A benchmark study for CFD solvers: simulation of air flow in livestock husbandry
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| Number of Parts | 20 | |
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| License | CC Attribution 3.0 Germany: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. | |
| Identifiers | 10.5446/35362 (DOI) | |
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Leibniz MMS Days 20184 / 20
00:00
Observational studyComputational fluid dynamicsMultiplication signDifferent (Kate Ryan album)Many-sorted logicComputer animationLecture/Conference
00:26
Observational studyComputational fluid dynamicsStochasticMathematical analysisScale (map)MathematicsNumerical analysisInterface (chemistry)Focus (optics)Element (mathematics)Different (Kate Ryan album)Flow separationPresentation of a groupCondition numberMass flow rateNumerical analysisGroup actionComputer animation
01:19
Operator (mathematics)ResultantMultiplication signProjective planeMereologyPhysical systemSet theoryComputer animation
01:51
Observational studyWind tunnelArithmetic meanMeasurementWind tunnelComputer animation
02:22
MathematicsDifferent (Kate Ryan album)ResultantPoint (geometry)Computer animation
02:51
MathematicsComputational fluid dynamicsElement (mathematics)Cartesian coordinate systemReal numberComputer animation
03:36
MathematicsElement (mathematics)TurbulenceScale (map)Element (mathematics)Wind tunnelState of matterTheoryComputer animation
03:52
MathematicsBoundary value problemSheaf (mathematics)Statistical hypothesis testingElement (mathematics)TurbulencePoint (geometry)Mathematical modelDifferent (Kate Ryan album)Line (geometry)Mass flow rateElement (mathematics)Sheaf (mathematics)TurbulenceVelocityWind tunnelCurveComputer animation
05:15
Nichtlineares GleichungssystemMathematicsTurbulenceDirected setNumerical analysisScale (map)Focus (optics)Large eddy simulationCalculus of variationsMultiplicationFlow separationNichtlineares GleichungssystemMultilaterationScaling (geometry)ModulformLarge eddy simulationObservational studyGroup actionFocus (optics)Mathematical analysisComputer animation
06:00
Large eddy simulationScale (map)MomentumFood energyMassSpectrum (functional analysis)TurbulenceLogical constantFiber (mathematics)Rule of inferenceScaling (geometry)Many-sorted logicModulformResultantLarge eddy simulationLengthTerm (mathematics)Logical constantGroup actionTensorStress (mechanics)AdditionVelocityComputer animation
06:47
Calculus of variationsScale (map)Angular resolutionFlow separationElement (mathematics)InfinityMultiplicationTurbulenceTensorSpacetimeScaling (geometry)Nichtlineares GleichungssystemSpacetimeMereologyFinite element methodFlow separationGroup actionStandard deviationPressureBounded variationFinitismusModulformVelocityINTEGRALTheory of relativityRule of inferenceFood energyNetwork topologyComputer animation
07:51
Randbedingung <Mathematik>AverageMeasurementBoundary value problemGreatest elementDifferent (Kate Ryan album)AverageMultiplication signMetreMereologyMeasurementGreatest elementPoint (geometry)Condition numberDimensional analysisWind tunnelBoundary value problemProfil (magazine)Closed setComputer animation
08:58
MathematicsComputational fluid dynamicsOpen setVolumeInfinityTurbulenceLarge eddy simulationNichtlineares GleichungssystemAdditionMereologyCartesian coordinate systemDifferent (Kate Ryan album)Nichtlineares GleichungssystemVolume (thermodynamics)CircleModulformSlide rulePhysical systemComputer animation
09:31
Open setComputational fluid dynamicsMathematicsInfinityVolumeLarge eddy simulationNichtlineares GleichungssystemTurbulenceBlock (periodic table)Vertex (graph theory)Adaptive behaviorThree-dimensional spaceTwo-dimensional spaceMeasurementVelocityRule of inferenceSequenceMatching (graph theory)Multiplication signComputer animation
10:24
Scale (map)MathematicsStokes' theoremInfinityVolumeCartesian productBlock (periodic table)Boundary value problemDisintegrationBlock (periodic table)Volume (thermodynamics)FluidCountingFilm editingComputer animation
10:54
MathematicsScale (map)Stokes' theoremInfinityVolumeCartesian productBlock (periodic table)Boundary value problemDisintegrationLarge eddy simulationTurbulenceElement (mathematics)Function (mathematics)TurbulenceResolvent formalismObservational studyBoundary value problemBoundary layerOrder (biology)Parameter (computer programming)VelocityFrictionApproximationLinearizationComputer animation
11:40
Local GroupMathematicsFocus (optics)InfinityElement (mathematics)TurbulenceLinear mapIterationDirected setCalculus of variationsScale (map)MultiplicationMass flow rateElement (mathematics)SpacetimeLinearizationFinite element methodFlow separationCartesian coordinate systemTurbulenceMultiplication signDifferent (Kate Ryan album)Computer animation
12:13
