Fire Science Show
Fire Science Show
210 - Fire Fundamentals pt. 16 - Turbulence with Randy McDermott
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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Hello everybody, welcome to the Fire Science Show. 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. We're actually jumping into some quite advanced concepts. I hope that doesn't scare you off too early. I can just say it's fun and useful. So in this episode I have invited Randy McDermott from NIST again. You may remember, a few episodes ago we've talked with Randy about FDS development. 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.
Wojciech Wegrzynski: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. It simply is the thing that characterizes flow that if you get it wrong, the entire image of your flow is wrong. 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. It's critical to fire modeling. We're also tackling some practical concepts. So you perhaps heard about a DSTAR criterion that people use to choose their mesh sizes for FTS simulations. In this episode we will go fairly deep into mesh resolutions and timescales, so you will hear a lot about that. 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. So, uh, yeah it's, it's a tough one, but I promise you it's worth it.
Wojciech Wegrzynski:I love randy, I love talking with Randy. We're both geeks, we both love fire science and I think you will simply enjoy this along with us. 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. It's mostly Randy and his part is awesome in the audio quality and in the technical content presented. So let's not prolong this anymore. Let's spin the intro and jump into the episode.
Wojciech Wegrzynski:Welcome to the Fire Science Show. My name is Wojciech Wigrzyński and I will be your host. 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. As the UK leading independent fire risk consultancy, ofar's globally established team have developed a reputation for preeminent Farr engineering expertise, with colleagues working across the world to help protect people, property and the plant. Established in the UK in 2016 as a startup business by two highly experienced Farr engineering consultants, the business continues to grow at a phenomenal rate, with offices across the country in eight locations, from Edinburgh to Bath, and plans for future expansions. If you're keen to find out more or join OFR Consultants during this exciting period of growth, visit their website at ofrconsultants. com.
Wojciech Wegrzynski:And now back to the episode. Hello everybody. I am joined today once again by Randy McDermott from NIST. Hey, randy, good to have you back. Hey, wojciech, good to see you. 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. 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. Like, come on, man, really turbulent combustion. But that's cool. That's cool. You already gave me the background last time.
Randy McDermott:I'm not going to get any better. You're not going to get any better answers out of me, though I know.
Wojciech Wegrzynski:Yeah, yeah, that's cool, that's cool. 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. So let's try to tackle the topic with the idea of bringing some fellow fire engineers up on speed on turbulent combustion. Why do we even care about that in fires? So perhaps before we go into combustion, let let's talk turbulence briefly and then we'll probably move into turbulent combustion. So if you had to define turbulence, how would you define to? I mean such a hard concept to define to me?
Randy McDermott: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.
Randy McDermott:It enhances.
Randy McDermott:It enhances things, whether it's mixing, whether it's heat transfer, you know it's turbulence, steepens gradients and and therefore destabilizes flows.
Randy McDermott: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.
Randy McDermott: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. 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. 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.
Wojciech Wegrzynski:Yeah, let's maybe try from stepping up from a simple laminar flow. 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. Yeah, those streamlines are like parallel. They're not interacting with each other. Everyone is flowing and everything is flowing in one single direction, and it's just, you know, a nice flow. Nothing's interacting with each other, it's just, you know, a nice flow. Nothing's interacting with each other, it's just flowing. 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.
Randy McDermott: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. 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. 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. 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.
Randy McDermott:Is the way that I used to think of it when I was trying to learn these things. 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. 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.
Wojciech Wegrzynski: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. They calculate your average velocity and ticket you based on average. So everyone is literally perfectly on the speed limit, Everyone's the same.
Randy McDermott:You might as well be on a train right?
Wojciech Wegrzynski:Yeah, it's like you are. Every vehicle is moving with the same velocity next to each other in one unison. And then there's a big intersection later on and a lot of vehicles start entering the traffic from the side. 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. 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. So I guess something like that happens in the flow. I'm not sure if that's an accurate description, but it felt like it.
Randy McDermott: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. I mean a lot of the same like flux limiting schemes and all that kind of stuff get used. 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? Like what is that? What is it that's actually turbulent, right, and it's the fluid elements.
Randy McDermott: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. 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. Right, as we heat liquids, right, their viscosity goes down and things will become more turbulent. 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.
