[Hr_kules]

Hey guys,


i want to simulate a turbulent flow through a pipe with heat exchange in a pipe.
I have made a pure heaxaeder mesh in gmsh and imported in OF. The simulation itself runs and converges. However the results are so far not okay. I want to validate my simulation with the Dittus Boelter equation that give the Nusselt Number as a function of Reynolds and Prandtl Number. The result of the equation is about 100, ym simulation results in 273.

I first examined the mesh. The checkMesh utility with additional flags resulted in following:

Mesh stats
    points:           2251612
    faces:            6693073
    internal faces:   6633527
    cells:            2221100
    faces per cell:   6
    boundary patches: 4
    point zones:      0
    face zones:       0
    cell zones:       1

Overall number of cells of each type:
    hexahedra:     2221100
    prisms:        0
    wedges:        0
    pyramids:      0
    tet wedges:    0
    tetrahedra:    0
    polyhedra:     0

Checking topology...
    Boundary definition OK.
    Cell to face addressing OK.
    Point usage OK.
    Upper triangular ordering OK.
    Face vertices OK.
    Topological cell zip-up check OK.
    Face-face connectivity OK.
    Number of regions: 1 (OK).

Checking patch topology for multiply connected surfaces...
    Patch               Faces    Points   Surface topology                   Bounding box
    inletFluid          3173     3212     ok (non-closed singly connected)   (-0.5 -0.5 0) (0.5 0.5 0)
    outletFluid         3173     3212     ok (non-closed singly connected)   (-0.5 -0.5 14) (0.5 0.5 14)
    wallEntrance        7600     7676     ok (non-closed singly connected)   (-0.5 -0.5 0) (0.5 0.5 2)
    wallDeveloped       45600    45676    ok (non-closed singly connected)   (-0.5 -0.5 2) (0.5 0.5 14)

Checking geometry...
    Overall domain bounding box (-0.5 -0.5 0) (0.5 0.5 14)
    Mesh has 3 geometric (non-empty/wedge) directions (1 1 1)
    Mesh has 3 solution (non-empty) directions (1 1 1)
    Boundary openness (3.44459e-17 6.30548e-16 -1.28511e-16) OK.
    Max cell openness = 3.28417e-16 OK.
    Max aspect ratio = 7.45032 OK.
    Minimum face area = 7.69428e-05. Maximum face area = 0.000826506.  Face area magnitudes OK.
    Min volume = 2.53194e-06. Max volume = 7.36883e-06.  Total volume = 10.9831.  Cell volumes OK.
    Mesh non-orthogonality Max: 38.9458 average: 6.83294
    Non-orthogonality check OK.
    Face pyramids OK.
    Max skewness = 1.52765 OK.
    Coupled point location match (average 0) OK.
    Face tets OK.
    Min/max edge length = 0.00384714 0.0413253 OK.
    All angles in faces OK.
    Face flatness (1 = flat, 0 = butterfly) : min = 0.999983  average = 1
    All face flatness OK.
    Cell determinant (wellposedness) : minimum: 0.149651 average: 3.62146
    Cell determinant check OK.
    Concave cell check OK.
    Face interpolation weight : minimum: 0.263644 average: 0.494385
    Face interpolation weight check OK.
    Face volume ratio : minimum: 0.365609 average: 0.971067
    Face volume ratio check OK.

Mesh OK.

End

I added function objetcs to examine the results:

wallHeatFlux wallHeatFlux1 write:
    writing object wallHeatFlux
    min, max, Q [W], q [W/m^2] for patch wallDeveloped = 999.817, 1000.27, 37688.5, 1000

surfaceFieldValue outletTemperature write:
    areaAverage(outletFluid) of T = 294.348

surfaceFieldValue wallDevelopedTemperature write:
    areaAverage(wallDeveloped) of T = 299.835

surfaceFieldValue wallEntranceTemperature write:
    areaAverage(wallEntrance) of T = 298.551

surfaceFieldValue inletTemperature write:
    areaAverage(inletFluid) of T = 293.15
End

Note that the inlet temperature and the wallheatflux are boundary conditions. My calculation of the Nusselt number is done in following way:


t_bulk = (t_inlet+t_outlet)*0.5
h = q/(t_wall - t_bulk)
with t_wall = areaAverage(wallDeveloped)
and q = wallHeatFlux


Nu = (h*d_h)/kappa
with d_h the hydraulic diameter of my pipe and kappa the thermal conductivity of the fluid at bulk temperature.


I have attached a few pictures from my results. I think (pure gut feeling) the the temperature of the outlet is too low and the wall temperature is too high.
In my T file the wall heat flux is defined as:

    wallEntrance
    {
        type            externalWallHeatFluxTemperature;
        mode            flux;
        q        uniform 1000;
        kappaMethod     fluidThermo;
        value           uniform 293.15;
    }
    wallDeveloped
    {
        type            externalWallHeatFluxTemperature;
        mode            flux;
        q        uniform 1000;
        kappaMethod     fluidThermo;
        value           uniform 293.15;
    }

Has anybody an idea what could be the mistake? Is the wall heat flux ill defined? Would a fixedGradient be better? If there is any more information required to answer this question i will proivde it of course.


Thanks in advance!




Image explanation:
The first image shows the temperature plot as seen from the outlet; the second from the inlet and the third a clip through the pipe.

[Hr_kules]

Has anybody an idea?

[Hr_kules]

Turned out that the wall temperature is too low instaed of too high, however i still have no idea how to resolve this.

I changed the thermophysical properties, so that the heat transport is not constant, but all the values for cp, rho and so on are now polynomials based on temperature.

The mesh has now in accordance with the used k-epsilon model a y+ between 30 and 300 and i checked all the wall functions.

With the used boundary conditions i should acutally reach a delta T of about 10.8 Kelvin so that the calculated Nusselt number is similar to the Nusselt Number of the Dittus Boelter equation given the same Reynolds and Prandtl Number.


Is there anything else i can look into? Its starting to get frustrating and a bit embarrassing that a pipe and a heat flux are so difficult to handle.


So, if you got an idea, please let know!