Evaluation of the basic systems of equations for turbulence measurements using the Monte Carlo technique

Abstract

A numerical experiment has been carried out to evaluate two of the methods available for finding the time-averaged mean velocity and the Reynolds stresses of a turbulent flow field using hot wires. The conventional method is based on the series expansion of the response equation, subsequent truncation of the series and time averaging. The improved method is based on squaring and time averaging without neglecting any terms. The method adopted to evaluate these two methods is based on the Monte Carlo simulation of a pseudo turbulent flow field using random-number generators and the corresponding hot-wire response, for a prescribed set of conditions, by assuming an appropriate model for the hot-wire response. The simulated hot-wire response and the calibration constants are then perturbed about their mean values to study the effects of errors in these quantities. The perturbed response is used to compute the time-averaged flow field by the two methods. The deviation of these values from the generated pseudo values, averaged over large number of trials, is used as the criterion to evaluate the methods. This procedure is also used to estimate the errors due to truncation in the conventional method, to study the effect of turbulence-intensity levels and to study the effects of measurement errors. The results indicate that the choice of the method for determining the time-averaged quantities should be based on the turbulence-intensity level and the measurement errors likely to be encountered. The conventional method yields reliable mean-velocity results for turbulence intensities as high as 50% with second-order turbulence correction. If measurement errors are within reasonable limits and the turbulence level is below 20%, the conventional method yields reliable results for Reynolds stresses. The improved method should be used to determine the time-averaged flow field for turbulence intensity above 40–50%. The error in the yaw sensitivity parameter k has an insignificant effect on the mean velocity and Reynolds stresses computed by both methods. By accurately determining the sensitivity s of the hot wire, the accuracy of the measured mean velocity and Reynolds stresses can be improved significantly. An improved method of carrying out the uncertainty analysis for measurements, based on the Monte Carlo technique, has also been outlined.