 A:middle L:90%
gonna see how those that profile changes with eggs and
1092
00:52:16.039 --> 00:52:17.980 A:middle L:90%
then we're gonna do the same at the below the
1093
00:52:17.980 --> 00:52:21.360 A:middle L:90%
rotor. You fix it? Why? And you
1094
00:52:21.360 --> 00:52:23.960 A:middle L:90%
see how the exchanges and this is the first,
1095
00:52:23.969 --> 00:52:27.320 A:middle L:90%
the first round. This is right here the second
1096
00:52:27.320 --> 00:52:29.019 A:middle L:90%
, the third and the fourth. So it's moving
1097
00:52:29.019 --> 00:52:30.440 A:middle L:90%
in this direction. And you could say from this
1098
00:52:30.440 --> 00:52:35.849 A:middle L:90%
picture, Well, that profile above the rotor doesn't
1099
00:52:35.849 --> 00:52:37.909 A:middle L:90%
quite seem to be fully developed. It seems to
1100
00:52:37.920 --> 00:52:42.139 A:middle L:90%
start changing. It seems to change, but this
1101
00:52:42.139 --> 00:52:44.090 A:middle L:90%
is the one that I love the most places.
1102
00:52:44.099 --> 00:52:46.269 A:middle L:90%
So if you look at this picture, remember,
1103
00:52:46.269 --> 00:52:47.619 A:middle L:90%
I mean, I don't know. Many of you
1104
00:52:47.630 --> 00:52:51.159 A:middle L:90%
may be willing could recognize this, but many of
1105
00:52:51.159 --> 00:52:53.380 A:middle L:90%
the profiles in a boundary layer looks like this.
1106
00:52:53.949 --> 00:52:58.130 A:middle L:90%
This list, this profile in the rotor swept looks
1107
00:52:58.130 --> 00:53:00.170 A:middle L:90%
very similar to what we know in boundary layers,
1108
00:53:00.179 --> 00:53:02.530 A:middle L:90%
and in fact, the variation here doesn't seem to
1109
00:53:02.530 --> 00:53:05.730 A:middle L:90%
be as much as what you see in the in
1110
00:53:05.730 --> 00:53:07.170 A:middle L:90%
the above the water. But if you look at
1111
00:53:07.170 --> 00:53:09.800 A:middle L:90%
below the rotor below the rotor, you see a
1112
00:53:09.800 --> 00:53:15.670 A:middle L:90%
significant variation in you. So it's very confusing,
1113
00:53:15.670 --> 00:53:16.510 A:middle L:90%
probably for you to look at all of this picture
1114
00:53:16.510 --> 00:53:19.369 A:middle L:90%
. But what the most important one that you want
1115
00:53:19.369 --> 00:53:22.519 A:middle L:90%
to see is that the the the the Rotor Swept
1116
00:53:22.530 --> 00:53:24.280 A:middle L:90%
seems to be more in what, in an equilibrium
1117
00:53:24.289 --> 00:53:29.409 A:middle L:90%
than above the rotor and below the rotor. So
1118
00:53:29.420 --> 00:53:31.679 A:middle L:90%
the reason why I'm putting this up is because France
1119
00:53:31.679 --> 00:53:36.949 A:middle L:90%
and in 1992 proposed that there's a two layers where
1120
00:53:36.949 --> 00:53:38.690 A:middle L:90%
the layer below the hub high and there's another layer
1121
00:53:38.699 --> 00:53:42.659 A:middle L:90%
above the hob high where those two layers are in
1122
00:53:42.659 --> 00:53:45.630 A:middle L:90%
equilibrium. And in fact, he proposed that the
1123
00:53:45.630 --> 00:53:47.389 A:middle L:90%
velocity profile in both of these letters could be longer
1124
00:53:47.389 --> 00:53:52.329 A:middle L:90%
. It me are logarithmic. This one could be
1125
00:53:52.340 --> 00:53:54.170 A:middle L:90%
, but there's no way that this profile is going
1126
00:53:54.170 --> 00:53:57.679 A:middle L:90%
to look great in any way in any way.
1127
00:53:58.150 --> 00:54:00.969 A:middle L:90%
And if you look at the V component, okay
1128
00:54:00.969 --> 00:54:01.659 A:middle L:90%
, This is the same velocity. So what we
1129
00:54:01.659 --> 00:54:05.989 A:middle L:90%
did here is that this is the same you velocity
1130
00:54:06.000 --> 00:54:07.980 A:middle L:90%
. We took this average velocity at the top tip
1131
00:54:07.980 --> 00:54:10.980 A:middle L:90%
, okay, for the entire region, the rotor
1132
00:54:10.980 --> 00:54:14.440 A:middle L:90%
swept up. And then this one represents below the
1133
00:54:14.440 --> 00:54:16.940 A:middle L:90%
rotor. And what this represents the maximum variation and
1134
00:54:16.940 --> 00:54:21.389 A:middle L:90%
the minimum variation over those profiles. What you can
1135
00:54:21.389 --> 00:54:23.170 A:middle L:90%
see here very clearly is that the maximum variation you
1136
00:54:23.170 --> 00:54:25.619 A:middle L:90%
can see a large variation above the tip. But
1137
00:54:25.619 --> 00:54:28.090 A:middle L:90%
look at this point. Oh, nine. That's
1138
00:54:28.090 --> 00:54:30.969 A:middle L:90%
the difference. This telling us the variation in the
1139
00:54:30.969 --> 00:54:34.769 A:middle L:90%
rotor swept along the entire X direction is what very
1140
00:54:34.769 --> 00:54:37.610 A:middle L:90%
, very small compared to what? Below the rotor
1141
00:54:37.619 --> 00:54:39.269 A:middle L:90%
and above the rotor. This is important. The
1142
00:54:39.269 --> 00:54:43.579 A:middle L:90%
rotor swept seemed to be more equilibrium than everything else
1143
00:54:43.670 --> 00:54:46.360 A:middle L:90%
. Okay? And so let's look at the V
1144
00:54:46.360 --> 00:54:49.670 A:middle L:90%
component. And if you look at the V,
1145
00:54:50.739 --> 00:54:52.039 A:middle L:90%
I'm gonna switch it because this is some interpretations that
1146
00:54:52.039 --> 00:54:53.530 A:middle L:90%
we have to do. But if you look at
1147
00:54:53.530 --> 00:54:55.599 A:middle L:90%
the V over the entire race, so this is
1148
00:54:55.599 --> 00:54:59.449 A:middle L:90%
the first profile is right here, and then you
1149
00:54:59.449 --> 00:55:01.500 A:middle L:90%
can see that all they are all scholars everywhere.
