Experiments in Fluids

, Volume 36, Issue 1, pp 214–216

Multi-mode fibre laser Doppler anemometer (LDA) with high spatial resolution for the investigation of boundary layers

Authors

    • Group Laser MetrologyLaser Zentrum Hannover e.V.
  • J. Czarske
    • Group Laser MetrologyLaser Zentrum Hannover e.V.
Short Communication

DOI: 10.1007/s00348-003-0684-z

Cite this article as:
Büttner, L. & Czarske, J. Exp Fluids (2004) 36: 214. doi:10.1007/s00348-003-0684-z

Abstract

A novel LDA system using laser diode arrays and multi-mode fibers in the transmitting optics is presented. The use of high numerical aperture multi-mode step-index fibres results in measurement volumes with, for example, 80 µm length and minimal speckle effects. Because of the high spatial resolution and low relative fringe spacing variation of Δd/d≈5×10−4 the multi-mode fibre LDA is predestined for investigating turbulent flows. Boundary layer measurements carried out show excellent agreement with theoretical velocity profiles.

1 Introduction

Usually, a short measurement volume ensuring high spatial resolution as well as a low variation of fringe spacing (known as "virtual turbulence") for a precise determination of turbulence data are required for measurements of laminar and turbulent boundary layers using the laser Doppler technique. Because of the wavefront curvature of the generally employed single-mode Gaussian beam, only one requirement can be fulfilled if no beam stops are used in the receiving optics. However, the multi-mode fibre laser Doppler anemometer presented in this contribution offers both features at the same time.

Normally, single-mode fibres have been employed in LDA systems for beam delivery from the laser to the measurement head as they preserve coherence properties from fundamental mode lasers. On the other hand, multi-mode fibres can transmit significantly higher power and need only low alignment effort for incoupling.

Because of these reasons experiments were carried out to employ multi-mode fibres even for beam delivery (Kaufmann and Fingerson 1985; Ruck and Durst 1983; Bopp et al. 1989), but because of the observed signal degeneration caused by speckles this technique could never become established. This work presents a multi-mode fibre LDA system, which minimises the speckle effect and allows the generation of short measurement volumes with low measurement errors. This is achieved by the use of light from multi-mode fibres with high numerical apertures. Because of its low degree of spatial coherence the length of the measurement volume is reduced drastically. The multi-mode radiation shows a behaviour similar to classical geometrical light with nearly plane wavefronts so that the fringe spacing variation is reduced to Δd/d≈ 5×10−4.

2 The principle

The aim of this work is to present the employment of multi-mode light with a poor degree of spatial coherence. The radiation emitted from the multi-mode fibre is regarded as an assembly composed of different phase cells that are mutually uncorrelated. Interference only occurs from light that originates from the same phase cell, each having ideal coherence properties. Considering the intersection volume of the two LDA partial beams in each point of this volume a certain cell of one beam overlaps with one cell of the other beam. Only different phase cells overlap in the marginal regions so that the interference is suppressed. In the centre region, identical phase cells coincide and an interference pattern develops. Consequently, the intersection volume of the laser beams and the measurement volume, i.e. the volume, where interference occurs, are no longer identical. This circumstance is depicted in Fig. 1, where lz indicates the length of the intersection volume and az the length of the measurement volume. At the bottom of Fig. 1 a measurement of the interference contrast is shown, illustrating the spatial restriction of the measurement volume.
Fig. 1.

Intersection volume and interference volume of two crossing multi-mode laser beams. The lines indicate the 1/e2 borders of the laser beams and the interference volume. The measurement of the interference contrast at the bottom demonstrates that the interference is restricted to the centre region of the intersection volume

The relative length az/lz is determined by the degree of spatial coherence of the light source. It is inverse proportional to the beam quality factor M2 (Buettner and Czarske 2001), which is determined by the core diameter D, the numerical aperture AN of the fibre and the wavelength λ, and is approximately given by:
$$ {M^{2} \approx {{\pi DA_{{\rm{N}}} } \over {2\lambda }}} $$
As a parasitic effect, intensity fluctuations in the far-field pattern arise from interference between different fibre modes. The visibility of the speckle pattern can be reduced by increasing the intermodal dispersion
$$ {L_{{\rm{D}}} = {\rm{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} }}LA^{2}_{{\rm{N}}} } $$
where LD means the path length difference between the lowest and the highest guided mode and L the fibre length. If this is large compared to the low temporal coherence lengths of the laser (Buettner and Czarske 2001; Morgan et al. 1993), the visibility of the speckle pattern is reduced. Experimentally, by using a 30 m, 0.37 NA fibre, a reduction of the speckle visibility down to 6% was achieved (Buettner and Czarske 2001). It is important to note, that a decrease of the coherence length leads only to a reduction of the speckle visibility, but not to a reduction of the visibility of the fringe pattern. Even at low temporal coherence lengths, the fringe system will show complete modulation (Buettner and Czarske 2001).

