¶ Critical Velocity in Tunnels
Hello everybody , welcome to the Fire Science Show . Finally , a Fire Science Show episode on critical velocity in tunnels that I actually look forward to .
This time I'm not going to be depressed about talking about critical velocity , which I don't really find very fond of , because we are talking about some very new interesting physics related to that , and this is brought by my guests , conrad Stacey and Michael Bayer from Stacey you Company , and thanks to my fantastic guests , this episode has it all .
It could be framed as fire fundamentals . There's a ton of physics , perhaps a little bit too much physics at the beginning , but please don't let that discourage you .
Even if Grascov , prong and Richardson numbers don't tell you much , you don't have to know their mathematical derivations to enjoy the beauty of someone finding a new mathematical relation that describes reality in a better way than the previous ones did . This episode could be framed as experiments that changed fire science for sure .
We're talking about one such experiment . That is , the memorial tunnel , a very big undertaking in the USA which changed the way how we design tunnels worldwide and was the source of a lot of data and a lot of knowledge that we are still using up to this day .
And actually revisiting it gives us even more knowledge , which is a beautiful aspect of fire science . This episode treats on a cutting edge fire science . We are discussing paper that is just being published as we speak . I hope it's already online , whether it's in its final version or not .
You will find a link in the show notes that will lead you either to a pre-print or the finished paper , so you will also be able to check out what we are geeking out about . And this episode also has a little bit of political drama and the kitchen of how standards are made , which I think makes it interesting for everyone , not just tunneling experts .
And if you are a tunneling expert boy , this episode is for you . I don't have to advertise it for you . So enough , with this , let's spin the intro and jump into the episode . With this , let's spin the intro and jump into the episode . Welcome to the Firesize Show . My name is Wojciech Wigrzyński and I will be your host .
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This year , get in touch at ofronsultantscom . Hello everybody , I am here today with two gentlemen Conrad and Stacey . Hello Conrad , hi Wojciech and Michel Beja , hi Michel . Hi , hi everybody , both from Stacey and you and guys . Welcome to the podcast .
I'm happy to find some colleagues from the underground in the fire science show and today we're going to have another podcast episode on tunnels .
In most of my conversations I have tried to avoid the subject of critical velocity , but today let's make a full episode on that , because I think it's the time that Fire Science Show covers this fundamental for fire safety engineering concept , at least in the tunneling space . So you're both involved in tunnels . You have so much experience doing tunnels worldwide .
Let's talk critical velocity First . Let's clear up the concept , perhaps because not all of the listeners are familiar with the worlds of tunnels . What is the concept of critical velocity and how it impacts the design of tunnel ventilation ?
The critical velocity is that airspeed along the tunnel that just stops smoke from back layering upstream of the fire . So as the smoke from the fire rises to the ceiling forms a buoyant layer . The buoyancy tends to want to make the smoke go both ways along the ceiling .
If you have an approaching airspeed at the critical velocity , the smoke will only go one way along the ceiling and it will not proceed further upstream , further upwind than the front of the fire . That's the definition that's understood in the industry of critical velocity .
The definition that's understood in the industry of critical velocity , and the reason it's significant , is , if you want to protect people on one side of a fire for example , a queue of cars that are stopped behind a fire then achieving critical velocity means that those people won't get any smoke over them , so it's almost like a value that guarantees you that
upstream remains smoke-free and downstream is used for smoke transport , right ?
That's the idea , yes , and what goes into establishing the critical velocity ? I know we were going to talk about your new developments in that , so I guess there's going to be a lot of physics in this episode . But historically , what variables were considered when you would establish the critical velocity ?
The primary variables are the height of the tunnel and the heat release rate , and historically the slope of the tunnel has been taken as being an important variable .
But I imagine we'll get to that a little bit further down that we think it's now not important at all that's a big claim , and that's that's also one of the reasons why you're here , so we will definitely get in there . And historically , for how long this concept has been used ? Can you even trace the the origins of that pretty ?
close . I think they they started looking into that in the early 1958 .
I think there was the first paper from Thomas who explained a little bit the different flow regimes , the inertia so that the momentum onto the fire and the buoyancy force , and he developed the first relation between the buoyancy force and the inertia and built up some correlations and came up with so-called Froude critical Froude number which is actually in fluid
dynamics . It's a Richardson number which is the ratio of Grasov number divided by Reynolds squared and the Grasov number is a measure for the buoyancy force and the Reynolds number for the inertia .
The 1958 , I think Michael said the first serious attempt to look at it for fire in tunnels . But prior to that I believe there were a number of people looking at methane back layering in mining tunnels .
If you want to clear methane out of a mine a mine that obviously has coal measures associated with it , which may be a coal mine then you need to achieve a velocity that stops the methane from building up , and going back upstream is part of building up .
You want it to all go away and be diluted and carried out of the mine , and so the critical velocity for methane back layering was of interest to people before . I think it was seriously of interest for fires in transport tunnels .
