Budgets of Reynolds stresses in film cooling with fan-shaped and cylindrical holes

The compressible budget terms in the transport equations of Reynolds stresses are examined from the large eddy simulation (LES) result of the film cooling. The capability of LES and the statistical post-processing procedure were first validated. The compressible Reynolds stress budget terms are then analyzed for both fan-shaped and cylindrical cooling films. The balance of all budget terms is shown. The effect of the blowing ratio on each budget term is examined. The mechanisms by which energy is extracted from the mean flow and distributed among the normal Reynolds stresses are highlighted. The sources of anisotropy in the Reynolds stress distributions are examined in detail, and their relation to the flow patterns of the mean and instantaneous flow is explored. The downstream development of the Reynolds stress budgets is studied, and it is shown that the jets of both fan-shaped and cylindrical films can be split into a near field and a far field with different properties. Far downstream of the cooling films, the Reynolds stress budgets near the wall present similarities with the Reynolds stress budgets in a boundary layer, while the Reynolds stress budgets further away from the wall resemble budgets in a free-shear flow. It is shown that the budgets of the Reynolds stress in the three-dimensional wall jets object of this study obey approximate similarity laws. These laws are based on easily obtained integral scales but need to be modified by suitable powers of the distance from the orifice producing the jet.