Velocity Of Individual Particles Research Articles

Overall kinetic parameters for combustion of a highly non-spherical carbon char

Overall kinetic parameters describing the combustion of an irregularly-shaped carbon char are obtained based on optical measurements of the temperature, size, and velocity of individual particles observed in an entrained-flow reactor. In addition, for one set of conditions, the mass loss profile is measured by quantitatively collecting samples of partially burned char at four different heights in the reactor. The combustion conditions investigated in this study range from 12 to 36 mole-% O2 with bulk gas temperatures from 1400 to 1800 K, resulting in particle temperatures from 1400 to 2100 K and overall burning rates from 8.9×10−3 to 1.3×10−1 gC/s·cm2 (based on the external surface of the particle). The kinetic mass loss profile. Good agreement between the measured and calculated profiles is achieved when CO2 formation near the particles is accounted for in the single-particle energy balance. Despite the uncertainty in the particle temperatures caused by the irregular shape of the particles, the kinetic paramters are relatively insensitive, to the simplifying assumption of a spherical particle. The measurements support an apparent reaction order of 0.7±0.2 and an apparent activation energy of 23±2 kcal/mol.

Experimental studies of particle‐laden plumes

Experiments are described in which buoyant plumes of fresh water and solid particles are generated in a tank of salt water. Dependence of the behavior of the plumes on particle concentration and grain size was studied. At low concentrations, behavior was similar to single‐component plumes, and the principal effect of the particles was to reduce the buoyancy flux. Measurements of particle concentration across the plumes demonstrated that there were substantial amounts of particle reentrainment from an outer sedimenting veil. Reentrainment caused the plume margins to become denser than the ambient fluid. Total particle flux in the plumes increased with height and can be several times greater than the flux at the plume source. Plumes with high particle concentration exhibit several kinds of convective instability, which generated gravity currents and rapid sedimentation. Gravity currents were generated at the margins of concentrated plumes. These flows are attributed to reentrainment, causing the flow margins to have excess density. When the plume density was close to but less than the density of the ambient fluid, a fountain forms high in the plumes which collapsed asymmetrically to generate a gravity current on one side of the plume. When the density of the particle‐laden flow was greater than the ambient fluid, a symmetrical fountain formed, and gravity currents moved across the tank floor, depositing sediment. At a well‐defined distance from the source, buoyant fluid ascended from the flow fronts to form a ring of plumes around the central fountain. These plumes coalesced to form a broad buoyant cloud. The plumes are generated by the sedimentation from the gravity currents, which resulted in the fresh water and some entrained particles being released. All the experimental plumes ascended to the top of the tank and spread out as gravity currents beneath the upper surface. Particles often fall from this layer in discrete parcels of particle‐rich fluid with shapes similar to thermals. The fall velocities were much greater than the terminal velocities of individual particles and the sedimenting region is inhomogeneous. These observations indicate that sedimentation is enhanced by convective instabilities when particle‐rich fluid is emplaced above particle‐free fluid. The experiments indicate that there may be several different mechanisms of generating pyroclastic flows and surges from the collapse of volcanic eruptions columns. The experiments also demonstrate that the sedimentation of particles from a plume has an important influence on dynamical behavior.

Novel approach for particle velocity and size measurement under plasma conditions

A novel technique is proposed for the simultaneous, in-flight, measurement of the velocity and size of individual particles under plasma conditions. The method is based on the observation of each particle through its own emission and the analysis, in the time domain, of the waveform of the light burst generated as it crosses an observation window of known dimensions. A theoretical analysis of the parameters affecting the visibility of the particles in an argon plasma showed that depending on the particle diameter and its surface temperature, its thermal visibility factor will drop sharply from 1.0 to almost zero, with the increase of the background plasma temperature. Measurements are carried out using nickel particles (d̄p=78 μm, σ=18.0 μm) injected axially into an inductively coupled rf plasma ( f=3 MHz, P=15 kW) operated using argon as the plasma gas at atmospheric pressure and under soft vacuum conditions (p=760 and 150 Torr). The results are in good agreement with particle velocity data obtained using laser Doppler anemometry. The measured, in-flight, particle size distribution is consistent with optical microscopic measurement of the particle size distribution of the injected powder.

