Numerical evaluation of the uncertainty of double-sensor conductivity probe for bubbly flow measurement

The double-sensor conductivity probe is one of the most commonly used techniques for obtaining the local time-averaged parameters in bubbly flows. The uncertainty of this measurement technique has not been well understood in the past as it involves many different steps and influential factors in a typical measurement. To evaluate the overall uncertainty of the double-sensor probe, a practical Monte Carlo simulation model is developed in this work. The actual measurement process and bubble characteristics are closely simulated in the model. The factors considered include bubble aspect ratio and inclination angle, the test section geometry, probe location in the measuring plane, the restrictions of wall boundary on bubble distribution and velocity fluctuation, and the effect of the sampling time, among others. The simulation results reveal that the measurement uncertainty may be significant for ellipsoidal bubbles with a small aspect ratio. Bubble inclination angle could also affect the measurement accuracy considerably. The uncertainty increases near the wall as several assumptions for the measurement model cannot hold due to wall restrictions. The random error in the time-averaged data is obtained by computing the standard deviation of 100 repeated simulations. The results indicate that convergence rate depends on velocity fluctuation magnitude and measurement location. In summary, the uncertainty in the data obtained by the double-sensor conductivity probe is evaluated based on the actual bubble characteristics and the measurement parameters including the probe location. This way of evaluating measurement uncertainty is a step improvement over the conventional ballpark estimate which does not consider these factors actually involved in the measurement.