Abstract

Investigating shear flows is important in technical applications as well as in fundamental research. Velocity measurements with high spatial resolution are necessary. Laser Doppler anemometry allows nonintrusive precise measurements, but the spatial resolution is limited by the size of the measurement volume to ∼ 50 µm. A new laser Doppler profile sensor is proposed, enabling determination of the velocity profile inside the measurement volume. Two fringe systems with contrary fringe spacing gradients are generated to determine the position as well as the velocity of passing tracer particles. Physically discriminating between the two measuring channels is done by a frequency-division-multiplexing technique with acousto-optic modulators. A frequency-doubled Nd:YAG laser and a fiber-optic measuring head were employed, resulting in a portable and flexible sensor. In the center of the measurement volume of ∼1-mm length, a spatial resolution of ∼5 µm was obtained. Spatially resolved measurements of the Blasius velocity profile are presented. Small velocities as low as 3 cm/s are measured. The sensor is applied in a wind tunnel to determine the wall shear stress of a boundary layer flow. All measurement results show good agreement with the theoretical prediction.

© 2005 Optical Society of America

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References

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  1. H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1987).
  2. M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
    [CrossRef]
  3. C. D. Meinhart, S. T. Wereley, J. G. Santiago, “Micron-resolution velocimetry techniques,” in Laser Techniques Applied to Fluid Mechanics, Selected Papers from the Ninth International Symposium, Lisbon, Portugal, July 1998 (Springer-Verlag, Berlin, 2000), pp. 57–70, paper I.4.
    [CrossRef]
  4. H. Abe, H. Kawamura, Y. Matsuo, “Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence,” Trans. ASME J. Fluids Eng. 123, 382–393 (2001).
    [CrossRef]
  5. D. Matovic, C. Tropea, “Spectral peak interpolation with application to LDA signal processing,” Meas. Sci. Technol. 2, 1100–1106 (1991).
    [CrossRef]
  6. J. Czarske, O. Dölle, “Quadrature demodulation technique used in laser Doppler anemometry,” Electron. Lett. 43, 547–549 (1998).
    [CrossRef]
  7. L. Büttner, J. Czarske, “A multimode-fiber laser-Doppler anemometer for highly spatially resolved velocity measurements using low-coherence light,” Meas. Sci. Technol. 12, 1891–1903 (2001).
    [CrossRef]
  8. V. Strunck, G. Grosche, D. Dopheide, “New laser Doppler sensors for spatial velocity information,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities ICIAF'93, Saint-Louis, France, 1993 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1993), pp. 36.1–36.5.
  9. V. Strunck, T. Sodomann, H. Müller, D. Dopheide, “How to get spatial resolution inside probe volumes of commercial 3D LDA systems,” Exp. Fluids 36, 141–145 (2004).
    [CrossRef]
  10. J. Czarske, “Laser Doppler velocity profile sensor using a chromatic coding,” Meas. Sci. Technol. 12, 52–57 (2001).
    [CrossRef]
  11. J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometer spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
    [CrossRef]
  12. D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fiber-optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
    [CrossRef]
  13. S. L. Kaufmann, L. M. Fingerson, “Fiber optics in LDV applications,” in Proceedings, International Conference on Laser Anemometry—Advances and Applications, Manchester, UK, 16–18 September 1985 (Springer-Verlag, Berlin, 1985), pp. 53–65.
  14. M. Stieglmeier, C. Tropea, “Mobile fiber-optic laser Doppler anemometer,” Appl. Opt. 31, 4096–4105 (1992).
    [CrossRef] [PubMed]
  15. J. Czarske, H. Müller, “Two-dimensional directional fiberoptic laser Doppler anemometer based on heterodyning by means of a chirp frequency modulated Nd:YAG miniature ring laser,” Opt. Commun. 132, 421–426 (1996).
    [CrossRef]
  16. H. Müller, H. Wang, D. Dopheide, “Fiber optical multi-component LDA-system using the optical frequency difference of powerful DBR-laser diodes,” in Developments in Laser Techniques and Fluid Mechanics, Selected Papers from the Eighth International Symposium, Lisbon, Portugal, 8–11 July 1996 (Springer-Verlag, Berlin, 1996), pp. 11–21, paper I.2.
  17. D. Dopheide, V. Strunck, H. J. Pfeifer, “Miniaturized multicomponent laser Doppler anemometers using high frequency pulsed diode lasers and new electronic signal acquisition systems,” Exp. Fluids 9, 309–316 (1990).
    [CrossRef]
  18. L. Büttner, “Untersuchung neuartiger Laser-Doppler-Verfahren zur hochauflösenden Geschwindigkeitsmessung,” Ph.D. dissertation (Cuvillier Verlag, Göttingen, Germany, 2004).
  19. H. Blasius, “Grenzschichten in Flüssigkeiten mit kleiner Reibung,” Z. Math. Phys. 56, 1–37 (1908), NACA Tech. Memo 1256.
  20. H-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
    [CrossRef]
  21. F. Durst, H. Kikura, I. Lekakis, J. Jovanovic, Q. Ye, “Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows,” Exp. Fluids 20, 417–428 (1996).
    [CrossRef]

