July 15, 2025
210 - Fire Fundamentals pt. 16 - Turbulence with Randy McDermott
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In the 16th part of the Fire Fundamentals series, we invite Randy McDermott from NIST to join us for a deep dive into turbulence and its critical role in fire dynamics modelling. We explore the physics behind turbulent combustion and how it fundamentally shapes fire behaviour, plume dynamics, and simulation accuracy.
In this episode we cover:
- Defining turbulence as the enhancement of mixing and heat transfer through the creation of eddies and instabilities
- Understanding length scales in turbulence from the integral scale to the Kolmogorov scale
- Practical considerations when choosing grid resolutions for different fire engineering applications
- How turbulence models work in Large Eddy Simulation (LES) and what they represent
- Limitations of the D* criterion for mesh sizing and why higher resolution may be needed
- Differences between pre-mixed and diffusion flames in turbulent combustion
- Time scales in fire and the concept of Damköhler number in determining combustion behaviour
- Entrainment physics at the base of fire plumes requires centimetre-scale resolution
- Why turbulence modelling ultimately determines the accuracy of fire simulations
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The Fire Science Show is produced by the Fire Science Media in collaboration with OFR Consultants. Thank you to the podcast sponsor for their continuous support towards our mission.
00:00 - Introduction to Fire Fundamentals
02:40 - Defining Turbulence in Fire Science
09:39 - Modeling Turbulence with DNS and LES
17:45 - Length Scales and D-Star Criterion
23:45 - Turbulent Combustion Fundamentals
32:40 - Time Scales in Fire Dynamics
39:20 - Entrainment and Plume Dynamics
48:50 - Practical Applications and Resolution Requirements
55:15 - Episode Wrap-up and Key Takeaways
WEBVTT
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Hello everybody, welcome to the Fire Science Show.
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For a long time I've promised you another episode of Fire Fundamentals and here we are with another episode in this series, though it's probably not just fundamentals that we're gonna cover.
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We're actually jumping into some quite advanced concepts.
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I hope that doesn't scare you off too early.
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I can just say it's fun and useful.
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So in this episode I have invited Randy McDermott from NIST again.
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You may remember, a few episodes ago we've talked with Randy about FDS development.
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Randy is a member of the NIST team that develops FDS and I promised Randy that we're going to talk about something more comfortable to him, which is turbulent combustion, apparently.
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So in this Fire Fundamentals we are covering the turbulence, and that's a really really tough topic to cover, because turbulence is even difficult to define it really.
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It simply is the thing that characterizes flow that if you get it wrong, the entire image of your flow is wrong.
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And in this episode we try to cut it into smaller pieces and digest on how modeling turbulence, how different phenomena in the flow change the fire behavior, change the combustion, change the products generation, change the entrainment all the phenomena that are necessary to really grasp the image of the fire itself.
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It's critical to fire modeling.
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We're also tackling some practical concepts.
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So you perhaps heard about a DSTAR criterion that people use to choose their mesh sizes for FTS simulations.
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In this episode we will go fairly deep into mesh resolutions and timescales, so you will hear a lot about that.
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We will discuss what it takes to model entrainment really well, model fire plumes really well and what you can really expect from your modeling.
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So, uh, yeah it's, it's a tough one, but I promise you it's worth it.
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I love randy, I love talking with Randy.
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We're both geeks, we both love fire science and I think you will simply enjoy this along with us.
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And a little warning on my end I battled terrible technical issues in this episode and barely recovered my part of the audio file, so it's a little worse quality than usual, but fortunately I'm not talking that much in this episode.
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It's mostly Randy and his part is awesome in the audio quality and in the technical content presented.
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So let's not prolong this anymore.
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Let's spin the intro and jump into the episode.
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Welcome to the Fire Science Show.
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My name is Wojciech Wigrzyński and I will be your host.
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The Firesize Show is into its third year of continued support from its sponsor, ofar Consultants, who are an independent, multi-award winning fire engineering consultancy with a reputation for delivering innovative safety-driven solutions.
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com.
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And now back to the episode.
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Hello everybody.
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I am joined today once again by Randy McDermott from NIST.