I think in general , the mining ventilation would be something perhaps precedes everything we do , because mines were always for the history of humanity .
So yeah , anyway , another thing that interests me is what led to establishing because it's also like a very interesting derivation , establishing , because it's also like a very interesting derivation that the fundamentals laws of physics , the dimensionless numbers , that goes into this analysis , but it also has been confirmed or studied with the use of different experimental
methods , full skill and small skill . Perhaps you can comment on the developments and confirmation that this critical velocity is there and for large fires as well as well , does exist , to the best of my knowledge , that that's perhaps one of the outcomes of the of the memorial tunnel project , but may be wrong ?
no , you're . You're exactly right . The memorial tunnel data are the best data for understanding critical velocity . It's the best recorded set of information . You discussed the scaling problem and the idea of doing small scale tests . Unfortunately , they're a waste of time and the reason is that there's so many different flow regimes involved in the problem .
You cannot simultaneously match all of your dimensionless parameters unless you also match the dimensions .
In other words , you make it full scale , which is why attempts to scale from tiny tunnels when I say tiny cross sections , like the sheet of an A4 paper you know really small tunnels and hoping that all of your physical behaviors are somehow balanced in the same way when you get to a tunnel that's 20 times as big is well , it's just hopeful , it's not
scientific and the net result is that the numbers that we've seen coming out of those tests , or the numbers out of the tests , are fine for making really small tunnels , and I've got a cartoon of Gulliver on his travels representing to the king of Lilliput that he's able to design their tunnels for them , armed with a copy of NFPA 502 2020 .
Directly Correct , but if you want to design real scale tunnels , then that wasn't very useful . So you may learn some things from studying small-scale tunnels .
You may learn some trends , but I wouldn't get too excited about relying on them for any answers that are relevant to design of full-size tunnels I've published papers criticizing or showcasing issues with small-scale research , especially that you're simply unable to keep Reynolds and Froude number Like that's number one thing
¶ Tunnel Smoke Control Standards Update
for me .
Like you cannot have a turbulent flow and the Froude number at the same time in the scale , because they simply scale at different rates with the geometrical size , Same with the heat transfers and stuff like that , Though I still find scale modeling a useful exercise to understand some physical phenomena , but perhaps , as you said , to have them as a source of the
numbers . Simply run the test in a small scale , scale up and here's your result for the full scale . That has been an issue and you've brought up NFPA 502 from 2020 . 502 from 2020 .
I'm not sure how many of our listeners understand this little pun , but perhaps it's important that we showcase that because the things that we discussed today have significant impact over a billion dollar industry , which is the smoke control in tunnels .
So in NFPA 502 , some physical relations based on small scale tunnels were introduced , superseding the previous I think it was Kennedy's relations for critical velocity . The outcome of that was that the velocities that were given by the standard were significantly higher , or higher in general , than the ones that you would receive previously .
That's my understanding , and the outcome of having your velocities higher means you need more fans . You need more speed in your tunnel to achieve that rate , and suddenly our tunnels started to cost a lot more . And then was it version 23 ? It was reverted right , so you were involved in 502 . How did that process look like ?
I think it was very brave to revert it .
While it was essential , the change in critical velocity from 2014 to 2017 for a typical road tunnel with , say , a 50 megawatt design fire , I think it was about a 40% increase and it resulted , if you do the sums with simple longitudinal ventilation using jet fans , it was something like a factor of 2.7 on the number of jet fans you would need .
Now you mentioned the billion dollar industry in ventilating the tunnels . There's a significant cost in those extra fans , but the real cost is in making space or changing the shape of the tunnel to accommodate those extra fans .
If you were doing a cut and cover tunnel through some boggy ground and you had to make your tunnel one and a half meters deeper in this marshland in order to accommodate roof in the ceiling space for more jet fans , or you needed to make a significant length of the tunnel deeper , then that's many billions of dollars possibly for the one tunnel , so certainly
hundreds of millions . So it was a really serious economic issue and , like all designers , we were very busy designing and you think , oh it went up a bit to 2017 . This is a bit more onerous . Do we really think this is real ? Oh , but it probably doesn't matter if it's real or not , because the client has specified it , so we'll design to that .
And then 2020 came along and it went up again , and the source of these equations was the same , but 2017 was moderated for whatever reason . And then in 2020 , it was just getting a bit ridiculous to say is it really right that this new equation is correct and Kennedy was a fool ? The answer , of course , is that Kennedy was not a fool .
He looked at the memorial tunnel data and , for the typical design value of about 50 megawatt heat release rate , his numbers were about right . And so we started looking at why was there this difference ?
Because we had the 2014 equation , which matched the memorial tunnel data , and we had the 2020 equation , which matched the memorial tunnel data , and yet there was a 40% difference . How could that be ? And the answer was that the 2020 equation , the memorial tunnel data , was shifted . They were not the original memorial tunnel data .
