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2D AND 3D FLOW ANALYSIS IN MICROFLUIDIC
CHANNELS INCLUDING MULITPLE SPECIES
TRANSPORT.
Written and Tested by: Scott Stelick
Alliance for NanoMedical Technologies
Cornell University
Last revision 10/2/02
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Problem Specification
Applicable ANSYS Products: ANSYS/Multiphysics, ANSYSIFLOTRAN, ANSYSIED
Level of Difficulty: advanced
Interactive Time Required: 1-112to 2 hours
Discipline: Computational Fluid Dynamics (CFD)
Analysis Type: steady-state
Element Types Used: FLUID141 and FLUID 142
ANSYS Features Demonstrated: Solid modeling, mapped meshing, defining an
abbreviation on the Toolbar, restart of FLOTRAN solution, multiple solutions, vector
displays, line graphs, path operations, trace particle animation, multiple species, fluidmixing in micro fluidic channels, fluid flow around obstacles in fluid channel.
Problem Description
This problem models laminar fluid flow in a small micro fluidic channel. Two input arms
combine in the design creating laminar flow out of the single output channel. You will
first run a 2D analysis of the design and after this is completed, a 3D analysis will be
done. The final analysis will be fluid flow around an obstruction in the channel. Added
information is given on how to model complex 3D structures.
Constants and dimensions
All parameters and constants are either given in the tutorial or in the table at the end of
this tutorial.
Approach and Assumptions
You will perform two and three-dimensional analyses using the FLOTRAN element
FLUID141 and FLUID 142, respectively. This problem is divided into three parts:
A laminar analysis of the 2D fluid flow and multiple species analysis of two different
fluids.
Extruding of the 2D model into a 3 dimensional design and multiple species analysis of
the two different fluids.
Velocity profiles of the fluids flowing in a micro fluidic channel with obstructions are
modeled.
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For all solutions, you will apply a uniform velocity profile at the inlet. This includes
specification of a zero velocity condition at the inlet in the direction normal to the inlet
flow. You will apply no-slip (zero velocity) conditions all
along the walls (including where the walls intersect the inlets and outlets). The fluid is
considered incompressible and you can assume that the properties will be constant. In
such cases, only the relative value of pressure is important, and a zero relative pressure isapplied at the outlet.
For the initial analysis, the flow is in the laminar regime (Reynold's number < 1000).
(Note that in a two-dimensional geometry, the hydraulic diameter is twice the inlet
height.)
For internal flows, the transition to turbulence occurs within the Reynolds number range
of 2000-3000.
Summary of Steps
Use the information in the problem description and the steps below as a guideline in
solving the problem on your own. Or, use the detailed interactive step-by-step solution
below.
Before you begin, delete any results files (.rfl) from previous CFD analyses that still
reside in your working directory. If you begin an ANSYS session to start a new CFD
analysis, and use the same jobname from a file stored from a previous CFD analysis, the
program will not start from scratch, but will restart and append to files with the same
name (Jobname.rfl and Jobname.pfl). To avoid this situation, delete these results files
when starting a newCFD analysis. Another way of avoiding this situation is to change the jobname to one that
was not used in a previous CFD analysis. You can change the jobname in the product
launcher before starting ANSYS, or during an ANSYS session by choosing Utility Menu
>File> Change Jobname
Preprocessing (Laminar Analysis)
1. Set preferences.
2. Define element type.
3. Units.
4. Create Keypoints.
5. Create Areas from Keypoints.
6. Making areas with curved lines example.
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7. Create the finite element mesh.
8. 2D meshing.
9. 3D meshing.
10. Extruding 2D models into 3D structures.
11. Unselecting 2D elements.
12. Establish Fluid properties.
13. Set execution controls.
14. Change reference conditions.
15. Multiple species setup.
16. Enter fluid properties.
17. Boundary conditions.
18. Execute FLOTRAN solution.
19. Post processing.
20. Plot velocity vectors.
21. Plot density variations.
22. Plot total pressure contours.
23. Animate velocity of trace particles instructions.
24. Path plot of velocity.
25. Construct single micro fluidic channel with obstacles.
26. Mesh regions.
27. Apply boundary conditions.
28. Execute FLOTRAN solution.
29. Complex 3D modeling.
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Launching ANSYS:
It is probably best to save your work on a Zip Disk inthe computer IOMEGA Zip Drive.
Then, simply click on the ANSYS icon on the Windows Desktop. The ANSYS Launcher
menu should appear. It is shown at the top of the next page. The only input you will
likely need on this menu is specification of the Zip Drive as your "Working Directory".If you don't have a Zip Disk, or if you prefer to work on the computer hard drive instead,
then specify any directory (or, "Folder") as your working directory. To browse and find
the desired working directory, click on the button with the three dots to the far right on
the Launcher Menu on the line that says "Working Directory". Once the working
directory is specified, click on "Run" at the bottom of the Launcher Menu.
The ANSYS menus
should open up. You
will see a Main Menu,
illustrated on the
following page, and a
large black graphics
window. You are now
ready to begin creating
the model and
performing the analysis.
Enter an initial jobname
here, no spaces are
allowed.
ANSYS Launcher
Menu:
ANSYS Main Menu:
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Note: Most of the required tasks are performed using menu picks from the ANSYS
Graphical User Interface, as specified in italics in the step-by-step instructions below. It
is sometimes more convenient, however, to enter certain commands directly at the
command line. The command line is seen on the screen as:
,f/\'ANSYS Input
Pich a ~epu ite~ o~ ente~ ANSYS command below (BEGIN)
The method of direct command line entry is used in some cases in this exercise,
whenever this method is more convenient than using menu picks.
****IMPORTANT***: AS YOU WORK THROUGH THIS EXERCISE, WITIDN
ANSYS, ON THE ANSYS TOOLBAR (UPPER RIGHT), CLICK ON "SAVE_DB"
OFTEN!!! THIS TOOLBAR APPEARS AS:
4 J AN5YS Toolbar _
S A I I E _ D B
R E S U M _ D B
Q U I T
POWRGRPH
At any point, if you want to resume from the previous time the model was saved, simply
click on "RESUM _DB" on this same Toolbar. Any information entered since the last
save will be lost, but this is a nice feature in the event that you make an input mistake,
and are unsure of how to correct it.
There are a number of ways to model a system and perform an analysis in ANSYS. The
steps below present only one method.
Set preferences.
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You will now set preferences in order to filter quantities that pertain to this discipline
only.
1. Main Menu~'
>
Preferences
2. Turn on FLOTRANCFD filtering
3. OK.
Define element type.
1. Main Menu> Preprocessor> Element Type> Add/Edit/Delete
2. Add an element type.
3. Choose 2D FLOTRAN element (FLUID141).
4. Choose 3D FLOTRAN element (FLUID142).
5. OK.
6. Close.
Units.
1. Main Menu> Preprocessor> Material prop
> material library> select units
2. Choose the cgs system
Note: All units shown in this tutorial are in cgs
units.
Main Menu > Preprocessor > Materials >
temperature unit
3. Choose the Celsius scale
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Create Keypoints:
In fluid modeling, it is best to have a single area defined. Original tests were done where
rectangles were made and merged together. This method did not work well and it was
decided to enter the coordinates of all the vertices of the design and connect all the points
to create a 2D area. This 2D area can then extruded to make the 3D design.
To add keypoints to a coordinate system:
Preprocessor -> -Modeling- Create -> Keypoints -> In Active CS...
Fill in the fields as shown below, then click "APPLY". When you click on "Apply", the
command is issued to create keypoint number I at (x,y)=(0.0501, -0.2645). Note that
when the Z field is left blank, in this case, the blank space defaults to zero, which is
desired. Since you clicked on "Apply", instead of "OK", then the keypoint creation box
remains open.
