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 u of the runner blades by using encoder signals relating a ®xed runner position to an arrival time. It is convenient to statistically evaluate the velocity information of the detected particles in an angular window u 0 À Du=2; u 0 Du=2 in order to obtain mean velocities and turbulence values for an angular position u 0 . This approach has the inconvenience that turbulence values calculated from standard deviations are in¯uenced by a possible variation in the mean velocity in the evaluation window. Other problems that arise with this``evaluation window'' method are the in¯uence 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 thè`e valuation window'' method wrt these problems based on ideas found in a paper by McDonald and Owen are presented. A con®dence interval calculation, generalizing the methods of Boutier, for all calculated values is included, which allows an appropriate window size Du to be chosen for each particular situation. The different methods are compared using examples from wake¯ows of axial hydraulic turbomachinery measured in air and water.

Study of the vortex-induced pressure excitation source in a Francis turbine draft tube by particle image velocimetry

“…The phase averaging suppresses the random turbulent fluctuations and isolates the periodical component of the velocity fields induced by the vortex precession. In the case of LDV data measured in rotating machinery, Glas et al (2000) proposed a statistical evaluation of the phase-averaged velocity values and the corresponding turbulent values computed in a phase window of width �φ. The confidence interval of these quantities is estimated for different averaging methods.…”

Frequency-resolved interferometric measurement of local density fluctuations for turbulent combustion analysis

“…When ensemble averaging is applied, classical uncertainty estimates can be performed (e.g. LDV, Glas et al [20]).…”

The application of laser measurement techniques to aerospace flows

“…This falls to an SNR of ¡ 8 dB for a sample size of 128. For data taken from reciprocating or rotating systems, Glas et al [164] have presented a smoothing method based on a statistical evaluation of the particle information in a given evaluation window. Subsequent recommendations were made for an appropriate window size given a particular measurement situation.…”