Wojciech Wegrzynski:What from the perspective of a flow, fluid flow? 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. But anyway, let's talk about movement of air. 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. What changes in the flow when it's more turbulent?
Randy McDermott: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. In a turbulent flow you usually have, you know, sort of what we call the integral length scale. So this is like some length scale in in fire, you know could be the base of the fire plume. 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.
Randy McDermott:Usually, it's usually connected to a physical thing, right? I mean the, the diameter of a pool fire or something like this is, is some is a length scale. That's that's relevant to the problem. You know, know the height of a doorway opening, the size of a window opening? I mean these things control to some degree the large-scale fluid motions in either a compartment or if it's an outdoor flow. You know you've got boundary layer heights, or even you know outdoor flows in the WUI, wild and urban interface. 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. These are these larger scale link scales that are one end of the spectrum, as we say in turbulence. 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.
Randy McDermott:Those usually correspond to some other physical link scale in the problem, right. And what about the smallest ones In the pipe? It's the diameter of the pipe, right, and so on. So you've got that length scale right, which is the fancy way to say that in turbulence is the integral length scale. And then of course, we have what we call.
Randy McDermott:There are two small length scales in turbulence that we have to worry about. One is what we call the Kamalgarov length scale, kamalgaroff length scale. 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. 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. 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. 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.
Wojciech Wegrzynski:The full amount of scale is like nanometers, like really tiny, right.
Randy McDermott: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.
Randy McDermott:The other, another link scale that we have to worry about, right, is flame thickness.
Randy McDermott: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.
Randy McDermott:So, right, schmidt number being the ratio of the scalar diffusivity to the kinematic viscosity. 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. So we inherit a lot of great research that has gone into that field.
Wojciech Wegrzynski:And how does? 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. So let's, let's even start with how do we model turbulence, because they mentioned. 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. So how do we?
Randy McDermott:So this sort of gets back to your original question of how do you define turbulence. So from my point of view as a modeler, I worry about turbulence when, or I have to worry about turbulence for whenever. 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. Um, because I don't, I don't have a subgrid model to deal with. I have other problems, right, you have computational costs and and and all kinds of things to to deal with. 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. 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?
Wojciech Wegrzynski:you have to make yourself small enough. Or is there any other trick to that right?
Randy McDermott:I mean there are in numerical methods. There are two types of adaptivity we call. We call them. One's called p adaptivity and the other is called h adaptivity. And then the p adaptivity. The p is, a is a fancy designation related to the order of the numerical method that you're using. 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. And then H-adaptivity is where you're just making your cells smaller and smaller, trying to reduce the error in your numerical solution. 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.
Randy McDermott: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. And maybe we could talk about that for just a quick second. 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. 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? Um, but there are some modeling problems. 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. You've got to get that right and that's a forecasting problem, right? So there's a difference between sort of modeling turbulence.
Randy McDermott: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.
Randy McDermott: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. 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. 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.
Wojciech Wegrzynski:It's also like the discussion between, from a practical simulation perspective, between the realism and the truth. 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. 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. It's a model statistics, not a real prediction. 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. Oh yeah, I can simulate how exactly the fire will you know behave in this compartment. I will give you like a prediction. And how will you do it? Oh, yeah, I'll put a burner in that BS. Well, that like yeah, it's that a burner in that BS. 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.
Wojciech Wegrzynski:So you told me that the audience follows and we promised them turbulence, combustion. I'm not sure if we can keep the combustion part, seeing the time. But let's talk more turbulence. 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. Engineers have to use turbulence models. So what exactly are you modeling when you're using a turbulence model? What exactly are you modeling when you're using a turbulence?
Randy McDermott:model Right. Well, what we're exactly modeling is? I mentioned these nonlinear terms in the Navier-Stokes equations and those are unclosed terms.
Randy McDermott: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. 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. There's a discrepancy and you have to account for that discrepancy and if you don't, you will just get things wildly wrong. 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. 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. 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.
Randy McDermott:Of course there's another, in fire, and this gets us into the turbulent combustion regime. There's also what we call the mean chemical source term on the right-hand side, which is a nonlinear term. 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. 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. And of course, in fire, that's everything. You have to get the heat. Really, I mean that, or at least it's not everything, but it's at least the first thing, right? 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. We were talking about what is turbulence. Well, the source of most turbulence in fire is that heat release rate term, because it's what generates the buoyancy and so on.