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Hey, randy, good to have you back.
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Hey, wojciech, good to see you.
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And the last time we spoke about FDS development, I appreciate that talk again because I've really listened to it and again I've learned something new about FDS.
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And in the talk you were not happy because I was asking you questions and questions outside of your scope of work, and you said you want something that you feel more comfortable with and that's turbulent combustion.
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Like, come on, man, really turbulent combustion.
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But that's cool.
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That's cool.
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You already gave me the background last time.
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I'm not going to get any better.
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You're not going to get any better answers out of me, though I know.
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Yeah, yeah, that's cool, that's cool.
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You gave me the intro where you came from and why actually turbulent combustion, and you makes a lot of sense how you became a fire scientist.
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So let's try to tackle the topic with the idea of bringing some fellow fire engineers up on speed on turbulent combustion.
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Why do we even care about that in fires?
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So perhaps before we go into combustion, let let's talk turbulence briefly and then we'll probably move into turbulent combustion.
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So if you had to define turbulence, how would you define to?
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I mean such a hard concept to define to me?
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yeah, yeah, I'm sure I'm gonna nail this better than you know all the other thousands of people who've tried before me I mean I think when, especially when we talk, you know, when we're talking fire and fluid mechanics, the key with turbulence, right, is it.
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It enhances.
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It enhances things, whether it's mixing, whether it's heat transfer, you know it's turbulence, steepens gradients and and therefore destabilizes flows.
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Therefore, you have, you know, these nice, pretty whorls and eddies and and also buoyant plumes and and whenever you have the, the, as you, as we were saying that the mixing of these different things which, in fire, of course, fuel and air are the things that that are, that are mixing, coming together so that enables the chemical reactions, it enables them to happen faster, usually, and yeah, so so enhanced fluxes, you know, which means heat transfer to surfaces, right, you've got these steeper gradients at near, near boundaries.
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It changes the nature of radiation because you know, you've got, you know, these very high temperatures, temperatures and species compositions and so on that are correlated with the higher temperatures and turbulence, and health is involved in sort of sculpting all of that and giving us the picture of a fire that we're used to seeing.
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So I mean, in a nutshell, that's kind of it, right, when you get back to, I mean when you go back to the fluid mechanics you know, we were talking in the prep here about.
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Obviously I have to define some things like okay, when you have high inertial forces and low viscosity, then you're probably going to get turbulence.
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Yeah, let's maybe try from stepping up from a simple laminar flow.
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So, when there are no forces that cause turbulence, I guess, or the forces are not strong enough, the particles of fluid, you can, I guess, stream, simplify it, or scientists like to call them streamlines also.
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Yeah, those streamlines are like parallel.
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They're not interacting with each other.
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Everyone is flowing and everything is flowing in one single direction, and it's just, you know, a nice flow.
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Nothing's interacting with each other, it's just, you know, a nice flow.
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Nothing's interacting with each other, it's just flowing.
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And eventually the amount of things in there is too big for this flow to go like this right, when the inertial forces get higher, then you know the viscous forces don't don't win.
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And you know, when you think in in terms of like I'm a modeler, right, I think, in terms of equations, in the, the navier-st equations, which are what govern the fluid mechanics, a term that is the inertial term, or the, you know, the advection term in the Navier-Stokes equations, and then you have a viscous term.
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The viscous stresses and the relative size of those terms is what determines, you know, whether the flow is going to become turbulent, the sort of initial term, the term is a nonlinear term, right, so there's a velocity squared in that term, whereas the viscous term is a linear term.
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And so you can, from a mathematical point of view or a modeling point of view, you know that these nonlinear terms can lead all kinds of more interesting solutions to the equations.
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From a physical point of view, it means that those terms start to dominate and that, basically, the you know the flow sort of trips on itself, right, it can't, it can't stabilize itself.
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Is the way that I used to think of it when I was trying to learn these things.
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I mean the you look at flow over a backward facing step, right, I mean, if the flow is viscous enough, if it is, you know, you know, really cold maple syrup then flow can just go around, even a very sharp expansion, and stay laminar, and that's because of such high viscosity, right.
