An Improved Method for Calibration of X-Probe Hot-wires

A new method for finding the direct calibration equation of the X-probes used in 2-D flow based on the genetic algorithm (GA) is presented. This GA method introduces a new way to find a format for the polynomials used as the calibration equation, which makes them most adaptive to the hot-wire data. The previous methods in direct calibration also used polynomials as the calibration equation but the polynomials had a pre-defined fixed format and their coefficients were obtained from the least square fitting method using the QR factorization algorithm. Each of the former methods of direct calibration suggested a new format for these polynomials to obtain a calibration equation with a less value of error in velocity calculation. But all of the suggested formats in the former methods had some restrictions in their application velocity range, and they were also not adaptive to any set of hot-wire data set. For comparison between the new suggested GA method and a well known former method in direct calibration of 2-D flow which uses one of the most frequent formats of polynomials will be explained in this paper (named in this paper as the QR method because of using the QR factorization algorithm), and it will be implemented on a set of experimental hot-wire data. Then the GA method will be presented, using a stochastic algorithm to find the most adaptive format of polynomial as the calibration equation to the same experimental hot-wire data set. Then a comparison will be made in the velocity calculation error between the two methods (GA & QR). The results show a decrease up to 10 times in error by the presented GA method relative to the QR method. Furthermore the GA method shows to keep the error small in a large range of velocities (10-100 m/s) while the QR method is restricted to a specified range of low velocities because of using a fixed format of polynomial for each set of hot-wire data.

Keywords:

Hot wire , Calibration , 2-D Flow , Genetic Algorithm