# Non Boussinesq approximation

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 January 30, 2013, 08:31 Non Boussinesq approximation #1 New Member   Hari Join Date: Jan 2013 Posts: 4 Rep Power: 5 Hi, I need to simulate natural convection in square cavity (bottom wall heated) without using Boussinesq approximation. I need to take the density changes into account with non-Boussinesq approximation. Can I solve this with an incompressible solver with treating density as constant? I need help about the formulation and way of solving. With regards, Hari

January 30, 2013, 09:15
#2
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Filippo Maria Denaro
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Quote:
 Originally Posted by design_amrita Hi, I need to simulate natural convection in square cavity (bottom wall heated) without using Boussinesq approximation. I need to take the density changes into account with non-Boussinesq approximation. Can I solve this with an incompressible solver with treating density as constant? I need help about the formulation and way of solving. With regards, Hari
if you are outside the hypothesis of linearity (small variation of temperature) required by Bousinnesq model, you must use the full compressible model

 February 5, 2013, 09:04 Non Boussinesq approximation #3 New Member   Hari Join Date: Jan 2013 Posts: 4 Rep Power: 5 Thank you for replying. I need to develop a pressure based solver without boussinesq approximation. Is it possible to work on incompressible flows without treating density as constant.

 February 5, 2013, 09:37 #4 Senior Member   Join Date: Jul 2009 Posts: 238 Rep Power: 11 If the density can vary, then the flow by definition is not incompressible. however, you can develop segregated solvers for variable density flows. One example of such a solver can be found in a JCP paper by Hou and Mahesh. If you put their names into google scholar, the second or third entry will point you to a pdf version of that paper.

 February 5, 2013, 10:42 Non Boussinesq approximation #5 New Member   Hari Join Date: Jan 2013 Posts: 4 Rep Power: 5 Thankyou for replying. I was referring to the following ASME J.heat transfer paper where they say the flow is incompressible with non boussinesq approximation in a differentially heated cavity. I have mentioned the details of the paper below. A Numerical Simulation of Combined Radiation and Natural Convection in a Differential Heated Cubic Cavity P. Kumar and V. Eswaran J. Heat Transfer,2010,Volume 132,Issue 2,

February 5, 2013, 11:28
Non Boussinesq approximation
#6
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Jonas T. Holdeman, Jr.
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Quote:
 Originally Posted by agd If the density can vary, then the flow by definition is not incompressible.
But doesn't "incompressible" just mean that the density is not a function of pressure? Isn't constant density just an additional simplification? I would think that an (idealized) incompressible fluid could still have the density a function of temperature or concentration. Isn't bouyancy just the result of density differences?

February 6, 2013, 10:01
#7
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p ding
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Quote:
 Originally Posted by Jonas Holdeman But doesn't "incompressible" just mean that the density is not a function of pressure? Isn't constant density just an additional simplification? I would think that an (idealized) incompressible fluid could still have the density a function of temperature or concentration. Isn't bouyancy just the result of density differences?
we should define the incompressible by "partial P/partial rho", in natural convecion problem, the density varies, but it is still a incompressible flow.

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