Approximate and Analytic Solutions for Deformation of Finite Porous Filters

1997 ◽  
Vol 64 (4) ◽  
pp. 929-934 ◽  
Author(s):  
S. I. Barry ◽  
G. N. Mercer ◽  
C. Zoppou
Keyword(s):  
Fluid Flow ◽  
Steady State ◽  
Porous Material ◽  
Deformation Behavior ◽  
Fluid Velocity ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Solid Stress ◽  
Side Walls

The deformation, using linear poroelasticity, of a two-dimensional box of porous material due to fluid flow from a line source is considered as a model of certain filtration processes. Analytical solutions for the steady-state displacement, pressure, and fluid velocity are derived when the side walls of the filter have zero solid stress. A numerical solution for the case where the porous material adheres to the side walls is also found. It will be shown, however, that simpler approximate solutions can be derived which predict the majority of the deformation behavior of the filter.

scholarly journals Analytic solutions for Long's equation and its generalization

2017 ◽  
Vol 24 (4) ◽  
pp. 727-735
Author(s):  
Mayer Humi
Keyword(s):  
Steady State ◽  
Gravity Waves ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Atmospheric Flow ◽  
Flow Over Topography ◽  
Isothermal Flows

Abstract. Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.

scholarly journals Liquid-liquid separation using steady-state bed coalescer

2016 ◽  
Vol 70 (4) ◽  
pp. 367-381 ◽  
Author(s):  
Radmila Secerov-Sokolovic ◽  
Dunja Sokolovic ◽  
Dragan Govedarica
Keyword(s):  
Fluid Flow ◽  
Steady State ◽  
Current Knowledge ◽  
Fluid Velocity ◽  
Engineering Application ◽  
Flow Mode ◽  
Liquid Separation ◽  
Emulsion Flow ◽  
Flow Through ◽  
Mode Fibre

This paper presents a literature review on the current understanding of liquid-liquid separation that is immensely widespread in practice, highlighting the steady-state bed coalescer being a good solution in various engineering application. Generally, the fibre bed coalescence has proven to be very effective separation method in the industry. Due to the complexity of bed coalescence phenomenon coalescer design and sizing procedure relies on experimental test. This review provides a research overview of the key phenomena essential for the efficient bed coalescence, such as mechanisms of droplet coalescence and emulsion flow through the fibre bed. In addition to this provides an overview of the current knowledge about coalescer?s design properties and variables such as: fluid velocity, fluid flow orientation/flow mode, fibre bed geometry, and bed length.

Three-Dimensional Steady-State String Motion in a Fluid Flow

2004 ◽  
Vol 71 (6) ◽  
pp. 894-895
Author(s):  
Roman Miroshnik
Keyword(s):  
Fluid Flow ◽  
Steady State ◽  
Three Dimensional ◽  
Initial Approximation ◽  
Invariant Curve ◽  
Perturbation Scheme ◽  
Two Dimensional ◽  
Flowing Medium ◽  
Steady State Motion ◽  
Existence Conditions

The phenomenon of three-dimensional (3D) steady-state motion of a string traveling along an invariant curve in a flowing medium is studied. Existence conditions are found using a perturbation scheme where a known two-dimensional (2D) solution is used as an initial approximation.

scholarly journals Analytic Solutions for Long's Equation and its Generalization

2017 ◽  
Author(s):  
Mayer Humi
Keyword(s):  
Steady State ◽  
Gravity Waves ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Atmospheric Flow ◽  
Flow Over Topography ◽  
Isothermal Flows

Abstract. Two dimensional, steady state, stratified, isothermal, atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic type solutions in addition to regular gravity waves. These new analytical solutions provide insights about the propagation and amplitude of gravity waves over topography.

