Sultan Anick Islam (100822163) | AERO 4304 Computation Fluid Dynamics | Due: Dec 1st, 2015
AERO 4304 CFD Term Project TURBULENT FLAT PLAT ANALSYS USING ANSYS CFX
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1.0 Introduction: Project Objective
The problem statement for this project is to analyze the turbulent flow of a flat
plate and validate the simulation to experimental data found on NASA’s website.
Furthermore the analysis will be extended to see the sensitivity of the skin friction
coefficient and velocity profile along the length of the plate. A sensitivity study will
be done to observe the changes of the values found when the Reynolds number
increases or decreases (as the fluid velocity fluctuates along the plate). This
simulation exercise helps us understand the fluid mechanics of turbulent flow
across a flat plate more intuitively, and can be used as a study aid for analyzing
more complex structures in engineering like blended body airfoils.
2.0 Literature Background and Previous Experiments
The flat plate simulation is based on previous experiments done by private
and government entities to study the formation of a turbulent boundary layer
across a flat plate. For this project I have used around 2 sources for
validating and setting up this simulation. The first one is the NASA turbulent
flat plate experimental study. They have specifically 2 studies for this but in
actuality they are the same studies done with a different approach. The final
source is from an experiment done by Caelus.
2.1 NASA FLAT PLATE SIMULATION
NASA ran two independent studies on the analysis of a turbulent flat plat
using computer simulation. In both studies a 16.7 ft long flat plate was
modeled using the following free stream conditions:
Table 1: NASA Freestream Condition
The mesh created was a 81 grid vertical by 111 grid horizontal. The first
study created a mesh for different non-dimensional Y+ while the second
study created mesh for one. The figure bellow illustrates the mesh. The
boundary conditions defined for both studies are show bellow in figure 1.
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Figure 1 Boundary Conditions
Using the above conditions, their simulation resulted in the following
relationship for skin friction vs. Reynolds number and for velocity profiles
for studies 1 and two respectively. (Please note that they used the K-
Epsilon and Mentors SST k-omega method for their solvers)
Figure 2: Skin Friction (SST Method)
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Figure 3 SST Velocity Profile
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Figure 4 K-epsilon and SST Skin friction (varying Y+)
The main influence of this project is from this NASA study. More detail of
the study and the results can be found at [1] [2].
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2.2 CAELUS TURBULENT FLAT PLATE MODEL
The Caelus model used a different geometry for the flat plate but the setup
and results are similar. Caelus uses a 2 meter long flat plate instead of the
16.7 ft (approx. 5 m long) plate that NASA uses. Caelus sets the
simulation by setting the air (our working fluid) as a perfect gas and uses
the following boundary conditions:
Table 2 Caelus Freestream Conditions
Caelus solves using Splart Almaras and k-omega SST methods, I focused
on the SST method. It is important to note that Caelus calculation for K-
omega is a bit different from the K-omega calculation computed using the
variables from the NASA case. The boundary conditions are similar as the
NASA case (see figure bellow) but instead of having a top free stream
condition, it is set to a symmetry condition. For the case of a flat plate, a
symmetry condition is equivalent to a free slip condition hence why the
lower left wall was also set as a symmetry condition.
Figure 5 Caelus Boundary Conditions
The computational grid used for the solver had a grid division of 544 cells
in the X and 384 in the Z (note that the surface of the flat plate here is the
XZ plane and not the XY plane like in the NASA case, it is due to the fact
that the solver used in Caelus case is 3D only while for the NASA case it
is 2D & 3D capable). Caelus only studied skin friction and thus the result
for the K-omega SST model can be found in Figure 6.
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Figure 6 Caelus Skin Friction SST
Just like the NASA case, full details on the simulation setup and results
can be found on [3].
3.0 Turbulent Flat Plate Ansys CFX Simulation
This section covers how the Turbulent flat plate simulation was set up using
the Ansys CFX Software suite. Note that some details for the computational
setup for both the NASA and Caelus experiments were left out so further
research was required to get those settings.
