Langevin Dynamics Study of the Mean Flow Rate-Energy Stochastic Fluid Intrusion Process in Porous Media

2019 ◽  
Vol 12 (6) ◽  
pp. 398
Author(s):  
Yassine Hariti ◽  
Ahmed Hader ◽  
Layla Amallah ◽  
Imad Achik ◽  
Yahia Boughaleb
Keyword(s):  
Porous Media ◽  
Flow Rate ◽  
Langevin Dynamics ◽  
Mean Flow ◽  
The Mean ◽  
Stochastic Fluid

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.

Oscillatory forcing of flow through porous media. Part 1. Steady flow

2002 ◽  
Vol 465 ◽  
pp. 213-235 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Media ◽  
Flow Rate ◽  
Stokes Equations ◽  
Nonlinear Flow ◽  
Navier Stokes ◽  
Full Time ◽  
Inertial Effects ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Oscillatory forcing of a porous medium may have a dramatic effect on the mean flow rate produced by a steady applied pressure gradient. The oscillatory forcing may excite nonlinear inertial effects leading to either enhancement or retardation of the mean flow. Here, in Part 1, we consider the effects of non-zero inertial forces on steady flows in porous media, and investigate the changes in the flow character arising from changes in both the strength of the inertial terms and the geometry of the medium. The steady-state Navier–Stokes equations are solved via a Galerkin finite element method to determine the velocity fields for simple two-dimensional models of porous media. Two geometric models are considered based on constricted channels and periodic arrays of circular cylinders. For both geometries, we observe solution multiplicity yielding both symmetric and asymmetric flow patterns. For the cylinder arrays, we demonstrate that inertial effects lead to anisotropy in the effective permeability, with the direction of minimum resistance dependent on the solid volume fraction. We identify nonlinear flow phenomena which might be exploited by oscillatory forcing to yield a net increase in the mean flow rate. In Part 2, we take up the subject of unsteady flows governed by the full time-dependent Navier–Stokes equations.

Cerebrospinal fluid formation in rats and cats during treatment with timolol

1982 ◽  
Vol 60 (8) ◽  
pp. 1138-1143 ◽  
Author(s):  
Betty P. Vogh ◽  
David R. Godman
Keyword(s):  
Cerebrospinal Fluid ◽  
Dose Level ◽  
Aqueous Humor ◽  
Flow Rate ◽  
Formation Rate ◽  
Time Study ◽  
Mean Flow ◽  
Dye Dilution ◽  
Fluid Formation ◽  
The Mean

The influence of timolol upon cerebrospinal fluid formation rate has been examined in rats by the measurement of 22Na+ entry into this fluid after 10, 100, or 1000 μg∙kg−1 i.v, and in cats by the dye-dilution measurement of new fluid formation after 30, or 3000 μg∙kg−1 i.v., or 250 μg∙mL−1 in ventricular perfusate. In rats no change from control rates occurred. In the cats there appeared to be no effect of intraventricular timolol; however, a significant decrease of ~ 25% in the mean flow rate was seen after 40 min when drug was given i.v. at either dose level. A time study showed that no further decrease occurred within 5 h and that the observed decrease continued for at least 3 h. These findings are of interest in view of the ability of topical, intraocular, and i.v. timolol to reduce aqueous humor formation rate.

MEAN FLOW OF A VERTICALLY VIBRATED HOURGLASS

1993 ◽  
Vol 07 (09n10) ◽  
pp. 1799-1805 ◽  
Author(s):  
Pierre EVESQUE ◽  
Wahib MEFTAH
Keyword(s):  
Time Constant ◽  
Flow Rate ◽  
Flow Dynamics ◽  
Mean Flow ◽  
Resonance Domain ◽  
The Mean ◽  
Vertical Vibrations

We have investigated the mean flow of a hourglass submitted to vertical vibrations as function of the amplitude a and frequency f=Ω/2π of the vibration (5Hz≤f≤100Hz) . We find that the time constant of the flow dynamics is longer than 0.2s, that the flow rate is weakly sensitive to vibrations as far as these ones have a small enough amplitude (aΩ2<g=10m/s2) . When aΩ2 becomes larger than g and when the frequency is located inside a resonance domain (10Hz<f<80Hz) , the flow rate decreases strongly; it even stops at large aΩ2 and when 40Hz<f<60Hz .

