# Natural convection on a vertical cylinder

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March 16, 2022, 14:12
Natural convection on a vertical cylinder
#1
New Member

Roxana Laspiur
Join Date: Jul 2021
Location: Salta-Argentina
Posts: 5
Rep Power: 4
Hi !

I am new to OpenFoam. I am trying to simulate internal natural convection on a vertical cylinder, but I have a problem with the result. I am working with the BuoyantBoussinesqPimpleFoam solver (transient case).
A time large (approx 30 min) quasi-steady, I get a full stratified fluid full but streamlines aren't expected (toroidal shape). I also compared the vertical velocity with radius, with a paper by Hess and Miller, did not come up to expectations.

I think my problem is in the Dict of fvSolution and fvSchemes.
I am working in the laminar regime Ra=10¹⁰.
BC:

• wall top and bottom isolated
• sidewall T= 296 K
Fluid is water and T_0= 293 K

Attached are the Dict and images of the T-profile and the streamlines.

blockMeshDict:
Code:
```l          0.30;
nl        -0.30;
s          0.35;
sn        -0.35; //longitud de la curvatura del cuadrado interior
// datos del cilindro
Rn         -0.5;
H           1;  //altura
//arcos del cilindro
X           0.353553;  //x=R*cos 45º
Xn         -0.353553;
Z           0.353553;  //z= R * sen 45º
Zn         -0.353553;

scale        1 ;
vertices
(
(\$l  0 \$l)  //0
(\$nl 0 \$l) //1
(\$nl 0 \$nl)//2
(\$l  0 \$nl) //3

(\$l  \$H \$l)  //4
(\$nl \$H \$l) //5
(\$nl \$H \$nl)//6
(\$l  \$H \$nl) //7
//cilindro externo
(\$X 0 \$Z)   //8
(\$X 0 \$Zn)  //9
(\$Xn 0 \$Zn) //10
(\$Xn 0 \$Z)  //11

(\$X \$H \$Z)   //12
(\$X \$H \$Zn)  //13
(\$Xn \$H \$Zn) //14
(\$Xn \$H \$Z)  //15
);
blocks
(
hex (0 3 2 1 4 7 6 5) (20 20 35) simpleGrading (1 1 1)
//block 1
hex (8 9 3 0 12 13 7 4) (20 10 35) simpleGrading (1 4 1)
//block 2
hex (9 10 2 3 13 14 6 7) (20 10 35) simpleGrading (1 4 1)
//block 3
hex (10 11 1 2 14 15 5 6) (20 10 35) simpleGrading (1 4 1)
//block 4
hex (11 8 0 1 15 12 4 5) (20 10 35) simpleGrading (1 4 1)
);

edges
(
arc 0 1 (0 0 \$s)
arc 1 2 (\$sn 0 0)
arc 2 3 (0 0 \$sn)
arc 3 0 (\$s 0 0)
arc 4 5 (0 \$H \$s)
arc 5 6 (\$sn \$H 0)
arc 6 7 (0 \$H \$sn)
arc 7 4 (\$s \$H 0)

//cilindro externo
arc 8 9   (\$R 0 0)
arc 9 10  (0 0 \$Rn)
arc 10 11 (\$Rn 0 0)
arc 11 8  (0 0 \$R)
arc 12 13 (\$R \$H 0)
arc 13 14 (0 \$H \$Rn)
arc 14 15 (\$Rn \$H 0)
arc 15 12 (0 \$H \$R)
);
boundary
(
wallTop
{
type wall;
faces
(
(4 7 6 5)
(12 13 7 4)
(13 14 6 7)
(14 15 5 6)
(15 12 4 5)
);
}
wallDown
{
type wall;
faces
(
(0 1 2 3)
(8 9 0 3)
(10 9 3 2)
(10 2 1 11)
(1 0 8 11)
);
}
sides
{
type wall;
faces
(
(11 8 12 15)
(10 11 15 14)
(9 10 14 13)
(8 9 13 12)
);
}
);

```

ControlDict:
Code:
```FoamFile
{
version     2.0;
format      ascii;
class       dictionary;
location    "system";
object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     buoyantBoussinesqPimpleFoam;

startFrom       latestTime;

startTime       0;

stopAt          endTime;

endTime         2000;

deltaT          0.03;

writeControl    timeStep;

writeInterval   1000;

purgeWrite      0;

writeFormat     ascii;
writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;

maxCo           0.5;

functions
{
#includeFunc singleGraph1
#includeFunc singleGraph2
}

```

fvSchemes:

Code:
```ddtSchemes
{
default         Euler;
}

{
default         Gauss linear;
}

divSchemes
{
default         none;

div(phi,U)      Gauss QUICK; //upwind
div(phi,T)      Gauss QUICK; //upwind
div(phi,k)      Gauss upwind;
div(phi,epsilon) Gauss upwind;
div(phi,R)      Gauss upwind;
div(R)          Gauss linear;
}

laplacianSchemes
{
default         Gauss linear uncorrected;
}

interpolationSchemes
{
default         linear;
}
{
default         uncorrected;
}

```

fvSolution:
Code:
```solvers
{
p_rgh
{
solver          PCG;
preconditioner  DIC;
tolerance       1e-6;
relTol          0.01;
}

p_rghFinal
{
\$p_rgh;
relTol          0;
}

"(U|T|k|epsilon|R)"
{
solver          PBiCGStab;
preconditioner  DILU;
tolerance       1e-6;
relTol          0.1;
}

"(U|T|k|epsilon|R)Final"
{
\$U;
relTol          0;
}
}
PIMPLE
{
momentumPredictor no;
nOuterCorrectors 1;
nCorrectors     2;
nNonOrthogonalCorrectors 0;
pRefCell        0;
pRefValue       0;
}

relaxationFactors
{
equations
{
"(U|T|k|epsilon|R)" 1;
"(U|T|k|epsilon|R)Final" 1;
}
}
```

Thanks for your help and sorry for my English.

Attached Images
 streamline1980s.png (133.2 KB, 3 views) T1980s.png (15.7 KB, 2 views)

 Tags buoyantbousspimplefoam, cylinder, natural convection, water

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