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And then if you have, you know, flow with very low viscosity, then it kind of, as it's going over that, it like trips over itself and it has to catch itself and it just starts tumbling.
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My real life example of turbulence that I think some people can relate, if you look at this phenomenon from this perspective, is I was once driving on a highway, you know, and everyone was driving because there was a speed limit and there was like this annoying system where they measure you know the time when you entered the section, the time when you exit the section.
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They calculate your average velocity and ticket you based on average.
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So everyone is literally perfectly on the speed limit, Everyone's the same.
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You might as well be on a train right?
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Yeah, it's like you are.
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Every vehicle is moving with the same velocity next to each other in one unison.
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And then there's a big intersection later on and a lot of vehicles start entering the traffic from the side.
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And then there's a lot of vehicles try to cross three or four lanes of road to reach another exit, you know, and everyone starts moving around me like I'm driving in the straight line, I'm trying to keep my lane, and there's people driving from the right, from the left around me, you know, and this madness continues for two, three kilometers and eventually they spread out and they again form one unison in which every vehicle moves the same.
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And to me that was a transition from a laminar flow in a highway into a turbulent intersection where a lot of turbulence was caused by those vehicles from the sides, and then it laminarized again and we were flowing.
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So I guess something like that happens in the flow.
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I'm not sure if that's an accurate description, but it felt like it.
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I mean the traffic flow equations are actually, you know, interesting numerical equations to solve and a lot of the there are even similar numerical methods that get used to solve the traffic flow, traffic density equations that we use in fluid mechanics.
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I mean a lot of the same like flux limiting schemes and all that kind of stuff get used.
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The interesting thing about you know, what you're pointing out is, if this is something that I I want to try to get a little bit into the details of the physics, right, like what in the fluid?
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Like what is that?
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What is it that's actually turbulent, right, and it's the fluid elements.
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Are really these collection of molecules, right, and so you know, when the molecules themselves are really bouncing around in all kinds of random motions, right, that's more of viscosity kind of a of a thing.
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Right, when you've got things really going all kinds of like random directions on the molecular level, these things are moving quite fast, you know 100 meters per second, but in all kinds of different directions, and these, you know those, that kind of adds to the viscosity of the flow, right, I mean one of the things that's a little bit weird about like a gas, right, versus a liquid, is that a gas, as you increase the temperature, the viscosity goes up, okay, whereas a liquid, that's not the case.
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Right, as we heat liquids, right, their viscosity goes down and things will become more turbulent.
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But like actually, you know, in fire one of the things that happens is, like, as you know, in the, the hotter the gas, the more viscous it gets, and that tends to some degree suppress the turbulence.
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What from the perspective of a flow, fluid flow?
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I guess we're fire engineers, so we're discussing things like air smoke, which is mostly the same thing, just with a little bit of flavor of soot and some species in it.
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But anyway, let's talk about movement of air.
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What does it mean that one flow is more turbulent than another flow, like how those two flows would be different if you had to investigate that.
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What changes in the flow when it's more turbulent?
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yeah, I mean the one of the things that people usually talk about is like the breadth of length scales that are present in the flow right, and so in a laminar flow you can usually think of like one dominant length scale.
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In a turbulent flow you usually have, you know, sort of what we call the integral length scale.
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So this is like some length scale in in fire, you know could be the base of the fire plume.
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Um, it could be the height of the fire plume but this is arbitrary or this is a physical thing this is a physical thing.
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Usually, it's usually connected to a physical thing, right?
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I mean the, the diameter of a pool fire or something like this is, is some is a length scale.
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That's that's relevant to the problem.
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You know, know the height of a doorway opening, the size of a window opening?
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I mean these things control to some degree the large-scale fluid motions in either a compartment or if it's an outdoor flow.
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You know you've got boundary layer heights, or even you know outdoor flows in the WUI, wild and urban interface.
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Houses and things like this are these roughness elements that basically lead to link scales that have to be dealt with and they create turbulence and so on.
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These are these larger scale link scales that are one end of the spectrum, as we say in turbulence.
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So it kind of gives you the size of the largest eddies in the turbulence, sort of the size of the largest eddies in the turbulence.
