Impulse Response Processing of Transient Heat Transfer Gauge Signals

A new, computationally efficient method is presented for processing transient thin-film heat transfer gauge signals. These gauges are widely used in gas turbine heat transfer research, where, historically, the desired experimental heat transfer flux signals, $q$⁠, are derived from transient measured surface-temperature signals, $T$⁠, using numerical approximations to the solutions of the linear differential equations relating the two. The new method uses known pairs of exact solutions, such as the $T$ response due to a step in $q$⁠, to derive a sampled approximation of the impulse response of the gauge system. This impulse response is then used as a finite impulse response digital filter to process the sampled $T$ signal to derive the required sampled $q$ signal. This is computationally efficient because the impulse response need only be derived once for each gauge for a given sample rate, but can be reused repeatedly, using optimized MATLAB filter routines and is highly accurate. The impulse response method can be used for most types of heat flux gauge. In fact, the method is universal for any linear measurement systems which can be described by linear differential equations where theoretical solution pairs exist between input and output. Examples using the new method to process turbomachinery heat flux signals are given.