1150
00:55:01.510 --> 00:55:04.760 A:middle L:90%
And part of the reason is because the velocity here
1151
00:55:04.760 --> 00:55:07.309 A:middle L:90%
seems to be lower. So this is positive.
1152
00:55:07.320 --> 00:55:08.829 A:middle L:90%
You have positive velocity, you have negative. But
1153
00:55:08.829 --> 00:55:12.420 A:middle L:90%
if you look at the sweat region, the profile
1154
00:55:12.420 --> 00:55:14.900 A:middle L:90%
seems to be covered up, which is consistent to
1155
00:55:14.900 --> 00:55:17.489 A:middle L:90%
wait to this. So this means that in the
1156
00:55:17.489 --> 00:55:19.980 A:middle L:90%
in the region, in the boundary, a lot
1157
00:55:19.980 --> 00:55:22.469 A:middle L:90%
of the energy is going what from the floor of
1158
00:55:22.940 --> 00:55:25.139 A:middle L:90%
and indeed, when we do the energy budget and
1159
00:55:25.150 --> 00:55:28.269 A:middle L:90%
we didn't show you here a lot of the energies
1160
00:55:28.269 --> 00:55:30.449 A:middle L:90%
coming vertical, but a lot of the energy,
1161
00:55:30.460 --> 00:55:32.550 A:middle L:90%
but the main vertical velocity is coming from the bottom
1162
00:55:32.559 --> 00:55:37.469 A:middle L:90%
up. And And if you look at the the
1163
00:55:37.480 --> 00:55:39.250 A:middle L:90%
below the rotor, you can see that this profile
1164
00:55:39.260 --> 00:55:42.789 A:middle L:90%
is gonna cover up and everything else needs to be
1165
00:55:42.800 --> 00:55:45.110 A:middle L:90%
not changing so much. I did not. Today
1166
00:55:45.119 --> 00:55:45.840 A:middle L:90%
, with all of this, is very hard for
1167
00:55:45.840 --> 00:55:50.070 A:middle L:90%
you to make a distinction whether or not all of
1168
00:55:50.070 --> 00:55:52.840 A:middle L:90%
these profiles are fully developed or not, or characterize
1169
00:55:52.840 --> 00:55:54.199 A:middle L:90%
this array. So if you take the average,
1170
00:55:54.210 --> 00:55:57.250 A:middle L:90%
so if you take the average, which is the
1171
00:55:57.260 --> 00:55:59.760 A:middle L:90%
solid line and this is the maximum, this is
1172
00:55:59.760 --> 00:56:01.210 A:middle L:90%
the minimum. The difference between this is a point
1173
00:56:01.219 --> 00:56:04.070 A:middle L:90%
Oh, nine. If you look at the rotor
1174
00:56:04.070 --> 00:56:07.710 A:middle L:90%
swept this point Serial 67 and then below the rotor
1175
00:56:07.719 --> 00:56:12.510 A:middle L:90%
is 670.15 The message here is that the rotor swept
1176
00:56:12.510 --> 00:56:15.469 A:middle L:90%
seems to be in a more equilibrium than everything else
1177
00:56:15.480 --> 00:56:17.010 A:middle L:90%
in terms of the main flow. Now what we
1178
00:56:17.010 --> 00:56:20.829 A:middle L:90%
want to do is to have Can we characterize this
1179
00:56:20.840 --> 00:56:22.670 A:middle L:90%
in a more rigorous way than what I show you
1180
00:56:22.670 --> 00:56:25.739 A:middle L:90%
here? And we can do that. I'm sure
1181
00:56:25.750 --> 00:56:28.250 A:middle L:90%
I'm going to show you hit this. We could
1182
00:56:28.250 --> 00:56:30.780 A:middle L:90%
do that by taking what we call the heroin.
1183
00:56:30.780 --> 00:56:32.539 A:middle L:90%
Or, in other words, you can look at
1184
00:56:32.539 --> 00:56:37.480 A:middle L:90%
the profile over the X, the vertical direction and
1185
00:56:37.480 --> 00:56:39.989 A:middle L:90%
horizontal direction in all of this plane and take the
1186
00:56:39.989 --> 00:56:44.099 A:middle L:90%
difference in the second velocity. So if you look
1187
00:56:44.099 --> 00:56:46.070 A:middle L:90%
at the profile in front and behind the 1st and
1188
00:56:46.070 --> 00:56:50.030 A:middle L:90%
2nd turbine, if you look at that difference,
1189
00:56:50.530 --> 00:56:52.630 A:middle L:90%
if this is very small, you could begin to
1190
00:56:52.630 --> 00:56:54.420 A:middle L:90%
make assessment whether this is fully developed, so were
1191
00:56:54.420 --> 00:56:58.389 A:middle L:90%
normalized. If we integrate the entire region here,
1192
00:56:58.400 --> 00:57:00.670 A:middle L:90%
we integrate the entire region in the second one,
1193
00:57:00.679 --> 00:57:04.230 A:middle L:90%
and we normalized by what the incoming flow. This
1194
00:57:04.230 --> 00:57:07.510 A:middle L:90%
could give you an assessment as to how small or
1195
00:57:07.519 --> 00:57:12.869 A:middle L:90%
how much the norm be, how much this flow
1196
00:57:12.880 --> 00:57:15.230 A:middle L:90%
will become fully developed. So what we did is
1197
00:57:15.230 --> 00:57:16.380 A:middle L:90%
that we did that for the mean velocity for the
1198
00:57:16.380 --> 00:57:20.659 A:middle L:90%
world number, velocity, reign of stresses and even
1199
00:57:20.659 --> 00:57:22.070 A:middle L:90%
the energy flux is, and this basically gives you
1200
00:57:22.070 --> 00:57:24.119 A:middle L:90%
a more complete picture. So let me let me
1201
00:57:24.119 --> 00:57:27.489 A:middle L:90%
explain you because I think I have dropped so much
1202
00:57:27.489 --> 00:57:30.119 A:middle L:90%
information. All right? What we have done is
1203
00:57:30.119 --> 00:57:35.079 A:middle L:90%
is we have performed well, control experiment right where
1204
00:57:35.079 --> 00:57:37.630 A:middle L:90%
we know there's not so many variables in the floor