Study about influence of doors’ opening degree on crowd evacuation based on simulation

2019 ◽  
Vol 30 (11) ◽  
pp. 1950096
Author(s):  
Yuanchun Ding ◽  
Falu Weng ◽  
Lizhong Yang
Keyword(s):  
Linear Relationship ◽  
Flow Rate ◽  
Saving Rate ◽  
Mean Square ◽  
Mean Flow ◽  
Time Saving ◽  
Evacuation Time ◽  
Crowd Evacuation ◽  
The Mean ◽  
Simulation Results

Based on simulation, the influence of the doors’ opening degree (DOD) on crowd evacuation is investigated in this paper. First of all, an evacuation model, which has one exit with two doors, is established by utilizing the software Pathfinder. Then, based on the obtained model, some evacuation scenarios are considered. The simulation results indicate, when the DOD is within 115∘–135∘, the time saving rate is more than 13%, and the maximum time saving rate is achieved when the DOD is 125∘. Furthermore, there is a linear relationship between the mean square error and the number of the evacuees. For a small number of evacuees, the total evacuation time is mainly influenced by the distributions of the evacuees, however, as the number of the evacuees increases, it is mainly influenced by the number of the evacuees. Moreover, when the DOD is 125∘, the mean flow rate per unit width (MFRPUW) decreases along with the increasing of exit’s width, however, it increases along with the increasing of exit’s width while the DOD is 180∘. Compared with the 180∘ DOD, the 125∘ DOD can always achieve a higher MFRPUW, and the narrower the exit is, the higher MFRPUW the 125∘ DOD achieves.

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.

Mechanics of machine milking: II. The flow-rate pattern within single pulsation cycles

1966 ◽  
Vol 33 (2) ◽  
pp. 177-191 ◽  
Author(s):  
C. C. Thiel ◽  
P. A. Clough ◽  
D. R. Westgarth ◽  
D. N. Akam
Keyword(s):  
Flow Rate ◽  
Response Rate ◽  
Sphincter Muscle ◽  
Mean Flow ◽  
Considerable Time ◽  
Flow Rates ◽  
Machine Milking ◽  
Closing Force ◽  
The Mean ◽  
Pulsation Cycle

SummaryThe milk flowing during a single pulsation cycle was collected in a circle of contiguous cups which rotated in a chamber at 1 rev/pulsation cycle just below the end of the teatcup liner. The mean flow rate during the time taken for each collecting cup to pass under the milk stream was calculated and the flow-rate curve for the milkflow period of the pulsation cycle plotted. Flow rates were measured at 130, 97, 65, 32 and 16 c/min, and also after the pulsator had been stopped with the liner open for 0·5 min (0 pulsation).It was concluded from the series of flow-rate curves at the different pulsation rates that flow rate from the teat increased in about 0·05 sec to a steady value which continued for 0·5 sec or so, and then declined over a period of about 1·5 sec to a new constant value approximately equal to that shown after milk had flowed continuously from the teat for 0·5 min.These results suggest that once the pressure difference across the streak canal during milking forces the teat sphincter open a considerable time elapses before the muscle control system responds, and that a further much longer period elapses before the full closing force of the sphincter is exerted. Thus, it would appear that at pulsation rates of about 50 c/min and above, the streak canal is closed by pressure exerted on the teat by the closing liner, the sphincter muscle playing no active part because its response rate is slow compared with the pulsation rate. At lower pulsation rates the flow rate declines during each cycle because the sphincter muscle has time to exert a closing force to a greater or lesser extent depending on the duration of the milkflow period.

scholarly journals Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170388 ◽  
Author(s):  
C. J. Cotter ◽  
G. A. Gottwald ◽  
D. D. Holm
Keyword(s):  
Large Scale ◽  
Particle Dynamics ◽  
Homogenization Theory ◽  
Small Scale ◽  
Mean Flow ◽  
Time Dynamics ◽  
Fluid Equations ◽  
Diffusive Limit ◽  
The Mean ◽  
Stochastic Fluid

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. ( doi:10.1098/rspa.2014.0963 )), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Pressure Propagation in Pulsatile Flow Through Random Microvascular Networks

1993 ◽  
Vol 115 (2) ◽  
pp. 180-186 ◽  
Author(s):  
X. S. He ◽  
J. G. Georgiadis
Keyword(s):  
Pressure Distribution ◽  
Flow Rate ◽  
Large Scale ◽  
Direct Method ◽  
Blood Flow Rate ◽  
Vessel Diameter ◽  
Mean Flow ◽  
Statistical Variation ◽  
Vascular Segment ◽  
The Mean

A microvascular network with random dimensions of vessels is built on the basis of statistical analysis of conjuctival beds reported in the literature. Our objective is to develop a direct method of evaluating the statistics of the pulsatile hydrodynamic field starting from a priori statistics which mimic the large-scale heterogeneity of the network. The model consists of a symmetric diverging-converging dentritic network of ten levels of vessels, each level described by a truncated Gaussian distribution of vessel diameters and lengths. In each vascular segment, the pressure distribution is given by a diffusion equation with random parameters, while the blood flow rate depends linearly on the pressure gradient. The results are presented in terms of the mean value and standard deviation of the pressure and flow rate waveforms at two positions along the network. It is shown that the assumed statistical variation of vessel lengths results in flow rate deviations as high as 50 percent of the mean, while the corresponding effect of vessel diameter variation is much smaller. For a given pressure drop, the statistical variation of lengths increases the mean flow while the effect on the mean pressure distribution is negligible.

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.

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