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Colin October 8, 2003 11:00

Gravity g's influence on Simulation Results
Hi, thank you in advance for your taking time and energy to give me your valuable proposals. The problem is as follows.

When we solve N-S equation to obtain the velocity and pressure fields, if gravity g has influence on the final simulation results?

If the answer is 'yes', how do we reflect gravity(g)'s influence on the results using Fluent? Or what should we do using Fluent to consider g's influence?

Any suggestions are highly appreciated.

steve October 9, 2003 02:06

Re: Gravity g's influence on Simulation Results
I won' be able to help you on how to modify the gravity in fluent but I can assure you that g has an influence on the results.

If you take a close look at the conservation of momentum which can be written as follow:

ro*(du/dt+(u*V)u)+V p = ro g + f + V tau

where u, g and f are vectors and V the diverent.

Imagine that the external force (excluding gravity) f is zero and that the viscous stress tensor tau is also equal to zero. Then you system of DE has for results on the right hand side (gx gy gz)'. In an 'normal' case where g only act along the z axis then you have (0 0 9.81)'.

I am simulating tunnel fires where ro if a function of the temperature. I usually build my tunnel horizontal and then modify g to take the effect of the sloop in consideration. Say the gradient of the tunnel is 5 then g = (0.85 0 9.77). The results between an horizontal and a 5 sloop tunnel are very different. If you are not convince search the web for 'Kaprun Cable Car fire'

Hope this has helped


Colin October 9, 2003 10:38

Re: Gravity g's influence on Simulation Results
Hi, Steve,

Your advice is very lightening and helpful. Thank you very much for your taking the time and effort to help me. Would please give me further suggestions?

Now I can see the importance of gravity in your research. Let's see another case: assume water flows in a tube. For the horizontally flow if we could say the gravity can be neglected, while for the vertical upward flow the gravity plays a role that can not be ignored?

steve October 10, 2003 02:00

Re: Gravity g's influence on Simulation Results
I would not say that gx is neglect, I would say that the componant in the x-direction of g gx is equal to zero: g = (0 0 -9.81). I agree I might be playing with the words but don't forget that g is a vector.

In a river it is gx that will move the flow forward !

Once again imagine a tunnel fire or a room fire (sorry to use once again a fire but...) . Ro is a function of the temperature. The hotter is the air the lower is the mass density ro. So in a fire the hot air which is 'lighter' tends to go up under the ceiling while colder air will be find at road level. Without the gz the hotter air would not know which way to go. In the NS equations how do you define up and down ?? by g = (0 0 -9.81). If you change g to (0 0 9.81) so gz point upward then the hotter air will be find at road level while the colder air will be find under the ceiling.

Hope this help.

PS: you can do the same comparaison with a hot air ballon.

jdc October 10, 2003 04:29

Re: Gravity g's influence on Simulation Results
Hi Colin and Steve,

The Froude number Fr (=V^2/(g.L) where V is a characteristic velocity, g the norm of the gravity forces and L a characteristic length) can help knowing wheter the gravity should be taken into account in the simulation.

I know this criteria is used for jet flows where V is the injection velocity and L the injector diameter.

Note: I wonder if there is not a formulation that also uses the density.

Hoppe this may help. Julien

Colin October 10, 2003 10:48

Re: Gravity g's influence on Simulation Results
Hi, Steve and Julien,

I much appreciate your kind help. Your advices are much important to me. I will deal with gravity carefully in my project.

Julien, would you please give me a clue that how the Froude Number is used as a criteria for jet flow?

Thank you, and have a nice weekend, you all.



Jannis D. November 2, 2003 15:13

Re: Gravity g's influence on Simulation Results
You have to consider gravitation when you have high temperture differences that result a suplementary motion in your system. This supplementary forces result from buoyancy forces. You can check it over the ratio of Rayleigh to reynolds number. If Re/Ra >10 000 you may ignore the gravitation.

best regards,


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