Yeh and Cummins (1964) first demonstrated that gas lasers could be used to measure the velocity of fluids by observing the Doppler shift in the frequency of light scattered from small particles moving with the fluid. Since then the technique, which became known as laser Doppler anemometry (LDA) has been greatly developed and today specialized optical and signal processing systems are routinely used in almost every fluid mechanics laboratory in the world.
Gas lasers provide the high energy monochromatic light source for most LDA systems, different optical techniques being used depending upon whether or not forward scatter or back scatter light is collected by the photodetector. In order to scatter light, particles are required in the flow. These may occur naturally in some situations; in other instances small seed particles have to be introduced into the flow. Small seed particles are usually larger than the laser wavelength and for conventional LDA, it is assumed that the small seed particles are capable of following the small scale fluctuations in the flow. The velocity of the particles is therefore taken to be the velocity of the flow at the point of measurement. A typical scattering diagram associated with a single particle is shown in Figure 1.
The intensity of scattered light received varies with angular position of the photodetector. An angle of 0° denotes forward scatter and 180° is known as backscatter. For forward scatter the flow has to be accessible through a minimum of two viewing directions, whereas with backscatter at 180° a single window is sufficient. The figure shows that the intensity of scattered light decreases with angular location of the detector, being a maximum at 0° and a minimum at 90°. The ratio of forward to backscattered light is of the order of 10^{2} to 10^{3}; a high powered laser is usually required for backscatter measurements.
Optical techniques based on forward scatter (reference beam, dual beam and dual scattered beam) and backscatter geometries have been fully developed, see Durst et al. (1976). All transmission optical components are corrected for spherical aberration, surfaces are coated to provide optimal transmission characteristics for the selected wavelengths. Today the dual beam optical geometry is most widely used for both forward and backscatter optical configurations.
The concept of the fringe model was introduced by Rudd (1969) to explain the operation of the dual beam LDA, in which each of the two, equal intensity, Gaussian beams can be considered to contain a series of wavefronts. When correctly aligned the two beams come to a focus or waist at their intersection, so that in this region the wavefronts are very nearly parallel. The wavefronts from each beam form a series of parallel interference fringes in the plane normal to the plane of the beams. The fringe spacing (Δx) is given by
where λ is the laser wavelength and θ is the intersection angle of the two focused beams. Figure 2 shows the interference fringes formed in the intersection region, as Equation 1 shows Δx decreases with increasing θ.
The characteristic dimensions of the length (2σ_{y}), width (2σ_{x}), and height (2σ_{z}) of the scattering control volume, are given by
F is the focal length of the focussing lens and B is the diameter of the laser beam at the e^{−1} point of the Gaussian intensity distribution. The introduction of beam expander units into the transmission optical geometry is essential for applications where the size of the measuring volume should be small. The beam expander expands both the laser beam diameter (B) and the beam spacing by the expansion ratio (E). θ is increased by the expansion ratio so that the measurement volume length decreases by a factor equal to the square of the expansion ratio. The light intensity in the control volume will be increased by the square of the expansion ratio. Particles in the flow cross the beam intersection region, which is known as the measurement volume, and scatter light with an intensity which is modulated by the Doppler frequency (f_{D}). A typical Doppler burst or signal from a particle is shown in Figure 3. If the optical system is correctly aligned the Doppler frequency f_{D} associated with each individual fringe (Δx), within the measurement volume is a constant. This means that the velocity of each individual particle may be represented as
V is the instantaneous velocity normal to the fringes and f_{D} is known as the instantaneous Doppler frequency. This leads to the relationship
from which it is clear that the instantaneous particle velocity V varies linearly with f_{D}, since for any optical geometry and laser λ/2sinθ/2 is a constant. This relationship also shows that no system calibration is necessary.
Representing the instantaneous quantities as the sum of a mean (V_{m}) plus a fluctuation (v'), then
and
or for mean quantities
and for fluctuating quantities
These relationships show that a one-dimensional LDA system is capable of providing the mean velocity as well as the corresponding Reynolds normal stress. In addition other turbulence parameters, such as the skewness and flatness factors, together with the spectrum of turbulence and the auto or cross-correlations, are available via sophisticated software packages.
For many measurements made by LDA the velocity statistics are compiled from N discrete instantaneous velocity measurements made at random time intervals, each of which corresponds to the passage of a particle through the measurement volume. Mean quantities are calculated by performing ensemble averages, that is
suffix i denotes the velocity from the ith Doppler burst in the sample.
The signal to be analyzed is provided by the photodetector, usually as a current plulse, which contains the required frequency information relating to the velocity. Photodetector tubes have a band width up to approximately 120 MHz. Interference filters are required to restrict the light reaching the photosensitive surface to that from the required wavelength or color.
Using the blue and green lines simultaneously from an Argon-ion laser enables a two-dimensional LDA system to be assembled, the blue and green fringes being orthogonal to one another. A particle crossing the orthogonal fringes will scatter blue and green light, providing two orthogonal velocity components. Again using two photodetectors and ensemble averaging, this optical configuration provides the capability to measure two mean velocity components (U_{m}, V_{m}), two normal stresses (u'^{2}, v'^{2}), and a Reynolds shear stress (u' v').
