On one-dimensional unsteady flow at infinite Mach number

1968 ◽  
Vol 304 (1478) ◽  
pp. 255-273 ◽  
Keyword(s):  
Asymptotic Expansion ◽  
Blast Wave ◽  
Outer Part ◽  
The Body ◽  
Viscous Boundary Layer ◽  
Outer Flow ◽  
Hypersonic Speeds ◽  
Set Up ◽  
Viscous Boundary ◽  
Infinite Set

The use of the blast-wave analogy, as an aid to the interpretation of experimental data on the motion of a fluid past an obstacle at hypersonic speeds, has led to the theoretical study of its role in an asymptotic expansion of the solution to the governing equations at large distances downstream of the body. In all attempts to set up such an expansion it has proved necessary to divide the flow régime into two parts, an outer part dominated by the blast wave and an inner part consisting of streamlines which, originally, pass close by the body. The matching of these two regions is apparently only possible if a certain integral vanishes. In the present paper a numerical integration, in one particular set of circumstances, is carried out to test the validity of the asymptotic expansion proposed. Formally, an unsteady problem is tackled, for ease of computation, but the steady analogue follows immediately and is of exactly the form discussed in the earlier investigations. It is found that the main results are in line with the theory and that the integral in question is indistinguishable from zero. However, a deeper investigation of the asymptotic expansion shows that, for an expansion of the type envisaged, an infinite set of integrals must each vanish. The next integral does not appear to be zero according to our computations but this result is not believed to be conclusive. Assuming that all the integrals do vanish, then it appears that the inner layer, which although inviscid, has many of the characteristics of a viscous boundary layer, has the addi­tional, surprising property that it can exert no direct influence on the outer flow at large distances downstream of the body.

scholarly journals On solitary waves forced by underwater moving objects

1999 ◽  
Vol 389 ◽  
pp. 119-135 ◽  
Author(s):  
DAOHUA ZHANG ◽  
ALLEN T. CHWANG
Keyword(s):  
Boundary Layer ◽  
Solitary Waves ◽  
Body Shape ◽  
Moving Objects ◽  
The Body ◽  
Wave Radiation ◽  
Two Dimensional ◽  
Viscous Effect ◽  
Viscous Boundary Layer ◽  
Viscous Boundary

The phenomenon of a succession of upstream-advancing solitary waves generated by underwater disturbances moving steadily with a transcritical velocity in two- dimensional shallow water channels is investigated. The two-dimensional Navier–Stokes (NS) equations with the complete set of viscous boundary conditions are solved numerically by the finite-difference method to simulate the phenomenon. The overall features of the phenomenon illustrated by the present numerical results are unanimous with observations in nature as well as in laboratories. The relations between amplitude and celerity, and between amplitude and period of generation of solitary waves can be accurately simulated by the present numerical method, and are in good agreement with predictions of theoretical formulae. The dependence of solitary wave radiation on the blockage and on the body shape is investigated. It furnishes collateral evidence of the experimental findings that the blockage plays a key role in the generation of solitary waves. The amplitude increases while the period of generation decreases as the blockage coefficient increases. It is found that in a viscous flow the shape of an underwater object has a significant effect on the generation of solitary waves owing to the viscous effect in the boundary layer. If a change in body shape results in increasing the region of the viscous boundary layer, it enhances the viscous effect and so does the disturbance forcing; therefore the amplitudes of solitary waves increase. In addition, detailed information of the flow, such as the pressure distribution, velocity and vorticity fields, are given by the present NS solutions.

On the motion of liquid in a spheroidal cavity of a precessing rigid body

1963 ◽  
Vol 17 (1) ◽  
pp. 1-20 ◽  
Author(s):  
K. Stewartson ◽  
P. H. Roberts
Keyword(s):  
Boundary Layer ◽  
Angular Velocity ◽  
Rigid Body ◽  
Steady Motion ◽  
Viscous Boundary Layer ◽  
Constant Vorticity ◽  
Spheroidal Cavity ◽  
Axis Of Symmetry ◽  
Set Up ◽  
Viscous Boundary

The flow set up in an oblate cavity of a precessing rigid body is examined under the assumptions that the ellipticity of the spheroidal boundary of the fluid is large compared with Ω/ω and that the boundary-layer thickness is small compared with the deviations of the boundary from sphericity (ωis the angular velocity of the rigid body about the axis of symmetry,Ωis the angular velocity with which this axis precesses).The motion of the fluid is found by considering an initial-value problem in which the axis of rotation of the spheroid is impulsively moved at a timet= 0; before that time this axis is supposed to be fixed in space, the fluid and envelope turning about it as a solid body. The solution is divided into a steady motion and transients, and, by evaluating the effects of the viscous boundary layer, the transients are shown to decay with time. The steady motion which remains consists of a primary rigid-body rotation with the envelope, superimposed on which is a circulation with constant vorticity in planes perpendicular toω× (ω×Ω), the streamlines being similarly situated ellipses.The possible effects of the luni-solar precession on the fluid motions in the Earth's core are discussed.

