Method for determining time-resolved heat transfer coefficient and adiabatic effectiveness waveforms with unsteady film cooling

摘要

A new method for determining heat transfer coefficient (h) and adiabatic effectiveness (η) waveforms h(t) and η(t) from a single test uses a novel inverse heat transfer methodology to use surface temperature histories obtained using prior art approaches to approximate the h(t) and η(t) waveforms. The method best curve fits the data to a pair of truncated Fourier series.

主权项

1. A method for determining heat transfer coefficient h and adiabatic effectiveness η waveforms h(t) and η(t) from a single test on a film cooled test article, wherein η is determined from adiabatic wall temperature Taw as a dimensionless numberη=T∞-TawT∞-Tc,comprising the steps of:
(a) soak the test article to a uniform and known temperature; (b) expose the test article to a freestream flow at a different and known temperature; (c) measure spatial surface temperature Ts as a function of time over a plurality of time steps, to determine Ts(t); (d) calculate surface heat flux qs(t) for each time step; and, (e) find periodic Taw(t) and h(t) functions that are least squares fits to:
qs(t)=h(t)(Taw(t)−Ts(t)), using truncated Fourier series as the periodic Taw(t) and h(t) functions; defined as:h⁡(t)=h^02+∑n=1N⁢⁢(h^n⁢cos⁢n⁢⁢π⁢⁢tL+h~n⁢sin⁢n⁢⁢π⁢⁢tL);and,⁢Taw⁡(t)=T^02+∑n=1N⁢⁢(T^n⁢cos⁢n⁢⁢π⁢⁢tL+T~n⁢sin⁢n⁢⁢π⁢⁢tL).