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Those usually correspond to some other physical link scale in the problem, right.
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And what about the smallest ones In the pipe?
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It's the diameter of the pipe, right, and so on.
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So you've got that length scale right, which is the fancy way to say that in turbulence is the integral length scale.
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And then of course, we have what we call.
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There are two small length scales in turbulence that we have to worry about.
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One is what we call the Kamalgarov length scale, kamalgaroff length scale.
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So, uh, andre Nikolai Nikolai Kamalgaroff, uh, his theories are still, you know, the sort of the dominant theories in in turbulence and and his, the length scale named after him, is the smallest length in fluid motion in the in the turbulent flow Right and around that length scale is.
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So in between these, you know the, the sort of the integral scale and the Kamalgaroff scale, there's what's what's interesting about turbulence is there aren't just these two scales.
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It's not like you just see eddies that are the size of the pipe and then you just see you know the smallest eddy in the flow which is less than a millimeter, or something like this.
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You see a spectrum, like a continuous spectrum of these of these length scales, and that has consequences for how we end up modeling these, uh, these, these flows, yeah, so I'll try to try to leave it at that.
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The full amount of scale is like nanometers, like really tiny, right.
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It's like more like, probably more like a millimeter, millimeter, okay, yeah, or less you know, less you know somewhere in that, in that, in that ballpark, the you know, the flame in a fire.
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The other, another link scale that we have to worry about, right, is flame thickness.
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Flame thickness is usually like, smaller than the komal garof scale, okay, or it can be, and, and so you know, if we were just talking like scalar mixing, there, there's another scale called the Batchelor scale, which is sort of the you know, the smallest link scale in terms of scalar mixing, and if you have a Schmidt number of one, then Batchelor and Kolongorov are the same and so on.
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So, right, schmidt number being the ratio of the scalar diffusivity to the kinematic viscosity.
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Anyway, so there are all these names of these small link scales, right, you know taylor micro scales, and and and so on, and they all start to get into they're they're all aimed at sort of trying under, trying to understand the physics, uh, of the scales at which these sort of small scale phenomena are happening, uh, in reacting flows, um, and Nixon, and mixing and scalar mixing, which scalar mixing is a problem not unique to fire, and and and combustion, right, I mean, uh, scalar mixing in the ocean, atmospheric astrophysics, um, all kinds of things, uh, scalar mixing is involved.
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So we inherit a lot of great research that has gone into that field.
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And how does?
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Because I know modeling is very dear to your heart and most of the things that you look at you also look from a modeler's perspective.
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So let's, let's even start with how do we model turbulence, because they mentioned.
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Let's even start with how do we model turbulence, because you mentioned Navier-Stokes equations and that's basically the basis of CFD modeling, but then again, we're not modeling all of the turbulence because they simply are too small.
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So how do we?
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So this sort of gets back to your original question of how do you define turbulence.
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So from my point of view as a modeler, I worry about turbulence when, or I have to worry about turbulence for whenever.
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I need a turbulence model, right, if I'm just doing direct numerical simulation, I mean you can say I'm modeling turbulence, but as a as a numerical analyst, those are, it's somewhat easier.
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Um, because I don't, I don't have a subgrid model to deal with.
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I have other problems, right, you have computational costs and and and all kinds of things to to deal with.
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But from that point of view, you know there the sort of cell Reynolds number, the link scale associated with a computational cell, is so small that the Reynolds number for that cell is small enough that that cell looks, for all practical purposes, as if it's laminar.
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The viscous forces in that cell are at least at the same order of the the inertial forces, and so how do we achieve that?
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you have to make yourself small enough.
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Or is there any other trick to that right?
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I mean there are in numerical methods.
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There are two types of adaptivity we call.
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We call them.
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One's called p adaptivity and the other is called h adaptivity.
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And then the p adaptivity.
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The p is, a is a fancy designation related to the order of the numerical method that you're using.
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So so in some cases you can increase the order of your numerical method and get closer and closer to the real solution, and we call that P-adaptivity.
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And then H-adaptivity is where you're just making your cells smaller and smaller, trying to reduce the error in your numerical solution.