1205
00:57:37.639 --> 00:57:39.030 A:middle L:90%
. Then we tie those want to what? The
1206
00:57:39.030 --> 00:57:43.590 A:middle L:90%
questions of motion simply to make assessment as to how
1207
00:57:43.590 --> 00:57:45.840 A:middle L:90%
much important turbulence could be in the floor and in
1208
00:57:45.840 --> 00:57:49.599 A:middle L:90%
the energy budget. And then I also took the
1209
00:57:49.599 --> 00:57:53.179 A:middle L:90%
same data and the what averages To understand what whether
1210
00:57:53.179 --> 00:57:57.440 A:middle L:90%
or not the profile becomes what fully developed. Okay
1211
00:57:57.449 --> 00:57:59.510 A:middle L:90%
, so is this in the same information in a
1212
00:57:59.510 --> 00:58:01.670 A:middle L:90%
different way. If you do this, this a
1213
00:58:01.679 --> 00:58:06.050 A:middle L:90%
r is Meanwhile, above the rotor r s is
1214
00:58:06.050 --> 00:58:08.059 A:middle L:90%
the rotor sweat and below the rotor. And this
1215
00:58:08.059 --> 00:58:12.400 A:middle L:90%
is the mean velocity war normal mean velocity. And
1216
00:58:12.400 --> 00:58:15.829 A:middle L:90%
this is the Rennes Uh normal citywide stresses. Reynolds
1217
00:58:15.860 --> 00:58:19.099 A:middle L:90%
stresses war, normal stresses and this is the energy
1218
00:58:19.099 --> 00:58:21.750 A:middle L:90%
flux. But let's pay attention to this as you
1219
00:58:21.750 --> 00:58:22.519 A:middle L:90%
go from the first turbine. In other words,
1220
00:58:22.530 --> 00:58:25.329 A:middle L:90%
if you go from here to this is the 1st
1221
00:58:25.340 --> 00:58:30.340 A:middle L:90%
and 2nd turbine sick 3rd and 4th and fourth and
1222
00:58:30.340 --> 00:58:31.579 A:middle L:90%
five. If you look at this, this is
1223
00:58:31.579 --> 00:58:35.219 A:middle L:90%
what you have the arrow nor in the first from
1224
00:58:35.219 --> 00:58:37.940 A:middle L:90%
the first turbine as you move in the X direction
1225
00:58:37.949 --> 00:58:40.630 A:middle L:90%
. Guess what happened? The flow as it gets
1226
00:58:40.639 --> 00:58:45.480 A:middle L:90%
bigger and bigger in X becomes what, more fully
1227
00:58:45.480 --> 00:58:49.460 A:middle L:90%
developed? Okay, so from the main perspective in
1228
00:58:49.460 --> 00:58:52.070 A:middle L:90%
the above the ray, this vital 0.3 is the
1229
00:58:52.070 --> 00:58:53.460 A:middle L:90%
norm. It goes down as you go from the
1230
00:58:53.460 --> 00:58:55.449 A:middle L:90%
rotor swept. You can see the rotors. It
1231
00:58:55.449 --> 00:58:58.059 A:middle L:90%
is about the same valley. It's a little bit
1232
00:58:58.059 --> 00:59:01.530 A:middle L:90%
smaller, but if you go below below the turbine
1233
00:59:01.590 --> 00:59:04.789 A:middle L:90%
, these points or nineties points or six, it
1234
00:59:04.789 --> 00:59:07.630 A:middle L:90%
tells you what very close to the wall. The
1235
00:59:07.630 --> 00:59:12.460 A:middle L:90%
main flow in the X direction is less in equilibrium
1236
00:59:12.469 --> 00:59:15.750 A:middle L:90%
than above, so above the array, these proteins
1237
00:59:15.750 --> 00:59:17.539 A:middle L:90%
to become more what in equilibrium and as you go
1238
00:59:17.539 --> 00:59:22.869 A:middle L:90%
downstream, it more evident that this becomes what more
1239
00:59:22.880 --> 00:59:24.989 A:middle L:90%
of a fully developed. But if you look at
1240
00:59:24.989 --> 00:59:28.260 A:middle L:90%
the V component, if you look at the B
1241
00:59:28.260 --> 00:59:30.670 A:middle L:90%
what you make, the first thing is that above
1242
00:59:30.670 --> 00:59:32.050 A:middle L:90%
the road and you see what the paranormal is a
1243
00:59:32.050 --> 00:59:35.719 A:middle L:90%
lot higher than in the main flow. So that
1244
00:59:35.719 --> 00:59:38.820 A:middle L:90%
immediately telling you tells you what the world number component
1245
00:59:38.949 --> 00:59:42.639 A:middle L:90%
is in less equilibrium, that the extreme wise component
1246
00:59:43.309 --> 00:59:45.300 A:middle L:90%
and also you can see that this one look at
1247
00:59:45.300 --> 00:59:49.829 A:middle L:90%
this this is 0.9 to 7.5 point 85 Guess what
1248
00:59:49.829 --> 00:59:53.550 A:middle L:90%
happened. The vertical velocity becomes worse as you move
1249
00:59:53.550 --> 00:59:57.280 A:middle L:90%
down. Three. Why? Because there is a
1250
00:59:57.280 --> 01:00:00.539 A:middle L:90%
bound layer growing a boundary for a boundary to grow
1251
01:00:00.539 --> 01:00:02.030 A:middle L:90%
. What happened to the vertical velocity has to be
1252
01:00:02.030 --> 01:00:06.869 A:middle L:90%
important. The velocity has to be critical. And
1253
01:00:06.869 --> 01:00:08.469 A:middle L:90%
if you look at the rotor swept, these values
1254
01:00:08.469 --> 01:00:12.869 A:middle L:90%
are higher, so closer to the wall, closer
1255
01:00:12.869 --> 01:00:15.980 A:middle L:90%
to the world, the violence becomes seems to be
1256
01:00:15.989 --> 01:00:17.260 A:middle L:90%
more or less the same. So very close to
1257
01:00:17.260 --> 01:00:20.880 A:middle L:90%
the world. The V velocity seems to be what
1258
01:00:20.889 --> 01:00:24.079 A:middle L:90%
morning equilibrium than the U. And if you look
1259
01:00:24.079 --> 01:00:25.630 A:middle L:90%
at the rain of stresses, look at this.