Wojciech Wegrzynski:But I'll try to play the difficult role of translator into more simple terms. 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. Otherwise your results are not correct or further away from the truth. What would happen if you just ignored those results?
Randy McDermott:Well, your mixing would be slower, right, so you would have this stretched flame. It wouldn't look anything like a real fire.
Wojciech Wegrzynski: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.
Randy McDermott:So it would run like. 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. Let's pick a fire size. You know a 50 kilowatt fire. 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. 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. What you'll see is you don't get as much mixing down low. You would still. If your domain is large enough, you would still eventually burn all 50 kilowatts. It would just take a lot longer and your flame height would be way, way longer.
Wojciech Wegrzynski: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. 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. It also defines the scale at which the subgrid model for turbulence will be introduced. 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.
Randy McDermott: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. It's a partial differential equation. You're going to solve that that equation. Okay, it's a partial differential equation, you're going to solve it. Now, what partial differential equation you actually write down depends on the filter width that you choose. Okay, so you imprint in the. Formally, what you do is you apply a filter, a mathematical filter, to the navier stokes equations of some specified width, delta. 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. Okay, so we never actually apply a mathematical filter to the equations in the practical les code. Okay. Now that introduces errors. It goes back to what we were talking about before whether or not we are really getting an accurate solution to the equations. These errors behave in all kinds of interesting ways and you can spend a career thinking about it. 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. So the first job of the turbulence model is to take the correct amount of kinetic energy off of the grid. Okay, that's the first order job of a turbulence model in an les code. 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. What that means is that you're going to see the, the plume as it's rising and starting to dissipate and and and changing from this sort of intense fire-looking turbulent fire into sort of the plume region where you get these larger billows and so on, that the scales are sort of dissipating at the right rate and we all know what we see when we watch, look at the code and we can see whether this is happening. We actually can measure this. There are verification you know the actual numerical verification cases and so on, experiments that we've run the code against to to make sure that these models are behaving and doing exactly this.
Randy McDermott:Again, this is the first order thing that the turbulence model has to do is take the right amount of energy off the grid. And what we mean by off the grid is we mean by the scales that are at about twice the filter width or twice the grid side, grid resolution, right, you've heard of the, the so-called energy cascade, where you know these things, you know the big worlds create little worlds and so on and so on, and we're trying, in the cascade picture, these things are creating smaller eddies that are not resolved, and once they be, once they get into the subgrid level, then, as far as we're concerned, they, they become dissipated. Okay, they just go, they go away. In physics, you just lose some energy and don't model them anymore. You lose energy and you don't model them anymore, and you know, in a low speed flows, these things dissipate into heat that you don't even record. Yeah, you have to worry about, okay, in high speed flows, of course, that the dissipation is is there's enough energy in that that they actually heat things? Right, that's why the spaceships, yeah, things re-entering the atmosphere, get hot. So, so this is where you know this issue of, of the grid resolution and the filter width starts to come into play.
Randy McDermott:Okay, and and like I said, the first order sort of approach here is is to allow the motions that are present on the grid at a scale dx or 2dx to live.
Randy McDermott:Okay, and what do I mean by live? If you do explicit filtering at, say, a scale of 2dx or 4dx, right, if you set your filter width when you're writing your equations down to be something some multiple of the actual grid resolution, then you kill all of the dynamics in that range. Okay, it's like a notch filter in. I don't know if you listen to music or whatever either, but it would be like taking a notch filter and just like taking out certain frequencies and you could just and they're just not heard.
Randy McDermott:Okay, and if those frequencies are important for dynamics, then usually they're just lost, and and in physics that's really what happens in turbulent flows. If you filter those things out, then you're relying on your turbulence model to somehow account for them. And my philosophy is basically that there is yet a turbulence model to be invented that does not do a better job than the discrete Navier-Stokes equations. Even if those Navier-Stokes equations are somehow under-resolved, they still do a better job than some algebraic turbulence model. You know they connect to the pressure equation and you are actually solving the Navier-Stokes equations on those scales.
