scholarly journals A multiscale method to calculate filter blockage

2016 ◽  
Vol 809 ◽  
pp. 264-289 ◽  
Author(s):  
M. P. Dalwadi ◽  
M. Bruna ◽  
I. M. Griffiths
Keyword(s):  
Homogenization Theory ◽  
Initial Porosity ◽  
Structure Evolution ◽  
Contaminant Removal ◽  
Unidirectional Flow ◽  
Average Porosity ◽  
Flow Through ◽  
As Adsorption ◽  
Asymptotic Reduction ◽  
Spatially Varying

Filters that act by adsorbing contaminant onto their pore walls will experience a decrease in porosity over time, and may eventually block. As adsorption will generally be greater towards the entrance of a filter, where the concentration of contaminant particles is higher, these effects can also result in a spatially varying porosity. We investigate this dynamic process using an extension of homogenization theory that accounts for a macroscale variation in microstructure. We formulate and homogenize the coupled problems of flow through a filter with a near-periodic time-dependent microstructure, solute transport due to advection, diffusion and filter adsorption, and filter structure evolution due to the adsorption of contaminant. We use the homogenized equations to investigate how the contaminant removal and filter lifespan depend on the initial porosity distribution for a unidirectional flow. We confirm a conjecture made by Dalwadi et al. (Proc. R. Soc. Lond. A, vol. 471 (2182), 2015, 20150464) that filters with an initially negative porosity gradient have a longer lifespan and remove more contaminant than filters with an initially constant porosity, or worse, an initially positive porosity gradient. In addition, we determine which initial porosity distributions result in a filter that will block everywhere at once by exploiting an asymptotic reduction of the homogenized equations. We show that these filters remove more contaminant than other filters with the same initial average porosity, but that filters which block everywhere at once are limited by how large their initial average porosity can be.

scholarly journals Understanding how porosity gradients can make a better filter using homogenization theory

2015 ◽  
Vol 471 (2182) ◽  
pp. 20150464 ◽  
Author(s):  
M. P. Dalwadi ◽  
I. M. Griffiths ◽  
M. Bruna
Keyword(s):  
Solute Transport ◽  
Homogenization Theory ◽  
Contaminant Removal ◽  
Computationally Efficient ◽  
Filter Efficiency ◽  
Second Stage ◽  
Advection Diffusion ◽  
Periodic Microstructure ◽  
Flow Through ◽  
Total Adsorption

Filters whose porosity decreases with depth are often more efficient at removing solute from a fluid than filters with a uniform porosity. We investigate this phenomenon via an extension of homogenization theory that accounts for a macroscale variation in microstructure. In the first stage of the paper, we homogenize the problems of flow through a filter with a near-periodic microstructure and of solute transport owing to advection, diffusion and filter adsorption. In the second stage, we use the computationally efficient homogenized equations to investigate and quantify why porosity gradients can improve filter efficiency. We find that a porosity gradient has a much larger effect on the uniformity of adsorption than it does on the total adsorption. This allows us to understand how a decreasing porosity can lead to a greater filter efficiency, by lowering the risk of localized blocking while maintaining the rate of total contaminant removal.

scholarly journals A Robust Flow-Through Platform for Organic Contaminant Removal

2021 ◽  
Vol 2 (1) ◽  
pp. 100296
Author(s):  
Long Chen ◽  
Akram N. Alshawabkeh ◽  
Shayan Hojabri ◽  
Meng Sun ◽  
Guiyin Xu ◽  
...  
Keyword(s):  
Organic Contaminant ◽  
Contaminant Removal ◽  
Flow Through

scholarly journals Viscous effects in two-layer, unidirectional hydraulic flow

2010 ◽  
Vol 644 ◽  
pp. 371-394
Author(s):  
MARTIN S. SINGH ◽  
ANDREW McC. HOGG
Keyword(s):  
Control Point ◽  
Lower Boundary ◽  
Internal Gravity Waves ◽  
Velocity Shear ◽  
Hydraulic Control ◽  
Viscous Effects ◽  
Unidirectional Flow ◽  
Boundary Case ◽  
Flow Through ◽  
Layer Flow

Hydraulic equations are derived for a stratified (two-layer) flow in which the horizontal velocity varies continuously in the vertical. Viscosity is included in the governing equations, and the effect of friction in hydraulically controlled flows is examined. The analysis yields Froude numbers which depend upon the integrated inverse square of velocity but reduce to the original layered Froude numbers when velocity is constant with depth. The Froude numbers reveal a critical condition for hydraulic control, which equates to the arrest of internal gravity waves.Solutions are presented for the case of unidirectional flow through a lateral constriction, both with and without bottom drag. In the free-slip lower boundary case, viscosity transports momentum from the faster to the slower layer, thereby shifting the control point downstream and reducing the flux through the constriction. However, while the velocity shear at the interface between the two layers is reduced, the top-to-bottom velocity difference of the controlled solution is increased for larger values of viscosity. This counter-intuitive result is due to the restrictions placed on the flow at the hydraulic control point. When bottom drag is included in the model, the total flux may increase, in some cases exceeding that of the inviscid solution.