We perhaps cannot say that they were shifted to exactly match the equation , but they were shifted and after they were shifted , they matched the equation .
And this was based on mostly this smaller scale , right Okay , memorial as a reference point . But I think that a lot of research that led to the re-establishment of those equations was based on a ton of paper . I remember that time . I am like a reviewer for tunneling and underground space technology .
I remember the flood of papers on critical velocity in that time , that that that was coming in in most odd combinations , usually based on on small skydive tunnels . Now this is one simple number or one small number , and we can argue whether it's three meters per second , two and a half or 1.7 meters per second .
Yet , as you said , the consequences for the real world , for engineering out there , are tremendous in all sorts of way , because it's also power supply , it's redundancy , it's backups , it its cables , like the electrical cable . People who are not designing this would not believe how much design goes in designing the electrical cables for large jet fans in the tunnels .
Even this starting sequence . This is all fun stuff . Anyway , one more thing that I think is very important for our further discussion 502 also introduced the rev revisions also introduced the concept of confinement velocity as something that's not critical velocity . I also think it's very relevant to talk about that .
So maybe I'll ask Michael to explain the idea of confinement velocity and how is that different from the critical velocity ?
When we started to look into the differences between the equation and the X-rated 2020 equation , then it ended up being one meter per second higher than it should be , or the Memorial Tunnel says that it's what's necessary . So we ended up with 4.2 meters per second for a tunnel that looks like a Memorial Tunnel , compared to three meters per second
¶ Tunnel Back Layering and Critical Velocity
.
And then there's also the other risks combined with that , because you would also overventilate your fire and that also mixes the smoke potential smoke layering in the tunnel and if there are people downstream of the fire , that wouldn't facilitate the egress or the self-rescue or the egress conditions for them , and so there's also a risk associated to having a velocity
that's too high in the tunnel . And when we started that discussion , we also ended the discussion is critic velocity actually the best way to do or to manage the fire or the smoke in the tunnel ?
So that's why the discussion about confinement velocity came into the NFDA and that actually means that we allow a little bit of a back layering , which is in a so-called tenable zone and in a zone where you have a very nice back layering anyways , because usually when you have a back layering , it's very nice to stratify it because it's a hot smoke adjacent to
the ceiling and you have usually clear air underneath and it doesn't restrict if it's confined to a specific length , it doesn't restrict your evocation and that's why we thought it's a good way to make it safer and not to over-ventilate the fire .
When some back layering is available . Are we speaking about like a meter of back layering or 50 meters of back layering or like 500 meters , or this is a point of assessment ?
The NFP defines the fire and the velocity as allowing 30 meter of back layering 30 meter . But it depends on the fire size . So if you design a tunnel for 100 megawatts then the radiation so you can't go , you know , five meters close to a fire and it will be uncomfortable there .
You have a tenable zone where you can't be anyways or where you're at risk because of the heat and the radiation of the fire . So 20 to 30 meters was more or less that base where you might be safe .
And when there is a smoke layer in that zone then that can be acceptable because you would experience a lot of high heat anyways from the fire and the radiation . And so if you had 100 megawatt fires or maybe 50 meter backlaying is then acceptable . But for 50 or 30 megawatt a 30 meter backlaying is then acceptable .
But for 50 or 30 megawatt 30 meter backlaying might be acceptable . The traffic situation in the tunnel if it's a bidirectional or unidirectional tunnel , they have a fixed velocity between one and three meters per second and so they control the velocity and accept the backlaying that can occur based on that velocity .
And actual fire heat is radiated in the tunnel because most of the fires might be small . You know you only have a car fire , maybe for five megawatts , and one meter per second might be okay and in some circumstances you might have a 30 megawatt fire and then your back layering might be longer .
But as long as it's stratified and you have good clearance under the layer , it's not a bad thing , especially when you have cars on both sides or can have cars on both sides of the tunnel for very high jet tunnels or , yeah , bi-directional tunnels and in those large fires the buoyancy is really strong .
It's it's like a really it could be a really sharp interface , the back glaring . I remember in some of the grass conferences they were doing this uh , heptane benzeneene smoke tests many years ago . I think you were there as well . That was very sharp smoke later on and it was a very interesting demonstration .
This concept is very profound to me because we stopped talking about one artificial value or one number of velocity . We stopped talking about engineering . We stopped considering safety . We stopped considering where you can be in in case of a fire off a tunnel to still be able to get out . We start to engineer . This is why I appreciate this , you know .
For me it opens the pathways showing that there's a spectrum of outcomes , there's a spectrum of fires and not just , you know , one fixated holy grail number for which you need to cut the trench one and a half meter more because you cannot feed your jet fan there . That was crazy . I'm really happy we've escaped those times .
Perhaps this is the time to to move into critical velocity and and revision of the concept . Let's try that . Conrad , you've mentioned the Memorial Tunnel . I know your recent research is also based on the Memorial Tunnel . You said it's the best experimental data set for studying critical velocity and back layering formation . Why is that ?