A third color and photodetector enables a fully three-dimensional system to be constructed which will measure, at a point in the flow, ensemble averages of the three mean velocity components (U_{m}, V_{m}, W_{m}) and all the components which represent Reynolds normal and shear stresses in the general form of the Navier Stokes equations.
Modern laser Doppler anemometer systems incorporate a Bragg cell for frequency shifting of a laser beam, at a frequency of 40 MHz, in order to remove any directional ambiguity. This facility enables regions of positive, zero and negative flow velocities to be clearly identified, the importance of this capability is highlighted in Figure 4. An exceptionally small control volume 30 × 17 × 15 μm was used to provide detailed measurements within the cavity between two 5 mm square ribs on a roughened surface, the pitch to height ratio (x/e) being 7.2. These near wall measurements to within 100 μm of the surface enable the various flow regimes to be clearly identified and confirms that flow reattachment does not occur along the base of the cavity [see Martin and Bates (1992)].
With recent advances in fiber optic technology a new generation of LDA probes have been introduced with the fiber used as a link between the laser and the optical head, which incorporates the focusing lens. The fibers which transmit the laser beams are polarization-preserving single mode fibers. A multimode fiber is then used to collect the scattered light for transfer to the photodetector. The use of fiber optics has improved the inherent safety of LDA systems, since the high powered laser beams are confined within the fiber which may be run through a laboratory from a centrally located high power laser.
Nonintrusive LDA measurements have been undertaken on a large number of carefully controlled experiments of laminar and turbulent flows which may be isothermal or combusting. Good quality experimental data has been used as a basis for comparison and validation of modern computational fluid dynamic codes based upon the numerical solution of the three-dimensional Navier-Stokes equations.
After a decade of research conventional LDA techniques have been successfully extended to measure simultaneously the size and velocity of spherical droplets and particles suspended in two-phase flows. Phase Doppler anemometry (PDA) is today the most widely used technique for two-phase flow investigations.
Modern PDA systems comprise two or more photodetectors which are located at different points in space, but each of the detectors sees the light scattered from the same particle as it travels across the measurement probe volume. Each detector will therefore generate an identical Doppler burst. As with conventional LDA the Doppler frequency provides the velocity of the particle or droplet. Each Doppler signal carries a phase difference with respect to one another. Saffman et al. (1984), Bachalo (1980), and Durst and Zareé (1975) showed, either theoretically or experimentally, that the phase difference varied linearly with particle or droplet diameter. The linear relationship between phase and diameter depends upon both the transmission and collection optical geometries, the angle at which the scattered light is collected as well as, for refraction only, the ratio of the refractive index of the droplet to that of the transporting medium. Two matched photodetectors enable phase differences up to 360° to be considered, whilst the inclusion of a third matched photodetector eliminates phase ambiguity and doubles the sizing range. Modern PDA receivers are integrated units, which accommodate up to four photodetectors. A range of micrometer screws control the size of the aperture, over which scattered light is collected, as well as the polarization of the system and the focusing of the unit. Drain (1985) showed how the scattered light intensity varied with the scattering angle at which the light was collected, taking into account refraction and reflection due to the droplet as well as the polarization of the laser. In general 30°, 70°, and 150° scattering angles, from the forward direction are the most appropriate for scattering from water droplets. Scattering at both 30° and 70° takes into account refraction and reflection associated with each droplet. The collection of scattered light at 70° minimizes the influence of reflection on the experimental measurements.
The most obvious advantages associated with the use of PDA techniques for multiphase flows are:
A small single-color control volume, such as that used in a one-dimensional conventional LDA system is capable of providing simultaneously the velocity and diameter of individual droplets suspended in a two-phase flow.
A relatively cheap low-power helium-neon laser is appropriate. To improve the PDA's sensitivity to small droplets a high powered laser may be required.
A relatively large dynamic range of 40:1 is possible, with a minimum and maximum droplet size of approximately 1 and 10,000 μm, respectively.
New high speed co-variance signal processors provide the ability to measure in real time at data rates of up to 200 kHz. The autocorrelation of a Doppler burst provides the Doppler frequency, whereas the cross-correlation of two Doppler bursts from a phase Doppler system provides the phase difference. The data processing software converts the phase difference into a droplet or particle diameter based on the linear calibration curve.
Tayali and Bates (1990) have rewiewed the development of optical techniques for particle sizing in multiphase flows. Detailed PDA experimental measurements, of the diameter and velocity of individual droplets or particles found in a wide range of two-phase and multiphase flows, have been published in the research literature. This data provides a new insight into the complex flow phenomena whereby droplets:
may break-up
may be entrained into a flow
may coalesce
may deposit on to a surface.
