Natural convection in an annulus

[Wenhao Xue]

Hello :

I am running a case that natural convection in an annulus. the outer cylinder maintains a uniform temperature T = 0, while the inner one has a heat flux at the surface with ∂T/∂n = m = −1. In the simulation, the radii ratio β = Ri/Ro is fixed at 0.5, where Ro and Ri are the radii of the inner and outer cylinders, respectively. The non-dimensional governing equation and nondimensional scaling are listed as follows.

The Pr=0.7, Ra=5700=, Q denotes heat flux, L=(Ro-Ri). I build a cylinder mesh and specify the boundaries as the annulus geometry. The .rea , .usr , SIZE , .box files are attached.  My problem is with these files I can't get the right result, comparing with the benchmark result.

My result:

Benchmark result[1]:

Could anyone help to find out where the problem is?

Kind regards

W.H.Xue

[1]: Tao S, Xu A, He Q, et al. A curved lattice Boltzmann boundary scheme for thermal convective flows with Neumann boundary condition[J]. International Journal of Heat and Mass Transfer, 2020, 150: 119345.

[Fischer, Paul]

Dear Wenho,

Normally surface flux would be:

k dT/dn = q"   ( = "flux" in userbc )

In Nek, we prescribe q" --- not dT/dn.

Does this help at all?

Best,

Paul

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Subject: [nek5000] Natural convection in an annulus

 

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[Wenhao Xue]

Dear Professor :

Thanks for your reply!

I noticed this problem. The heat flux Q=-k dT/dn .  

In this simulation,  dT/dn = m = −1, so the value of heat flux at the inner surface was Q=-k (-1)=k = sqrt(1/(Ra*Pr)) (="flux" in  userbc).

Is it correct? 

Kind regards

W.H.Xue

[Wenhao Xue]

Hello :

Sorry to ask this question again. I found the one previous mistake that I ever make. For the buoyance, the buoy = temp/(QL/kappa), using its dimensionless form. So it should be rewritten as buoy=temp/(Ro-Ri)(rhoCp=1,  dT/dn =  −1, Q=-kdT/dn=k = kappa*rhoCp = kappa). The new .usr file is attached

 But I still can not get the correct result. 

 Could anyone give me some suggestions?

Kind regards

W.H.Xue