Improved Heat Transfer Coefficient Data for Gas Turbine Cooling Channels Using Inverse Methods

Determination of heat transfer in channel flow is important in many fields, with particular interest to this research being the cooling channels in gas turbine engine blades. Validation of gas turbine engine design is an essential step in their development process. Accurate knowledge of heat transfer that occurs within turbine blades during their operation allows for reduction of thermal stresses, increasing blade life and energy efficiency. Measuring heat flux, q, directly is difficult, so it is often calculated based on Newton‟s Law of Cooling. Use of thermochromic liquid crystals (TLCs) in determining heat transfer coefficients h is common, as they allow full-field temperature measurement by allowing the experimenter to measure surface temperatures in a non-invasive fashion. Direct measurement of bulk flow temperature is T∞ difficult, with computation requiring detailed upstream information. T∞ and h are known for established geometries, but become uncertain in complex geometries. The goal of this study was to develop a technique using inverse methods to estimate h and T∞ simultaneously using experimental transient TLC surface temperature data. To apply this method to complex geometries, it was first desired to develop it on a simple geometry. An experimental apparatus was designed, immersing a flat plate in a wind tunnel capable of varying fluid flow speed and temperature. The surface of the plate was coated with TLCs and recorded with a digital camera. The plate was subjected to a sudden heating of the air flow, and the TLC response was recorded. The hue camera data was converted to temperature data, being validated by an array of thermocouples. Analytical models were developed that related surface temperature to time, h, and T∞, in which the profile of T∞ in time was assumed first to be a step function, then a series of ramps. These surface convection formulations were used with a conjugate gradient inverse method to estimate h and T∞ using TLC hue temperature data as the input. The inverse method was tested with models and data of increasing complexity at three plate positions at various distances from the plate leading edge. First, a step change model was used to verify h and T∞ could be estimated simultaneously. Then, experimental hue temperature data was used with the series of ramps model to estimate these parameters. The lead position (Position 1) worked very well with the step function, producing T∞ values within 4% of true values, and h values within accepted ranges. Positions 2 and 3 had relatively successful results, predicting T∞ with 10% accuracy but with h values greater than accepted correlation ranges. Use of generated data with the series of ramps formulation predicted algorithm convergence with large error, which was corroborated with parameter estimation using experimental data. Experimental data produced large variances in initial T∞ slopes, but was still able to minimize the objective function in a stable way. It was concluded that the method works but will require additional constraints for increased accuracy