1 Introduction This is the second assignment for the Computational FluidDynamics (CFD) section of the ME40001 Computer Aided Engineering module,investigating the different turbulence models of cross-flow ventilation inbuildings.

The validation paper that will be used to make numerical comparisonof results is the work of ww N. Meroney, the Professor of Civil Engineering atColorado State University. 1This paper considers the effectiveness of ComputationalFluid Dynamics (CFD) to reproduce the results found in a physical wind tunnelexperiment performed by Karava, in which the airflow within and around a scalemodel building is considered. 2The three turbulence models being compared are the standardk-?, the Reynold’s Stress Model (RSM), and the LargeEddy Simulation (LES).The first two models are consideredclassic turbulence models which find the mean flow without first calculatingthe time-dependant flow field. 3 These are based onthe Reynolds Average Navier-Stokes (RANS) equations, which offer meanquantities with engineering accuracy at moderate cost for a wide range of flowtypes. 4 The third model however is time-dependant,which means it can perform better with fewer modelling uncertainties to thoseof RANS models. LES also provides unsteady flow data which enables it to beused for a wide range of situations where RANS models would not providesufficient enough accuracy.

It unfortunately costs ten to one hundred times asmuch as running RANS models, and provides mean values of unsteady flow bycomputing with a small time step over a long sampling time, 4 much longer than fora RANS simulation.Generally, this is why it issuggested to use RANS models for reliability and efficiency, whilst LESprovides more detail in regions of interest. 4This paper will evaluate this claimand compare qualitative and quantitative results to see what the differencesbetween the three turbulence models actually are.1.1 LiteratureReview The investigation ofcross-ventilation flow in buildings has been made by a wide variety ofacademics, ensuring that the results in this article are verifiable against thework of others.

One such source of useful information are papers which coverthe differences between the turbulence models, such as the ‘Hybrid LES/RANSMethods forthe Simulation of Turbulent Flows’ by Jochen Frohlich and Dominic von Terzi 4 which looks at howthe costs of running LES simulations can be reduced. Another useful source is the ‘Comparison of different turbulence modelsin simulating unsteady flow’ by Feng Gao 5which looks at how the accuracy of unsteady simulation can be improved when thefluid flow characteristics change into natural convection. Both papers lookclosely at how the difference turbulence models can be used in a variety ofdifferent problems/conditions for optimal results to be obtained. Studies that are closer linked to the problem setup at hand include the’Wind tunnel experiments on cross-ventilation flow of a generic building withcontaminant dispersion in unsheltered and sheltered conditions’ by YoshihideTominaga 6. This is a physicalexperimental setup of a model building under various wind conditions for CFDsimulations run by other scholars to validate against. Though you would thinkthis paper ideal for validation, a lack of any actual CFD calculations tocompare with make it hard to include.

The second study is the ‘Validation with wind tunnel measurements andanalysisof physical and numerical diffusion effects on different isolatedbuilding configurations’ by R. Ramponi 7is a physical and computational study based on Particle Image Velocimetry (PIV)measurements for four different building configurations. It is comparing thedifferences between the numerical and physical diffusion rates.

Though ofobvious importance, there are few papers available in the public domain relatedto this study to make an accurate comparison against. One other paper which was a contender for validation is the ‘Comparisonof RANS, LES and experiments on the accuracy of CFD simulations ofcross-ventilation flows for a generic isolated building’ by T. van Hooff 8 which seeks to validateCFD simulations for both RANS and LES turbulence models against physicalexperimental data. This paper has not been used as direct validation but as ithas a very similar problem setup, it has been used for general comparison. The validation paper that has been used is the ‘CFDPrediction of Airflow in Buildings for Natural Ventilation’ by Robert N.Meroney 9 which uses variousstrategies to analyse how well CFD can reproduce the findings of the recentwind tunnel experiment performed by Karava 2. These strategiesinclude the comparison of 2D/3D models and the use of different turbulence models.The paper is detailed enough to make a good attempt at reproducing the resultswith minor arbitrariness for the domain and meshing.

Along with this validation paper is apresentation again produced by Robert N. Meroney 9, which includesfigures of the path lines and flow fields which are not available within hisofficial article. 1.2 CFD Turbulence Models Turbulence models are computational procedures to close thesystem of mean flow equations.

