We have been discussing on flow past bodies
various shapes and if we recollect that in
our previous class we identified that there
could be bodies of different shapes, which
are generated out of considerations of various
elementary flows if you start with a potential
flow consideration.
May be one of the important things of concern
for such cases is that if you have a wall
or if you want to represent the existence
of a wall how do you represent that?
For example, say you have a wall like this
and say you have some source located at this
point say A which is basically on the y axis
where wall is the x axis.
So you have a source of a given strength located
at A, wall is not given to you, say only the
location of source is given to you.
Now you are told that now we have a wall,
we should have a combination of super position
of flows which would represent the effect
of this wall.
So how do you do that?
Given this source is already existing.
We have to keep one thing in mind what is
that?
We are talking about a potential flow in this
example, when we are talking about a potential
flow it means that no penetration boundary
condition is the only boundary condition that
we have to satisfy at the wall.
So if you have a source like this, see the
source radially emits flow in all possible
direction.
That means it also emits a flow radially in
the downward direction.
Now from this do you have a clue that what
we should do to make sure that there is 0
normal component of velocity at the wall?
No, phi=0 or rather stream line or a stream
function=0 represents a body of a particular
shape because the surface of the body is a
reference stream line that is true but how
do you ensure that with this physical example.
What more you have to get to ensure that yes
this is such a line where you have no penetration.
So it is the inverse problem.
It is not that you generate a body of a given
shape given a body or given a wall what extra
thing you need to have with this to ensure
that you satisfy no penetration at the wall.
Let us say this is a plain wall just as an
example.
Just think like this, it is a very common
sense thing.
Say you have just like a reflection you have
image source located at this point.
So if you have an image source located at
this point see that it will also have its
own radially diverging field and one of the
velocity directions is this I mean it will
be perpendicular to the wall.
So if these two sources are of equal strength
and located at equal distance from the wall,
then these two effects will nullify each other
to have resultant normal component of velocity
0 at the wall.
So this is a very simple concept but maybe
implemented in practice very easily.
So it will now become a superposition of a
particular say source and an image source
where the image is with respect to the deflection
as if the wall is like a mirror.
So a superposition of that so this is known
as method of images, very convenient method
and one can generate the effect of the wall
using this.
Now we have also discussed that not all flows
are potential flows in fact no flow in reality
is the potential flow but potential flows
are important because if it is a boundary
layer theory that you are applying then outside
the boundary layer you may apply the concept
of potential flow and whatever pressure gradient
that you calculate out of that the same pressure
gradient is imposed on the fluid within the
boundary layer.
But because of the existence of the boundary
layer, you have the viscous effects also important
and that dictates what should be the drag
force on a body.
Of course if you have very high Reynolds number
flow and a bluff body or a body of such a
shape that flow separation occurs quite quickly
then the form drag or pressure drag remains
to be the more important concern than the
skin friction drag.
And then the drag coefficient sort of may
become independent of Reynolds number at a
very high Reynolds number.
Now if you have say a flow where viscous effects
are important then you represent that with
a drag coefficient where the drag coefficient
is the combination of the skin friction drag
and the form drag or pressure drag.
Now the drag coefficient will have in general
a dependence on Reynolds number.
In certain cases for very high Reynolds number
flow because the form drag effect is very
important, so it may become virtually independent
of Reynolds number but otherwise because of
the skin friction effect it becomes a strong
function of the Reynolds number otherwise.
So let us look into one or two problems where
we illustrate or we try to see that what are
the consequences of that.
So let us consider one example say you have
a flat plate but this plate is oriented in
a bit of a special way, the dimension of the
plate is given.
The dimension of the plate is given as the
height is delta and the width is L and you
have a free stream velocity.
The free stream velocity is not a uniform
velocity but the incipient stream is like
a boundary layer already developed by itself.
And assume that this is a turbulent boundary
layer where you have the velocity profile
given by u/u infinity=y/delta to the power
of 1/7, this is given.
You have to find out that what is the total
drag coefficient of the net drag coefficient
because of the interaction between the fluid
and the solid plate.
What is given is that for a turbulent flow
you may assume that the CD is 0.031/rho uL/mu
to the power 1/7 that is given.
This is the CD based on a local velocity,
this is the CD net that is the net effect
on the plate what is the equivalent CD that
you have to find out okay.
So to find out the CD what you require?
You require to find out what is the total
drag force.
So to find out what is the total drag force
which is there acting on the body how you
should go about it.
