1 Introduction

This is the second assignment for the Computational Fluid

Dynamics (CFD) section of the ME40001 Computer Aided Engineering module,

investigating the different turbulence models of cross-flow ventilation in

buildings. The validation paper that will be used to make numerical comparison

of results is the work of ww N. Meroney, the Professor of Civil Engineering at

Colorado State University. 1

This paper considers the effectiveness of Computational

Fluid Dynamics (CFD) to reproduce the results found in a physical wind tunnel

experiment performed by Karava, in which the airflow within and around a scale

model building is considered. 2

The three turbulence models being compared are the standard

k-?, the Reynold’s Stress Model (RSM), and the Large

Eddy Simulation (LES).

The first two models are considered

classic turbulence models which find the mean flow without first calculating

the time-dependant flow field. 3 These are based on

the Reynolds Average Navier-Stokes (RANS) equations, which offer mean

quantities with engineering accuracy at moderate cost for a wide range of flow

types. 4

The third model however is time-dependant,

which means it can perform better with fewer modelling uncertainties to those

of RANS models. LES also provides unsteady flow data which enables it to be

used for a wide range of situations where RANS models would not provide

sufficient enough accuracy. It unfortunately costs ten to one hundred times as

much as running RANS models, and provides mean values of unsteady flow by

computing with a small time step over a long sampling time, 4 much longer than for

a RANS simulation.

Generally, this is why it is

suggested to use RANS models for reliability and efficiency, whilst LES

provides more detail in regions of interest. 4

This paper will evaluate this claim

and compare qualitative and quantitative results to see what the differences

between the three turbulence models actually are.

1.1 Literature

Review

The investigation of

cross-ventilation flow in buildings has been made by a wide variety of

academics, ensuring that the results in this article are verifiable against the

work of others. One such source of useful information are papers which cover

the differences between the turbulence models, such as the ‘Hybrid LES/RANS

Methods for

the Simulation of Turbulent Flows’ by Jochen Frohlich and Dominic von Terzi 4 which looks at how

the costs of running LES simulations can be reduced.

Another useful source is the ‘Comparison of different turbulence models

in simulating unsteady flow’ by Feng Gao 5

which looks at how the accuracy of unsteady simulation can be improved when the

fluid flow characteristics change into natural convection. Both papers look

closely at how the difference turbulence models can be used in a variety of

different 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 with

contaminant dispersion in unsheltered and sheltered conditions’ by Yoshihide

Tominaga 6. This is a physical

experimental setup of a model building under various wind conditions for CFD

simulations run by other scholars to validate against. Though you would think

this paper ideal for validation, a lack of any actual CFD calculations to

compare with make it hard to include.

The second study is the ‘Validation with wind tunnel measurements and

analysis

of physical and numerical diffusion effects on different isolated

building configurations’ by R. Ramponi 7

is a physical and computational study based on Particle Image Velocimetry (PIV)

measurements for four different building configurations. It is comparing the

differences between the numerical and physical diffusion rates. Though of

obvious importance, there are few papers available in the public domain related

to this study to make an accurate comparison against.

One other paper which was a contender for validation is the ‘Comparison

of RANS, LES and experiments on the accuracy of CFD simulations of

cross-ventilation flows for a generic isolated building’ by T. van Hooff 8 which seeks to validate

CFD simulations for both RANS and LES turbulence models against physical

experimental data. This paper has not been used as direct validation but as it

has a very similar problem setup, it has been used for general comparison.

The validation paper that has been used is the ‘CFD

Prediction of Airflow in Buildings for Natural Ventilation’ by Robert N.

Meroney 9 which uses various

strategies to analyse how well CFD can reproduce the findings of the recent

wind tunnel experiment performed by Karava 2. These strategies

include 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 results

with minor arbitrariness for the domain and meshing.

Along with this validation paper is a

presentation again produced by Robert N. Meroney 9, which includes

figures of the path lines and flow fields which are not available within his

official article.