2004

V. Strunck, T. Sodomann, H. Müller, D. Dopheide, “How to get spatial resolution inside probe volumes of commercial 3D LDA systems,” Exp. Fluids 36, 141–145 (2004).
[CrossRef]

2002

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometer spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

2001

J. Czarske, “Laser Doppler velocity profile sensor using a chromatic coding,” Meas. Sci. Technol. 12, 52–57 (2001).
[CrossRef]

M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
[CrossRef]

H. Abe, H. Kawamura, Y. Matsuo, “Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence,” Trans. ASME J. Fluids Eng. 123, 382–393 (2001).
[CrossRef]

L. Büttner, J. Czarske, “A multimode-fiber laser-Doppler anemometer for highly spatially resolved velocity measurements using low-coherence light,” Meas. Sci. Technol. 12, 1891–1903 (2001).
[CrossRef]

1998

J. Czarske, O. Dölle, “Quadrature demodulation technique used in laser Doppler anemometry,” Electron. Lett. 43, 547–549 (1998).
[CrossRef]

1996

J. Czarske, H. Müller, “Two-dimensional directional fiberoptic laser Doppler anemometer based on heterodyning by means of a chirp frequency modulated Nd:YAG miniature ring laser,” Opt. Commun. 132, 421–426 (1996).
[CrossRef]

F. Durst, H. Kikura, I. Lekakis, J. Jovanovic, Q. Ye, “Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows,” Exp. Fluids 20, 417–428 (1996).
[CrossRef]

1992

1991

D. Matovic, C. Tropea, “Spectral peak interpolation with application to LDA signal processing,” Meas. Sci. Technol. 2, 1100–1106 (1991).
[CrossRef]

1990

D. Dopheide, V. Strunck, H. J. Pfeifer, “Miniaturized multicomponent laser Doppler anemometers using high frequency pulsed diode lasers and new electronic signal acquisition systems,” Exp. Fluids 9, 309–316 (1990).
[CrossRef]

1984

D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fiber-optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
[CrossRef]

1908

H. Blasius, “Grenzschichten in Flüssigkeiten mit kleiner Reibung,” Z. Math. Phys. 56, 1–37 (1908), NACA Tech. Memo 1256.

Abe, H.

H. Abe, H. Kawamura, Y. Matsuo, “Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence,” Trans. ASME J. Fluids Eng. 123, 382–393 (2001).
[CrossRef]

Albrecht, H-E.

H-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
[CrossRef]

Blasius, H.

H. Blasius, “Grenzschichten in Flüssigkeiten mit kleiner Reibung,” Z. Math. Phys. 56, 1–37 (1908), NACA Tech. Memo 1256.

Borys, M.

H-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
[CrossRef]

Büttner, L.

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometer spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

L. Büttner, J. Czarske, “A multimode-fiber laser-Doppler anemometer for highly spatially resolved velocity measurements using low-coherence light,” Meas. Sci. Technol. 12, 1891–1903 (2001).
[CrossRef]

L. Büttner, “Untersuchung neuartiger Laser-Doppler-Verfahren zur hochauflösenden Geschwindigkeitsmessung,” Ph.D. dissertation (Cuvillier Verlag, Göttingen, Germany, 2004).