1260
01:00:25.639 --> 01:00:29.090 A:middle L:90%
The reign of stress is the norm is what a
1261
01:00:29.090 --> 01:00:30.610 A:middle L:90%
lot higher than the V. A lot higher than
1262
01:00:30.610 --> 01:00:32.690 A:middle L:90%
you. So that tells you what If you go
1263
01:00:32.690 --> 01:00:37.269 A:middle L:90%
from the first two first 22 wine to the three
1264
01:00:37.269 --> 01:00:38.309 A:middle L:90%
and four. What happened to the euro? Norm
1265
01:00:38.320 --> 01:00:42.769 A:middle L:90%
gets smaller. So as you move above the array
1266
01:00:42.780 --> 01:00:45.159 A:middle L:90%
, the air norms becomes smaller in X because the
1267
01:00:45.159 --> 01:00:47.780 A:middle L:90%
flow becomes more fully developed. But the other important
1268
01:00:47.780 --> 01:00:51.480 A:middle L:90%
issue is a very close to the world. What
1269
01:00:51.480 --> 01:00:53.710 A:middle L:90%
happened to the paranormal is a lot smaller than in
1270
01:00:53.710 --> 01:00:58.659 A:middle L:90%
the mean velocity. Why the rhino stresses, even
1271
01:00:58.659 --> 01:01:00.559 A:middle L:90%
though you have very close to the world, are
1272
01:01:00.559 --> 01:01:02.340 A:middle L:90%
reducing the magnitude. But more importantly, the smaller
1273
01:01:02.340 --> 01:01:06.980 A:middle L:90%
scale seems to be what more homogeneous so that very
1274
01:01:06.980 --> 01:01:08.329 A:middle L:90%
close to the world they tend to be what,
1275
01:01:08.340 --> 01:01:12.239 A:middle L:90%
more in a fully developed than when you look at
1276
01:01:12.239 --> 01:01:15.230 A:middle L:90%
the V component or the U component. So with
1277
01:01:15.230 --> 01:01:17.019 A:middle L:90%
all of this picture, basically, we have make
1278
01:01:17.019 --> 01:01:21.590 A:middle L:90%
some assessment that clearly this boundary layer is not what
1279
01:01:21.599 --> 01:01:23.460 A:middle L:90%
fully developed Number two, that there is a boundary
1280
01:01:23.460 --> 01:01:28.320 A:middle L:90%
layer growing above theory is that we make the hypothesis
1281
01:01:28.329 --> 01:01:31.269 A:middle L:90%
and we still don't know yet. I still have
1282
01:01:31.269 --> 01:01:34.429 A:middle L:90%
not shown you What happened to the large scale?
1283
01:01:34.440 --> 01:01:36.739 A:middle L:90%
So what is the first part? The first part
1284
01:01:36.739 --> 01:01:38.150 A:middle L:90%
is that the Rennes Shear stresses is a very,
1285
01:01:38.150 --> 01:01:42.769 A:middle L:90%
very critical component. Remember that All of that energy
1286
01:01:42.769 --> 01:01:45.420 A:middle L:90%
that isn't training to the array is coming from the
1287
01:01:45.420 --> 01:01:49.059 A:middle L:90%
above array and that this is not fully developed.
1288
01:01:49.070 --> 01:01:51.219 A:middle L:90%
But we still need to find when you look at
1289
01:01:51.219 --> 01:01:53.300 A:middle L:90%
the second statistics, what happened to them? Those
1290
01:01:53.300 --> 01:01:57.119 A:middle L:90%
second statics is telling you that they have more.
1291
01:01:57.130 --> 01:02:00.010 A:middle L:90%
They need more developing region to become what fully developed
1292
01:02:00.900 --> 01:02:04.150 A:middle L:90%
. But I'm still have not answered one question to
1293
01:02:04.150 --> 01:02:07.489 A:middle L:90%
you. Remember about the land skills. So I'm
1294
01:02:07.489 --> 01:02:10.260 A:middle L:90%
gonna go briefly over that. Okay, so this
1295
01:02:10.260 --> 01:02:13.099 A:middle L:90%
is what I'm gonna do. Okay, I see
1296
01:02:13.099 --> 01:02:14.329 A:middle L:90%
that time, right? Well, do we have
1297
01:02:14.329 --> 01:02:21.219 A:middle L:90%
time? Okay, so if you look at this
1298
01:02:21.219 --> 01:02:22.239 A:middle L:90%
this line scale So what we're gonna do is to
1299
01:02:22.239 --> 01:02:23.449 A:middle L:90%
look at the p. O. D. Analysis
1300
01:02:23.449 --> 01:02:25.610 A:middle L:90%
. We're gonna do a low dimension analysis of this
1301
01:02:25.610 --> 01:02:29.269 A:middle L:90%
data, and then we're gonna try to analyze the
1302
01:02:29.360 --> 01:02:31.369 A:middle L:90%
kinetic energy question. Remember the kinetic energy question?
1303
01:02:31.380 --> 01:02:35.190 A:middle L:90%
Those the energy flux is worthy one critical for the
1304
01:02:35.190 --> 01:02:37.570 A:middle L:90%
internment of the energy and what we're gonna do there
1305
01:02:37.579 --> 01:02:39.980 A:middle L:90%
is to find a characteristic length scale from that model
1306
01:02:39.980 --> 01:02:43.940 A:middle L:90%
, the composition. And then then after that,
1307
01:02:43.949 --> 01:02:45.309 A:middle L:90%
find what is the contribution of the large scales.
