2-D Transient Flow
Geometry: Transient Plates Ta
Wall Inlet Ta Pa
h
Outlet Pa
Water μ, ρ q
Wall
vb
L • Laminar flow through parallel plates w/ impulsed velocity and heat flux on bottom wall. • Initially at zero velocity and atmospheric temperature.
Parameters Parameter
Symbol
Value
height
h
10 mm
length
L
50 mm
wall velocity
vb
100 mm/s
viscosity
μ
1.831E-5 kg/m-s
density
ρ
1.185 kg/m3
specific heat
c
1004.4 J/kg-K
thermal conductivity
k
0.0261 W/m-K
atmospheric pressure
Pa
1 atm
atmospheric temperature
Ta
298 K
heat flux
q
1000 W/m2
Workbench 1. Create new directory •
called Transient Plates
2. Open ANSYS CFX in this new directory 3. Create New Model •
File – New Simulation
•
New Simulation window appears.
•
Select General. Select OK.
4. Save file in new directory: transient_plates.cfx •
File – Save Simulation
5. Import Geometry •
Geometry is same as previously created for Parallel Plates example.
•
Copy and paste the refined parallel_plates2.gtm into current directory. Rename it transient_plates.gtm.
•
In Outline View, right-click on Mesh. Select Import Mesh. In Import Mesh window, selected transient_plates.gtm. Click Open.
6. Set Simulation Type •
When CFX opens, in Tree Outline double-click on Simulation Type.
•
Simulation Type Tab appears.
•
In Basic Settings Tab under Simulation Type, set Option to Transient.
•
In Basic Settings Tab under Time Duration, set Total Time to 2 s.
•
In Basic Settings Tab under Time Steps, set Timesteps to 0.1 s.
•
Click Apply. Click OK.
7. Define Model Data •
Double-click on Default Domain in Tree Outline. Domain: Default Domain Tab appears.
•
In General Options Tab under Basic Settings, set Fluids List to Air at 25 C.
•
In General Options Tab under Domain Models, ensure Reference Pressure is set to 1 atm.
•
In Fluid Models Tab under Heat Transfer, ensure Option is set to Thermal Energy.
•
In Fluid Models Tab under Turbulence, set Option to None (Laminar).
•
Click Apply. Click OK.
8. Define Model Data •
Double-click on Default Domain in Tree Outline. Domain: Default Domain Tab appears.
•
In Initialisation Tab, select Domain Initialisation. Select Initial Conditions.
•
Under Cartesian Velocity Components, enter 0 m/s for U, V, and W.
•
Under Static Pressure, enter 0 Pa for Relative Pressure.
•
Under Temperature, enter 298 K for Temperature.
•
Click Apply. Click OK.
9. Check Material Properties •
Outline – Simulation – Materials. Double-click Air at 25 C. Material: Water Tab appears.
•
In Basic Settings Tab, ensure that Material Group is set to Constant Property Gases.
•
In Material Properties Tab under Equation of State, ensure that Density is set to 1.185 kg/m3.
•
In Material Properties Tab under Specific Heat Capacity, ensure that Specific Heat Capacity is set to 1004.4 J/kg-K.
•
In Material Properties Tab under Transport Properties, ensure that Dynamic Viscosity is set to 1.831E-5 kg/m-s.
•
In Material Properties Tab under Transport Properties, ensure that Thermal Conductivity is set to 0.0261 W/m-K.
•
Click Apply. Click OK.
10. Create Inlet Boundary Condition •
Toolbar – Create a Boundary Condition. Enter LetIn for Name. Click OK.
•
Boundary: LetIn – Basic Settings – Boundary Type. Select Inlet.
•
Boundary: LetIn – Basic Settings – Location. Select LetIn.
•
Boundary: LetIn – Boundary Details – Mass and Momentum – Option. Select Static Pressure.
•
Boundary: LetIn – Boundary Details – Mass and Momentum – Relative Pressure. Enter 0 Pa.
•
Boundary: LetIn – Boundary Details – Heat Transfer – Static Temperature. Set to 298 K.
•
Click Apply. Click OK.
11. Create Outlet Boundary Condition •
Toolbar – Create a Boundary Condition. Enter LetOut for Name. Click OK.
•
Boundary: LetOut – Basic Settings – Boundary Type. Select Outlet.
•
Boundary: LetOut – Basic Settings – Location. Select LetOut.
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Boundary: LetOut – Boundary Details – Mass and Momentum – Option. Select Average Static Pressure.
•
Boundary: LetOut – Boundary Details – Mass and Momentum – Relative Pressure. Enter 0 Pa.
•
Click Apply. Click OK.
