Unsteady Effects on the Experimental Determination of Overall Effectiveness

An increasingly common experimental method allows determination of the overall effectiveness of a film cooled turbine component. This method requires the Biot number of the experimental model to match that of the engine component such that the nondimensional surface temperature, ϕ, is matched to that of the engine component. The matched Biot number requirement effectively places a requirement on the thermal conductivity of the model and the traditional implementation places no requirement on the model's density or specific heat. However, such is not the case if such a model is exposed to unsteadiness in the flow such as with film cooling unsteadiness. In this paper, we develop an additional nondimensional parameter that must also be theoretically matched to conduct overall effectiveness experiments with unsteady film cooling. Since finding suitable materials with an acceptable combination of thermodynamic properties for a typical low temperature experiment can be difficult, simulations were conducted to determine the impact of imperfectly matched parameters achievable with common materials. Because the disparity between the diffusion and the unsteadiness time scales can hinder numerical simulation, a novel analytical solution to the heat equation with relevant unsteady Robin type boundary conditions is developed. Particular solutions are examined to determine the sensitivity of the temperature response of a turbine blade (or a model of one) to its material properties and the form of the unsteady variation in the convection parameters. It is shown that it is possible to obtain useful experimental results even with imperfectly matched parameters.