Experimental studies in magneto-fluid dynamics: pressure distribution measurements around a sphere

1968 ◽  
Vol 31 (4) ◽  
pp. 801-814 ◽  
Author(s):  
T. Maxworthy
Keyword(s):  
Boundary Layer ◽  
Pressure Distribution ◽  
Experimental Studies ◽  
The Body ◽  
Surface Boundary ◽  
Viscous Boundary Layer ◽  
Surface Boundary Layer ◽  
Reference Velocity ◽  
Viscous Boundary ◽  
Inertia Forces

Measurements of the pressure distribution around a sphere placed in aligned magnetic and velocity fields show that an increase in drag is mainly due to a decrease in the pressure on the base of the body. When magnetic forces are large compared to inertia forces, this decrease is due to a loss in total pressure along streamlines just outside the surface boundary layer and an acceleration of the flow to a velocity much larger than the reference velocity. Separation of a viscous boundary layer takes place behind the equator and still, to a large extent, controls the magnitude of the base pressure and the drag experienced by the sphere. A model consistent with these findings is presented.

The axisymmetric Prandtl-Batchelor eddy behind a circular disc in a uniform stream

1998 ◽  
Vol 377 ◽  
pp. 253-266
Author(s):  
J. F. HARPER
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Bluff Body ◽  
The Body ◽  
Circular Disc ◽  
Axially Symmetric ◽  
Viscous Boundary Layer ◽  
Disc Diameter ◽  
Viscous Boundary ◽  
Uniform Stream

Analytical support is given to Fornberg's numerical evidence that the steady axially symmetric flow of a uniform stream past a bluff body has a wake eddy which tends towards a large Hill's spherical vortex as the Reynolds number tends to infinity. The viscous boundary layer around the eddy resembles that around a liquid drop rising in a liquid, especially if the body is a circular disc, so that the boundary layer on it does not separate. This makes it possible to show that if the first-order perturbation of the eddy shape from a sphere is small then the eddy diameter is of order R1/5 times the disc diameter, where R is the Reynolds number based on the disc diameter. Previous authors had suggested R1/3 and lnR, but they appear to have made unjustified assumptions.

Measurements of turbulent crossflow separation created by a curved body of revolution

2007 ◽  
Vol 589 ◽  
pp. 353-374 ◽  
Author(s):  
P. A. GREGORY ◽  
P. N. JOUBERT ◽  
M. S. CHONG
Keyword(s):  
Flow Visualization ◽  
Skin Friction ◽  
Cross Sections ◽  
Separated Flow ◽  
Surface Flow ◽  
The Body ◽  
Body Of Revolution ◽  
Outer Flow ◽  
Friction Measurements ◽  
Surface Flow Visualization

Using the method pioneered by Gurzhienko (1934), the crossflow separation produced by a body of revolution in a steady turn is examined using a stationary deformed body placed in a wind tunnel. The body of revolution was deformed about a radius equal to three times the body's length. Surface pressure and skin-friction measurements revealed regions of separated flow occurring over the rear of the model. Extensive surface flow visualization showed the presence of separated flow bounded by a separation and reattachment line. This region of separated flow began just beyond the midpoint of the length of the body, which was consistent with the skin-friction data. Extensive turbulence measurements were performed at four cross-sections through the wake including two stations located beyond the length of the model. These measurements revealed the location of the off-body vortex, the levels of turbulent kinetic energy within the shear layer producing the off-body vorticity and the large values of 〈uw〉 stress within the wake. Velocity spectra measurements taken at several points in the wake show evidence of the inertial sublayer. Finally, surface flow topologies and outer-flow topologies are suggested based on the results of the surface flow visualization.

