Pressure drop due to viscous flow through cylinders

1959 ◽  
Vol 6 (4) ◽  
pp. 542-546 ◽  
Author(s):  
Howard Brenner
Keyword(s):  
Pressure Drop ◽  
Circular Cylinder ◽  
Viscous Fluid ◽  
Viscous Flow ◽  
Steady Flow ◽  
Equations Of Motion ◽  
Point Force ◽  
Flow Through ◽  
Bounding Surfaces ◽  
Simple Fashion

A general formula is developed which permits a calculation of the pressure drop arising from the slow steady flow of a viscous fluid through a circular cylinder for arbitrarily assigned conditions of velocity on the bounding surfaces of the cylinder. In particular, the diminution in pressure can be calculated directly from the prescribed boundary velocities without requiring a detailed solution of the equations of motion. Hence it is possible to compute, in comparatively simple fashion, the magnitude of this macroscopic parameter for a large variety of complex motions which would normally present great analytical difficulties.By way of illustration the additional pressure drop arising from the presence of a point force situated along the axis of a cylinder is calculated. The additional force required to maintain the motion in the presence of the obstacle is exactly twice the magnitude of the point force itself.

Calculations of unsteady viscous flow past a circular cylinder

1958 ◽  
Vol 4 (1) ◽  
pp. 81-86 ◽  
Author(s):  
R. B. Payne
Keyword(s):  
Circular Cylinder ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Viscous Flow ◽  
Steady Flow ◽  
Reynolds Numbers ◽  
A Value ◽  
Unsteady Viscous Flow ◽  
Starting Flow ◽  
Forward Integration

A numerical solution has been obtained for the starting flow of a viscous fluid past a circular cylinder at Reynolds numbers 40 and 100. The method used is the step-by-step forward integration in time of Helmholtz's vorticity equation. The advantage of working with the vorticity is that calculations can be confined to the region of non-zero vorticity near the cylinder.The general features of the flow, including the formation of the eddies attached to the rear of the cylinder, have been determined, and the drag has been calculated. At R = 40 the drag on the cylinder decreases with time to a value very near that for the steady flow.

scholarly journals On compressible and piezo-viscous flow in thin porous media

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170601 ◽  
Author(s):  
F. Pérez-Ràfols ◽  
P. Wall ◽  
A. Almqvist
Keyword(s):  
Porous Media ◽  
Pressure Drop ◽  
Viscous Fluid ◽  
Linear Equation ◽  
Nonlinear Function ◽  
Viscous Fluids ◽  
Total Flow ◽  
Thin Porous Media ◽  
Flow Through ◽  
The One

In this paper, we study flow through thin porous media as in, e.g. seals or fractures. It is often useful to know the permeability of such systems. In the context of incompressible and iso-viscous fluids, the permeability is the constant of proportionality relating the total flow through the media to the pressure drop. In this work, we show that it is also relevant to define a constant permeability when compressible and/or piezo-viscous fluids are considered. More precisely, we show that the corresponding nonlinear equation describing the flow of any compressible and piezo-viscous fluid can be transformed into a single linear equation. Indeed, this linear equation is the same as the one describing the flow of an incompressible and iso-viscous fluid. By this transformation, the total flow can be expressed as the product of the permeability and a nonlinear function of pressure, which represents a generalized pressure drop.

scholarly journals The steady flow of viscous fluid past a fixed spherical obstacle at small reynolds numbers

1929 ◽  
Vol 123 (791) ◽  
pp. 225-235 ◽  
Keyword(s):  
Viscous Fluid ◽  
Steady Flow ◽  
Kinematic Viscosity ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Great Distance ◽  
Small Reynolds Numbers

It was proposed by Oseen that, in considering the steady flow of a viscous fluid past a fixed obstacle, the velocity of disturbance should be considered small, and terms depending on its square neglected. This approximation is to be taken to hold not only at a great distance from the obstacle, but also right up to its surface; and involves the assumption that U d/v is small, where d is some representative length of the obstacle, which in the case of a sphere is taken to be its diameter, U is the undisturbed velocity of the stream, and v the kinematic viscosity of the fluid. With this approximation, the equations of motion become linear, and can be solved; the condition of no slip at the boundary is then applied to complete the solution. We take the obstacle to be a sphere of radius and take the origin of coordinates at its centre.

Impulsive Motion of a Moving Circular Cylinder in a Viscous Flow by the Numerical Simulation

1998 ◽  
Vol 14 (3) ◽  
pp. 119-123
Author(s):  
D. L. Young ◽  
J. T. Chang
Keyword(s):  
Circular Cylinder ◽  
Viscous Fluid ◽  
Viscous Flow ◽  
Drag Force ◽  
Moving Boundary ◽  
Stokes Equations ◽  
Flow Theory ◽  
Infinite Domain ◽  
Constant Acceleration ◽  
Element Method

ABSTRACTAn innovative computation procedure is developed to solve the external flow problems for viscous fluids. The method is able to handle the infinite domain so that it is convenient for the external flows. The code is based on the projection method of the Navier-Stokes equations. We use the three-step explicit finite element method to solve the momentum equation by extracting the boundary effects from the finite computation domain. The pressure Poisson equation for the external field is treated by the boundary element method. The arbitrary Lagrangian-Eulerian (ALE) scheme is employed to incorporate the present algorithm to deal with the moving boundary, such as the motion of an impulsively moving circular cylinder in a viscous fluid. The model demonstrates that drag force is well predicted for a circular cylinder moving in a still viscous fluid starting from rest, to a constant acceleration, and then maintaining at a uniform velocity. In the constant acceleration phase, the drag force is closed to the added mass effect from the ideal flow theory. On the other hand, the drag force is equal to viscous flow theory in the constant velocity phase.

