approach to heat transfer coefficients
 

The problem with usage heat transfer coefficient obtained from CFD

q = h •(Tnw – Tw) (1)

is that h is useless outside CFD. The problem is that Tnw is a function of Tw. This way to calculate flux one has to know not only HTC but Tnw as well ( in other words for each wall temperature CFD simulation have be run). It is inconvenient for practical tasks. It looks that there is more convenient way to use CFX results.

Let there are exist such local hå è Tå that next equation will be true for a range of wall temperature values Tw:

q = hå •(Tå – Tw i.e. hå è Tå are independent of Tw. (2)

The system of two equation may be written down :

q1 = hå •(Tå – Tw1) (3)

q2 = hå •(Tå – Tw2) (4)

The solution is:

hå = (q1 – q2)/( Tw2 – Tw1); (5)

Tå = Tw1 + q1/ hå (6)

It may be presented as a strait line in (T, Q,) plain, that passed through points (q1, Tw1) (q2, Tw2) and crossed X-axes in T=Te point.

This idea was checked on case of gas turbine nozzle vane simulation. Tree cases was ran , Tå and hå values were calculated with two cases results and verified with third case. Calculated Tå and hå values remains stable in 300C range of wall temperature.

Next check was done by direct definition of Tå with CFD simulation. The wall BC was defined as q=0 (adiabatic wall). For this case Tå= Tw= Tnw.

The found Tw and Tnw distributios along vane cross-section curves well coincide with calculated Tå values.

Does anyone see hidden problems in solution mentioned above ?