1308
01:02:45.900 --> 01:02:49.920 A:middle L:90%
And I will go very quickly on this because I'm
1309
01:02:49.920 --> 01:02:51.869 A:middle L:90%
not gonna bother you with this, but this is
1310
01:02:51.869 --> 01:02:53.219 A:middle L:90%
the energy flux. Is that we can remember Dominican
1311
01:02:53.219 --> 01:02:55.869 A:middle L:90%
Eric Energy. This is the index notation. This
1312
01:02:55.869 --> 01:02:59.659 A:middle L:90%
is the terms that were very responsible for a lot
1313
01:02:59.659 --> 01:03:00.610 A:middle L:90%
of the energy and training. So what we're going
1314
01:03:00.610 --> 01:03:02.949 A:middle L:90%
to do is to use that one the mobile expansion
1315
01:03:02.949 --> 01:03:06.619 A:middle L:90%
of this term. This is the three wise component
1316
01:03:06.789 --> 01:03:07.989 A:middle L:90%
. This is a very emotional stresses. And this
1317
01:03:07.989 --> 01:03:10.510 A:middle L:90%
one r D v. Okay, so this is
1318
01:03:10.510 --> 01:03:14.239 A:middle L:90%
the second order term. We're only gonna worry about
1319
01:03:14.250 --> 01:03:17.010 A:middle L:90%
the the the energy flux is that we saw before
1320
01:03:17.019 --> 01:03:19.500 A:middle L:90%
. And what we're going to do is to do
1321
01:03:19.500 --> 01:03:22.800 A:middle L:90%
this rendered decomposition. I'm sorry. We're going to
1322
01:03:22.800 --> 01:03:23.840 A:middle L:90%
use the rest of the composition of the Rada stresses
1323
01:03:23.849 --> 01:03:27.510 A:middle L:90%
in a mobile expansion. So these are the iron
1324
01:03:27.510 --> 01:03:29.920 A:middle L:90%
functions that we could get from the data. So
1325
01:03:29.929 --> 01:03:31.670 A:middle L:90%
we will expand the range of stresses in a model
1326
01:03:31.670 --> 01:03:35.250 A:middle L:90%
expansion. Okay. And then from that, we're
1327
01:03:35.250 --> 01:03:37.550 A:middle L:90%
going to determine which are the moat that are gonna
1328
01:03:37.550 --> 01:03:39.619 A:middle L:90%
contribute to most of the energy that is entrained.
1329
01:03:40.000 --> 01:03:44.460 A:middle L:90%
And if you do this, um, this is
1330
01:03:44.460 --> 01:03:46.250 A:middle L:90%
the rain of stresses. This is only 100 times
1331
01:03:46.250 --> 01:03:49.070 A:middle L:90%
steps, and you can see that a lot of
1332
01:03:49.070 --> 01:03:52.010 A:middle L:90%
the energy in the food fields capture above the array
1333
01:03:52.699 --> 01:03:53.820 A:middle L:90%
. If you take the 1st 30 mode, you
1334
01:03:53.820 --> 01:03:57.750 A:middle L:90%
can see regions of high range of stresses. That's
1335
01:03:57.750 --> 01:03:59.550 A:middle L:90%
what you saw before. And if you look at
1336
01:03:59.550 --> 01:04:01.150 A:middle L:90%
the first mode, you can see, uh,
1337
01:04:01.159 --> 01:04:04.070 A:middle L:90%
concentration behind the second turbine. Now, the question
1338
01:04:04.070 --> 01:04:08.119 A:middle L:90%
is what are dealing skills that could contribute to a
1339
01:04:08.119 --> 01:04:10.539 A:middle L:90%
lot of the energy and what I'm going to show
1340
01:04:10.539 --> 01:04:14.010 A:middle L:90%
you. Uh, this is the key component.
1341
01:04:14.389 --> 01:04:15.170 A:middle L:90%
What? I'm we're going to show you. I'm
1342
01:04:15.170 --> 01:04:16.900 A:middle L:90%
sorry. What we're going to show you is that
1343
01:04:16.900 --> 01:04:19.449 A:middle L:90%
you can decompose all of the reign of stresses.
1344
01:04:19.460 --> 01:04:21.639 A:middle L:90%
These are all the rain of stresses in the model
1345
01:04:21.639 --> 01:04:25.489 A:middle L:90%
expansion, and you could sum all of the energy
1346
01:04:25.500 --> 01:04:27.429 A:middle L:90%
. In other words, you could represent a fraction
1347
01:04:27.429 --> 01:04:30.809 A:middle L:90%
of the energy for every mode over the entire field
1348
01:04:30.820 --> 01:04:32.070 A:middle L:90%
. And from that, you get what the fractional
1349
01:04:32.070 --> 01:04:35.980 A:middle L:90%
contribution of energy for every mode. Okay, And
1350
01:04:35.989 --> 01:04:41.269 A:middle L:90%
if you do this, what you show is following
1351
01:04:41.280 --> 01:04:42.820 A:middle L:90%
. This is a fraction of energy due to the
1352
01:04:42.820 --> 01:04:45.329 A:middle L:90%
Reno stresses that the first mode contains about 13% of
1353
01:04:45.329 --> 01:04:48.230 A:middle L:90%
the energy. And if you look at the the
1354
01:04:48.239 --> 01:04:50.710 A:middle L:90%
the DK, this DK is a rapid decay.
1355
01:04:50.719 --> 01:04:54.449 A:middle L:90%
But what you can see the first night mode contained
1356
01:04:54.449 --> 01:04:57.639 A:middle L:90%
54% of the energy. Okay, so from that
1357
01:04:57.639 --> 01:05:00.699 A:middle L:90%
perspective, this is a very, very valuable information
1358
01:05:00.710 --> 01:05:03.599 A:middle L:90%
, and you could actually use this to get what
1359
01:05:04.090 --> 01:05:08.420 A:middle L:90%
a characteristic length scale. So you could say that
1360
01:05:08.429 --> 01:05:12.079 A:middle L:90%
the highest space here we represent a characteristic landscape for
1361
01:05:12.079 --> 01:05:14.710 A:middle L:90%
mode one for more than 20. You could do
1362
01:05:14.710 --> 01:05:16.760 A:middle L:90%
the same. And this space here is what a
1363
01:05:16.760 --> 01:05:19.539 A:middle L:90%
characteristic landscape for that mode. So I can represent
1364
01:05:19.539 --> 01:05:23.750 A:middle L:90%
for every single mode what is the characteristic length scale
1365
01:05:23.760 --> 01:05:26.590 A:middle L:90%
. And from that rations of skills over the entire
1366
01:05:26.590 --> 01:05:29.340 A:middle L:90%
domain, I can have what, the variation of
1367
01:05:29.340 --> 01:05:30.530 A:middle L:90%
the energy and that's that's the end of this.