Wojciech Wegrzynski:Well, the risk is here put on the user, Randy, because if this size is determined by the cell size, which is a choice of the user, then the user chooses what gets modeled and what gets filtered right. So if the user is unaware that they're going to remove or turn into a model some scale that perhaps would have been very impactful to their solution, they could cause an error. That's my understanding. Yeah, that's, and that brings us to D-star, because people use D-star.
Randy McDermott:That brings us to D-star. So what is D-star? So D-star is a length scale where we apply the Froude number scaling and it gives us sort of the effective diameter of a pool or a plume right with a plume source. Now you know there's a lot of lore, you know suggesting that okay, we need. You know, d star over dx equals 10, or whatever. Four to 16, four to 16. Four to 16.
Wojciech Wegrzynski:Yeah.
Randy McDermott:It's written down somewhere. Okay, so that's one link scale. I, like you know, when you're looking at problems, I, like my colleague you know, arnaud Trivet, likes to point out that, like there are many link scales in these problems and more or less from a signal processing point of view, you need about 10 cells to resolve any signal. Okay, um, to get a reasonable picture of of a of a signal and if and to under to understand what that means, you know, take some random collection of points, any signal that you want, and just start, you know, sampling on a different sheet of paper what from from that signal and until you get to about 10 points, you really don't have a good picture of what that signal looks like you could buy luck, but it becomes consistent by look but right.
Randy McDermott:I mean, if you know the signal is a sine wave, then it doesn't take 10 points okay yeah, that's where that's why we have, you know, spectral methods and so on.
Randy McDermott:But if you have some, you know, completely random signal. So anyway, so that's one. So d star or the pool, you know diameter, are, are just, you know, one of many potential link scales in in a fire problem that need to to be considered, uh, and and resolved and you're going back to sort of you know some of the things we were talking about in the other lecture. I mean, my experience with the DSTAR criterion is that when you're looking at sort of again these global quantities, flame height and so on for prescribed heat release rates, it can do somewhat of a reasonable job. When we start getting into, you know again, trying to predict fire growth and so on, trying to predict in flame properties or near wall properties, near wall heat feedbacks and so on, my experience is you need much better resolution than the star or DX.
Wojciech Wegrzynski:My bottom line is that when mechanical ventilation comes into play, like jet fumes, Like foot number doesn't it's not a valid term to define anything Jetson-related, like you don't have Williams in it so it's a mechanical injection of, especially at high velocities. So when you're talking about a phenomenon that's really close to a fire plume, yeah sure, perhaps it's adequate, Perhaps it's not, but it's probably a good guess, a good first estimate. But if you're enforcing flow, especially at higher velocities than we would seeing fires and the jet fan can go like 40 meters per second easily inside the jet fan, that's completely different things. Okay, we've got a lot of things to think of. Perhaps let's let's let's move into um, the, the turbulent combustion itself. So we already said that turbulence is important for a lot of phenomenon. Why is it important for combustion? What's so important about turbulence?
Randy McDermott:that that you have the entire field of combustion well, again it goes back to if you don't account for it, then you're not going to get anything right?
Randy McDermott:um yeah, from a model, from a modeling point of view, you know again, you know, if we're talking about flames, we're talking about combustion, then of course we have to, we have to back up a step and say, like, what kind of flames are we talking about? Right, so there are pre-mixed flames. There are, you know, diffusion flames. Um, there are partially pre-mixed flames, so there's also. So, basically, there's pure pre-mix, there's pure diffusion and there's really, from an engineering point of view, there's everything in between can you quickly define them for blue first?
Randy McDermott:the one line definition. So a pre-mix.
Randy McDermott:In a pre-mix combustion, the fuel and the oxidizer are mixed together before they are ignited okay so, um, think of your, if you have a gas stove in your, in your kitchen, for example, those are pre-mixed burners and you know there's a venturi mixer where there's a, an orifice injecting your natural gas and those it's it's entraining air.
Randy McDermott:Also, there's a lot, you know, fuel injected automobiles and so on, that that use this same same concept now, and then you have, and then you have the spark, um, and then where the flame rests, usually in pre-mix combustion, is there's some flame speed, right, so you've got, you've got a pre-mixture and and when you ignite the, the, the pre-mix fuel and air, then it wants to propagate back against the direction of the flow and there's some speed at which that happens and the flame stabilizes where the flame speed and the speed of the flow have matched too low, then the flame will can what they call pop back, or a flashback to, you know, to the source of wherever the fuel is being injected and so on.
