Abstract
A method is presented for the cancellation of wide band contaminating noise occurring within internal flow configurations such as rectangular channels and pipes. Facility generated noise within these flow systems contaminates the turbulent wall pressure signature at low frequencies thus preventing the possible extraction of useful information. The proposed methodology utilizes the signals from two flush mounted wall pressure transducers. A first estimate for the one-point spectral density is obtained using a least mean square algorithm. A secondary correction to this estimate is obtained by taking advantage of the planar homogeneity of the turbulence. The application of the technique is demonstrated in a fully developed turbulent channel flow for which a more than 40 dB cancellation is obtained at low frequencies. In this low frequency range, the power spectral density is shown to have an approximate quadratic dependence, substantiating past theoretical predictions reported in the literature.
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Abbreviations
- d :
-
transducer diameter
- d + :
-
non-dimensional transducer diameter, \(d^ + = du^* /v\)
- f :
-
frequency (Hz)
- h :
-
channel half-height
- l :
-
spanwise separation of transducers
- p N (t) :
-
signal due to contaminating noise
- p q (t) :
-
system output signal
- p R (t) :
-
turbulent wall pressure signal at reference transducer
- p 1(t):
-
turbulent wall pressure signal at primary transducer
- R h :
-
channel Reynolds number, \(R_h = U{\text{ }}H/v\)
- s R (t) :
-
pressure signal from reference transducer
- s 1 (t):
-
pressure signal from primary transducer
- t :
-
time
- U :
-
channel centerline velocity, (maximum velocity)
- u * :
-
shear velocity, \(u^* = \sqrt {\tau _{wall} /\rho }\)
- W(f) :
-
optimized filter function used for cancellation (Fourier transform)
- α:
-
correction factor, (noise to signal ratio)
- γ 2 :
-
coherence function
- λ z :
-
lateral turbulence macro-scale
- λ N :
-
correlation length scale of contaminating noise
- v :
-
kinematic viscosity
- ϱ :
-
fluid density
- τ wall :
-
wall shear stress
- Φ pN (f) :
-
auto spectral density of p N (t)
- Φ pR (f) :
-
auto spectral density of p R (t)
- Φ 1 p :
-
auto spectral density of p 1(t)
- Φ sR (f) :
-
auto spectral density of s R (t)
- Φ 1 s(f):
-
auto spectral density of s 1(t)
- φ 1ssr :
-
cross spectral density of s 1 (t) with s R (t)
References
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Galib, T. A.; Zandina, A. 1984: Turbulent pressure fluctuations with conventional piezoelectric and miniature piezoresistive transducers. 108th Meeting of the Acoustical Society of America, Mpls., Minnesota. JASA. Suppl. 1 (76)
Horne, M. P. 1990: Physical and computational investigation of the wall pressure fluctuations in a channel flow. NRL Memorandum Report 6628. Naval Research Laboratory
Leehey, P. 1989: Dynamic wall pressure measurements. Lecture Notes in Engineering, Advances in Fluid Mechanics Measurements, M. Gad-el-Hak (ed.)
Panton, R. L. et al. 1980: Low-frequency pressure fluctuations in axisymmetric turbulent boundary layers. JFM, Vol. 97
Widrow, B. et al 1954: Adaptive noise cancelling: principles and applications. ARRAY PROCESSING Applications to Radar. Haykin, S. (ed.), Dowden, Hutchinson and Ross, Inc.
Wiener, N. 1949: Extrapolation, interpolation and smoothing of stationary time series, with engineering applications. Wiley, New York
Willmarth, W. W. 1975: Pressure fluctuations beneath turbulent boundary layers. Annual Review of Fluid Mechanics. No 7
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Home, M.P., Handler, R.A. Note on the cancellation of contaminating noise in the measurement of turbulent wall pressure fluctuations. Experiments in Fluids 12, 136–139 (1991). https://doi.org/10.1007/BF00226580
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DOI: https://doi.org/10.1007/BF00226580