3 The results

A fibre-coupled laser diode array with 700 mW output power at λ=810 nm wavelength and a step-index fibre with D=100 µm core diameter and AN=0.22 numerical aperture were used to set up the multi-mode fibre LDA. A measurement volume of 80 µm length, 300 µm lateral extension and 100 fringes resulted. Laser power of 100 mW was available in the measurement volume. The beam quality factor of M2≈43 led to a ratio of only az/lz=3.5% between the length of the interference volume and the length of the intersection volume. The relative variation of fringe spacing Δd/d was measured to less than 5×10−4, see Fig. 2.
Fig. 2.

Fringe spacing along the optical axis in a measurement volume of 80 µm (full 1/e2) length. The total relative variation is less than 5×10−4

This demonstrates, that the multi-mode fibre LDA offers both a high spatial resolution and a low variation of fringe spacing ("virtual turbulence") at the same time, which, in the case of LDA's with single-mode radiation, are complementary features.

The function of the multi-mode fibre LDA was verified in a Göttingen-type wind tunnel, in which a glass plate was inserted to generate the well-known Blasius boundary layer (Buettner and Czarske 2002). DEHS (diethylhexyl sabacate) droplets of 2.5 µm mean diameter, generated with an atomizer, acted as scattering particles. The laminar boundary layer was measured by scanning the multi-mode fibre LDA perpendicular to the glass plate along the boundary layer. The receiving optics were placed in a forward scattering arrangement but approximately 20° inclined with respect to the plane of the partial beams so that reflections from the glass plate had less influence. Avalanche photodetectors were used for signal detection. The measured velocity profiles are shown in Fig. 3 for three different free stream velocities with corresponding Reynolds numbers of Rex=5.8×103, 2.3×104 and 5.8×104. Coordinates were normalised in order to compare the measured boundary layers with the theoretical Blasius profile. The Reynolds numbers are significantly smaller than 3.5×105...1×106, which is considered as the critical range for laminar to turbulent transition, so that laminar boundary layers can be assumed. All measurements are in excellent agreement with theory.
Fig. 3.

Measured velocity profiles of boundary layer flows for different Reynolds numbers in normalised co-ordinates v/v and η=z(v/(2νx))1/2. A good agreement with the theoretical Blasius boundary layer occurs

Figure 4 demonstrates the influence of an obstacle (a wire with 1 mm diameter) to the flow profile that was placed upstream on the glass plate and induced a turbulence. Figure 4a shows the velocity profile, which in the undisturbed case corresponds to the Blasius boundary layer. The obstacle turns it to an unsteady function with an increased gradient in the vicinity of the wall. Figure 4b shows the turbulence intensity profile, which in the undisturbed case is nearly constant at 0.4%. It increases significantly when the obstacle is introduced.
Fig. 4a, b.

Induced turbulence caused by a small obstacle. a Velocity profile, b turbulence intensity profile

4 Conclusion

The features of the multi-mode fibre LDA can be summarised as follows. A high spatial resolution is achieved owing to the low degree of spatial coherence of the multi-mode light, which reduces the length of the measurement volume to a few tens of micrometers in length. A small variation of fringe spacing of less than 5×10−4 and 100 signal periods ensures a small uncertainty for the velocity measurement. Turbulence data can be determined precisely. The parasitic speckle effect can be suppressed sufficiently by choosing fibres with high intermodal dispersion. A reduction of the speckle visibility down to 6% was demonstrated experimentally. The use of multi-mode fibres in the LDA-sending optics allows the employment of high power and low cost laser diode arrays with poor beam quality usually used for laser material processing. Only low alignment effort is needed to couple the light into multi-mode fibres, so that a simple and robust set-up can be realised. The principle can be extended by means of a two-wavelength technique to achieve a directional discrimination by the quadrature-homodyne technique (Buettner and Czarske 2002; Büttner and Czarske 2003). The multi-mode fibre LDA was applied in wind tunnel experiments to measure flat-plate Blasius boundary layers. All measurements are in excellent agreement with the theory. Measurements of a turbulent boundary layer were presented.

Acknowledgement

The support from the Deutsche Forschungsgemeinschaft (FKZ Cz55/4-4) is greatly acknowledged.

Copyright information

© Springer-Verlag 2004