Chan, R. K. Y.

D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fiber-optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
[CrossRef]

Czarske, J.

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometer spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

J. Czarske, “Laser Doppler velocity profile sensor using a chromatic coding,” Meas. Sci. Technol. 12, 52–57 (2001).
[CrossRef]

L. Büttner, J. Czarske, “A multimode-fiber laser-Doppler anemometer for highly spatially resolved velocity measurements using low-coherence light,” Meas. Sci. Technol. 12, 1891–1903 (2001).
[CrossRef]

J. Czarske, O. Dölle, “Quadrature demodulation technique used in laser Doppler anemometry,” Electron. Lett. 43, 547–549 (1998).
[CrossRef]

J. Czarske, H. Müller, “Two-dimensional directional fiberoptic laser Doppler anemometer based on heterodyning by means of a chirp frequency modulated Nd:YAG miniature ring laser,” Opt. Commun. 132, 421–426 (1996).
[CrossRef]

Damaschke, N.

H-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
[CrossRef]

Dölle, O.

J. Czarske, O. Dölle, “Quadrature demodulation technique used in laser Doppler anemometry,” Electron. Lett. 43, 547–549 (1998).
[CrossRef]

Dopheide, D.

V. Strunck, T. Sodomann, H. Müller, D. Dopheide, “How to get spatial resolution inside probe volumes of commercial 3D LDA systems,” Exp. Fluids 36, 141–145 (2004).
[CrossRef]

D. Dopheide, V. Strunck, H. J. Pfeifer, “Miniaturized multicomponent laser Doppler anemometers using high frequency pulsed diode lasers and new electronic signal acquisition systems,” Exp. Fluids 9, 309–316 (1990).
[CrossRef]

H. Müller, H. Wang, D. Dopheide, “Fiber optical multi-component LDA-system using the optical frequency difference of powerful DBR-laser diodes,” in Developments in Laser Techniques and Fluid Mechanics, Selected Papers from the Eighth International Symposium, Lisbon, Portugal, 8–11 July 1996 (Springer-Verlag, Berlin, 1996), pp. 11–21, paper I.2.

V. Strunck, G. Grosche, D. Dopheide, “New laser Doppler sensors for spatial velocity information,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities ICIAF'93, Saint-Louis, France, 1993 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1993), pp. 36.1–36.5.

Durst, F.

M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
[CrossRef]

F. Durst, H. Kikura, I. Lekakis, J. Jovanovic, Q. Ye, “Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows,” Exp. Fluids 20, 417–428 (1996).
[CrossRef]

Fingerson, L. M.

S. L. Kaufmann, L. M. Fingerson, “Fiber optics in LDV applications,” in Proceedings, International Conference on Laser Anemometry—Advances and Applications, Manchester, UK, 16–18 September 1985 (Springer-Verlag, Berlin, 1985), pp. 53–65.

Fischer, M.

M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
[CrossRef]

Grosche, G.

V. Strunck, G. Grosche, D. Dopheide, “New laser Doppler sensors for spatial velocity information,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities ICIAF'93, Saint-Louis, France, 1993 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1993), pp. 36.1–36.5.

Jackson, D. A.

D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fiber-optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
[CrossRef]

Jones, J. D. C.

D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fiber-optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
[CrossRef]

Jovanovic, J.

M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
[CrossRef]

F. Durst, H. Kikura, I. Lekakis, J. Jovanovic, Q. Ye, “Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows,” Exp. Fluids 20, 417–428 (1996).
[CrossRef]

Kaufmann, S. L.

S. L. Kaufmann, L. M. Fingerson, “Fiber optics in LDV applications,” in Proceedings, International Conference on Laser Anemometry—Advances and Applications, Manchester, UK, 16–18 September 1985 (Springer-Verlag, Berlin, 1985), pp. 53–65.

Kawamura, H.