scholarly journals Fluid mechanical valving of air flow in bird lungs

1988 ◽  
Vol 136 (1) ◽  
pp. 1-12 ◽  
Author(s):  
D. O. Kuethe
Keyword(s):  
High Pressure ◽  
Flow Rate ◽  
Pressure Difference ◽  
Air Flow ◽  
Low Pressure ◽  
Physical Models ◽  
Unidirectional Flow ◽  
Air Sacs ◽  
Caudal Portion ◽  
Flow Through

The unidirectional flow through the gas-exchanging bronchi of bird lungs is known to be effected by (1) the structure of the major bronchi and (2) a pressure difference between the cranial and caudal air sacs. To study the effects of bronchial structure, simple physical models of bird lungs were constructed. They suggested that, to achieve unidirectional flow, air in the caudal portion of the primary bronchus must be directed towards the orifices of the mediodorsal bronchi. To study the effect of air sac pressures, a controllable pressure difference was produced between the air sac orifices of fixed duck lungs. The cranial orifices had a higher pressure than the caudal ones during inhalation and vice versa during exhalation. There was a set of pressure differences for which the paleopulmo received the same flow rate during inhalation as during exhalation. High pressure differences caused more flow in the paleopulmo during exhalation than during inhalation; low pressure differences had the converse effect.

scholarly journals Numerical study of heat transfer in a porous medium of steel balls

2019 ◽  
Vol 23 (1) ◽  
pp. 271-279
Author(s):  
Mehmet Pamuk
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Numerical Study ◽  
Fluid Phase ◽  
Commercial Software ◽  
Number Range ◽  
Unidirectional Flow ◽  
Flow Through ◽  
Steel Balls

In this study, heat transfer in unidirectional flow through a porous medium with the fluid phase being water is analyzed using the commercial software Comsol?. The aim of the study is to validate the suitability of this package for similar problems regarding heat transfer calculations in unidirectional flow through porous media. The porous medium used in the study is comprised of steed balls of 3 mm in diameter filled in a pipe of 51.4 mm inner diameter. The superficial velocity range is 3-10 mm/s which correspond to a Reynolds number range of 150-500 for an empty pipe. Heat is applied peripherally on the outer surface of the pipe at a rate of 7.5 kW/m2 using electrical ribbon heaters. The numerical results obtained using the commercial software Comsol? are compared with those obtained in the experiments once conducted by the author of this article. Results have shown that Comsol? can generate reliable results in heat transfer problems through porous media, provided all parameters are selected correctly, thus making it unnecessary to prepare expensive experimental set-ups and spending extensive time to conduct experiments.

scholarly journals The wave-induced flow of internal gravity wavepackets with arbitrary aspect ratio

2017 ◽  
Vol 834 ◽  
pp. 385-408 ◽  
Author(s):  
T. S. van den Bremer ◽  
B. R. Sutherland
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Mean Flow ◽  
One Dimensional ◽  
Unidirectional Flow ◽  
Aspect Ratios ◽  
Non Local ◽  
Flow Through ◽  
Induced Flow ◽  
Wave Induced

We examine the wave-induced flow of small-amplitude, quasi-monochromatic, three-dimensional, Boussinesq internal gravity wavepackets in a uniformly stratified ambient. It has been known since Bretherton (J. Fluid Mech., vol. 36 (4), 1969, pp. 785–803) that one-, two- and three-dimensional wavepackets induce qualitatively different flows. Whereas the wave-induced mean flow for compact three-dimensional wavepackets consists of a purely horizontal localized circulation that translates with and around the wavepacket, known as the Bretherton flow, such a flow is prohibited for a two-dimensional wavepacket of infinite spanwise extent, which instead induces a non-local internal wave response that is long compared with the streamwise extent of the wavepacket. One-dimensional (horizontally periodic) wavepackets induce a horizontal, non-divergent unidirectional flow. Through perturbation theory for quasi-monochromatic wavepackets of arbitrary aspect ratio, we predict for which aspect ratios which type of induced mean flow dominates. We compose a regime diagram that delineates whether the induced flow is comparable to that of one-, two- or compact three-dimensional wavepackets. The predictions agree well with the results of fully nonlinear three-dimensional numerical simulations.

Application of a Momentum Integral Model to the Study of Parallel Channel Boiling Flow Oscillations

1963 ◽  
Vol 85 (1) ◽  
pp. 1-9 ◽  
Author(s):  
J. E. Meyer ◽  
R. P. Rose
Keyword(s):  
Method Comparison ◽  
Analytical Models ◽  
Integral Model ◽  
Flux Flow ◽  
Comparison With Experiment ◽  
Boiling Flow ◽  
Flow Oscillations ◽  
Flow Through ◽  
Momentum Integral ◽  
Spatially Varying

A method is discussed for treating oscillations in flow through a heated boiling channel which connects two plenum regions of constant pressure difference. The approach is based on a numerical solution of pointwise difference equations representing conservation laws in fluid and metal. It is appropriate for spatially varying heat flux, flow with or without slip, and large perturbations. Details of the method, comparison with experiment, and features which distinguish it from other analytical models are discussed.

Sign in / Sign up

Export Citation Format

Share Document