A critical review of the fundamental equations of a mixture of a gas and small solid particles
Gas-solid particles flow pseudofluid equations, discussing difference of species and partial density and various flow phases
Pai, S. I.↗
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Fundamental equations of a mixture of gas and small spherical solid particles from simple kinetic theory.
The fundamental equations of a mixture of a gas and pseudofluid of small spherical solid particles are derived from the Boltzmann equation of two-fluid theory. The distribution function of the gas molecules is defined in the same manner as in the ordinary kinetic theory of gases, but the distribution function for the solid particles is different from that of the gas molecules, because it is necessary to take into account the different size and physical properties of solid particles. In the proposed simple kinetic theory, two additional parameters are introduced: one is the radius of the spheres and the other is the instantaneous temperature of the solid particles in the distribution of the solid particles. The Boltzmann equation for each species of the mixture is formally written, and the transfer equations of these Boltzmann equations are derived and compared to the well-known fundamental equations of the mixture of a gas and small solid particles from continuum theory. The equations obtained reveal some insight into various terms in the fundamental equations. For instance, the partial pressure of the pseudofluid of solid particles is not negligible if the volume fraction of solid particles is not negligible as in the case of lunar ash flow.
Pai, S. I.↗
A review of fundamental equations of the mixture of a gas with small solid particles
Fluid dynamics of gas-particle flow and solid particle behavior in mixed flow
Pai, S. I.↗
Effects of solid particles suspended in fluid flow through an axial flow compressor stage
An approximate method for calculating the flow properties of gas-particle mixture flowing over blades in a cascade is studied. Using an analytical method, the solid particle trajectory and location of collisions between the solid particles and the blade surfaces are determined. In addition an experimental investigation of the trajectories and velocities of solid particles suspended in a fluid passing through an axial flow compressor cascade was performed. The cascade blades were made of 2024 aluminum alloy and the solid particles used were quartz sand with average diameter of 165 microns. The following parameters were investigated: blade pressure distribution, and total pressure loss coefficient, both depending on the degree of erosion. In addition, a theoretical estimation of the blade erosion is compared with the experimental data.
Tabakoff, W.↗
A tenfold increase in the abundance of large solid particles in the stratosphere, as measured over the period 1976-1984
Representative chemical, structural, and morphological analyses of the large (greater than 1 micron diameter) solid particles from three impaction collection surfaces have been performed. These collections sampled the stratosphere at approximately 17-19 km in altitude during 1976, 1981, and 1984. For these sampling periods, the stratospheric solid-particle number densities have been determined to be 0.089, 0.16, and 1.7 particles/cu m of air, respectively, for particles of greater than 1 micron diameter. This rise in solid-particle number density for the stratosphere over the collection period is likely due to the influx of solid rocket exhaust and rocket and satellite debris into the atmosphere in increasingly larger amounts with time. Some of this material is shed from spacecraft during ascent through the atmosphere, but the majority is probably provided during the descent of material from earth's growing belt of debris in low-earth orbit.
Zolensky, Michael E.↗
Launch Vehicle Performance with Solid Particle Feed Systems for Atomic Propellants
An analysis of launch vehicle Gross Liftoff Weight (GLOW) using high energy density atomic propellants with solid particle feed systems was conducted. The analyses covered several propellant combinations, including atoms of aluminum (Al), boron (B). carbon (C), and hydrogen (H) stored in a solid cryogenic particle, with a cryogenic liquid as the carrier fluid. Several different weight percents (wt%) for the liquid carrier were investigated and the gross lift off weight (GLOW) of the vehicles using the solid particle feed systems were compared with a conventional 02/H2 propellant vehicle. The potential benefits and effects of feed systems using solid particles in a liquid cryogenic fluid are discussed.
