Development of Two-Frequency Planar Doppler Velocimetry

Tom O. H. Charrett and Ralph P. Tatam

Engineering Photonics Group, Centre for Photonics and Optical Engineering,

School of Engineering, Cranfield University,

Cranfield, Bedford,

MK43 0AL, UK.

Abstract. This paper describes recent developments in the 2n-PDV flow measurement technique. A method of approximately doubling the sensitivity compared to a conventional PDV system and previously demonstrated 2n-PDV techniques. The construction of 3D 2n-PDV system capable of making time averaged velocity measurements is described and used to make measurements demonstrating this increased sensitivity 2n-PDV method.

1. Introduction

Planar Doppler Velocimetry (PDV)[1], also known as Doppler Global Velocimetry (DGV)[2] is a non-intrusive planar flow measurement technique that allows up to three components of the flow velocity to be measured simultaneously over a plane defined by a laser light sheet. The technique is capable of making either instantaneous flow measurements using a pulsed laser source or time-averaged measurements using a continuous wave laser to form the illuminating laser sheet.

PDV works on the principle of measuring the Doppler frequency shift of light scattered from particles seeded in the flow being measured. Using a single observation direction allows the measurement of a single component of the velocity. To measure multiple components requires either multiple illumination directions[3] or more usually multiple observation directions[4] which allows the velocity components to be measured simultaneously. This would usually require the use of multiple imaging systems however the use of imaging fibre bundles, pioneered at Cranfield[1], allows several observation directions, and thus velocity components, to be measured simultaneously by spatially multiplexing on to a single CCD camera. This approach has since been adopted by other groups in the field including DLR[5] and NASA[6].

The optical frequency shift,, is given by the Doppler equation:

(1)

Where is the optical frequency, and are unit vectors in the observation and illumination directions respectively, is the velocity vector and c is the free space speed of light.

In PDV the Doppler shift is measured using a molecular filter as an intensity-to-frequency transducer. This consists of a glass cell containing a molecular gas, usually iodine through which the flow is imaged. Iodine has a large number of absorption lines over the visible spectrum[7] and the laser frequency is tuned to coincide with one such line. The optical intensity at any position in the camera image is a function of the Doppler shift experienced at the corresponding position in the flow. For example Figure 1 shows a typical absorption feature in the iodine spectrum. If the illuminating frequency is tuned to point A then a Doppler shift will result in lower image intensities point A'.

Figure 1. Relative positions of the laser frequency and the shift frequency on a typical absorption feature. A and B/C denote the position of the illumination frequencies and A' and B'/C' the Doppler shifted frequency / Figure 2. Schematic of a conventional PDV imaging head arrangement.

However the intensity in a PDV image is also affected by other factors such as the intensity profile of the illuminating laser sheet, spatial variations in the seeding density and imperfections in the optical surfaces. These variations are generally of similar amplitude to those resulting from absorption in the iodine cell, and can obscure the information about flow velocity that is contained within the camera image. It is therefore usual to amplitude-divide the image beam onto two cameras, Figure 2; from one of the two imaging paths the iodine cell is omitted, and the resulting image acts as a reference to normalize the signal image carrying the velocity information.

2. Two-frequency Planar Doppler Velocimetry (2n-PDV)

In the two-frequency Planar Doppler Velocimetry (2n-PDV) technique[8-10] the need for a second camera to normalise the intensity is removed by capturing sequential images of the flow under different illumination frequencies. This overcomes the significant problem of image misalignment with conventional PDV, for errors to be minimised superposition of the two images to sub-pixel accuracy is necessary. For example an image misalignment of 0.1 pixels can lead to velocity errors of up to 5ms-1[11]. The 2n-PDV method also eliminates the problem of polarisation sensitivity of the split ratio of the beam splitter used in a conventional PDV imaging head. Ideally the beam splitter used in a conventional PDV imaging head would split the incoming light 50:50 between the signal and reference cameras with no variation for different polarizations of light. However even the 'non-polarizing' beam splitters typically used retain a slight sensitivity to polarization[12], typically quoted as ±3% variation in the split ratio for S and P polarized light, leading to typical velocity errors of ±7ms-1.

