Properties of inviscid, recirculating flows

1965 ◽  
Vol 22 (2) ◽  
pp. 337-346 ◽  
Author(s):  
W. W. Wood
Keyword(s):  
Velocity Gradient ◽  
Inviscid Flow ◽  
Rotating Cylinder ◽  
Fluid Particle ◽  
Inviscid Fluid ◽  
Viscous Forces ◽  
Rotation Axes ◽  
Total Head ◽  
Recirculating Flows ◽  
Integral Relations

Integral relations are derived for steady, incompressible recirculating motions with small viscous forces. The circuit time of a fluid particle on a closed streamline in steady, inviscid flow is shown to be the same for all the closed streamlines on a surface of constant total head.The discontinuities of velocity and velocity gradient that occur in the motion of inviscid fluid filling a closed, rotating cylinder set in a rotating support with the two rotation axes slightly misaligned are then investigated.

The Estimation of Laminar Skin Friction, including the Effects of Distributed Suction

1960 ◽  
Vol 11 (1) ◽  
pp. 1-21 ◽  
Author(s):  
N. Curle
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Simple Formula ◽  
Outer Part ◽  
Order Correction ◽  
Viscous Effects ◽  
Viscous Forces ◽  
Exact Theory ◽  
Total Head

SummaryStratford's analysis of the laminar boundary layer near separation uses two physical ideas. In the outer part of the boundary layer, where viscous effects are small, the development is given by the condition that the total head is constant along streamlines, apart from a second-order correction for viscosity. Near the wall, however, viscous forces must balance the pressure forces, and the profile adjusts itself accordingly. Quantitatively these ideas yield a simple formula for predicting separation, which has been found to be particularly accurate.In this paper it is indicated how the same approach may be used to yield the full distribution of skin friction along the wall. Further, the effects of suction may be incorporated into the method. Physically, suction affects the outer part of the boundary layer in that the streamlines are drawn towards the wall when suction is applied. At the wall, the balance between viscous and pressure forces is influenced by the momentum of the fluid which is sucked away. When these effects are accounted for quantitatively, the resulting formula for the skin friction is still very simple.Several examples are considered, and comparison is made with exact theory and with approximate results by other methods. It is indicated that the method has a useful range of validity.

Viscous and inviscid flows in a channel with a moving indentation

1989 ◽  
Vol 209 ◽  
pp. 543-566 ◽  
Author(s):  
M. E. Ralph ◽  
T. J. Pedley
Keyword(s):  
Flow Rate ◽  
Small Amplitude ◽  
Inviscid Flow ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Generation Process ◽  
Vorticity Distribution ◽  
Downstream Flow ◽  
Upstream Flow

The flow in a channel with an oscillating constriction has been studied by the numerical solution of the Navier-Stokes and Euler equations. A vorticity wave is found downstream of the constriction in both viscous and inviscid flow, whether the downstream flow rate is held constant and the upstream flow is pulsatile, or vice versa. Closed eddies are predicted to form between the crests/troughs of the wave and the walls, in the Euler solutions as well as the Navier-Stokes flows, although their structures are different in the two cases.The positions of wave crests and troughs, as determined numerically, are compared with the predictions of a small-amplitude inviscid theory (Pedley & Stephanoff 1985). The theory agrees reasonably with the Euler equation predictions at small amplitude (ε [lsim ] 0.2) as long as the downstream flow rate is held fixed; otherwise a sinusoidal displacement is superimposed on the computed crest positions. At larger amplitude (ε = 0.38) the wave crests move downstream more rapidly than predicted by the theory, because of the rapid growth of the first eddy (‘eddy A’) attached to the downstream end of the constriction. At such larger amplitudes the Navier-Stokes predictions also agree well with the Euler predictions, when the downstream flow rate is held fixed, because the wave generation process is essentially inviscid and the undisturbed vorticity distribution is the same in each case. It is quite different, however, when the upstream flow rate is fixed, as in the experiments of Pedley & Stephanoff, because of differences in the undisturbed vorticity distribution, in the growth rate of the vorticity waves and in the dynamics of eddy A. A further finite-amplitude effect of importance, especially in an inviscid fluid, is the interaction of an eddy with its images in the channel walls.