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In FHIR, as most of us practice, since we're all using second order codes, h-adaptivity and H-refinement is pretty much all we ever mess with.
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But there are reasons for doing P-adaptivity, especially if you're trying to make your models more like, if you're trying to do forecasting versus engineering level modeling.
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And maybe we could talk about that for just a quick second.
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Because, like there's there's an interesting thing when you're trying to model turbulence right at some level, especially when we're modeling fires, we don't really try to forecast a a real as at any specific realization of a fire.
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Like we have just an intuitive understanding that there's no possible way that the numerical solution that we're going to get is one-to-one, exactly a realization that we see in the in the real world, right?
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Um, but there are some modeling problems.
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When you're trying to forecast the track of a hurricane, for example, like where you really want to, actually you know whether this thing steers right or steers left.
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You've got to get that right and that's a forecasting problem, right?
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So there's a difference between sort of modeling turbulence.
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For the sake of you know, getting mean statistics of the engineering problem Correct, okay, I want to get the mean flame height Correct, I want to get the mean heat transfer from the flame Correct, and so on versus, I have to predict the rate of spread of this fire from this compartment to this compartment to this compartment, and so on, right to this compartment to this compartment, and so on, right.
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So there's one realization where this happens and those can be very different types of modeling approaches that you might use, because you know turbulence is chaotic and it can go in all kinds of different directions when you're trying to just model the means and get the mean answers, then these low order models tend to work well because you can, you can get good resolution on them, um, and the statistics end up being being pretty good.
00:21:54.023 --> 00:22:10.178
When you're trying to like forecast something, this kind of gets back to the things that we were talking about in the last episode, where there are these nonlinear feedbacks that happen at the surface with pyrolysis and and so on, and that becomes a very much more difficult problem.
00:22:10.178 --> 00:22:18.788
But that's where you might want higher order methods, um, to try and try and handle those things and reduce those, those errors that you can't tolerate.
00:22:19.229 --> 00:22:26.211
It's also like the discussion between, from a practical simulation perspective, between the realism and the truth.
00:22:26.211 --> 00:22:44.006
You know, if you simulate a fire, it may look very realistic and the way, for example, how FDS solves turbulence with larger dissimulation, it creates those beautiful fires with those big worlds, I mean they look realistic.
00:22:44.006 --> 00:22:55.387
But it's not a prediction of how exactly a fire will be in this particular space, in this particular set of phenomenon, in terms of the exact flows, because it's just an approximation.
00:22:55.387 --> 00:23:00.319
It's a model statistics, not a real prediction.
00:23:00.319 --> 00:23:13.359
I mean, I get annoyed because you know, the more and more we get into the competitive market on fire modeling as engineers, the more kinds of snake hole vendors you have to battle.
00:23:13.359 --> 00:23:19.326
Oh yeah, I can simulate how exactly the fire will you know behave in this compartment.
00:23:19.326 --> 00:23:20.894
I will give you like a prediction.
00:23:20.894 --> 00:23:21.900
And how will you do it?
00:23:21.900 --> 00:23:24.000
Oh, yeah, I'll put a burner in that BS.
00:23:24.000 --> 00:23:25.813
Well, that like yeah, it's that a burner in that BS.
00:23:25.813 --> 00:23:32.268
Well, that's like yeah, that's not exactly what you're claiming you're going to do, but let's maybe not deviate too much.
00:23:32.861 --> 00:23:36.347
So you told me that the audience follows and we promised them turbulence, combustion.
00:23:36.347 --> 00:23:39.288
I'm not sure if we can keep the combustion part, seeing the time.
00:23:39.288 --> 00:23:41.407
But let's talk more turbulence.
00:23:41.407 --> 00:23:55.932
So I guess DNS, the direct numerical solution to those turbulence problems, is something available to you and perhaps not that many people around the world who have the abilities, resources and knowledge necessary for that.
00:23:55.932 --> 00:23:58.448
Engineers have to use turbulence models.
00:23:58.448 --> 00:24:00.786
So what exactly are you modeling when you're using a turbulence model?
