Velocimetry

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Dye in a fluid can help illuminate the fluids motion paths. This is the most simple example of Velocimetry. Summer School Fluid Dynamics of Sustainability and the Environment (34874208054).jpg
Dye in a fluid can help illuminate the fluids motion paths. This is the most simple example of Velocimetry.

Velocimetry is the measurement of the velocity of fluids. This is a task often taken for granted, and involves far more complex processes than one might expect. It is often used to solve fluid dynamics problems, study fluid networks, in industrial and process control applications, as well as in the creation of new kinds of fluid flow sensors. Methods of velocimetry include particle image velocimetry and particle tracking velocimetry, Molecular tagging velocimetry, laser-based interferometry, ultrasonic Doppler methods, Doppler sensors, and new signal processing methodologies.

Contents

In general, velocity measurements are made in the Lagrangian or Eulerian frames of reference (see Lagrangian and Eulerian coordinates). Lagrangian methods assign a velocity to a volume of fluid at a given time, whereas Eulerian methods assign a velocity to a volume of the measurement domain at a given time. A classic example of the distinction is particle tracking velocimetry, where the idea is to find the velocity of individual flow tracer particles (Lagrangian) and particle image velocimetry, where the objective is to find the average velocity within a sub-region of the field of view (Eulerian). [1]

History

Velocimetry can be traced back to the days of Leonardo da Vinci, who would float grass seeds on a flow and sketch the resulting trajectories of the seeds that he observed (a Lagrangian measurement). [2] Eventually da Vinci's flow visualizations were used in his cardio vascular studies, attempting to learn more about blood flow throughout the human body. [3]

Smoke used as a visualizer similarly to the technique Marey popularized. Flow around sphere, being visualized by seeding flow with smoke.jpg
Smoke used as a visualizer similarly to the technique Marey popularized.

Methods similar to da Vinci's were carried out for close to four hundred years due to technological limitations. One other notable study comes from Felix Savart in 1833. Using a stroboscopic instrument, he sketched water jet impacts. [3]

In the late 19th century a huge breakthrough was made in these technologies when it became possible to take photographs of flow patterns. One notable instance of this is Ludwig Mach using particles unresolvable by the naked eye to visualize streamlines. [4] Another notable contribution occurred in the 20th century by Étienne-Jules Marey who used photographic techniques to introduce the concept of the smoke box. This model allowed both for the directions of the flow to be tracked but also the speed, as streamlines closer together indicated faster flow. [3]

More recently, high speed cameras and digital technology has revolutionized the field. allowing for the possibility of many more techniques and rendering of flow fields in three dimensions. [3]

Methods

Today the basic ideas established by Leonardo are the same; the flow must be seeded with particles that can be observed by the method of choice. The seeding particles depend on many factors including the fluid, the sensing method, the size of the measurement domain, and sometimes the expected accelerations in the flow. [5] If the flow contains particles that can be measured naturally, seeding the flow is unnecessary. [6]

Spatial reconstruction of fluid streamtubes using long exposure imaging of tracer can be applied for streamlines imaging velocimetry, high resolution frame rate free velocimetry of stationary flows. [7] Temporal integration of velocimetric information can be used to totalize fluid flow. For measuring velocity and length on moving surfaces, laser surface velocimeters are used. [8]

Vector field created by a PIV analysis of vortexes PIVlab multipass.jpg
Vector field created by a PIV analysis of vortexes

The fluid generally limits the particle selection according to its specific gravity; the particles should ideally be of the same density as the fluid. This is especially important in flows with a high acceleration (for example, high-speed flow through a 90-degree pipe elbow). [9] Heavier fluids like water and oil are thus very attractive to velocimetry, whereas air ads a challenge in most techniques that it is rarely possible to find particles of the same density as air.

