# Measurement Principles of PDA

#### Introduction

Phase Doppler anemometry (PDA) measurements are performed on single particles, allowing for detailed analysis of particulate flows. The distribution of statistical size and velocity moments in a flow field can be measured, as well as particle concentration and local size-velocity correlation.

Movement of the measurement point in the flow allows mapping of entire flow fields.
The underlying principle of phase Doppler anemometry is based on light-scattering interferometry and therefore requires no calibration.

The measurement point is defined by the intersection of two focused laser beams and the measurements are performed on single particles as they move through the sample volume. Particles thereby scatter light from both laser beams, generating an optical interference pattern.

A receiving optics placed at a well-chosen off-axis location projects a portion of the scattered light onto multiple detectors. Each detector converts the optical signal into a Doppler burst with a frequency linearly proportional to the particle velocity. The phase shift between the Doppler signals from different detectors is a direct measure of the particle diameter.

#### Principles

The PDA technique is an extension of laser Doppler anemometry and is based upon phase Doppler principles.

Two or more detectors collect the light scattered by single particles passing through the measurement volume.

#### Light scattering

The phenomena of light scattering can be visualised by ray tracing. For example, the light which is incident on a water droplet is partially reflected from the surface and partially transmitted and refracted in both forward and backward directions after one internal reflection. The scattered light intensity is not uniform in all directions and also depends on the relative refractive index:

#### Scattering angle

The position of the receiver (scattering angle j) must therefore be carefully selected to ensure that one light scattering mode is dominant.

Commonly used scattering angle ranges are:
A: 30° – 70° for refraction
B: 80° – 110° for reflection
C: 135° – 150° for 2nd order refraction

#### Particle velocity

The particle velocity U is calculated from the Doppler frequency fD of the signal from any one of the detectors:

#### Particle size

The particle size D is derived from the phase difference F between the signals from two detectors.

If light scattering is dominated by reflection:

If light scattering is dominated by refraction:

#### Three detectors

The maximum particle size that can be unambiguously measured with two detectors corresponds to a phase shift of F 1-2 = 360°. Reducing the distance between the detectors can extend the particle size range. This however, will also reduce the measurement resolution. Using three detectors provides both a large measurable size range (F 1-3) and a high measurement resolution (F 1-2).

State-of-the-art PDA receivers have three pre-aligned receiving apertures integrated into one fibre optical probe.