7.2 Laser Doppler velocimetry

Laser Doppler velocimetry is a powerful technique for measuring fluid velocities in multiphase flows. It uses laser light scattered by particles to determine velocity through the Doppler effect. This non-intrusive method provides high-resolution data on flow behavior.

LDV systems create interference fringes where laser beams intersect. As particles cross these fringes, they scatter light at frequencies proportional to their velocity. By analyzing this scattered light, LDV can measure velocity components with great precision in complex multiphase systems.

Principles of laser Doppler velocimetry

• Laser Doppler velocimetry (LDV) is a non-intrusive optical technique for measuring fluid velocity at a point in a flow field
• Based on the Doppler effect and the interference of laser light scattered by particles in the fluid
• Provides high spatial and temporal resolution velocity measurements in multiphase flows

Doppler effect in LDV

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• When light is scattered by a moving particle, the frequency of the scattered light is shifted proportional to the particle's velocity
• The Doppler frequency shift $f_D$ is given by $f_D = (2 v \sin(\theta/2))/\lambda$, where $v$ is the particle velocity, $\theta$ is the angle between the incident and scattered light, and $\lambda$ is the laser wavelength
• Measuring the Doppler frequency shift allows the determination of the particle velocity component perpendicular to the bisector of the incident and scattered light directions

Interference fringes for velocity measurement

• LDV systems create an interference fringe pattern at the intersection of two laser beams
• As a particle passes through the fringes, it scatters light with an intensity modulation at the Doppler frequency
• The fringe spacing $d_f$ is given by $d_f = \lambda/(2 \sin(\theta/2))$, where $\lambda$ is the laser wavelength and $\theta$ is the angle between the intersecting beams
• The particle velocity $v$ is related to the Doppler frequency $f_D$ and fringe spacing $d_f$ by $v = f_D \cdot d_f$

LDV system components

• A typical LDV system consists of a laser source, beam splitter, transmitting and receiving optics, and a signal processing unit
• These components work together to create the interference fringe pattern, collect the scattered light, and extract the velocity information

Laser source and beam splitting

• Continuous wave lasers (Helium-Neon, Argon-ion, or laser diodes) are commonly used in LDV systems for their high intensity, monochromaticity, and coherence
• A beam splitter divides the laser beam into two or more beams of equal intensity
• Acousto-optic modulators (Bragg cells) are often used to introduce a frequency shift between the beams, allowing the determination of flow direction

Transmitting and receiving optics

• Transmitting optics, such as a focusing lens, direct the laser beams to intersect at the measurement point, forming the interference fringe pattern
• Receiving optics, typically a lens or a fiber optic probe, collect the scattered light from the particles passing through the measurement volume
• The collected light is then focused onto a photodetector (photomultiplier tube or avalanche photodiode) for conversion into an electrical signal

Signal processing unit

• The photodetector output is processed by a signal processor to extract the Doppler frequency information
• High-pass and low-pass filters remove noise and isolate the Doppler signal
• A burst detector identifies the presence of a particle in the measurement volume and triggers the data acquisition
• Fast Fourier Transform (FFT) or autocorrelation techniques are used to determine the Doppler frequency and calculate the particle velocity

Measurement techniques

• Various LDV configurations and techniques are employed depending on the specific application and flow conditions
• These include reference beam vs dual beam LDV, forward vs backward scatter modes, and 1D, 2D, or 3D velocity measurements

Reference beam vs dual beam LDV

• Reference beam LDV uses a single laser beam intersecting with a reference beam at the measurement point
• Dual beam LDV, also known as fringe mode LDV, employs two intersecting laser beams to create the interference fringe pattern
• Dual beam LDV is more commonly used due to its higher signal-to-noise ratio and reduced sensitivity to vibrations

Forward vs backward scatter modes

• Forward scatter mode collects the scattered light in the direction of the transmitted laser beams, resulting in a higher signal intensity but requiring optical access on both sides of the flow
• Backward scatter mode collects the scattered light from the same side as the incident beams, allowing measurements in flows with limited optical access but with reduced signal intensity