Why is it the best one Because they recorded everything so carefully , with so many thermocouple trees and so many time histories of velocity , and that you're able now to go back and reanalyze all of that data .
So it's not just a question of the summary papers that were produced at the time , but the raw data are available and we've been back into it and reanalyzed it to see what we think the critical velocity was .
Because velocity varies over time during these tests and the back layering varies over time and you look at the time instance when you think it's steady and when the smoke just starts coming forward again but it's still not changing too fast , and you say , well , that's a good time to pick where the critical velocity is .
So all of those data are available for anybody to reanalyze .
¶ Memorial Tunnel Study With CFD
And there was a large number of tests , not just one or two , and a large number of couple trees so you can calibrate your CFD to the downstream temperature profiles . And , yes , as Michael says , it's got very high heat release rates . You know there are equal velocity tests with three megawatt fires and you say , well , what use are they in a road tunnel ?
And that was a real tunnel right . It was a full-scale , large , proper tunnel right . What was the size of it ?
The height of the memorial tunnel is 7.86 meters . It's about 7.9 . And the height of the fuel pans they have used is 0.8 meters .
And the shape was a horseshoe , and then they put the ceiling .
Yeah , so it was a horseshoe shape , a TVM tunnel basically , and it had a full ceiling and they did a lot of tests with the transversal ventilation system .
And then they removed the ceiling , put all the equipment and measurement stuff in the tunnel again , placed the loops they had in place , they put back and did a lot of tests with tetraends and longitudinal ventilation .
Then Wow , and why did they run this project ? What was the origin of the Memorial Tunnel project ?
Art Vendelius used to love telling the story of myself coming to chat with him and a chap who was then unknown to me at the Boston BHR as it was then the ISAF , the conference in 2000 , and they were talking about the memorial tunnel tests , which were not that long before , a few years , three , four years before and I asked weren the Memorial Tunnel tests just
about proving to Americans that jet fans worked ? And there was , oh yes , well , that was part of it , and you know the very dry answer .
And the other person who was in the conversation at this welcome drinks was Tony Caserta , who was the secretary for the Department of Transportation for the US federal government , who was responsible for funding these tests and whose department was also responsible for policies that said you probably shouldn't use jet fans in tunnels .
So the glib answer , or the glib understanding that I had as to what the Memorial Tunnel tests were about at that time wasn't entirely inaccurate , in that there was essentially a prohibition on US tunnel projects that expected federal funding .
There was a prohibition on using jet fans , and so showing that you could control smoke in fact using jet fans was a really useful thing to do . But they were also studying the transverse or the semi-transverse ventilation of the smoke , before they then took the ceiling down and ran with the jet fans and just understanding the heat downstream from the fire etc .
Etc . So there were a few other . Obviously you get all the information you can out of it , out of a series of tests like that . But how to control smoke with longitudinal ventilation was certainly central , and showing that jet fans even worked in America was part of that .
They seem to just work globally . That's good , that physics in America even though the physics in there is in feet and stones , it still works .
And the good thing of those tests is actually that they had long lasting fires so they didn't use fuel pans and just filled them up and burned them out till the fuel is gone .
They had actually pumps and they were constantly pumping fuel into the fire pan so that they were able to have more or less a constant heat rate over a long time , and it was up to 30 minutes per test test . Okay .
And the variety of the fire size was also very good , because it started with 10 megawatts up to 100 megawatts and 100 megawatt fire over 30 minutes .
It's a really good test starter actually to validate realistic design fires again , and also for and it was the whole procedure was designed to analyze critical velocity , because they had jet fans and they changed the velocity in the tumble very careful and very close to the crit velocity and when it was a bit higher and there was no backlaying , they slowly or
slightly changed the air speed down until the backlaying started , and they did that during the test a couple of times just to pinpoint the actual velocity when the backlayiding occurs or when it's back to the fireside , and so you can actually , in a very narrow range , tell what the cryptic velocity was during those tests . Fantastic .
Okay , let's move to your recent study . So you said you were revisiting the data from Memorial . To my best understanding , you were doing that using modern CFD methodology . So if you could comment on the software and choices like how did you approach that ? Did you build like a detailed model of the tunnel ? How did you model the fire , etc .
Yeah , so we started with recreating the Memorial Tunnel model with all the details we have gotten . So we also got from Joe Gonzalez , who was there during the tests , some notes about loops and all the obstacles that were there .
You know we measured the units and all that sort of stuff and the precise location was of all those loops and what the potential blockage was , and also we implemented all the tetrains .
So all the details that are available in the report we implemented in the models and then we started first exploring the fire based on the volumetric heat source , because that was when we started , it was more or less the agreed best practice in simulating fire with Fluent or with CFD other than FDS , and then we realized that it actually the answer depends on how
you define the volume .
¶ Importance of Fire Intensity in Tunnels
If you define the volume exactly in that area where the fire pan was , but just you can change the height of that volume and depending on the height change , the result changed .