For the majority of the time in engineeringapplications, it is unnecessary to resolve intricate details of the turbulencefluctuations. One important aspect however is simplifying the expressions ofthe Reynold’s stresses. For most CFD scenarios, the usefulness of a turbulencemodel depends on; how applicable it is to different flow types, how accurateits numerical results are, how simple the setup of the equation is, and howeconomical it is to run. 31.2.

1 Standard K-? (Epsilon) This classic turbulence model is a based on ReynoldsAveraged Navier-Stokes (RANS) equations, which follow the same fundamentallimits explained in the first report for this module. 10 This is a twoequation model, where the number of equations that a turbulence model hasrepresents the number of partial derivatives that need to be solved. 3This two equation model can account for history effects includingconvection and diffusion of turbulent energy.

The first variable denoted as ‘k’is the turbulent kinetic energy, with the second variable ‘?’ given as theturbulent dissipation. This second variable is what determines the scale ofturbulence whilst the first accounts for the energy in turbulence. 11 (1) These two equations are derived here, with ‘k’ as: (2) The second variable ‘?’ is derived as: (3) The constants for this turbulence model include:This models is useful for its simplicity, likeliness ofconvergence, and wide range of applications. Its drawbacks are poor predictionsfor swirling/rotating flows, axisymmetric jets, and flows with strongseparation. 31.2.2 Reynolds Stress Model (RSM) This is a seven equation model which develops on the k-?model by solving additional transport equations of the remaining Reynold’sstresses 3, representing themost complete classical turbulence model available.

12For this type of turbulence model, the eddy viscosity methodis avoided in preference of directly computing the individual components of theReynolds stress tensor. As this means that the model does not suffer fromlimited states of turbulence, the model can account for complicatedinteractions in turbulent flow fields, like the directional effects of Reynoldsstresses. 12 The transport equations used in the RSM turbulence model areas follows: (4) (5) Recommended constants for this model are: The strengths of this model are that it is the physicallymost complete model allowing the history, transport and anisotropy of theturbulent stresses to be accounted for. The drawbacks are the two to three foldincrease in CPU effort required to complete simulations, and the closelycoupled momentum and turbulence equations. 31.

2.3 Large Eddy Simulation (LES) This LES turbulence model is different to RANS turbulencemodels because the averaging is performed locally over a set space, a smallarea around each point, which makes the variables in LES time-dependant. Thisdiffers to RANS because its averaging is performed over time which bydefinition means they are not time-dependant.

13It seeks to be more detailed than typical RANS models butnot as detailed as Direct Numerical Simulation (DNS) which can resolve thewhole spectrum of turbulent scales. This however requires a very largehigh-resolution mesh which means a large computational cost. LES lies betweenDNS and RANS by solving large eddies directly with smaller eddies being modelled. 14Large eddies are problem-dependant, decided by the geometryand boundary conditions set by the user. Smaller eddies are more isotropic andhence are more universal. This all leads to a mesh size requirement of at leastone order of magnitude smaller than DNS, with much reduced time step sizesalso. 14The main advantage of LES is more detailed results than RANSmodels but shorter computing time than DNS.

However, a very fine mesh is stillrequired and a considerable amount of computing power is needed for it to beeven considered for engineering calculations. 141.3 Objectives The aim for this article is to try and replicate the resultsof the validation paper, before comparing the three turbulence models side byside with numerical and visual data. The numerical data is the pressurecoefficient values at the centre of the building, using a graphicalrepresentation.

The visual data is pressure coefficient contours around thebuilding within the domain. 2 ResearchMethodology Finding a validation paper that provides enough detail to berecreated with a respectable amount of accuracy is important when conducting aCFD analysis. Thankfully, the validation paper used for this article containedsaid information with the setup for the problem described below.2.1 Geometry The physical wind tunnel experiment used a scale modelbuilding of 10 x 10 x 8cm high with 2mm thick walls, which corresponds to a1:200 scale of a 20 x 20 x 16m high building. These same dimensions were usedin this investigation, first created using SOLIDWORKS and then importing thisis as a ‘Para solid’ file into ANSYS Fluent 14.5.

7. The surrounding enclosurewas to represent a wind-tunnel and has dimensions of 100 x 150 x 50cm tall, asseen in figure 1.Figure 1 – the computational domainThe building contains two windows which are the same sizeand are aligned parallel with each other, according to case E 1.