1368
01:05:30.539 --> 01:05:32.840 A:middle L:90%
Okay, and this is what you have. This
1369
01:05:32.840 --> 01:05:36.110 A:middle L:90%
is all over the the line scale over the rotor
1370
01:05:36.110 --> 01:05:39.550 A:middle L:90%
ratio, and what you see here is the first
1371
01:05:39.559 --> 01:05:42.960 A:middle L:90%
nine mode contain about 50% of the energy. And
1372
01:05:42.960 --> 01:05:45.719 A:middle L:90%
this is what we call what? Adjusting chromatic mode
1373
01:05:45.090 --> 01:05:47.090 A:middle L:90%
. This is basically the large skills of energy.
1374
01:05:47.090 --> 01:05:49.260 A:middle L:90%
In fact, the argument here is that the large
1375
01:05:49.260 --> 01:05:53.300 A:middle L:90%
skills are in homogeneous and they contain most of the
1376
01:05:53.309 --> 01:05:56.940 A:middle L:90%
energy in the entire flow. The decay here for
1377
01:05:56.940 --> 01:06:00.639 A:middle L:90%
the smaller scales dedicated for your modes. And that
1378
01:06:00.639 --> 01:06:02.139 A:middle L:90%
tells you that the smaller skills and that's the case
1379
01:06:02.139 --> 01:06:04.539 A:middle L:90%
, like one over N that the smaller skills are
1380
01:06:04.539 --> 01:06:09.420 A:middle L:90%
what homogeneous in annex. So this homogeneity, the
1381
01:06:09.420 --> 01:06:11.960 A:middle L:90%
case, have won over end, and they contribute
1382
01:06:11.960 --> 01:06:15.010 A:middle L:90%
to what? Very little portion of the energy of
1383
01:06:15.010 --> 01:06:16.119 A:middle L:90%
the entire Ray. And this is indeed the most
1384
01:06:16.119 --> 01:06:19.239 A:middle L:90%
important part of this discussion here. And this was
1385
01:06:19.239 --> 01:06:23.690 A:middle L:90%
consistent to watch uh um, Ron, Adrian Beltre
1386
01:06:23.690 --> 01:06:27.260 A:middle L:90%
show for, uh, internal flow. So with
1387
01:06:27.260 --> 01:06:28.730 A:middle L:90%
this, I would like to conclude. Guys,
1388
01:06:28.730 --> 01:06:30.539 A:middle L:90%
I'm very sorry. What we found here is the
1389
01:06:30.539 --> 01:06:32.090 A:middle L:90%
first nine modes produce the land skills about what,
1390
01:06:32.099 --> 01:06:35.519 A:middle L:90%
13 rotor diameter, and they produce 54% of the
1391
01:06:35.519 --> 01:06:41.230 A:middle L:90%
energy and we're done. Thank you. I'm sorry
1392
01:06:41.230 --> 01:06:43.329 A:middle L:90%
that if I went too fast in all of this
1393
01:06:46.780 --> 01:07:00.989 A:middle L:90%
, Okay. What? Yes, if we had
1394
01:07:01.980 --> 01:07:06.210 A:middle L:90%
servings differently. Damages. So I one roll 100
1395
01:07:06.210 --> 01:07:10.429 A:middle L:90%
m play and the other 1 50. What is
1396
01:07:10.429 --> 01:07:13.250 A:middle L:90%
the effect of that? Because getting back to the
1397
01:07:13.260 --> 01:07:15.699 A:middle L:90%
blinds induced laws that regulate problem flows if we have
1398
01:07:15.710 --> 01:07:19.369 A:middle L:90%
jets are different strengths. The entrainment Yes, yes
1399
01:07:19.369 --> 01:07:21.449 A:middle L:90%
. Example. The weaker guy will try to go
1400
01:07:21.449 --> 01:07:26.210 A:middle L:90%
and merge with the stronger guy. So yes,
1401
01:07:26.579 --> 01:07:29.489 A:middle L:90%
six of them. He had the the for example
1402
01:07:29.489 --> 01:07:31.550 A:middle L:90%
, the the we took. Not this data and
1403
01:07:31.550 --> 01:07:33.099 A:middle L:90%
other data that we took in a winter now,
1404
01:07:33.480 --> 01:07:36.050 A:middle L:90%
uh, many years ago. And we share that
1405
01:07:36.050 --> 01:07:39.420 A:middle L:90%
with the group in Syracuse, and what they show
1406
01:07:39.420 --> 01:07:42.309 A:middle L:90%
is that they did optimization design, and what they
1407
01:07:42.309 --> 01:07:45.130 A:middle L:90%
were able to show is that by doing exactly taking
1408
01:07:45.130 --> 01:07:47.610 A:middle L:90%
care of the different jets are placed that you could
1409
01:07:47.610 --> 01:07:50.019 A:middle L:90%
, actually, if you the idea is that if
1410
01:07:50.019 --> 01:07:54.170 A:middle L:90%
you have different altitude, different rotor diameters, different
1411
01:07:54.170 --> 01:07:56.599 A:middle L:90%
hope, high and different locations, that is the
1412
01:07:56.599 --> 01:07:59.199 A:middle L:90%
best way to do it from the perspective of the
1413
01:07:59.199 --> 01:08:02.230 A:middle L:90%
power generation. But perhaps it's not economically survival right
1414
01:08:02.230 --> 01:08:05.079 A:middle L:90%
, because it would have to deploy different grid line
1415
01:08:05.090 --> 01:08:08.989 A:middle L:90%
, location and the construction. So in many cases
1416
01:08:09.000 --> 01:08:11.539 A:middle L:90%
, that may not be the most viable from the
1417
01:08:11.539 --> 01:08:15.260 A:middle L:90%
economic standpoint, but it is indeed the best way
1418
01:08:15.269 --> 01:08:16.229 A:middle L:90%
. I mean, you would for no, there's
1419
01:08:16.229 --> 01:08:20.140 A:middle L:90%
no There's no doubt that they would produce about 10%
1420
01:08:20.140 --> 01:08:24.560 A:middle L:90%
more, uh, performance capacity, factor in the
1421
01:08:24.560 --> 01:08:28.550 A:middle L:90%
performance. Really interested in knowing the work that we
1422
01:08:28.560 --> 01:08:30.840 A:middle L:90%
do here? Or does that come work that has
1423
01:08:30.850 --> 01:08:35.529 A:middle L:90%
been done in classical jet floor? Yeah. Yeah
1424
01:08:35.539 --> 01:08:38.239 A:middle L:90%
. I haven't looked at that from that perspective.
