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.

Numerical Prediction of the Pipeline Flow Characteristics of Thixotropic Liquids

1967 ◽  
Vol 7 (04) ◽  
pp. 369-376 ◽  
Author(s):  
R.A. Ritter ◽  
J.P. Batycky
Keyword(s):  
Shear Rate ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Pressure Gradient ◽  
Rheological Properties ◽  
Flow Rate ◽  
Time Dependent ◽  
Flow Rates ◽  
Instantaneous Pressure ◽  
Pipeline Design

Abstract A numerical technique has been developed to permit establishing the pressure gradient associated with laminar flow of thixotropic liquids through long pipelines. For this purpose the pipeline is divided into a number of radial and longitudinal increments within which rheological properties of the fluid may be considered as constant at any time. Then, provided only that the fluid flow curve is defined at every duration of shear, it is possible to predict the instantaneous pressure gradient at any cross-section along the pipeline for each desired flow rate and pipe size. The technique consists of an iterative integration of shear rate to establish the appropriate value of the wall shear stress at each location. Consistency of fluid in the increment is determined by the flow history of that increment, while the radial flow) associated with variations in velocity profile is accounted for by adjusting the width and radial position of the increment. A number of pressure profiles, computed at each of several flow rates, provide a convenient basis for pipeline design and pump selection. Introduction In recent years, considerable attention has been given to predicting pressure drop associated with the isothermal laminar flow of time-independent non-Newtonian fluids in pipes and annuli. The approach generally has been m develop analytical relationships between flow rate and pressure drop based on simple constitutive models which hopefully provide an approximate description of the rheological properties of the fluid. Analytical solutions are highly desirable since the influence of all pertinent parameters can be readily determined. Unfortunately, however, this approach is restricted to simple flow geometries and frequently leads to erroneous results due to inadequacies in the model. In certain cases a solution may be obtained through applying appropriate numerical techniques For example, a digital computer program is available for predicting the velocity profile and pressure drop encountered by any Newtonian or time-independent non-Newtonian fluid flowing under laminar conditions in a cylindrical pipe or annulus. In this paper the consistency behavior of the fluid need only be described in terms of basic rheological data. Analyzing flow systems involving fluids with time-dependent rheological characteristics is considerably more complicated since substantial changes in consistency may occur because of sustained shear action. This sensitivity to shear frequently persists for several hours. Consequently, variations in pressure drop and/or flow rate resulting from the aging process and addition of unsheared or partially sheared fluid to the system must be considered for purposes of pipeline design. This paper outlines a numerical method for predicting the transient and steady-state laminar flow behavior of a thixotropic liquid in a pipeline of arbitrary length (i.e., at a specified constant flow rate, the instantaneous pressure gradient may be determined at any time after start up and at any location along the pipeline). Several such pressure gradient profiles computed at several flow rates, may be combined to produce a complete portrait of the system response. This flow portrait provides a reasonable basis for pipeline design and for selecting a suitable pump characteristic. TIME-DEPENDENT RHEOLOGICAL BEHAVIOR The most familiar time-dependent rheological properties are those exhibited by thixotropic liquids. Many of these materials, particularly thixotropic crude oils, generally display an apparent yield stress in that a finite pressure gradient is required to initiate flow. Then, under the influence of sustained shear at a constant shear rate, the consistency systematically decreases to some final limiting value. SPEJ P. 369ˆ

Effects of an external constant pressure gradient on a steady incompressible laminar flow through a semi-porous annular pipe

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Guy Leopold Mbogba ◽  
Elisabeth Ngo Nyobe ◽  
Maurice Lamara ◽  
Yves Christian Mbono Samba ◽  
Elkana Pemha
Keyword(s):  
Laminar Flow ◽  
Pressure Gradient ◽  
Steady Flow ◽  
Constant Pressure ◽  
Stokes Equations ◽  
Outer Wall ◽  
Optimization Method ◽  
External Pressure ◽  
Injection Velocity ◽  
Annular Pipe

Abstract In this paper, we examine a steady laminar flow for an incompressible fluid located in a semi porous annular pipe and subjected to a favorable constant pressure gradient applied between the two borders of the pipe. The inner wall is impermeable and the fluid is sucked or injected at the outer wall at constant and uniform velocity, orthogonally to the wall. The problem under study depends on three parameters: the pipe gap ratio, the dimensionless external pressure gradient, and the Reynolds number defined from the sum of the suction or injection velocity and the maximum Hagen–Poiseuille velocity. The conservation of mass induces the zero-divergence velocity field which allows replacing the steady-flow Navier–Stokes equations with a single equation satisfied by the stream function and called the vorticity equation. Assuming the similarity-solution hypothesis, the problem under consideration is reduced to a fourth-order nonlinear ordinary differential equation with two boundary conditions at each wall. The numerical shooting technique including the Runge–Kutta algorithm and the Newton–Raphson optimization method is applied to obtain the solution for the steady flow. For various values of the dimensionless external pressure gradient, the profiles of the velocity components are found and investigations on the wall shear stress for both walls are performed. The results obtained are discussed and physical understandings for the problem studied are derived.

scholarly journals ANALYTICAL SOLUTION FOR TRANSIENT ONEDIMENSIONAL COUETTE FLOW CONSIDERING CONSTANT AND TIME-DEPENDENT PRESSURE GRADIENTS

2009 ◽  
Vol 8 (2) ◽  
pp. 92 ◽  
Author(s):  
A. A. Mendiburu ◽  
L. R. Carrocci ◽  
J. A. Carvalho
Keyword(s):  
Pressure Gradient ◽  
Couette Flow ◽  
Stokes Equations ◽  
Transient State ◽  
Integral Transforms ◽  
Time Dependent ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Navier Stokes Equations ◽  
The One

This paperaims to determine the velocity profile, in transient state, for a parallel incompressible flow known as Couette flow. The Navier-Stokes equations were applied upon this flow. Analytical solutions, based in Fourier series and integral transforms, were obtained for the one-dimensional transient Couette flow, taking into account constant and time-dependent pressure gradients acting on the fluid since the same instant when the plate starts it´s movement. Taking advantage of the orthogonality and superposition properties solutions were foundfor both considered cases. Considering a time-dependent pressure gradient, it was found a general solution for the Couette flow for a particular time function. It was found that the solution for a time-dependent pressure gradient includes the solutions for a zero pressure gradient and for a constant pressure gradient.

