The problem is a simple vertical rectangle that has a temperature gradient across the breadth. To working fluid is air. I can get the simulation running on any fluid software but the velocity vector field seems to vary when I input force due to the graviy as an external force to the equation or force due to the variation in desity as an external force. Both the forces bear opposite signs. Only one force can be input to the the eqn at a time.
I have 2 questions now from the perspective of the physical process:
1. If I gave the force due to gravity as an input, and plug in values of air density with ref to Temp it should give me the flow of natural convection where the flow is bottom up. This doesn't happen. At the face of it, it seems like the gravity force is overpowering the inertial and shear forces. Does any one have a feel of it?
2. When I gave the force due to the density variations, I am eventually not plugging the force due to gravity. This way I am asking the simulation to just simulate the flow bottom up..
Which one is closer to reality?
One more question is, if u simulated the low field of air in free convection process, what is the maximum velocity of air at Far field?
Durga;
From these explanations; i hope, you are trying to simulate natural convection flow in a rectangular enclosure with bottom side being heated up.
1) First of all, which software are you using for simulation (is it Ansys FLUENT)
2) The first method is apt, in the physical sense. You are trying to use Boussinesq approximation for modeling the flow. If gravity force seems to overpower the other forces, then check out the sign convention according to your model or solver definition stage. Moreover, if you are using ANSYS FLUENT, then there are seperate drop down menus to choose density of the fluid (i.e air) to model by using Boussinesq approx: (i hope you are aware of that)
Best Regards
Akr
Hey Arun,
Thank you for the response. Please check the link here.
https://www.comsol.co.in/blogs/using-the-boussinesq-approximation-for-natural-convection/
There are 3 equations:
1. NS equation - rho*g is the force due to gravity pointing downwards if the net flow is bottom - up
2. NS equation - I did not understand this. What shift are they talking about? Are they talking about pressure - flow velocity compensation? Where does this equation find its application?
3. This is the approximation you are talking about. The sign on the last term in all the three equations is based on the convention that the force due to gravity is against the motion of the fluid and the bouyant force is in the direction of the motion!! Am I right?
Could you explain the last term in approach 2 and 3?
I have modeled rho as a f(T) w.r.t : http://www.engineeringtoolbox.com/air-temperature-pressure-density-d_771.html
and used the 1st equation. This is not the approximation you are talking about. I have spatial gradient of density. i have not neglected the density changes like in the Boussunesq approx.
Dear Mr. Sravan,
I will not go into simulation details because it depends on the software that your are using and its interfaces. physically speaking the forces on your fluid particles are gravity friction (shear stress) and buoyancy (this force is due to the change in air density). the later one in the motor for free convection. so in the simulation you should try to model all three in order to obtain the closest results to reality.
Look at the attached pdf file in section 9.2. The governing equation of a laminar boundary layer for free convection, is well explained. this chapter is part of "Introduction to heat transfer", sixth edition by Theodore L. Bergman, Adrienne S. Lavine, David P. Dewitt and Franck P. Incropera.
Concerning the maximum velocity of air at far field for having always free convection I assume, might be determined using the conditions of section 9.3 (last paragraph) or 9.9.
Good luck.
Kind regards,
Kifah SARRAF
Thank you very much for the explanation Sarraf.
It is very kind of you for the attachment.
This is the kind of material I have been looking for. I'll try to plug all the forces to calculate the velocity field.
If air satisfies the Boussinesq approximation, the buoyancy force will be :
beta*g*(T-T0) where beta is the thermal expansion coefficient, g the gravity, T the local temperature and T0 a reference temperature.
I hope this shoud be helpful.
Best regards,
The terminology is some what, mis-understood. In natural convection, it is the 'buoyancy' force that drives the flow. It is a result of density variation. If the eqns are correctly written, the whether the buoyancy aids or opposes the flow is decided. If, in a rectangular enclosure, sides are insulated and the bottom is heated, it is common sense to recognise that the buoyancy aids, the fluid raises. On the other hand, if the botton side is cooled, the buoyancy opposes, upward movement, In a way the fluid sits cool at the cool bottom. This is easy to visulise in a 2-D approx, like the above rectangular enclosute, with sides being insulated and is infinite in z- or perpendicular to the plane of the board (in a class room) or plane of the paper. if all the sides are differentially heated, well, the situation demands a 3D modelling and not easy to physically visualize. You may consult books on Free convection by Bejan or Jaluria. You may find natural convection ( though in porous media) articles by yours faithfully et al. You may Google. I am not sure, whether IITKGP website still hosts my publications etc., since I have retired.
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