1425
01:08:38.239 --> 01:08:40.140 A:middle L:90%
To be honest with you, I have not think
1426
01:08:40.140 --> 01:08:43.689 A:middle L:90%
about the looking at the jet studies. And,
1427
01:08:44.270 --> 01:08:45.939 A:middle L:90%
yes, build a model. Yes. And you're
1428
01:08:45.939 --> 01:08:48.220 A:middle L:90%
correct. And that's probably actually from this. You
1429
01:08:48.220 --> 01:08:50.699 A:middle L:90%
can see that you saw it, right? A
1430
01:08:50.699 --> 01:08:54.590 A:middle L:90%
lot of the growth of the entrainment comes from across
1431
01:08:54.590 --> 01:08:58.390 A:middle L:90%
the radius, right? And, for example,
1432
01:08:58.869 --> 01:09:00.590 A:middle L:90%
to just me, what is the pressure that was
1433
01:09:01.170 --> 01:09:04.750 A:middle L:90%
, and how does that mean? And and actually
1434
01:09:04.750 --> 01:09:06.850 A:middle L:90%
, it shouldn't be that bad. Because if we
1435
01:09:06.850 --> 01:09:10.699 A:middle L:90%
borrow a lot of that knowledge and and look at
1436
01:09:10.699 --> 01:09:13.859 A:middle L:90%
the V component because I mean, I'm sure it
1437
01:09:13.859 --> 01:09:15.770 A:middle L:90%
will be quite easy to show in the vertical direction
1438
01:09:15.770 --> 01:09:20.770 A:middle L:90%
that yes, yes, models exist. Interesting to
1439
01:09:20.770 --> 01:09:25.250 A:middle L:90%
compare. Never have somebody tell me about the jet
1440
01:09:25.260 --> 01:09:27.439 A:middle L:90%
comparison. Actually never thought about it, to be
1441
01:09:27.439 --> 01:09:29.329 A:middle L:90%
honest with you, but it's a very good point
1442
01:09:29.340 --> 01:09:30.939 A:middle L:90%
. Very good. Yes, We had a second
1443
01:09:30.939 --> 01:09:36.989 A:middle L:90%
question. Yes, yes. Why? It could
1444
01:09:38.000 --> 01:09:40.779 A:middle L:90%
be nice, but I'm not familiar. Oh,
1445
01:09:41.270 --> 01:09:43.260 A:middle L:90%
why is it that they are always placed in a
1446
01:09:43.270 --> 01:09:45.189 A:middle L:90%
regular, you know, really, like, especially
1447
01:09:45.569 --> 01:09:48.779 A:middle L:90%
? Why can't we just explore more random arrangement?
1448
01:09:49.369 --> 01:09:56.369 A:middle L:90%
See if that the second question is I'm not sure
1449
01:09:56.369 --> 01:10:00.619 A:middle L:90%
if they take into consideration in dynamic orientation of the
1450
01:10:00.619 --> 01:10:09.829 A:middle L:90%
rotor blades and things like what? Um, yeah
1451
01:10:09.840 --> 01:10:14.159 A:middle L:90%
, so the okay. The first question the example
1452
01:10:14.159 --> 01:10:16.020 A:middle L:90%
that I show you here are the exception. Actually
1453
01:10:16.020 --> 01:10:17.449 A:middle L:90%
, if you go to any wind farm, if
1454
01:10:17.449 --> 01:10:19.560 A:middle L:90%
you I wish you could do that sometime, fly
1455
01:10:19.560 --> 01:10:24.930 A:middle L:90%
to Dallas and drive from Dallas to Lubbock is the
1456
01:10:24.939 --> 01:10:28.109 A:middle L:90%
most fascinating trade. And and the reason is because
1457
01:10:28.109 --> 01:10:30.890 A:middle L:90%
what you get is an ocean of turbines. Everywhere
1458
01:10:30.899 --> 01:10:32.520 A:middle L:90%
is an ocean literally notion. And if you if
1459
01:10:32.520 --> 01:10:33.939 A:middle L:90%
you look at them, actually, if you look
1460
01:10:33.939 --> 01:10:36.880 A:middle L:90%
very carefully, they're not placed like this. Actually
1461
01:10:38.260 --> 01:10:40.909 A:middle L:90%
, the best scientific way to have done this correctly
1462
01:10:40.909 --> 01:10:44.699 A:middle L:90%
is to use proper optimization designed to place them.
1463
01:10:44.710 --> 01:10:45.949 A:middle L:90%
Many of them are placed randomly. Many of them
1464
01:10:45.949 --> 01:10:48.659 A:middle L:90%
are placed simply because of the I mean you have
1465
01:10:48.659 --> 01:10:53.329 A:middle L:90%
a 57 diameters rotor distance. That's standard, but
1466
01:10:53.329 --> 01:10:56.000 A:middle L:90%
they're placed in the way of degree more than anything
1467
01:10:56.000 --> 01:11:00.609 A:middle L:90%
else. Okay, the so there's not reason behind
1468
01:11:00.619 --> 01:11:01.770 A:middle L:90%
. This one is because it's offshore, and sometimes
1469
01:11:01.770 --> 01:11:04.789 A:middle L:90%
you see them in a line in Denmark. But
1470
01:11:04.800 --> 01:11:06.399 A:middle L:90%
when you look at them in United States are not
1471
01:11:06.399 --> 01:11:09.289 A:middle L:90%
necessarily like this, and most of them are not
1472
01:11:09.659 --> 01:11:13.310 A:middle L:90%
, Um so the second question was the effects of
1473
01:11:13.310 --> 01:11:17.750 A:middle L:90%
what? The dynamics control. Yeah, so right
1474
01:11:17.750 --> 01:11:23.090 A:middle L:90%
now the turbines have those controls embedded where and and
1475
01:11:23.100 --> 01:11:25.270 A:middle L:90%
they're working. Okay, What? The future is
1476
01:11:25.270 --> 01:11:26.710 A:middle L:90%
moving. I don't know if you're in control.