Create keypoint number 2 at (x,y)=(0.0678,-0.2822), using the input shown below. After
entering the input, again, click on "APPLY":
Enter all of your keypoints in this manner. Units are in cm and for this design the
channel is 8.5 mm long and 250 microns wide.
Keypoint # X Coordinate Y Coordinate
3 0.34916 0
4 0.85 0
5 0.85 0.025
6 0 0.025
7 0 0
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1 8 I 0.3146 1 0
When the final keypoint is entered, click on "OK" instead of "APPLY". "OK" issues the
command and also closes the keypoint creation box.
Before moving on, it is probably a good idea to check the keypoint locations. Along thetop toolbar:
U§hjiiff l l j ir i"iJi#,rl lt lf ,t inH4,ui'
Choose: List -> Keypoints -> Coordinates Only. A box should open up with the keypoint
location information. If any keypoint is not in the correct location, at this point, you can
just re-issue the keypoint creation command for that particular keypoint. To do this,
choose: Preprocessor -> -Modeling- Create -> Keypoints -> In Active CS...
Fill in the correct information for that particular keypoint in the box, and click "OK".
The keypoint will be moved to the correct location. If you have some keypointincorrectly numbered above number 12, this will not cause a problem. Just be sure you
have keypoint numbers 1 thru 12 located correctly.
You can close the box listing the keypoint locations, by clicking, in that listing box, on
"File-> Close".
Create areas.
In this design, all lines connecting the keypoints are straight lines so the following
command is used. If in your design, curved lines are used, the next section gives an
example of the process.
Main Menu> Preprocessor> -Modeling- Create> -Areas- Arbitrary> By Lines
Connect the points in numerical order and when done click "OK" on the picking menu.
The following area is created.
Curved lines will not be used in this tutorial but I will include information for reference.
If you have a curved line in your design the following example will show you how to
connect a tangent line between keypoints. This will make the analysis a little more
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difficult because the areas are broken up but should still work fine. The example is from
another gas flow tutorial that is available in the ANSYS help menu.
Making areas with curved lines
1. Main Menu> Preprocessor> -Modeling- Create> -Lines- Lines> Tan to 2 Lines
line of left rectangle).
3.0K (in picking menu).
end of the first line (upper right comer).
5.0K (in picking menu).
6.Pick the second line (upper line of the larger rectangle.
7.0K (in picking menu).
8.Pick the tangency end of the second line.
9.0K to create the line
The result is a smooth line between the two areas.
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Now create the third area as an arbitrary area through keypoints.
10.Main Menu> Preprocessor> -Modeling- Create> -Areas- Arbitrary> Through
KPs
l l.Pick 4 corners in counterclockwise order.
12.0K.
13.Toolbar: SAVE DB
Meshing
Of all the steps in this process, meshing is by far the most important step to
get an accurate modeling of your system. Meshing breaks up the areas of
your design into user defined shapes. The smaller the shape the more
accurate the analysis will be but the downside being the finer the mesh, the
longer the processing time. A good balance is needed between processing
time and resolution of the solution.
For most fluid modeling applications, only a 2D model is required so fromnow on I will separate the 2D and 3D commands.
2D Meshing (Do not use if modeling in 3D)
1. Utility Menu> Plot> Lines
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...,'
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2. Main Menu> Preprocessor> Mesh Tool
3. Choose Lines Set.
4. Pick all lines (in the picking menu).
Note (You can separate different regions of your design and mesh them differently if
you want, you will have to play with that stuffby yourself).
5. Apply (in the picking menu).
6. Enter 100 as the No. of
element divisions.
8. On the meshtool
menu, pick the option
for "free" mesh and
also "quad shape".
7. Enter 1 as the Spacing
ratio (-2 produces smaller
elements near both ends of
the line).
7. Apply.
9. Click "Mesh"
10. Pick all lines (in the picking menu)
11. Close the meshtool menu
This will mesh the entire design and for 2D designs and should look like the following
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If only modeling in 2D, you can skip the next section and start again at adding boundary
conditions.
3D Meshing
1. Main Menu> Preprocessor> Mesh Tool
The next step is to specify mesh controls in order to obtain a particular
mesh density.
2. Set global size controls.
3. Enter 0.005 for element edge length.
4. OK.
5. Mesh.
6. Pick All (in picking menu).
7. Close.
8. Close Mesh Tool.
9. SAVE DB
Some error messages might
pop up because of irregular
size elements but ignore these for now.
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Extrude the meshed area into a 3D meshed volume.
In this step, first changing the element type to Fluid 142, which is defmed as element type
2, and then extruding the area into a volume generates the 3-D volume.
1. Main Menu> Preprocessor> -Modeling- Operate> Extrude> Elem Ext Opts
2. Choose 2 (FLOTRAN 142) for Element type number.
3. Enter 30 for the No. of
element divisions.
4. OK.
5. Main Menu> Preprocessor>
-Modeling- Operate> Extrude>
-Areas- By XYZ Offset
6. Pick All (in picking menu).
7. Enter 0,0,0.002 (Where 0.002
if the height of your channel in em,
20 microns high) for offsets for
extrusion in the Z direction.
8. OK.
9. Close.
To examine the extruded design, use the commands in steps 10-11 below.
10. Utility Menu> PlotCtrls > Pan,
Zoom, Rotate
11. Choose ISO, then box zoom.
12. Close.
13. Toolbar: SAVE DB.
Unselect 2-D elements.
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Before applying boundary values to the micro fluidic channels, unselect all FLOTRAN
141 elements used in the 2-D area mesh since they will not be used for
the analysis.
1. Utility Menu> Select> Entities
2. Choose Elements.
3. Choose By Attributes.
4. Choose Elem type num.
5. Enter 1 for the element type number.
6. Choose Unselect.
7. Apply.
The 3D modeling design should now be constructed. The FLOTRAN parameters must
now be setup and added to the model.
Multiple species Laminar Analysis (both 2D and 3D)
Establish fluid properties.
Fluid properties will be established for water in
the cgs system.
1. Main Menu > Solution > FLOTRAN Set
Up > Fluid Properties
2. Choose CMIX for density. Leave
viscosity and conductivity and specific
heat as constant.
3. Click "yes" for allow density variations.
4. OK.
5. Enter 0.01 for viscosity and 0.04 for
conductivity. Leave specific heat at -1.
6. OK. (for next screen that pops up)
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Set execution controls.
Choose the execution control from the FLOTRAN
SetUp Menu.
tJILiIIIfl:U.11ER 1_. __ 1
EQC 61ol>llI_I.... 2 f' "
0I1iJII _vl"l PH ~it.. J>..... ==
1. Main Menu> Solution> FLOTRAN Set Up > - ..1 _ · .v --'
Execution Ctrl .. ..l......._,
2. Enter 40 Global iterations (Note: 40 global PRBO ....... _
iterations is arbitrary with no guarantee of 1'9IP I_~-convergence.) - fnlo_ ~iMt1~ .......,.. ' 1 '; . : . : ; ", : : :: : : '
BaI't: 'tWllb..l_t. .h .....JM.l::i_ t'..I~i,
Mu: 'I-Mh!.IIlI;lM 1IoJtN,Jt; 1,,"~ f.,. "~OOJ'~-u - at::I: tcI'W .... t : t . . ~'I"""Z"a. :b. -.pt:w
3. OK to apply and close.
Change reference conditions.
"""""""""""""""""" ', ., '"1'LDllo11l51.<MIP __ Opt. _
_ Ootpot -.lI bo_,~ jill~-...I
At the end of this tutorial there is a table of constants and reference conditions for water.
The reference conditions will have be changed to suit your design and units used.