Also , we couldn't get a good agreement on the temperature , the distribution up and down from the fire , and so we started to look a little bit into the details of combustion and did a little bit of research of what could be available or a good , reliable combustion model that is not too computationally expensive but still accurate enough to get the holistic behavior
of the fire and to actually release the heat . In the model , the verdimere , most fuel is mixed with the air and gets burned , which is also a function of the temperature , a function of how much is combusted , what is the species there and how much oxygen you have .
So that was actually really important to have the heat released in the tunnel where the combustion is happening , to get an accurate temperature distribution downstream of the fire and also to predict the smoke backlighting downstream of the fire and also to predict the smoke back layering . Yeah .
And so we looked at different combustion models and there was one that is not too computational expensive , which is the eddy dissipation combustion model EDC , yeah , yeah , correct , and it was very robust . And , as you always have to , you're not after the data of a fire where some fluctuations and temperature increase happens local to the fire .
You are more after a time average or holistic temperature field to get the steady state backfiring predicted accurately . And that's why Rand's turbulence model was really good in finding good answers compared to the memorial tunnel in a more average sense .
But it always depends what you're after if you're using safety , because if you want to know what the maximum lane temperature is , then maybe that approach is not the best , but if you want to know what the smoke is doing in a steady state sense , then that was a really good model to use .
Were you using that around as a steady state or you were having transient simulation following the development of events at the memorial ?
Yeah , during the research we used a transient model and also RANS and we compared the transient with RANS and we found that there were no differences If you look in the , say , five-minute time average . Because we averaged the test data the velocity , the heat risk rate and all the important parameters were stable for a specific time .
So we averaged all those measured parameters over that time and then we did a steady-state simulation to see if we can confirm with that .
Because the problem is that if your heat risk rate changes and your velocity changes and also your temperature downstream changes depending on what was the heat risk rate at that time and the travel distance and speed at that time , so it's really hard to compare time .
So you it's really hard to compare and that's why I was after a period where everything was pretty constant , so that I can make sure that down to the fire , the temperature profile is well established and can be compared to the simulation we're after , because the aim is to analyze critical velocity in in a steady state sense .
So we want to know what the critical velocity is for a 50 MW fire that lasts , say , half an hour or an hour or whatever the design parameters are .
And the software is Ansys Fluent , right , yeah , we use Ansys .
Fluent for that .
Good , good Fellow Ansys users . It's also our software of choice . Now let's move to the formulations of your conclusions . So you've spoiled it a little bit . You said that slope used to be an important factor , but you believe it is not .
I also always put the slopes into my critical ventilation calculations and I know the impact it creates on the number of jet fans I have to put , which disturbs my clients . So please tell me what's up with slope . It creates the number of jet ones I have to put , which disturbs my clients . So please tell me what's up with slope .
Why do you think it's not as an important factor as we attributed it before ? I have a feeling it's a longer story .
It is a long story . I'll start , but the details of the flow are probably Michael's to tell . In short , if you are blowing smoke downhill from a major fire , the back layering that wants to proceed uphill at , say , a 4% grade , is very much more energetic than if the ceiling of the tunnel was flat .
And that energy of the back layer , with a roughly similar flow coming onto it , enhances the mixing to the point where the back layer self-defeats . And I'm not sure that that's a full and erudite explanation . But it seems that the answer is somewhere there in the more energetic mixing generated by the adverse gradient .
And while it's still certainly true that you need more ventilation power to achieve a certain velocity because you've got the buoyancy head of the smoke blowing downhill , the velocity that you need to achieve is actually not very different at all and may in fact be less when you've got a downgrade length of tunnel .
I always consider this as a battle of two wedges . Like you have two triangles that touch each other and the answer is the momentum transfer between those wedges .
Yeah , michael , add to that yeah , if you look at the local plume dynamics . So if you had a flat tunnel , you have the fire and the fire is inducing some momentum towards the ceiling and the gravity sector onto that flame and plume is the maximum when it's a flat tunnel .
You get the maximum speed hitting the tunnel when it's flat and as soon as you incline it the gravity vector onto that fire plume is decreasing so that the resulting pressure on the ceiling , which is then relevant for creating back layering or at least spreading a smoke in both ways decreases with the tunnel slope .
And that is one indication why it's decreasing or why it's about maximum when the tunnel is flat . And then of course you have different , as Conrad said , you also have a different mixing behavior because your flames also changes , because they deflect a bit more when when you're inclining the tunnel , and so you have also mixing effects .
But in the cfd what we found is that the pressure on the ceiling , because of the plume hitting the ceiling , decreases when you increase the tunnel slope .
It doesn't matter which way okay , good , in your paper , which I will link link in the show notes , one that triggered our conversation are also other aspects that you bring up , like the orientation of the fire source , the width of the fire source . I found that to be quite interesting .
So perhaps you can introduce us to factors that we perhaps have not recognized before or not recognized enough . That truly impacts the formulation of back layering and , as a consequence , the critical velocity itself .