Still, even large-field measurement techniques like PIV have been performed successfully in air. [10] Particles used for seeding can be both liquid droplets or solid particles. Solid particles being preferred when high particle concentrations are necessary. [9] For point measurements like laser Doppler velocimetry, particles in the nanometre diameter range, such as those in cigarette smoke, are sufficient to perform a measurement. [6]

In water and oil there are a variety of inexpensive industrial beads that can be used, such as silver-coated hollow glass spheres manufactured to be conductive powders (tens of micrometres diameter range) or other beads used as reflectors and texturing agents in paints and coatings. [11] The particles need not be spherical; in many cases titanium dioxide particles can be used. [12]

Relevant Applications

PIV has been used in research for controlling aircraft noise. This noise is created by the high speed mixing of hot jet exhaust with the ambient temperature of the environment. PIV has been used to model this behavior. [13]

Additionally, Doppler velocimetry enables noninvasive techniques of determining whether fetuses are the proper size at a given term of pregnancy. [14]

Basis for Four-Dimensional Pulmonary Imaging

Velocimetry has also been applied to medical images in order to obtain regional measurements of blood flow and tissue motion. Initially, standard PIV (single plane illumination) was adapted to work with x-ray images (full volume illumination), enabling the measurement of opaque flows such as blood flow. This was then extended to investigate the regional 2D motion of lung tissue, and was found to be a sensitive indicator of regional lung disease. [15]

Velocimetry was also expanded to 3D regional measurements blood flow and tissue motion with a new technique – computed tomographic x-ray velocimetry – which uses information contained within the PIV cross-correlation to extract 3D measurements from 2D image sequences. [16] Specifically, computed tomographic x-ray velocimetry generates a model solution, compares the cross-correlations of the model to the cross-correlation from the 2D image sequence, and iterates the model solution until the difference between the model cross-correlations and the image sequence cross-correlations are minimised. This technique is being used as a non invasive method to quantify functional performance of the lungs. It is being used in a clinical setting, [17] and is being utilised in clinical trails conducted by institutions including Duke University, [18] Vanderbilt University Medical Center [19] and Oregon Health Science University [20]

Related Research Articles

Flow measurement is the quantification of bulk fluid movement. Flow can be measured using devices called flowmeters in various ways. The common types of flowmeters with industrial applications are listed below:

<span class="mw-page-title-main">Time of flight</span> Timing of substance within a medium

This information can then be used to measure velocity or path length, or as a way to learn about the particle or medium's properties. The traveling object may be detected directly or indirectly. Time of flight technology has found valuable applications in the monitoring and characterization of material and biomaterials, hydrogels included.

Particle image velocimetry (PIV) is an optical method of flow visualization used in education and research. It is used to obtain instantaneous velocity measurements and related properties in fluids. The fluid is seeded with tracer particles which, for sufficiently small particles, are assumed to faithfully follow the flow dynamics. The fluid with entrained particles is illuminated so that particles are visible. The motion of the seeding particles is used to calculate speed and direction of the flow being studied.

<span class="mw-page-title-main">Laser Doppler velocimetry</span> Optical method of measuring fluid flow

Laser Doppler velocimetry, also known as laser Doppler anemometry, is the technique of using the Doppler shift in a laser beam to measure the velocity in transparent or semi-transparent fluid flows or the linear or vibratory motion of opaque, reflecting surfaces. The measurement with laser Doppler anemometry is absolute and linear with velocity and requires no pre-calibration.

<span class="mw-page-title-main">Stokes number</span> Dimensionless number characterising the behavior of particles suspended in a fluid flow

The Stokes number (Stk), named after George Gabriel Stokes, is a dimensionless number characterising the behavior of particles suspended in a fluid flow. The Stokes number is defined as the ratio of the characteristic time of a particle to a characteristic time of the flow or of an obstacle, or

<span class="mw-page-title-main">Molecular tagging velocimetry</span>

Molecular tagging velocimetry (MTV) is a specific form of flow velocimetry, a technique for determining the velocity of currents in fluids such as air and water. In its simplest form, a single "write" laser beam is shot once through the sample space. Along its path an optically induced chemical process is initiated, resulting in the creation of a new chemical species or in changing the internal energy state of an existing one, so that the molecules struck by the laser beam can be distinguished from the rest of the fluid. Such molecules are said to be "tagged".