1D, 2D, and 3D velocity measurements

• 1D LDV measures a single velocity component perpendicular to the bisector of the two laser beams
• 2D LDV uses two pairs of intersecting beams with different wavelengths (colors) to measure two orthogonal velocity components simultaneously
• 3D LDV employs three pairs of beams with different wavelengths to measure all three velocity components, providing a complete velocity vector at the measurement point

Seeding particles for LDV

• Seeding particles are introduced into the flow to scatter light and enable velocity measurements
• The choice of seeding material depends on the fluid properties, flow conditions, and the laser wavelength used

Ideal particle characteristics

• Seeding particles should be small enough to faithfully follow the fluid motion without altering the flow characteristics
• They should be large enough to scatter sufficient light for detection
• Particles should have a high refractive index relative to the fluid to enhance light scattering
• They should be non-toxic, non-corrosive, non-abrasive, and chemically inert to avoid damaging the flow system or the LDV components

Common seeding materials

• Liquids: Titanium dioxide (TiO2), aluminum oxide (Al2O3), glass microspheres, polymer microspheres (polystyrene, polyamide)
• Gases: Oil droplets (olive oil, silicon oil), smoke particles, titanium dioxide (TiO2), aluminum oxide (Al2O3)
• Multiphase flows: Naturally occurring particles or bubbles in the flow can be used as seeding, or tracer particles can be added to one or both phases

Particle size and concentration effects

• Particle size affects the scattered light intensity and the ability to follow the fluid motion accurately
• Smaller particles (0.1-5 μm) are typically used in gas flows, while larger particles (1-100 μm) are used in liquid flows
• The seeding concentration should be high enough to ensure a sufficient data rate but low enough to avoid multiple particle scattering and signal attenuation
• Optimal particle concentration depends on the measurement volume size, laser power, and the flow velocity range

Data acquisition and processing

• LDV data acquisition involves detecting and validating the Doppler burst signals, extracting the frequency information, and converting it to velocity
• Various signal processing techniques are employed to improve the accuracy and reliability of the velocity measurements

Burst signal detection and validation

• A burst detector identifies the presence of a particle in the measurement volume by comparing the signal amplitude to a threshold level
• Burst validation techniques, such as the 5/8 rule or the burst envelope matching, ensure that only complete and high-quality bursts are processed
• The arrival time and transit time of each validated burst are recorded for further analysis

Frequency domain analysis

• Fast Fourier Transform (FFT) is commonly used to extract the Doppler frequency from the burst signal
• The power spectrum of the signal is computed, and the peak frequency is identified as the Doppler frequency
• Interpolation techniques (parabolic, Gaussian, or centroid) are used to improve the frequency resolution and accuracy

Velocity bias and correction methods

• Velocity bias occurs when faster particles are more likely to be measured than slower ones, resulting in an overestimation of the mean velocity
• Correction methods, such as the transit time weighting or the residence time weighting, assign higher weights to slower particles to compensate for the bias
• The arrival time method, which uses the time between consecutive bursts, can also be used to correct the velocity bias

Applications in multiphase flows

• LDV is widely used for velocity measurements in various multiphase flow systems, providing insights into the flow behavior and interactions between phases
• Applications include liquid-liquid and gas-liquid flows, particle-laden flows, sprays, and turbulent and high-speed flows

Liquid-liquid and gas-liquid flows

• LDV can measure the velocity of each phase separately by using seeding particles with different characteristics (size, material) for each phase
• In gas-liquid flows, such as bubble columns or pipe flows, LDV can provide information on the gas and liquid velocity profiles, slip velocity, and turbulence properties
• For liquid-liquid flows, such as oil-water mixtures, LDV can help characterize the flow patterns, phase distribution, and mixing behavior