scholarly journals Lie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
R. Sadat ◽  
Praveen Agarwal ◽  
R. Saleh ◽  
Mohamed R. Ali
Keyword(s):  
Euler Equations ◽  
Inviscid Flow ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Inviscid Fluid ◽  
Analysis Method ◽  
Governing Equations ◽  
Lie Symmetry Analysis ◽  
Cartesian Plane ◽  
Intensive Observation

AbstractThrough the Lie symmetry analysis method, the axisymmetric, incompressible, and inviscid fluid is studied. The governing equations that describe the flow are the Euler equations. Under intensive observation, these equations do not have a certain solution localized in all directions $(r,t,z)$ ( r , t , z ) due to the presence of the term $\frac{1}{r}$ 1 r , which leads to the singularity cases. The researchers avoid this problem by truncating this term or solving the equations in the Cartesian plane. However, the Euler equations have an infinite number of Lie infinitesimals; we utilize the commutative product between these Lie vectors. The specialization process procures a nonlinear system of ODEs. Manual calculations have been done to solve this system. The investigated Lie vectors have been used to generate new solutions for the Euler equations. Some solutions are selected and plotted as two-dimensional plots.

Vibrations of Circular Cylindrical Shells With Nonuniform Constraints, Elastic Bed and Added Mass Coupled to Internal, External and Annular Flow

2002 ◽  
Author(s):  
M. Amabili ◽  
R. Garziera
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Computer Code ◽  
Inviscid Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Forces ◽  
Added Masses ◽  
Circular Cylindrical Shells ◽  
Lumped Masses

The effect of steady viscous forces on vibrations of shell with internal and annular flow has been considered by using the time-mean Navier-Stokes equations. The model developed by Amabili & Garziera (2000), capable of simulating shells with non-uniform boundary conditions, added masses and partial elastic bed, has been extended to include non-uniform prestress. The effect of steady viscous forces has been added to the inviscid flow formulation considered by Amabili & Garziera (2002). The computer code DIVA has been developed by using the model developed in the present study. It has been validated by comparison with available results for shells with uniform constraints and has been used to study shells with non-uniform constraints and added lumped masses.

Boundary-layer flow around a submerged circular cylinder induced by free-surface travelling waves

1996 ◽  
Vol 316 ◽  
pp. 241-257 ◽  
Author(s):  
B. Yan ◽  
N. Riley
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Wave Amplitude ◽  
Perturbation Methods ◽  
Travelling Waves ◽  
Inviscid Flow ◽  
Steady Streaming ◽  
Viscous Forces ◽  
Layer Flow ◽  
Streaming Motion

We consider the fluid flow induced when free-surface travelling waves pass over a submerged circular cylinder. The wave amplitude is assumed to be small, and a suitably defined Reynolds number large, so that perturbation methods may be employed. Particular attention is focused on the steady streaming motion, which induces circulation about the cylinder. The viscous forces acting on the cylinder are calculated and compared with the pressure forces which are solely responsible for the loading on the cylinder in a purely inviscid flow.

Aerodynamics of slot-film cooling: theory and experiment

1985 ◽  
Vol 160 ◽  
pp. 15-27 ◽  
Author(s):  
A. D. Fitt ◽  
J. R. Ockendon ◽  
T. V. Jones
Keyword(s):  
Integral Equation ◽  
Film Cooling ◽  
Nonlinear Integral Equation ◽  
Free Stream ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Total Head ◽  
Slot Film Cooling ◽  
Range Of Values ◽  
Theory And Experiment

A simple model is proposed for the two-dimensional injection of irrotational inviscid fluid from a slot into a free stream. In a certain range of values of the ratio of free-stream to injection total heads, the film thickness satisfies a nonlinear integral equation whose solution enables the mass flow in the film to be found. Some experiments are described which both agree with this theory when it is relevant and indicate its deficiencies at other values of the total head ratio.