H. Abe, H. Kawamura, Y. Matsuo, “Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence,” Trans. ASME J. Fluids Eng. 123, 382–393 (2001).
[CrossRef]

Kikura, H.

F. Durst, H. Kikura, I. Lekakis, J. Jovanovic, Q. Ye, “Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows,” Exp. Fluids 20, 417–428 (1996).
[CrossRef]

Lekakis, I.

F. Durst, H. Kikura, I. Lekakis, J. Jovanovic, Q. Ye, “Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows,” Exp. Fluids 20, 417–428 (1996).
[CrossRef]

Matovic, D.

D. Matovic, C. Tropea, “Spectral peak interpolation with application to LDA signal processing,” Meas. Sci. Technol. 2, 1100–1106 (1991).
[CrossRef]

Matsuo, Y.

H. Abe, H. Kawamura, Y. Matsuo, “Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence,” Trans. ASME J. Fluids Eng. 123, 382–393 (2001).
[CrossRef]

Meinhart, C. D.

C. D. Meinhart, S. T. Wereley, J. G. Santiago, “Micron-resolution velocimetry techniques,” in Laser Techniques Applied to Fluid Mechanics, Selected Papers from the Ninth International Symposium, Lisbon, Portugal, July 1998 (Springer-Verlag, Berlin, 2000), pp. 57–70, paper I.4.
[CrossRef]

Müller, H.

V. Strunck, T. Sodomann, H. Müller, D. Dopheide, “How to get spatial resolution inside probe volumes of commercial 3D LDA systems,” Exp. Fluids 36, 141–145 (2004).
[CrossRef]

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometer spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

J. Czarske, H. Müller, “Two-dimensional directional fiberoptic laser Doppler anemometer based on heterodyning by means of a chirp frequency modulated Nd:YAG miniature ring laser,” Opt. Commun. 132, 421–426 (1996).
[CrossRef]

H. Müller, H. Wang, D. Dopheide, “Fiber optical multi-component LDA-system using the optical frequency difference of powerful DBR-laser diodes,” in Developments in Laser Techniques and Fluid Mechanics, Selected Papers from the Eighth International Symposium, Lisbon, Portugal, 8–11 July 1996 (Springer-Verlag, Berlin, 1996), pp. 11–21, paper I.2.

Pfeifer, H. J.

D. Dopheide, V. Strunck, H. J. Pfeifer, “Miniaturized multicomponent laser Doppler anemometers using high frequency pulsed diode lasers and new electronic signal acquisition systems,” Exp. Fluids 9, 309–316 (1990).
[CrossRef]

Razik, T.

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometer spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

Santiago, J. G.

C. D. Meinhart, S. T. Wereley, J. G. Santiago, “Micron-resolution velocimetry techniques,” in Laser Techniques Applied to Fluid Mechanics, Selected Papers from the Ninth International Symposium, Lisbon, Portugal, July 1998 (Springer-Verlag, Berlin, 2000), pp. 57–70, paper I.4.
[CrossRef]

Schlichting, H.

H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1987).

Sodomann, T.

V. Strunck, T. Sodomann, H. Müller, D. Dopheide, “How to get spatial resolution inside probe volumes of commercial 3D LDA systems,” Exp. Fluids 36, 141–145 (2004).
[CrossRef]

Stieglmeier, M.

Strunck, V.

V. Strunck, T. Sodomann, H. Müller, D. Dopheide, “How to get spatial resolution inside probe volumes of commercial 3D LDA systems,” Exp. Fluids 36, 141–145 (2004).
[CrossRef]

D. Dopheide, V. Strunck, H. J. Pfeifer, “Miniaturized multicomponent laser Doppler anemometers using high frequency pulsed diode lasers and new electronic signal acquisition systems,” Exp. Fluids 9, 309–316 (1990).
[CrossRef]

V. Strunck, G. Grosche, D. Dopheide, “New laser Doppler sensors for spatial velocity information,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities ICIAF'93, Saint-Louis, France, 1993 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1993), pp. 36.1–36.5.

Tropea, C.