3.1 GEOMETRY OF FLATPLATE The geometry of the simulation is a rectangular prism with a small amount of
thickness. Refer to figure 1 for the geometry sketch used in Ansys 15. From
the NASA reference the geometric requirements of the plate are given to be
approximately 5.09016 m or about 16.7 ff. However there is a certain length
before where the flat plate begins which allows the flow to build by via a free
slip surface, thus the actual length of the plate is 5.0906+Build up length
which for our case was 0.5m. The document also cited multiple Y+ (non-
dimensional distance to wall), but based on other similar experiments, a Y+
value of 50 was chosen for the SST solver. The thickness and width aren’t
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given but can be found using the Reynolds Number expression. The
Reynolds number in question is Rex (which is the Reynolds Number based
on length of the plate). Rex was given to be 2.29x107. Using Rex the boundary
layer thickness was found using fluids theory to be 0.0656 m and it is also
known from theory that the width of the plate can be found to be about 10
times ½ the boundary layer thickness, thus we now have a thickness of 0.328
m. All that is left is the height, which was found to be 0.00109 m, this can be
found using the above values (the height is the distance between the wall
and the first node) but was cited from the NASA document. Y+ is also used to
define the mesh itself which can be found in the later sections. In order to get
the geometry illustrated in figure 7, a box function was used to create a box
with the end points at (-0.5,0,0) m &(5.09016,0.328,0.00109) m, then in order
to divide the flow build up section and the flat plate, a box with the
dimensions of 0.5 m by 0.328 m was sketched on the XY plane and then
imprinted onto the surface. With the geometry created, we can move onto
meshing.
Figure 7 Geometry of flat plate
3.2 COMPUTATIONAL GRID
Originally the grid division was chosen to be 50 in the Y direction with 60
in the X with a bias factor of 70 along the wall. Since the Y+ value was
cited to be 50, it was safely assumed that a minimum grid division of 50 is
required for the Y direction. Though this was deemed not suffice to
capture the flow changes across the plate so the grid division was
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changed. Instead the grid division in the Y direction was chosen to be 200
while for the X direction the grid division was chosen to be 220 with a bias
factor of 220. Using mapped face meshing on the two surfaces and edge
sizing on the edges a structured mesh with node concentration along the
wall was attained. The figures bellow illustrates where each technique was
used.
Figure 8 Mesh setting
Next using named selections, each boundary location was defined (i.e. the
no slip wall, free slip wall, inlet, outlet, symmetry), figure 9 illustrates the
mesh and the named selections.
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Figure 9 Mesh and Named Selection
With the meshing done, we can move onto the physics setup of this
problem.
3.3 BOUNDARY AND PHYSICS SETUP
This is where things get a bit complicated, the boundary conditions are
based on the following freestream conditions,
Table 3 Ansys CFX Pre Freestream Condition
PARAMETER VALUE
UPSTREAM VELOCITY 68 m/s or Mach 0.2
PRESSURE 14.7 psia
TEMPERATURE 530 R
ANGLE OF ATTACK 0 deg
ANGLE OF SIDESLIP 0 deg
REYNOLDS NUMBER 2.29x107
A custom material was created from the already existing Air at 25C in the
cfx post setting. The reference temperature and pressure was set to the
values found in Table 3 and Table 1, an air density of 1.192 kg/m3 was
chosen based on the temperature and pressure of the free stream. After
the material was set up, boundary conditions were defined based on
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figure’s 1 and 5. The inlet condition is a velocity inlet with a freestream
velocity of 68.8m/s in the X direction, while velocities in the Y and Z are
set to 0. Unfortunately the NASA simulation did not supply a K and Omega
value for the freestream that are needed for the turbulence modelling, K
and Omega are calculated using a supplementary report [3] and [4]. In
the report, the K and Omega equations are based of Wilcox report in
1998, the value for K is given as
𝐾𝑖𝑛𝑙𝑒𝑡 =3
2(𝑈𝑖𝑛𝑙𝑒𝑡𝐼)2 EQ1 [4] [5]
where I is the turbulence intensity. Similarly omega at the inlet can be
found using the equation bellow
𝜔 = 𝐶𝜇1/4 √𝑘
𝑙 EQ2 [4] [5]
where l is the turbulence length scale which is set to 0.22 in general for wall bounded inlets such as in our case. The derivation of these equations are based of Wilcox work which is beyond this course, the values calculated used approximations given in [4] and [5]. This yielded a K=26.3 m2/s2 and ω= 12.83 1/s. For the K-epsilon model, a turbulent intensity of 5% was used and K and omega were not used. For the outlet a static pressure outlet was chosen with a gauge pressure of 0 psig. The first portion of the bottom wall was set as inviscid (i.e free slipping) while the second portion of the bottom wall was set as viscous (no slip) for the plate. The two surfaces of the plate were set as symmetry conditions. The top of the plate was set as an opening boundary condition to the inlet freestream using the values for K and omega with a velocity of 68.6 m/s. The figure bellow illustrates the boundary conditions set in CFX-Pre.
