[Pastukhov]

Dear CFD-online community!

I have a question that I was hoping you might be able to help me with.
I'm trying to calculate temperature distribution in isolated volume of
air in high-raise staircase in the stationary implementation.
I get converged solution with settings being described downwards.
So the problem is a strange temperature distribution: it looks like reversed
stratification and it's definitely counter-intuitive and illogical. At the top of staircase the temperature is lower than at it's bottom part. But the air in the volume being adjoined the warm convectors predictably raises up.

Do you have any ideas how is it possible?

Model description:

- Steady-state;
- Air Ideal gas;
- k-eps model;
- Buoyancy Model: Buoyant, gravity Dirn.: (0, -g, 0);
- Buoyancy Ref. Density: 1.2 kg*m^-3;
- Heat Transfer: Thermal Energy;
- Thermal Radiation: Discrete transfer, S-to-S;

BCs:
- Initial temperaure: 16°C;
- 3 x convector heating units:
- Radiation flux: 111 W*m^-2;
- Convective flux: 443 W*m^-2;
- external (outer) wall:
- Heat Trans. Coeff.: 0.32 W*m^-2*K^-1;
- Outside Temp.: -28°C;
- 15 + 15 interfaces (each floor is certain meshed volume);
- other surfaces are adiabatic no-slip walls.

The first solution was started with automatic timestep, then changed to physical TS
with separated timestep values for each equation. That brought better convergence
and faster temperature distribution convergence.

Best regards,
Ivan.

interf.jpg

mesh_1.jpg

conve.jpg

temperature_1+convect_1.jpg

mons.jpg

[evcelica]

Even Though it does look strange with the reverse stratification, I think it makes sense. You have a heat source on the bottom, 5th, and 10th floors. The floor furthest away from the heat source is the 15th, and it is the coldest. If you moved the heaters up a few floors: 3, 8, 13 maybe, I would expect it to be more uniform.

[ghorrocks]

I suspect Erik is correct.

A slightly related issue, not quite on topic but hopefully interesting anyway:

There was a fire in Kings Cross Station, London in 1987 (https://en.wikipedia.org/wiki/King's_Cross_fire). The fire in the escalator shaft spread far more rapidly than was expected and this caused a people to be trapped and over 30 deaths. A CFD simulation was done as part of the investigation and showed that the hot plume from the fire entered the escalator shafts, but rather than travelling along the top wall of the diagonal escalator shaft as expected it stuck to the bottom wall due to the Coanda effect. This means the hot plume ignited the escalators very quickly and spread beyond the escalator shafts very quickly.

I think the paper is: Jones, I. P., Simcox, S. and Wilkes, N. S. Computer simulation of
the flows of hot gases from fire at King’s Cross underground station. IMechE Seminar on The King’s Cross underground fire: fire dynamics and the organization of safety, July 1989, pp. 19-26 (Mechanical Engineering Publications, London).

This is another example of the hot gas being at the bottom, not the top. In this case the Coanda effect causes the apparent inversion of the temperature field. A very different scenario.

[Pastukhov]

Thank you for your replies!
But I still can’t understand why warm air doesn’t raise up though tends to be more buoyant.
Temperature difference between ground floor and 15’th floor is equal ∆T = 11°K; buoyancy of the air on the ground floor is 0.055 N/(m^3), and -0.325 N/(m^3) on the 15th floor.
I can’t spot the cause why cold air doesn’t fall and warm one doesn’t raise up like air bubbles in water. Is that because of drag forces or sort of?
Anyway, solution for case with heaters on 2nd, 8th and 14th is coming up.

P.s. Streamlines visualisation of air moving from the heaters. https://youtu.be/ASK807GIvQo

[ghorrocks]

Your outside temperature is very cold, so heat is being lost at the walls. The heat getting to the top of the stairs is being lost to the outside, so by the time it gets to the top of the stairs it is pretty cold. In other words, the rate heat is lost to the outside is faster than the rate heat from the hot plume can work its way up the stairs by buoyancy.

If you made the outside temperature higher this would not happen and you will start to make it hotter as you go up. Alternately, if you had a heat source on every floor you would also make the temperature profile increase with height (as long as the heat source is strong enough to overcome heat lost to the outside).

[Pastukhov]

Originally Posted by ghorrocks

Your outside temperature is very cold, so heat is being lost at the walls. The heat getting to the top of the stairs is being lost to the outside, so by the time it gets to the top of the stairs it is pretty cold. In other words, the rate heat is lost to the outside is faster than the rate heat from the hot plume can work its way up the stairs by buoyancy.

If you made the outside temperature higher this would not happen and you will start to make it hotter as you go up. Alternately, if you had a heat source on every floor you would also make the temperature profile increase with height (as long as the heat source is strong enough to overcome heat lost to the outside).

Thank you for your explanation, Glenn!