Investigation of the heat transfer coefficient in a transpiration film cooling with chemical reactions

In modern high performance engines (gas turbines, rocket combustors) the probability of chemical reactions inside a cooling film increases. In the past, the enhanced heat flux in a reactive cooling film is estimated usually using the difference between the hottest temperature inside the boundary layer and the wall temperature as driving temperature difference, assuming the heat transfer coefficient to be the same as in an inert configuration. However, experiments have shown that the heat transfer coefficient of a reactive cooling film differs from an inert one. The objective of this work is to investigate the heat transfer coefficient in a reactive boundary layer in more detail. The surface heat flux of a reactive laminar boundary layer on a transpiration cooled flat plate is analytically derived using boundary layer theory. The results of the simplified boundary layer theory are compared to CFD data for different reactive mixtures. In a reactive cooling film emanating with a mixture fraction Z=1 from a porous surface assuming Burke-Schumann chemistry, the heat transfer coefficient is mainly enhanced by a factor of 1/(1-Zst), where Zst is the mixture fraction at stoichiometric mixture. This factor represents the location of the maximum temperature within the boundary layer.