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 http://www.cheresources.com/convection.shtml 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?

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'.

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.

How are you calculating the Nusselt number?

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.

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.

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)?

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.