00:24:00.786 --> 00:24:04.037
What exactly are you modeling when you're using a turbulence?
00:24:04.076 --> 00:24:04.859
model Right.
00:24:04.859 --> 00:24:07.424
Well, what we're exactly modeling is?
00:24:07.424 --> 00:24:13.906
I mentioned these nonlinear terms in the Navier-Stokes equations and those are unclosed terms.
00:24:14.028 --> 00:24:29.605
Okay, because you have the primitive variables that we solve for on the grid, the values that we store are single components of velocity, and then you have to multiply those together right in the nonlinear term.
00:24:29.605 --> 00:24:48.707
But you need, in the world of large-eddy simulation, we say you need a filtered value of this unclosed, this nonlinear term, and people will remember from their school that, you know, the square of the mean is not the mean of the square, the square, okay, and so those two things are not the same.
00:24:48.707 --> 00:24:56.461
There's a discrepancy and you have to account for that discrepancy and if you don't, you will just get things wildly wrong.
00:24:56.461 --> 00:25:23.220
And so these, what happens is, mathematically, there's this term that we put on the you know the other side of the equation, and we say, hey, this, we need to somehow model this, this difference, this residual term that is going to account for the added or subtracted fluxes that that aren't quite right from just, you know, multiplying these resolved values of velocity.
00:25:23.220 --> 00:25:36.923
Or, in the case of scalar transport, um, scalar transport meaning, like the species compositions and so on, um, you know, then there's a species composition times, a velocity, that's a, that's a non-linear, unclosed term that has to be modeled.
00:25:36.923 --> 00:25:48.296
So those are the terms that show up, the so-called subgrid terms, in the equations that we then have to write models for and then implement these.
00:25:49.037 --> 00:25:55.535
Of course there's another, in fire, and this gets us into the turbulent combustion regime.
00:25:55.535 --> 00:26:02.215
There's also what we call the mean chemical source term on the right-hand side, which is a nonlinear term.
00:26:02.215 --> 00:26:21.296
So if you're doing arenous kinetics with any sort of, even a simple chemical mechanism, even a one-step chemical mechanism, it will be a function of the local composition, which includes temperature, and so the, the temperatures and species are not resolved.
00:26:21.296 --> 00:26:32.384
And so you're, if you just use mean values or cell average values, uh, for the temperature and the species, you will not, uh, get that term correct.
00:26:32.384 --> 00:26:35.076
And of course, in fire, that's everything.
00:26:35.076 --> 00:26:36.059
You have to get the heat.
00:26:36.059 --> 00:26:39.377
Really, I mean that, or at least it's not everything, but it's at least the first thing, right?
00:26:39.377 --> 00:26:49.803
If you don't get the, the heat release rate, correct in a fire, um, then nothing else follows, and then we can go back to circle, back to the beginning of the podcast.
00:26:49.803 --> 00:26:51.028
We were talking about what is turbulence.
00:26:51.028 --> 00:26:57.182
Well, the source of most turbulence in fire is that heat release rate term, because it's what generates the buoyancy and so on.
00:26:59.433 --> 00:27:05.324
But I'll try to play the difficult role of translator into more simple terms.
00:27:05.324 --> 00:27:31.459
So in LES and let's narrow this podcast episode to larger dissimulation, because that's the default thing most of our engineers would work with I understand that you basically resolve all the large vortices with Navier-Stokes equation because you solve them, and then there is some smaller discrepancy with residuals, as you call them, that you would have to include in the overall image.
00:27:31.459 --> 00:27:36.698
Otherwise your results are not correct or further away from the truth.
00:27:36.698 --> 00:27:39.660
What would happen if you just ignored those results?
00:27:41.314 --> 00:27:47.179
Well, your mixing would be slower, right, so you would have this stretched flame.
00:27:47.179 --> 00:27:50.098
It wouldn't look anything like a real fire.
00:27:51.972 --> 00:28:00.809
So basically, those discrepancies also happen at length scales that are important for some of the phenomena that we are encountering in the fire, like combustion.
00:28:01.752 --> 00:28:02.556
So it would run like.
