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Jervds November 18, 2008 05:20

Natural Convection in a storage tank - boussinesq?

I'm trying to simulate a transient storage tank of water in natural convection, at the first moment my source is a constant temperature at 90C and the water initial temperature is 25C.

I didn't understand yet one thing in CFX, if I just put the option "buoyant" CFX will use a boussinesq model? Can I use this option for these conditions? because in CFX tutorial "Buoyant Flow in a Partitioned Cavity" he has a difference of temperature equal to 70C for air and if I well understand CFX use boussinesq to solve this problem. But the boussinesq is for a small temperature difference, ok?

My other doubt… in another case I used a CEL expression to simulate the density with temperature, I just put the CEL value in "density" in the material properties of Water… in this case, how CFX will calculate? He will negligence the boussinesq or use a combination?

I hope that I explained my problem!!

Thanks & Regards


Rogerio Fernandes Brito November 18, 2008 06:07

Re: Natural Convection in a storage tank - boussin
Boussinesq Model:

For buoyant flows where the density variation is driven only by small temperature variations, the Boussinesq model is used. In this model, a constant reference density is used for all terms other than the buoyancy source term. The buoyancy source term is approximated as:

See equation 116 and equation 117.

Example 2: Feedback to Control Inlet Temperature.

In this example, a feedback loop is used to control the outlet temperature by varying the temperature at an inlet.

Fluid from a main and a side inlet enter at temperatures of 275 K and 375 K respectively. The temperature of the fluid entering from the third inlet depends on the outlet temperature. When the outlet temperature is greater than 325 K, the fluid from the third inlet is set to 275 K. When the outlet temperature is less than 325 K, the fluid from the third inlet is set to 375 K. In addition an expression is used to set the dynamic viscosity to be a linear function of temperature.

The LIBRARY section of the CCL (CFX Command Language) file appears as follows. Note that the the "\" character indicates a line continuation in CCL.


MATERIAL: Water at STP Modified

Option = Pure Substance


Option = General Fluid

Density = 9.999E2 [kg m^-3]

Dynamic Viscosity = VisT

Specific Heat Capacity = 4.21E3 [J kg^-1 K^-1]

Thermal Conductivity = 5.69E-1 [W m^-1 K^-1]


END # MATERIAL Water at STP Modified



Tupper = 375.0 [ K ] # Upper temp.

Tlower = 275.0 [ K ] # Lower temp.

Visupper = 0.000545 [ N s m^-2 ] # Vis. at Tupper

Vislower = 0.0018 [ N s m^-2 ] # Vis. at Tlower

VisT = Vislower+(Visupper-Vislower)*(T-Tlower)/ \


# Vis.-Temp. relationship


Tout=areaAve(Water at STP Modified.T)@outlet

Tcontrol=Tlower*step((Tout-Tm)/1[K]) \



END # CEL END # LIBRARY The first four expressions, Tupper, Tlower, Visupper and Vislower are simply constant values to define temperature and viscosity values. The expression VisT produces a linear function for the dynamic viscosity taking a value of Visupper at Tupper and a value of Vislower at Tlower. The expression Tm sets the desired value of the outlet temperature. In this case it is set to a mean value of the two inlet temperatures.

Tout calculates the outlet temperature using the areaAve function. This function can be selected in ANSYS CFX-Pre in the Expression details view. For details, see Expressions.

Finally the expression Tcontrol is used to set the temperature of the third inlet. Two step functions are used so that the temperature is equal to Tlower when Tout-Tm is positive (i.e., the outlet temperature is greater than Tm), and is equal to Tupper when Tout-Tm is positive.

Jervds November 18, 2008 08:55

Re: Natural Convection in a storage tank - boussin

So… if I understood, I can consider 100C as a small difference of temperature for water? And CFX use automatically the boussinesq, is that?

But if I don't want use the boussinesq, how can I do that? Some ideas? With the CEL expressions for density will work?

Thanks & Regards


pmp77 November 18, 2008 10:25

Re: Natural Convection in a storage tank - boussin
Hello Jervds,

I have found this in the help:

>>> ANSYS CFX-Solver Modeling Guide | Basic Capabilities Modeling | Material Properties | Buoyancy Properties

Thermal Expansivity

Thermal Expansivity (or coefficient of thermal expansion),[[Beta]] , describes how a fluid expands with temperature. It is used in the Boussinesq approximation for buoyant flow and has dimensions of [[temperature^-1]] (where [[temperature]] is temperature). For details, see Buoyancy. This parameter will only be used by the flow solver if the fluid has a constant density. Otherwise, the full buoyancy model will be used for which thermal expansivity is not a required parameter. <<<

I can select fluid buoyancy model for my fluids (Air/Pur multiphase) on the fluid details tab. To do this I need to define buoyancy on the general options tab, and to be able to select Boussinesq bouyancy model I have selected Thermal energy (Fluid Models, Heat Transfer, option)

I also have a question about this:

Is that mean, if you do have density as a funcition of (T) then no thermal expansion (and convection) is calculated?

I am new to CFX, and write to you because I have just trying something similar. I am going to write about it in a new thread.

May I ask for what you have used the CEL function in changing the density of water? Did you try to simulate the thermal expansivity?

All the best:


Glenn Horrocks November 18, 2008 18:03

Re: Natural Convection in a storage tank - boussin

Whether your temperature difference means the Boussinesq approximation is valid will depend on the level of accuracy you expect from the results.

If you want to go beyond the Boussinesq approximation then you should go to a fully compressible (for a gas) or density as a function of temperature and/or pressure (for a liquid). In this case the Boussinesq assumption is not used and the buoyancy forces are calculated directly though density variations.

If you are doing this you should also include variable properties for viscosity, thermal conductivity and specific heat. Often the changes due to variable properties are of a similar magnitude as the changes due to fully compressible flow.

Regards, Glenn Horrocks

Jervds November 19, 2008 07:01

Re: Natural Convection in a storage tank - boussin
Thanks a lot, I'll try the both possibility and check the results!!!

Regards, Jervds

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