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Underestimation of turbulence / heat transfer - Capillary tube

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Old   December 8, 2015, 12:27
Default Underestimation of turbulence / heat transfer - Capillary tube
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Phil Gadsby
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Hi,

I am at something of a brick wall with my simulation and hopefully somebody can suggest a reason why my model is not reproducing experimental results.

In my experiment I pumped heptane through an electrically heated capillary tube (clamped vertically between bus bars) and recorded the external wall temperature with a thermal camera and the fluid exit temperature with a TC at the tube outlet. This was repeated for 3 currents (40-60A). System pressure is 2MPa.

By my calculation, the inlet Re should be around 4000:
Tube diameter = 530um
Flow rate = 65ml/min = 1.08E-06m^3/s
Area = 2.21E-07m^2
u avg = Q/A = 4.91m/s
@20oC:
rho = 685kg/m^3
kinematic viscosity = 6.16E-07m^2/s
thus Re = V*D/k visc = 4.91 * 530E-06 / 6.16E-07 = 4224.

I run a simulation without heat to calculate the fully developed velocity profile and apply at the inlet. I also run simulations to check my measured values of friction factor, from which I calculate a roughness height by using the colebrook white equation. Then I apply the profile at the inlet, and run a simulation with heat generation in the tube wall.

Therefore my model boundary conditions (2D axisymmetric):

Inlet:
Velocity: 4.91m/s
Tuburbulence intensity: 6%
Hydraulic diameter: 530um
Temp: 300K

Outlet: outflow
Axis: axis

Inner wall:
Roughness height: 19.5um, roughness constant = 0.5

Solid wall:
Egen = ~6E8 W/m^3

Outer wall:
Mix of convection and radiation: 17W/m^2K, E=0.95 (free stream T = 300K)

Tube ends: insulated

Fluid properties:
Temp dependent properties for heptane at 2MPa from NIST database. Applied as UDF for rho, visc, Cp and k

My first port of call was k-w SST. The solution converges without issue, but the flow remains laminar across the whole length, despite being 4000 at the inlet(??). As a result, i get much higher than observed tube wall temperatures (up to 700oC for the 50A case, in my experiment the max was 200oC in the 60A case) and much lower than observed fuel exit temperature - being around 100oC in the experiment but only a degree or two over ambient in the model (measured at the centreline).

Then i tried the k-w SST transition model to see if this would allow transition to take place (even though it should already be turbulent!?) and enhance heat transfer to give me a closer result to what i have observed experimentally. The model did introduce turbulent ke, but it hasn't made a huge amount of difference - the fuel exit temperature from the model increased to around 320K.

My model has around 800K cells and y+ is well below 1.

I am now completely stumped - having checked my BC values and material properties repeatedly I can't see an obvious issue there.

Can anybody think of anything I might have missed along the way?

I can upload further information if required.

Thanks
Phil.
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Old   December 9, 2015, 15:36
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Lucky Tran
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It seems like you are blaming the CFD results not matching the experimental ones on the flow being laminar.

But how do you verify whether your flow is laminar or turbulent? What variables are you looking at?
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Old   December 10, 2015, 10:16
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Phil Gadsby
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I have outlined my calculation of Re above.


Inlet Re is around 4000 and should only increase from inlet to outlet due to change in fluid properties with temperature (density and viscosity).

Last edited by Gadders; December 10, 2015 at 11:37.
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Old   December 10, 2015, 11:11
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Ok your Reynolds number is 4000. Then you go and run the simulation and find that the flow is laminar."" How do you conclude that the flow is laminar if the Re=4000 ? So I ask again, what criteria are you using to say "but the flow remains laminar" ?
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Old   December 10, 2015, 11:31
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Phil Gadsby
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By plotting any turbulence value (k, i etc) along the tube, or looking at the radial distribution of temperature (very high radial temperature gradient)... i can see that turbulence wasn't predicted.

I have since re-built my UDF and applied temperature dependent polynomials for all fluid properties (density, viscosity, cp and k) which seems to have produced a more sensible flow field; turbulence from inlet, not requiring the transition model and a more even radial distribution of temperature. Before, i had either not loaded the UDF correctly (i think values for kerosene were still in libudf) and/or had left cp and k as constant values.

I re ran my simulation, and now for the same power I have a more sensible external wall temperature profile when compared to fluid temperature profile along the centreline. However, the model still grossly underestimates the fluid temperature increase from inlet to outlet.

Applying 5.5e8 W^m3, my fluid temperature increases by only 2K, and my tube external wall T varies from 336-343K (inlet-outlet). In the experiment, the fluid T increase was around 80K and the external wall temperature was 394-418K.

What could be the reason for the underprediction of heat transfer from wall to fluid?
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