See if you take a thin strip say at a distance
y you take a thin strip of width dy.
What is the drag force that is acting on the
strip?
See why we are taking such a strip because
we want to use our knowledge of boundary layer
for flow over a flat plate.
For flow over a flat plate which is oriented
just instead of this say oriented in such
a way that a uniform flow is flowing on the
top of that then the reference drag coefficient
is based on uniform u infinity.
Here as if the u infinity which is coming
on the top of this plate is varying.
It is varying from 0 to u infinity as you
are moving along the height of the plate.
So if you take a small strip over which the
local u infinity is the local u.
What is there what is this u?
So then if you calculate that what is the
local drag force, the local drag force is
the local CD*1/2 rho local u square*the area
L dy.
Of course, in practice if it is a slender
plate like this fluid is flowing on both the
front and at the back.
So you may multiply this by 2 for the 2 sides
and you can substitute CD as the function
of u and the total drag force you may integrate
dFD from y=0 to y=delta and u as a function
of y is given.
So that you have to substitute for doing the
integration.
So I am not going through all the integration,
but if you calculate the total drag force
it is 0.031*49/62*rho nu to the power 1/7
L to the power 6/7 u infinity to the power
13/7*delta.
This is the final answer to this problem and
of course the net CD is something which is
artificial.
What is more important is the drag force because
you may just use any reference velocity say
you may use the reference velocity as u infinity
and very easily find out the CD by the drag
force/1/2 u infinity square*delta*L is the
area of the plane but important is what is
the drag force effectively that is what is
more important.
Let us workout another problem.
So you have a sphere which is moving in a
liquid.
The sphere has the density as rho s and the
liquid has the density of rho.
The radius of the sphere is R. So you have
to find out how the velocity of the sphere
varies as the function of time if it starts
from a velocity V0 at time=0.
Assume that it is moving in the vertical direction
okay.
So now if you see just if you consider the
free body diagram of this sphere.
So what are the important forces that you
see on this sphere?
So if you draw the free body diagram you have
the weight, you have the buoyancy force and
drag force.
So if it is tending to move upwards the drag
force is trying to make it move downwards.
So when we say that when the sphere is tending
to move upwards, it means relative to the
fluid.
That means it might be so that the sphere
is stationary.
But the fluid is moving downwards from the
top it is all the same but when we are writing
equation of motion for this sphere, we are
writing its velocity as velocity of it relative
to the fluid that means as if the fluid is
stationary.
So if it is moving upwards relative to the
fluid then you have the drag force.
So you have the buoyancy force-the weight-the
drag force=the mass of this sphere*dv/dt that
is the Newton second law right.
So these things the buoyancy you can very
easily write what is the buoyancy?
4/3 pi R cube*rho*g-4/3 pi R cube rho of this
sphere*g drag force.
It depends on the relative velocity that is
what is important.
So you cannot say what it is, you can just
write it as say CD*1/2 rho v square*the reference
area.
So that is pi R square right.
Again the projected area is the reference
area for these cases, so not 4 pi R square
that you have to keep in mind.
So that is equal to 4/3 pi R cube*rho of this
sphere*dv/dt.
So the whole attention now is that what is
the CD right and that depends on the Reynolds
number of flow.
So this is the function of Reynolds number.
If the Reynolds number is very, very low,
say Reynolds number<1 then the Stokes law
is approximately valid.
So if Reynolds number is much, much<1 you
have the CD is 24/Reynolds number based on
the diameter of this sphere.
And there will come another velocity.
If on the other hand Reynolds number is very,
very large, very large Reynolds number, CD
may be approximately a constant independent
of Reynolds number because at very high Reynolds
number, we have seen that the effect of the
form drag for bodies with curvatures become
more and more important and the reason is
as you say as you increase the Reynolds number
what happens?
What happens with the boundary layer?
Boundary layer becomes thicker or thinner?
If you increase the Reynolds number, the boundary
layer becomes thinner.
So when the boundary layer becomes thinner
then when the surface effects of the fluid
at there then are penetrate into the outer
fluid outside the boundary layer and they
may part a bit sufficiently and that of course
it becomes more and more important.
So form of the geometry of the surface tend
to become more and more important as you increase
the Reynolds number.
Now at very large Reynolds number CD is approximately
constant independent of Reynolds number.
So if you draw say CD what is its Reynolds
number for flow past as sphere?
So what we will get out of this?
So what you get is something approximately
like this.
So let us say we plot with the log of Reynolds
number.