1.2 CFD Turbulence Models

Turbulence models are computational procedures to close the

system of mean flow equations. For the majority of the time in engineering

applications, it is unnecessary to resolve intricate details of the turbulence

fluctuations. One important aspect however is simplifying the expressions of

the Reynold’s stresses. For most CFD scenarios, the usefulness of a turbulence

model depends on; how applicable it is to different flow types, how accurate

its numerical results are, how simple the setup of the equation is, and how

economical it is to run. 3

1.2.1 Standard K-? (Epsilon)

This classic turbulence model is a based on Reynolds

Averaged Navier-Stokes (RANS) equations, which follow the same fundamental

limits explained in the first report for this module. 10 This is a two

equation model, where the number of equations that a turbulence model has

represents the number of partial derivatives that need to be solved. 3

This two equation model can account for history effects including

convection and diffusion of turbulent energy. The first variable denoted as ‘k’

is the turbulent kinetic energy, with the second variable ‘?’ given as the

turbulent dissipation. This second variable is what determines the scale of

turbulence 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 of

convergence, and wide range of applications. Its drawbacks are poor predictions

for swirling/rotating flows, axisymmetric jets, and flows with strong

separation. 3

1.2.2 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’s

stresses 3, representing the

most complete classical turbulence model available. 12

For this type of turbulence model, the eddy viscosity method

is avoided in preference of directly computing the individual components of the

Reynolds stress tensor. As this means that the model does not suffer from

limited states of turbulence, the model can account for complicated

interactions in turbulent flow fields, like the directional effects of Reynolds

stresses. 12

The transport equations used in the RSM turbulence model are

as follows:

(4)

(5)

Recommended constants for this model are:

The strengths of this model are that it is the physically

most complete model allowing the history, transport and anisotropy of the

turbulent stresses to be accounted for. The drawbacks are the two to three fold

increase in CPU effort required to complete simulations, and the closely

coupled momentum and turbulence equations. 3

1.2.3 Large Eddy Simulation (LES)

This LES turbulence model is different to RANS turbulence

models because the averaging is performed locally over a set space, a small

area around each point, which makes the variables in LES time-dependant. This

differs to RANS because its averaging is performed over time which by

definition means they are not time-dependant. 13

It seeks to be more detailed than typical RANS models but

not as detailed as Direct Numerical Simulation (DNS) which can resolve the

whole spectrum of turbulent scales. This however requires a very large

high-resolution mesh which means a large computational cost. LES lies between

DNS and RANS by solving large eddies directly with smaller eddies being modelled. 14

Large eddies are problem-dependant, decided by the geometry

and boundary conditions set by the user. Smaller eddies are more isotropic and

hence are more universal. This all leads to a mesh size requirement of at least

one order of magnitude smaller than DNS, with much reduced time step sizes

also. 14

The main advantage of LES is more detailed results than RANS

models but shorter computing time than DNS. However, a very fine mesh is still

required and a considerable amount of computing power is needed for it to be

even considered for engineering calculations. 14

1.3 Objectives

The aim for this article is to try and replicate the results

of the validation paper, before comparing the three turbulence models side by

side with numerical and visual data. The numerical data is the pressure

coefficient values at the centre of the building, using a graphical

representation. The visual data is pressure coefficient contours around the

building within the domain.

2 Research

Methodology

Finding a validation paper that provides enough detail to be

recreated with a respectable amount of accuracy is important when conducting a

CFD analysis. Thankfully, the validation paper used for this article contained

said information with the setup for the problem described below.

2.1 Geometry

The physical wind tunnel experiment used a scale model

building of 10 x 10 x 8cm high with 2mm thick walls, which corresponds to a

1:200 scale of a 20 x 20 x 16m high building. These same dimensions were used

in this investigation, first created using SOLIDWORKS and then importing this

is as a ‘Para solid’ file into ANSYS Fluent 14.5.7. The surrounding enclosure

was to represent a wind-tunnel and has dimensions of 100 x 150 x 50cm tall, as

seen in figure 1.

