Unsteady Flow of Two Immiscible Fluids under an Oscillatory Time-dependent Pressure Gradient in a Channel with One Porous Floor

2006 ◽  
Vol 1 (2) ◽  
pp. 194-203 ◽  
Author(s):  
Sai K.S., . ◽  
N.S. Swamy . ◽  
H.R. Nataraja . ◽  
S.B. Tiwari . ◽  
B. Nageswara Rao .
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Immiscible Fluids ◽  
Time Dependent

On the Unsteady Flow of Two Incompressible Immiscible Second Grade Fluids between Two Parallel Plates

2014 ◽  
Vol 1016 ◽  
pp. 546-553
Author(s):  
Abdul M. Siddiqui ◽  
Maya K. Mitkova ◽  
Ali R. Ansari
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Analytical Solutions ◽  
Interface Velocity ◽  
Time Dependent ◽  
Second Grade ◽  
Parallel Plates ◽  
Governing Equations ◽  
Layer Flow ◽  
Second Grade Fluids

Unsteady, pressure driven in the gap between two parallel plates flow of two non-Newtonian incompressible second grade fluids is considered. The governing equations are established for the particular two-layer flow and analytical solutions of the equations that satisfy the imposed boundary conditions are obtained. The velocity of each fluid is expressed as function of the material constants, time dependent pressure gradient and other characteristics of the fluids. As part of the solution, an expression for the interface velocity is derived. We analyze the shift of the velocity maximum from one to another fluid as a function of variety of values of fluids’ parameters.

scholarly journals Numerical Study of Interface Tracking for the Unsteady Flow of Two Immiscible Micropolar and Newtonian Fluids Through a Horizontal Channel with an Unstable Interface

2021 ◽  
Vol 10 (4) ◽  
pp. 552-563
Author(s):  
Rajesh Kumar Chandrawat ◽  
Varun Joshi ◽  
O. Anwar Bég
Keyword(s):  
Shear Stress ◽  
Unsteady Flow ◽  
Pressure Gradient ◽  
Constant Pressure ◽  
Immiscible Fluids ◽  
Wave Number ◽  
Horizontal Channel ◽  
Surface Model ◽  
Fluid Interface ◽  
The Waves

The dynamics of the interaction between immiscible fluids is relevant to numerous complex flows in nature and industry, including lubrication and coating processes, oil extraction, physicochemical separation techniques, etc. One of the most essential components of immiscible flow is the fluid interface, which must be consistently monitored. In this article, the unsteady flow of two immiscible fluids i.e., an Eringen micropolar and Newtonian liquid is considered in a horizontal channel. Despite the no-slip and hyper-stick shear stress condition at the channel edge, it is accepted that the liquid interface is dynamic, migrating from one position to the next and possibly get absolute change; as a result, The CS (continuum surface) model is integrated with the single moment equation based on the VOF (volume of fluid) approach to trace the interface. The immiscible fluids are considered to flow under three applied pressure gradients (constant, decaying, and periodic) and flow is analyzed under seamless shear stress over the entire interface. The modified cubic b-spline differential quadrature method (MCB-DQM) is used to solve the modeled coupled partial differential equations for the fluid interface evolution. The advection and tracking of the interface with time, wave number, and amplitude are illustrated through graphs. It is observed that the presence of micropolar parameters affects the interface with time. The novelty of the current study is that previous studies (which considered the smooth and unstable movement of the micropolar fluid, the steady stream of two immiscible fluids, and interface monitoring through different modes) are extended and generalized to consider the time-dependent flow of two immiscible fluids namely Eringen micropolar and Newtonian with a moving interface in a horizontal channel. For the decaying pressure gradient case, which requires more time to achieve the steady-state, the peak of the waves resembles those for the constant pressure gradient case. The interface becomes steady for a more extensive time when a constant pressure gradient is applied. The interface becomes stable quickly with time as the micropolar parameter is decreased for the constant pressure gradient case i.e., weaker micropolar fluids encourage faster stabilization of the interface. With periodic pressure gradient, the interface takes more time to stabilize, and the crest of the waves is significantly higher in amplitude compared to the constant and decaying pressure cases. The simulations demonstrate the excellent ability of MCB-DQM to analyze complex interfacial immiscible flows.

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.

scholarly journals Steady and unsteady flow of non-newtonian fluid in curved pipe with triangular

2006 ◽  
Vol 3 (3) ◽  
pp. 470-480
Author(s):  
Baghdad Science Journal
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Curved Pipe ◽  
First Case ◽  
Stable Flow ◽  
Flow Cross

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

Time-Dependent Laminar Flow in Curved Channels

1970 ◽  
Vol 37 (3) ◽  
pp. 838-843 ◽  
Author(s):  
R. J. Nunge
Keyword(s):  
Laminar Flow ◽  
Pressure Gradient ◽  
Constant Pressure ◽  
Time Dependent ◽  
Pressure Gradients ◽  
Straight Channel ◽  
Curvature Ratio ◽  
Curved Channels ◽  
Developing Flow ◽  
Time Required

The velocity distribution for time-dependent laminar flow in curved channels is derived. The analysis applies to flows with pressure gradients which are arbitrary functions of time. Numerical results are obtained for developing flow due to a constant pressure gradient. Developing flow in a straight channel is also discussed and it is found that the curvature ratio has only a small effect on the time required to reach the fully developed state.

Comparisons of time dependent pier scour models under unsteady flow conditions

2014 ◽  
pp. 473-481
Author(s):  
J Hong ◽  
Y Chiew ◽  
P Yeh
Keyword(s):  
Unsteady Flow ◽  
Time Dependent ◽  
Flow Conditions ◽  
Pier Scour

Magnetorheological Flow in Pipes: An Exploration of the Time-Variation of Herschel-Bulkley Parameters

2007 ◽  
Author(s):  
Mario F. Letelier ◽  
Juan S. Stockle ◽  
Dennis A. Siginer
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Unsteady Flow ◽  
Yield Stress ◽  
Magnetic Fluid ◽  
Time Variation ◽  
Power Index ◽  
Time Structure ◽  
Time Dependent ◽  
Constitutive Parameters

In this paper it is analyzed the effects on the flow of the time-variation of Herschel-Bulkley model of fluid constitutive parameters. In this way, the influence of a varying magnetic field on the unsteady flow of a magnetic fluid is explored. Yield stress, viscosity and power index are assumed time-dependent. In particular, linear variations in time of these parameters are considered. The characteristics of the velocity field is analyzed for different values of the constants that determine the time structure of the constitutive parameters.

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