Particle collision efficiencies for a sphere

1969 ◽  
Vol 37 (3) ◽  
pp. 565-575 ◽  
Author(s):  
D. H. Michael ◽  
P. W. Norey
Keyword(s):  
Velocity Profile ◽  
Potential Flow ◽  
Analytic Solution ◽  
Numerical Procedure ◽  
Stokes Number ◽  
Critical Value ◽  
Particle Collision ◽  
Small Particles ◽  
Axis Of Symmetry ◽  
Good Agreement

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.

LDA Measurements and Numerical Prediction of Pulsatile Laminar Flow in a Plane 90-Degree Bifurcation

1988 ◽  
Vol 110 (2) ◽  
pp. 129-136 ◽  
Author(s):  
J. M. Khodadadi ◽  
N. S. Vlachos ◽  
D. Liepsch ◽  
S. Moravec
Keyword(s):  
Laminar Flow ◽  
Numerical Study ◽  
Numerical Procedure ◽  
Stokes Number ◽  
Flow Rate Ratio ◽  
Velocity Measurements ◽  
Numerical Predictions ◽  
Dependent Variables ◽  
Separation Zones ◽  
Good Agreement

An experimental and numerical study of pulsatile laminar flow in a plane 90-degree bifurcation is presented. Detailed LDA velocity measurements of the oscillatory flow field have been carried out. The numerical predictions, which are based on an iterative, finite-difference numerical procedure using primitive dependent variables, are in good agreement with the measurements. The results show that one separation zone is established near the bottom wall of the main duct and another near the upstream wall of the branch. The location and size of the separation zones vary within the cycle and are influenced by the Reynolds number, the flow rate ratio, and the Stokes number.

Large-eddy simulation of turbulent gas–particle flow in a vertical channel: effect of considering inter-particle collisions

2001 ◽  
Vol 442 ◽  
pp. 303-334 ◽  
Author(s):  
Y. YAMAMOTO ◽  
M. POTTHOFF ◽  
T. TANAKA ◽  
T. KAJISHIMA ◽  
Y. TSUJI
Keyword(s):  
Gas Flow ◽  
Vertical Channel ◽  
Stokes Number ◽  
Particle Collision ◽  
Experimental Measurements ◽  
Particle Collisions ◽  
Two Phase ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Good Agreement

The interaction between a turbulent gas flow and particle motion was investigated by numerical simulations of gas–particle turbulent downward flow in a vertical channel. In particular the effect of inter-particle collision on the two-phase flow field was investigated. The gas flow field was obtained by large-eddy simulation (LES). Particles were treated by a Lagrangian method, with inter-particle collisions calculated by a deterministic method. The spatial resolution for LES of gas–solid two-phase turbulent flow was examined and relations between grid resolution and Stokes number are presented. Profiles of particle mean velocity, particle wall-normal fluctuation velocity and number density are flattened as a result of inter-particle collisions and these results are in good agreement with experimental measurements. Calculated turbulence attenuation by particles agrees well with experimental measurements for small Stokes numbers, but not for large Stokes number particle. The shape and scale of particle concentrations calculated considering inter-particle collision are in good agreement with experimental observations.

scholarly journals The Stationary Concentrated Vortex Model

Climate ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 39
Author(s):  
Oleg Onishchenko ◽  
Viktor Fedun ◽  
Wendell Horton ◽  
Oleg Pokhotelov ◽  
Natalia Astafieva ◽  
...  
Keyword(s):  
Vortex Structure ◽  
Radial Direction ◽  
Symmetry Axis ◽  
Outer Part ◽  
Vertical Direction ◽  
Axially Symmetric ◽  
New Model ◽  
Vortex Model ◽  
Axis Of Symmetry ◽  
Good Agreement

A new model of an axially-symmetric stationary concentrated vortex for an inviscid incompressible flow is presented as an exact solution of the Euler equations. In this new model, the vortex is exponentially localised, not only in the radial direction, but also in height. This new model of stationary concentrated vortex arises when the radial flow, which concentrates vorticity in a narrow column around the axis of symmetry, is balanced by vortex advection along the symmetry axis. Unlike previous models, vortex velocity, vorticity and pressure are characterised not only by a characteristic vortex radius, but also by a characteristic vortex height. The vortex structure in the radial direction has two distinct regions defined by the internal and external parts: in the inner part the vortex flow is directed upward, and in the outer part it is downward. The vortex structure in the vertical direction can be divided into the bottom and top regions. At the bottom of the vortex the flow is centripetal and at the top it is centrifugal. Furthermore, at the top of the vortex the previously ascending fluid starts to descend. It is shown that this new model of a vortex is in good agreement with the results of field observations of dust vortices in the Earth’s atmosphere.