So CD=24/Reynolds number if you plot it as
a log of Reynolds number, it will be like
a straight line but that is valid only for
very low Reynolds number.
Then there is a significant deviation from
this and so it will come down like this.
And there will be a sudden transition at a
particular Reynolds number when the CD goes
down.
Before this transition, the CD was approximately
as the constant, so it is not really an exact
constant but it is almost like an asymptotic
like it is almost approaching a constant.
Then suddenly there is a transition again
it increases.
This is roughly say for a sphere maybe it
is of the order of 10 to the power 5 this
Reynolds number.
Now what happens here?
Here there is a transition to turbulence,
because of a transition to turbulence what
happens the boundary layer separation is delayed.
We have seen that like when the shape of the
body is important in terms of the form drag,
boundary layer separation is what matters
because early separation will induce a lot
of form drag but later separation will reduce
the form drag.
So when the boundary layer becomes turbulent,
the separation is delayed.
So it reduces the form drag and since at very
high Reynolds number form drag is what is
important the reduction of form drag is what
is prominent here but beyond that if you increase
the Reynolds number further then many interesting
things may occur because I mean it is a change
of the state of turbulence from one state
to another state where the point of separation
again shifts more towards the upstream.
That is why this is all related to the boundary
layer separation, so what we are trying to
understand is that towards the high Reynolds
number for flow past bodies with curvature,
the boundary layer separation is the very
important phenomenon that dictates the total
drag force and the similar behavior is there
for flow past cylinders and let us try to
understand what happens for flow past circular
cylinders as special example.
So we now look into some of the animated representations
or movies related to flow past circular cylinders.
So one by one we will see and we start with
a particular visualization where it is almost
like a potential flow.
So if you see that these green colored lines
this represent sort of stream lines and if
you see that these stream lines are very symmetrically
coming from one side and they are also symmetrically
merging in the other side the front and the
back side.
So almost a perfect symmetry is maintained
so just like what a potential flow could predict.
Now if you increase the Reynolds number what
happens?
So let us say that the Reynolds number is
increased beyond say 4 or something like that.
See at very low Reynolds number the solution
is always like stokes flow solution.
So the solution does not consider the fluid
flow or the advection terms in the left hand
side of the Navier-Stokes equation.
So the advection effects are totally neglected
in that solution.
But in reality the advection terms maybe important
typically as you go for downstream and what
happens is see physically what happens the
wall is the source of vorticity because wall
generates a cross velocity gradient and that
vorticity is transmitted within the fluid.
So if there is a strong advection then the
advection transmits the vorticity from one
place to another place and creates an asymmetry
in the flow.
So if advection effects are totally neglected
that asymmetry is totally neglected then vorticity
is just diffused in all directions equally
but if the advection effects are there then
vorticity is preferentially transmitted or
advected towards the wake side or the low
pressure on the back side and what is the
consequence?
So whatever we showed as a visualization example.
Let us see it as a simulated example.
So if you see two Eddies of counter rotating
nature are formed at the back or in the low
pressure region or in the wake side of the
cylinder.
We are talking about still low Reynolds number
cases.
Now if you say increase the Reynolds number
you see certain interesting things.
So if you see these are like staggered vortices,
which are forming so there is one row of staggered
vortex interacting with another row of staggered
vortex and these are sort of rolling in the
opposite direction.
So if we want to look into it in a bit more
detailed manner.
Let us try to look into another movie.
And with that movie what we will try to see
is that what are the implications of these
alternately rotating vortices?
So these alternately rotating structures they
have sort of an impression of footprints on
a road and this was first observed by Von
Karman and that is why this is known as Von
Karman Vortex Street.
So if you see that basically what is happening
is these vortex streets or these vortex lines
so to say are interacting with the small eddies
the two counter rotating eddies which were
formed close to the cylinder.
Because with increase in Reynolds number these
vortices are coming very close to the back
of the cylinder and they are interacting with
those small eddies and so alternately you
are having sort of staggered rolls of vortices
rotating one against the other.
Now so we will look into one interesting flow
visualization of vortex shedding.
This phenomenon is known is vortex shedding.
That is as if there is a flow past a cylinder,
it is not just for a cylinder it could be
for body of any similar shape but cylinder
is just a demonstration.
So what we want to see first before going
into the phenomenon of vortex shedding in
more details that what types of vortex rolls
are formed in the back of the cylinder, so
in the wake region or the low pressure region.
So like animated description of the Von Karman
Vortex Street.