1. Main Menu> Solution > FLOTRAN
Set Up > Flow Environment > Ref
Conditions
2. Change the reference pressure to
101350 (cgi units, equivalent to 1
atmosphere).
3. Change the nominal, stagnation, and
reference temperatures to 20°C.
4. Change bulk modulus to 0.21xl011
5. Change the temperature offset from
absolute 0 to 273.
7. OK.
8. Toolbar: SAVE DB.
Species Setup
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There are a lot of steps that will have to be completed for this process. Itis the same for
2D and 3D designs.
1. Main Menu > Preprocessor>
FLOTRAN Set Up>solution options
2. Highlight the multiple species
transport box.
3. OK
This turns on the multiple species
transport. Now you have to define all
the parameters for each liquid that is
added to the system.
First define the number of different liquids that are added to the system. In this case, two
different liquids are being modeled.
1. Main Menu > Solution > FLOTRAN
Set Up > Multiple species
In this case 2 species were used.
2. Enter 2 for Number of
species
3. Make sure the Algebraic
species number is set at 2.
4. OK
After clicking ok, the following
screen appears. For each species all
the parameters have to input.
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These windows are all connected so when "OK" is pressed it just brings you back to this
screen.
Main Menu> Solution > FLOTRAN
Set Up > Multiple species> Species#1 > general the following window
appears:
1. Change the "species name" to
something you can
remember.
2. Change the molecular weight
of the fluid to the one you are
using (18 in this case).
3. Leave mass fraction to 0.5 if
there is 2 species. If you
have 3 then change it to 0.3, 0.3, and 0.4 for the different species. This number
has to add up to 1, regardless of how many species there are.
4. OK
1. Main Menu > Solution >
FLOTRAN Set Up >
Multiple species > Species
#1 > solver
2. Set to "Precond conj re"
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3. OK
(preconditioned conjugate residual method) for both species, The other solver
options have not really been tried.
4. Change "No of search
vectors used" from 2
to 3.
5. OK
Species relaxation
1. Main Menu > Solution >
FLOTRAN Set Up > Multiple
species > Species #1 >
relaxation
2 . Change concentration relaxation
to 1.
3. OK
Enter fluid properties.
Main Menu> Solution> FLOTRAN Set Up > Multiple species> Species #1 >properties menu.
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Enter all density,
viscosity, conductivity,
mass fraction constants
and change the solution
options.
Enter all the
information you can on
all the constants.
All the data here is very important. To solve for density variations In the fluid
flow/mixing region.
1. Select density. . : . : I
2. OK.
3. For Density type enter
"liquid" .
4. For nominal value
enter the density (for
water it is 1 g/cm3)
5 . Also enter first and
second coefficients if
you have them.
6 . Click vary density yes.
7. OK
Do the same thing for the rest of the variables that you want solved and the parameters.
For constant inputs, enter CONSTANT for the "type" and enter the nominal value.
HINT! ! If you want to plot density differences in the graphs later on, let the nominal
value for density of species 1 be 1.0 and the density of species 2 to be 1.001. Ansys will
apply colors to the two densities (red and blue) and with this little difference, mixing can
be plotted. You can also do the same for viscosity if that is to be plotted also.
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1. Main Menu> Solution> FLOTRAN Set Up >Multiple species> Species #1 >fluid properties> mass diffusion.
3. OK
2. Enter 0.000013 for
the nominal value.
4. SAVE DB
The mass diffusion constant
IS the most important
constant for mixmg
modeling. Make sure the
constant for this IS as
accurate as possible. (See
sheet at end of tutorial).
Click "EXIT Properties Panels" when done. Enter properties for both species.
One last thing to change:
1. Main Menu> Solution> FLOTRAN Set Up >Multiple species> Capping
2. Click "yes" for cap mass fraction.
3. OK
Click "cancel" to exit the main "multiple Species" panel.
Boundary Values
Now comes the fun part, adding velocities and pressures to the lines and areas.
It is slightly different for adding boundary values to 2D and 3D designs but for the most
part, it is similar so I will cover both at the same time.
A velocity of 0.1 cm/s is applied in the X direction (VX) at the inlet, and a zero velocity
is applied in the transverse direction at the inlet (VY in the Y direction). Zero velocities in
both directions are applied all along the walls, and a zero pressure is applied at the outlet.
Apply the inlet boundary condition.
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1. Main Menu > Preprocessor > Loads > -Loads- Apply > -FluidlCFD- Velocity >
On Lines (2D) [On Areas (3D)].
2. Pick the inlet line (the vertical JtJ
line at the far left).
3. OK
4. Enter 0.1 for VX. (2D and 3D).
5 . Enter 0.0 for VY. (2D and 3D).
6. Enter 0.0 for VZ (3D only)
7. OK
Select the second arm of the
micro fluidic design.
1. Main Menu > Preprocessor> Loads > -Loads- Apply> -Fluid/CFD- Velocity >
On Lines (2D) [On Areas (3D)].
2. Pick the inlet line (angled line on the lower left).
3. OK
4. Enter 0.0707 for VX. (2D and 3D).
5. Enter 0.0707 for VY. (2D and 3D).
6. Enter 0.0 for VZ (3D only).
7. OK
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The following picture should appear.
Next, apply the wall boundary conditions. Choose the lines that make up the walls and
then apply zero velocities in the X and Y directions.
1. Main Menu > Preprocessor > Loads > -Loads- Apply > -FluidlCFD- Velocity >
On Lines (2D) - [On Areas (3D)]
2. Pick the five lines
(or 8 areas) on the
top and bottom.
3. OK
4. Enter 0.0 for vx :and VY. [Enter
0.0 for VZ (3D)].
5. OK
One of the following pictures should appear for 2D or 3D.
2D
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3D
Apply the outlet condition.
1. Main Menu > Preprocessor > Loads > -Loads- Apply > -Fluid/CFD- Pressure
DOF> On Lines. [On Areas (3D)).
2. Pick the outlet line (vertical line on the far right) or (output areas for 3D).
3 . OK
4. Enter 0 for the
pressure value.
5 . Set endpoints
to yes.
6. OK
7. Toolbar:
SAVE DB.
After the flow rates and pressures are added to the model, the species will now be added.
In multiple species transport, there are 2 or more inputs and a single output so mixing can
be studied. For each input arm, both species have to be added.
Main Menu > Preprocessor > Loads >
-Loads- Apply > -Fluid/CFD-Species >
On Lines (2D) [on Areas (3D)]
Apply Species.
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1. Click on the left vertical line.
2. APPLY
3 . Pick species #1. ~
4. OK
5. Enter percentage of that species
for that input location. (1 IS
100%). 1 in this case.
6. OK
7. Highlight "yes" for another
species.
8 . OK
9. Click species #2
10. OK
11. Enter other loading factor
(0 for this case).
12. OK
13. Highlight "No"
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14. OK
15. Repeat for the angled input. But reverse the species, 0 is now species I and 1.0 is
species 2.
16. SAVE DB
Both species are now added to the two inputs and the image should look like the
following.
Everything should be setup up now and the solution can now be run.
Execute FLOTRAN solution.
1. Main Menu> Solution> Run FLOTRAN
2. Close the information window when the solution is done.
While running the FLOTRAN solution, ANSYS will plot the "Normalized Rate of
Change" as a function of the "Cumulative Iteration Number." This is the Graphical
Solution Tracker, which allows visual monitoring of the solution for convergence.
This step might take some time so be patient, especially the 3D modeling.
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Post processing (Laminar Analysis)
Read in the results for post processing.
Enter the general postprocessor and read in the latest set of solution results, and then
create a vector plot.
1. Main Menu> General Postproc > -Read Results- Last set
Plot velocity vectors.
