Minimizing recalibration using a non-linear regression technique for thermal anemometry

A new method to minimize recalibration in thermal anemometry using a non-linear regression technique is investigated. This method finds potential applications in cases of correcting for non-thermal calibration drifts in long measurements and scenarios where direct calibration of the hot films/hot wires is not possible or suffers significant uncertainties. The essential input for this technique is the a priori knowledge of the first three or four moments of velocity or wall-shear stress for a given Reynolds number. These can be obtained from a separate database (experimental or numerical) in cases where this technique is used as an alternative to direct calibration, or from a previous or simultaneous set of experiments when correcting for non-thermal calibration drifts. Using this input, the coefficients for the assumed calibration functional form can be obtained by an error minimization process. Illustrative results are shown for channel flows where glue-on hot-film probes and hot-wire probes are used for wall-shear stress and streamwise velocity measurements, respectively. There is found to be a good agreement between the velocity and wall-shear stress obtained using regression and prior calibration, which is confirmed using both time history and probability density function plots. Sensitivity to the form of calibration relationship, number of moments, and number of samples required for the regression are conducted. Through examples, it is observed that this method works well in estimating the data when moments obtained from a numerical database are used and also works well in correcting for non-thermal calibration drifts. This technique is also shown to work well for the estimation of data from the voltage signals if moments are available for a Reynolds number “close” to, but not the same as, the measured Reynolds number. One additional potential scenario for application related to the measurement in external flows is then discussed. Graphic abstract: [F