12. Create Top Wall Boundary Condition •
Toolbar – Create a Boundary Condition. Enter TopWall for Name. Click OK.
•
Boundary: TopWall – Basic Settings – Boundary Type. Select Wall.
•
Boundary: TopWall – Basic Settings – Location. Select TopWall.
•
Boundary: TopWall – Boundary Details – Heat Transfer – Option. Set to Temperature.
•
Boundary: TopWall – Boundary Details – Heat Transfer – Fixed Temperature. Set to 298 K.
•
Click Apply. Click OK.
13. Create Bottom Wall Boundary Condition •
Toolbar – Create a Boundary Condition. Enter BottomWall for Name. Click OK.
•
Boundary: BottomWall – Basic Settings – Boundary Type. Select Wall.
•
Boundary: BottomWall – Basic Settings – Location. Select BottomWall.
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Boundary: BottomWall – Boundary Details. Select checkbox next to Wall Velocity. Enter 0.1 m/s for Wall U, 0 m/s for Wall V, and 0 m/s for Wall W.
•
Boundary: TopWall – Boundary Details – Heat Transfer. Set to Heat Flux. For Heat Flux in, enter 1000 W/m2.
•
Click Apply. Click OK.
14. Create First Symmetry Boundary Condition •
Toolbar – Create a Boundary Condition. Enter Sym1 for Name. Click OK.
•
Boundary: Sym1 – Basic Settings – Boundary Type. Select Symmetry.
•
Boundary: Sym1 – Basic Settings – Location. Select Sym1.
•
Click Apply. Click OK.
15. Create Second Symmetry Boundary Condition •
Toolbar – Create a Boundary Condition. Enter Sym2 for Name. Click OK.
•
Boundary: Sym2 – Basic Settings – Boundary Type. Select Symmetry.
•
Boundary: Sym2 – Basic Settings – Location. Select Sym2.
•
Click Apply. Click OK.
File – Save Simulation. transient_plates.cfx.
16. Set Solver Controls •
In Toolbar, select Solver Control
icon.
•
Solver Control tab appears.
•
Solver Control – Basic Settings – Timestep Initialisation – Option. Ensure is set to Automatic.
•
Solver Control – Basic Settings – Convergence Control – Max. Coeff. Loops. Ensure is set to 10.
•
Solver Control – Basic Settings - Convergence Criteria – Residual Target. Ensure is set to 1.E-4.
•
Click Apply. Click OK.
17. Set Output Controls •
Note warning message under Viewer. “No intermediate results files...”
•
In Tree Outline, double-click on Output Control.
•
Output Control tab appears.
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Output Control – Trn Results – Transient Results. Select Add New Item box.
•
Transient Results window appears. Click OK.
•
Output Control – Transient Results – Output Frequency. Set Option to Every Timestep.
•
Click Apply. Click OK.
18. Write Solver File •
In Toolbar, select Write Solver File
•
Write Solver File window appears.
•
Save file as transient_plates.def.
•
Click Save.
icon.
19. Start Run •
Define Run window appears.
•
Select Start Run.
20. Open CFX-Post •
Once solution is completed, ANSYS CFX Solver Finished Normally window will appear.
•
Select Yes when asked whether you’d like to post-process results now.
21. Create Plane •
In Toolbar, select Location down menu, select Plane.
icon. In drop-
•
Insert Plane window appears. Click OK.
•
Details View – Geometry – Definition – Method. Set to XY Plane.
•
Details View – Geometry – Definition – Z. Set to 0.0005 m.
•
Deselect check mark next to Plane 1 in Outline Workspace.
22. Create Vector Plot •
In Toolbar, select Vector
icon.
•
Insert Vector window appears. Select OK.
•
In Details View under Geometry tab, for Definition – Locations select Plane 1.
•
In Details View under Geometry tab, for Definition – Variable ensure that Velocity is selected.
•
Click Apply.
•
Right-click in Viewer. Select Predefined Camera – View towards -Z.
23. Alter Legend •
In Outline Workspace under User Locations and Plots, double-click on Default Legend View 1.
•
In Details View under Definition tab, select Horizontal.
•
In Details View under Definition tab, for Location – X Justification, select Center.
•
In Details View under Definition tab, for Location – Y Justification, select Bottom.
•
In Details View under Appearance tab, for Text Parameters – Precision set 3 and Fixed.
•
Click Apply.
24. View Other Timesteps •
The default timestep for viewing is the final timestep.
•
In Toolbar, select Timestep Selector
•
Timestep Selector window appears.
•
Select the timestep associated with 0 s. Click Apply.
•
Repeat for timestep associated with 1 s.