<span class="mw-page-title-main">Particle tracking velocimetry</span>

Particle tracking velocimetry (PTV) is a velocimetry method i.e. a technique to measure velocities and trajectories of moving objects. In fluid mechanics research these objects are neutrally buoyant particles that are suspended in fluid flow. As the name suggests, individual particles are tracked, so this technique is a Lagrangian approach, in contrast to particle image velocimetry (PIV), which is an Eulerian method that measures the velocity of the fluid as it passes the observation point, that is fixed in space. There are two experimental PTV methods:

<span class="mw-page-title-main">Flow visualization</span> Visualization technique in fluid dynamics

Flow visualization or flow visualisation in fluid dynamics is used to make the flow patterns visible, in order to get qualitative or quantitative information on them.

Planar Doppler Velocimetry (PDV), also referred to as Doppler Global Velocimetry (DGV), determines flow velocity across a plane by measuring the Doppler shift in frequency of light scattered by particles contained in the flow. The Doppler shift, Δfd, is related to the fluid velocity. The relatively small frequency shift is discriminated using an atomic or molecular vapor filter. This approach is conceptually similar to what is now known as Filtered Rayleigh Scattering.

<span class="mw-page-title-main">Seeding (fluid dynamics)</span>

Seeding a material is a concept used in fluid dynamics to describe the act of introducing specific particulates or other foreign substances into a stream of fluid being evaluated. An altered fluid will be described as having a seeded flow.

An engine test stand is a facility used to develop, characterize and test engines. The facility, often offered as a product to automotive OEMs, allows engine operation in different operating regimes and offers measurement of several physical variables associated with the engine operation.

<span class="mw-page-title-main">Planar laser-induced fluorescence</span>

Planar laser-induced fluorescence (PLIF) is an optical diagnostic technique widely used for flow visualization and quantitative measurements. PLIF has been shown to be used for velocity, concentration, temperature and pressure measurements.

Turbulent diffusion is the transport of mass, heat, or momentum within a system due to random and chaotic time dependent motions. It occurs when turbulent fluid systems reach critical conditions in response to shear flow, which results from a combination of steep concentration gradients, density gradients, and high velocities. It occurs much more rapidly than molecular diffusion and is therefore extremely important for problems concerning mixing and transport in systems dealing with combustion, contaminants, dissolved oxygen, and solutions in industry. In these fields, turbulent diffusion acts as an excellent process for quickly reducing the concentrations of a species in a fluid or environment, in cases where this is needed for rapid mixing during processing, or rapid pollutant or contaminant reduction for safety.

Acoustic Doppler velocimetry (ADV) is designed to record instantaneous velocity components at a single-point with a relatively high frequency. Measurements are performed by measuring the velocity of particles in a remote sampling volume based upon the Doppler shift effect.

Matched Index of Refraction is a facility located at the Idaho National Laboratory built in the 1990s. The purpose of the fluid dynamics experiments in the MIR flow system at Idaho National Laboratory (INL) is to develop benchmark databases for the assessment of Computational Fluid Dynamics (CFD) solutions of the momentum equations, scalar mixing, and turbulence models for the flow ratios between coolant channels and bypass gaps in the interstitial regions of typical prismatic standard fuel element or upper reflector block geometries of typical Very High Temperature Reactors (VHTR) in the limiting case of negligible buoyancy and constant fluid properties.

In scientific visualization, Lagrangian–Eulerian advection is a technique mainly used for the visualization of unsteady flows. The computer graphics generated by the technique can help scientists visualize changes in velocity fields. This technique uses a hybrid Lagrangian and Eulerian specification of the flow field. It is a special case of a line integral convolution.

<span class="mw-page-title-main">Laser Doppler imaging</span>

Laser Doppler imaging (LDI) is an imaging method that uses a laser beam to scan live tissue. When the laser light reaches the tissue, the moving blood cells generate doppler components in the reflected (backscattered) light. The light that comes back is detected using a photodiode that converts it into an electrical signal. Then the signal is processed to calculate a signal that is proportional to the tissue perfusion in the scanned area. When the process is completed, the signal is processed to generate an image that shows the perfusion on a screen.