There are two approaches to the positioning of the illumination frequencies relative to the iodine absorption line, the first is similar in concept to conventional PDV and the second provides a method of approximately doubling the sensitivity compared with conventional PDV. In the first approach a signal image and a reference image are captured and processed in the same manor as conventional PDV images. The signal image is acquired under the first illumination frequency that is tuned to a position on the absorption line, Figure 1, point A. This is normalised using a reference image acquired under the second frequency that is tuned to lie in a 100% transmission region, Figure 1, point B.

The second tuning scheme increases the sensitivity of the system by tuning the two frequencies to positions A and C in Figure 1. With one frequency tuned to the falling slope and the other on the rising slope, a constant Doppler shift will result in the further attenuation of one image to a lower signal level and the rise in signal level in the other image. Dividing the difference of the images by the sum, and taking into account any difference in the gradients will give a result that has approximately double the sensitivity of the current PDV methods.

3. Development of a 3D 2n-PDV system

In our previous work a single component 2n-PDV system capable of making time-averaged measurements was demonstrated with measurements on a seeded air jet in the laboratory[8], however this system was unable to provide the frequency separation required for the increased sensitivity tuning scheme. Here a modified system is described, using image fibre bundles to make multiple component measurements, that is capable of making measurements using both of the sensitivity schemes described above.

Figure 3. Schematic showing the experimental arrangement used for the three dimensional velocity measurements. HWP - λ/2 plate; AOM – acousto-optic modulator; PBS – polarising beam splitter; BS – beam splitter; HWP – half wave plate Shifted (locking) beam path Un-shifted (illumination) beam

3.1. Illumination system

Figure 3 shows a schematic of the experimental arrangement. The light source was a tunable argon-ion laser (Spectra Physics Beamlok 2060), incorporating a temperature-stabilized etalon to ensure single-mode operation at 514.5 nm. Changing the optical path length of the intra cavity etalon generates the illumination frequencies. This was stabilized using a locking system consisting of a second iodine cell with signal and reference photodiode detectors and locking electronics to adjust the laser etalon temperature and ensure the laser frequency is stable based upon the transmission through this cell. An acousto-optic modulator (AOM) is used to shift the frequency by 260MHz and allow the locking system to operate when the frequency is tuned to 100% transmission. The locking beam will be shifted onto the absorption line so that any frequency fluctuations will result in an associated transmission fluctuation seen by the photodiodes and can then be corrected for.

The beam is then coupled into the high birefringent single mode polarization maintaining fiber used to guide the light to the beam scanning light sheet generator. This rapidly scanning the beam over the sheet to provide a top-hat intensity profile in the light sheet rather than the Gaussian distribution formed if using cylindrical lenses.

This arrangement increased the illumination power available over previous setups[8] however the images are now captured with a separation of minutes rather than seconds limited by the laser tuning time. For time-averaged measurements with constant seeding density this has not proved to be a problem.

3.2. Imaging head and fibre bundles

The imaging head used is greatly simplified compared to conventional PDV and consists of a single 12-bit peltier cooled CCD camera and iodine cell (25mm diameter by 50mm long operating as a starved cell above 40oC) with the views ported to the imaging head via the imaging fibre bundles.

Figure 4. The individual arms of the imaging fibre bundles. / Figure 5. The combined end of the imaging fibre bundles. / Figure 6. An example image of a view through the imaging bundles of a calibration target

The custom made imaging fibre bundles in use at Cranfield use a coherent array of fibres that is spilt into four channels (Figure 4). Each channel is 4m long, and has 600x500 fibres that are 8mm in diameter and positioned at 10mm centres. The losses through the bundle are ~50% for the 4m length used. The four views are combined at the detector head, with each occupying a quarter of the CCD image (Figure 5). An example of the image formed is shown in Figure 6. This is a view of a calibration target used to de-warp the image to a common view and determine the observation directions for each view.