Palaszewski, Bryan↗
A Stochastic Model Study of the Movement of Solid Particles
Stochastic transport model for suspended solid particle flow in corner of rectangular channel
PARTICLE MOTION↗
Measurements of Turbulence Attenuation by a Dilute Dispersion of Solid Particles in Homogeneous Isotropic Turbulence
This research addresses turbulent gas flows laden with fine solid particles at sufficiently large mass loading that strong two-way coupling occurs. By two-way coupling we mean that the particle motion is governed largely by the flow, while the particles affect the gas-phase mean flow and the turbulence properties. Our main interest is in understanding how the particles affect the turbulence. Computational techniques have been developed which can accurately predict flows carrying particles that are much smaller than the smallest scales of turbulence. Also, advanced computational techniques and burgeoning computer resources make it feasible to fully resolve very large particles moving through turbulent flows. However, flows with particle diameters of the same order as the Kolmogorov scale of the turbulence are notoriously difficult to predict. Some simple flows show strong turbulence attenuation with reductions in the turbulent kinetic energy by up to a factor of five. On the other hand, some seemingly similar flows show almost no modification. No model has been proposed that allows prediction of when the strong attenuation will occur. Unfortunately, many technological and natural two-phase flows fall into this regime, so there is a strong need for new physical understanding and modeling capability. Our objective is to study the simplest possible turbulent particle-laden flow, namely homogeneous, isotropic turbulence with a uniform dispersion of monodisperse particles. We chose such a simple flow for two reasons. First, the simplicity allows us to probe the interaction in more detail and offers analytical simplicity in interpreting the results. Secondly, this flow can be addressed by numerical simulation, and many research groups are already working on calculating the flow. Our detailed data can help guide some of these efforts. By using microgravity, we can further simplify the flow to the case of no mean velocity for either the turbulence or the particles. In fact the addition of gravity as a variable parameter may help us to better understand the physics of turbulence attenuation. The experiments are conducted in a turbulence chamber capable of producing stationary or decaying isotropic turbulence with nearly zero mean flow and Taylor microscale Reynolds numbers up to nearly 500. The chamber is a 410 mm cubic box with the corners cut off to make it approximately spherical. Synthetic jet turbulence generators are mounted in each of the eight corners of the box. Each generator consists of a loudspeaker forcing a plenum and producing a pulsed jet through a 20 mm diameter orifice. These synthetic jets are directed into ejector tubes pointing towards the chamber center. The ejector tubes increase the jet mass flow and decrease the velocity. The jets then pass through a turbulence grid. Each of the eight loudspeakers is forced with a random phase and frequency. The resulting turbulence is highly Isotropic and matches typical behavior of grid turbulence. Measurements of both phases are acquired using particle image velocimetry (PIV). The gas is seeded with approximately 1 micron diameter seeding particles while the solid phase is typically 150 micron diameter spherical glass particles. A double-pulsed YAG laser and a Kodak ES-1.0 10-bit PIV camera provide the PIV images. Custom software is used to separate the images into individual images containing either gas-phase tracers or large particles. Modern high-resolution PIV algorithms are then used to calculate the velocity field. A large set of image pairs are acquired for each case, then the results are averaged both spatially and over the ensemble of acquired images. The entire apparatus is mounted in two racks which are carried aboard NASA's KC-135 Flying Microgravity Laboratory. The rack containing the turbulence chamber, the laser head, and the camera floats freely in the airplane cabin (constrained by competent NASA personnel) to minimize g-jitter.