In experimental fluid mechanics, Lagrangian Particle Tracking refers to the process of determining trajectories of small neutrally buoyant particles that are freely suspended within a turbulent flow field. These are usually obtained by 3-D Particle Tracking Velocimetry. A collection of such particle trajectories can be used for analyzing the Lagrangian dynamics of the fluid motion, for performing Lagrangian statistics of various flow quantities etc.

<span class="mw-page-title-main">Magnetic resonance velocimetry</span>

Magnetic resonance velocimetry (MRV) is an experimental method to obtain velocity fields in fluid mechanics. MRV is based on the phenomenon of nuclear magnetic resonance and adapts a medical magnetic resonance imaging system for the analysis of technical flows. The velocities are usually obtained by phase contrast magnetic resonance imaging techniques. This means velocities are calculated from phase differences in the image data that has been produced using special gradient techniques. MRV can be applied using common medical MRI scanners. The term magnetic resonance velocimetry became current due to the increasing use of MR technology for the measurement of technical flows in engineering.

<span class="mw-page-title-main">Joseph Katz (professor)</span> American fluid dynamicist

Joseph Katz is an Israel-born American fluid dynamicist, known for his work on experimental fluid mechanics, cavitation phenomena and multiphase flow, turbulence, turbomachinery flows and oceanography flows, flow-induced vibrations and noise, and development of optical flow diagnostics techniques, including Particle Image Velocimetry (PIV) and Holographic Particle Image Velocimetry (HPIV). As of 2005, he is the William F. Ward Sr. Distinguished Professor at the Department of Mechanical Engineering of the Whiting School of Engineering at the Johns Hopkins University.