1477
01:11:26.720 --> 01:11:30.369 A:middle L:90%
What the future is isn't predicting what the velocity is
1478
01:11:30.369 --> 01:11:32.079 A:middle L:90%
going to be 23 minutes for now and then do
1479
01:11:32.079 --> 01:11:35.090 A:middle L:90%
all the control strategies not only in the in this
1480
01:11:35.090 --> 01:11:39.279 A:middle L:90%
direction but also in in inside of the air force
1481
01:11:39.279 --> 01:11:41.569 A:middle L:90%
themselves, similar to what we have in the airplanes
1482
01:11:41.579 --> 01:11:44.180 A:middle L:90%
with flaps and everything. This is if it's predicting
1483
01:11:44.180 --> 01:11:45.800 A:middle L:90%
what the flow will be 23 minutes and do the
1484
01:11:45.800 --> 01:11:49.029 A:middle L:90%
controls that that's because at that time it's not.
1485
01:11:49.039 --> 01:11:51.340 A:middle L:90%
It's not late, right? And the question right
1486
01:11:51.340 --> 01:11:54.579 A:middle L:90%
when you are reacting to what happened right now is
1487
01:11:54.590 --> 01:11:56.609 A:middle L:90%
is a bit late and and that's what it is
1488
01:11:56.609 --> 01:11:59.800 A:middle L:90%
. But more than that is can you develop contract
1489
01:11:59.800 --> 01:12:02.069 A:middle L:90%
strategies like where you're discussing not just for one turbine
1490
01:12:02.079 --> 01:12:04.170 A:middle L:90%
, but will be optimal for the entire A.
1491
01:12:04.750 --> 01:12:06.710 A:middle L:90%
So when you're looking at the end, you're asking
1492
01:12:06.710 --> 01:12:10.579 A:middle L:90%
me about the location. For example, when we
1493
01:12:10.579 --> 01:12:13.199 A:middle L:90%
show the the importance of the reign of stresses that
1494
01:12:13.199 --> 01:12:15.939 A:middle L:90%
tells you Look, I can change the the the
1495
01:12:15.939 --> 01:12:17.850 A:middle L:90%
geometry To maximize this, I can also, from
1496
01:12:17.850 --> 01:12:19.880 A:middle L:90%
the growth of the boundary layer away from the first
1497
01:12:19.880 --> 01:12:24.590 A:middle L:90%
few turbines, I can gradually change the altitude or
1498
01:12:24.590 --> 01:12:28.380 A:middle L:90%
change the rotor such that I'm always attracted more energy
1499
01:12:28.449 --> 01:12:30.979 A:middle L:90%
from the floor above. So So there are many
1500
01:12:30.979 --> 01:12:32.489 A:middle L:90%
parameters. Actually, this is a very complex brand
1501
01:12:32.489 --> 01:12:34.609 A:middle L:90%
. This is why we like the winter because you
1502
01:12:34.609 --> 01:12:38.609 A:middle L:90%
have less variability than what you would normally we have
1503
01:12:38.609 --> 01:12:41.260 A:middle L:90%
in the field. And I didn't even talk about
1504
01:12:41.270 --> 01:12:43.539 A:middle L:90%
. And you're working on that with this certification.
1505
01:12:43.550 --> 01:12:45.550 A:middle L:90%
Eric graduate, you have the simulations with the stratification
1506
01:12:45.560 --> 01:12:47.930 A:middle L:90%
and the effects on the wig. So So this
1507
01:12:47.930 --> 01:12:50.670 A:middle L:90%
is something I didn't even touch it. Thanks.
1508
01:12:55.649 --> 01:12:58.310 A:middle L:90%
Long time ago. You know Robert Taylor have a
1509
01:12:58.319 --> 01:13:00.220 A:middle L:90%
junior at Cornell. He was looking at the effect
1510
01:13:00.220 --> 01:13:04.300 A:middle L:90%
of turbulence on the corn. The growth of one
1511
01:13:04.319 --> 01:13:06.239 A:middle L:90%
. Suppose you had the corn? I'm in the
1512
01:13:06.250 --> 01:13:10.449 A:middle L:90%
Midwest, You know, fields of suppose you place
1513
01:13:10.449 --> 01:13:13.449 A:middle L:90%
these wind tunnels there. What is the effect of
1514
01:13:13.460 --> 01:13:16.380 A:middle L:90%
this draft on the growth of corn? Oh,
1515
01:13:18.449 --> 01:13:23.149 A:middle L:90%
mhm. You're a tough guy. Um, actually
1516
01:13:23.159 --> 01:13:24.970 A:middle L:90%
, actually, and I had to be honest with
1517
01:13:24.970 --> 01:13:29.170 A:middle L:90%
you, we were discussing a proposal to see because
1518
01:13:29.180 --> 01:13:30.979 A:middle L:90%
again, you have this This jet, these waves
1519
01:13:30.979 --> 01:13:35.319 A:middle L:90%
propagate several kilometers downstream. And we were discussing about
1520
01:13:35.319 --> 01:13:40.010 A:middle L:90%
a proposal to see the agricultural impact, the micro
1521
01:13:40.010 --> 01:13:43.380 A:middle L:90%
climate and and those expressions. But But that will
1522
01:13:43.380 --> 01:13:45.050 A:middle L:90%
definitely change the micro climate. I know for sure
1523
01:13:45.060 --> 01:13:47.300 A:middle L:90%
, but we don't know exactly what are the benefit
1524
01:13:47.310 --> 01:13:58.210 A:middle L:90%
? Uh, 1990 changes here. Ricardo, you
1525
01:13:58.210 --> 01:14:02.579 A:middle L:90%
had another. Quick, You had a question there
1526
01:14:04.850 --> 01:14:10.079 A:middle L:90%
. Let's thank Oh, thank you. Mhm.
1527
01:14:12.449 --> A:middle L:90%
I