Computer Simulation of Rapid Granular Flow Through an Orifice

2006 ◽  
Vol 74 (1) ◽  
pp. 111-118 ◽  
Author(s):  
Hojin Ahn
Keyword(s):  
Computer Simulation ◽  
Normal Stress ◽  
Solid Fraction ◽  
Granular Flow ◽  
Discharge Rate ◽  
Tube Length ◽  
Granular Temperature ◽  
Mean Flow ◽  
Flow Through ◽  
The Mean

Rapid granular flow through an orifice (nozzle-shaped flow restrictor) located at the bottom of a vertical tube has been studied using three-dimensional direct computer simulation with the purpose of investigating (1) characteristics of rapid granular flows through the flow restrictor, (2) the choking condition of rapid flow at the orifice and thus conditions at which the maximum discharge rate takes place for the given orifice, and (3) a functional relationship between the discharge rate and flow quantities such as granular temperature and solid fraction. In the present simulation, where the frictional hard-sphere collision operator was employed, it was possible to obtain both rapid and slow (choked) flows through the orifice by controlling the number of particles in the system. The results show that the profile of granular temperature in the vicinity of the orifice plays an important role in determining the choking condition at the orifice. Flow appears to be choked when an adverse granular conduction occurs locally at the orifice in the direction opposite to the mean flow. On the other hand, flow is not choked when the fluctuation energy is conducted in the mean flow direction near the orifice. When flow is not choked, the discharge rate through the orifice increases with increasing solid fraction or normal stress. Once the flow becomes choked, however, the discharge rate decreases as the solid fraction or normal stress increases. Also for inelastic, rough particles, the discharge rate is found to be proportional to the granular temperature to the power of 1.5 and inversely proportional to the gravitational acceleration and the tube length.

The dispersion of matter in turbulent flow through a pipe

1954 ◽  
Vol 223 (1155) ◽  
pp. 446-468 ◽  
Keyword(s):  
Turbulent Flow ◽  
Capillary Tube ◽  
Resistance Coefficient ◽  
Mean Flow ◽  
Combined Action ◽  
Flow Through ◽  
The Mean ◽  
Coefficient Of Diffusion ◽  
Good Agreement ◽  
Made In

The dispersion of soluble matter introduced into a slow stream of solvent in a capillary tube can be described by means of a virtual coefficient of diffusion (Taylor 1953 a ) which represents the combined action of variation of velocity over the cross-section of the tube and molecluar diffusion in a radial direction. The analogous problem of dispersion in turbulent flow can be solved in the same way. In that case the virtual coefficient of diffusion K is found to be 10∙1 av * or K = 7∙14 aU √ γ . Here a is the radius of the pipe, U is the mean flow velocity, γ is the resistance coefficient and v * ‘friction velocity’. Experiments are described in which brine was injected into a straight 3/8 in. pipe and the conductivity recorded at a point downstream. The theoretical prediction was verified with both smooth and very rough pipes. A small amount of curvature was found to increase the dispersion greatly. When a fluid is forced into a pipe already full of another fluid with which it can mix, the interface spreads through a length S as it passes down the pipe. When the interface has moved through a distance X , theory leads to the formula S 2 = 437 aX ( v * / U ). Good agreement is found when this prediction is compared with experiments made in long pipe lines in America.

A theoretical study of viscous effects in peristaltic pumping

1994 ◽  
Vol 279 ◽  
pp. 177-195 ◽  
Author(s):  
Alden M. Provost ◽  
W. H. Schwarz
Keyword(s):  
Wave Propagation ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Mean Flow ◽  
Viscous Effects ◽  
Transverse Waves ◽  
Peristaltic Pumping ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Intuition and previous results suggest that a peristaltic wave tends to drive the mean flow in the direction of wave propagation. New theoretical results indicate that, when the viscosity of the transported fluid is shear-dependent, the direction of mean flow can oppose the direction of wave propagation even in the presence of a zero or favourable mean pressure gradient. The theory is based on an analysis of lubrication-type flow through an infinitely long, axisymmetric tube subjected to a periodic train of transverse waves. Sample calculations for a shear-thinning fluid illustrate that, for a given waveform, the sense of the mean flow can depend on the rheology of the fluid, and that the mean flow rate need not increase monotonically with wave speed and occlusion. We also show that, in the absence of a mean pressure gradient, positive mean flow is assured only for Newtonian fluids; any deviation from Newtonian behaviour allows one to find at least one non-trivial waveform for which the mean flow rate is zero or negative. Introduction of a class of waves dominated by long, straight sections facilitates the proof of this result and provides a simple tool for understanding viscous effects in peristaltic pumping.

