1_-_behaviour_of_real_fluids [compatibility mode].pdf

7/25/2019 1_-_Behaviour_of_Real_Fluids [Compatibility Mode].pdf

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1 Behaviour of Real

Fluids


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Real Fluids

Real Fluids Tangential or shearing forces always develop whenever

there is motion relative to a solid body creating fluidfriction

Friction forces gives rise to a fluid property called

viscosity Compressible

Viscous in nature

Certain amount of resistance is always offered by these

fluids when they move


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Ideal Fluids

Ideal Fluids

A fluid with no friction

Also referred to as an inviscid (zero viscosity)

fluid Internal forces at any section within are

normal (pressure forces)

Practical application: many flows approximatefrictionless flow away from solid boundaries


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Viscous Flow

Viscous is basically referring to internal friction in a

fluid.

A true non-viscous fluid would flow along a solid wall

without any slowing down because of friction.

A viscous fluid has a lot of friction, even parts of the fluiditself, flowing at different rates, will have friction between

them.

If a viscous fluid were flowing past a wall, the friction at

the wall would be transmitted inward. The fluid right atthe wall would not be flowing at all, as you moved away

from the wall, the fluid would be flowing faster.


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Ideal & real flow around a cylinder


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Viscous Flow In Fig 2, fluids are both sandwiched between a fixed solid surface

on one side and a movable belt on the other.

Effect of shear force on fluid


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If the belt is set in motion, experimentalmeasurements will indicate:

Ideal Fluid The force required to move the belt is negligible

The movement of the belt has no effect whatsoever onthe ideal fluid, which remains stationary.

Real Fluid A considerable force is required to maintain belt motion,

even at low speed. The whole body of fluid is deforming and continues to

deform as long as belt motion continues. Closerinvestigation will reveal that deformation pattern consists

in the shearing, sliding, of one layer of fluid over another.Between the solid surface and the belt the fluid velocityis assumed to vary linearly.


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Reynolds Number


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Reynolds Number


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The stability of laminar flows and theonset of turbulence

The flows examined so far involved only low

speeds.

If the speed of the belt increased, the pattern of

linearly sheared flow will continue to exist only up

to a certain belt velocity. Above that velocity a

dramatic transformation takes place in the flowpattern. WHY?

Effects of disturbance on a viscous flow


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Effects of disturbance in a sheared flow Consider a slowly moving sheared flow. If a small

disturbance happened (a small local vibration),

the pathlines will be slightly deflected, bunching

together at A and opening out correspondingly at

B.

This implies that the local velocity at A, uA,

increases slightly compared with the upstreamvelocity u, while at the same time uB reduces.

From Bernoulli equation,

gu

gP

gu

gP

gu

gP BBAA

222

222


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Therefore PB>PA. It can thus be reasonedthat the disturbance will produce a small

transverse resultant force acting from B

towards A. The lateral components of velocitywill also produce a corresponding component

of viscous shear force, which acts in the

opposite sense to the resultant disturbingforce.

As long as the fluid is moving slowly, the

resultant disturbing force tends to beoutweighed by the viscous force.

Disturbances are therefore damped out.


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As the rate of shear increases, the effect ofthe disturbance becomes morepronounced:

1. The difference between uA and uB increases

2. The pressure differences (PA-PB) increases with(uA

2-uB2), so the deflection of the pathline

becomes more pronounced

3. The greater shear results in a deformation ofthe crest of the pathline pattern. When theshear is sufficiently great, the deformation iscarried beyond the point at which the rectilinear

pattern of pathlines can cohere. The flowdisintegrates into a disorderly pattern of eddiesin place of the orderly patterns of layers.


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The Boundary Layer

When a fluid enters a pipe, viscous effects due to the

pipe wall will develop. The region where viscous effects are important is

referred to as the boundary layer.


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The Boundary Layer

The velocity profile will vary due to the growth of this

boundary layer. When the velocity profile reaches a constant (i.e.,

velocity profile no longer changes along the pipe), the

flow is said to be fully developed.

The length required for the flow to reach fully developed

conditions is called the entrance length (Le), and can be

determined from the following empirical relations:

For laminar flow: Le/D = 0.06Re

For turbulent flow: Le/D = 4.4(Re)1/6


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The Boundary layer

To develop the boundary layer concept, it is helpfulto begin with a flow bounded on one side only.Consider, a rectilinear flow passing over a stationaryflat plate which lies parallel to the flow. The incidentflow (i.e. the flow just upstream of the plate) has auniform velocity, U

.

Development of a boundary layer


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As the flow comes into contact with the plate, the layer of fluid

immediately adjacent to the plate decelerates (due to viscousfriction) and comes to rest.

This follows from the postulate that in viscous fluids a thin layerof fluid adhere to a solid surface. There is then a considerableshearing action between the layer of fluid on the plate surface

and the second layer of fluid. The second layer is therefore forced to decelerate (it is not quiet

brought to rest), creating a shearing action with the third layer offluid and so on. As the fluid passes further along the plate, the

zone in which shearing action occurs tends to spread furtheroutwards.

This zone is known as a boundary layer. Outside the boundarylayer the flow remains effectively free of shear, so the fluid hereis not subjected to viscosity-related forces.


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The flow within the boundary layer may be viscous or

turbulent, depending on value of Reynolds Number.

To evaluate Re we need a typical dimension and in

boundary layers this dimension is usually the distance inthe x-plane from the leading edge of the solid boundary.

The Reynolds number becomes Rex

=U

x/.

The structure of the boundary layer is shown in the

following figure.


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A graph (distribution) of velocity variation with y may be drawn,and will reveal that:

In laminar zone there is a smooth velocity distribution towhich a mathematical function can be fitted with good

accuracy In the turbulent zone the mixing action produces a steeply

sheared profile near the surface of the plate, but flatter,more uniform profile further out towards the boundary layeredge.

Structure of a boundary layer


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Implications of the boundary layer concept

Different material exhibit different degrees of roughness. Doesthis have any effect on the boundary layer?

In laminar flow, the friction is transmitted by pure shearing action.

Consequently, the roughness of the solid surface has no effect,except to trap small pools of stationary fluid in the interstices,and thus slightly increase the thickness of the stationary layer offluid.

In a turbulent flow, a laminar sub-layer forms close to the solidsurface. If the average height of the surface roughness is smallerthan the height of the laminar sub-layer, there will be little or noeffect on the overall flow.

Turbulent flow embodies a process of momentum transfer from

layer to layer. Consequently, if the surface roughness protrudesthrough the laminar region into the turbulent region, then it willcause additional eddy formation and therefore greater energyloss in the turbulent flow. This implies that the apparent frictionalshear will be increased.

1_-_behaviour_of_real_fluids [compatibility mode].pdf

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