MathematicsLocal GroupFocus (optics)Element (mathematics)InfinityMultiplicationCalculus of variationsScale (map)TurbulenceLinear mapDirected setIterationTriangleVertex (graph theory)Group actionBDF-VerfahrenBoundary value problemDifferential equationTriangleMass flow rateMultiplication signStability theoryBoundary value problemResultantOrder (biology)Computer animation
12:57
VelocityOrder of magnitudeNumerical analysisResultantCausalityMass flow rateComputer animation
13:18
Vector spaceVelocityNumerical analysisStreamlines, streaklines, and pathlinesWater vaporKörper <Algebra>Image resolutionArithmetic meanVelocityAlgebraic structureStatuteComputer animation
13:37
Parameter (computer programming)Numerical analysisParameter (computer programming)FrictionVelocitySupremumComputer animationDiagram
14:03
Numerical analysisOpen setResultantDifferent (Kate Ryan album)Arithmetic meanAlgebraic structureGrothendieck topologyComputer animation
14:44
Numerical analysisVelocityOrder of magnitudeVelocityAlgebraic structurePairwise comparisonResultantComputer animation
15:14
Line (geometry)Sample (statistics)Wind tunnelClique-widthOpen setNumerical analysisMortality rateResultantWind tunnelBoundary layerMereologyPoint (geometry)CurveTurbulenceVelocityInsertion lossFiber bundleTheoryComputer animation
16:33
Unstrukturiertes GitterBoundary value problemApproximationNumerical analysisApproximationResultantBoundary layerComputer animation
17:07
Boundary value problemSheaf (mathematics)Function (mathematics)FrictionVelocityStatistical hypothesis testingTurbulenceParameter (computer programming)Open setScale (map)Numerical analysisLinear mapDifferent (Kate Ryan album)Statistical hypothesis testingScaling (geometry)FrictionBoundary layerMass flow rateWind tunnelVelocityMany-sorted logicResultantMortality rateComputer animation
18:08
Complex (psychology)Observational studyResultantState of matterObservational studySet theoryComputer animation
19:56
Computer animationLecture/Conference
Transcript: English(auto-generated)
00:01
Good afternoon. It's my third MMS day, or days. I'm happy to be here this time to present not only my work, but the work with other people from different institutes. I think you should see this. Either you present your work in a very specific way,
00:22
or if you want to present different views, then you have to be a little bit more general. This is a presentation of several general topics together, joined in a nice collaboration with different institutes. The people involved were David Young and Delia Willing from ATB in Potsdam.
00:44
ATB is an institute working on research in agricultural engineering, and then Oswald Knoth from Leipzig. You know, Anthropos is very advanced in the research on atmospheric flows. Myself and another colleague, which is now left, V.S. and Navid,
01:05
and we are, to our group, working on research of numerical methods for flows. In particular, Navid is very expert in turbulent modeling, and this is the topic of this work. I want to first tell what did we do and why and how,
01:24
and then I want to show some results. I put the dates here because in this time, we had an aberration in the ATB also, so it means that we were all involved in other works, a part of this scientific work. Since this was a side project for all of us, this means that we had to advance in a very limited time.
01:43
That's why I wanted to highlight that it was very difficult to work on a side project in this time for us. Okay, so what are we going to study? Livestock husbandry means animal care, basically. These are cow houses,
02:02
and the people from ATB had a wind tunnel model, which is a scaled model, 1 to 100, of this barn in Germany. The possibility of doing wind tunnel experiments and measurements. Then the collaboration started last year in Hanover.
02:24
During a poster session, David came and said they had this problem. He was interested in seeing other people working on the same topic. We started discussing, and the first question was how to do a nice and adaptive mesh. This was our first point in contact.
02:42
Then we started interacting and said, okay, why don't we just try to study the same problem with different codes and try if we can see how the different codes perform in the same problem. Of course, each of us has different motivation, so each institute from the ATB side, they wanted to share knowledge with our institutes.
03:01
They wanted to understand better what the safety solvers were doing, and also they were interested in open source software. From the trouble side into the one motivation, they were already giving the software to ATB, so the motivation was to disseminate the software more than for their own application.
03:22
From our side, it was very interesting to be able to benchmark our solver with real data because we develop always new methods, but we rarely have data to compare with. What is the real experiment? As I said, it's a 100-scale model of a barn.