An Asymptotic Model of Viscous Flow Limitation in a Highly Collapsed Channel

1998 ◽  
Vol 120 (4) ◽  
pp. 544-546 ◽  
Author(s):  
O. E. Jensen
Keyword(s):  
Pressure Drop ◽  
Viscous Flow ◽  
External Pressure ◽  
Asymptotic Model ◽  
Flow Limitation ◽  
Two Dimensional ◽  
Inertial Effects ◽  
Channel One ◽  
Narrow Region ◽  
Flow Through

A viscous flow through a long two-dimensional channel, one wall of which is formed by a finite-length membrane, experiences flow limitation when the channel is highly collapsed over a narrow region under high external pressure. Simple approximate relations between flow rate and pressure drop are obtained for this configuration by the use of matched asymptotic expansions. Weak inertial effects are also considered.

Viscous flow through a grating or lattice of cylinders

1964 ◽  
Vol 18 (1) ◽  
pp. 94-96 ◽  
Author(s):  
Joseph B. Keller
Keyword(s):  
Pressure Drop ◽  
Viscous Flow ◽  
Lubrication Theory ◽  
Cross Sectional ◽  
Flow Through ◽  
Square Array

Viscous flow perpendicular to a line (or ‘grating’) of evenly spaced identical cylinders is considered in the case when the spacing between the cylinders is much smaller than their cross-sectional dimensions. Lubrication theory is used to find the pressure drop across the grating and hence the force on each cylinder. A square array (or ‘lattice’) of closely packed cylinders is similarly treated.

Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100

1970 ◽  
Vol 42 (3) ◽  
pp. 471-489 ◽  
Author(s):  
S. C. R. Dennis ◽  
Gau-Zu Chang
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Steady Flow ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Reliable Data ◽  
Time Dependent ◽  
Cylinder Surface ◽  
Number Range

Finite-difference solutions of the equations of motion for steady incompressible flow around a circular cylinder have been obtained for a range of Reynolds numbers from R = 5 to R = 100. The object is to extend the Reynolds number range for reliable data on the steady flow, particularly with regard to the growth of the wake. The wake length is found to increase approximately linearly with R over the whole range from the value, just below R = 7, at which it first appears. Calculated values of the drag coefficient, the angle of separation, and the pressure and vorticity distributions over the cylinder surface are presented. The development of these properties with Reynolds number is consistent, but it does not seem possible to predict with any certainty their tendency as R → ∞. The first attempt to obtain the present results was made by integrating the time-dependent equations, but the approach to steady flow was so slow at higher Reynolds numbers that the method was abandoned.

The Reaction of a Stream of Viscous Fluid on a Rotating Circular Cylinder

1925 ◽  
Vol 29 (170) ◽  
pp. 100-104
Author(s):  
A. R. Low
Keyword(s):  
Angular Velocity ◽  
Circular Cylinder ◽  
Viscous Fluid ◽  
Special Reference ◽  
Steady Flow ◽  
Experimental Investigations ◽  
Rotating Circular Cylinder ◽  
Wing Profile ◽  
Small Correction ◽  
The Subject

At the request of the Council the following notes on the subject have been prepared, with special reference to the Flettner “rotor ship” and to possible applications in aeronautics.While it is necessarily somewhat provisional, the data available are pretty full, and it is hoped that no serious modifications will be required as a result of further experimental investigations.In the now well-known Joukowsky transformation from a circle to a wing profile, maintaining the circulation G and the steady flow at a distance U, unaltered, the diameter of the cylinder 2a, its angular velocity ω, the chord of the profile 4a. (subject to a small correction of about – 5 per cent) and the effective incidence (β are connected by the relations G = 2πa2ω = 4πa sin βU so that aω/2U = sin β.

scholarly journals The existence of steady flow in a collapsed tube

1989 ◽  
Vol 206 ◽  
pp. 339-374 ◽  
Author(s):  
O. E. Jensen ◽  
T. J. Pedley
Keyword(s):  
Pressure Drop ◽  
Energy Loss ◽  
Steady Flow ◽  
Flow Rate ◽  
Transmural Pressure ◽  
Tube Model ◽  
Collapsible Tube ◽  
One Dimensional ◽  
Flow Through ◽  
Range Of Values

Self-excited oscillations arise during flow through a pressurized segment of collapsible tube, for a range of values of the time-independent controlling pressures. They come about either because there is an (unstable) steady flow corresponding to these pressures, or because no steady flow exists. We investigate the existence of steady flow in a one-dimensional collapsible-tube model, which takes account of both longitudinal tension and jet energy loss E downstream of the narrowest point. For a given tube, the governing parameters are flow-rate Q, and transmural pressure P at the downstream end of the collapsible segment. If E = 0, there exists a range of (Q, P)-values for which no solutions exist; when E ≠ 0 a solution is always found. For the case E ≠ 0, predictions are made of pressure drop along the collapsible tube; these solutions are compared with experiment.

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