Explicit solution for the potential flow due to an assembly of stirrers in an inviscid fluid

An analysis of the lift augmentation properties of a vertical solid two-dimensional subsonic jet due to the presence of the ground is presented. The jet efflux is assumed to behave as an ideal, inviscid fluid, and familiar potential flow techniques are used to solve the resultant problems. The factors controlling the phenomenon are height from the ground, nozzle wall angle, and compressibility. The results in the form of curves of lift augmentation against height from ground show that, whereas the effects of compressibility are very small, the effect of nozzle wall angle is important and can be a useful design-control parameter.

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Potential Flow Past a Circular Cylinder of a Homogeneous Inviscid Fluid

Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences ◽

10.1007/978-3-319-73518-4_12 ◽

2017 ◽

pp. 263-301

Author(s):

David J. Wollkind ◽

Bonni J. Dichone

Keyword(s):

Circular Cylinder ◽

Potential Flow ◽

Inviscid Fluid ◽

Flow Past

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A Bernoulli equation for potential flow of incompressible materials with an inherent material characteristic length

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2012.0641 ◽

2013 ◽

Vol 469 (2151) ◽

pp. 20120641 ◽

Cited By ~ 2

Author(s):

M. B. Rubin

Keyword(s):

Circular Cylinder ◽

Constitutive Equations ◽

Potential Flow ◽

Size Dependence ◽

Characteristic Length ◽

Inviscid Fluid ◽

Bernoulli Equation ◽

Material Characteristic ◽

Velocity Gradients ◽

Incompressible Materials

A general simple continua can be enhanced by constitutive equations which depend on the acceleration and velocity gradients to model the effects of a material characteristic length. This paper shows that for irrotational flows of a class of incompressible materials this model yields a Bernoulli equation. Consequently, for this class of materials and flows, it is possible to satisfy the balance of linear momentum exactly, including the effect of a material characteristic length which introduces size dependence of solutions. An example of a rigid circular cylinder moving through an inviscid fluid is considered to demonstrate dependence of the motion on the size of the cylinder.

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Adiabatic transverse waves in a rotating fluid

Journal of Fluid Mechanics ◽

10.1017/s0022112069002515 ◽

1969 ◽

Vol 38 (4) ◽

pp. 657-671 ◽

Cited By ~ 17

Author(s):

C. Sozou ◽

J. Swithenbank

Keyword(s):

Angular Velocity ◽

Potential Flow ◽

The Other ◽

Inviscid Fluid ◽

Fast Wave ◽

Harmonic Waves ◽

Cylindrical Container ◽

Rotating Fluid ◽

Transverse Waves ◽

The Core

Adiabatic disturbances propagating as transverse waves in an inviscid fluid rotating as a Rankine vortex about the axis of its cylindrical container are considered. The propagation of the first mode of the first two harmonic waves has been investigated. Relative to a fixed co-ordinate system, for each harmonic, there are three waves. Two waves are rotating in the same direction as the fluid, one faster and the other slower than the core of the fluid, and one wave rotates in the opposite direction. The latter is stable and relative to the core of the rotating fluid it is the fastest wave. Relative to the container, the other two waves are speeded up by rotation. However, relative to the rotating core, the angular velocity of the fast wave decreases when the fluid is speeded up, and when it is zero the wave breaks down. As the region of potential flow decreases the angular velocity of the slow wave increases and its amplitude decreases, and in the limit of vanishing potential flow, the wave rotates as fast as the fluid and its amplitude tends to zero.

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Hydrodynamics of locomotion in the squid Loligo pealei

Journal of Fluid Mechanics ◽

10.1017/s0022112001004037 ◽

2001 ◽

Vol 436 ◽

pp. 249-266 ◽

Cited By ~ 7

Author(s):

ERIK J. ANDERSON ◽

WILLIE QUINN ◽

M. EDWIN DE MONT

Keyword(s):

Skin Friction ◽

Potential Flow ◽

High Speed ◽

Flow Analysis ◽

Whole Body ◽

Working Fluid ◽

Inviscid Fluid ◽

Fluid Forces ◽

Loligo Pealei ◽

Unsteady Effects

Potential flow analysis, including unsteady effects, has been applied to live swimming squid, Loligo pealei. Squid were modelled as slender, axisymmetric bodies. High-speed video records, recorded at frame rates of 125 to 250 Hz, provided time-varying body outlines which were digitized automatically. Axisymmetric renderings of these body outlines and the real motion of the squid were used as the input of the potential flow analysis. Axial and lateral inviscid fluid forces simply due to the flow past the squid body were calculated from pressures coefficients obtained from the unsteady Bernoulli equation. Lateral forces were found to play virtually no role in determining muscle stresses in squid jet propulsion. Axial pressure forces were also found to be small in comparison to both net force (based on the observed whole body kinematics) and estimations of skin friction. These findings demonstrate the effects of the highly adapted shape of squid with regard to hydrodynamics. The work suggests that skin friction and working fluid intake are the most significant sources of drag on a swimming squid.

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Viscous potential flow analysis of Kelvin–Helmholtz instability in a channel

Journal of Fluid Mechanics ◽

10.1017/s0022112001005572 ◽

2001 ◽

Vol 445 ◽

pp. 263-283 ◽

Cited By ~ 142

Author(s):

T. FUNADA ◽

D. D. JOSEPH

Keyword(s):

Surface Tension ◽

Critical Velocity ◽

Potential Flow ◽

Critical Value ◽

Neutral Curve ◽

Shear Stresses ◽

Inviscid Fluid ◽

Neutral Stability ◽

Viscous Potential Flow ◽

The Stability

We study the stability of stratified gas–liquid flow in a horizontal rectangular channel using viscous potential flow. The analysis leads to an explicit dispersion relation in which the effects of surface tension and viscosity on the normal stress are not neglected but the effect of shear stresses is. Formulas for the growth rates, wave speeds and neutral stability curve are given in general and applied to experiments in air–water flows. The effects of surface tension are always important and determine the stability limits for the cases in which the volume fraction of gas is not too small. The stability criterion for viscous potential flow is expressed by a critical value of the relative velocity. The maximum critical value is when the viscosity ratio is equal to the density ratio; surprisingly the neutral curve for this viscous fluid is the same as the neutral curve for inviscid fluids. The maximum critical value of the velocity of all viscous fluids is given by that for inviscid fluid. For air at 20°C and liquids with density ρ = 1 g cm−3 the liquid viscosity for the critical conditions is 15 cP: the critical velocity for liquids with viscosities larger than 15 cP is only slightly smaller but the critical velocity for liquids with viscosities smaller than 15 cP, like water, can be much lower. The viscosity of the liquid has a strong effect on the growth rate. The viscous potential flow theory fits the experimental data for air and water well when the gas fraction is greater than about 70%.

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