03:44
This is a wind tunnel model, and there is a turbulent flow inside due to these small roughness elements. This is a sketch. This is the wind tunnel here the flow comes in. This small element here creates turbulence,
04:01
so that when the flow is far enough from the inflow, it's fully developed turbulent flow. Inside, there is a small model of a house, an obstacle.
04:22
This one, we call it the inflow section. We start simulating from here where the flow is turbulent, and these are called roughness elements. The experimental data says that when the flow is here, then it's really turbulent, so this is a typical curve of a developed turbulent flow.
04:43
I'm not a turbulent person, I'm a turbulent flow person, so I must say that it's not completely meaningful. Then we measure the flow at different lines to these sampling points where we can measure the velocity inside the wind tunnel.
05:04
We want to compare at the end the simulation data with this data measured here. I want to say some words about the mathematical model that we are going to consider. It's, of course, Navier-Sox equation for incompressible fluids. As we want to model turbulent flow, then we have to consider different approaches.
05:22
Of course, the DNS, the right numerical simulation, might be very costly if you want to simulate all the scales, the very small and the very large one. The software that we considered in our study has two different approaches. One is the LES.
05:40
We had already before about this. Basically, we focus on large scales, then try to model the effect of small scales onto the large scales. There's a called Variational Multiscale Method, which is a similar idea, but somehow formulated in a variational form. I will go in some detail later.
06:01
We'll first talk about the LES. Basically, the LES that most of you already know. You separate the scales in the coarse and the solid scale and the small and hard-to-solid scales. You filter the velocity in the coarse and the fine velocity, then you solve the Navier-Stokes for only the coarse scales, then try to model the effect of the small scales
06:23
using an additional stress term. For example, the Smogorowski model has this form. These additional stresses depend on the tensor of the coarse scale. There are two constants.
06:40
One is the filter length for the scale filter, and one is the model constant. The Variational Multiscale is a similar idea, but the scales now are three. There are three different scales. The large resolvable scale, the small resolvable scale, and the small unresolved scales. This separation is embedded in the variational formulation,
07:02
which means you can write the variational form of the equation in this way. This part here will be a standard Navier-Stokes formulation, where Q and V are standard finite space for velocity and pressure. This blue part here is the effect of small scales on the coarse scale.
07:28
Here, this space, LH, is the space of the small resolvable scales. This new T is a viscosity model, which can be, for example, a Smogorowski model.
07:43
It's very similar to the LES, but there are three scales, and this is very natural, formulated in a finite element setting. What is the simulation setup? The domain is a channel, 265 meters by 100 meters,
08:01
and there is a small obstacle here, which is relatively small compared to the size of the domain. Also, if you look at the dimension of the obstacle itself, the roof of the house is very thin. This requires, at least here, close to the obstacle, very fine meshes.
08:24
Boundary conditions with the inlet profile prescribed here, coming from the wind tunnel measurement. We took the measurement here and put this as inlet measurement. Then we have a do-nothing condition on the outlet part,
08:40
and then here is a no-slip boundary condition on the bottom, and a slip boundary condition on the top. We simulate, say, a relatively large time interval, and then compute the average at different points, so it's compared with the experimental data. The next part is I want to introduce a different code that we tried to compare.
09:04
The first solver is OpenFoam, which is an open-source safety solver based on finite volume. It's widely used in several applications. The Tubernetes model is a so-called one-like equation, which is similar to Smagorowski, but it's very similar to Smagorowski,
09:24
with the slight difference that they solve an additional transport equation to compute the tuberant part. It works only with block-structured three-dimensional exciter meshes, which means if you want to resolve the obstacle, you have to do a very fine mesh.
09:42
This is a zoom near the roof, so it requires a very fine discretization. In the case of our simulation, there were about 500,000 mesh nodes. The time excretization is an explicit, backward method,
10:04
adapted in time, so it means that you have to choose the time step always depending on the velocity, so it can be very small if the velocity is very high. In this case, one simulation took up to four days, even on 32 CPUs,
10:21
due to the fine mesh required. The second solver is ASAM from TROPOS. This is made for simulating different regimes of fluid. It's based on FORTRAN. Correct me if I say something which is wrong. Fine volume block Cartesian meshes,
10:42
where the obstacles are taken into account using the cut-cell approach, which means the mesh doesn't need to resolve the obstacle, so they are just lying within the mesh. So in this case, the mesh doesn't resolve exactly the obstacle.
11:01
The turbulence model is an LES-Magrisski model, and then there is an additional parameter that the ASAM user can tune, which is related to the boundary condition near the wall. There is a parameter which says, which can be used to tune the shape of the boundary layer near the wall. This I learned during this study.
11:22
If you want to match the blue for the turbulent curve, you can turn your friction velocity in order to have a better approximation, and this you can do in the ASAM solver. The third solver is the one developed by the VES called PARMOON.