Approximate Calculation of Pressure Drop in Laminar Flow of Generalized Newtonian Liquid Through Channel of Noncircular Cross Section

1994 ◽  
Vol 59 (3) ◽  
pp. 603-615 ◽  
Author(s):  
Václav Dolejš ◽  
Ivan Machač ◽  
Petr Doleček
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Numerical Solution ◽  
Cross Section ◽  
Approximate Calculation ◽  
Newtonian Liquid ◽  
Straight Channel ◽  
Suggested Procedure ◽  
Noncircular Cross Section ◽  
Calculation Results

The paper presents a modification of the equations of Rabinowitsch-Mooney type for an approximate calculation of pressure drop in laminar flow of generalized Newtonian liquid through a straight channel whose cross section forms a simple continuous area. The suitability of the suggested procedure of calculation of pressure drop is demonstrated by the comparison of calculation results with both the published and original results of numerical solution and experiments.

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 Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces

1985 ◽  
Vol 40 (10) ◽  
pp. 959-967
Author(s):  
A. Salat
Keyword(s):  
Magnetic Field ◽  
Hamiltonian System ◽  
Magnetic Fields ◽  
Constant Pressure ◽  
Time Dependent ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Mhd Equilibrium ◽  
Magnetic Surfaces ◽  
Rotational Transform

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

scholarly journals Determinants of valve gating in collecting lymphatic vessels from rat mesentery

2011 ◽  
Vol 301 (1) ◽  
pp. H48-H60 ◽  
Author(s):  
Michael J. Davis ◽  
Elaheh Rahbar ◽  
Anatoliy A. Gashev ◽  
David C. Zawieja ◽  
James E. Moore
Keyword(s):  
Pressure Gradient ◽  
Muscle Tone ◽  
Lymphatic Vessels ◽  
Vessel Diameter ◽  
Intraluminal Pressure ◽  
Pressure Gradients ◽  
Rat Mesentery ◽  
Temporal Relationships ◽  
Wide Range ◽  
Valve Opening

Secondary lymphatic valves are essential for minimizing backflow of lymph and are presumed to gate passively according to the instantaneous trans-valve pressure gradient. We hypothesized that valve gating is also modulated by vessel distention, which could alter leaflet stiffness and coaptation. To test this hypothesis, we devised protocols to measure the small pressure gradients required to open or close lymphatic valves and determine if the gradients varied as a function of vessel diameter. Lymphatic vessels were isolated from rat mesentery, cannulated, and pressurized using a servo-control system. Detection of valve leaflet position simultaneously with diameter and intraluminal pressure changes in two-valve segments revealed the detailed temporal relationships between these parameters during the lymphatic contraction cycle. The timing of valve movements was similar to that of cardiac valves, but only when lymphatic vessel afterload was elevated. The pressure gradients required to open or close a valve were determined in one-valve segments during slow, ramp-wise pressure elevation, either from the input or output side of the valve. Tests were conducted over a wide range of baseline pressures (and thus diameters) in passive vessels as well as in vessels with two levels of imposed tone. Surprisingly, the pressure gradient required for valve closure varied >20-fold (0.1–2.2 cmH2O) as a passive vessel progressively distended. Similarly, the pressure gradient required for valve opening varied sixfold with vessel distention. Finally, our functional evidence supports the concept that lymphatic muscle tone exerts an indirect effect on valve gating.

Time Dependent Magnetic Switching in Spin Valve Structures

1995 ◽  
Vol 384 ◽  
Author(s):  
J. B. Restorff ◽  
M. Wun-Fogle ◽  
S. F. Cheng ◽  
K. B. Hathaway
Keyword(s):  
Giant Magnetoresistance ◽  
Spin Valve ◽  
Time History ◽  
Time Dependent ◽  
Si Substrates ◽  
Magnetic Switching ◽  
Magnetic Aftereffect ◽  
Magnetron Sputter Deposition ◽  
History Of ◽  
Time Required

ABSTRACTWe have observed time dependent magnetic switching in spin-valve sandwich structures of Cu/Co/Cu/Fe films grown on silicon and Kapton substrates and Permalloy/Co/Cu/Co films grown on NiO or NiO/CoO coated Si substrates. The giant magnetoresistance (MR) values ranged from 1 to 3 percent at room temperature. The films were grown by DC magnetron sputter deposition. Measurements were made on the time required for the MR to stabilize to about 1 part in 104 after the applied field was incremented. This time depends almost linearly on the amplitude of the timedependent MR change with a slope (time / ΔMR) of 20 000 to 30 000 s. Some samples took as long as 70 s to stabilize. The time dependent effects may be important for devices operating in these regions of the magnetoresistance curve. In addition, measurements were made on the time history of the MR value for a period of 75 s following a step change in the field from saturation. We observed that the time dependent behavior of the MR values of both experiments produced an excellent fit to a function of the form ΔMR(t) = α + β;ln(t) where ɑ and β are constants. This time dependence was consistent with the behavior of the magnetic aftereffect.

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