Eaton, John↗
Global Evolution of Solid Matter in Turbulent Protoplanetry Disks: Aerodynamics of Solid Particles - Part 1
The problem of planetary system formation and its subsequent character can only be addressed by studying the global evolution of solid material entrained in gaseous protoplanetary disks. We start to investigate this problem by considering the space-time development of aerodynamic forces that cause solid particles to decouple from the gas. The aim of this work is to demonstrate that only the smallest particles are attached to the gas, or that the radial distribution of the solid matter has no momentary relation to the radial distribution of the gas. We present the illustrative example wherein a gaseous disk of 0.245 solar mass and angular momentum of 5.6 x 10(exp 52) g/sq cm/s is allowed to evolve due to turbulent viscosity characterized by either alpha = 10(exp -2) or alpha = 10(exp -3). The motion of solid particles suspended in a viscously evolving gaseous disk is calculated numerically for particles of different sizes. In addition we calculate the global evolution of single-sized, noncoagulating particles. We find that particles smaller than 0.1 cm move with the gas; larger particles have significant radial velocities relative to the gas. Particles larger than 0.1 cm but smaller than 10(exp 3) cm have inward radial velocities much larger than the gas, whereas particles larger than 10(exp 4) cm have inward velocities much smaller than the gas. A significant difference in the form of the radial distribution of solids and the gas develops with time. It is the radial distribution of solids, rather than the gas, that determines the character of an emerging planetary system.
Stepinski, T. F.↗
A continuum theory of a lubrication problem with solid particles
The governing equations for a two-dimensional lubrication problem involving the mixture of a Newtonian fluid with solid particles at an arbitrary volume fraction are developed using the theory of interacting continuua (mixture theory). The equations take the interaction between the fluid and the particles into consideration. Provision is made for the possibility of particle slippage at the boundaries. The equations are simplified assuming that the solid volume fraction varies in the sliding direction alone. Equations are solved for the velocity of the fluid phase and that of the solid phase of the mixture flow in the clearance space of an arbitrary shaped bearing. It is shown that the classical pure fluid case can be recovered as a special case of the solutions presented. Extensive numerical solutions are presented to quantify the effect of particulate solid for a number of pertinent performance parameters for both slider and journal bearings. Included in the results are discussions on the influence of particle slippage on the boundaries as well as the role of the interacting body force between the fluid and solid particles.
Dai, Fuling↗
Environmental solid particle effects on compressor cascade performance
The effect of suspended solid particles on the performance of the compressor cascade was investigated experimentally in a specially built cascade tunnel, using quartz sand particles. The cascades were made of NACA 65(10)10 airfoils. Three cascades were tested, one accelerating cascade and two diffusing cascades. The theoretical analysis assumes inviscid and incompressible two dimensional flow. The momentum exchange between the fluid and the particle is accounted for by the interphase force terms in the fluid momentum equation. The modified fluid phase momentum equations and the continuity equation are reduced to the conventional stream function vorticity formulation. The method treats the fluid phase in the Eulerian system and the particle phase in Lagrangian system. The experimental results indicate a small increase in the blade surface static pressures, while the theoretical results indicate a small decrease. The theoretical analysis, also predicts the loss in total pressure associated with the particulate flow through the cascade.
Tabakoff, W.↗
Fundamental studies of the solid-particle erosion of silicon
The predictions of the theories of solid-particle erosion of brittle materials are compared to experimental results of studies in which angular Al2O3 particles with mean diameters D of 23 to 270 microns are used to erode (111) surfaces of silicon single crystals at impact angles alpha from 20 to 90 deg and velocities v from 30 to 150 m/s. The description of the steady state erosion rate by a power law, delta W varies directly as (v sin alpha)(n)D(m) must be modified to include threshold and plasticity effects. Furthermore the velocity exponent n depends on D. Results using abrasives of different sizes mixed together can be explained using a logarithmic-normal distribution. The results of transient experiments can be used to explain the synergistic effects which are observed using a biomodal distribution of abrasives.
Routbort, J. L.↗
Effect of surface configuration during solid particle impingement erosion
A study of the progression of erosion and its detrimental effects due to solid particle impingement requires a detailed understanding of the erosion process and morphology of real surfaces of ductile metals. A series of experiments was conducted to investigate the erosion characteristics of aluminum alloy surfaces during spherical glass bead and angular crushed glass particle impingement. The effects of particle shape on cylindrical surfaces and surfaces with pre-existing holes and slits were determined. An attempt was made to understand the relationship between erosion rate and pit morphology. Based on the experimental observations, an empirical relationship between erosion rate and volume loss is presented. This technique provides an improved prediction method for a wide spectrum of ductile materials.
