scholarly journals The time evolution of the maximal horizontal surface fluid velocity for an irrotational wave approaching breaking

2015 ◽  
Vol 768 ◽  
pp. 468-475 ◽  
Author(s):  
A. Constantin
Keyword(s):  
Pressure Gradient ◽  
Time Evolution ◽  
Deep Water ◽  
Fluid Velocity ◽  
Horizontal Surface ◽  
Wave Profiles ◽  
Breaking Time ◽  
Spilling Breaker ◽  
Irrotational Wave

We derive an equation that relates the evolution in time of the maximum of the horizontal fluid velocity at the surface of an irrotational deep-water plunging or spilling breaker to the first component of the pressure gradient at the surface. The approach applies to overhanging wave profiles, up to breaking time.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

Addressing the siphoning effect in new shunt designs by decoupling the activation pressure and the pressure gradient across the valve

2013 ◽  
Vol 11 (2) ◽  
pp. 181-187 ◽  
Author(s):  
Tobias A. Mattei ◽  
Martin Morris ◽  
Kathleen Nowak ◽  
Daniel Smith ◽  
Jeremy Yee ◽  
...  
Keyword(s):  
Pressure Gradient ◽  
Flow Rate ◽  
Fluid Velocity ◽  
Component System ◽  
The Past ◽  
Benchmark Tests ◽  
Final Design ◽  
Actual Flow Rate ◽  
Actual Flow ◽  
Labview Program

Object Although several improvements have been observed in the past few years in shunt technology, currently available systems still present several associated problems. Among these, overdrainage along with its complications remains one of the great challenges for new shunt designs. To address the so-called siphoning effect, the authors provide a practical example of how it is possible to decouple the activation pressure and the pressure gradient across the valve through a 3–key component system. In this new shunt design, the flow is expected to depend only on the intracranial pressure and not on the pressure gradient across the valve, thus avoiding the so-called siphoning effect. Methods The authors used computer models to theoretically evaluate the mechanical variables involved in the operation of the newly designed valve, such as the fluid's Reynolds number, proximal pressure, distal pressure, pressure gradient, actual flow rate, and expected flow rate. After fabrication of the first superscaled model, the authors performed benchmark tests to analyze the performance of the new shunt prototype, and the obtained data were compared with the results predicted by the previous mathematical models. Results The final design of the new paddle wheel valve with the 3–key component antisiphoning system was tested in the hydrodynamics laboratory to prove that the siphoning effect did not occur. According to the calculations obtained using the LabVIEW program during the experiments, each time the distal pressure decreased without an increase in the proximal pressure (despite the range of the pressure gradient), the pin blocked the spinning of the paddle wheels, and the calculated fluid velocity through the system tended to zero. Such a situation was significantly different from the expected flow rate for such a pressure gradient in a siphoning situation without the new antisiphon system. Conclusions The design of this new prototype with a 3–key component antisiphoning system demonstrated that it is possible to decouple the activation pressure and the pressure gradient across the valve, avoiding the siphoning effect. Although further developments are necessary to provide a model compatible to clinical use, the authors believe that this new prototype illustrates the possibility of successfully addressing the siphoning effect by using a simple 3–key component system that is able to decouple the activation pressure and the pressure gradient across the valve by using a separate pressure chamber. It is expected that such proof of concept may significantly contribute to future shunt designs attempting to address the problem of overdrainage due to the siphoning effect.