1. Main Menu> General Postproc > Plot Results> -VectorPlot- Predefined
2. Choose DOF solution.
3. Choose Velocity V.
4. OK.
1. Main Menu> General Postproc > Plot Results> -VectorPlot- Predefined
2. Choose Nodal solution.
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3. Choose Velocity Vx or Vy.
4. OK.
2DVx
2DVy
This gives the velocity
profiles for the x and y
direction in the
channels. Red is the
highest pressure.
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3DVx
These images show a generalized velocity profile in the micro fluidic system. Ifusing 3D
you can rotate the design to get a better angle.
Plot total density variations.
1. Main Menu> General Postproc > Plot Results> -Contour Plot- Nodal Solu
2. Choose other quantities.
3. Choose Density, DENS.
4. OK.
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2D Density variations
3D Density
variations
These results show the mixing of the two species. If viscosity is varied, you can plot that
also. The degree of mixing depends on the mass diffusion constant. For this model that
constant was 0.00001, which is not accurate. I used this number to show off the mixing
modeling and this is not a real world model. Do some research for the fluids you are
using and make sure this constant is accurate.
Plot total pressure contours.
1. Main Menu> General Postproc > Plot Results> -Contour Plot- Nodal Solu
2. Choose Other quantities.
3. Choose Total Pressure, PTOT.
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4. OK.
The resulting contour plot shows the total static and dynamic pressures that occur in the
system.
Animate velocity of trace particles.
Animation cannot be used with this design because of the small size. But in a larger
micro fluidic channel a movie can be made of the motion. The following procedure can
be used to do that.
1. Main Menu> General Postproc > Plot Results> -Flow Trace- Defi Trace Pt
2. Pick two or three points around the inlet region and one or two points in the
recalculation region (along the upper wall of the transition region).
3. OK (in picking menu).
4. Utility Menu> PlotCtrls > Animate> Particle Flow
5. Choose nOF Solution.
6. Choose Velocity VX.
7. OK.
Ignore any warning messages about maximum number ofloops (Choose Close).
The resulting trace plot shows the path of flow particles.
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8. Make choices in the Animation Controller (not shown), if necessary, then choose
Close.
Make a path plot of velocity through the outlet.
1. Main Menu> General Postproc > Path Operations> Define Path> By Nodes
2. Pick the lowest
and then the highest
point just on the other
side where the two
fluids come together.
3. OK (in picking
menu).
4. Enter Mixers for
the Path Name.
5. OK.
6. File> Close (Windows)
Now specify the velocity in the X direction (VX) to map onto the path.
7. Main Menu> General Postproc > Path Operations> Map onto Path
8. Enter DENSITY as label.
9. Choose other quantities.
10. Choose DENS.
11. OK.
12. Main Menu> General Postproc > Path Operations> -Plot Path Item- On Graph
13. Choose the label DENSITY that you previously defined.
14. OK.
15. Close any warning messages.
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This is the density profile immediately after the intersection of the two flows.
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Fluid flow modeling with obstructions in the channel.
This tutorial is a simple model to show the important features for modeling fluid flow
with pillars and shapes in the fluid flow. The beginning is similar to the 2D model shown
above with few important differences. The design is a 250 urn wide by 5 mm long
channel which has two 50 urn square pillars evenly spaced in the channel.
Start the ANSYS program with a new jobname.
Set preferences.
You will now set preferences in order to filter quantities that pertain to this discipline
only.
1. Main Menu >Preferences
2. Turn on
FLOTRAN CFD
filtering
3. OK.
Define element type. (2D)
4. Main Menu> Preprocessor> Element Type> Add/Edit/Delete
5. Add an element type.
6. Choose 2D FLOTRAN element (FLUID14l).
7. OK.
8. Close.
Units
9. Main Menu > Preprocessor > Material
prop > material library> select units
10. Choose the cgs system
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11. Main Menu> Preprocessor> Materials > temperature unit
12. Choose the Celsius scale
Create Keypoints:
In fluid modeling, it is best to have a single area defined. Original tests were done where
rectangles were made and merged together. This method did not work well and it was
decided to enter the coordinates of all the vertices of the design and connect all the points
to create a 2D area. This 2D area can then extruded to make the 3D design.
To add keypoints to a coordinate system:
Preprocessor -> -Modeling- Create -> Keypoints -> In Active CS...
Fill in the fields as shown below, then click "APPLY". When you click on "Apply", thecommand is issued to create keypoint number 1 at (x,y)=(O, 0). Note that when the Z
field is left blank, in this case, the blank space defaults to zero, which is desired. Since
you clicked on "Apply", instead of "OK", then the keypoint creation box remains open.
Enter all of your keypoints in this manner. Units are in cm and for this design the
channel is 8.5 mm long and 250 microns wide.
Keypoint # X Coordinate Y Coordinate
2 0.025 0
3 0.025 0.5
4 0 0.5
5 0.005 0.56 0.010 0.5
7 0.015 0.5
8 0.020 0.5
9 0.005 0.45
10 0.010 0.45
11 0.015 0.45
12 0.020 0.45
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When the final keypoint is entered, click on "OK" instead of "APPLY". "OK" issues the
command and also closes the keypoint creation box.
Before moving on, it is probably a good idea to check the keypoint locations. Along the
top toolbar:
U A b f ii ff ll j' d iq q i ,i tl ii t! n W ; ; ; ,
Choose: List -> Keypoints -> Coordinates Only. A box should open up with the keypoint
location information. If any keypoint is not in the correct location, at this point, you can
just re-issue the keypoint creation command for that particular keypoint. To do this,
choose:
Preprocessor -> -Modeling- Create -> Keypoints -> In Active CS...
Fill in the correct information for that particular keypoint in the box, andclick "OK". The keypoint will be moved to the correct location. If you
have some keypoint incorrectly numbered above number 12, this will
not cause a problem. Just be sure you have keypoint numbers 1 thru 12
located correctly.
You can close the box listing the keypoint locations, by clicking, in that
listing box, on "File-> Close".
Create areas
In this design, all lines connecting the keypoints are straight lines so the
following command is used.
Main Menu> Preprocessor> -Modeling- Create> -Areas- Arbitrary >
By Lines
Connect the four outside points to form the outside area then connect the
other keypoints so it forms two squares as shown in the picture at the
right. The following area is created.
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Area subtraction.
To form the model system, the two small squares have to be subtracted from the larger
channel.
1. Main Menu> Preprocessor> -Modeling- Operate> Subtract
2. Itask you first for the area to subtract from so pick the larger area.
3. OK
4. Pick both of the small squares.
5. OK
You can always unpick an object by changing the setting on the picking
menu. This might have to be down in Step 1. Usually one square is also
highlighted so just it from "pick" to "unpick" in
the menu, un-highlight the square and click OK.
When done properly the following image should
be seen.
Meshing
II II
Of all the steps in this process, meshing is by far the most important step to get an
accurate modeling of your system. Meshing breaks up the areas of your design into user
defined shapes. The smaller the shape the more accurate the analysis will be. With the
downside being the finer the mesh, the longer the processing time. A good balance is
needed between processing time and resolution of the solution.
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Meshing for this is design slightly different than the channels in the first tutorial. The
regions around the square have to be meshed differently than the rest of the channel for
the modeling to be accurate.
1. Utility Menu> Plot> Lines
2. Main Menu> Preprocessor> Mesh Tool
3. Choose Lines Set.
4. Pick the four lines that surround the full channel.
5. Apply (in the picking
menu).
6. Enter 100 as the No. ofelement divisions.
7. Enter 1 as the Spacing ratio
(-2 produces smaller elements
near both ends of the line).
8. Apply.
9. No pick the 8 lines that
form the squares.
10. OK
11. Enter 15 for the No. of element divisions.
12.Enter -2 as the spacing ratio. (The reason for the two-mesh
spacing is to make the mesh element for the larger rectangle
and the space between the squares comparable. If this is not
done and all the lines are meshed the same, there will be no
flow between the squares and that is incorrect.)