Rao, P. V.↗
The effects of solid rocket motor effluents on selected surfaces and solid particle size, distribution, and composition for simulated shuttle booster separation motors
A series of three tests was conducted using solid rocket propellants to determine the effects a solid rocket plume would have on thermal protective surfaces (TPS). The surfaces tested were those which are baselined for the shuttle vehicle. The propellants used were to simulate the separation solid rocket motors (SSRM) that separate the solid rocket boosters (SRB) from the shuttle launch vehicle. Data cover: (1) the optical effects of the plume environment on spacecraft related surfaces, and (2) the solid particle size, distribution, and composition at TPS sample locations.
Jex, D. W.↗
Lidar observations of Arctic polar stratospheric clouds, 1988 - Signature of small, solid particles above the frost point
The paper presents recent (January 1988) Arctic airborne lidar data which suggest that Type I polar stratospheric clouds (PSCs) are composed of small solid particles with radii on the order of 0.5 micron. PSCs were observed remotely in the 21-24 km altitude range north of Greenland during a round-trip flight from Andenes, Norway on January 29, 1988, aboard the NASA Wallops Flight Facility P-3 Orion aircraft. Synoptic analyses at the 30-mb level show local temperatures of 191-193 K, which are well above the estimated frost point temperature of 185 K; this suggests that the PSCs were probably of the binary HNO3-H2O (Type I) class.
Poole, L. R.↗
Overview of solid particle LV seeding techniques used at UTRC
Due to the failure of existing seeders to meet the stringent specifications required for benchmark experiments in high pressure, high temperature, rapidly accelerating flowfields, an effort is made to improve an existing solid particle seeder. The goal is to produce a more monodisperse seed from the 0.3 micro alumina powder with more than 99 percent of the particles in the submicron range while maintaining a high seeding rate. Coiled-wire inserts are installed within the ends of the nitrogen injection lines in the primary seeder to produce swirling conical jets to vigorously agitate the seed bed. A secondary swirler, constructed from a 25 cm length of 3.8 cm ID steel pipe having threaded end caps, is connected to the output line of the primary seeder. The seeded nitrogen from the primary seeder is injected tangentially at near sonic velocity into the secondary swirler 9.4 cm above its base. Independently controlled auxiliary nitrogen used to increase the swirl in the secondary chamber is also injected tangentially 2.5 cm below the seeded nitrogen lines. Large seed particles are collected by bleeds in the swirler cap and directed overboard. The remaining seeded nitrogen is collected on the center line of the secondary swirler and ducted to the rig.
Patrick, W. P.↗
Trajectories of solid particles spalled from a carbonaceous heat shield
Trajectories are calculated of solid carbon particles that spall from a carbonaceous heat shield and travel through a given flow field. The mathematical model takes into account mass, momentum, and energy conservation during evaporation of the particles in an effort to understand spallation phenomena and their consequences in a physical way. The solution technique is applied to available Galileo Probe flow field solutions. Plots of trajectories and other particle parameters are presented for a range of initial particle sizes and velocities. It is shown that a significant amount of gaseous carbon is deposited in the inviscid region and ahead of the bow shock as well as in the ablation layer.
Davies, C. B.↗
Large, solid particles in the clouds of Venus - Do they exist?
The evidence for solid mode 3 particles in the clouds of Venus is reexamined. The sampling characteristics of the cloud particle size spectrometer (LCPS) are reviewed, and reasons are pointed out for believing that relatively small differences in interpreting the measurements of this instrument could produce systematic errors. It is shown that all of the Pioneer Venus and Venera measurements can be understood if it is assumed that the large particles observed by the LCPS form the tail of the mode 2, H2SO4 size distribution.
Toon, O. B.↗