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Pressure correction schemes and the use of the Wiener deconvolution method in pneumatic systems with short tubes

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Abstract

Experiments are conducted to evaluate the ability of various schemes to correct for pressure distortion caused by a finite tubing length between the pressure tap and the transducer. This study focuses on relatively short tubes, such as those encountered in multi-hole probes. Experimentally determined dynamic response is compared to the analytical model of Berg and Tijdeman with and without the Wiener filter. Bench-top experiments show that, for pneumatic systems with relatively short tubes, the addition of the Wiener filter carries no advantage over the Berg and Tijdeman model. The true advantage of the Wiener deconvolution method is observed for pressure tubes longer than ∼150 mm. Finally, the mean axial velocity and three Reynolds stress distributions from three correction schemes are compared to particle image velocimetry (PIV) results in a shear flow experiment. The statistical results ascertain the advantage of the Berg and Tijdeman and the Wiener deconvolution method over the generally noise-dominated inverse transfer function method.

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Abbreviations

A c :

Cross-sectional area of tube (cm2)

c :

Sonic velocity (m/s)

D :

Tube diameter (cm)

f :

Cyclic frequency (Hz)

G :

Wiener deconvolution function

G 00 :

Power spectrum from p 0

G 0L :

Cross-spectra from p 0 and p L

H :

Irwin et al. experimental deconvolution function

ITF :

Inverse transfer function (H)

L :

Tube length (cm)

N :

Frequency-domain noise (Pa/s)

P :

Fourier-transformed pressure (Pa· s)

p :

Time-domain pressure (Pa)

p 0 :

Input (surface) pressure (Pa)

p static :

Static pressure (Pa)

p total :

Total pressure (Pa)

P 00 :

Variance of surface pressure (Pa2)

p L :

Sensed transducer pressure (Pa)

SRM :

System response model of Berg and Tijdeman

S/N :

Signal-to-noise ratio

t :

Time (s)

V :

Transducer volume (cm3)

WF–SRM :

Wiener filtered system response model

\(\Upgamma_p\) :

Wave propagation factor

\(\Upupsilon\) :

Berg and Tijdeman deconvolution function

w :

Angular frequency (rad/s)

\(\hat{}\) :

Reconstructed signal

* :

Complex conjugate

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Authors and Affiliations

  1. Institut für Strömungsmechanik, Technische Universität Braunschweig, Braunschweig, Germany

    Richard Semaan & Peter Scholz

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  1. Richard Semaan
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  2. Peter Scholz
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Correspondence to Richard Semaan.

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Semaan, R., Scholz, P. Pressure correction schemes and the use of the Wiener deconvolution method in pneumatic systems with short tubes. Exp Fluids 53, 829–837 (2012). https://doi.org/10.1007/s00348-012-1332-2

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  • DOI: https://doi.org/10.1007/s00348-012-1332-2

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