13. On the meshtool menu, pick the option for "free" mesh and
also "quad shape".
14. Click "Mesh"
15. Pick all lines (in the picking menu)
16. Close the meshtool menu
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This will mesh the entire design and for should look like the following image.
Establish fluid properties.
Fluid properties will be established for
water in the cgs system.
NOTE: The images that follow in the
instructions below so not have the
correct values entered. The images
are from the tutorial above, change
the numbers accordingly.
1. Main Menu > Solution >
FLOTRAN Set Up > Fluid Properties
8. Choose Liquid for density,
viscosity and conductivity. Leave
specific heat as constant.
9. There should be no variations in
the modeling so they should be all
"no"
10. OK
11. Enter 1.0 for density, 0.01 for viscosity and 0.04 for conductivity. Leave specific
heat at-1.
5. OK
Set execution controls.
IlILNIUJ, I TER l't"fttfti_ c..t:-r.l
IIPPE .)'-fl -flU oWppiM f , . . . .
Choose the execution control from the FLOTRAN
SetUp Menu.
1. Main Menu> Solution> FLOTRAN Set Up >
Execution CtrlPREI ,., .. .. . .. .. .
DaIS t.wl.:w.t . 1 - . . . . .1,"t1_
" " t . = ''I')'flllliMtw.- c - ' M o e ' J i . 1", ~ r .) " . . . DGf
u - at:l: tcl'WWt:t . . ~ ' I " " " Z " " ":b. ~t:w.""""""""""""""""" ', ., '"
LPl..Uit..sl~aI1P o.t.p.t. Opt..i-1
39 ~ OIII~:pIIII~~» f~,~
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2. Enter 40 Global iterations (Note: 40 global iterations is arbitrary with no guarantee
of convergence.)
3. OK to apply and close.
Change reference conditions.
At the end of this tutorial there is a table of constants and reference conditions for water.
The reference conditions will have be changed to suit your design and units used.
1. Main Menu > Solution >
FLOTRAN Set Up > Flow Environment>
Ref Conditions
2. Change the reference pressure to
101350 (cgi units, equivalent to 1
atmosphere).
3. Change the nominal, stagnation,
and reference temperatures to 20°C.
4. Change bulk modulus to 0.21x1011
5. Change the temperature offset from
absolute 0 to 273.
17. OK.
7. Toolbar: SAVE DB.
Boundary Values
--- - -- --
Now comes the fun part, adding velocities and pressures to the lines.
A velocity of 0.1 cm/s is applied in the Y direction (VY) at the inlet, and a zero velocity is
applied in the transverse direction at the inlet (VX in the X direction). Zero velocities in
both directions are applied all along the walls and squares, and a zero pressure is applied
at the outlet.
Apply the inlet boundary condition.
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1. Main Menu > Preprocessor> Loads > -Loads- Apply > -Fluid/CFD- Velocity >
On Lines
2. Pick the inlet line (the horizontal line at the bottom).
7 . OK
3. OK
4. Enter 0.0 for Vx.
5. Enter 0.1 for Vy.
6. Leave Vz blank
Wall boundary conditions
Choose the lines that make up the vertical walls and also the lines that form the squares
and apply zero velocities in the X and Y directions.
1. Main Menu > Preprocessor> Loads > -Loads- Apply > -Fluid/CFD- Velocity >
On Lines
2. Pick All.
3. OK
4. Enter 0.0 for Vx and Vy.
5. OK
Apply the outlet condition
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6. Main Menu > Preprocessor > Loads > -Loads- Apply > -FluidlCFD- PressureDOF> On Lines.
7. Pick the outlet line (horizontal line on the top).
8. OK
10. Set endpoints to Yes
9. Enter 0 for the pressure value.
11. OK
12. Toolbar: SAVE DB.
When all the boundary conditions are inputted, the design should look
like the following.
Execute FLOTRAN solution.
1. Main Menu> Solution> Run FLOTRAN
2. Close the information window when the solution is done.
While running the FLOTRAN solution, ANSYS will plot the "Normalized Rate of
Change" as a function of the "Cumulative Iteration Number." This is the Graphical
Solution Tracker, which allows visual monitoring of the solution for convergence.
Post processing
Read in the results for post processing.
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Enter the general postprocessor and read in the latest set of solution results, and then
create a vector plot.
1. Main Menu> General Postproc > -Read Results- Last set
Plot velocity vectors.
1. Main Menu > General Postproc > Plot
Results> -VectorPlot- Predefined
2. Choose DOF solution.
3. Choose Velocity V.
4. OK.
1. Main Menu> General Postproc > Plot Results> -VectorPlot- Predefined
2. Choose Nodal solution.
3. Choose Velocity Vx or Vy.
4. OK.
Vx
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Vy
These images show the velocity profile for the micro fluidic system above.
Make a path plot of velocity through the outlet.
1. Main Menu> General Postproc > Path Operations> Define Path> By Nodes
2. Pick the nodes near the outlet of the squares.
3. OK (in picking menu).
4. Enter Velocity for the Path Name.
5. OK.
6. File> Close (Windows)
Now specify the velocity in the Y direction (Vy) to map
onto the path.
7. Main Menu> General Postproc > Path Operations>
Map onto Path
8. Enter Velocity as label.
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9. Choose nOF solution.
10. Choose Velocity Vy.
11. OK.
12. Main Menu> General Postproc >
Path Operations> -Plot Path Item- On
Graph
13. Choose the label Velocity that you
previously defined.
14. OK.
15. Close any warning messages.
Make a path plot of velocity through the outlet (second location).
1. Main Menu> General Postproc > Path Operations> Define Path> By Nodes
5. OK.
2. Pick the nodes near the outlet of the squares.
3. OK (inpicking menu).
4. Enter Velocity for the Path Name.
6. File> Close (Windows)
Now specify the velocity in the Y direction (Vy) to
map onto the path.
7. Main Menu> General Postproc >Path Operations> Map onto Path
8. Enter Velocity as label.
9. Choose nOF solution.
10. Choose Velocity Vy.
11. OK.
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12. Main Menu> General Postproc > Path Operations> -Plot Path Item- On Graph
13. Choose the label Velocity that
you previously defined.
14. OK.
15. Close any warning messages.
These graphs show the velocity
profiles for two slices in the
modeling. Any area can be analyzed
in this way.
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Complex 3D structure modeling
In this set of instructions, the steps for modeling fluid flow in complex 3D structures are
described. Many of the steps are similar to one shown above with several important
differences. I will model a simple microfluidic channel that has large interconnect
reservoirs on the ends of the channels. This will demonstrate what happens to the fluid
when needles and reservoirs are used in conjunction with small micro fluidic channels.
Start a new ANSYS filename as shown above.
Set preferences.
You will now set preferences in order to filter quantities that pertain to this discipline
only.
1. Main Menu >
Preferences
2. Turn on FLOTRAN
CFD filtering
3. OK.
Define element type.
4. Main Menu> Preprocessor> Element Type> Add/Edit/Delete
5. Add an element type.
6. Choose 2D FLOTRAN element (FLUIDI41).
7. Choose 3D FLOTRAN element (FLUID 142).
8. OK.
9. Close.
Units.
10. Main Menu > Preprocessor > Material
prop >material library > select units11. Choose the cgs system
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Note: All units shown in this tutorial are in cgs units.
Main Menu > Preprocessor > Materials >
temperature unit
12. Choose the Celsius scale
~ ICreate Keypoints:
Keypoints for the design will be entered here. What will be entered are the coordinate for
the channel, reservoirs and needle inputs. 2D areas will first be made then extruded into
the 3D design.