Pulsatile flow in rigid tubes

1965 ◽  
Vol 20 (5) ◽  
pp. 1078-1082 ◽  
Author(s):  
Robert G. Linford ◽  
Norman W. Ryan
Keyword(s):  
Fluid Flow ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Pulsatile Flow ◽  
Fluid Velocity ◽  
Fluid Flow Rate ◽  
Tube Radius ◽  
Low Frequencies ◽  
Time Relationship ◽  
Fluid Properties

The purpose of this study was to examine critically the theoretical equations derived for pulsatile laminar flow in rigid straight tubes. These equations, presented in their most useful form by J. R. Womersley in 1955, give the fluid flow rate as a function of the pressure gradient-time relationship, pulse frequency, fluid properties, and tube radius, and they give the fluid velocity as a function of the above quantities and the radial position in the tube. A pulsatile flow apparatus was constructed which would allow measurement of all the variables mentioned above, and a computer program based on Womersley's equations was used to calculate the fluid flow rate and velocity profile from the pressure gradient-time relationship, fluid properties, and tube radius. Thus a comparison between measured and calculated values of flow and velocity could be made. Calculations and data agree within the estimated experimental error, thus providing evidence of the applicability of the theoretical equations to actual flow with large pulse amplitudes. The analog computer “pressure gradient technique” of D. Fry and associates was compared with the exact solution for straight rigid tubes and found to deviate less than 20% in amplitude and phase except at very low frequencies. hydrodynamics, pulsatile flow; blood flow, arterial; hemodynamics, pulse characteristics Submitted on April 6, 1964

Capsule Transport in Coal Slurry Medium

1995 ◽  
Vol 117 (4) ◽  
pp. 691-695 ◽  
Author(s):  
J. Seaba ◽  
G. Xu
Keyword(s):  
Pressure Gradient ◽  
Total Pressure ◽  
Fluid Velocity ◽  
Optimal Operation ◽  
Coal Slurry ◽  
Pressure Gradients ◽  
Velocity Range ◽  
Aspect Ratios ◽  
Potential Benefits ◽  
Lift Off

The use of coal slurry instead of water in a coal log pipeline (CLP) is investigated for the first time. This investigation reveals significant differences and possible benefits by using coal slurry instead of water in CLPs. The lift-off velocity, and capsule and total pressure gradients are presented for a 51 mm pipeline using two capsule geometries. The fluid velocity was tested from 1 to 3 m/s, which includes the lift-off velocity of the capsule train. The diameter ratio (k) and specific gravity (S) are held constant at 0.75 and 1.3, respectively. Two capsule lengths were studied corresponding to aspect ratios (a) of 2 and 4. Aluminum-Plexiglas capsules are used to simulate the coal logs. The coal slurry significantly lowered the lift-off velocity, and transported more coal per total pressure gradient than coal logs in water. The capsule pressure gradient was nearly constant over the velocity range investigated. This indicates that the optimal operation velocity range may be much larger for coal slurry compared to water. Further tests and abrasion studies are required to fully assess the potential benefits of using coal slurry.

Two Types of Nonlinear Pressure-Drop Versus Flow-Rate Relation Observed for Saturated Porous Media

1997 ◽  
Vol 119 (3) ◽  
pp. 700-706 ◽  
Author(s):  
J. L. Lage ◽  
B. V. Antohe ◽  
D. A. Nield
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Hydrostatic Pressure ◽  
Pressure Gradient ◽  
Fluid Velocity ◽  
Rate Of Change ◽  
Transition To Turbulence ◽  
Abnormal Behavior ◽  
Hydrostatic Pressure Gradient ◽  
Transition Speed

Previous reports of experiments performed with water (Fund et at., 1987 and Kececioglu and Jiang, 1994) indicated that beyond the Forchheimer regime the rate of change of the hydrostatic pressure gradient along a porous medium suddenly decreases. This abnormal behavior has been termed “transition to turbulence in a porous medium.” We investigate the relationship between the hydrostatic pressure gradient of a fluid (air) through a porous medium and the average seepage fluid velocity. Our experimental results, reported here, indicate an increase in the hydrostatic pressure rate beyond a certain transition speed, not a decrease. Physical arguments based on a consideration of internal versus external incompressible viscous flow are used to justify this distinct behavior, a consequence of the competition between a form dominated transition and a viscous dominated transition. We establish a criterion for the viscous dominated transition from consideration of the results of three porous media with distinct hydraulic characteristics. A theoretical analysis based on the semivariance model validation principle indicates that the pressure gradient versus fluid speed relation indeed departs from the quadratic Forchheimer-extended Darcy flow model, and can be correlated by a cubic function of fluid speed for the velocity range of our experiments.