4. Results

The system was initially used to measure the velocity field of a rotating disc. This provides a well-known velocity field with which to characterize the system as well as facilitating a comparison between the two sensitivity schemes described above. Each arm of the imaging fibre bundle was used with a 35mm SLR camera lens to view the rotating disc. The disc itself was 200mm in diameter, although the common field of view of each observation direction was an approximate disc 100mm in diameter. The rotation of the disc was measured using an optical tachometer giving a maximum velocity in the field of view of ~±34ms-1.

Figure 7. A single measured velocity component of a rotating disc, calculated using the normal sensitivity scheme. / Figure 8. A single measured velocity component of a rotating disc, calculated using the increased sensitivity scheme. / Figure 9. Histograms showing the error for + Normal and * Increased sensitivity

An example of a measured velocity component can be seen in Figure 7, using the normal sensitivity scheme, and Figure 8 using the increased sensitivity scheme. Here it can be seen that the measurement using the increased sensitivity scheme is visibly less noisy than that using the normal sensitivity scheme. To allow a comparison between the two schemes a theoretical velocity component (calculated from view geometry and the discs rotation) was subtracted from each of the measured components leaving only the remaining error. A histogram of this remaining error is shown in Figure 9, which shows that the resulting error is smaller for the increased sensitivity scheme. This was done for all four measured components and the standard deviations are shown in Table 1. It can be seen that there is approximately a 40% reduction in the level of error when using the increased sensitivity scheme over the normal sensitivity scheme.

Table 1. Standard deviations of the variation between the measured and theoretical velocity components, and the calculated reduction in error when using the increased sensitivity scheme.
Standard deviation / View 1 / View 2 / View 3 / View 4
Normal sensitivity / 4.6 ms-1 / 4.9 ms-1 / 2.4 ms-1 / 3.9 ms-1
Increased sensitivity / 2.5 ms-1 / 2.9 ms-1 / 1.6 ms-1 / 2.3 ms-1
% Reduction / 45.7% / 40.8% / 33.3% / 41.0%

5. Discussion and future development of the technique.

The use of the increased sensitivity 2n-PDV method has been demonstrated and shown to reduce the error level by approximately 40%. As both signal and reference images are captured on a single camera the image misalignment problem in conventional PDV is overcome. As noted in our previous work[8,9] this means that there is no need to use a 'white card' type correction that is commonly applied in PDV measurements, this simplifies the processing and removes a potential source of systematic error. However the images used in the normalisation process are now captured sequentially, unlike in conventional PDV where they are captured simultaneously. This was not found to be an issue when making measurements on the rotating disc or in further[8] measurements on seeded air jets, shown in Figure 10 .

Figure 10. 3D 2n-PDV cross section measurements on a seeded air jet. Vectors represent the in plane velocities (every 12th x 12th vector shown) and colour the out-of-plane velocity. Cross sections were measured at 60,80,100 and 120mm distances from the jet nozzle exit

The combination of the 2n-PDV technique with the imaging fibre bundles approach allows 3D velocity measurements to be made using only a single camera and iodine cell, greatly reducing the cost and complexity associated with conventional PDV techniques which require six cameras and three iodine cells for 3D measurements.

In a rapidly time-varying flow, averaging over long integration times is not an option; a pulsed laser would be required for this type of flow, to freeze the motion of the particles. An implementation of the 2n-PDV technique using two closely spaced pulses at the two frequencies combined with a dual-frame CCD is currently being investigated[10]. The dual frame CCD camera is capable of capturing two frames with a time separation of around ~200ns allowing the two images required by the two-frequency technique to be captured with a delay small enough to effectively freeze the motion of the seed particles

6. Acknowledgement

This work was funded by the Engineering and Physical Sciences Research Council (EPSRC), UK

7. References

[1]  Nobes, D.S., Ford, H.D., and Tatam, R.P., 2004, Experiments in Fluids, 36, 1, 3-10.

[2]  Meyers, J.F. and Komine, H., 1991, Laser Anemometry, 1, 273-277.

[3]  Roehle, I., Willert, C., Schodl, R., and Voigt, P., 2000, Measurement Science and Technology, 11, 1023-1035.