The dimensions ofthe window are 4.6 x 1.8cm tall positioned 4cm (halfway) up the height of thebuilding. Though other window configurations were used, this configuration hadthe most data available within the paper, as well as being the same setup asthe other similar paper being used for comparison.

8 2.2 Mesh Arguably one of the most important aspects of the problemsetup, the mesh resolution and shape had to be roughly replicated due to someissues between the validation paper and what the student version of ANSYSFluent running on the university computers can handle. The mesh used in the validation paper equated to 1-2 millioncells with a duopoly of hexagonal and tetrahedral shapes.

The maximum number ofcells that the student version can run is 512,000 which meant from the startthat the resolution was 2-4 times less. The other problem was that errors werevery prevalent within the software when a mesh of 400,000+ elements was used,so this had to be reduced further to keep the program stable. Figure 2 – 3d perspective of meshAfter much trial and error, the final mesh used for allthree turbulence models had 336,080 elements with 61,112 nodes. This kept agood balance of stability, accuracy, and reasonable computing time. The 3D meshcan be seen in fig. 2, which had elements concentrated on the building withinthe ‘enclosure’, particularly around the two windows where the air flow wouldenter and exit. Fig. 3 shows the mesh from a directly central planarperspective, showing largely triangular shaped cells.

Figure 3 – planar perspective of meshAnother point to make is that the comparison paper 8 used roughly 5million elements in their mesh which allows much greater detail to beconcentrated in regions of interest, including the flow over the top of thebuilding as shown in fig.4. Figure 4 – mesh of building in comparison paper 8Considerations to scale down the model building intodimensions of millimetre scale, as well as using axisymmetric techniques toonly study half of the building flow and then mirror the results, were made.However, though this may increase the quality of the meshing by having highercell density, this was not done in the validation paper so was left out to bestreplicate their procedure.2.3 SolutionSetup To keep things simple the constants used in all threeturbulence models were kept as the default values defined by the program. Theresiduals were set as 0.0001 for steady state calculations, k-epsilon and RSM, thenchanged to 0.

001 for unsteady state (LES Model). The turbulence intensity wasset at a value of 10%, and the inlet velocity at 8.6ms-1 inaccordance with the validation paper. The LES model solution setup required the most intervention,including changing the time solver from steady to transient. The time steppingmethod was set as fixed with the time step size as 0.001 seconds, the maximumiterations per time step as 10, and the number of time steps as 10,000representing 10 seconds of simulation.

All models were initialized with respectto conditions at the inlet, and for k-epsilon and RSM, the number of iterationsset as 1000. All turbulence models completed simulation without error 2.4 Validation To numerically validate the results of the validation paperagainst those of this investigation, the internal pressure coefficient of themodel building was found. Though other numerical validation methods wereavailable, the pressure coefficient was the least complex to model and had themost data for comparison to be made.

The pressure coefficient values within thevalidation paper were found using both CFD graphical figures and the use of aprediction equation denoted as equation (6) below 1. This equation isfrom the external sealed building pressure coefficients 1 and gives anestimated value for the internal pressure dependant on the inlet and outletpressure coefficients of the first window and second window respectively. (6) The values for the inlet and outlet pressure coefficients alongwith the resulting internal pressure coefficient values can be seen in fig. 5.Along with this quantitative analysis, a qualitative analysis was made withpressure coefficient contours along a central plane passing through both thefirst and second windows of the model building. By comparing and discussing thesefigures and values side-by-side, a supported argument was made to best describethe happenings of the simulation for each of the three turbulence models andwhy they were/were not different. Turbulence Model CP(Inlet) CP(Outlet) CP(Internal) Standard k- ? 0.

66375 0.002857 0.333 Reynolds Stress Model (RSM) 0.6651 -0.1175 0.274 Large Eddy Simulation (LES) 0.

61125 -0.097 0.257 Figure 5 – table of calculated pressure coefficientsusing equation (6)The method used to find the inlet and outlet pressurecoefficients ,shown in fig.

5, was to place ‘points’ in the centre of the inletwindow and outlet window, then plot an XY graph of pressure coefficient againstx-distance. This gives a single point on the graph where the pressurecoefficient value can be read off of. Evidence of this can be seen in the AppendixB. The internal pressure coefficients for the ‘This CFD’ heading in fig. 5 aretaken from the XY plots in Appendix A at 5cm x-position.

