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Spatio-temporal correlation analysis of turbulent flows using global and single-point measurements

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Abstract

A method to extract whole-field spatio-temporal correlations by combining global and single-point measurement techniques of different time resolutions is proposed. For fluid mechanics applications, the emphasis is on the combination of low repetition rate particle image velocimetry (PIV) results with experimental data obtained at largely higher sampling frequencies. The experimental feasibility of the procedure is established from results obtained in the wake of a cylinder, using PIV and constant temperature hot wire anemometry (CTA). The method is then applied to examine the shear layer in the core of a round subsonic jet using PIV and laser Doppler velocimetry (LDV). The accuracy of the cross-correlation functions is compared to the auto- and cross-correlation functions obtained from series of LDV and CTA measurements.

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Abbreviations

B :

Bandwidth (Hz)

B s :

Statistical bandwidth (Hz)

D :

Diameter of the cylinder/jet (m)

f :

Frequency (Hz)

R D :

Diameter-based Reynolds number

R xy :

Cross-correlation function (m2/s2)

\(\hat R_{xy} \) :

Cross-correlation function estimator (m2/s2)

U :

Longitudinal (cylinder) or axial (jet) velocity component (m/s)

V :

Normal (cylinder) or radial (jet) velocity component (m/s)

u, v:

Fluctuating part of U and V (m/s)

tu,i, tv,j:

Arrival time of LDV series U and V (s)

x :

Longitudinal coordinate in the cylinder wake (m)

y :

Normal coordinate in the cylinder wake (m)

z :

Axial coordinate in the jet (m)

ϕ uu , ϕ vv :

Phases of \(\hat R_{uu} \) and \(\hat R_{vv} \) in the frequency domain (rad)

τ :

Time delay (s)

τ c :

Convection-corrected time delay (s)

ω :

Angular velocity (rad/s)

η :

Radial coordinate in the jet shear layer (m)

〈·〉:

Expected value

\(\bar \cdot \) :

Time average

BSA:

Burst spectrum analyser

CTA:

Constant temperature hot wire anemometry

DAQ:

Data acquisition system

LDV:

Laser Doppler velocimetry

PIV:

Particle image velocimetry

PRGC:

Point-referenced global correlation

PTU:

Programmable time unit

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Acknowledgements

This work was completed under a Marie Curie EU Research Program FP5, contract no. HPMD-CT-2000-00022. The fuzzy slotting routines have been written using the freely available Meschach 1.2 library (Meshach Matrix Library, copyright David E. Stewart and Zbigniew Leyk) and Bloodshed Dev-C++ 5 integrated development environment (Bloodshed Dev-C++, copyright Bloodshed Software), which the authors gratefully acknowledge.

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  1. Fluid and Vibrations Group, Mechanical and Manufacturing Engineering, Trinity College, Dublin 2, Ireland

    Ludovic Chatellier & John Fitzpatrick

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  1. Ludovic Chatellier
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  2. John Fitzpatrick
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Correspondence to Ludovic Chatellier.

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Chatellier, L., Fitzpatrick, J. Spatio-temporal correlation analysis of turbulent flows using global and single-point measurements. Exp Fluids 38, 563–575 (2005). https://doi.org/10.1007/s00348-004-0910-3

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