Randy McDermott:But those are not fires, those are not. Those are not fires, those are, but those are important applications in the turbulent combustion world, in petrochemical industry and so on. You know, that's the world that I lived in um for many years. So in fires almost you know all you know. Most of the phenomena we're interested in are our diffusion flames um backdrafts are a different situation where you can get um.
Randy McDermott:You know partially and even pre-mixed situations, so pre-mixed combustion does matter in fire for those situations, and so the behavior of these flames are different.
Randy McDermott:You know, the stabilization mechanisms for these flames are somewhat different and ultimately like you need, it still comes down to the fire triangle, right? I mean, it's still ultimately like the fuel and oxidizer have to mix together and they have to be raised to some kind of ignition temperature In a flammability limit, within their flammability limits, and so usually at the point where things are, you know, stabilizing, there is always some sort of like combination of. This is kind of usually a partially premixed kind of situation.
Wojciech Wegrzynski:If you have a diffusion flame, how will it change if somehow you increase the turbulence? What's going to happen with, with the, with the chemistry, with the, with the fire, with the generation of species like?
Randy McDermott:what happens, right? So a couple of things happen. First of all, when things are turbulent, then the, the, the fluid sort of gets stretched and, as I my mental model of this is again, things sort of trip over one another and, and you know, when you get Eddie's taking place, you've got, you know, fresh oxygen mixing in with unburned fuel and so you've got sort of an increased surface area for the fuel in the air to to come into contact and and mix, and and again to come into contact and mix, and again this all goes to sort of enhance the rate at which the reaction takes place. For most fire applications still, like you know, fast chemistry is a good approximation until we start talking about extinction, until we start talking about formation of what do you mean by fast chemistry?
Randy McDermott:We mean Okay, so now we've talked a lot about link scales. Yeah, so far in this, in this episode, right, but what always comes along with link scales is a time scale. And when you're thinking about the chemistry versus mixing, it's good to to think about the, the time scales at which these things are happening. And for the most part, when temperatures are high, in combustion, in fire, the chemistry is happening very fast. So it means that the time scales are very short. By short, I mean order 10 to the minus 4, 10 to the minus 5 seconds, compared with the time scale for the fuel and the air to actually mix, okay, so, which is probably on the order of, you know, 0.01 seconds, okay, or something like this.
Randy McDermott:So, a hundredth of a second, tenth of a second. So even those, even though those things seem very fast, even those things, even though those things seem very, very fast, you know, fractions of a second, um, they're a lot slower than the rate at which the chemistry is happening. So, um, so, in chem, in chemical reaction, engineering, what you learn is like the slowest part of a process is what dictates the overall rate at which that process happens. Right, and so, in diffusion flames, when the mixing is slower than the chemistry, then the rate at which mixing takes place is really what's controlling the rate of chemical reaction. And then, since the chemical reaction is what controls the heat release rate, the rate of mixing is really what's controlling the heat release rate.
Wojciech Wegrzynski:Okay, in terms of chemical generation of energy right in terms of generation of chemical energy which again is the first order, you know important in a fire.
Randy McDermott:And so the way I think about all of this is again this sort of like hierarchy of physical processes, right, so you've got the, the fluid mechanics and that's sort of the momentum, and then of an obvious Stokes equations going into control, the mixing, okay, which is the fuel and the air. Are these species that are that flow, you know, with a fluid, but then, because of turbulence, they're getting mixed up right and coming in contact with one another at a molecular level, okay, and of course, when that happens in a diffusion flame there's this thin flame sheet. You know they're generating products. These things are folding up on one another. These products are then hot and and also, you know, getting flowing around and then moving around and then going to ignite other parts of the flow, and that heat generation is generating buoyancy which you know generates more turbulence and sort of the process sustains itself.
Wojciech Wegrzynski:With this increased turbulence, would there be any differences in terms of different species production?