Well , I think the biggest thing , Michael , is the focus on the intensity of the fire .
Yeah , I mean , there's a little bit of a story behind , because when we thought of issues with the small scale tunnels , we looked into the details and said , okay , what is actually the reason for that ? And one of them was , of course , of the scaling rules they have used .
So we are relying on the Froude number , and that is a little bit of a confusion , because Thomas used the critical Froude number , which is a rigid number and includes the density change on the temperature , and the Froude number used for scaling is actually a different Froude number .
It's the Froude number also used for fluid dynamics and it doesn't actually include the temperature other than the density change .
It's used for free surface waves and for particle suspension and various other things where temperature is not an issue .
It's a ratio of the inertia force to the gravity force and it's only for isothermal fluid flow . And when you look at the Navier-Stokes equation , as soon as you have buoyancy forces , that Froude number in the body force gets replaced by the Richardson's number , which is the cross of divided by Reynolds squared .
And that's when you talk about the mixed convection or in general , when you talk about convection or forced mixed or natural convection , and if those numbers are very similar the Grashof number and the Reynolds squared number then you have a mixed convection problem .
So to come back to the scaling , so the Froude number used for scaling is actually not the number that is representative for buoyancy forces , and that's the main problem , which means actually that your fire or your temperature field in the small scale tunnel is not scaled . So it has to be exactly the same as in the real tunnel and that doesn't happen .
Okay , in that way . Okay , now I got it .
Yeah , yeah and the second problem was that the fire size , because they used , or most of them used , small burner , or especially that one that is um the um the the problematic one .
Yeah , lee lay and ingerson 2010 is the problematic paper .
Okay , yeah and and they use the fixed burner size . But all the other researchers use the fixed burner size and increase the heat risk rate on that fixed area , which automatically increases the fire intensity .
And when you compare that to the Memorial Tunnel , then there's a problem , because in the Memorial Tunnel they have increased the heat risk rate by increasing the area and extending the fire pan in longitudinal direction to get more heat into the tunnel or more heat risk rate With a high intensity , which means the heat risk rate per square meter was constant in the
memorial tunnel tests but it was not , or is not , in the small skill tests , or most of them yeah , I remember we had similar discussions in the european commission for uh designing standards for car box , like how do we define the fires , whether we like to have a constant heat release rate by unit area and scale up the area , or we want to have the same
area and scale up the intensity , and uh , that was a very interesting conversation that took like six or seven years and I'm not sure if we even reached an agreement in the end , which one we like , but it certainly was enlightening
¶ Fire Intensity Impact on Tunnel Design
. So here you would say that the intensity actually is the impactful thing when you start to formulate the critical velocity and back layering . Why ?
is that ? Primarily because it determines the temperatures that you're going to get in the first part of the plume . Okay , because it's a buoyancy driven phenomenon and obviously that means temperature is a critical parameter .
And if you have a low intensity fire you don't get a very high temperature rise in your plume , you don't get a big density deficit , so you don't get the drivers of back layering .
And the analogy which I used some time ago to useful effect is you could make a 50 megawatt fire by soaking a ship's mooring rope in oil or in petrol and stretching it along a tunnel far enough oil or in petrol and stretching it along a tunnel far enough .
And clearly it's only the first bit of that burning mooring rope that's going to affect any back layering from it . So it's the intensity at the front of the fire that really matters in terms of generating back layering .
So if you've got a 25 meter long truck that's all burning , the first 12.5 meters are going to pretty much determine the backlayering that happens , because that determines the intensity , the density deficit that's hitting the ceiling , and the second 12.5 meters is just getting washed downstream by the flow that's already established to control the backlayering from the 12
and a half meters , so you might have doubled the fire size to a 25 meter long truck , but you haven't affected the intensity at the front of the fire , which is what really matters . And so that leads us to the second part of our modeling , second third , which is the influence of the length of the fire .
And there's a decaying influence of the length of the fire downstream , and we had no particular wisdom as to what that decay rate was , other than looking at useful data .
And again , the memorial tunnel data because they had fire pans of varying lengths gave us a good handle on that , and so we simply synthesized a decay curve that seemed to be of the appropriate form and that went into our formula , and then that got calibrated empirically along with the other parameters .
But there was some calibration we could do on that decay curve independently .
Yeah , and I just wanted to add that the indication of that thinking was also because of the memorial tunnel results and what was observed there , because for lower heat-per-haze rate between 10 and 20 megawatts , the crit velocity was about 3 meters per second . For 50 megawatts it was 3 meters per second and for 100 megawatts it was also 3 meters per second .
For 50 megawatts it was 3 meters per second and for 100 megawatts it was also 3 meters per second . And all the models always tried to calculate critical velocity based on the total heat release rate or on the convective heat release rate .
And so that's why most of the models were under-predicting critical velocity for low heat release rates and over-predicting for high heat release rates , because it increased the value when the hit-risk rate was increased .