11:46
We focus mainly on several applications in flow and transport, also turbulent flow. It's a finite element solver, and we have a lot of options for finite element spaces in 2D and 3D, lots of different time discretization, different linear solvers.
12:04
In this case, we use a turbulence model, which was the Varasian multi-scale method, with P1, P1 stabilized fine elements, and so we could have a mesh which was fully adaptive. This was much coarser than the other mesh we measured before,
12:22
it's only 80,000 triangles and only 40,000 nodes. Time discretization is second order of BDF, and time step also relatively coarse. For us, the simulation was much shorter, I think five, six hours for a full simulation.
12:41
We also could add stabilization on the open boundary, which is useful to mesh these cores, not to get the stability when the flows start to come in at the open boundary. Now I want to show you some nice pictures and video of the results. This is the ASAM result.
13:05
This is nothing more than showing what happened. This is the flow that we obtained. For this now you can just have a look, and I will compare more in detail the different cores. This is a picture of the mean velocity field close to the obstacle.
13:28
These are the streamlines, so you can see a very nice resolution of the water structures near the obstacle. This is what I mentioned before.
13:42
This is the parameter which regulates the velocity near the wall. This is the one which was used for the simulation. Delia was the one who used the ASAM software, so she compared different cases to see what happens if you change this friction parameter.
14:04
Then I want the results of open foam. In this case, the mesh is much finer, so you see much finer structure, because it's much more costly and much more resolved. You can see more fine structure in the simulation.
14:27
We have different layouts for all the software, so you cannot really see the difference. The cores can be different, meaning from each software. As I said, this was a kind of side project, so this is not completely finished.
14:43
Again, if you just focus on one snapshot, this is the one velocity snapshot and this is the average velocity. I just want to show the video for the last software, which, as I said, the mesh was much coarse, so you cannot resolve all the structure that you solved with the other software,
15:04
but you can say the results are at least in the I-norm comparable. If you go more in detail with the experimental results, so this is the open foam results. The green points here are the wind tunnel data,
15:26
and the red curves are the simulation data, so it's relatively close. What you see here is it's common for all software, so the boundary layer is not well resolved,
15:44
so the simulated velocity is always slower than the data near the wall. This is a problem of all our solvers. This is the ASAM result. It looks a little bit better than the other one if you compare.
16:00
It's closer to the wind tunnel data, but again, if you look close to the wall, the velocity is smaller than the real data one. This is the parmon performance. I'm sorry, the cores are different from the other one, so it's comparable to the ASAM.
16:22
Again, here this part is very nice, and near the wall we have a problem with the boundary layer of turbulent flow. It's just all together once more. We have a good overall agreement of the results, and then ASAM has a more flexible possibility for the physical modeling,
16:45
and this gives better approximation of boundary layer at least here, near the inflow, before the obstacle. Parmon is faster. It's probably due to the fact that we have better discretization available,
17:01
and we can also have a certain mesh. This makes the problem much easier to solve. This is where we are now, and the next step will be to simulate the flow before coming to the obstacle, just to see how can we reproduce the boundary layer in a better way.
17:24
I also tried to test different friction models, for example in our software. The option would be to simulate the problem at the wind tunnel scale. We have an experiment on the Scotland model, and we simulated the real model. This is based on the assumption that the velocity can be scaled.
17:45
This was an observation of David when we started. Maybe it's not fully decayed, so the other option would be to simulate the model at the wind tunnel scale, or the small 100 scale. Of course, we are trying to write also a publication, which will be a nice end of the first step of this MMS collaboration.
18:06
Coming to the conclusion, just a few statements. I think this benchman problem in general is important, not always because it can be as helpful as developing new methods,
18:21
because you can help people learning the state of the art, doing a nice benchmark, more than doing a new method. Also, they are key for reproducible research, which is a topic which we are talking about a lot, at least in this framework.
18:41
I learned that benchmark can be much more complex than expected, so when we started, I thought, OK, we just give me the data and I can simulate it. When we start talking with other people, you see that there are different ways of talking about things, so we learn. Before we could really set up a simulation, it took three months. Before, everybody was doing the same thing. I think this says that we have to learn how to talk to each other,
19:04
and this, for me, was a nice opportunity. I think the benchmark results are always good, no matter if you match the data or not. I think you will always learn what you can do better, what we are doing good and what you can do better, in any case.
19:22
It's not the problem of who is giving the best results, but more or less what you can do better in your software. The other thing is that the benchmark studies are always ongoing, so even if we finish this collaboration, it would be good to update this with other methods, other software.
19:44
Of course, there are other people interested. This is a thing that would not have happened without the MMS network. This is for us, so it would be nice if there are other people interested. You are welcome to join the benchmarking. Thank you for your attention.