ON THE SERIES EXPANSION OF HOT-WIRE RESPONSE EQUATION

This paper discusses the characteristics of the relative errors of the measured values of the mean velocity and the Reynolds stress derived from the approximation of the hot-wire response equations when those values are measured by I and X probes using the conventional method. The general hot-wire response equations and their series expansions are shown first. The conditions for the convergence of the series equations and the convergence domain expressed in the turbulence velocity space are also shown. By numerical simulation, based on approximation of the distribution of turbulence velocities by the Gaussian distribution, the relative errors of the measured values derived from the approximation of the hot-wire response equations by the series equations were shown to decrease, not necessarily monotonically, as the numbers of terms of the series equations were increased when the turbulence intensity was high. Apart from the problems of approximation by the series equations, the method of measurement of the mean velocity direction and characteristics of the measured angles by the I probe are also discussed.