IMPORTANT!! When doing 3D modeling, the areas have to overlap slightly. Areas
that butt up against each other WILL NOT work with this simulation. Be aware of thiswhen inputting your points.
To add keypoints to a coordinate system:
Preprocessor -> -Modeling- Create ->Keypoints -> In Active CS...
Fill in the fields as shown below, then click "APPLY". When you click on "Apply", the
command is issued to create keypoint number 1 at (x,y)=(-0.06, 0.00625). Note that
when the Z field is left blank, in this case, the blank space defaults to zero, which is
desired. Since you clicked on "Apply", instead of "OK", then the keypoint creation box
remains open.
Enter all of your keypoints in this manner.
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Keypoint# X Coordinate Y Coordinate Keypoint# X Coordinate Y Coordinate
2 0 0.075 17 0.95 -0.075
3 -0.15 0.075 18 0.95 0.075
4 -0.15 -0.075 19 0.8 0.075
5 0 -0.075 20 0.86 0.006256 -0.06 -0.00625 21 -0.075 -0.01
7 0.3 -0.00625 22 -0.075 0.01
8 0.29375 -0.36 23 -0.095 0.01
9 0.225 -0.3 24 -0.095 -0.01
10 0.225 -0.45 25 0.29 -0.375
11 0.375 -0.45 26 0.29 -0.395
12 0.375 -0.3 27 0.31 -0.375
13 0.30625 -0.36 28 0.31 -0.395
14 0.3125 -0.00625 29 0.895 -0.01
15 0.8 -0.00625 30 0.875 -0.01
16 0.8 -0.075 31 0.875 0.0132 0.895 0.01
When the final keypoint is entered, click on "OK" instead of "APPLY". "OK" issues the
command and also closes the keypoint creation box.
Before moving on, it is probably a good idea to check the keypoint locations. Along the
top toolbar:
i M § j ? i E J b : H F t ,l d i j ' iO " ; i §! ,
Choose: List -> Keypoints -> Coordinates Only. A box should open up with the keypointlocation information. If any keypoint is not in the correct location, at this point, you can
just re-issue the keypoint creation command for that particular keypoint. To do this,
choose: Preprocessor -> -Modeling- Create -> Keypoints -> In Active CS...
Fill in the correct information for that particular keypoint in the box, and click "OK".
The keypoint will be moved to the correct location. If you have some keypoint
incorrectly numbered above number 12, this will not cause a problem. Just be sure you
have keypoint numbers 1 thru 12 located correctly.
You can close the box listing the keypoint locations, by clicking, in that listing box, on
"File-> Close".
The keypoints should look like the image below.
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Create areas.
In this design, all lines connecting the keypoints are straight lines so the following
command is used.
Main Menu> Preprocessor> -Modeling- Create> -Areas- Arbitrary> By Lines
There are seven separate regions that have to be made into areas. There are 3 small
squares that represent the needle inputs, 3 larger squares that are the reservoirs and the
micro fluidic channeL So make three small square using the above command, three larger
squares and the micro fluidic channel so it looks like the image below.
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Save your work Toolbar: SAVE_DB
Extrude the meshed area into a 3D meshed volume.
In this step, first changing the element type to Fluid 142, which is defmed as element type
2, and then extruding the area into a volume the 3-D volume.
1. Main Menu> Preprocessor>
-Modeling- Operate> Extrude>
Elem Ext Opts
2. Choose 2 (FLOTRAN 142) for
Element type number.
3. Enter 20 for the No. of element
divisions.
4. OK.
5. Main Menu> Preprocessor>
-Modeling- Operate> Extrude>
-Areas- By XYZ Offset
6. Choose the small squares that
represent the needles and extrude then 0.21 cm in the Z direction.
7. Apply
8 . Choose the 3 larger
squares that represent the
reservoirs and extrude
then 0.20 em in the Z
direction.
9 . Apply
10. Choose the micro fluidic
channel and extrude it
0.01 em m the Z
direction.
11. OK
12. Close
The resulting 3D model should
look like the following:
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Unselect 2-D elements.
Before applying boundary values to the micro fluidic channels, unselect all FLOTRAN
141 elements used in the 2-D area mesh since they will not be used for the analysis.
1. Utility Menu> Select> Entities
2. Choose Elements.
3. Choose By Attributes.
4. Choose Elem type num.
5. Enter 1 for the element type number.
6. Choose Unselect.
7. Apply.
Overlap 3D volumes.
This step you overlap the seven different volumes. I tried adding together the volumes
but that does not seem to work.
1. Main Menu> Preprocessor> -Modeling- Operate> Overlap
2. Pick all seven volumes.
3. OK.
The 3D modeling design should now be constructed.
Meshing
Of all the steps in this process, meshing is by far the most important step to
get an accurate modeling of your system. Meshing breaks up the areas of
your design into user defined shapes. The smaller the shape the more
accurate the analysis will be but the downside being the finer the mesh, the
longer the processing time. A good balance is needed between processing
time and resolution of the solution.
The next step is to specify mesh controls in order to obtain a particular mesh
density.
1. Main Menu> Preprocessor> Mesh Tool
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2. Set global size controls.
3. Enter 0.005 for element
edge length.
4. OK.
5. Mesh.
6. Pick All (in picking menu).
7. Close.
8. Close Mesh Tool.
9. SAVE DB
Boundary Values
Now comes the fun part, adding velocities and pressures to the areas.
IMPORTANT!! Do not add velocities to the areas inside the volumes. Only the areas
that are exposed to the outside get boundary values.
A velocity of -0.1 cm/s is applied in the Z direction (VZ) at the inlet, and a zero velocity
is applied in the transverse direction at the inlet (VX, VY). Zero velocities in all three
dimensions are applied on all exterior areas, and a zero pressure is applied at the outlet.
Apply the inlet boundary condition.
1. Main Menu > Preprocessor > Loads > -Loads- Apply > -Fluid/CFD- Velocity >
On Areas.
2. Pick the two needle inlets areas.
3. OK.
4. Enter 0.0 for VX.
5. Enter 0.0 for VY.
6. Enter -0.1 for VZ.
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7. OK
Now, doing a couple of areas at a time, select all other outside areas (except for the
needle outlet) and apply a 0.0 to VX, VY and VZ.
8. OK
Apply the outlet condition.
1. Main Menu> Preprocessor> Loads> -Loads- Apply> -Fluid/CFD- Pressure
DOF> On Areas.
2. Pick the outlet needle area.
3. OK.
4. Enter 0 for thepressure value.
5. Set endpoints to
yes.
6. OK.
7. Toolbar: SAVE DB.
After all the pressures and
velocities have been addedto the model, the following
picture will appear. This is
the most difficult step so be
careful and take your time.
If you miss an area, the simulation will not work.
Establish fluid properties.
Fluid properties will be established for water in the cgs system.
1. Main Menu> Solution> FLOTRAN Set Up > Fluid Properties
2. Choose liquid for density and viscosity. Leave conductivity and specific heat as
constant.
3. OK.
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4. Enter 1.0 for density, 0.01 for viscosity and 0.04 for conductivity. Leave specific
heat at-1.
Choose the execution control from the FLOTRAN
SetUp Menu.
1. Main Menu> Solution> FLOTRAN Set Up > - ..,_ ----,
Execution Ctrl .. .., ~-'
2. Enter 40 Global iterations (Note: 40 global P " "" . .. .. .. _
iterations is arbitrary with no guarantee of 1"911' I_~-convergence.) - Tnllo_. ~iMU~.......,..
5. OK.
Set execution controls.
3. OK to apply and close.
Change reference conditions.
At the end of this tutorial there is a table of
constants and reference conditions for water.
The reference conditions will have to be
changed to suit your design and units used.