Experimentally determined overall burning rates of pulverized-coal chars in specified O 2 and CO 2 environments

Measurements of the size, temperature and velocity of individual pulverized-coal char particles are used to determine the overall burning rates of particles flowing in gaseous environments of specified O2 and CO2 contents. The overall burning rates of the char particles are essentially unaffected by the carbon dioxide content of the ambient gas. When the single film model of a burning carbon particle with CO as the sole heterogeneous reaction product is employed, the chemical reaction rate coefficients determined in gaseous environments of fixed CO2 levels but varying O2 levels exhibit the same temperature dependence. For the Missouri bituminous coal studied, a reaction rate coefficient of 28.4 exp (−2000/RT) g/cm2-s is determined for the C−O2 heterogeneous reaction. The apparent activation energy is in the range expected for burning limited by the combined effects of pore diffusion and the intrinsic chemical reactivity of the particle material. Based on the overall particle burning rates determined, the Thiele modulus estimated for each particle size is in the range which suggests little penetration of oxygen into the particle pores. The results support the single film model of a burning particle with CO as the sole reaction product for coal chars burning under typical pulverized-coal combustion conditions. The results indicate that the double film model of a burning carbon particle is not applicable for particles less than about 130 μm burning under such conditions. A reaction rate constant for the C−CO2 heterogeneous reaction a thousand times greater than the rate constants reported in the literature is required in order to get agreement between measured and calculated temperatures for a given particle size when the double film model is employed.

A three-parameter markov model for sedimentation II. Simulation of transit times and comparison with experimental results

An adequate description of the global behavior of sedimenting suspensions requires a knowledge of not only the mean velocity, but also the variation and autocorrelation of the velocities of individual particles. Much of the published information on these two parameters is encoded in transit times. For example, Koglin measured the length of time for individual spheres to traverse a fixed distance x and found that sedimentation velocities based on these transit times satisfied a log-normal distribution. Computer simulations, which yield the distribution of transit times as a function of the three parameters of the parent distribution, are an effective method of decoding these data. Our three-parameter Markov model yields first-passage times which are approximately log-normal, and the convergence to log-normality as x increases is remarkably fast. Thus, Koglin's data provide strong support for the Markov model, experimentally verifying theoretical predictions based (via simulations) on it.

The Use of Calibration Techniques for the Development and Application of Optical Particle Sizing Instruments

AbstractThis paper describes seven different methods of calibrating optical particle sizing instruments based on single particle scattering theory. The results presented were obtained from a Laser Doppler Anemometer (LDA) using two concentric probe volumes of different diameters and colours. Measurements of the Doppler signal frequency, amplitude and visibility can yield the absolute particle size and velocity of individual particles providing that the optics and processor are correctly designed and implemented.The requirements for signal processing without validation bias are discussed together with the use of a Doppler signal generator for testing the processor. Calibration of the system is then described using a scanning pinhole unit, calibration plate and aerosols of bronze spheres. The other techniques described are the use of glass spheres mounted on thin stalks, Berglund‐Lui monodisperse particle generator and latex spheres entrained in a recirculating cell. The discussion indicates the sizing range over which the above techniques are applicable. This covers a total size range from 1 micron to 1 millimetre.

Optically determined temperatures, sizes, and velocities of individual carbon particles under typical combustion conditions

This study utilizes an in situ optical method to determine the temperature, size, and velocity of individual particles of burning pulverized fuels. Temperature-size and velocity-size correlations were determined for both nonreacting and ignited suspensions of a spherical, nonvolatile, molecular sieve carbon flowing in one dimension. The measurements at three axial positions when no oxygen was present illustrate the strong sensitivity to particle size in the transient temperatures. A comparison with predictions from a heat transfer model with no adjustable parameters assesses the experimental errors. Sizes were determined to within 10 μm (120 < d p, μm < 240), temperatures to within 50K (1150 < T p, K < 1950), and velocities to within 5% (150 < ν p, cm/s < 300). Four temperature-size correlations for suspensions burning in 24% excess oxygen show that heterogeneous reaction steepens the correlations beyond their levels for conduction heating alone. For a 75 μm size range, the observed ranges of temperature during heatup and ignition span several hundred degrees, which raises serious doubts about the utility of using average temperatures and sizes to assign kinetic parameters throughout the first 100–150 ms of this process.