scholarly journals USE OF GALERKIN TECHNIQUE TO THE ROLLING OF A PLATE IN DEEP WATER

2021 ◽  
Vol 26 (2) ◽  
pp. 209-222
Author(s):  
Swagata Ray ◽  
Soumen De ◽  
B. N. Mandal
Keyword(s):  
Integral Equation ◽  
Deep Water ◽  
Water Waves ◽  
Vertical Plate ◽  
Fluid Velocity ◽  
Galerkin Approximation ◽  
Horizontal Component ◽  
Wave Number ◽  
Small Oscillations ◽  
Surface Water Waves

The classical problems of surface water waves produced by small oscillations of a thin vertical plate partially immersed as well as submerged in deep water are reinvestigated here. Each problem is reduced to an integral equation involving horizontal component of velocity across the vertical line outside the plate. The integral equations are solved numerically using Galerkin approximation in terms of simple polynomials multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge(s) of the plate. Fairly accurate numerical estimates for the amplitude of the radiated wave at infinity due to rolling and also for swaying of the pate in each case are obtained and these are depicted graphically against the wave number for various cases.

Analysis On the Inception of the Magnetohydrodynamic Flow Instability in the Annular Linear Induction Pump Channel

2021 ◽  
Author(s):  
Ruijie Zhao ◽  
Xiaohui Dou ◽  
Qiang Pan ◽  
ZHANG Desheng ◽  
Bart van Esch
Keyword(s):  
Magnetic Field ◽  
Pressure Gradient ◽  
Lorentz Force ◽  
Flow Rate ◽  
Flow Instability ◽  
Fluid Velocity ◽  
Magnetic Reynolds Number ◽  
Wave Number ◽  
Magnetic Flux Density ◽  
Linear Induction

Abstract Flow instability is the intricate phenomenon in the Annular Linear Induction Pump when the pump runs at off-design working condition. A 3D numerical model is built to simulate the flow in the pump channel. The pump heads at different flow rates are accurately predicted by comparing with experiment. The simulation results show the fluid velocity is circumferentially non-uniform in the pump channel even at the nominal flow rate. The flow in the middle sector continuously decelerates to nearly zero with the reducing flow rate. Reversed flow occurs in the azimuthal plane, followed by vortex flow. The reason for the heterogeneous velocity field is attributed to the mismatch between non-uniform Lorentz force and relatively even pressure gradient. It is seen that the flow in the region of small Lorentz force has to sacrifice its velocity to match with the pressure gradient. An analytic expression of the axial Lorentz force is then developed and it is clearly demonstrated the Lorentz force could be influenced by the profiles of velocity and radial magnetic flux density. The coupling between velocity and magnetic field is studied by analyzing the magnitudes of different terms in the dimensionless magnetic induction equation. It is found the dissipation term is determined not only by the magnetic Reynolds number but the square of wave number of the disturbance in each direction. The smaller disturbing wave number weakens the dissipating effect, resulting in the larger non-uniform magnetic field and axial Lorentz force.

Darcy's law for slow viscous flow past a stationary array of bubbles

1990 ◽  
Vol 114 (1-2) ◽  
pp. 71-79 ◽  
Author(s):  
Robert Lipton ◽  
Marco Avellaneda
Keyword(s):  
Pressure Gradient ◽  
Viscous Flow ◽  
Body Force ◽  
Darcy’S Law ◽  
Fluid Velocity ◽  
Darcy's Law ◽  
Slow Viscous Flow ◽  
Flow Past

SynopsisWe examine slow viscous flow past a concentrated bed of small stationary viscous bubbles of a second fluid, and derive Darcy's law relating the average fluid velocity to the overall pressure gradient and body force.

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