Randy McDermott:I don't know, different chemical reactions being possible then yeah, for sure, for sure, because again it goes back to and this you know, this gets back to the, the time scale issue. So you know when the rate at which the chemistry happens eventually can get to be about the same order as the rate at which things mix, okay, and so there's, like we had a Reynolds number, you know that talked about the. You know whether things are turbulent because there's an inertial force and a viscous force. So on the chemistry side there's what's called the Dahlmkohler number, which is the rate of flow, sort of the flow, the mixing time scale over the chemical time scale, right. And so when, when the chemistry is happening very fast, the chemical time scale is small, then it's in the denominator. So your dom color number is high and and in that that's our typical situation in fire, right.
Randy McDermott:And when the mixing and the chemistry start to become on the same order as one another, now your Dom Kohler number is like approaching one and your mixing can get to the point where it's very fast, okay, you can think of like things that are stretched you know flames that are stretched, or you're blowing out a candle or whatever, right, so you've got these like really high strain rates and there you're, you know the chemistry can't keep up, okay, and and in that case you're that you know the heat transfer and and so on becomes basically, you're mixing faster than they can burn through, so you're mixing half burn products eventually, because they didn't exactly it's like you're taking cold stuff and you're and you're pushing it into the flame zone at a rate that's too high for the flame to sustain, and and then you can get extinction Right and during that process you know there's again, there's it's all, even though the extinction in fire is is not.
Randy McDermott:It's a fairly binary process. Things are usually either close to burning or kind of go, or they kind of go out, either close to burning or kind of go, or they kind of go out. But there is some like range there where you're sort of you know, as you get sort of under ventilated, you get more pockets of these, these regions where you know you get high CO production and and and other toxics. That that is where you know the chemistry comes in, when, when it's um, when the chemistry is happening at a time scale that's sort of you know, on the same order as of the mixing scale.
Wojciech Wegrzynski:One more thing that I wanted to ask. It perhaps spins us a little bit outside of the combustion, but it's very important to me as a smoke control engineer also. I guess a thing that defines entrainment into smoke plumes and and how the the smoke plume is growing in, let's say, a smoke model right.
Randy McDermott:So so entrainment in a plume is a is a fascinating topic um yeah, it is the sort of picture, the mental picture that I cling to, is one that was taught to me by Sheldon Teason. I don't know if you've ever met Sheldon. He was at Sandia National Labs for a long time and really, really smart guy and he did a lot of work in this area to kind of like illuminate the picture of what happens at the base of a fire plume and like what you really need to resolve to to get plume dynamics right. And his version, his vision of this is like, as you know, as you, okay, we, we kind of know that, okay, there's, there's something that gets the fire plume going, which means that there's. So now you've got buoyancy that's kind of driving up the flow.
Randy McDermott:Now that, obviously, as you, as you have the fire plume rising, you start to get entrainment. You get a boundary layer that forms as the entrained air is coming toward the base of the plume and that boundary layer, as the air is meeting the fuel, creates a shear layer between the fuel and and the incoming air and that that shear layer has has oscillations in it, okay, which are, um, in the turbulence world we call these kelvin helmholtz oscillations. So this is what you see when you see, like cloud formations and things, the cloud rolls and and things, or of carmen, vortex street, right as a car, as a kelvin helmholtz instability. So those density variations eventually get large enough that they can lead to rayleigh taylor instabilities, right? So the rayleigh taylor instability is where you get a lower density fluid that's, that's buoyant and and push in, pushing up right on, and then you've got the, the colder, colder fluids on on the side. So right there at the base of the plume you've got. You get this helman helmholtz instability leading to rayleigh taylor instabilities and those.
Randy McDermott:That picture of entrainment to me is what drives the puffing behavior of of the plume. And what sheldon showed is like to get the right kelvin helmholtz instability, you need something like a sound centimeter grid resolution, right, because this, these density variations that lead to the, to the instabilities that drive entrainment, happen on that, happen on that length scale. So that's, I don't think it's any coincidence. Then, because of that, you'll see, like, when we to get, if you're, if you start looking at, like trying to match data inside the plume or inside the, the flame region I'm inside the core region of a plume velocity measurements and so on. You need to be all of the simulations that get this stuff right are down at centimeter scale resolution. So you need to get those disabilities at the bottom. Yeah, you've got to be resolving the physics of that in entrainment near the near the bottom, in order to kind of like an initiation to those vertices that flow and grow and then build up right.