References

  1. ↑ Batchelor, G. K. (George Keith) (2002). An introduction to fluid dynamics. Cambridge University Press. ISBN   0-521-66396-2. OCLC   800027809.
  2. ↑ Gharib, M.; Kremers, D.; Koochesfahani, M.; Kemp, M. (2002). "Leonardo's vision of flow visualization". Experiments in Fluids. 33 (1): 219–223. Bibcode:2002ExFl...33..219G. doi:10.1007/s00348-002-0478-8. ISSN   0723-4864. S2CID   9577969.
  3. 1 2 3 4 Fermigier, Marc (September 2017). "The use of images in fluid mechanics". Comptes Rendus Mécanique. 345 (9): 595–604. Bibcode:2017CRMec.345..595F. doi: 10.1016/j.crme.2017.05.015 . ISSN   1631-0721.
  4. ↑ Raffel, Markus; Willert, Christian E.; Wereley, Steve T.; Kompenhans, Jürgen (2007). Particle Image Velocimetry. doi:10.1007/978-3-540-72308-0. ISBN   978-3-540-72307-3.
  5. ↑ Reeder, Mark F.; Crafton, Jim W.; Estevadeordal, Jordi; DeLapp, Joseph; McNiel, Charles; Peltier, Don; Reynolds, Tina (2009-11-18). "Clean seeding for flow visualization and velocimetry measurements". Experiments in Fluids. 48 (5): 889–900. doi:10.1007/s00348-009-0784-5. ISSN   0723-4864. S2CID   120422467.
  6. 1 2 Miles and, Richard B.; Lempert, Walter R. (1997). "Quantitative Flow Visualization in Unseeded Flows". Annual Review of Fluid Mechanics. 29 (1): 285–326. Bibcode:1997AnRFM..29..285M. doi:10.1146/annurev.fluid.29.1.285. ISSN   0066-4189.
  7. ↑ Keinan, Eliezer; Ezra, Elishai; Nahmias, Yaakov (2013-08-05). "Frame rate free image velocimetry for microfluidic devices". Applied Physics Letters. 103 (6): 063507. Bibcode:2013ApPhL.103f3507K. doi:10.1063/1.4818142. ISSN   0003-6951. PMC   3751964 . PMID   24023394.
  8. ↑ Truax, Bruce E.; Demarest, Frank C.; Sommargren, Gary E. (1983). "Laser Doppler velocimeter for velocity and length measurements of moving surfaces". Conference on Lasers and Electro-Optics. Washington, D.C.: OSA: WN6. doi:10.1364/cleo.1983.wn6.
  9. 1 2 Melling, A (1997-12-01). "Tracer particles and seeding for particle image velocimetry". Measurement Science and Technology. 8 (12): 1406–1416. Bibcode:1997MeScT...8.1406M. doi:10.1088/0957-0233/8/12/005. ISSN   0957-0233. S2CID   250844330.
  10. ↑ Adrian, Ronald J. (1991). "Particle-Imaging Techniques for Experimental Fluid Mechanics". Annual Review of Fluid Mechanics. 23 (1): 261–304. Bibcode:1991AnRFM..23..261A. doi:10.1146/annurev.fl.23.010191.001401. ISSN   0066-4189.
  11. ↑ Techet, Alexandra H.; Belden, Jesse L. (2007). "Imaging across the interface of small-scale breaking waves". APS. 60: GK.001. Bibcode:2007APS..DFD.GK001T.
  12. ↑ JONES, GREGORY; GARTRELL, LUTHER; KAMEMOTO, DEREK (1990-01-08). "An investigation of the effects of seeding in laser velocimeter systems". 28th Aerospace Sciences Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics. Bibcode:1990aiaa.meetV....J. doi:10.2514/6.1990-502.
  13. ↑ "Shedding light on the mysteries of high-speed hot jets". Nasa. 2019. Archived from the original on 2006-10-05.
  14. ↑ Kaponis, Apostolos; Harada, Takashi; Makrydimas, George; Kiyama, Tomoiki; Arata, Kazuya; Adonakis, George; Tsapanos, Vasilis; Iwabe, Tomio; Stefos, Theodoros; Decavalas, George; Harada, Tasuku (2011). "The Importance of Venous Doppler Velocimetry for Evaluation of Intrauterine Growth Restriction". Journal of Ultrasound in Medicine. 30 (4): 529–545. doi: 10.7863/jum.2011.30.4.529 . ISSN   1550-9613. PMID   21460154.
  15. ↑ Fouras, Andreas; Allison, Beth J.; Kitchen, Marcus J.; Dubsky, Stephen; Nguyen, Jayne; Hourigan, Kerry; Siu, Karen K. W.; Lewis, Rob A.; Wallace, Megan J.; Hooper, Stuart B. (2012-05-01). "Altered Lung Motion is a Sensitive Indicator of Regional Lung Disease". Annals of Biomedical Engineering. 40 (5): 1160–1169. doi:10.1007/s10439-011-0493-0. ISSN   1573-9686. PMID   22189492. S2CID   254193228.
  16. ↑ Dubsky, S.; Jamison, R. A.; Irvine, S. C.; Siu, K. K. W.; Hourigan, K.; Fouras, A. (2010-01-11). "Computed tomographic x-ray velocimetry". Applied Physics Letters. 96 (2): 023702. Bibcode:2010ApPhL..96b3702D. doi:10.1063/1.3285173. ISSN   0003-6951.
  17. ↑ "XV Technology | A new modality for detecting lung disease". 4DMedical. Retrieved 2022-09-15.
  18. ↑ Duke University (2022-07-27). "4DX Functional Lung Imaging in the Diagnosis of Chronic Lung Allograft Dysfunction After Lung Transplantation". 4D Medical.{{cite journal}}: Cite journal requires |journal= (help)
  19. ↑ Richmond, Bradley (2022-08-29). "Utility of a Novel Imaging Algorithm (4DX) for the Diagnosis of Constrictive Bronchiolitis". Vanderbilt University Medical Center, 4D Medical.{{cite journal}}: Cite journal requires |journal= (help)
  20. ↑ Khan, Akram (2021-06-30). "Ventilation Imbalances in Mild to Moderate Chronic Obstructive Pulmonary Disease". Oregon Health and Science University, 4DMedical.{{cite journal}}: Cite journal requires |journal= (help)
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