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Considerations for high resolution laser Doppler measurements in very small circular tubes

When performing laser Doppler measurements in channels and tubes of very small dimensions, the velocity gradient across the measurement volume cannot always be neglected in estimating the mean velocity or the variance of the velocity fluctuations. This effect and the corresponding estimator corrections have been previously documented for plane channels and nozzles of diameter much larger than the measurement volume dimensions. However, for very small pipes and microtubes, for instance holes in fuel injection nozzles, additional corrections are required. These corrections are derived for a generalized geometry and their magnitude is computed in dimensionless form for laminar and turbulent flow profiles. One experimental example will be shown. For large tube diameters the solution approaches asymptotically the result for a plane flow geometry.