Film Cooling: a Comparative Study of Different Heater- Foilconfigurations for Liquid Crystals Experiments

A new measurement technique for the determination of the heat transfer coefficient and the film cooling effectiveness is presented. It is based on a regression of multiple transient liquid crystals experiments using an electrical heater-foil producing a nonhomogeneous surface heat flux. This is particularly interesting for film-cooled surfaces where each cooling hole in the heater-foil leads to a non-homogeneous heat flux distribution. The method and its theoretical basis are described. Results on two different heater-foil configurations for one row of film cooling holes are presented. The first heater-foil configuration deals with a longitudinal electrical current relatively to the main flow direction, while the second one is considering a transversal electrical current. NOMENCLATURE BR [-] blowing ratio cp [J/(kgK)] specific heat at constant pressure d [m] film cooling hole diameter G [-] gain factor h [W/(mK)] convective heat transfer coefficient k [W/mK] thermal conductivity L [m] wall thickness N [-] number of experiments P [m] pitch cooling holes q [W/m] surface reference heat flux T [K] temperature t [s] time x [m] spatial coordinate into the material y,z [m] surface coordinates on the plate Submitte ASME Turb 3-6 June 2002, Amster 1 GREEK α [m/s] thermal diffusivity α=k/(ρ cp) η [-] film cooling effectiveness ρ [kg/m] density SUBSCRIPTS 0 initial condition (t=0) aw adiabatic wall i index of experiment LC liquid crystal rg recovery gas tg total gas tc total coolant w wall (x=0) INTRODUCTION In modern gas turbine design, there is a strong desire to increase the inlet hot-gas temperature of the turbine. This would lead to much higher blade temperatures than the maximum allowable metal temperature of the gas turbine blades. In order to protect the turbine blades from melting, the blades need extensive cooling by internal air flow. Usually a combination of internal convective cooling and external film cooling is employed. The cooling designs of these parts have to be highly efficient, because a larger cooling mass flow rate degrades the thermal efficiency of the thermodynamic cycle of the gas turbine. This is especially true for the application of film cooling, where a protective film of cold air is spread around the blade and large cooling mass flows are required. Because of the importance of film cooling for turbine blade design, the subject has been studied d for the o Expo 2002 dam, The Netherlands 1 Copyright © 2002 by ASME Copyright © 2002 by ASME extensively over the past 35 years [1-3]. Most of the studies concentrate on flat plate configurations with film injection through slots, cylindrical or shaped holes [4,5]. When film cooling is considered on airfoil type flows [6-8], numerical methods and correlations have been developed to predict the adiabatic film cooling effectiveness and the increase in heat transfer coefficients, a large number of parameters influencing the film cooling process (such as cooling hole geometry, blowing and momentum flux ratio and main stream turbulence effects). Several models can be found in literature and are used for specific applications only [9-11]. In order to further develop the cooling schemes for gas turbine blades, high quality experimental data are required. Today, in order to obtain these data, a large number of heat transfer experiments are performed by using the liquid crystals technique. Herewith, it is possible to obtain the film cooling performance (adiabatic film cooling effectiveness and increase in film cooling heat transfer coefficients) either by two separate experiments, or by transient experiments. If two separate experiments are performed, the increase in heat transfer coefficient is measured by using the steady-state liquid crystals method for a film cooling injection experiment, where the coolant temperature and the free stream temperature are identical. The increase in heat transfer due to film cooling is obtained by applying a heater-foil at the wall. The adiabatic film cooling effectiveness is additionally measured by using an adiabatic wall and by blowing with a different coolant temperature than the main stream temperature [12]. Using the transient liquid crystals approach, film cooling performance can be obtained by varying the coolant temperature for several runs and employing a regression analysis. These transient experiments are generally performed by the rapid insertion of a preconditioned model [13,14] or by using heater grids in the main flow. Because of the demand to obtain high quality experimental data, new liquid crystals measurement techniques have been developed. One is given in [15] where a step heating technique is described for heat transfer measurements without film cooling. The method has the advantage that uncertainties and losses in the power for the heater-foil do not influence the measured heat transfer coefficient. The objective of the present paper is to introduce a new transient heater-foil method for film cooling situations. By using this new method, the film cooling effectiveness and the heat transfer augmentation can be obtained simultaneously. An analytical theory of this new method is developed. Experimental results on a flat plate with cylindrical film cooling holes are shown for two heater-foil configurations. Results are compared to a correlation issued from experimental data given in the literature. MEASUREMENT TECHNIQUE: THEORY Consideration is given to a flat plate geometry covered by a heater-foil having a row of film cooling holes. The flat plate is subjected to a longitudinal main flow. A transient measurement technique as shown in Fig 1 is developed: at t0=0, a step change in the surface heat flux q(t) is generated by the heater-foil and at the same time a coolant gas is injected at a constant blowing ratio but with a temperature evolution Ttc(t). 2 2 Fig 1: Schematic drawing of the considered flat plate experiment. The equation describing the spatio-temporal evolution of the temperature at a specific location in the plate is given by the onedimensional heat conduction equation without source terms: