Measurement Principles of LDA

Introduction

The Laser Doppler Anemometer, or LDA, is a widely accepted tool for fluid dynamic investigations in gases and liquids and has been used as such for more than three decades. It is a well-established technique that gives information about flow velocity.

Its non-intrusive principle and directional sensitivity make it very suitable for applications with reversing flow, chemically reacting or high-temperature media, and rotating machinery where physical sensors are difficult or impossible to use. It requires tracer particles in the flow.

The method’s particular advantages are: non-intrusive measurement, high spatial and temporal resolution, no need for calibration, and the ability to measure in reversing flows.

image of laser doppler anemometry principle
LDA principle

Principles

The basic configuration of an LDA consists of:

  • A continuous wave laser
  • Transmitting optics, including a beam splitter and a focusing lens
  • Receiving optics, comprising a focusing lens, an interference filtre and a photodetector
  • A signal conditioner and a signal processor.

Advanced systems may include traverse systems and angular encoders. A Bragg cell is often used as the beam splitter. It is a glass crystal with a vibrating piezo crystal attached. The vibration generates acoustical waves acting like an optical grid.

iamge of the Bragg cell used as a beam splitter.
The Bragg cell used as a beam splitter.

The output of the Bragg cell is two beams of equal intensity with frequencies f0 and fshift. These are focused into optical fibres bringing them to a probe.

In the probe, the parallel exit beams from the fibres are focused by a lens to intersect in the probe volume.

The probe volume

image of the probe and the probe volume.
The probe and the probe volume.

The probe volume is typically a few millimeters long. The light intensity is modulated due to interference between the laser beams. This produces parallel planes of high light intensity, called fringes. The fringe distance df is defined by the wavelength of the laser light and the angle between the beams:

image of fringe distance equation

Each particle passage scatters light proportional to the local light intensity.

Flow velocity information comes from light scattered by tiny “seeding” particles carried in the fluid as they move through the probe volume. The scattered light contains a Doppler shift, the Doppler frequency fD, which is proportional to the velocity component perpendicular to the bisector of the two laser beams, which corresponds to the x-axis shown in the probe volume.

The scattered light is collected by a receiver lens and focused on a photo-detector. An interference filtre mounted before the photo-detector passes only the required wavelength to the photo-detector. This removes noise from ambient light and from other wavelengths.

Signal processing

The photo-detector converts the fluctuating light intensity to an electrical signal, the Doppler burst, which is sinusoidal with a Gaussian envelope due to the intensity profile of the laser beams.

The Doppler bursts are filtered and amplified in the signal processor, which determines fD for each particle, often by frequency analysis using the robust Fast Fourier Transform algorithm.

The fringe spacing df provides information about the distance traveled by the particle

The Doppler frequency fD provides information about the time: t = 1/fD

Since velocity equals distance divided by time, the expression for velocity thus becomes: Velocity V = df* fD

Determination of the sign of the flow direction

Image of Doppler frequency to velocity transfer function for a frequency shifted LDA system.
Doppler frequency to velocity transfer function for a frequency shifted LDA system.

The frequency shift obtained by the Bragg cell makes the fringe pattern move at a constant velocity. Particles which are not moving will generate a signal of the shift frequency fshift. The velocities Vpos and Vneg will generate signal frequencies fpos and fneg, respectively.

LDA systems without frequency shift cannot distinguish between positive and negative flow direction or measure 0 velocity.

LDA systems with frequency shift can distinguish the flow direction and measure 0 velocity.

Two- and three-component measurements

To measure two velocity components, two extra beams can be added to the optics in a plane perpendicular to the first beams.

All three velocity components can be measured by two separate probes measuring two and one components, with all the beams intersecting in a common volume as shown below. Different wavelengths are used to separate the measured components. Three photo-detectors with appropriate interference filters are used to detect scattered light of the three wavelengths.

Image of LDA optics
LDA optics for measuring three velocity components.

Modern LDA systems employ a compact transmitter unit comprising the Bragg cell and colour beam splitters to generate up to 6 beams: unshifted and frequency shifted beams of three different colours. These beams are passed to the probes via optical fibres.

Seeding particles

Liquids often contain sufficient natural seeding, whereas gases must be seeded in most cases.

Ideally, the particles should be small enough to follow the flow, yet large enough to scatter sufficient light to obtain a good signal-to-noise ratio at the photo-detector output.

Typically the size range of particles is between 1 µm and 10 µm. The particle material can be solid (powder) or liquid (droplets).

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