Figure 10 Boundary Conditions
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With the boundary conditions set, the working fluid was set to air at 21 c
and the advection model was set to a blend factor of 1 while the
turbulence model was set to higher order, Finally the turbulent models
were chosen as SST and k-epsilon and the maximum iteration was set to
5000 and the solver was ran.
3.4 RESULTS
The solver ran for about 1000 iteration before converging at an RMS value
of 10-6. A velocity vector was created along the plate with a pressure
contour as well. A line was plotted along the outlet of the plate to capture
the velocity profile along the Y-axis. A sample of 100 was used and figure
bellow illustrated the resulting velocity profile.
Figure 11 Velocity Profile
Next a point was plotted to probe the freestream velocity at the inlet, the points
location was set as (-0.5,0.328,0) in the XYZ coordinates system. A wall line was
plotted along the wall of the plate itself with a length of 5.09016m. In order to
show the skin friction, we need a custom function for that, using the skin friction
equation found bellow a custom function was created to calculate Cf.
𝐶𝑓 = 𝜏𝑤
1
2𝜌𝑈∞
2 EQ2 [6]
The Reynolds number was also computed using a custom function with the
equation bellow.
𝑅𝑒𝑥 =𝜌𝑉𝐿
𝜇 EQ3 [6]
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With both the skin friction and Reynolds number computed, a plot was created
along the wall line that was plotted previously (a sample size of 65 was used for
this one).
Figure 12 Skin Friction
This concludes the results of the simulation.
4.0 Grid Convergence, Sensitivity and Validation of the Results
With the results of the simulation computed the next step is check the
convergence, sensitivity and validation with the target data both from NASA
and Caelus. It is important to note that there are other papers as well but for
this report only 2 will be used.
4.1 GRID CONVERGENCE Initially the grid division chosen was 50 by 60 but it was not enough to
fully capture the skin friction and velocity profile. The Nasa website
used a grid division of 111 by 81 while other sources used grids of 100
by 100, 200 by 200, etc. The grid division was increased one by one
until the results converged and the results appeared exactly the same.
This occurred at a grid division of 200 by 220. The table below
illustrates this for the SST case. (Note the k-epsilon solutions also
converged at the same grid division, more on this on the sensitivity
section)
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Table 4 Grid Convergence
# Of Elements
44000 (200 by 220) 48000 (220 by 220)
Normalized Velocity Profile
Skin Friction
As one can see the results look identical, thus for the final mesh
setting, a 200 by 220 grid division was chosen (as in the meshing
section).
4.2 MODEL SENSITIVITY The order of accuracy for the turbulence and advection model did
effect the results in a big way. Accurate results were only possible
using a higher order models. For the advection model both the use of
a higher order or a blend factor of 1 achieved the same result. There is
a miniscule difference between the use of Mentors k-omega SST
(Sheer Stress Transport) and k-epsilon. The table below illustrated it.
