1 be used for a wide range of situations

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

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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


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

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



These two equations are derived here, with ‘k’ as:



The second variable ‘?’ is derived as:



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:






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


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


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.



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.





k- ?




Stress Model (RSM)




Eddy Simulation (LES)




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-?





Reynolds Stress Model (RSM)





Large Eddy Simulation (LES)





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:



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.