Figure 1 – the computational domain

The building contains two windows which are the same size

and are aligned parallel with each other, according to case E 1. The dimensions of

the window are 4.6 x 1.8cm tall positioned 4cm (halfway) up the height of the

building. Though other window configurations were used, this configuration had

the most data available within the paper, as well as being the same setup as

the other similar paper being used for comparison. 8

2.2 Mesh

Arguably one of the most important aspects of the problem

setup, the mesh resolution and shape had to be roughly replicated due to some

issues between the validation paper and what the student version of ANSYS

Fluent running on the university computers can handle.

The mesh used in the validation paper equated to 1-2 million

cells with a duopoly of hexagonal and tetrahedral shapes. The maximum number of

cells that the student version can run is 512,000 which meant from the start

that the resolution was 2-4 times less. The other problem was that errors were

very 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 mesh

After much trial and error, the final mesh used for all

three turbulence models had 336,080 elements with 61,112 nodes. This kept a

good balance of stability, accuracy, and reasonable computing time. The 3D mesh

can be seen in fig. 2, which had elements concentrated on the building within

the ‘enclosure’, particularly around the two windows where the air flow would

enter and exit. Fig. 3 shows the mesh from a directly central planar

perspective, showing largely triangular shaped cells.

Figure 3 – planar perspective of mesh

Another point to make is that the comparison paper 8 used roughly 5

million elements in their mesh which allows much greater detail to be

concentrated in regions of interest, including the flow over the top of the

building as shown in fig.4.

Figure 4 – mesh of building in comparison paper 8

Considerations to scale down the model building into

dimensions of millimetre scale, as well as using axisymmetric techniques to

only 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 higher

cell density, this was not done in the validation paper so was left out to best

replicate their procedure.

2.3 Solution

Setup

To keep things simple the constants used in all three

turbulence models were kept as the default values defined by the program. The

residuals were set as 0.0001 for steady state calculations, k-epsilon and RSM, then

changed to 0.001 for unsteady state (LES Model). The turbulence intensity was

set at a value of 10%, and the inlet velocity at 8.6ms-1 in

accordance with the validation paper.

The LES model solution setup required the most intervention,

including changing the time solver from steady to transient. The time stepping

method was set as fixed with the time step size as 0.001 seconds, the maximum

iterations per time step as 10, and the number of time steps as 10,000

representing 10 seconds of simulation. All models were initialized with respect

to conditions at the inlet, and for k-epsilon and RSM, the number of iterations

set as 1000. All turbulence models completed simulation without error

2.4 Validation

To numerically validate the results of the validation paper

against those of this investigation, the internal pressure coefficient of the

model building was found. Though other numerical validation methods were

available, the pressure coefficient was the least complex to model and had the

most data for comparison to be made. The pressure coefficient values within the

validation paper were found using both CFD graphical figures and the use of a

prediction equation denoted as equation (6) below 1. This equation is

from the external sealed building pressure coefficients 1 and gives an

estimated value for the internal pressure dependant on the inlet and outlet

pressure coefficients of the first window and second window respectively.

(6)

The values for the inlet and outlet pressure coefficients along

with the resulting internal pressure coefficient values can be seen in fig. 5.

Along with this quantitative analysis, a qualitative analysis was made with

pressure coefficient contours along a central plane passing through both the

first and second windows of the model building. By comparing and discussing these

figures and values side-by-side, a supported argument was made to best describe

the happenings of the simulation for each of the three turbulence models and

why 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 coefficients

using equation (6)

The method used to find the inlet and outlet pressure

coefficients ,shown in fig. 5, was to place ‘points’ in the centre of the inlet

window and outlet window, then plot an XY graph of pressure coefficient against

x-distance. This gives a single point on the graph where the pressure

coefficient value can be read off of. Evidence of this can be seen in the Appendix

B. The internal pressure coefficients for the ‘This CFD’ heading in fig. 5 are

taken from the XY plots in Appendix A at 5cm x-position. This represents the

centre of the building and is therefore the most ‘central’ part to take the

readings 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 validation

paper is comparing against does not use the ‘Case E’ building configuration for

internal pressure coefficient measurements. This means only a comparison

against the results found by Meroney 1 can be made. Had

there been more time, the dimensionless flow rate would have been calculated

too, which is compared inside the same table within the validation paper.

