A REVISED EQUATION FOR HEAT FLUX REDUCTION IN FILM COOLING STUDIES AND DISCUSSION OF ITS APPLICATIONS

摘要

In film cooling experimental studies, due to the difficulty in measuring the surface heat flux variation, a Heat Flux Ratio (HFR) equation originally derived by Mick and Mayle [1], has been widely employed to calculate the surface heat flux distribution using the measured adiabatic film effectiveness and surface temperature. A close examination of the derivation process and applications of the HFR equation reveals two issues of concern. First, an implicit assumption was introduced by letting the wall surface temperature of the system without-film be the same as that which would occur with a film-cooled condition. A revised equation is then derived by removing this implicit assumption and incorporating the wall temperature change due to film cooling Secondly, a uniform value of the non-dimensional metal temperature (p (or film cooling effectiveness) has been used in all the previous applications of the HFR equation. This practice implicitly implies that a uniform wall temperature is distributed throughout the entire surface under film cooling, which is usually not the case in real conditions. A series of computational experiments are conducted to verify the revised HFR equation under different conditions as well as examine the validity of using a constant surface temperature in the HFR equation. Results reveal that using a constant value of (0.5 ~ 0.7) to calculate surface heat flux may result in a negative HFR in some simulated cases showing the commonly adopted value Φ=0.5~0.7. This could induce errors and give false HFR. The error is reduced in 3D cases because the streamwise wall temperature becomes more uniform than 2D cases. The difference between the old and new equations can reach about 20%. A conjugate wall cooling simulation shows negative HFR is possible in the region close to the film hole due to the heat conduction from the downstream hotter region into the cooler region near the film hole. Using the actual wall temperature as the Φ-value, the newly revised HFR equation produces the exact heat flux as calculated by CFD including the correct calculation of negative heat flux caused by the conjugate wall.