[Arttis]

I am modelling a buoyancy-driven in an inclined rectangular cavity and I'd appreciate some help.

1. I am confused whether the flow is laminar or turbulent. I've read literature and I am familiar with Rayleigh and Grashof numbers. However, I get Rayleigh number of magnitude 10^5 which indicates laminar flow, while Grashof number is 10^12, which indicates turbulent flow.

Dimensions: L=2m, W=1m, H=0.007m (space between plates), Tupper wall = 310, Tlower wall = 305, Tfluid = 300.

Ra=( g*B* (Tu-Tf)*L^3 ) / (v*a)

where Tu - upper plate temperature
Tf - fluid temperature
L - Length of the cavity
g - 9.81m/s
B - thermal expansion coeff for WATER @ 20C (0.0033 [1/K])
v - kinematic viscosity
a - thermal diffusivity

Gr = (g*B (Tu-Tf)*H^3) / (v^2)
where H - distance between two plates - 7mm

2. Also, based on ANSYS guide and posts in this forum, I am simulating a Businessq approximation and gradually increasing gravity from 0.00981 to 9.81 m/ss as suggested.
Could anyone tell me, why is it necessary to follow this approach? Why can't gravity be specified as 9.81m/ss in the first place?

[Cryo1991]

So the problem comes from different characteristic length. one use L one use H
i'm not sure the model you describe . is it a rectangular closure without inlet and outlet(if so Tf is not necessary for steady state result)
or it is a tunnel flow

in my opinion increasing G gradually is just make sure solution procedure more steady. if convergence can be reached then just 9.8 is OK

[Arttis]

Originally Posted by Cryo1991

So the problem comes from different characteristic length. one use L one use H
i'm not sure the model you describe . is it a rectangular closure without inlet and outlet(if so Tf is not necessary for steady state result)
or it is a tunnel flow

in my opinion increasing G gradually is just make sure solution procedure more steady. if convergence can be reached then just 9.8 is OK

Thanks for your response. There is inlet and outlet. Yes, I understand that I use different characteristic length - that's because I found it like this in the literature. L in Grashof number is given as the length of the plate while for Rayleigh number it is the distance between the plates (H) that is taken into account.

Do you think I should assume H for Grashof number too?

[LuckyTran]

You can use H or L but you'll have different criteria. Btw you usually use H or L in very different contexts. You usually use H when it's an internal flow (e.g. fully developed) and L for external flow (where boundary layers are still growing).

Originally Posted by Arttis

2. Also, based on ANSYS guide and posts in this forum, I am simulating a Businessq approximation and gradually increasing gravity from 0.00981 to 9.81 m/ss as suggested.
Could anyone tell me, why is it necessary to follow this approach? Why can't gravity be specified as 9.81m/ss in the first place?

It's just a user hack to improve convergence. You can start with 9.81. In fact I recommend to do so so that any divergence will happen quickly. If it is a problem, then you can worry about how to deal with it.

[Arttis]

Originally Posted by LuckyTran

You can use H or L but you'll have different criteria. Btw you usually use H or L in very different contexts. You usually use H when it's an internal flow (e.g. fully developed) and L for external flow (where boundary layers are still growing).



It's just a user hack to improve convergence. You can start with 9.81. In fact I recommend to do so so that any divergence will happen quickly. If it is a problem, then you can worry about how to deal with it.

In my case, the flow is fully developed, inside a rectangular cavity between two heated plates. Does that mean I must use H for both Rayleigh and Grashof numbers, meaning that based on my boundary conditions, the flow is laminar? I am not saying you're incorrect but I couldn't find such expression in the literature...

I appreciate your help.

[LuckyTran]

If you use H, you wouldn't compare Gr with 10^12 but another number. I don't know what is though.

For example, the critical Reynolds number for a flat plate based on L is 500,000 whereas the critical Reynolds number for pipes based on tube diameter is 2300.

[Arttis]

Originally Posted by LuckyTran

You can use H or L but you'll have different criteria. Btw you usually use H or L in very different contexts. You usually use H when it's an internal flow (e.g. fully developed) and L for external flow (where boundary layers are still growing).



It's just a user hack to improve convergence. You can start with 9.81. In fact I recommend to do so so that any divergence will happen quickly. If it is a problem, then you can worry about how to deal with it.

Is it possible to get the correct result with the reduced gravity? When I impose 9.81m/ss, the residuals drop to 1e-02 but the velocity that I get in the cavity is too large comparing to other researches that I refer to. However, when I set lower gravity, the results make sense.