Figure 6 – table of internal pressure

coefficients comparing the validation paper and this investigation

The predicted values using equation (6) are very similar in

the results of the validation paper but have a much larger difference in the

findings of this investigation. The Reynolds Stress Model (RSM) was not used in

the validation paper so has been left as not applicable. The reasons for the

large differences between the validation paper and this investigation are most

likely the lack of similarity between problem setups. There is talk of having

different inlet air flow angles which were not replicated in this study as it

is unknown how to make this within ANSYS Fluent. Through further research into

this area, and greater time spent on grasping the computer software, the

problem setup could be better replicated and so the similarity in results would

be more apparent. The pressure coefficient is the ratio of pressure forces to inertial

forces 15 and is expressed as:

(7)

In this expression, ‘P’ represents pressure, ‘?’ is

density, and ‘v’ is velocity. What this shows is that the sign of the value of

the pressure coefficient, as in negative or positive, is dependent on the

numerator (change in pressure) as the denominator (density multiplied by

velocity squared all over two) will always be positive. This can be seen

visually in fig. 7 where, starting from the front of the rooftop of the

building leading to the rear, the pressure coefficient is negative. This shows the

point of flow separation as the fluid passes over the roof before re-joining

beyond the building.

The difference in internal pressure coefficient between

k-epsilon and LES in the validation paper was zero, suggesting that the

turbulence model chosen has zero effect on the outcome of the results. Compare

this to the results of this investigation and the changes between turbulence

models are very significant. The conclusion of the validation paper was that

the cross-ventilation flow through the building ‘appear to be fairly

insensitive to choice of turbulence model’. The reasons for the differences

between turbulence models could be to do with the suitability of each model for

different flow types. As outlined in the description of the three turbulence

models earlier in this paper, the k-epsilon model is fairly robust and can give

mediocre accuracy for results using a wide range of flow types. However,

complex flows like those within the building in this case, can suffer from the

lack of information that this two constant equation takes into account.

The RSM model however uses seven different equations and is

therefore better suited to more complex flow types and should perform better

than k-epsilon in this case. The LES model is supposed to give a more detailed

solution in regions of large eddies within the fluid flow, though the mesh must

be suitable quality and size to benefit from this. As the mesh was kept the

same for all three turbulence models in this investigation, the LES model most

likely suffered from this. If this investigation was repeated, it may be

necessary to alter the mesh for the LES simulation to benefit from the more

detailed results considering the longer computing time cost that the user has

to pay.

The negative correlation of internal pressure coefficient in

fig. 6 starting from k-epsilon down to LES does not seem to be repeated in the

values taken from equation (6) and is certainly not apparent in the validation

paper. This is especially surprising considering the pressure coefficient

contours of fig. 7 show a relative similarity with the differences between them

definitely nowhere near as pronounced as the numerical data would suggest.

3 Conclusion

The conclusions taken from this investigation are that

generally, for simpler fluid problems, the differences between these three

turbulence models are few. Though this was not the case for the results found

in this investigation, or for those found in the work of T. v. Hooff 8 who found that the

differences for internal kinetic energy between the RANS and LES models were

quite significant. Perhaps the differences are more substantial for some

numerical validation methods and not so for others. In the case of the internal

pressure coefficients, the validation paper found very little differences

whilst the changes in this investigation where very large. Through further use

of the ANSYS Fluent software, a greater understanding of the program and the

turbulence models involved will be developed which can only improve my ability

to write reports like this later on in life.