[Paper Review] Limitations of estimating turbulent convection velocities from PIV

Roeland de Kat, Lian Gan+2 more|arXiv (Cornell University)|Nov 25, 2013

Fluid Dynamics and Turbulent Flows9 references9 citations

TL;DR

This paper investigates the limitations of estimating turbulent convection velocities from particle image velocimetry (PIV) data using a phase-spectral approach. It demonstrates that while measurement noise, flow development, and finite domain effects spread the convection velocity probability density function (pdf), the mode of the pdf reliably matches the true convection velocity, with the most probable velocity equaling the local mean flow in turbulent boundary layers.

ABSTRACT

This paper deals with determination of turbulent convection velocities from particle image velocimetry (PIV). Turbulent convection velocities are of interest because they can be used to map temporal information into space. Convection velocity can be defined in several different ways. One approach is to use the phase-spectrum of two signals with a time-separation. Obtaining convection velocity per wavenumber involves determining a spatial spectrum. PIV data is limited in spatial resolution and sample length. The influence of truncation of both spatial resolution and frequency resolution is investigated, as well as the influences of spatial filtering and measurement noise. These issues are investigated by using a synthetic data set obtained by creating velocity-time data with an imposed spectrum. Results from the validation show that, when applying a Hamming window before determining the phase spectrum, there is a usable range of wavenumbers for which convection velocities can be determined. Simulation of flow evolution, movement into and out of the measurement plane, and measurement noise show that these result in a spread in convection velocities using the current approach. Despite this spread, the most probable calculated convection velocity coincides with the imposed convection velocity. Application of the phase-spectral approach to a turbulent boundary layer with $Re_τ\approx 2700$, shows there is a range of convection velocities and that the most probable convection velocity is equal to the local mean velocity.

Motivation & Objective

• To assess the reliability of estimating turbulent convection velocities from PIV data under practical limitations such as finite spatial and temporal domains.
• To investigate how spatial resolution, sample length, measurement noise, and flow evolution affect convection velocity estimation.
• To evaluate whether the phase-spectral method can accurately recover convection velocities in the presence of spectral leakage and filtering effects.
• To determine the range of wavenumbers for which convection velocity can be reliably estimated using PIV data.
• To validate the method using synthetic data and apply it to real turbulent boundary layer flows at Reτ ≈ 2700.

Proposed method

• A phase-spectral approach is used to estimate convection velocity by computing the phase difference between velocity signals at different spatial and temporal separations.
• The method computes convection velocity as $ u_c = -rac{ ext{phase difference}}{ ext{time separation}} imes ext{spatial separation} $, avoiding reliance on power spectra.
• Synthetic velocity data with imposed spectra are generated to simulate PIV conditions and validate the method under controlled noise and resolution constraints.
• A Hamming window is applied before phase-spectrum computation to reduce spectral leakage and improve resolution in the wavenumber-frequency domain.
• The probability density function (pdf) of instantaneous convection velocities is computed per wavenumber to assess spread and central tendency.
• The method is applied to experimental PIV data from a turbulent boundary layer at $ Re_ au \approx 2700 $, using both large and small field-of-view configurations.

Experimental results

Research questions

• RQ1 To what extent do spatial resolution and finite sample length in PIV data limit the accurate estimation of convection velocities?
• RQ2 How do measurement noise and flow evolution (e.g., structures entering/exiting the field of view) affect the distribution of estimated convection velocities?
• RQ3 Can the phase-spectral method reliably recover the true convection velocity despite spectral leakage and filtering effects inherent in PIV?
• RQ4 What is the range of wavenumbers for which convection velocity can be accurately estimated using the phase-spectral approach?
• RQ5 Does the mode of the convection velocity pdf correspond to the local mean velocity in real turbulent boundary layers?

Key findings

• The phase-spectral method enables convection velocity estimation in wavenumber ranges where traditional power-spectrum-based methods fail due to low-pass filtering in PIV.
• Measurement noise and flow development cause a symmetric spread in the convection velocity pdf, but do not bias the mode of the distribution.
• The mode of the convection velocity pdf per wavenumber coincides with the imposed convection velocity in synthetic data, confirming method reliability within the usable wavenumber range.
• In real turbulent boundary layer data, the most probable convection velocity (mode of pdf) matches the local mean velocity at $ y/\delta = 0.1 $, consistent with prior findings on coherent structure convection.
• The spread in convection velocities is larger in the small field-of-view experiment, likely due to higher noise amplification and fewer temporal samples per scale.
• Despite signal degradation from noise and finite domain effects, the mode of the convection velocity pdf remains robust and unbiased, indicating its utility as a reliable estimator.