Particle-laden flows and sprays

• In particle-laden flows, such as fluidized beds or pneumatic conveyors, LDV can measure the velocity of both the fluid and the particles
• The slip velocity between the phases and the particle velocity fluctuations can be determined, providing insights into the particle-fluid interactions and the flow dynamics
• For sprays and atomization processes, LDV can measure the droplet velocities and help characterize the spray structure, penetration, and mixing

Turbulent and high-speed flows

• LDV's high temporal resolution makes it suitable for measuring velocity fluctuations and turbulence properties in multiphase flows
• Turbulent statistics, such as mean velocity, Reynolds stresses, and turbulent kinetic energy, can be obtained from the velocity time series
• In high-speed flows, such as supersonic gas-particle flows or cavitating liquids, LDV can provide velocity measurements without disturbing the flow, as long as optical access is available

Advantages and limitations

• LDV has several advantages over other velocity measurement techniques, but it also has some limitations that should be considered when planning experiments

Non-intrusive and high spatial resolution

• LDV is a non-intrusive technique, meaning it does not disturb the flow during measurements, as it relies on light scattering from particles
• It offers high spatial resolution, with measurement volumes typically on the order of 50-500 μm, allowing velocity measurements in small-scale flows or near walls and interfaces
• The non-intrusive nature and high spatial resolution make LDV suitable for studying delicate or complex flow structures in multiphase systems

Velocity range and accuracy

• LDV can measure a wide range of velocities, from very low (< 1 mm/s) to supersonic (> 1000 m/s), depending on the laser wavelength, optical configuration, and signal processing techniques used
• The velocity measurement accuracy is typically within 0.1-1% of the measured value, making LDV one of the most accurate velocity measurement techniques
• The high accuracy is particularly useful for validating computational fluid dynamics (CFD) models and studying flow phenomena in multiphase systems

Optical access and seeding requirements

• LDV requires optical access to the flow, which can be a limitation in some applications, such as dense multiphase flows or opaque systems
• The need for transparent windows or immersion probes may restrict the operating conditions (pressure, temperature) or the geometry of the flow system
• Seeding the flow with tracer particles is necessary for LDV measurements, which can be challenging in some multiphase flows, such as high-temperature or chemically reactive systems

Advanced LDV techniques

• Several advanced LDV techniques have been developed to extend the capabilities of standard LDV and address specific measurement challenges in multiphase flows
• These include dual-mode LDV for turbulence measurements, laser Doppler phase anemometry (LDPA) for simultaneous size and velocity measurements, and micro-scale LDV for near-wall measurements

Dual-mode LDV for turbulence measurements

• Dual-mode LDV combines the reference beam and dual beam techniques to measure the velocity and the velocity fluctuations simultaneously
• A reference beam is used to measure the instantaneous velocity, while a dual beam (fringe mode) is used to measure the transit time of the particles
• By correlating the velocity and transit time information, the turbulent velocity fluctuations and the Reynolds stresses can be determined with high accuracy

Laser Doppler phase anemometry (LDPA)

• LDPA is an extension of LDV that allows simultaneous measurement of particle size and velocity
• It uses two or more detectors at different scattering angles to measure the phase difference of the Doppler signals
• The phase difference is related to the particle size, while the Doppler frequency provides the velocity information
• LDPA is particularly useful for studying particle-laden flows, sprays, and multiphase systems with a wide range of particle sizes

Micro-scale LDV for near-wall measurements

• Micro-scale LDV systems use smaller measurement volumes (< 50 μm) and shorter focal length optics to measure velocities near walls or interfaces
• The reduced measurement volume size allows for higher spatial resolution and reduces the influence of velocity gradients within the volume
• Micro-scale LDV has been used to study wall-bounded multiphase flows, such as particle deposition, bubble-wall interactions, and liquid-liquid interfaces
• Advanced signal processing techniques, such as deconvolution or correlation-based methods, are often employed to improve the accuracy and resolution of micro-scale LDV measurements