Measurement error of tracer-based velocimetry in single-phase turbulent flows with inhomogeneous refractive indices

TL;DR

This study quantifies measurement errors in tracer-based velocimetry caused by inhomogeneous refractive indices in turbulent flows using ray tracing simulations, highlighting the dominant error types and their magnitudes.

Contribution

It provides a detailed analysis of how three-dimensional, spatio-temporal refractive index gradients affect velocity and acceleration measurements in turbulent mixing flows.

Findings

Random errors dominate measurement inaccuracies.

Velocity measurement errors are around 1% for small index differences.

Acceleration errors can reach over 100,000% with larger index differences.

Abstract

Inhomogeneous refractive index fields lead to errors in optical flow velocity measurements. Former respective studies are mostly in quasi two-dimensional flows, and attribute the measurement errors to spatial gradients in the refractive index field, while less attention has been paid to flows with three-dimensional refractive index fields which usually change in space and in time. In this study, ray tracing simulations were carried out in a three-dimensional flow, which is from a direct numerical simulation of single-phase turbulent mixing of two fluids. Given the data of the numerical simulation as reference, the ray tracing simulation is used to quantify the measurement errors of the flow velocity and flow acceleration for tracer-based velocimetry, i.e. particle tracking velocimetry in this study. The errors of both flow velocity and flow acceleration are attributed to the spatial and the spatio-temporal gradients of the refractive indices, respectively, which are closely inherited from flow characteristics. While the dominant type of error depends on the studied flow, the main measurement error for the considered turbulent mixing flow is caused by the random error. When the maximum spatial difference of the refractive indices is about 10 to the power of -6, the relative random measurement error is about 1 % in velocity and about 200 % in acceleration, respectively. When the maximum index difference is about 0.01 (water), the relative random measurement errors of velocity and acceleration are 2000 % and 100,000%, respectively, for the flow considered in this study.