Skip to main content
SpringerLink
Log in

Integrating Mach–Zehnder interferometry with TPIV to measure the time-resolved deformation of a compliant wall along with the 3D velocity field in a turbulent channel flow

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

A system combining tomographic PIV (TPIV) and Mach–Zehnder interferometry (MZI) simultaneously measures the time-resolved 3D flow field and 2D distribution of wall-normal deformation in a turbulent channel flow over a transparent compliant surface. This paper focuses on the experimental techniques and data analysis procedures, but includes sample results. Standard TPIV analysis resolves the log layer of the mean velocity and the linear decrease in total shear stress with distance from the wall. Single-pixel ensemble correlations reveal the buffer layer and top of the viscous sublayer. Analysis of the MZI data consists of two steps, namely critical spatial filtering of interferograms to remove noise and phase demodulation to calculate the surface shape. A new technique to improve the filtration of noise from interferograms based on spatial correlations of small windows is introduced and optimized. Taking advantage of this enhancement, the phase/deformation distribution is calculated directly from arccosines of the intensity, which avoids edge artifacts affecting spectral calculations. Validations using synthetic noisy interferograms indicate that errors associated with correlation-based enhancement are consistently lower and much less sensitive to fringe shape than spectral band-pass filtering. The experimental wavenumber–frequency spectra show that the deformation consists of patterns that are larger than the field of view, surface waves and small-scale patterns. Some of the latter are advected at the freestream velocity, but mostly at 70 % of the freestream, the mean speed at 10 % of the channel half height. Indeed, spatial correlations of the deformation with velocity components peak at this elevation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  • Atkinson C, Soria J (2009) An efficient simultaneous reconstruction technique for tomographic particle image velocimetry. Exp Fluids 47:553–568

    Article  Google Scholar 

  • Bartelt H, Lohmann AW, Wirnitzer B (1984) Phase and amplitude recovery from bispectra. Appl Opt 23(18):3121–3129

    Article  Google Scholar 

  • Benjamin TB (1960) Effects of a flexible boundary on hydrodynamic stability. J Fluid Mech 9:513–532

    Article  MATH  MathSciNet  Google Scholar 

  • Benjamin TB (1963) The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows. J Fluid Mech 16:436–450

    Article  MATH  Google Scholar 

  • Benjamin TB (1966) Fluid flow with flexible boundaries. Applied mechanics: proceedings of the eleventh international congress of applied mechanics, Munich (Germany), pp 109–128

  • Blake WK (1986) Mechanisms of flow-induced sound and vibration. Academic Press, New York

    Google Scholar 

  • Blick EF, Walters RR (1968) Turbulent boundary-layer characteristics of compliant surfaces. J Aircraft 5(1):11–16

    Article  Google Scholar 

  • Boggs FW and Hahn ER (1962) Performance of compliant skins in contact with high velocity flow in water. Proceedings of 7th joint army-navy-air force conference on elastomer research and development, San Francisco, vol 2, p 443

  • Bone DJ, Bachor HA, Sandeman RJ (1986) Fringe-pattern analysis using a 2-D Fourier transform. Appl Opt 25(10):1653–1660

    Article  Google Scholar 

  • Bushnell DM, Hefner JN, Ash RL (1977) Effect of compliant wall motion on turbulent boundary layers. Phys Fluids 20:31–48

    Article  Google Scholar 

  • Butters JN, Leendertz JA (1971) Holographic and video techniques applied to engineering measurement. Meas Control 4(12):349–354

    Google Scholar 

  • Castellini P, Martarelli M, Tomasini EP (2006) Laser doppler vibrometry: development of advanced solutions answering to technology’s needs. Mech Syst Signal Process 20:1265–1285

    Article  Google Scholar 

  • Choi KS, Yang X, Clayton BR, Glover EJ, Atlar M, Semenov BN, Kulik VM (1997) Turbulent drag reduction using compliant surfaces. Proc R Soc Lond A 453:2229–2240

    Article  MATH  Google Scholar 

  • Dinkelacker A, Hessel M, Meier GEA, Schewe G (1977) Investigation of pressure fluctuations beneath a turbulent boundary layer by means of an optical method. Phys Fluids 20:S216–S224

    Article  Google Scholar 

  • Elsinga GE, Scarano F, Wieneke B, van Oudheusden BW (2006) Tomographic particle image velocimetry. Exp Fluids 41:933–947

    Article  Google Scholar 

  • Fisher DH, Blick EF (1966) Turbulent damping by flabby skins. J Aircraft 3(2):163–164

    Article  Google Scholar 

  • Gad-el-Hak M (1986) The response of elastic and viscoelastic surfaces to a turbulent boundary layer. J Appl Mech 53:206–212

