An investigation of particle trajectories in two-phase flow systems
TL;DR: In this article, the authors describe a theoretical investigation into the response of a spherical particle to a one-dimensional fluid flow, and the motion of the spherical particle in a uniform 2D fluid flow about a circular cylinder.
Abstract: This paper describes a theoretical investigation into (i) the response of a spherical particle to a one-dimensional fluid flow, (ii) the motion of a spherical particle in a uniform two-dimensional fluid flow about a circular cylinder and (iii) the motion of a particle about a lifting aerofoil section. In all three cases the drag of the particle is allowed to vary with (instantaneous) Reynolds number by using an analytical approximation to the standard experimental drag-Reynolds-number relationship for spherical particles.
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TL;DR: In this article, a method is presented which enables the computation of the bed-load transport as the product of the saltation height, the particle velocity and the bed load concentration.
Abstract: A method is presented which enables the computation of the bed-load transport as the product of the saltation height, the particle velocity and the bed-load concentration. The equations of motions for a solitary particle are solved numerically to determine the saltation height and particle velocity. Experiments with gravel particles (transported as bed load) are selected to calibrate the mathematical model using the lift coefficient as a free parameter. The model is used to compute the saltation heights and lengths for a range of flow conditions. The computational results are used to determine simple relationships for the saltation characteristics. Measured transport rates of the bed load are used to compute the sediment concentration in the bed-load layer. A simple expression specifying the bed-load concentration as a function of the flow and sediment conditions is proposed. A verification analysis using about 600 (alternative) data shows that about 77% of the predicted bed-load-transport rates are within 0.5 and 2 times the observed values.
1,653 citations
Cites methods from "An investigation of particle trajec..."
...For the drag coefficient the (empirical) expressions given by Morsi and Alexander (29) were used....
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TL;DR: The physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices are reviewed.
Abstract: The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols This article presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices We also discuss the physics of wind-blown sand and dune formation on Venus and Titan
1,175 citations
Cites background from "An investigation of particle trajec..."
...The drag coefficient (CD) is a function of the particle Reynolds number, Re = ρavRDp/µ (e.g. Morsi and Alexander 1972)....
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TL;DR: In this article, an extensive review of the physics of wind-blown sand and dust on Earth and Mars is presented, including a review of aeolian saltation, the formation and development of sand dunes and ripples, dust aerosol emission, weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices.
Abstract: The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols. This paper presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars. Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices. We also discuss the physics of wind-blown sand and dune formation on Venus and Titan.
1,069 citations
Ferdowsi University of Mashhad1, Xi'an Jiaotong University2, King Mongkut's University of Technology Thonburi3, University of Monastir4, Shahid Beheshti University5, University of Rennes6, Clarkson University7, North Carolina State University8, University of Vermont9, Iran University of Science and Technology10, University of New South Wales11, Royal Society12, King Abdulaziz University13, Quaid-i-Azam University14, University of Tehran15, Babeș-Bolyai University16
TL;DR: A review of the latest developments in modeling of nanofluid flows and heat transfer with an emphasis on 3D simulations can be found in this paper, where the main models used to calculate the thermophysical properties of Nanofluids are reviewed.
659 citations
TL;DR: In this paper, a semi-empirical formula is developed for estimating the total amount of surface material moving in eolian saltation, surface traction, and suspension on the surface of Mars, and the ratio of final particle speed to the particle threshold friction speed is found to be several times that of saltation on earth.
Abstract: Results of low-pressure wind tunnel testing and theoretical considerations are used to estimate the eolian transport of surface material on Mars Saltation on Mars, equations of particle motion, computational results, and analytical determination of surface material movement are considered A semiempirical formula is developed for estimating the total amount of surface material moving in eolian saltation, surface traction, and suspension Numerical solutions of the equations of motion for particle trajectories on the surface of Mars are presented The ratio of final particle speed to the particle threshold friction speed is found to be several times that of saltation on earth
449 citations
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TL;DR: In this article, it was shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamline moving in the direction opposite to V.
Abstract: It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segree & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.
2,912 citations
TL;DR: In this article, the Stokes number σc is calculated for small particles introduced upstream into a fluid flowing past a fixed sphere, and the effect of gravity is included in the formulation when it acts along the axis of symmetry.
Abstract: Trajectories are calculated for small particles introduced upstream into a fluid flowing past a fixed sphere. Unseparated potential flow is taken as the velocity profile for the fluid, and the effect of gravity is included in the formulation when it acts along the axis of symmetry. Using a numerical procedure, particle trajectories which graze the sphere, and the corresponding collision efficiencies, are calculated for values of the Stokes number σ. When gravity is neglected, an analytic solution is obtained for large values of σ which is in good agreement with the numerical results for σ as low as 5. These results are compared with those of Sell (1931) and Langmuir & Blodgett (1946). When gravity is included, a critical value of the Stokes number σc is calculated for which no collisions occur until σ > σc.
62 citations
TL;DR: In this paper, an approximate analytical solution is made for a number of gas particle flows to determine broadly the features on which particle trajectory depends and some experimental results are given which confirm the theoretical computations.
Abstract: Among the parameters which determine the erosion damage sustained by the walls of a nozzle in which a mixture of gas and particles is flowing, is the angle between the direction of the particle flow and the wall surface at the moment of impact. In this work an approximate analytical solution is made for a number of gas particle flows to determine broadly the features on which particle trajectory depends and some experimental results are given which confirm the theoretical computations. It is shown that the divergent region of a conical nozzle is unlikely to suffer a severe particle attack but that for parallel flow convergent-divergent nozzles the convex region near the exit may be affected. The choke, on the other hand, is most susceptible to particle attack even by fairly small particles. It may be said, in general, that any particle which enters the choke section with a velocity which, in the absence of effects from the gas would allow the particle to strike the choke wall, will in fact hit the wall at some point along the length of the choke.
53 citations
TL;DR: In this paper, the authors provided some possible explantions for certain observed phenomena associated with the mean-velocity profile of a turbulent boundary layer which undergoes a rapid yawing.
Abstract: The purpose of this paper is to provide some possible explantions for certain observed phenomena associated with the mean-velocity profile of a turbulent boundary layer which undergoes a rapid yawing. For the cases considered the yawing is caused by an obstruction attached to the wall upon which the boundary layer is developing. Only incompressible flow is considered.§1 of the paper is concerned with the outer region of the boundary layer and deals with a phenomenon observed by Johnston (1960) who described it with his triangular model for the polar plot of the velocity distribution. This was also observed by Hornung & Joubert (1963). It is shown here by a first-approximation analysis that such a behaviour is mainly a consequence of the geometry of the apparatus used. The analysis also indicates that, for these geometries, the outer part of the boundary-layer profile can be described by a single vector-similarity defect law rather than the vector ‘wall-wake’ model proposed by Coles (1956). The former model agrees well with the experimental results of Hornung & Joubert.In §2, the flow close to the wall is considered. Treating this region as an equilibrium layer and using similarity arguments, a three-dimensional version of the ‘law of the wall’ is derived. This relates the mean-velocity-vector distribution with the pressure-gradient vector and wall-shear-stress vector and explains how the profile skews near the wall. The theory is compared with Hornung & Joubert's experimental results. However at this stage the results are inconclusive because of the lack of a sufficient number of measured quantities.
41 citations