Review—Combined Measurements of Particle Velocities, Size Distributions, and Concentrations

The present paper describes combined laser Doppler particle sizing systems which permit simultaneous velocity and size measurements of individual particles. Combined measurements of these properties are achieved by extended laser Doppler anemometers. These extensions require the physics of laser Doppler signal generation to be clarified. A system for measurements of small particles and one to measure the properties of large particles is described. Some applications of these instruments are given.

Measurements of charged precipitation in a New Mexico thunderstorm: lower positive charge centers

We designed an instrument to measure the charge and vertical velocity of individual precipitation particles inside thunderclouds. A balloon carried the particle charge instrument, an electric field meter, and a standard meteorological radiosonde upward into thunderclouds over Langmuir Laboratory in central New Mexico. During one balloon flight the instruments encountered two regions of positive charge below the main negative charge center. We identify these positive regions with the lower positive charge centers that have been described in the literature for many years. We find the following points: (1) One region had an estimated total charge of 0.4 C. The other had 2 C. (2) The charge resided on precipitation particles. The particles' charges typically ranged between 10 and 200 pC, but a few particles had charges up to 400 pC. Their diameters lay between an estimated 1–3 mm. The charges were too large to be explained by the polarization induction mechanism. We favor the hypothesis that lightning provided the positive charge in the lower positive charge centers. (3) The motion of the lower positive charge centers enhanced the electrical energy of the storm, but their contribution to the overall electrical budget was small. (4) The field excursions (at the ground) associated with precipitation (FEAWPs) described by C. B. Moore and B. Vonnegut are probably caused by lower positive charge centers descending on precipitation. The larger (2 C) lower positive charge center caused a FEAWP. Negatively charged precipitation particles passed through our instrument near the top of its trajectory just before the balloon was struck by lightning. The charge density on precipitation particles was substantial, but we do not have enough information to comment on the role the particles may have had in generating the main region of negative charge.

A laser Doppler anemometer using photon correlation to measure the velocity of individual particles

A laser Doppler anemometer is described in which a photon correlator is used to measure the velocity of individual scattering particles. The mean velocity and the turbulence intensity found in this way are compared with the values obtained by fitting curves to the autocorrelation function averaged over many particles. The two methods agree to within 1% provided the turbulence intensity is not greater than 10%. At higher levels of turbulence agreement is less good due to various sources of systematic bias in the way the velocity is sampled when individual particle velocities are measured. The method is most likely to be useful when the density of scattering particles, and the intensity of the scattered light are low.

Spectral analysis of signals from a laser Doppler anemometer operating in the burst mode

Recently developed methods of spectral analysis for randomly sampled signals are applied to data acquired by a laser Doppler anemometer (LDA) operating in the burst mode, where the velocity of individual particles is computed. The measurements, which were obtained in a seeded air jet, support the adoption of a Poisson model for the distribution of the particle arrival times. Spectral estimates formed from the LDA data are found to agree well with corresponding estimates obtained from a hot wire probe, and have a variability which conforms with theoretical predictions. The advantages and limitations of a simple method of reducing the variability of the spectral estimates is discussed.

Settling velocities of particulate systems, 1. Settling velocities of individual spherical particles

Combining boundary-layer theory and experimental data for the pressure distribution and boundary-layer thickness over the surface of a sphere, the following expression was obtained for the drag coefficient: C D= 1+ 9.06 R e 1 2 2 Using this formula as a basis, an expression was developed for relating the settling velocity of spherical particles to their diameter at any value of the Reynolds Number. The validity of such expressions discussed and compared with experimental data.

Measurement of Falling Velocity of Snow Using a Laser Doppler Velocimeter

Using a newly deviced laser Doppler velocimeter, measurements of falling velocity of large flakes of snow, powdery snow flakes, sleet and rain in Nagaoka city were made. Measured falling velocities are almost similar to the values reported by other investigators. This method is superior in real time recording to the conventional method using stroboscopic photography. Comparing with the ultrasonic Doppler method, this method is capable of measuring the falling velocity of individual particle because the sampling volume is smaller than the particle size.