Application of Potential Flow Theory to Plane-Strain Extrusion

1967 ◽  
Vol 89 (3) ◽  
pp. 503-511 ◽  
Author(s):  
A. Shabaik ◽  
S. Kobayashi ◽  
E. G. Thomsen
Keyword(s):  
Plane Strain ◽  
Potential Flow ◽  
Flow Line ◽  
Flow Theory ◽  
Flow Fields ◽  
Potential Flow Theory ◽  
Good Agreement

Theoretical and experimental flow fields of several extrusion ratios of lead in plane strain were compared. It was found that, for extrusion ratios where dead metal exists, the agreement between the potential and experimental flow nets was better for small reductions when a modified boundary approaching a flow line was used. It was also found that when the flow changed direction gradually, the potential flow net was in good agreement with the experimental one. The solution obtained is unique and complete.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

scholarly journals On the evolution of solutions of Burgers equation on the positive quarter-plane

2019 ◽  
Vol 52 (1) ◽  
pp. 237-248
Author(s):  
Esen Hanaç
Keyword(s):  
Boundary Condition ◽  
Analytic Solution ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Condition ◽  
Quarter Plane ◽  
Initial Boundary Value ◽  
Good Agreement

AbstractIn this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane; $\matrix{ {{v_t} + v{v_x} - {v_{xx}} = 0,\,\,\,x > 0,\,\,\,t > 0,} \cr {v\left( {x,0} \right) = {u_ + },\,\,\,x > 0,} \cr {v\left( {0,t} \right) = {u_b},\,\,t > 0,} \cr }$ where x and t represent distance and time, respectively, and u+ is an initial condition, ub is a boundary condition which are constants (u+ ≠ ub). Analytic solution of above problem is solved depending on parameters (u+ and ub) then compared with numerical solutions to show there is a good agreement with each solutions.

Determination of Small Bone Particles in Meat

1968 ◽  
Vol 51 (6) ◽  
pp. 1175-1177 ◽  
Author(s):  
Robert M Hill ◽  
B D Hites
Keyword(s):  
Carbon Tetrachloride ◽  
Meat Products ◽  
The Other ◽  
Small Particles ◽  
Bone Content ◽  
Bone Particles ◽  
Small Bone ◽  
Good Agreement

Abstract Very small particles of bone can be separated from ground meats and meat products by the following procedure: The bulk of the meat is solubilized by digestion with papain and the bone is separated from the other nondigestible material according to its ability to settle in a carbon tetrachloride: acetone mixture. Turkey samples with widely varying bone content were analyzed, with good agreement between duplicate samples.

On the Aeroelastic Instability of Bluff Cylinders

1961 ◽  
Vol 28 (2) ◽  
pp. 252-258 ◽  
Author(s):  
G. V. Parkinson ◽  
N. P. H. Brooks
Keyword(s):  
Nonlinear Damping ◽  
Critical Value ◽  
Aerodynamic Coefficients ◽  
Static Test ◽  
Aeroelastic Instability ◽  
Near Resonance ◽  
Theoretical Predictions ◽  
All Speeds ◽  
Uniform Stream ◽  
Good Agreement

The validity of quasi-steady theory, using experimental aerodynamic coefficients, to explain the observed aeroelastic instability of bluff cylinders in a uniform stream is examined for several cylinder sections. Only plunging oscillation is considered, and the analytical model is an oscillator with nonlinear damping dependent on the aerodynamic coefficients. Static and dynamic wind-tunnel tests were made of cylinder models of square, rectangular, and D-section. The D-section and the short rectangular sections behaved dynamically like the circular cylinder, showing plunge instability only near resonance with the von Karman vortex street. In complete contrast, the square and long rectangular sections showed plunge instability with amplitude increasing with wind speed for all speeds above a critical value. These dynamic results were in quite good agreement with the theoretical predictions, using the static test data.

Density Distribution in Stagnation Region of Saffman Equation for Dusty Gas

2002 ◽  
Author(s):  
Kazuhiro Tsuboi
Keyword(s):  
Flow Field ◽  
Particle Density ◽  
Stokes Number ◽  
The Body ◽  
Particle Flow ◽  
Particle Phase ◽  
Primary Interest ◽  
Stagnation Region ◽  
Two Fluid ◽  
Good Agreement

We investigate the behaviour of flow field around an obstacle placed in uniform particle flow based on two-fluid Saffman equation. Particle density in the vicinity of the front stagnation point is, in particular, the primary interest in the present study. In the case of small Stokes number, in which particle impingement does not occur, there exists the exact solution of the flow field of particle phase is obtained. Perturbed solution is also obtained in the reciprocal of Stokes number when Stokes number is large enough. Comparison between numerical results and these solutions shows good agreement and the peak of particle density appears near the threshold of partide impingement to the body surface.

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