00:28:02.556 --> 00:28:11.035
I mean, you could try it in FDS, right, you could, and FDS being the fire dynamic simulator, so it's a code you could put in a you know whatever.
00:28:11.035 --> 00:28:12.198
Let's pick a fire size.
00:28:12.198 --> 00:28:14.962
You know a 50 kilowatt fire.
00:28:14.962 --> 00:28:22.741
Fire size you know a 50 kilowatt fire, and we all sort of have an intuitive understanding for what that 50 kilowatt fire, that's with a one meter base, should look like.
00:28:22.741 --> 00:28:34.637
Right, if you put that fire, if you put that heat so-called heat release rate but if you put that fuel, that same amount of fuel in, and you turned off the turbulence model, it's a simple thing to do.
00:28:34.637 --> 00:28:37.703
What you'll see is you don't get as much mixing down low.
00:28:37.703 --> 00:28:38.490
You would still.
00:28:38.490 --> 00:28:43.078
If your domain is large enough, you would still eventually burn all 50 kilowatts.
00:28:43.078 --> 00:28:46.317
It would just take a lot longer and your flame height would be way, way longer.
00:28:46.898 --> 00:29:04.159
Yes, and brought me to one thing that I forgot that we need to talk about, and that's the concept of scales in fires and also the d-star number, because you previously said that the integral length scale could be the base of the fire or diameter of the fire.
00:29:04.159 --> 00:29:28.298
Many people would use this kind of calculations based on the square root of foot number, or d-square like people like to call it, to assume their scale at which important things are happening, because often this is also related to the size of the mesh they are choosing in their numerical simulation and by the nature of how FBS is built.
00:29:28.298 --> 00:29:35.049
It also defines the scale at which the subgrid model for turbulence will be introduced.
00:29:35.049 --> 00:29:43.136
So maybe first let's clear out how the scale leads to a specific solution for turbulence and then let's discuss the B star.
00:29:44.152 --> 00:29:55.259
Okay, so you have some numerical method and you're discretizing that equation with some cell size dx, dy, so on on a grid and you're going to solve that equation.
00:29:55.259 --> 00:29:56.266
It's a partial differential equation.
00:29:56.266 --> 00:29:56.900
You're going to solve that that equation.
00:29:56.900 --> 00:29:58.849
Okay, it's a partial differential equation, you're going to solve it.
00:29:58.849 --> 00:30:04.816
Now, what partial differential equation you actually write down depends on the filter width that you choose.
00:30:04.816 --> 00:30:07.340
Okay, so you imprint in the.
00:30:07.340 --> 00:30:15.240
Formally, what you do is you apply a filter, a mathematical filter, to the navier stokes equations of some specified width, delta.
00:30:15.240 --> 00:30:23.849
In practice, we always choose delta to be the same size as the grid, and okay, and that means that we are doing implicit filtering.
00:30:23.849 --> 00:30:31.324
Okay, so we never actually apply a mathematical filter to the equations in the practical les code.
00:30:31.324 --> 00:30:32.391
Okay.
00:30:32.391 --> 00:30:34.432
Now that introduces errors.
00:30:34.432 --> 00:30:42.856
It goes back to what we were talking about before whether or not we are really getting an accurate solution to the equations.
00:30:42.856 --> 00:30:53.144
These errors behave in all kinds of interesting ways and you can spend a career thinking about it.
00:30:53.144 --> 00:31:23.512
In practice, what we do I come from the school of using low order energy conserving numerics, which means using central, second order, central differencing for the momentum equations, and what that means is that whenever we're applying that means I can turn off viscosity completely, the turbulent viscosity, the molecular viscosity, and I can run the calculation and the flow will stay stable because all of the energy gets contained on the grid and it doesn't blow up.
00:31:23.512 --> 00:31:32.074
So the first job of the turbulence model is to take the correct amount of kinetic energy off of the grid.
00:31:32.074 --> 00:31:38.263
Okay, that's the first order job of a turbulence model in an les code.
00:31:38.263 --> 00:31:46.016
Okay, in these smagrinsky type models or the deardorff type model, these eddie viscosity models that we use in principle, that's more or less what they do.
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