Discussion about the Practice of Using a Heated Surface in Film Cooling Studies

It is found in many film-cooling experiments and computational analyses that a heated surface is employed to simulate the actual film-cooling condition with a cooling jet and a hot main flow. Considering that the dominant energy passage in turbine airfoil film cooling is always from the hot combustion gas flowing into the airfoil, employing a heated surface to simulate the actual film cooling condition does not provide the correct physics of the heat flow under an actual film cooling condition, and therefore, the results are questionable. The objective of this paper is to investigate the consequent results associated with the practice of employing a heated surface by comparing its result with actual conditions including a conjugate metal wall and internal cooling via a series of computational simulations. When the surface is heated, in some conditions, negative film cooling effectiveness can be found as a result of a higher surface temperature than the main gas stream temperature. This is unrealistic for an operational turbine system. The heated wall acts as an active heat source; as a result, the concept of using the adiabatic wall temperature (Taw) as the driving temperature potential is no longer valid because an artificially created competing heat source is added into the system, and the heat transfer mechanism on the airfoil is not solely determined by Taw. Heating the surface to simulate the film cooling boundary condition, although it does not provide correct physics, can provide the heat transfer coefficient value within 10-15% of the value calculated from the correct boundary conditions. Using a heated surface is only correct under one condition: when all the conditions are reversed, i.e. with a hot jet and cold main gas flow. The practice of using a jet flow with the same temperature of the hot gas (isoenergetic jet) to obtain the film heat transfer coefficient will result in about 20-25% discrepancy from the cooling jet case. The uniformly cooled wall cases fair better than heated cases because it provides correct physics in most part of the surface. NOMENCLATURE b coolant injection slot width (mm) haf adiabatic film heat transfer coefficient (haf = q" / (TawTw)) (W/mK) HFR heat flux ratio (q" / q"o) l chord length (mm) M blowing ratio, (ρu)j/(ρu)g Nux Nusselt number, hx/λ NHFR net heat flux reduction (1q" / q"o) Pr Prandtl number (ν/α) q" heat flux (W/m), positive value for heat flowing from gas into the wall r recovery factor Re l Reynolds number based on chord length, ul/ν Taw adiabatic wall temperature (K) Tw wall surface temperature in contact with gas (K) Tg main gas flow temperature (K) Tj coolant temperature at the cooling jet hole exit (K) Tci internal coolant temperature (K) Tr recovery temperature (K) Tu turbulence intensity Greek Letters η adiabatic film cooling effectiveness, (Tg-Taw)/(Tg-Tj) λ heat conductivity (W/mK) φ film cooling effectiveness, φ = (Tg-Tw) / (Tg-Tj) (or non-dimensional metal temperature) Subscript aw adiabatic wall ci internal cooling conj conjugate blade f with film cooling g main flow of hot gas/air j coolant or jet flow o without film w wall INTRODUCTION Film cooling has been widely used in high-performance gas turbines to protect turbine airfoils from being damaged by hot flue gases. Film injection holes are placed in the body of the airfoil to allow coolant to pass from the internal cavity to the external surface. The ejection of coolant gas results in a layer or