Abstract
A noninvasive optical method is described which allows the measurement of the vertical component of the instantaneous displacement of a surface at one or more points. The method has been used to study the motion of a passive compliant layer responding to the random forcing of a fully developed turbulent boundary layer. However, in principle, the measurement technique described here can be used equally well with any surface capable of scattering light and to which optical access can be gained. The technique relies on the use of electro-optic position-sensitive detectors; this type of transducer produces changes in current which are linearly proportional to the displacement of a spot of light imaged onto the active area of the detector. The system can resolve displacements as small as 2 μm for a point 1.8 mm in diameter; the final output signal of the system is found to be linear for displacements up to 200 μm, and the overall frequency response is from DC to greater than 1 kHz. As an example of the use of the system, results detailing measurements obtained at both one and two points simultaneously are presented.
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Abbreviations
- C t :
-
elastic transverse wave speed = (G/ρ)1/2
- d + :
-
spot diameter normalized by viscous length scale
- G :
-
frequency average of G′(ω)
- G′(ω) :
-
shear storage modulus
- G″(ω) :
-
shear loss modulus
- l. :
-
viscous length scale = v/u *
- N :
-
total number of sampled data values
- r :
-
separation vector for 2-point measurements = (ξ, ζ)
- rms :
-
root-mean-square value
- R θ :
-
momentum thickness Reynolds number = θ U t8/v
- t :
-
time
- u (y) :
-
mean streamwise component of velocity in boundary layer
- u * :
-
friction velocity = (t w/ρ)1/2
- U ∞ :
-
free-stream velocity
- x, y, z :
-
longitudinal, normal and spanwise directions
- y o :
-
undisturbed surface position
- δ :
-
vertical component of compliant surface displacement
- δ 99 :
-
boundary layer thickness for which u(y) = 0.99 U t8
- δ l :
-
viscous sublayer thickness ∼ 5 l *
- η :
-
frequency average of G″(ω)/ω
- θ :
-
boundary layer momentum thicknes =\(\int\limits_0^\infty {\frac{{u(y)}}{{U_\infty }}} \left( {1 - \frac{{u(y)}}{{U_\infty }}} \right)dy\)
- μ :
-
fluid dynamic viscosity
- v :
-
fluid kinematic viscosity = μ/ρ
- ξ, ζ :
-
longitudinal, spanwise components of separation vector r
- ρ :
-
fluid density
- τ :
-
time delay
- τ w :
-
wall shear stress
References
Adair, D.; Madigosky, W. M.; Mease, N. E. 1991: An electro-optical sensor for surface displacement measurements of compliant coatings. Rev. Sci. Instrum. 62, 1652–1653
Benjamin, T. B. 1963: The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows. J. Fluid Mech. 16, 436–450
Bushnell, D. M.; Hefner, J. N.; Ash, R. L. 1977: Effect of compliant wall motion on turbulent boundary layers. Phys. Fluids, 20, S31-S48
Cerwin, S. A. 1984: A noncontacting electro-optic displacement sensor for piezoelectrically driven active surfaces. In: Symposium on Flow-Induced Vibrations, ASME Winter Annual Meeting, pp. 1–7
Chu, C. C.; Falco, R. E.; Wiggert, D. C. 1984: Experimental determination of drag modifications due to an elastic compliant surface using quantitative visual techniques. Ninth Symp. Turbul., University of Missouri, Rolla, USA, pp. 42–1 to 42–7
Duncan, J. H. 1986: The response of an incompressible viscoelastic coating to pressure fluctuations in a turbulent boundary layer. J. Fluid Mech. 171, 339–363
Duncan, J. H.; Waxman, A. M.; Tulin, M. P. 1985: The dynamics of waves at the interface between a viscoelastic coating and a fluid flow. J. Fluid Mech. 158, 177–197
Gad-cl-Hak, M. 1986a: Boundary layer interactions with compliant coatings: An overview. Appl. Mech. Rev. 39, 511–524
Gad-el-Hak, M. 1986b: The response of elastic and viscoelastic surfaces to a turbulent boundary layer. J. Appl. Mech. 53, 206–212
Gad-el-Hak, M.; Blackweldcr, R. F.; Riley, J. J. 1984: On the interaction of compliant coatings with boundary layer flows. J. Fluid Mech. 140, 257–280
Hansen, R. J.; Hunston, D. L. 1983: Fluid-property effects on flow generated waves on a compliant surface. J. Fluid Mech. 133, 161–177
Hansen, R. J.; Hunston, D. L.; Ni, C. C.; Reischman, M. M. 1980: An experimental study of flow generated waves on a flexible surface. J. Sound Vib. 68, 317–334
Hess, D. E. 1990: An experimental investigation of a compliant surface beneath a turbulent boundary layer. Ph.D. thesis, Johns Hopkins University, Baltimore, MD.
Kendall, J. M. 1970: The turbulent boundary layer over a wall with progressive surface waves. J. Fluid Mech. 41, 259–281
Krämer, M. O. 1957: Boundary layer stabilization by distributed damping. J. Aeronaut. Sci. 24, 459–460
Landahl, M. T. 1962: On the stability of a laminar incompressible boundary layer over a flexible surface. J. Fluid Mech. 13, 609–632
Landahl, M. T.; Kaplan, R. E. 1965: The effect of compliant walls on boundary layer stability and transition. Proc. of AGARD Fluid Dynamics Panel Conf. on Boundary Layer Technology. AGAR Dograph 97, 363–394
Riley, J. J.; Gad-el-Hak, M.; Metcalfe, R. W. 1988: Compliant coatings. Ann. Rev. Fluid Mech. 20, 393–420
Sengupta, T. K.; Lekoudis, S. G. 1985: Calculation of two-dimensional turbulent boundary layers over rigid and moving wavy surfaces. AIAA J. 23, 530–536
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Hess, D.E., Peattie, R.A. & Schwarz, W.H. A noninvasive method for the measurement of flow-induced surface displacement of a compliant surface. Experiments in Fluids 14, 78–84 (1993). https://doi.org/10.1007/BF00196991
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DOI: https://doi.org/10.1007/BF00196991