Axonal transport of organelles visualized by light microscopy: Cinemicrographic and computer analysis

Rapid movements of intra-axonal organelles in acutely isolated single myelinated fibers from bullfrog sciatic nerve were visualized by dark-field microscopy. The movements were recorded by cinemicrography, and analyzed by computer-based methods. The movements are saltatory and bidirectional, but each particle moves mainly in a single direction. For more than 90% of the particles, the predominant movement direction is retrograde, i.e. toward the cell body. Quantitative measurements on a variety of parameters of the organelle movements are presented. Different particles in the same axon show a broad range of mean speeds. The average mean speed of movement in the retrograde direction at 28 degrees C was 1.08 micrometer/sec (S.D. - 0.41), equivalent to an axonal transport rate of 93 mm/day. Disperse distributions were also found for other parameters such as the instantaneous velocities of individual particles. Quantal velocities, periodic movement patterns, and specific 'channels' were not detected. When the data from a population of particles is treated statistically, the average mean speed, the distribution of velocities, and other statistical parameters are found to be similar in different axons studied at the same temperature. Direct microscopical observation of axonal organelle movement is a technique which provides information about axonal transport which is different from and complementary to that obtained from enzyme accumulation of radioactive tracer methods.

Fast-moving suspended particles: measurements of their size and velocity

A simple optical instrument is developed to measure remotely the size as well as the velocity of individual particles suspended in a fast-moving stream. The instrument consists of dual laser beams, each directed toward one phototransistor. The size and velocity are determined from the signals produced by particles passing through the laser beams. The measuring range of the particle size of the present unit is between 30 microm and 800 microm; both the upper and the lower ranges, however, are adjustable.

Instrumentation techniques for studying heterogeneous combustion

Diagnosis of heterogeneous combustion systems requires the measurement of physical and chemical properties in flames laden with liquid and solid particles. For liquid-fuelled combustors, the characteristics of the spray require to be determined, including the trajectories of individual droplets and their interaction with gas streams. Vaporization rates can be determined from measurement of the rate of change of diameter of individual droplets. Particulate matter emitted from combustion chambers is mainly in the solid phase and consists of both unburned fuel and non-burnable material. With heavy fuel oils, particles of the order of 100 μm can be emitted while, for the lighter fuels, particulate emissions are mainly in the sub-micron size region. The laser anemometer can be used for simultaneous measurement of velocity and particle size of individual droplets and particles in spray flames. Laser diffraction techniques can be used for measurement of over-all size distributions. Laser Raman spectroscopy offers the possibility of simultaneous measurement of temperature and species concentration in flames. Presence of particles results in laser irradiated particulate heating and incandescence, which can lead to the swamping of signals. The use of coherent anti-Stokes Raman and near-resonant Raman offers possibilities for making laser Raman measurements in particle laden flames. Solid probes for measuring temperature and species concentration require special adaptation when used in particle laden flows. Particles may damage probes by direct impingement and cause blockage of orifices. Thermocouples can be used in sprays, but the effects of direct droplet impingement must be considered. Diagnostic techniques have been developed in which thermocouple signals are digitized and recorded on a computer. This system permits the rapid measurement of time constants and, subsequently, digital frequency compensation of temperature time histories, providing a frequency response of the order of 1 kHz. Information on spray boundaries is provided by both laser anemometer and thermocouple measurements. Gas sampling probes, specially designed to separate liquid and solid particles from the gas, are used for removal of samples from within the flame. Size analysis of particles is made by microphotography and computer image analyser. Species concentration in the gas is measured by gas phase chromatography, flame ionization detectors, non-dispersive infrared and ultraviolet detectors and chemiluminescent analysers. All measurement diagnostic techniques are affected by the presence of large-scale coherent eddy structures in the turbulent flow systems. The need for increasing frequency response, recording and analysis of variations with time, and the use of conditional sampling in intermittent flows is emphasized. The coupling of high-speed movies with laser optical proves to give simultaneous recording of visual and signal events is recommended.

