# Effective Size of the Measuring Cross-Section of a Phase-Doppler Anemometry

## Abstract

The paper presents a technique for measuring particle mass flux in dispersed two-phase flows with improved accuracy of mass flux measurements by a *standard* phase-Doppler anemometer (PDA) with an AID converter-based signal processor. The purpose was achieved by improved estimation of the effective area of the probe volume. The area of probe volume was calculated by a geometrical optics approximation after considering two major influences namely ‘trajectory ambiguity’ and ‘slit effect’. The calculation results showed that the effective measuring area in the present optical configuration can be determined as a simple function of the probe diameter, size of the spatial filter of the receiving optics and particle diameter by considering only refracted light when ‘phase validation’ is applied. In addition careful setting of the trigger level of the signal processor resulted in reducing number of rejected signals owing to low signal to noise ratio (SNR) within the defined effective measuring area and as a consequence the accuracy of mass flux measurement was improved by 15% compared with our earlier work. The flux measurement of a hollow-cone spray indicated that the error did not exceed 20%, at a volume fraction of 2 × 10^{−4}%

## Keywords

Phase Doppler anemometry Mass flux measurement Trajectory ambiguity Slit effect Geometrical optics approximation## Preview

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## References

- Aizu, Y., Durst, F., Grehan, G., Onofri, F. and Xu, T., H.: PDA-system without Gaussian beam defects, 3rd Int. Cong, on Optical Particle Sizing, Yokohama, Japan, pp. 461–470, 1993.Google Scholar
- Bachalo, W., D., Rudoff, R., C. and Breña de la Rosa: A mass flux measurements of a high number density spray system using the phase Doppler particle analyzer, AIAA 88–0236, 1988.Google Scholar
- Domnick, J., Durst, F., Meiling, A., Qiu, H. -H., Sommerfeld, M. and Ziema, M.: A new generation of phase-Doppler instruments for particle velocity, size and concentration measurements, 3rd Int. Cong, on Optical Particle Sizing, Yokohama, pp. 407–414,. 1993.Google Scholar
- Durst, F., Tropea, C. and Xu, T.-H.: The Slit Effect in Phase Doppler Anemometry, 2nd Int. Conf. on Fluid Dynamic Measurement and its Applications, Bejing, Chaina, pp. 38–43, Oct. 1994.Google Scholar
- Gouesbet, G. and Gréhan, G.: Gaussian beam errors in phase-Doppler Anemometry and their elimination, 5th Int. Symp. on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, 11.6., pp. 243–259, 1990. Hardalupas, Y., Ph.D. Thesis, Imperial College, 1989.Google Scholar
- Hardalupas, Y. and Taylor, A. M. K. P.: Phase validation criteria of size measurements for the phase Doppler technique″, Exp. in Fluids, 17, pp. 253–258, 1994.ADSCrossRefGoogle Scholar
- Higuchi, M., Shirakawa, T., Morikita, M., Hishida, K. and Maeda, M.: Experimental study of multiple interacting sprays by phase Doppler anemometry, 7th Int. Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, paper 31.2, 1994.Google Scholar
- Hishida, K., Kobashi, K. and Maeda, M.: Improvement of LDA/PDA using a digital signal processing systems, Third Int. Conf. on Laser Anemometry, Advances and Applications, Swansea, UK, 1989.Google Scholar
- Kobashi, K., Hishida, K. and Maeda, M.: Measurement of Fuel Injector Spray Flow of I.C. Engine by FFT Based Phase Doppler Anemometer, in R. J. Adrian, D. F. G. Durao, F. Durst, M. Maeda, J. H. Whitelaw (Eds.) Applications of Laser Technique to Fluid Mechanics, Springer-Verlag, pp. 268–287, 1990.Google Scholar
- Kobashi, K. Hishida, K. and Maeda, M.: Multi-purpose high speed signal processor for LDA/PDA using DSP array, Sixth International Symposium (eds) Applications of Laser Techniques to Fluid Mechanics, paper 21.6, Lisbon, Portugal, 1992.Google Scholar
- Panidis, Th. and Sommerfeld, M.: The locus of centres method for LDA and PDA measurements, 8th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics, paper 12.5, Lisbon, Portugal, 1996.Google Scholar
- Qiu, H. H. and Sommerfeld, M.: A reliable method for determine the measurement volume size and particle mass fluxes using phase-Doppler anemometry, Exp. in Fluids, 13, pp. 393–404, 1992.ADSCrossRefGoogle Scholar
- Saffman, M.: Automatic calibration of LDA measurement volume size, Appl. Opt., Vol. 26, No. 13, pp. 2592, 1987.ADSCrossRefGoogle Scholar
- Sanker, S. V., Inenaga, A. S. and Bachalo, W. D.: Trajectory Dependent Scattering in Phase Doppler Interferometry: Minimizing and Eliminating Sizing Error, in R. J. Adrian, D. F. G. Durao, F. Durst, H. V. Heitor, M. Maeda, J. H. Whitelaw (Eds.) Laser Techniques and Applications in Fluid Mechanics, Springer-Verlag, pp. 75–89, 1992.Google Scholar
- Sanker, S. V., Bachalo, W. D. and Robart, D. A.: An adaptive intensity validation technique for minimizing trajectory dependent scattering errors in phase Doppler interferometry, 4th Int. Congress on Optical Particle Sizing, Nürnberg, Germany, pp. 1–14, 1995.Google Scholar
- Schöne, F., Bauckhage, K. and Wriedt, T.: Size of the detection area of a phase-Doppler anemometer for Reflecting and Refracting particles, Part. Part. Syst. Charact., 11, pp. 327–338, 1994.CrossRefGoogle Scholar
- Sommerfeld, M. and Qiu, H. -H.: Particle concentration measurements by phase-Doppler anemometry in complex dispersed two-phase flows, Exp. in Fluids, 18, pp. 187–198, 1995.ADSCrossRefGoogle Scholar
- Tropea, C. and Xu, T.-H., Onofri, F., Grehan, G., Haugen, P. and Stieglmeier, M.: Dual mode phase Doppler anemometer, 4th Int. Congress Optical Particle Sizing, Nürnberg, Germany, pp. 287–296, 1995.Google Scholar
- Willmann, M., Kneer, R., Eigenmann, L., Wittig., S and Hirleman, E.: Experimental investigations on the effect of trajectory dependent scattering on phase Doppler particle sizing with a standard instrument, 7th. Int. Symp. on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 18.1, 1994.Google Scholar
- Xu. T.-H. and Tropea, C.: Improving the performance of two-component phase Doppler anemometers, Meas. Sci. Technol. 5, pp. 969–975, 1995ADSCrossRefGoogle Scholar