3D Natural Convection Log Out | Topics | Search
Moderators | Register | Edit Profile

FlexPDE User's Forum » User Postings » 3D Natural Convection « Previous Next »

Author Message
Top of pagePrevious messageNext messageBottom of page Link to this message

Nathan Cheng (nathan_cheng)
New member
Username: nathan_cheng

Post Number: 1
Registered: 07-2008
Posted on Wednesday, July 16, 2008 - 12:42 pm:   

Does anyone have any tips on applying the Navier-Stokes Equations in 3D to a natural convection problem? Essentially I am trying to model a heated steel cylinder immersed in a tank of water.

I've been able to modify the "BUOYANT" sample file to get a very good model in 2D however using the stream function format of the NS equations doesn't seem like it translates into 3D.

Just using the NS equations in cartesian 2space with the Boussinesq approximation is already troublesome and tends to diverge. Does anyone have any suggestions?? Any help would be much appreciated!

Thanks
Top of pagePrevious messageNext messageBottom of page Link to this message

Marek Nelson (mgnelson)
Moderator
Username: mgnelson

Post Number: 52
Registered: 07-2007
Posted on Friday, July 18, 2008 - 03:08 pm:   

1)
The stream function model of fluid flow in 3D becomes complicated. The equipotentials are surfaces, not flow lines. Flow lines are given by intersection of surfaces.

2)
When the viscocity is low, the solution can support small vortices, causing the solution to go unstable. In steady-state systems, it is often necessary in this case to stage the density, starting at 0 to remove the non-linear terms and getting more dense at each stage. Also, the initial values for the system are critical. They must be something close to the actual solution or the system can have difficulty converging. You should start at an equilibrium condition and slowly turn on the driving terms.

The particular approach depends on the specifics of your system.

If you have a script started, you can post it and we will take a look.
Top of pagePrevious messageNext messageBottom of page Link to this message

Georgios Florides (gflo)
New member
Username: gflo

Post Number: 1
Registered: 12-2009
Posted on Saturday, December 19, 2009 - 03:38 pm:   

I am a new user and I would appreciate your help to simulate the temperature drop of a hot fluid running in an un-insulated pipe. I would like to plot the temperature drop of the fluid along the z axis and also observe the temperature increase of the pipe at the inlet (z=0) and outlet (Z= 0.07) as the time passes. I include a 2D version turned to 3D which lacks some important equation concerning Tfluid.
application/octet-stream3d flow in pipe
3d flow in pipe.pde (2.3 k)
Top of pagePrevious messageNext messageBottom of page Link to this message

Marek Nelson (mgnelson)
Moderator
Username: mgnelson

Post Number: 170
Registered: 07-2007
Posted on Sunday, December 20, 2009 - 07:23 pm:   

You can use a HISTORY plot to monitor the change at a specific location. i.e.
HISTORY(temp) AT (0,0,0) (0,0,0.07)

See "Histories" in the Help index and the example problem "two_histories.pde" (the directory "Samples|Usage" in V6, "Samples|Misc" in V5.)
Top of pagePrevious messageNext messageBottom of page Link to this message

Georgios Florides (gflo)
New member
Username: gflo

Post Number: 2
Registered: 12-2009
Posted on Tuesday, December 22, 2009 - 01:07 pm:   

Dear Mr. Nelson,

Thank you for your reply. The main concern is the convection heat loss from the fluid to the pipe and the calculation of the fluid temperature (Tfluid). Let me clarify the matter.

