Laser-Doppler Velocimeter Measurements in Nonuniform Flow: Error Estimates

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Abstract
An approximate technique is described for estimating errors in velocity measurements obtained by laser-Doppler velocimeter (LDV) techniques due to flow variation within the finite dimensions of the scattering volume. The analysis is applicable to steady laminar or turbulent velocity profiles of arbitrary form. By suitable adjustments in the evaluation of the equations, the technique is also applicable to both cw and individual realization LDV applications. In the LDV technique, the velocities of many particles are observed, either simultaneously or sequentially depending on the particle concentration. The velocity measured at a point is thus some type of mean velocity that is not necessarily equal to the velocity at the center of the scattering volume. The analysis presents a mathematical model for approximating the above averaging process from which estimates of errors in LDV measurements are obtained due to a nonuniform velocity distribution within the scattering volume. In addition, the analysis is extended to allow estimation of errors obtained when velocity measurements are made at locations sufficiently near the wall that part of the scattering volume is truncated by the wall. Example calculations are presented for an arbitrary second order velocity profile, for laminar parabolic flow, and for turbulent flow in a pipe for both cw and individual realization signals.