But it wasn't observed during the Memorial Tunnel tests and we were thinking about the differences between Memorial Tunnel and the small-scale tests and what could be the parameter or the reason for that , and one of them is the high-intensity , as Conrad discussed .
And the way how they did add those additional megawatts in the memorial was adding pan after pan , after pan after pan . So it was increasing the length of the fire source , right ? You can't ?
increase the fire because it's a physical parameter . You can't have a five , say , a fire intensity of five megawatts per square meter because you can't get that feed into that area , because the fuel has a specific combustion value and based on that , that's the intensity you get out and the return .
Fire , for example , has a different intensity than a diesel fire or a gasoline fire . And we found that the fuel oil they used in the moral tunnel is already on the upper limit of a fire intensity because I mean , if you look at all fire , it's it's a very intense fire already and how about the width of the fire ?
how is that impactful ?
in a couple of ways . The first impact , I guess , is that it determines the shape of the plume and how much of the air that's coming down the tunnel interacts with the plume .
In most of the prior models the temperature that was put into the model is the average mixed downstream temperature , which then embodies the total heat release rate rather than just the intensity of the front bit .
So when we looked at dividing the heat released amongst the air that was likely to interact with the plume , with the rest of the air going around the plume , you get a different answer for the temperature rise , and that was one of the problems that people had with all of the prior models .
There was lots of discussion about aspect ratio corrections , correcting for wider tunnels , because the answer's not quite right .
Well , if you take a very wide tunnel and you pretend that the temperature fully mixed by the time the temperature has fully mixed , well , downstream of the fire in a very wide tunnel , that temperature is clearly irrelevant to the back layering , and so we could see that and we took as our temperature rise a temperature argued from an idealized shape of the plume
and taking that frontal area of the plume as representing the air that went through the plume to give us our temperature rise with the rest of the air going around it . So that's the genesis of the effective temperature , or the effective plume temperature rise . That's in our model .
The other part of the fire is what we please to call the curtain effect , which is , if you make a fire completely across the tunnel , there is no ability for the air to bypass the plume .
All of the air is pushing on the fire plume in the same way or a similar way , and so the whole thing leans over and the wider the fire is beyond some optimum or worst case value . As the fire width approaches a significant fraction of the tunnel width , the critical velocity goes down .
Because of this curtain effect , there's no ability for the free flow to bypass the plume .
Basically , the incoming air becomes more and more efficient because it just mixes with more and more of the back layering .
Well , it's just the physical inability for the plume to rise in between the stream of air . There is no in between .
If you have curtains and you pull them shut across an open window and the breeze is blowing in the window , the curtains will all pull back enough distance for the air to go underneath the curtain and into the room , whereas as soon as you create a tiny gap in the curtain , they can hang vertically for a modest breeze coming in through that gap and so making
the fire wider . For the same , fire intensity didn't actually increase the velocity required to stop back layering . It actually decreased it .
That's a really like . This is a challenging observation , but it kind of makes sense .
If you put it like that , it's quite easy to think about this very narrow fire , because when you have a very narrow fire there's a lot of space because the plume , you can see the plume is an obstacle and the air , the approaching air , is trying to not actually hit the obstacle , it's trying to go around easier .
There's a lot of space towards the left and the right of the fire and the air says I go around that , opening up a space , a vacuum , or kind of a vacuum for the plume and the smoke to propagate upstream , kind of a vacuum for the plume and the smoke to propagate upstream .
That's why you need much more air speed to push that back , compared to a very wide fire where all of the approaching air is actually hitting the full plume .
Fantastic . So , as we're approaching the end of our time , I would love to .
Basically , the outcome is you have proposed a revision of the critical velocity model based on your observation , on the careful investigation of the memorial tunnel and a parametric cfd study that followed again , there's a massive paper out there that's linked in the shown us , if anyone wants to get into the details of this , of this derivation .
You proposed a model . What is the from practical point of view , not not explaining physics like , what's the practical take for an engineer from this new model ? How does it differentiate from the existing model ? If you could figure out like one important change in the lives of engineers with this , besides being closer to the truth , hopefully .
Well , that is the fundamental benefit . As engineers , we're getting close to the truth . And this model is closer to the truth than all the previous equations have been .
It's closer to the truth than the Kennedy equations that were up to 2014 , primarily because of the recognition of intensity , and it allowed the formula to lose the heat release rate to the one-third power relation that had always dominated everything .
And it's closer to the truth than the more recent equations because it doesn't involve any fudging of data , and it's just closer to the truth for the range of heat release rates and tunnel sizes that people are interested in designing for . And why do we think it's close to the truth ?
We think it's close to the truth because it matches not only the memorial tunnel data very well , but it also works in Lilliput . The really small scale data are also matched , not by scaling rules , but by putting in the real dimensions of those small test tunnels .
Ah , considering small scale ones as full scale ones , but just little ones , correct , yeah , you just compare the measured values with the equation Nice , nice , nice .