1. Main Menu> Solution> FLOTRAN Set
Up > Flow Environment> Ref Conditions
2. Change the reference pressure to 101350
(cgs units, equivalent to 1 atmosphere).
3. Change the nominal, stagnation, and
reference temperatures to 20°C.
4. Change bulk modulus to 0.21x1011
5. Change the temperature offset from
absolute 0 to 273.
I:JILIIiITI:U.lrER 1_ __ 1
EQC 61o>l_I ....
Mu: 'I-Mh!.IIlI;lM 1f,JtN,Jt; 1,,"~ f.,. .. oopU it::I: -tc.. .... th ~I"'"Z"ka h. -.ptw
"""""""""""""""""" ', ., '"L I'L DIIoI1 l51 .< MlP _ _ Opt. _
_., Oo~po~ -.lI £..._~ ' = - - , 9 _ ' _..I
- ~ ----~----
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6. OK.
7. Toolbar: SAVE DB.
The modeling should be ready to be run.
Execute FLOTRAN solution.
1. Main Menu> Solution> Run FLOTRAN
2. Close the information
window when the solution
is done.
While running the
FLOTRAN solution,ANSYS will plot the
"Normalized Rate of
Change" as a function of
the "Cumulative Iteration
Number." This is the
Graphical Solution Tracker,
which allows visual
monitoring of the solution
for convergence.
This step might take sometime so be patient, the output should look similar to the following.
Post processing (Laminar Analysis)
Read in the results for post processing.
Enter the general postprocessor and read in the latest set of solution results, and then
create a vector plot.
1. Main Menu> General Postproc > -Read Results- Last set
Plot velocity vectors.
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1. Main Menu> General Postproc > Plot Results> -VectorPlot- Predefined
2. Choose DOF solution.
3. Choose velocity v.
4. OK.
1. Main Menu> General Postproc > Plot Results> -VectorPlot- Predefined
2. Choose Nodal solution.
3. Choose Velocity Vx or Vy.
4. OK.
Vx
" . : . . ' . _ I I I~- ,
. . . .~ . ; , , : :# .; ,~,~ I
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Vy
This gives the velocity profiles for the x and y direction in the channels. Red is the
highest pressure. These images show that the output is turbulent.
These images show a generalized velocity profile in the micro fluidic system. Ifusing 3D
you can rotate the design to get a better angle.
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Constant tables:
DIFFUSION COEFFICIENTS T N LIQUID ATr 1' 1 11'E DIL nON
T h ~t ub lc I l~ 1 Sd if Ji Is io n c oe mc ic nl s D J Ji :H l nf in iu : d ih n io n f or s om e h iM ! ,} ' l iq uI d n 1i .'c C Ur d.I \Hhough V3.1ua: iIlIrcCiVtlllO [W'O d ec ima l p l ~ .
me as ur em e nt s i n I he : J t l tt ; ; :nute e re o f te n i n p o or a g re emc sn, 1 1 1 cr e fo r c: r ll O : f lV8 lu ~ I n Ihr: t IIblc c:aDtlCI be re [itd upon 10 MUtt' ' h J : In 11 )%.Sol\'CI1t,,~nre l i $ 1 c t d i n ! I ~p . h a bct . ie a l o r de r. i ! : ! ! . a ft th e S i Qh H ~~w h hl ll e ll en s e lv e m g r ou p .
IlEFEREl'iCIl
ullnloll·ll<lrns'cil1. ~ufi.Itrim' Data ( 1 1 m FtU lc l J 'ohaJ Rel t l li tJ tl ,S l tt } ) ' :' f ilf .5cie1f~i!and Tedmofoxy . S i xt h E d ni on . Vol . 1 1 JS : :t .1 9 6 9 .
D ., D .,S()lul~ S!!Jln_r l ! IfC I~t.lu~:vj .Su l u ( ( SoI .. . 1 ti"C lO~mllf·1
ACdic :8dd A , c : c : ' O U c 2 .1 >,)1 Awono T~rolC 'bk l rnmrth l ln l : 2~ I.n
IJrnDilk-itid A~I-mc: 25 2.62 1kni:l:11t1 l'drncll~hnnc l.l 1.A2
ronnu;.\Cid A_ n ),77 C~oh""",,, Te.ratliloromc=lh:lne 2.1 1,)0
NImJb:.I!I1.tn.; A_ 2D 2.94 EUunol T e c l " l l C h t o t o r n e c h : I n C l l~ LW
TCtniCh'Poro:mcLham:: Ar:ctOf1; II 3 . 1 : 9 l-odjrl( TCJI':1ltb'I01(ImCtM:Iono ro 1.6l
Trictllorvr:Mtti':lri;:: Amonl.1 2~ )064 T m : M 6 t o 1 1 m ' t 'l u J w : : Ttt r .ach lMome:th~l_e 25 I,U
w" ' ' ' " A«lol. 'lc 2) 4 _ 5 0 6 Aei:'ll('ldd -rol~ ~ 2,26
ACC li c . . rd Dcozene: l.) 2.09 Ikn>rc< Toluene ~ l,)4
l\lfuliN: B= a s 1.0il 1I<n<cI"ckI Toluene: U 1..9
~a.cid
-25 L l S Cy<.l ........ Te tueee ~ 2.'2
B romobcn1.cnc
-S L~S l)1mieacid TollJ""1:: IS 2.6~
],.p- ~ 30 2.0\1 Wllct To l uene lS 1,19
Chtornd~yl{!'tll!' s....:" R 1.17 I I o e c - t a n c Tric.nktn:ttn:~ a s L,
C y < I o he . . .. B~;r&:tie 25 l.Z, Ik.n.~"c T r i : t d " ro l ' i' l C !l : h .l ! n t 2~ 2,89
E_I Ikmcn. 2S 1.02 2~Uu1anonc ,irich~oo 15 1,1l
FonniC"lci6 Brnl(tle 15 2ol I ! IhIrylo'!ledmc T r l f J l 1 . l . o r W ' I l l d h o : r i n l O t '2l 1.71
I[lfrrt~ B~·.IlO 25 1.71 OlL'tli), lrl'hCt ' r r i e h l i l l l 'C l l f t e 1 N . n l i ! l lS 2.11
Mlt! lunDl Bcn1i.fIIt U ),00 "'-!w",1 Trieh'orOmclh;[lICI 15 noTo!""", !k.=1. U I.5 i!Ihyl"[!(I~I(! Tric.1:dorolfidh=-ltJO z s 1.02
I .! . . . •"1r i -chlOrobe tlUM .EkrrV1JlC! S 1 . .1< AC.:'tLCo.e!d W'l ' t lC l r rs 1.29
TriddQmlnr:tt1:mtl lfc:llCN:' 25 2 .26 Accl IDm: ' \V.ln 2.1 1,2
Adip l<>< id Hlijlam .'ll 30 0.4' A~10Bllrih: W.t« IS 1.1£- • • B l . l ll n o l 25 1.00 Allmir.rc Water IS 0.91
EH.~n)1 1-8utn rml IS, 0.6. AII)'liIIlmfral WltJ:'r IS 0 '1<)
But)'ritolcld ' · 6 V : t i U ' l r ; ) 1 )0 O , ~ l Aal l i l ' lCl W tc" t 20 Og;!