M. Stieglmeier, C. Tropea, “Mobile fiber-optic laser Doppler anemometer,” Appl. Opt. 31, 4096–4105 (1992).
[CrossRef] [PubMed]

D. Matovic, C. Tropea, “Spectral peak interpolation with application to LDA signal processing,” Meas. Sci. Technol. 2, 1100–1106 (1991).
[CrossRef]

H-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
[CrossRef]

Wang, H.

H. Müller, H. Wang, D. Dopheide, “Fiber optical multi-component LDA-system using the optical frequency difference of powerful DBR-laser diodes,” in Developments in Laser Techniques and Fluid Mechanics, Selected Papers from the Eighth International Symposium, Lisbon, Portugal, 8–11 July 1996 (Springer-Verlag, Berlin, 1996), pp. 11–21, paper I.2.

Wereley, S. T.

C. D. Meinhart, S. T. Wereley, J. G. Santiago, “Micron-resolution velocimetry techniques,” in Laser Techniques Applied to Fluid Mechanics, Selected Papers from the Ninth International Symposium, Lisbon, Portugal, July 1998 (Springer-Verlag, Berlin, 2000), pp. 57–70, paper I.4.
[CrossRef]

Ye, Q.

F. Durst, H. Kikura, I. Lekakis, J. Jovanovic, Q. Ye, “Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows,” Exp. Fluids 20, 417–428 (1996).
[CrossRef]

Appl. Opt.

Electron. Lett.

J. Czarske, O. Dölle, “Quadrature demodulation technique used in laser Doppler anemometry,” Electron. Lett. 43, 547–549 (1998).
[CrossRef]

Exp. Fluids

V. Strunck, T. Sodomann, H. Müller, D. Dopheide, “How to get spatial resolution inside probe volumes of commercial 3D LDA systems,” Exp. Fluids 36, 141–145 (2004).
[CrossRef]

D. Dopheide, V. Strunck, H. J. Pfeifer, “Miniaturized multicomponent laser Doppler anemometers using high frequency pulsed diode lasers and new electronic signal acquisition systems,” Exp. Fluids 9, 309–316 (1990).
[CrossRef]

F. Durst, H. Kikura, I. Lekakis, J. Jovanovic, Q. Ye, “Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows,” Exp. Fluids 20, 417–428 (1996).
[CrossRef]

J. Phys. E

D. A. Jackson, J. D. C. Jones, R. K. Y. Chan, “A high-power fiber-optic laser Doppler velocimeter,” J. Phys. E 17, 977–980 (1984).
[CrossRef]

Meas. Sci. Technol.

J. Czarske, “Laser Doppler velocity profile sensor using a chromatic coding,” Meas. Sci. Technol. 12, 52–57 (2001).
[CrossRef]

J. Czarske, L. Büttner, T. Razik, H. Müller, “Boundary layer velocity measurements by a laser Doppler profile sensor with micrometer spatial resolution,” Meas. Sci. Technol. 13, 1979–1989 (2002).
[CrossRef]

L. Büttner, J. Czarske, “A multimode-fiber laser-Doppler anemometer for highly spatially resolved velocity measurements using low-coherence light,” Meas. Sci. Technol. 12, 1891–1903 (2001).
[CrossRef]

D. Matovic, C. Tropea, “Spectral peak interpolation with application to LDA signal processing,” Meas. Sci. Technol. 2, 1100–1106 (1991).
[CrossRef]

Opt. Commun.

J. Czarske, H. Müller, “Two-dimensional directional fiberoptic laser Doppler anemometer based on heterodyning by means of a chirp frequency modulated Nd:YAG miniature ring laser,” Opt. Commun. 132, 421–426 (1996).
[CrossRef]

Phys. Fluids

M. Fischer, J. Jovanovic, F. Durst, “Reynolds number effects in the near-wall region of turbulent channel flows,” Phys. Fluids 13, 1755–1767 (2001).
[CrossRef]

Trans. ASME J. Fluids Eng.