Improved κ-ɛ Modelling of Impeller Flow Performance of a Mixed-Flow Pump under off-Design Operating States

1993 ◽  
Vol 207 (4) ◽  
pp. 219-229 ◽  
Author(s):  
S M Fraser ◽  
Y Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Navier Stokes ◽  
Mean Flow ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
The Mean ◽  
Flow Pump

Three-dimensional turbulent flow through the impeller passage of a model mixed-flow pump has been simulated by solving the Navier-Stokes equations with an improved κ-ɛ model. The standard κ-ɛ model was found to be unsatisfactory for solving the off-design impeller flow and a converged solution could not be obtained at 49 per cent design flowrate. After careful analysis, it was decided to modify the standard κ-ɛ model by including the extra rates of strain due to the acceleration of impeller rotation and geometrical curvature and removing the mathematical ill-posedness between the mean flow turbulence modelling and the logarithmic wall function.

Oscillatory forcing of flow through porous media. Part 2. Unsteady flow

2002 ◽  
Vol 465 ◽  
pp. 237-260 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Flow Through Porous Media ◽  
Mean Flow ◽  
Two Fluids ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Numerical computations are employed to study the phenomenon of oscillatory forcing of flow through porous media. The Galerkin finite element method is used to solve the time-dependent Navier–Stokes equations to determine the unsteady velocity field and the mean flow rate subject to the combined action of a mean pressure gradient and an oscillatory body force. With strong forcing in the form of sinusoidal oscillations, the mean flow rate may be reduced to 40% of its unforced steady-state value. The effectiveness of the oscillatory forcing is a strong function of the dimensionless forcing level, which is inversely proportional to the square of the fluid viscosity. For a porous medium occupied by two fluids with disparate viscosities, oscillatory forcing may be used to reduce the flow rate of the less viscous fluid, with negligible effect on the more viscous fluid. The temporal waveform of the oscillatory forcing function has a significant impact on the effectiveness of this technique. A spike/plateau waveform is found to be much more efficient than a simple sinusoidal profile. With strong forcing, the spike waveform can induce a mean axial flow in the absence of a mean pressure gradient. In the presence of a mean pressure gradient, the spike waveform may be employed to reverse the direction of flow and drive a fluid against the direction of the mean pressure gradient. Owing to the viscosity dependence of the dimensionless forcing level, this mechanism may be employed as an oscillatory filter to separate two fluids of different viscosities, driving them in opposite directions in the porous medium. Possible applications of these mechanisms in enhanced oil recovery processes are discussed.

The influence of mean shear on unsteady aperture flow, with application to acoustical diffraction and self-sustained cavity oscillations

1981 ◽  
Vol 109 ◽  
pp. 125-146 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Leading Edge ◽  
Vortex Sheet ◽  
Mean Flow ◽  
Kutta Condition ◽  
Sustained Oscillations ◽  
Linearized Theory ◽  
Flow Through ◽  
The Mean ◽  
Theoretical Results ◽  
Disturbed Motion

This paper discusses the linearized theory of unsteady flow through a two-dimensional aperture in a thin plate in the presence of a grazing mean flow on one side of the plate. The mean shear layer is modelled by a vortex sheet, and it is predicted that at low mean-flow Mach numbers there is a transfer of energy from the mean flow to the disturbed motion of the vortex sheet provided (i) the Kutta condition is imposed at the leading edge of the aperture, resulting in the unsteady shedding of vorticity from the edge, and (ii) the width of the aperture 2s satisfies ½ < 2s/λ < 1.1, where λ is the hydrodynamic wavelength of the disturbance on the vortex sheet within the aperture. The theory is used to examine the effect of mean shear on the diffraction of sound by a perforated screen, and to predict the spontaneous excitation and suppression of self-sustained oscillations in a wall-cavity beneath a nominally steady mean flow. In the latter case support for the proposed theory is provided by a favourable comparison of theoretical results with experimental data available in the literature.