p-DKhkmlben: l !C f i .e 1 ·0 ... .. 1 n 0,12 AruiDOK W:l.la 20 0 . 6 1 1
" '. . . . . . . . . , - B u u u 1 I Q 1 l< l OJ99 ._ W.II ler 1. 1m
OI",.dIl l~lJlilll:looL )0 0.2S I · U L i l ! I J . .o [ \ \ · , . , , ! r o : r z s oJ6
P""_ I-OLJIIJiol II I.S) Cop<QI, . . . .. \V:alcr l.l .,It)
'A'I.1~ ,.BUl i lJ lol 1$ 056 O IfDn)C tbyk'nc W .te:r 25 134
Bcnzmt Cy<_ Il 1 .41 Cy<. loh • . . . . , w , , , , , 20 0,3- l
'fC'f.I 'IoI!hl«ortll,; 'thOLI.'ICI C y< .1 01 >= . . 11 149 D i d b ) o l n . m [ t ' I C ' W"' tL'1 '
' " M
Tal..... C)'eloh':j(.m~ 2.1 I.l1 "tlm",,1 Wm: t c r lS 1.:24
All)'lol_1 &1 ' : I : ' 1 l O 1 I. 0,98 HlhiinotuniJX' WltCf II Uli
Ik.",.. _I 1! r.s: C-Ihyt l l ta:tatr,! W.nlJ: r I. 1.00
I W i n e . Ellunol 2$ U2 61hylbor=lI< W I I I , ; : : r 20 O,iIlodobcRtnKI
-2. 1.00 " ,h yl . . , 1 1 1, .. .. Wall:t 2 .1 1.1&
J.hlc--tlri)'I·'''''utl1nol "'....I 20 031 01"""" WltJ:'f 2S 0.6.1
Pyndo.. ~,.. . , . 20 1.\. OI)Wnll Wttf:_, 2l 1,06
y.C'~rO«lft' lCthnnr: ElhInol 1l 1.50 (j1)~jJ]1:i W i I o l . C : r 2S L O S
w..t ~l 2S 1 .2 . UiCl(l3 lC' Willet IS O.JS
" ' c : c n ~ add IWIrt~tc 2 . 2.11 M; . tm~ Wnl-ct 1 5 OJ8
1Lr;:-d(In(! I'lh)'l_'''' 2 . 1.li Ml l I 1 l 1 i l l J o l \Vlt.~r IS 0,)0
2 · B U I S r J O n C a J ry l : ! L ( ct l L lc 3. l_9J MI;L}iMF; \"'all:r ~ 1,<9
E'h)"I_. Elhylll(let.'II-C' 2 . tSl Ml. " ' lhmol W.tDf II 1,21
N_ ! ; ol ly l ~ . ~ . . . ID US Hltohrl,I·~." ...1 WII[~ 10 0.69
Wilki E!h)i~1tCUll: M no MCO.ylcycl""", , , . . . , WiIIllI;l.r 10 0.1$
B_ "_, 2S l.91 f 'M'nol WILl"'" 20 0.89
T o l u e R C ' tkpt&oll: 2S l.n I-Pt"", ...1 Wtl~_'r IS 0 , 1 1 7
~~ H e . ( ; ; U I 1 l l B 2.60 1- W.ft lt :r 21 I,"
).B_ U~I,' ! 30 ).1' 1')'''.1.. Wal C l r II 0.18
~ IItJ,.ane 2~ UJ R A f f i l l D M ! W •• o r IS 033
[cdiM Ue~ 25 4,4, !t KIWC W.~C' f zs 0,l2
Mor:\lJ~ 11t=un ;t : : 25 O,O~ Tnfu~r.r~ Wirer l:Q o,!l
rr,gpmt Ilenne 2S 4.81 U" " W:Hl:l zs 1.3
TtuxblOroml:<thimc 1I"1m: 25 3.70 Umbant Watet IS 0.80
TQh!~r.rc: n~.nc: 21 OJ
6 ·181
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PROPERTtES OF WATER IN THE RA 10 0 - 100 "c
T h is ' ab le summa riz cs , he b "" , a v a ; l ab le v al u es 0 r 1]1( , densi I)" s p ec i l ie I ! e a , C I ! J ' I ' c O ty 3' e< l 1 l S1 lJ t p ressure (Cp l , v"'I 'O' j N ' e " S s u r r : , vi.soosJ!)', themlal
condu , t I;vi.y" d le lc et ri e c on su a u , 3 n d s ur fa ce t en si on f o r l iq u id w a re r In lI le rang" 0 - 1 00 "c . Al l v a l ue s (c' ' ' 'evl " " I ' ' ' ' p re ss ur e r ef e' 10 a p r es su r eor 100 kP II (I ~r). 1 1te I cm p" nllU '< : s ea le is 1 (> 1'5 -6 8.
Density Cp V_po pres, Vise. · r b or, ccad, Sorf. (en.· c w(m
'J/~K 1<1'. l iP , " , mWI.K,J1, O l e l. e ons t, n.N/nl
0 0.99984 4.2116 O . 6 1 1 J 1793 ;';61,0 87.'10 75.641,0 0,99970 4 .1 92 1 I.ngl 1 3 1 1 7 S 8 0 , Q 83.96 141320 0.99821 4.1818 2 .3JSS 1 002 :19M 80 .20 12.7S~O 0 .99565 H18A 4.2455 7 97 . 7 615.4 16 .60 71.2041) 0.99212 4.1785 7.3814 65).2 630.5 73.17 69 .6050 0 .98803 4.1805 ]2.34<1 547.0 643.) 69.S8 67 .9460 0.98320 '1 .1184) 1 '} ,9 :J2 466 .5 654.3 6 6 . i 1 66 .2 410 0 .97 7 78 4.l895 31.176 404.0 663.1 63.73 64.4780 0.97182 4.l963 47 .373 3S4 .4 670 .0 60.86 6Ui190 0.965.35 4.2050 70 .1 1 7 31:4.5 675.3 5~.12 6 Q . 3 210 0 0.95$.>10 4.2159 101.32;; 2J!!.S 61 9 .1 55.51 58.91
Ref . )-3 2 1,3 3 J 4 5
ItE" l;;JtF.N'CES
I. L. Hanr . J. S . G~lln l lher , " nil G . S . K dl, N8S1NI lC $1"""" TQb l<M- , Hemisphe r e E"u l .> li s h il li l :orp . , 1984.
2. K . N. Mars h" E d . • TkcOJIJ"IIl ruldl !d "ef~r~IICI!-~fole"l(Jbfor Ihe R( ! b ./ i J! a liO l ! a [P } ,) , si ro r ;lwm i (! < 1 / P r vp eN i e s , Blackwell Scientific Pnh!' icat ionl t ,
Oxford, 1987.
3. J. V . S " " g c fl I a n d J. T . :R . W~ . l oo' " l r n pmv ed i n tcma ti o na l f <Hmu l~ t io n sto r d\ e viscosily aM t h < :n n o lr o~dy c' i' ~ (y o fw a( ~ r ' 'llbslam:>c.J. Ph " • .
CI,,,,,,.R~f [)ura, 1 5 , 1 2 9 1 ,1 9 8 6 .
4. D . G . A rd,, , •• n.d '1'. W'''!!; ' Th.ediel"ouiecons, ," , , (ofwlue, .nd Debye·Hfu:l<ellimilillg I, ;wslop<:s, . l PI, , ,$ . C I t ! ! " ,. I te [. DCI(l. 19 .371 .1990 .
S. N. 3 . V e r g l l1 li k . 01 o J . . Internaticnal ( abIes or Ih~sYrfl lCC tension of w ale r , .1 . Pllys,Oem. R~f DrlI l l , 12, 811. 19BJ.
Density Coeff Coeff2 Molecular Viscosity Mass Conductivity
1wt
Micro Pa Diffusion
N2gas 1.1381 300 101325 28.018 .00001786 .0000160 0.02598
1
H2 gas 0.0819 300 101325 2.016 .00000894 .0000496 0.1815
H2O 1.0 300 101325 18 10 0.00001 0.04
02 gas 1.2998 300 101325 31.99 .00001206 .0000214 0.02674
7 9
For other constants check out the CRC handbook online at:
http://www.hbc1.netbase.com/hbc1./default.j S 1 '
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