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Fast PSP measurements of wall-pressure fluctuation in low-speed flows: improvements using proper orthogonal decomposition

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Abstract

Fast pressure-sensitive paint (PSP) is very useful in flow diagnostics due to its fast response and high spatial resolution, but its applications in low-speed flows are usually challenging due to limitations of paint’s pressure sensitivity and the capability of high-speed imagers. The poor signal-to-noise ratio in low-speed cases makes it very difficult to extract useful information from the PSP data. In this study, unsteady PSP measurements were made on a flat plate behind a cylinder in a low-speed wind tunnel (flow speed from 10 to 17 m/s). Pressure fluctuations (ΔP) on the plate caused by vortex–plate interaction were recorded continuously by fast PSP (using a high-speed camera) and a microphone array. Power spectrum of pressure fluctuations and phase-averaged ΔP obtained from PSP and microphone were compared, showing good agreement in general. Proper orthogonal decomposition (POD) was used to reduce noise in PSP data and extract the dominant pressure features. The PSP results reconstructed from selected POD modes were then compared to the pressure data obtained simultaneously with microphone sensors. Based on the comparison of both instantaneous ΔP and root-mean-square of ΔP, it was confirmed that POD analysis could effectively remove noise while preserving the instantaneous pressure information with good fidelity, especially for flows with strong periodicity. This technique extends the application range of fast PSP and can be a powerful tool for fundamental fluid mechanics research at low speed.

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Abbreviations

A :

Matrix consists of mode coefficients

A(T):

PSP calibration coefficient

B(T):

PSP calibration coefficient

D :

Diameter of the cylinder

I :

Intensity

I ref :

Intensity at reference condition

K :

Discrete matrix of field parameter

M :

Finite number of POD modes

Ma :

Mach number

P :

Pressure

P ref :

Pressure at reference condition

P rms :

Root-mean-square of pressure fluctuation

R :

Temporal correlation matrix

St :

Strouhal number

V ∞ :

Freestream velocity

a n :

Mode coefficients

c :

Length of the flat plate

d :

Thickness of the flat plate

k :

Instantaneous field parameter

\(\bar{k}\) :

Time-average field parameter

k′:

Fluctuation of field parameter

n pe_ref :

Full-well capacity of a CCD at reference condition

t :

Time from the start of PSP data recording

x :

Coordinate in streamwise direction

y :

Coordinate in spanwise direction

ΔP :

Pressure fluctuation

ΔP min :

Noise floor of PSP measurement

Δt :

Time interval of instantaneous pressure data

Λ :

Diagonal matrix with eigenvalues

σ n :

Spatial eigenfunctions

φ :

Phase

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Acknowledgments

This work was supported by the young faculty startup fund from Shanghai Jiao Tong University, National Natural Science Foundation of China (NSFC No. 11502144), and funding from Gas Turbine Research Institute of Shanghai Jiao Tong University.

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Authors and Affiliations

  1. Gas Turbine Research Institute, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Rd., Shanghai, 200240, China

    Di Peng, Shaofei Wang & Yingzheng Liu

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  1. Di Peng
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  2. Shaofei Wang
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  3. Yingzheng Liu
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Correspondence to Yingzheng Liu.

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Peng, D., Wang, S. & Liu, Y. Fast PSP measurements of wall-pressure fluctuation in low-speed flows: improvements using proper orthogonal decomposition. Exp Fluids 57, 45 (2016). https://doi.org/10.1007/s00348-016-2130-z

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