The run-off condition for coating and rimming flows

1988 ◽  
Vol 187 ◽  
pp. 99-113 ◽  
Author(s):  
Luigi Preziosi ◽  
Daniel D. Joseph
Keyword(s):  
Critical Condition ◽  
Rotating Cylinder ◽  
Critical Value ◽  
Centripetal Acceleration ◽  
Coating Flows ◽  
Viscous Forces ◽  
Rimming Flow ◽  
Run Off ◽  
Coating Layers ◽  
The Given

A layer of liquid can be supported on the inside or outside of a horizontal rotating cylinder if the viscous forces pulling the liquid around with the cylinder are large enough to overcome the force of gravity. If there are places on the cylinder where the thickness of the layer is larger than a critical value, the excess fluid will run off. For a given maximum thickness the critical condition may be expressed as the minimum speed at which the given layer can be maintained. An approximation of the critical condition using lubrication theory was given by Wallis (1969) and by Deiber & Cerro (1976) for rimming flow and by Moffatt (1977) for coating and rimming flow. Here we address the question of the axial variations of the free surface on the coating layers, and show that they are dominated by the same type of balance between capillarity and centripetal acceleration which determines the shape of rotating drops and bubbles in the absence of gravity. The main results of this paper are the experiments which establish the validity of approximations used to describe the underlying fluid mechanics involved in rimming and coating flows.

Vortex formation in front of a piston moving through a cylinder

2000 ◽  
Vol 416 ◽  
pp. 1-28 ◽  
Author(s):  
J. J. ALLEN ◽  
M. S. CHONG
Keyword(s):  
Boundary Layer ◽  
Vortex Formation ◽  
Field Measurements ◽  
Inviscid Flow ◽  
Cylinder Wall ◽  
Viscous Effects ◽  
Viscous Forces ◽  
Vorticity Distribution ◽  
Piston Speed ◽  
Self Similar

This paper contains the details of an experimental study of the vortex formed in front of a piston as it moves through a cylinder. The mechanism for the formation of this vortex is the removal of the boundary layer forming on the cylinder wall in front of the advancing piston. The trajectory of the vortex core and the vorticity distribution on the developing vortex have been measured for a range of piston velocities. Velocity field measurements indicate that the vortex is essentially an inviscid structure at the Reynolds numbers considered, with viscous effects limited to the immediate corner region. Inviscid flow is defined in this paper as being a region of the flow where inertial forces are significantly larger than viscous forces. Flow visualization and vorticity measurements show that the vortex is composed mainly of material from the boundary layer forming over the cylinder wall. The characteristic dimension of the vortex appears to scale in a self-similar fashion, while it is small in relation to the apparatus length scale. This scaling rate of t0.85+0.7m, where the piston speed is described as a power law Atm, is somewhat faster than the t3/4 scaling predicted by Tabaczynski et al. (1970) and considerably faster than a viscous scaling rate of t1/2. The reason for the structure scaling more rapidly than predicted is the self-induced effect of the secondary vorticity that is generated on the piston face. The vorticity distribution shows a distinct spiral structure that is smoothed by the action of viscosity. The strength of the separated vortex also appears to scale in a self-similar fashion as t2m+1. This rate is the same as suggested from a simple model of the flow that approximates the vorticity being ejected from the corner as being equivalent to the flux of vorticity over a flat plate started from rest. However, the strength of the vorticity on the separated structure is 25% of that suggested by this model, sometimes referred to as the ‘slug’ model. Results show that significant secondary vorticity is generated on the piston face, forming in response to the separating primary vortex. This secondary vorticity grows at the same rate as the primary vorticity and is wrapped around the outside of the primary structure and causes it to advect away from the piston surface.

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