H. Abe, H. Kawamura, Y. Matsuo, “Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence,” Trans. ASME J. Fluids Eng. 123, 382–393 (2001).
[CrossRef]

Z. Math. Phys.

H. Blasius, “Grenzschichten in Flüssigkeiten mit kleiner Reibung,” Z. Math. Phys. 56, 1–37 (1908), NACA Tech. Memo 1256.

Other

H-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer-Verlag, Berlin, 2003).
[CrossRef]

L. Büttner, “Untersuchung neuartiger Laser-Doppler-Verfahren zur hochauflösenden Geschwindigkeitsmessung,” Ph.D. dissertation (Cuvillier Verlag, Göttingen, Germany, 2004).

H. Müller, H. Wang, D. Dopheide, “Fiber optical multi-component LDA-system using the optical frequency difference of powerful DBR-laser diodes,” in Developments in Laser Techniques and Fluid Mechanics, Selected Papers from the Eighth International Symposium, Lisbon, Portugal, 8–11 July 1996 (Springer-Verlag, Berlin, 1996), pp. 11–21, paper I.2.

S. L. Kaufmann, L. M. Fingerson, “Fiber optics in LDV applications,” in Proceedings, International Conference on Laser Anemometry—Advances and Applications, Manchester, UK, 16–18 September 1985 (Springer-Verlag, Berlin, 1985), pp. 53–65.

H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1987).

C. D. Meinhart, S. T. Wereley, J. G. Santiago, “Micron-resolution velocimetry techniques,” in Laser Techniques Applied to Fluid Mechanics, Selected Papers from the Ninth International Symposium, Lisbon, Portugal, July 1998 (Springer-Verlag, Berlin, 2000), pp. 57–70, paper I.4.
[CrossRef]

V. Strunck, G. Grosche, D. Dopheide, “New laser Doppler sensors for spatial velocity information,” in Proceedings of the International Congress on Instrumentation in Aerospace Simulation Facilities ICIAF'93, Saint-Louis, France, 1993 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1993), pp. 36.1–36.5.

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Figures (13)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Difference frequencies between the four frequency shifted laser beams. The carrier frequencies are in boldface.

Fig. 3
Fig. 3

Fringe systems tilted against each other because of the quadratic beam arrangement at the sensor head.

Fig. 4
Fig. 4

Top, right half plane of the outline of two elliptical fringe systems of 1.5-mm length tilted by 7.2° against each other. Bottom, coincidence probability along the z axis for different tilt angles.

Fig. 5
Fig. 5

Top, time-domain burst signal for the 20-MHz channel after down mixing and the low-pass filter and, bottom, the corresponding power spectrum. No dc pedestal exists.

Fig. 6
Fig. 6

Caustic curves for all four partial beams.

Fig. 7
Fig. 7

Fringe spacings versus position.

Fig. 8
Fig. 8

Calibration function q(z).

Fig. 9
Fig. 9

Power density of the Doppler frequency spectral lines of the burst signals.

Fig. 10
Fig. 10

Left, standard deviation of the position δ(z) and, right, relative measurement uncertainty in the velocity δυ/υ over the z position.

Fig. 11
Fig. 11

Blasius profile measured in 10 steps by traversing the sensor head, left, depicted in absolute units and, right, in comparison with theory in normalized units. The wall is located at z = η = 0.

Fig. 12
Fig. 12

Measurements, left, at the slope, at ∼1-mm distance from the wall and, right, in the free-stream region of the Blasius profile for different speeds of the wind tunnel.

Fig. 13
Fig. 13

Measured wall shear stress for different flow speeds of the wind channel in comparison with theory.

Tables (1)

Tables Icon

Table 1 Measured Beam Parameters for Four Partial Beams

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

q ( z ) = f 2 ( υ , z ) f 1 ( υ , z ) = υ ( z ) / d 2 ( z ) υ ( z ) / d 1 ( z ) = d 1 ( z ) d 2 ( z ) ,
υ ( z ) = f 1 ( υ , z ) d 1 ( z ) = f 2 ( υ , z ) d 2 ( z ) .
δ z 2 | q ( z ) z | 1 δ f f .
δ υ υ ( 3 2 ) 1 / 2 δ f f .
υ υ υ , z η = z ( υ 2 ν x ) 1 / 2
τ = μ ν z | z = 0 .

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