Influence of inhomogeneous refractive index fields on particle image velocimetry

The influence of inhomogeneous refractive index fields on particle image velocimetry (PIV) measurements is a well known problem, which leads to an unknown measurement uncertainty in, e.g., flame flows, shock waves and super sonic flows. Previous studies give only rough estimations of the measurement error due to inhomogeneous refractive index fields, and quantitative information is only available for special conditions such as a gradient of the refractive index independent of the viewing direction. Hence, the assessment of the spatial distribution of the quantitative measurement errors inside inhomogeneous refractive index distributions especially for stereoscopic and tomographic PIV is an open question. For this purpose, the flow measurement inside a hot jet flow is considered as an example, and a general analytic description of the error of the measured particle positions inside the hot jet flow is derived, numerically evaluated and finally validated by experiments. In particular, the determination of the particle position with triangulation is investigated, which is performed in stereoscopic and tomographic PIV. As a result, the measurement error is generally larger than for standard PIV without triangulation. The theoretically predicted errors of the measured particle position are validated with experiments and here amount to 11.7 µm for standard PIV and 17.3 µm for triangulation at the same distance from the center of the flow, respectively. Note that the error estimation requires the knowledge of the refractive index field that was determined by temperature measurements in the flow. Furthermore, the error analysis shows that for triangulation the measured particle position depends on the gradient and the curvature of the refractive index field, whereas for standard PIV the measured particle position only depends on the gradient of the refractive index. For the given temperature profile with a maximum temperature of 191 °C, the resulting flow velocity error is maximally 0.8 % with standard PIV, 1.7 % for the in plane and 2.9 % for the out of plane direction with stereoscopic PIV and 1.1 % with triangulation which is performed in tomographic PIV.