Measurement of Internal Channel Heat Transfer Coefficients and Fluid Temperature Using Inverse Methods

The cooling systems found in gas turbine blades and combustor liners often employ the use of convective cooling channels. The heat flux along the wall of an internal channel is typically computed using Newton’s Law of Cooling requiring knowledge of the local heat transfer coefficient and fluid bulk temperature at that location. Experimentally, the measurement of a heat transfer coefficient and the associated driving temperature difference is often difficult. By tracking the surface temperature response to a change in the fluid temperature during a transient experiment, sufficient data can be obtained to determine both the fluid temperature and heat transfer coefficient using inverse methods provided an appropriate mathematical model of the surface temperature response is employed. This procedure avoids the difficult measurement and tedious calculation for the determination of the fluid bulk temperature. To validate the technique, experiments were conducted for the ‘sudden’ heating of a flat plate in a small wind tunnel. The fluid temperature rise was measured with a ‘rapid’ response thermocouple while both thermocouple and thermo-chromic liquid crystal surface temperature history data were obtained on the surface of the plate. Results indicate that for data sets containing sufficient transient surface temperature history, the method can accurately measure heat transfer coefficients and the asymptotic temperature of the fluid temperature rise (within 5% to 10% depending on the surface temperature model used). In many situations the fluid temperature rise is not a ‘step change’. For example, for axial positions far downstream in a channel the assumption introduces bias due to the cooling along the channel walls upstream. The bias generated by the data analysis in the heat transfer coefficient and fluid temperature is examined and compared to more appropriate models describing the temperature rise. A similar situation was simulated in the tunnel and the results analyzed