Note that a sub-directory appears in the Transient Plates directory containing a results file for each timestep.
icon.
25. Create Animation •
The default timestep for viewing is the final timestep.
•
In Toolbar, select Timestep Selector
•
Timestep Selector window appears.
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Select the timestep associated with 0 s. Click Apply.
•
In Toolbar, select Animation
•
Animation window appears.
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To create first Keyframe, select New icon.
•
KeyframeNo1 appears in window. Select it and update # of Frames to 21.
icon.
icon.
25. Create Animation (cont.) •
In Timestep Selector window, select timestep associated with 2 s. Click Apply.
•
In Animation window, select New icon.
•
Click Play the animation
•
Select checkbox next to Save MPEG.
•
Click Play the animation icon again.
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Note that a MPG file called cfxMovie.mpg appears in the working directory. This animation may be viewed with Windows Media Player.
icon.
26. Create Contour Plot •
Ensure that 2 s timestep is selected.
•
In Toolbar, select Contour
•
Insert Contour window appears. Click OK.
•
Details View – Geometry – Locations. Set to Plane 1.
•
Details View – Geometry – Variable. Set to Temperature.
•
Turn off visibility of vector plot.
•
Click Apply.
icon.
27. Create Point •
In Toolbar, select Location down menu, select Point.
icon. In drop-
•
Insert Point window appears. Click OK.
•
Details View – Geometry – Definition – Method. Ensure it is set to XYZ.
•
Details View – Geometry – Definition – Point. Set to 0.025 m, 0.005 m, 0 m.
•
Click Apply.
28. Create Chart •
In Toolbar, select Chart
icon.
•
Insert Chart window appears. Click OK.
•
In Details View under Chart tab, ensure that Type is set to Time.
•
In Details View under Chart Line 1 tab, set Location to Point 1.
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In Details View under Chart Line 1 tab, set Time Variable – Variable to Temperature.
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Click Apply.
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Click Export. Save file to trans_temp.csv.
Transient Temperature Profile 330
Temperature (K)
325 320 315 310 305 300 295 0
0.5
1
1.5
2
Time (s)
•
Temperature increases as thermal wave passes location.
29. Save State file •
Select File – Save State As, transient_plates.cst.
Analytical Verification •
Penetration depth (δ) of momentum flux from moving wall may be approximated by:
µt δ =4 ρ •
where t is the time since the initial start of the plate.
•
For time = 0.1 s, the penetration depth is 5.0 mm.
30. Create Line •
In Toolbar, select Location down menu, select Line.
icon. In drop-
•
Insert Line window appears. Click OK.
•
Details View – Geometry – Definition – Method. Ensure it is set to Two Points.
•
Details View – Geometry – Definition – Point 1. Set to 0.05 m, 0 m, 0.0005 m.
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Details View – Geometry – Definition – Point 2. Set to 0.05 m, 0.01 m, 0.0005 m.
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Details View – Geometry – Line Type – Samples. Set to 20.
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Click Apply.
31. Create Chart •
Use Timestep Selector to select results associated with 0.1 s.
•
In Toolbar, select Chart
•
Insert Chart window appears. Click OK.
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In Details View under Chart tab, ensure that Type is set to XY.
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In Details View under Chart Line 1 tab, set Location to Line 1.
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In Details View under Chart Line 1 tab, set X Axis – Variable to Velocity u.
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In Details View under Chart Line 1 tab, set Y Axis – Variable to Y.
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Click Apply.
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Click Export. Save file to trans_vel.csv.
icon.
Velocity Profile time = 0.1 s 10
y (mm)
8
6
4
δ ≈ 6.0 mm
2
0 0
20
40
60
80
100
x-velocity (mm/s)
•
Velocity increases from wall as momentum flux propagates across gap.
Analytical Verification (cont.) •
An analytical expression exists for the x-velocity profile (u) as a function of space (y) and time (t).
u y ∞ 2 = 1 − − ∑ vb h n =1 n π
2 2 µt exp − n π 2 ρ h
y sin n π h
•
Note for long times, the velocity profiles approaches a linear dependence on y.
•
Further note, that only the first few terms of the infinite sum actually contribute.
Velocity Profile time = 0.1 s 10
CFX Analytical
y (mm)
8
6
4
2
0 0
20
40
60
80
100
x-velocity (mm/s)
•
Good agreement between numerical and analytical results.
Practice •
Create an animation of the developing temperature contours.
•
Does a similar analytical check on the thermal penetration depth yield good agreement?
•
Why does the plot of transient temperatures at y = 5 mm decrease after the initial increase?
•
Does the model reach steady-state? How could you predict the time it would take for this geometry to reach steady-state?