And that was the aim to validate it with small-scale data as well , because then it's the only indication that you get the proportion right , because everything is proportional to something . So you can't have an absolute number , saying after 10 meters it doesn't matter anymore if the fire is longer or not , you need it proportional to some other parameters .
And it's the same with the width . You can't say two meters is enough , it depends on the tunnel area itself . So all of those parameters have dependencies and , as we have established that , you can use it for very small tunnels , it is valid . You can use it for real small tunnels , it is valid . You can use it for real tunnels , it's valid .
And that's maybe the benefit of it . It's more universal equations and should represent more accurately the situation in real tunnels .
As a connoisseur of mathematical models and tunnel safety enthusiast , I'll tell you what I like about it the most .
So the consequence that I like the most is that when you drop the heat release rate relation , when you actually recognize the fact , it's the intensity and that's the first part of the fire at which the mixing with incoming air happens , that that's the important part , etc . Etc . Which led to establishment of your model .
Now , if I look at your plots , they're pretty flat . You know they , they reach , you know there's there's a very high spike when you go from small fires to to large fires , but then it to some extent flens out . And then I go into a tunnel and I'm a designer , I know that there's a concept of consistent level of crudeness .
I do all my fancy calculations , but the number I put into my calculations the 50 megawatt fire , the 100 megawatt fires , this is a guess , this is a design fire that we to some , some extent have agreed upon . Whether in my tunnel is gonna be 1725 or 133 megawatts fire , I have no clue .
But what your model shows to me is that if I design for this 50 or 100 megawatt fire and that fire becomes a different one 150 or 70 or 35, .
¶ New Physical Model for Critical Velocity
The differences in critical velocities are not that big . They're like 0.2 , 0.3 meters per second .
Yes , you're correct , the heat release rate makes very little difference to the critical velocity beyond some minimum where it's growing from tiny . But you must still design your ventilation to cope with the buoyancy and the additional velocity from the expanded gas , et cetera , et cetera . The heat release rate affects those things very strongly .
So they affect the achievement of critical velocity , but they don't affect the critical velocity much . And then to control that heat release rate you can do as we do in Australia and put in a fixed fire suppression system . Oh yeah , I would recommend that . And then you've got it covered .
I like where this is going . Let's restart the discussion .
I just wanted to add with that what you just said with the 50 , 100 and 200 megawatt . It also more or less represents the real situation , because you don't have a fire a 200 megawatt fire in a square meter you usually have a real tunnel and a real accident .
A 200 megawatt fire means an involvement of several cars or some substantial fuel spill or whatever , and you always have to extend in a longer direction because it's restricted in the width . So if you have such a fire , then you also have a huge area and that's what is recognized by our equations .
Fantastic Gentlemen . Thank you so much for coming to the Fire Science Show and sharing your interesting insight into the world of critical velocity , and I wish you a lot of success with your model . We're going to test it out . I'll tell you how it went on the next project , so let's stay in touch .
Three of our colleagues on the NFPA working group have been doing exactly that , and they started before the final submission of our paper , and so they were able to give some very helpful pointers to what we hadn't explained clearly in the paper . So , yeah , that's going really well . Thank you guys . Thanks Wojciech .
Thanks for the invitation and you've been a great part of your show .
And that's it . You cannot believe what joy it was for me to record this episode as someone dealing with tunnels , to find people that understand your language and understand what you're doing and are doing way more impressive things than you and you can talk about them and geek out . That is just fantastic feeling .
I hope it was not too tough on you if you're not a tunneling expert and it was not too tough on you if you are a tunneling expert . There was a lot of physics in this episode , but there's a good reason for it .
Michael and Conrad propose a new physical model for establishment of the critical velocity in tunnels and they give very sound in my opinion , very sound explanation behind the physical phenomena that justify what they say , and the model seems to match small scale data , large scale data .
I have not tested it yet on any of our data , but we definitely will with my student yakub . So we are looking forward to implementing this in the future . And if you wonder what the impact would be of what we have discussed today , boy , the standards will be rewritten . The books will be rewritten . That's the impact that research like this carries with it .
I hope the paper is published by the moment we release the episode . I know when we were recording it was getting the final touches , so I'm sure that it went well . I just hope that the timelines have matched well . We'll see on the release date .
Anyway , in the podcast show notes you will have an access to a paper , either in a pre-print or in its final form , and I highly recommend that you check it out .
¶ Tunnel Enthusiasm and Farewell
So that would be it for today's episode . I'm still hyped about the discussion . We've spent like 20 minutes after the podcast talking with Michael and Conrad about tunnels . It was really , really a lot of fun and , yeah , I'm hyped , I'm enthusiastic and for the next week I'm preparing another hopefully fantastic episode for you to enjoy .
So I hope you will be there with me and for today , that would be it . Thank you for being here with me . Cheers , bye . This was the Fire Science Show . Thank you for listening and see you soon .