final report turbulant flat plate ansys

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

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.

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)

Figure 3 SST Velocity Profile

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].

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.

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

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

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.

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

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

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]

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)

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.

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

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

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

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:


[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



http://www.caelus-cml.com/userdoc/3_Validation.html

http://www.caelus-cml.com/userdoc/2_Theory.html

https://bib.irb.hr/datoteka/718199.LucaManganiPhD2008.pdf

final report turbulant flat plate ansys

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