Randy McDermott:Okay, now that doesn't mean that you have to have a centimeter scale resolution to do every to those vertices that flow and grow and build up Right. Okay, now, that doesn't mean that you have to have a centimeter scale resolution to do every fire problem. It just means that if you're going to try to get in-flame metrics right, that tends to be where Because you're moving from forecast into statistical outcome and an averaged image, which is perhaps fine for your problem.
Wojciech Wegrzynski:We we made a full circle on this, but this is this is fire science and fire modeling in principle, yeah, I mean.
Randy McDermott:So to get back to the practical side of things, obviously you know, doing everything at centimeter scale resolution is not what, not what we can do today. But today we have a range of models, we have a range of problems and I think just be aware of what, what we're asking of the model and to to see you know what kind of resolution we need. It ultimately does I mean turbulence from a modeling point of view most of the time does come down to resolution I'll put that on the cover.
Wojciech Wegrzynski:Well, uh, randy, I think we can. We can stop on this. I think we you've done a great job on explaining turbulence and turbulent combustion. I mean, it's not an easy lecture to have and it's definitely not easy for the listener to grasp everything that has been said, but this is a good explanation of why we need modeling turbulence and how we can kind of do it and what factors come into play. I think it was a very valuable contribution and a lot of people just need to hear those things because for them, you know, it's a simple model. I just applied les and I put my cell because of this star, and then it happened and it's, it's fine. Why are you? You asking me those difficult questions what does it matter?
Randy McDermott:Now, in this podcast episode, you've heard on what it matters, so thank you a lot for bringing that to the yeah, I feel like we laid out a lot of the problems and not solved any of them, so Ah, yeah classical fire engineers. There's still, you know, a lot of work to be done in this field.
Wojciech Wegrzynski:No, definitely, definitely. But I'm very, very happy that also competent people like you are the ones who are developing the tools, because it also increases the trust to the tool, which is also a very important thing. Randy, it's fun talking with you over turbulence. We need to continue that in a pub one day. That's always a fun thing. I've heard about Doomcaller numbers. There's a special pub somewhere in Germany that I need to visit. I bet mine is lower than yours. Well, that calls for experimental validation eventually. Okay, randy, thank you so much for coming to the FireSense show again, and see you somewhere soon.
Randy McDermott:Yeah, yeah, enjoy your holiday, and so everybody knows that you're working on your holiday and that's it.
Wojciech Wegrzynski:I hope you enjoyed this one. Indeed, I am working on my holidays, or perhaps I'm just having fun. This is my idea of fun One extremely capable geek explaining to an extremely curious geek about what turbulence is and how impactful it is on the field of science that we both love. That's kind of fun to me. Now, this episode, it was very technical, very difficult, and I've re-listened to it twice already while editing, and I admit it is hard. So if you feel a lot of what has been said is difficult for you to comprehend, it just is.
Wojciech Wegrzynski:The understanding of the turbulence combustion and the turbulence phenomenon by Randy is really out of this world. But that's the reason why I wanted him to speak about this, because he's really capable in this subject and why it is important. I think Randy nailed it perfectly because if we do not model turbulence correctly, we get wrong results from our simulations, and that has been a case in many, many simulations that I've seen. Just the wrong application of the turbulence model changes everything Far plumes, far spread rates. If you model that entrainment into the plumes, smoke control, mixing, jet funds, really anything flow related when you miss on the turbulence, you're missing the grand picture and your solution is nowhere close to reality and of course, we want our solutions to be as close to reality as possible. I still believe there was a lot of practical takes in this episode. The role of the D-star criterion that a lot of people apply I think that was a very interesting one. The discussion about the length scale, the time scales I think it was very important to me to understand and refresh knowledge on those, so I think it's something that you can directly apply to your modeling.
Wojciech Wegrzynski:We have not covered most of the turbulence models in this episode, so Randy mostly focuses on large eddy simulation, les, which is the default model for FDS software. There's another family of turbulence models called Reynolds, average, navier-stokes, rans, and it's something that other softwares use. That's a whole field of science. Perhaps I'll go one day into the turbulence model episode, but for now I think that's enough turbulence knowledge for you, and I really hope you are enjoying your summer. I'm done with this episode, so time to go for a pool or something and enjoy the last days of my holidays in here with the family. I hope you're also having a great time and if you like great time, well then there's gonna be some great podcast episode coming your way next wednesday. See you there. Cheers bye, thank you.