New data collected using PDA systems will enable the performance of existing empirical models to be investigated. Figure 5 shows measurements of the correlation of droplet velocity versus droplet diameter for an air/water annular two- phase flow, the pipe diameter being 32 mm and the hydrodynamic development length is 228 diameters. The figure confirms that the larger droplets lag the smaller ones and clearly shows the effect of the variation of the gas mass flux, on the correlation, at a constant water flux. The size range of the droplets observed in the flow decreases with increasing gas flowrate [Bates and Sheriff (1992), Bates and Ayob (1994)].
REFERENCES
Bachalo. W. D. (1980) Method for Measuring the Size and Velocity of Spheres by Dual Beam Light Scattering Interferometry, Appl. Opt. 193:p363.
Bates, C. J. and Ayob, R. (1995) Annular Two-Phase Flow Measurements using Phase Doppler Anemometry with Scattering Angles of 30° and 70°, Flow Meas. Instrum. (6):21. DOI: 10.1016/0955-5986(95)93454-3
Bates, C. J. and Sheriff, J. M. (1992) High Data Rate Measurements of Droplet Dynamics in a Vertical Gas-Liquid Annular Flow, Flow Meas. Instrum. (3):247.
DOI: 10.1016/0955-5986(92)90023-XDrain, I. E. (1985) Laser Anemometry and Particle Sizing, Int. Conf. on Laser Anemometry—Advances and Applications, 7.
Durst, F., Melling, A., and Whitelaw, J. H. (1976) Principles and Practice of Laser Doppler Anemometry, Academic Press.
Durst, F. and Zaré, M. (1975) Laser-Doppler Measurements in Two-Phase Flows, Proc. LDA Symp., Copenhagen, 403.
Martin, S. R. and Bates, C. J. (1992) Small Probe Volume Laser Doppler Anemometry Measurements of Turbulent Flow near the Wall of a Rib Roughened Channel, Flow Meas. Instrum. 2, 81. DOI: 10.1016/0955-5986(92)90004-O
Rudd, M. J. (1969) A New Theoretical Model for the Laser Doppler Meter, J. Phys E: Sci. Instrum. 2, 55.
Saffman, M., Buchhave, P., and Tanger, H. (1984) Simultaneous Measurement of Size, Concentration and Velocity of Spherical Particles by a Laser-Doppler Method, 2nd ISALAFM, Lisbon, Paper 8.1.
Tayali, N. E. and Bates, C. J. (1990) Particle Sizing Techniques in Multiphase Flows: A Review, Flow Meas. Instrum. 1, 77. DOI: 10.1016/0955-5986(90)90032-3
Yeh, Y. and Cummins, H. Z. (1964) Localized Fluid Flow Measurements with a He-Ne Laser Spectrometer, Appl Phys Lett. 4, 176.
Использованная литература
- Bachalo. W. D. (1980) Method for Measuring the Size and Velocity of Spheres by Dual Beam Light Scattering Interferometry, Appl. Opt. 193:p363.
- Bates, C. J. and Ayob, R. (1995) Annular Two-Phase Flow Measurements using Phase Doppler Anemometry with Scattering Angles of 30Â° and 70Â°, Flow Meas. Instrum. (6):21. DOI: 10.1016/0955-5986(95)93454-3
- Bates, C. J. and Sheriff, J. M. (1992) High Data Rate Measurements of Droplet Dynamics in a Vertical Gas-Liquid Annular Flow, Flow Meas. Instrum. (3):247.
- Drain, I. E. (1985) Laser Anemometry and Particle Sizing, Int. Conf. on Laser Anemometryâ€”Advances and Applications, 7.
- Durst, F., Melling, A., and Whitelaw, J. H. (1976) Principles and Practice of Laser Doppler Anemometry, Academic Press.
- Durst, F. and ZarÃ©, M. (1975) Laser-Doppler Measurements in Two-Phase Flows, Proc. LDA Symp., Copenhagen, 403.
- Martin, S. R. and Bates, C. J. (1992) Small Probe Volume Laser Doppler Anemometry Measurements of Turbulent Flow near the Wall of a Rib Roughened Channel, Flow Meas. Instrum. 2, 81. DOI: 10.1016/0955-5986(92)90004-O
- Rudd, M. J. (1969) A New Theoretical Model for the Laser Doppler Meter, J. Phys E: Sci. Instrum. 2, 55. DOI: 10.1088/0022-3735/2/1/313
- Saffman, M., Buchhave, P., and Tanger, H. (1984) Simultaneous Measurement of Size, Concentration and Velocity of Spherical Particles by a Laser-Doppler Method, 2nd ISALAFM, Lisbon, Paper 8.1.
- Tayali, N. E. and Bates, C. J. (1990) Particle Sizing Techniques in Multiphase Flows: A Review, Flow Meas. Instrum. 1, 77. DOI: 10.1016/0955-5986(90)90032-3
- Yeh, Y. and Cummins, H. Z. (1964) Localized Fluid Flow Measurements with a He-Ne Laser Spectrometer, Appl Phys Lett. 4, 176.