Abstract
Measurements have been made of the effect of flow turbidity on the visibility and pedestal amplitude of an anemometer signal when incident laser beams are interrupted by particulate flow. The purpose is to assess the likely accuracy of particle sizing and the reliability of discrimination between continuous and particulate phase velocities. Optical depths of field were varied between 2.5 × 10−2 and 14 × 10−2 mm the diameter of the interrupting particles ranged between 14 and 800 μm in six discrete ranges and the corresponding void fractions lay between 0.003% and 0.378%. The incident beam diameter was approximately 400 μm.
The measured size is subject to both systematic and random errors when inferred from measurements of pedestal amplitude: the random error increases as the ratio of the incident beam diameter to that of the particulate phase decreases. Systematic errors corresponding to a 10% underestimation of diameter occur at void fractions of 0.003%, 0.01% and 0.018% for particles below 40 μm 75 μm and 105 μm respectively over a 5 cm depth of field. The r.m.s. error is smaller than 7% for particles below 40 μm for all conditions studied but increases with increasing diameter and exceeds 10% at void fractions greater than 0.1% for particles above about 100 μm. The random error in measured diameter derived from measurements of visibility is influenced mostly by the flow turbidity over the 5 cm of the incident beams closest to the measuring volume. For interrupting particles smaller than about 100 μm the r.m.s. error is similar to that for measurements based on the pedestal amplitude.
Discrimination of the velocity signal between the particulate and dispersed phase, based on the separation of pedestal amplitudes, is likely to be unreliable if the particle diameter is comparable to the diameter of the incident beams and if the probability of two particles simultaneously present in each beam is not negligible. A method for estimating the level of turbidity at which discrimination is no longer possible is described.
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Abbreviations
- b :
-
beam diameter
- d :
-
particle diameter
- D :
-
amplitude of high passed Doppler signal (equation 7)
- D 1 :
-
depth of field of water tank
- E :
-
particle extinction coefficient (= 2)
- I 1,2 :
-
instantaneous light intensity at LDA measuring volume of each incident beam
- n :
-
particle concentration (number per unit volume)
- N :
-
number of particles in the incident beam
- P :
-
maximum amplitude of pedestal component of Doppler signal
- T :
-
Transmittance of beam {(attenuated/unattenuated) beam intensity}
- V :
-
signal visibility (equation 8)
- ε:
-
relative error in measured particle diameter {(truemeasured)/true)}
- λ:
-
wavelength of laser beam (632.8 nm)
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Kliafas, Y., Taylor, A.M.K.P. & Whitelaw, J.H. Errors in particle sizing by LDA due to turbidity in the incident laser beams. Experiments in Fluids 5, 159–176 (1987). https://doi.org/10.1007/BF00298456
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DOI: https://doi.org/10.1007/BF00298456