Summary
A model is developed that allows the prediction of the film cooling effectiveness produced by slot injection into a uniform cross flow. The model relies on the fact that when the slot pressure exceeds the cross flow pressure by a small amount only so that injection is weak, the resulting small parameter may be exploited to solve the flow problem. The energy equation for the flow may then be solved to determine how much protection cold gas injection gives to the wall downstream of a slot. Although the leading order energy equation must be solved numerically, a simple asymptotic expression may also be derived to allow predictions of heat transfer at large distances from the injection slot.
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Fitt, A.D., Stefanidis, V. Film cooling effectiveness for subsonic slot injection into a cross flow. Acta Mechanica 128, 233–242 (1998). https://doi.org/10.1007/BF01251893
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DOI: https://doi.org/10.1007/BF01251893