# Boussinesq approximation in closed system

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 July 4, 2006, 22:35 Boussinesq approximation in closed system #1 Nitesh Guest   Posts: n/a Hi all I have to simulate a buoyancy driven flow inside spherical vessel. My task is to calculate heat transfer through walls of closed spherical vessel. The wall temperature are at 300 K and the fluid is filled at 310 K at operating pressure 5bar. There are no pressure, velocity boundary conditions. Kindly let me know 1. Can I use Boussinesq approx to calculate heat transfer from wall in closed system? (We have neglected radiation and conduction. . 2. If unsteady state analysis of this problem is possible? I tried the unsteady analysis but its taking lot of time about 17 hrs and still could not reproduce the experimental results. Thanks in advance

 July 5, 2006, 03:35 Re: Boussinesq approximation in closed system #2 Ahmed Guest   Posts: n/a 1- what is the diameter of that spherical vessel? 2- Where the 5 bar pressure is measured? top bottom where! 3- What exactly is your problem? Why are using unsteady analysis? Are you pressurising the vessel or what ? 4- Yes you can use the Boussinesq approx , but where your reference temperature is located? 5- Are you using a general CFD solver or writting your own code 6- Why are you neglecting convection and Radiation effects

 July 5, 2006, 21:43 Re: Boussinesq approximation in closed system #3 Nitesh Guest   Posts: n/a Hi 1. The diameter is .3368 m. 2. I have specified pressure in terms of operating pressure with the reference located at origin which is also the centre of spherical vessel in my case. 3. The problem is I couldnot understand when I increase the operating pressure to lets say 20 bar, the computation time time increase drastically in comparison to that at 5bar as operating pressure even though I have specified the constant material property. Its a general axisymmetric problem in fluent 2d. 4. This analysis is basically to validate the experimental results and my guide is interested in observing the heat tranfer pattern in time. 5. I am using Fluent to simulate my problem. 6.Well in principle I should include conduction and radiation effect but they are too small to be included in my case as the Rayleigh number is considerably high. P.S. Whether a high Rayleigh number (~ 10^9 or 10) has anything to do with the computational time Nitesh

 July 6, 2006, 06:04 Re: Boussinesq approximation in closed system #4 Shubidu Guest   Posts: n/a Nitesh, I think you might struggle to obtain a converged solution because of the inherently unsteady physcis of rotating cavity flows (i.e. the flow is likely to be non-axisymmetric!!). Check that your cavity dows not contain any non-axisymmetric elements (bolts, gaps, dents, steps, etc.) and that you set the correct fluid pressure (isenchoric system, i.e. internal pressure set at the time of closing the cavity). You might have to go 3D!!! I suggest you take a close look at the paper by Snowsill, G.D and Young, C, ASME Turbo Expo 2005, "Towards Defining Objective Criteria for assessing the Adequacy of assumed Axisymmetry and steadiness of flows in rotating cavities". I am pretty sure this paper was subsequently also published in the ASME J. Heat Transer or ASME J. Turbomachinery. Regards Shubidu PS: Now, I have a question for you: How will you validate your model? Are you using experimental data of your own or are you refering to any previously published data (references)?

 July 10, 2006, 09:23 Re: Boussinesq approximation in closed system #5 Ahmed Guest   Posts: n/a So you are dealing with an "Isolated system" (Check your thermodynamics book for the definition), you have a sealed spherical vessel, no inlets or outlets and you have neglected the radiation and convection heat transfers, the only heat transfer mode left is conduction to the surrounding air through the mechanism of diffusion. As you know diffusion is a very slow process. The pressure difference between the top and bottom of the sphere is the piezometric pressure (density times acceleration of gravity times the diameter of the sphere) how much it is? My recommendation is very simple, make your mathematical model more physical. Please correct me if I am wrong. If you get any convergence, it is because of the rounding errors every iteration but not because of any physical mechanism, could you describe the residual plot especially the Energy plot. If you need further assistance you can either upload a picture of your mesh or use the Email button and send me your mesh file Have fun

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