1.The fluid running in the pipe loses heat by convection to the pipe. The inside film heat transfer coefficient, given by
hf=0.023(kf/dp)Re0.8Pr0.35
depends on the mass flow and temperature so it can be calculated and considered as a constant.
2.For the convection heat transfer, every time step and for every x,y,z position at the boundary, the temperature of the fluid (Tfluid) and the pipe (Tpipe) must be known. Then the boundary condition will be
natural(Tpipe)= hf (Tfluid- Tpipe)
3.If we define Tpipe as a variable then Tfluid must be a variable at the right position for every time step.
4.The question then is how to define Tfluid in Flex language. The method I used in the attached file is not probably correct since the fluid temperature at the boundary exceeds the max. temp which is 350K
application/octet-stream
3d flow in pipe 22-12-09.pde (2.6 k)
Top of pagePrevious messageNext messageBottom of page Link to this message

Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 1314
Registered: 06-2003
Posted on Tuesday, December 22, 2009 - 02:23 pm:   

1.
I don't understand what you are trying to do with your "tfluid" quantity.
One would assume that "tpipe" would be the value of "temp" in the pipe material and "tfluid" would be the value of "temp" in the fluid material. The heat flux flowing across the interface will be determined by the conductivities in the two materials.

2.
A Natural boundary condition on an interior boundary defines a surface energy source, energy which is provided by some external means. I don't think this is what you want.

3.
Your item 1 implies that there is a contact resistance between the fluid and the pipe. This kind of effect can be modeled using the CONTACT boundary condition. See "Contact" in the Help Index.

Top of pagePrevious messageNext messageBottom of page Link to this message

Georgios Florides (gflo)
Junior Member
Username: gflo

Post Number: 3
Registered: 12-2009
Posted on Tuesday, December 22, 2009 - 04:39 pm:   

Dear Mr. Nelson,
This solves the problem. Thank you very much.
Top of pagePrevious messageNext messageBottom of page Link to this message

gflo
Member
Username: gflo

Post Number: 4
Registered: 12-2009
Posted on Saturday, May 29, 2010 - 02:28 pm:   

Dear Mr. Nelson,
There are cases in problems where the value of a cell is needed in the calculations or where the mean value of a variable over an area is needed. For instance assume that for the attached example, the value of temp in the centre line of the fluid will be used in the calculations for every time step and for every z position. I created unsuccessfully a feature on the centre line (Feature-start (0,0,0) line to(0,0,length) and I tried to save the temp value { Tcentrefluid=value(temp)} at every time step and use it in the following calculation {natural(temp)=ho*(temp-Tcentrefluid)}. Could you please demonstrate the correct way of doing this? Also, in the case that the mean value of the temp over the cross section of the fluid is required per time step per z position how will it be calculated?
application/octet-streamex.1
con-1.pde (2.2 k)
Top of pagePrevious messageNext messageBottom of page Link to this message

rgnelson
Moderator
Username: rgnelson

Post Number: 1372
Registered: 06-2003
Posted on Monday, May 31, 2010 - 08:06 pm:   

1. There is no mechanism for integrating over a vertical line in 3D. You can integrate over any gridding surface or any compartment (Region/Layer). See "Integrals in Three Dimensions" in the Help Index.

2. Internal Natural boundary conditions are surface sources or sinks. Unless there is some skin source, you do not want to insert energy at an interior boundary. The default interior boundary conditions conserve heat energy and partition fluxes according to relative conductivities. The interior natural you have indicated will simply drive the entire temperature to zero by magically sucking energy out at the interface.

3. You can use VAL() to find the value of any expression at any point in the domain.

4. Your MONITOR print time is not reset for PLOTS and requests saving 20,000 full sets of plots. I hope you have a large disk. Perhaps fewer plots would be sufficient.

5. The MONITOR print time selection (every 0.5) also limits the maximum timestep, severly slowing the execution time of the problem. Less frequent plots or plots on cycle numbers will allow the timestep to increase as appropriate to the problem.

6. The problem as you show it is azimuthally symmetric, and could be run much more economically in 2D cylindrical coordinates.

Add Your Message Here
Post:
Username: Posting Information:
This is a private posting area. Only registered users and moderators may post messages here.
Password:
Options: Enable HTML code in message
Automatically activate URLs in message
Action:

Topics | Last Day | Last Week | Tree View | Search | Help/Instructions | Program Credits Administration