External work in level and grade walking on a motor-driven treadmill

1960 ◽  
Vol 15 (5) ◽  
pp. 759-763 ◽  
Author(s):  
J. W. Snellen
Keyword(s):  
Heat Loss ◽  
Heat Production ◽  
Total Energy Expenditure ◽  
The Body ◽  
External Work ◽  
Thermal Exchange ◽  
Level Walking ◽  
The Subject ◽  
Set Up ◽  
Physical Laws

When studying a walking subject's thermal exchange with the environment, it is essential to know whether in level walking any part of the total energy expenditure is converted into external mechanical work and whether in grade walking the amount of the external work is predictable from physical laws. For this purpose an experiment was set up in which a subject walked on a motor-driven treadmill in a climatic room. In each series of measurements a subject walked uphill for 3 hours and on the level for another hour. Metabolism was kept equal in both situations. Air and wall temperatures were adjusted to the observed weighted skin temperature in order to avoid any heat exchange by radiation and convection. Heat loss by evaporation was derived from the weight loss of the subject. All measurements were carried out in a state of thermal equilibrium. In grade walking there was a difference between heat production and heat loss by evaporation. This difference equaled the caloric equivalent of the product of body weight and gained height. In level walking the heat production equaled heat loss. Hence it was concluded that in level walking all the energy is converted into heat inside the body. Submitted on April 26, 1960

scholarly journals Moisture gradients form a vapor cycle within the viscous boundary layer as an organizing principle to worker termites

2018 ◽  
Vol 66 (2) ◽  
pp. 193-209 ◽  
Author(s):  
R. Soar ◽  
G. Amador ◽  
P. Bardunias ◽  
J. S. Turner
Keyword(s):  
Boundary Layer ◽  
Viscous Boundary Layer ◽  
Viscous Boundary

Viscous boundary layers in reversing flow

1976 ◽  
Vol 74 (1) ◽  
pp. 59-79 ◽  
Author(s):  
T. J. Pedley
Keyword(s):  
Boundary Layer ◽  
Shear Rate ◽  
Leading Edge ◽  
Wall Shear Rate ◽  
Viscous Boundary Layer ◽  
Large Molecules ◽  
Displacement Thickness ◽  
The Mean ◽  
Wall Shear ◽  
Viscous Boundary

The viscous boundary layer on a finite flat plate in a stream which reverses its direction once (at t = 0) is analysed using an improved version of the approximate method described earlier (Pedley 1975). Long before reversal (t < −t1), the flow at a point on the plate will be quasi-steady; long after reversal (t > t2), the flow will again be quasi-steady, but with the leading edge at the other end of the plate. In between (−t1 < t < t2) the flow is governed approximately by the diffusion equation, and we choose a simple solution of that equation which ensures that the displacement thickness of the boundary layer remains constant at t = −t1. The results of the theory, in the form of the wall shear rate at a point as a function of time, are given both for a uniformly decelerating stream, and for a sinusoidally oscillating stream which reverses its direction twice every cycle. The theory is further modified to cover streams which do not reverse, but for which the quasi-steady solution breaks down because the velocity becomes very small. The analysis is also applied to predict the wall shear rate at the entrance to a straight pipe when the core velocity varies with time as in a dog's aorta. The results show positive and negative peak values of shear very much larger than the mean. They suggest that, if wall shear is implicated in the generation of atherosclerosis because it alters the permeability of the wall to large molecules, then an appropriate index of wall shear at a point is more likely to be the r.m.s. value than the mean.

scholarly journals An experimental and theoretical investigation of particle–wall impacts in a T-junction

2013 ◽  
Vol 727 ◽  
pp. 236-255 ◽  
Author(s):  
D. Vigolo ◽  
I. M. Griffiths ◽  
S. Radl ◽  
H. A. Stone
Keyword(s):  
Flow Direction ◽  
Three Dimensional ◽  
Stokes Number ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Viscous Boundary Layer ◽  
Particle Tracing ◽  
Two Dimensional Model ◽  
Viscous Boundary ◽  
The Impact

AbstractUnderstanding the behaviour of particles entrained in a fluid flow upon changes in flow direction is crucial in problems where particle inertia is important, such as the erosion process in pipe bends. We present results on the impact of particles in a T-shaped channel in the laminar–turbulent transitional regime. The impacting event for a given system is described in terms of the Reynolds number and the particle Stokes number. Experimental results for the impact are compared with the trajectories predicted by theoretical particle-tracing models for a range of configurations to determine the role of the viscous boundary layer in retarding the particles and reducing the rate of collision with the substrate. In particular, a two-dimensional model based on a stagnation-point flow is used together with three-dimensional numerical simulations. We show how the simple two-dimensional model provides a tractable way of understanding the general collision behaviour, while more advanced three-dimensional simulations can be helpful in understanding the details of the flow.

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