This represents thecentre of the building and is therefore the most ‘central’ part to take thereadings from.3 Results & Discussion Turbulence Model CP(Internal) (Validation CFD) CP(Internal) (Validation Eq.2) CP(Internal) (This CFD) CP(Internal) (This Eq.

2) Standard k-? 0.305 0.315 0.500 0.333 Reynolds Stress Model (RSM) N/A N/A 0.390 0.

274 Large Eddy Simulation (LES) 0.305 0.315 0.

175 0.257 Unfortunately, the wind tunnel experiment by Karava 2 that the validationpaper is comparing against does not use the ‘Case E’ building configuration forinternal pressure coefficient measurements. This means only a comparisonagainst the results found by Meroney 1 can be made. Hadthere been more time, the dimensionless flow rate would have been calculatedtoo, which is compared inside the same table within the validation paper. Figure 6 – table of internal pressurecoefficients comparing the validation paper and this investigationThe predicted values using equation (6) are very similar inthe results of the validation paper but have a much larger difference in thefindings of this investigation.

The Reynolds Stress Model (RSM) was not used inthe validation paper so has been left as not applicable. The reasons for thelarge differences between the validation paper and this investigation are mostlikely the lack of similarity between problem setups. There is talk of havingdifferent inlet air flow angles which were not replicated in this study as itis unknown how to make this within ANSYS Fluent. Through further research intothis area, and greater time spent on grasping the computer software, theproblem setup could be better replicated and so the similarity in results wouldbe more apparent.

The pressure coefficient is the ratio of pressure forces to inertialforces 15 and is expressed as: (7) In this expression, ‘P’ represents pressure, ‘?’ isdensity, and ‘v’ is velocity. What this shows is that the sign of the value ofthe pressure coefficient, as in negative or positive, is dependent on thenumerator (change in pressure) as the denominator (density multiplied byvelocity squared all over two) will always be positive. This can be seenvisually in fig.

7 where, starting from the front of the rooftop of thebuilding leading to the rear, the pressure coefficient is negative. This shows thepoint of flow separation as the fluid passes over the roof before re-joiningbeyond the building.The difference in internal pressure coefficient betweenk-epsilon and LES in the validation paper was zero, suggesting that theturbulence model chosen has zero effect on the outcome of the results. Comparethis to the results of this investigation and the changes between turbulencemodels are very significant. The conclusion of the validation paper was thatthe cross-ventilation flow through the building ‘appear to be fairlyinsensitive to choice of turbulence model’.

The reasons for the differencesbetween turbulence models could be to do with the suitability of each model fordifferent flow types. As outlined in the description of the three turbulencemodels earlier in this paper, the k-epsilon model is fairly robust and can givemediocre accuracy for results using a wide range of flow types. However,complex flows like those within the building in this case, can suffer from thelack of information that this two constant equation takes into account.The RSM model however uses seven different equations and istherefore better suited to more complex flow types and should perform betterthan k-epsilon in this case. The LES model is supposed to give a more detailedsolution in regions of large eddies within the fluid flow, though the mesh mustbe suitable quality and size to benefit from this. As the mesh was kept thesame for all three turbulence models in this investigation, the LES model mostlikely suffered from this.

If this investigation was repeated, it may benecessary to alter the mesh for the LES simulation to benefit from the moredetailed results considering the longer computing time cost that the user hasto pay.The negative correlation of internal pressure coefficient infig. 6 starting from k-epsilon down to LES does not seem to be repeated in thevalues taken from equation (6) and is certainly not apparent in the validationpaper. This is especially surprising considering the pressure coefficientcontours of fig. 7 show a relative similarity with the differences between themdefinitely nowhere near as pronounced as the numerical data would suggest.3 Conclusion The conclusions taken from this investigation are thatgenerally, for simpler fluid problems, the differences between these threeturbulence models are few. Though this was not the case for the results foundin this investigation, or for those found in the work of T. v.

Hooff 8 who found that thedifferences for internal kinetic energy between the RANS and LES models werequite significant. Perhaps the differences are more substantial for somenumerical validation methods and not so for others. In the case of the internalpressure coefficients, the validation paper found very little differenceswhilst the changes in this investigation where very large. Through further useof the ANSYS Fluent software, a greater understanding of the program and theturbulence models involved will be developed which can only improve my abilityto write reports like this later on in life.