Mean velocity of optically detected intraaxonal particles measured by a cross-correlation method.

A method which uses by the cross correlation of optical signals is described for the determination of the mean velocity of somatopetally moving particles within nerve fibers. The method was validated by simulation experiments and by comparing the results with those obtained by averaging collections of velocities of individual particles. The significant contribution of the method is that it allows objective and rapid serial evaluation of mean particle velocity within individual nerve fibers with good accuracy and precision. A series of results from normal myelinated nerve fibers from Xenopus laevis is presented. Considerable variation (up to 50%) in mean velocity was found between individual nerve fibers. The mean of all determinations indicates that the mean velocity of somatopetally moving particles in axons with diameters greater than 10mum is in the region of 1.14 mum/s at a temperature of 22-24 degrees C. The findings are compared with small collection of such determinations which have been reported in the literature.

Measurements of individual alumina particle velocities and the relative slip of different-sized particles in a vertical gas - solid suspension flow using a laser - anemometer system

Particle velocities in a vertically upward gas-solid suspension flow have been measured using a laser-Doppler anemometer system. The electronic signal-processing equipment enables individual particle slip velocities to be measured, which in turn allows mixtures of different-sized particles to be successfully studied. Alumina particles in the size range 15-200 μm were used. In laminar pipe flow of fine particles (15 μm) the particle velocity profile is parabolic, but with increasing pipe Reynolds' number the profile becomes flatter. Near the pipe wall smaller particles were unexpectedly found to have greater slip than larger particles. Reasonable agreement was found between the measured centre-line slip velocities and those computed by extensive theoretical considerations. For alumina particles in excess of 30 μm diameter, Stokes' law is no longer applicable, and great care must be taken in order to obtain an accurate estimation of the slip.

Approximate statistical theory of a fluidized bed

Under the conditions of developed fluidization there are intensive fluctuations both in the fluidizing medium and in the dispersed solid phase. These motions have a decisive effect on the rheologlcal properties of the fluidized bed, and on the chemical reactions and transport processes taking place in it [1], Thus, for example, in the experiments of Wicke and Fetting [2], who investigated the heat transfer between a fluidized bed and the walls of a heated container, the effective heat transfer coefficient was found to be higher by an order of magnitude than the corresponding result for a fluidized bed held down by a wire grid so that the random motion of the solid phase was reduced. It is clear that the initial stage of any study of the structure of the fluidized bed as a whole, and of the subsequent development of any model, must involve an investigation of local structural properties, including the above fluctuations. The time variation of the individual particle velocities is due to two different causes. First, there is the interaction between the particles both through direct collisions and through the medium of the liquid phase, and, secondly, there is the interaction with the viscous fluid. These two factors are not independent, so that the set of fluidized particles has certain features characteristic for both a dense gas, with a potential intramolecular interaction, and a set of particles executing Brownian motion in a continuous medium. Any detailed statistical theory of a system of fluidized particles must be based on a representation of the random particle motions in the medium by a stochastic process with some definite properties (see, for example, [3–4]). Ideally, this theory should lead to the formulation of a transport equation which, in view of the above properties of the system, should have some of the features of both the usual Boltzman transport equation and the Fokker-Planck equation. The solution of this final equation is, of course, more difficult than the solution of the Boltzman or Fokker-Planck equations. Moreover, there is also the problem of applying this equation to different special cases. An alternative approach is to develop an approximate, but still sufficiently effective, theory of the local properties of the fluidized bed, which would combine relative simplicity in application with sufficient rigor and generality. This kind of theory is put forward in the present paper. The conclusions to which it leads are in good qualitative agreement with experiment.

Flow Equations for Composite Gases

J M Burgers New York: Academic Press 1969 pp xiv + 332 price £8 13s Differential equations describing the behaviour of very general mixtures are derived by Prof Burgers from the starting point of the Maxwell–Boltzmann equation which governs the individual particle velocity distribution functions. The moment method is employed throughout, so that it is necessary at some stage to truncate the scheme by representing higher moments as suitably chosen functions of lower moments, and there is not much discussion of the limitations of this approach.