Smoothing and statistical evaluation of laser Doppler velocimetry data of turbulent flows in rotating and reciprocating machinery

Abstract Arbitrarily time-distributed velocity information acquired by laser Doppler velocimeter systems needs special care when evaluated wrt. the mean velocity and the components of the Reynolds stress tensor. In rotating machinery, the arrival time information can be uniquely mapped to the angular position ϕ of the runner blades by using encoder signals relating a fixed runner position to an arrival time. It is convenient to statistically evaluate the velocity information of the detected particles in an angular window [ϕ0−Δϕ/2,ϕ0+Δϕ/2] in order to obtain mean velocities and turbulence values for an angular position ϕ0. This approach has the inconvenience that turbulence values calculated from standard deviations are influenced by a possible variation in the mean velocity in the evaluation window. Other problems that arise with this “evaluation window” method are the influence of unevenly angular-distributed velocity information on the mean velocity or the poor resolution of maxima and minima of the mean velocity, which is similar to the problem pointed out by Jakoby et al. but being of second-order nature. In this paper, different improvements in the “evaluation window” method wrt these problems based on ideas found in a paper by McDonald and Owen are presented. A confidence interval calculation, generalizing the methods of Boutier, for all calculated values is included, which allows an appropriate window size Δϕ to be chosen for each particular situation. The different methods are compared using examples from wake flows of axial hydraulic turbomachinery measured in air and water.