    Article  Google Scholar 

  • Gad-el-Hak M, Blackwelder RF, Riley JJ (1984) On the interaction of compliant coatings with boundary-layer flows. J Fluid Mech 140:257–280

    Article  Google Scholar 

  • Ghiglia DC, Pritt MD (1998) Two-dimensional phase unwrapping. Wiley, New York

    MATH  Google Scholar 

  • Ghiglia DC, Mastin GA, Romero LA (1987) Cellular-automata method for phase unwrapping. J Opt Soc Am A 4(1):267–280

    Article  Google Scholar 

  • Goldstein RM, Zebker HA, Werner CL (1988) Satellite radar interferometry: two-dimensional phase unwrapping. Radio Sci 23(4):713–720

    Article  Google Scholar 

  • Hansen RJ, Hunston DL (1974) An experimental study of turbulent flows over compliant surfaces. J Sound Vib 34:297–308

    Article  Google Scholar 

  • Hansen RJ, Hunston DL (1983) Fluid-property effects on flow-generated waves on a compliant surface. J Fluid Mech 133:161–177

    Article  Google Scholar 

  • Hansen RJ, Hunston DL, Ni CC, Reischman MM (1980) An experimental study of flow-generated waves on a flexible surface. J Sound Vib 68:317–334

    Article  Google Scholar 

  • Harris FJ (1978) On the use of windows for harmonic analysis with the discrete Fourier transform. Proc IEEE 66:51–83

    Article  Google Scholar 

  • Harris GL, Lissaman PBS (1969) Turbulent skin friction on compliant surfaces. AIAA J 7(8):1625–1627

    Article  Google Scholar 

  • Hecht E (2002) Optics, 4th edn. Addison-Wesley, San Francisco

    Google Scholar 

  • Hess DE, Peattie RA, Schwarz WH (1993) A noninvasive method for the measurement of flow-induced surface displacement of a compliant surface. Exp Fluids 14:78–84

    Article  Google Scholar 

  • Hong J, Katz J, Schultz MP (2011) Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow. J Fluid Mech 667:1–37

    Article  MATH  Google Scholar 

  • Ichioka Y, Inuiya M (1972) Direct phase detecting system. Appl Opt 11(7):1507–1514

    Article  Google Scholar 

  • Itoh K (1982) Analysis of the phase unwrapping algorithm. Appl Opt 21(14):2470

    Article  Google Scholar 

  • Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94

    Article  MATH  MathSciNet  Google Scholar 

  • Jones R, Wykes C (1983) Holographic and speckle interferometry. Cambridge University Press, Cambridge, pp 178–179

    Google Scholar 

  • Joshi P, Liu X, Katz J (2014) Effect of mean and fluctuating pressure gradients on boundary layer turbulence. J Fluid Mech 748:36–84

    Article  Google Scholar 

  • Kim E, Choi H (2014) Space-time characteristics of a compliant wall in a turbulent channel flow. J Fluid Mech 756:30–53

    Article  MathSciNet  Google Scholar 

  • Kramer MO (1957) Boundary layer stabilization by distributed damping. J Aeronaut Sci 24:459–460

    Google Scholar 

  • Kramer MO (1962) Boundary layer stabilization by distributed damping. Naval Eng J 2:341–348

    Article  Google Scholar 

  • Landahl MT (1962) On the stability of a laminar incompressible boundary layer over a flexible surface. J Fluid Mech 13:609–632

    Article  MATH  Google Scholar 

  • Lee T, Fisher M, Schwarz WH (1993a) Investigation of the stable interaction of a passive compliant surface with a turbulent boundary layer. J Fluid Mech 257:373–401

    Article  Google Scholar 

  • Lee T, Fisher M, Schwarz WH (1993b) The measurement of flow-induced surface displacement on a compliant surface by optical holographic interferometry. Exp Fluids 14:159–168

    Article  Google Scholar 

  • Lee T, Fisher M, Schwarz WH (1995) Investigation of the effects of a compliant surface on boundary-layer stability. J Fluid Mech 288:37–58

    Article  Google Scholar 

  • Luhar M, Sharma AS, McKeon BJ (2015) A framework for studying the effect of compliant surfaces on wall turbulence. J Fluid Mech 768:415–441

    Article  Google Scholar 

  • Maidanik G, Reader WT (1968) Filtering action of a blanket dome. J Acoust Soc Am 44:497–502

    Article  Google Scholar 

  • Mark JE (ed) (1999) Polymer data handbook. Oxford University Press, Oxford

    Google Scholar 

  • McMichael JM, Klebanoff PS, Mease NE (1980) Experimental investigation of drag on a compliant surface. In: G. R. Hough (ed) Viscous flow drag reduction. American Institute of Aeronautics and Astronautics Inc, New York, pp 410–438