Effect of Parallel Plane Walls on Vortex-Induced Oscillations of a Cylinder

2006 ◽  
Author(s):  
Shuichi Kato ◽  
Shunsuke Aritomi ◽  
Shinichi Maruyama ◽  
Masatsugu Yoshizawa
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Time History ◽  
Narrow Channel ◽  
Particle Image Velocimetry System ◽  
Blockage Ratio ◽  
Two Dimensional ◽  
Spring Stiffness ◽  
Lock In

This paper addresses the vortex-induced oscillations of a spring-supported cylinder in a narrow channel. The characteristics of the two-dimensional laminar fluid flow in a narrow channel deeply depend on the oscillations of the cylinder. The main purpose of this paper is to clarify the effects of channel walls on the nonlinear interaction between transverse oscillations of the cylinder and the unsteady fluid flow in a narrow channel. The following two problems were investigated in order to estimate the effect of channel walls. First, the spring stiffness, which supports a cylinder in a narrow channel, is varied. As the spring stiffness becomes weak, the time history of the cylinder displacement includes not only an oscillating component (A.C.), but also a constant component (D.C.). The numerical results indicated that the D.C. component is generated by viscous force. Second, the frequency and amplitude of the cylinder oscillation and vortex-shedding frequency are measured in and around the lock-in region in case of a blockage ratio w = 2.5. The blockage ratio is the ratio of the channel width to the cylinder diameter. The results in the lock-in region in a narrow channel are different than in the general wall-less lock-in region where such behaviors have never been observed. In this study, the experiments are also performed at Reynolds numbers Re below 200. The cylinder motion and the fluid velocity are simultaneously measured with an angular displacement meter and a PIV (Particle Image Velocimetry) system, respectively. Furthermore, the experimental results are compared with the theoretical results that are obtained from the numerical calculation of the two-dimensional incompressible Navier-Stokes equations.

scholarly journals Hydrodynamical Study of Creeping Maxwell Fluid Flow through a Porous Slit with Uniform Reabsorption and Wall Slip

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1852
Author(s):  
Hameed Ullah ◽  
Dianchen Lu ◽  
Abdul Majeed Siddiqui ◽  
Tahira Haroon ◽  
Khadija Maqbool
Keyword(s):  
Fluid Flow ◽  
Physical Phenomenon ◽  
Fluid Velocity ◽  
Axial Flow ◽  
Maximum Velocity ◽  
Maxwell Fluid ◽  
Two Dimensional ◽  
Mathematical Basis ◽  
Analytical Technique ◽  
The Impact

The present theoretical study investigates the influence of velocity slip characteristics on the plane steady two-dimensional incompressible creeping Maxwell fluid flow passing through a porous slit with uniform reabsorption. This two-dimensional flow phenomenon is governed by the mathematical model having nonlinear partial differential equations together with non-homogeneous boundary conditions. An analytical technique, namely the recursive approach, is used successfully to find the solutions of the problem. The explicit expressions for stream function, velocity components, pressure distribution, wall shear stress and normal stress difference have been derived. The axial flow rate, leakage flux and fractional reabsorption are also found out. The points of maximum velocity are identified. Non-dimensionalization is carried out and graphs are portrayed at different positions of the channel to show the impact of pertinent parameters: slip parameter, Maxwell fluid parameter and absorption parameter, on flow variables and found that the fluid velocity is affected significantly due to these parameters. This study provides a mathematical basis to understand the physical phenomenon for fluid flows through permeable boundaries which exists in different problems like gaseous diffusion, filtration and biological mechanisms.

Approximate solutions of transient and two-dimensional flame phenomena: constant-enthalpy flames

1958 ◽  
Vol 245 (1242) ◽  
pp. 352-372 ◽  
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Exact Solutions ◽  
Approximate Solutions ◽  
Large Mass ◽  
Boundary Layer Theory ◽  
Two Dimensional ◽  
Hot Gas ◽  
Finite Slab ◽  
Better Than

The ‘profile’ methods of boundary-layer theory are adapted to predict the behaviour of the transient flames resulting from contact of semi-infinite burnt and unburnt gas masses, contact of unburnt gas with an adiabatic catalyst, immersion of a finite slab of unburnt gas in a large mass of hot gas, and immersion of a finite slab of burnt gas in a large mass of unburnt. Comparison with some exact solutions suggests that the accuracy is normally better than 20%. The method is simple to use. The results are also relevant to two-dimensional steady-state flames.

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