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EJH November 2, 2010 10:40

Petukhov, Gnielinski HTC
I have a "simple" simulation that's driving me nuts. I'm trying to prove the accuracy of the Petukhov-Gnielinski heat transfer coefficient correlation for thermal-entry length in a pipe (see under section 1-3) using the following model: A 2.2m long pipe with inner diameter of 9.7mm. There's an unheated section 1.6m long (to achieve a fully-developed velocity profile), followed by a 0.6m long section with constant wall heat flux. Water is the fluid, and I'm using SST turbulence model. The Reynolds number is around 52000. The pipe wall temperature, mass-flow averaged mean temperature, and the resulting Nusselt number all have the correct shape, but the Nusselt number magnitude is off by a few thousand. I've tried all sorts of meshes. Any advice?

stumpy November 2, 2010 11:50

Are you using the default wall heat transfer coefficient, which would be based on the near-wall temperature? If so, you probably want to set a reference temperature for the HTC calculation using the expert parameter 'tbulk for htc'.

EJH November 2, 2010 12:50

Unfortunately, I can't use the near-wall temp, nor a constant value for 'tbulk'. It needs to be a velocity-averaged temperature (since water is incompressible, I can use mass-averaged temp.). Basically I have a bunch planes marching down the pipe and use the equation massFlowAve(Temperature)@Plane1 to find tbulk throughout the axial length of pipe.

michael_owen November 4, 2010 13:20

How are you calculating the Nusselt number?

EJH November 4, 2010 13:34

Nu = h*dia./k
q" = h(Twall - Tmean)

q" and the pipe diameter are constant input values. k is a constant material property.

Twall I get from a line generated at the wall, and Tmean comes from "massFlowAve(Temperature)@Plane x" where I have multiple planes normal to the flow at various axial locations in the pipe. Then I calculate the heat transfer coefficient from q", Twalls (at the same axial locations as my planes), and Tmeans, then get the Nusselt Numbers along the pipe length.

michael_owen November 4, 2010 14:44

Twall should be the solid surface temperature. This is NOT the fluid temperature at the wall; there is a discontinuity in temperature at the fluid solid interface. Using the fluid temperature will give you an artificially small delta T in the calculation, meaning your heat transfer coefficient and hence your Nusselt number will be artificially high.

EJH November 4, 2010 15:53

I originally had the model as three domains: two solids (one heated pipe and one unheated pipe), and one fluid (water). The heated pipe had a constant heat flux boundary condition at its OD. I saw back-effects of the heated portion of the pipe into the water prior to the water entering the heated portion even though I had an adiabatic wall separating the two pipes. Also, the resultant heat flux on the inner pipe wall was not constant. Therefore, I switched to two domains: one unheated water and one heated water which has the heat flux boundary at the OD (which would be the ID of the pipe, if it were there). I adjusted my heat flux value to account for the difference in area of the original pipe OD and the new water OD, although that shouldn't change the Nusselt Number. Should I put the pipe back in? If so, how could I ensure no energy gets transferred to the water prior to my x=0 point (the point where the heated wall starts)?

michael_owen November 4, 2010 16:23

Yeah. The problem is that you don't know the temperature of the pipe, which is the temperature that goes into the heat transfer coefficient calculation.

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