    Google Scholar 

  • Meinhart CD, Wereley ST, Santiago JG (2000) A PIV algorithm for estimating time-averaged velocity fields. J Fluids Eng 122:285–289

    Article  Google Scholar 

  • Nakayama S, Toba H, Fujiwara N, Gemma T, Takeda M (2009) Fourier-transform method with high accuracy by use of iterative technique narrowing the spectra of a fringe pattern. In: Osten W, Kujawinska M (eds) Fringe 2009. Springer, Berlin

    Google Scholar 

  • Pedrini G, Tiziani H (1994) Double-pulse electronic speckle interferometry for vibration analysis. Appl Opt 33(34):7857–7863

    Article  Google Scholar 

  • Pedrini G, Pfister B, Tiziani H (1993) Double pulse-electronic speckle interferometry. J Mod Opt 40(1):89–96

    Article  Google Scholar 

  • Pope SB (2000) Turbulent flows. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Roddier C, Roddier F (1987) Interferogram analysis using Fourier transform techniques. Appl Opt 26(9):1668–1673

    Article  Google Scholar 

  • Scarano F (2013) Tomographic PIV: principles and practice. Meas Sci Technol 24:012001

    Article  Google Scholar 

  • Scharnowski S, Hain R, Kahler CJ (2012) Reynolds stress estimation up to single-pixel resolution using PIV-measurements. Exp Fluids 52:985–1002

    Article  Google Scholar 

  • Servin M, Quiroga JA, Padilla JM (2014) Fringe pattern analysis for optical metrology. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

    Book  Google Scholar 

  • Soria J, Willert C (2012) On measuring the joint probability density function of three-dimensional velocity components in turbulent flows. Meas Sci Technol 23:065301

    Article  Google Scholar 

  • Tabatabai H, Oliver DE, Rohrbaugh JW, Papadopoulos C (2013) Novel applications of laser doppler vibration measurements to medical imaging. Sens Imag 14:13–28

    Article  Google Scholar 

  • Takeda M, Ina H, Kobayashi S (1982) Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. J Opt Soc Am 72(1):156–160

    Article  Google Scholar 

  • Totsky AV, Kurbatov IV, Lukin VV, Egiazarian KO, Astola JT (2003) Combined bispectrum-filtering techniques for radar output signal reconstruction in ATR applications. Proc SPIE 5094:301–312

    Article  Google Scholar 

  • Totsky AV, Zelensky AA, Kravchenko VF (2015) Bispectral methods of signal processing: applications in Radar, telecommunications and digital image restoration. Walter de Gruyter GmbH, Berlin

    Book  Google Scholar 

  • Uzol O, Chow YC, Katz J, Meneveau C (2002) Unobstructed particle image velocimetry measurements within an axial turbo-pump using liquid and blades with matched refractive indices. Exp Fluids 33:909–919

    Article  Google Scholar 

  • Westerweel J, Geelhoed PF, Lindken R (2004) Single-pixel resolution ensemble correlation for micro-PIV applications. Exp Fluids 37:375–384

    Article  Google Scholar 

  • Wieneke B (2008) Volume self-calibration for 3D particle image velocimetry. Exp Fluids 45:549–556

    Article  Google Scholar 

  • Wu H, Miorini RL, Katz J (2011) Measurements of the tip leakage vortex structures and turbulence in the meridional plane of an axial water-jet pump. Exp Fluids 50(4):989–1003

    Article  Google Scholar 

  • Yañez-mendiola J, Servín M, Malacara-hernández D (2001) Reduction of the edge effects induced by the boundary of a linear-carrier interferogram. J Mod Opt 48(4):685–693

    Article  Google Scholar 

Download references

Acknowledgments

This project is funded by the Office of Naval Research under Grant No. N000140910621. Dr. Debbie Nalchajian is the program officer. The author would also like to thank W. Blake for many constructive discussions and Dr. Rui Xiao for his help to measure the mechanical properties of PDMS.

Author information

Author notes

  1. Rinaldo Miorini

    Present address: General Electric Global Research Center, One Research Circle, Niskayuna, NY, 12309, USA

Authors and Affiliations

  1. Johns Hopkins University, Baltimore, MD, 21218, USA

    Cao Zhang, Rinaldo Miorini & Joseph Katz

Authors
  1. Cao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rinaldo Miorini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joseph Katz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joseph Katz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, C., Miorini, R. & Katz, J. Integrating Mach–Zehnder interferometry with TPIV to measure the time-resolved deformation of a compliant wall along with the 3D velocity field in a turbulent channel flow. Exp Fluids 56, 203 (2015). https://doi.org/10.1007/s00348-015-2072-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00348-015-2072-x

Keywords

Search

Navigation