How is the Wall Adjacent Temperature or near wall temperature calculated (Tnw) in ANSYS CFX?




The answer depends upon whether the flow is laminar or turbulent. In any case, the near wall temperature is definitely not just the temperature at the first node off the wall.

For turbulent flow, Tnw is the conservative temperature for the wall node. This is what is used to close the wall heat flux when using turbulent wall functions.

For laminar flow, it is taken from averaging the vertex temperatures in the element adjacent to the wall.

When the k-e model is used, the near wall temperature is calculated using wall functions. If the SST model is used and the grid is such that wall functions are not used, then Tnw will approach the average of the hybrid wall temperature and the temperature of the first node off the wall.

Here are the results of a simple demonstration calculation:

A test case with an inlet flow rate of 1 m/s and inlet temperature of 150 F (338.71 K). The walls had a specified temperature of 70 F (294.26 K). A polyline is created to examine the temperature distribution near the outlet.

For all cases, the hybrid wall temperature at the wall was 294.26 K.

With the k-epsilon model, the conservative value at the wall was 321.22 K (Tnw) and the temperature at the first node off the wall was 322.38 K.

With the SST model (the y-plus value was around 3), the conservative temperature at the wall was 299.76 K and the temperature at the first node
off the wall was 305.09 K.

So, when the k-e model is used, the near wall temperature is calculated using wall functions. In this case you should expect the near wall temperature and the temperature at the first node off the wall to be reasonably close to each other, but not exactly equal.

When the SST model is used and the grid is such that wall functions are not used, then you should expect Tnw to be close to the average of the hybridwall temperature and the temperature of the first node off the wall. Checking the latter for the SST model for the demo case, the average for the hybridwall temperature and first node off the wall temperature is (294.26 + 305.09)/2 = 299.675 which is very close to the conservative value reported at the wall (299.76 K).

If the inlet velocity is increased to 4 m/s, the yplus downstream for the demo case increased to near 12. It is now expected that the SST model will use wall functions. The hybrid wall temperature was still 294.26 K. For the demo case with the increased velocity, the conservative temperature at the wall for the SST model was 309.79 K and the temperature at the first node off the wall was 314.92 K. A straight average would have been close to 305 K.

To summarize, then, you shouldn`t expect the temperature at the first node off the wall to be equal to the near wall temperature. For standard wall function grids (i.e. y+ > 11), the two values will probably be close.

If a grid is used to bring y+ down to 2 or 3 and the SST model is used, then the near wall temperature will tend towards the average of the wall temperature and the first node off the wall.



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