Effects of Fluid Inertia and Compressibility on the Performance of Valves and Flow Meters Operating under Unsteady Conditions

1966 ◽  
Vol 8 (1) ◽  
pp. 52-61 ◽  
Author(s):  
D. McCloy
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Flow Measurement ◽  
Fluid Inertia ◽  
Mean Flow ◽  
Flow Meters ◽  
Orifice Area ◽  
Flow Through ◽  
The Mean ◽  
Compressibility Effects

Incompressible flow theory is used in the investigation of the effects of fluid inertia on unsteady flow through valves and flow meters. Two types of oscillatory disturbance are considered, one being due to valve oscillation at constant pressure drop and the other to pressure pulsation at constant orifice area. With the former type of disturbance it is shown that the mean flow rate decreases with frequency of oscillation. When the pressure drop pulsates the mean flow rate increases with frequency. These phenomena are shown to be of importance in hydraulic servomechanisms and in dynamic flow measurement. Compressibility effects are considered and it is shown that cavitation can occur at the valve during oscillation.

scholarly journals Flow in a Centrifugal Fan of the Squirrel Cage Type

1989 ◽  
Author(s):  
R. J. Kind ◽  
M. G. Tobin
Keyword(s):  
Flow Field ◽  
Reverse Flow ◽  
Field Measurements ◽  
Centrifugal Fan ◽  
Performance Measurements ◽  
Mean Flow ◽  
Velocity Measurements ◽  
Squirrel Cage ◽  
Flow Through ◽  
The Mean

This paper presents the results of performance measurements and detailed measurements of the mean flow field at rotor inlet and rotor exit in three squirrel cage fan configurations. The flow-field measurements were taken with a five-hole probe and yield total pressure, static pressure and the three components of velocity. Measurements were taken for two casing throat areas and for two different rotors. For each configuration the flow field was measured for flow rates below, near and above the best-efficiency point. Flow patterns are complex and there is reverse flow through the rotor blading even at the best-efficiency operating condition. Although complex, the main features of flow behaviour can be understood. They were common to all three fan configurations.

Flow in a Centrifugal Fan of the Squirrel-Cage Type

1990 ◽  
Vol 112 (1) ◽  
pp. 84-90 ◽  
Author(s):  
R. J. Kind ◽  
M. G. Tobin
Keyword(s):  
Flow Field ◽  
Reverse Flow ◽  
Flow Behavior ◽  
Field Measurements ◽  
Centrifugal Fan ◽  
Performance Measurements ◽  
Mean Flow ◽  
Squirrel Cage ◽  
Flow Through ◽  
The Mean

This paper presents the results of performance measurements and detailed measurements of the mean flow field at rotor inlet and rotor exit in three squirrel-cage fan configurations. The flow-field measurements were taken with a five-hole probe and yield total pressure, static pressure, and the three components of velocity. Measurements were taken for two casing throat areas and for two different rotors. For each configuration the flow field was measured for flow rates below, near, and above the best-efficiency point. Flow patterns are complex and there is reverse flow through the rotor blading even at the best-efficiency operating condition. Although complex, the main features of flow behavior can be understood. They were common to all three fan configurations.

scholarly journals The Dynamic Behavior and Compliance of a Stream of Cavitating Bubbles

1973 ◽  
Vol 95 (4) ◽  
pp. 533-541 ◽  
Author(s):  
C. Brennen
Keyword(s):  
Thermal Effects ◽  
Pressure Fluctuations ◽  
Distribution Functions ◽  
Careful Examination ◽  
Mean Flow ◽  
Reduced Pressure ◽  
Flow Through ◽  
The Mean ◽  
Bubble Number ◽  
Bubble Number Density

The role played by turbopump cavitation in the POGO instability of liquid rockets motivates the present study on the dynamic response of streams of cavitating bubbles to imposed pressure fluctuations. Both quasistatic and more general linearized dynamic analyses are made of the perturbations to a cavitating flow through a region of reduced pressure in which the bubbles first grow and then collapse. The results when coupled with typical bubble number density distribution functions yield compliances which compare favorably with the existing measurements. Since the fluids involved are frequently cryogenic, a careful examination was made of the thermal effects both on the mean flow and on the perturbations. As a result the discrepancy between theory and experiment for particular engines could be qualitatively ascribed to reductions in the compliance caused either by these thermal effects or by relatively high reduced frequencies.

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