Otherwise the results do not differential as much with a use of a
different model.
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Table 5 Comparing Turbulence Models
Turbulence Model
k-omega SST k-epsilon
Normalized Velocity Profile
Skin Friction
4.3 RESULT VALIDATION The results obtained in this simulation will be validated by the results
from NASA and Caelus (figures 2, 4 and 6). Unfortunately the results
given for those graph use a Fortran compiler to do post processing
and I do not have that thus a comparison is made by directly
comparing the results between the figures given and the figures
obtained from the simulation. The general curve is exactly what the
NASA website and Caelus has obtained. It is important to note that
they didn’t run a simulation for anything with a Y+ of 50 but the results
should be similar. The initial skin friction value from my simulation is
larger than their because of the flow build up section of the flat plate.
They did not document how long the free slip portion of their
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computational domains were and I have a theory that my build up
portion may be greater. Due to this, the actual velocity reaching the
plate is greater which causes a sharp increase in the wall shear (which
was evident in the solutions). Figure 13 bellow illustrates the boundary
layer formation after the free slip section, where one can see the jump
in wall shear and velocity.
Figure 13 Skin Friction jump due to a velocity boundary layer
Otherwise looking at the skin friction at the Reynolds number of 5x106,
the skin friction values between the theoretical values given by NASA
and Caelus are exactly the same as what Ansys CFX gives. As
previously stated, the plots given by both sources do not have a text
file which I can compare my data file to but upon comparing them side
by side the results appear accurate (accept of the initial skin friction
coefficient at Re=0). Finally I want to talk about that slight decrease in
velocity at the end of plate and to an extent a miniscule decrease in
the skin friction plot, referring to figure 14, looking at the end of the flat
plate, there seems to be a back flow at the outlet due to the turbulence
nature of our model, this backflow causes a slight decrease in the
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velocity boundary the end of the plate which caused the dip in our
velocity profile.
Figure 14 Velocity Boundary at the end of the plate
Before we continue on to the Discussion and Conclusion I would like
to note that the non-dimensional velocity and Y distance was not
calculated for Ansys as for some reason the solver refused to output a
value, so more emphasis on the skin friction was taken, though one
can note that for similar simulations that cited a velocity profile with
just U vs Y, the profile matches exactly.
5.0 Conclusion
The main focus of this simulation was to analyze the effects of
turbulence on the boundary layer. It is noted that skin friction is related
to the pressure and hence why the skin friction was a point of interest
for our simulation. Judging from the simulation, the skin friction
distribution was almost as exactly as it was predicted by the theory
and previous simulations and experiments. Sources of error were
explained and illustrated in the section above. It was shown that even
with different models, the solution converged and illustrated that the
farther you go down the plat the less pressure is applied on the wall
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from the turbulent forces and that velocity boundary layer quickly
grows by the outlet and reaches a free stream in a short amount of
time. This concludes this project.
6.0 References
[1] NASA (2011), Simulation of Turbulent Flat Plate Study 1 [Online], Available:
http://www.grc.nasa.gov/WWW/wind/valid/fpturb/fpturb01/fpturb01.html
[2] NASA (2011), Simulation of Turbulent Flat Plate Study 2 [Online], Available:
http://www.grc.nasa.gov/WWW/wind/valid/fpturb/fpturb02/fpturb02.html
[3] Caelus Documentation 4.10 (2015), Validation and Verification [Online],
Available: http://www.caelus-cml.com/userdoc/3_Validation.html
[4] Caelus Documentation 4.10 (2015), Theory [Online], Available:
http://www.caelus-cml.com/userdoc/2_Theory.html
[5] Ing. Luca Mangin (2008), Development and Validation of an Object Oriented
CFD Solver for Heat Transfer and Combustion Modeling in Turbomachinery
Applications [PDF], Available:
https://bib.irb.hr/datoteka/718199.LucaManganiPhD2008.pdf
[6] F.M. White, Fluid Mechanics, 7th Edition., 2010
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