ANSYS Mixer Tutorial1

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2D AND 3D FLOW ANALYSIS IN MICROFLUIDIC

CHANNELS INCLUDING MULITPLE SPECIES

TRANSPORT.

Written and Tested by: Scott Stelick

sjs [email protected]

Alliance for NanoMedical Technologies

Cornell University

Last revision 10/2/02

mailto:[email protected]

mailto:[email protected]



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.

2



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.

3



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.

4



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.

6



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

7



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

8



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

9



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).


6.Pick the second line (upper line of the larger rectangle.


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.

10



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

11

...,'



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

12



If only modeling in 2D, you can skip the next section and start again at adding boundary

conditions.

3D Meshing


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.

13



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


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.

14



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)

15



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.


Species Setup

16



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.

~-----------------------



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"



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


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.

19



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.

20



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.

21



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

22



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

23



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.



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"



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.

26



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.


2. Choose Nodal solution.

27



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.



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.

29



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.

30



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.

31



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.

32



This is the density profile immediately after the intersection of the two flows.

33



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.


only.

1. Main Menu >Preferences

2. Turn on

FLOTRAN CFD

filtering

3. OK.

Define element type. (2D)



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

34



11. Main Menu> Preprocessor> Materials > temperature unit


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.



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

35





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


choose:


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.

36



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.

37



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


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

38



This will mesh the entire design and for should look like the following image.


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.


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


IlILNIUJ, I TER l't"fttfti_ c..t:-r.l

IIPPE .)'-fl -flU oWppiM f , . . . .


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~,~



2. Enter 40 Global iterations (Note: 40 global iterations is arbitrary with no guarantee

of convergence.)



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.


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


absolute 0 to 273.

17. OK.


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.


40



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

41



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


When all the boundary conditions are inputted, the design should look

like the following.



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


42







1. Main Menu > General Postproc > Plot

Results> -VectorPlot- Predefined


3. Choose Velocity V.

4. OK.




4. OK.

Vx



Vy

These images show the velocity profile for the micro fluidic system above.

Make a path plot of velocity through the outlet.


2. Pick the nodes near the outlet of the squares.

3. OK (in picking menu).

4. Enter Velocity for the Path Name.

5. OK.


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.

44



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.


Make a path plot of velocity through the outlet (second location).


5. OK.

2. Pick the nodes near the outlet of the squares.

3. OK (inpicking menu).

4. Enter Velocity for the Path Name.


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.

45



12. Main Menu> General Postproc > Path Operations> -Plot Path Item- On Graph

13. Choose the label Velocity that

you previously defined.

14. OK.


These graphs show the velocity

profiles for two slices in the

modeling. Any area can be analyzed

in this way.

46



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.


only.

1. Main Menu >

Preferences

2. Turn on FLOTRAN

CFD filtering

3. OK.

Define 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

47



Note: All units shown in this tutorial are in cgs units.

Main Menu > Preprocessor > Materials >

temperature unit


~ 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.


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.

48



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



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


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.

49



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.



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.



Elem Ext Opts

2. Choose 2 (FLOTRAN 142) for

Element type number.

3. Enter 20 for the No. of element

divisions.

4. OK.



-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:

51



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.


52



2. Set global size controls.

3. Enter 0.005 for element

edge length.

4. OK.

5. Mesh.


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.


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.

53



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.


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.


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.

54



4. Enter 1.0 for density, 0.01 for viscosity and 0.04 for conductivity. Leave specific

heat at-1.


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.




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


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

- ~ ----~----

55



6. OK.


The modeling should be ready to be run.



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)






56





3. Choose velocity v.

4. OK.




4. OK.

Vx

" . : . . ' . _ I I I~- ,

. . . .~ . ; , , : :# .; ,~,~ I



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.

58



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

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IJrnDilk-itid A~I-mc: 25 2.62 1kni:l:11t1 l'drncll~hnnc l.l 1.A2

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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,

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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

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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

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-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

59



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 '

60

http://www.hbc1.netbase.com/hbc1./default.j

http://www.hbc1.netbase.com/hbc1./default.j

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