So just look into this very carefully because
this gives you an idea that what sort of vorticities
are there not in a quantitative sense but
at least qualitatively what is the nature
of rotation of this individual vortices and
this vortices may be of quite complicated
nature.
And one of the important things that comes
out of this experiments is that although the
flow that came towards the cylinder was steady
but there is an unsteadiness in terms of appearance
and disappearance and the frequency of the
rolls which are appearing.
So although the incipient flow is steady but
flow at the back of the cylinder is unsteady
and it has a sort of a frequency or it has
a sort of a periodicity in terms of the happenings.
That is the vortices are appearing disappearing
again appearing disappearing.
So vortex of one particular directional rotationality
is appearing, then vortex of an opposite rotationality
is appearing.
And the previous one is disappearing, so alternately
vortices of opposite signs are appearing and
disappearing and this phenomenon is known
as vortex shedding and is one of the very
important phenomena that you can see in flow
past bodies of these shapes.
Now you can generate these types of flows
in using computational techniques also and
this illustration will give you an idea of
like how the vortices of different rotating
nature are shed from the cylinder as if they
have been shed from the cylinder towards the
fluid.
So you can see this clearly from this illustration.
Now we will see some more examples of the
vortex shedding.
This is also an animated description, you
can see that are like alternating vortices
are shed in the fluid from the cylinder and
that occurs for quite a large range of Reynolds
number and it si important for many reasons
because we will see through one example that
what effect it has on the cylinder itself.
So with the width of the higher Reynolds number,
this oscillation frequency where this also
changes and we may have different experimental
visualizations of these ones.
So this is one experimental visualization
unlike the computational visualizations that
we saw in some of the previous examples.
This is an experimental visualization of the
same thing.
So we are just trying to look into this vortex
shedding phenomenon from different visualization
perspective.
This is a computational way of like generating
the similar type of behavior and you can see
from this example clearly that these vortices
are as if rolling upwards and downwards, upwards
and downwards like that and that creates an
alternating sort of frequency in the flow.
So this is a flow itself is inducing some
nature of rotationality or some nature of
frequency in the system and if you see that
because of this sort of transience in the
flow, the cylinder may itself start oscillating.
So this is called as flow induced vibration
of the cylinder.
So it was a steady flow, it was not an unsteady
flow, so if something vibrates because of
unsteadiness in a flow that is intuitive but
here the flow that was incipient to the cylinder
was steady.
But because of this physical phenomenon of
vortex shedding, you are now having some phenomenon
which is occurring with the frequency and
that is forcing the cylinder to oscillate
and it may be very critical if that forcing
frequency becomes same as the natural frequency
of the cylinder because that can give rise
to very high amplitude and sort of resonance.
And that is one of the important consequences
that may occur in a very strong fluid structure
interaction.
So you may have even multiple cylinders and
with multiple cylinders these types of effects
you can see with like as if one effect is
getting superimposed on the other.
Here the symmetry sort of is very well preserved
because the Reynolds number is not that large
but the symmetry may be destroyed by advection
of vorticity if the Reynolds number is substantially
larger.
Now if you want to look it in the form of
a 3-dimensional structure so you can see that
by the example that we will be seeing here,
let us try to see this example, may be we
just play it again okay.
So if you see this is a 3-dimensional structure,
so here the vortex shedding phenomenon is
shown in 3 dimensions but the basic phenomenon
is very, very similar to the 2-dimensional
flow visualization observation that we have
seen.
Now if you want to say see the behavior so
these like the vortex shedding frequencies
are very, very critical for the design of
a say structural system and it may be possible
that there is a wide range of Reynolds number
to which the flow is subjected so if you want
to look into the flow past a circular cylinder,
we could see that first there were some small
vortices which were formed close to the back
of the cylinder.
Then these vortices almost periodically appeared
and disappeared and interacted with the main
flow and created a vortex shedding phenomenon.
Now if you increase the Reynolds number to
a very large value then beyond a critical
Reynolds number, which is roughly like maybe
of the order of 5*10 to the power 5 or so,
there may occur a transition to turbulence.
So if you want to plot the pressure distribution
around the cylinder, so when we plot a pressure
distribution we basically plot the Cp versus
theta so Cp is the pressure coefficient p-p
infinity/1/2 rho u infinity square.
So the physical situation that we are considering
is there is the circular cylinder and there
is a flow past this circular cylinder.
Flow is coming with the velocity of u infinity.
And theta is a sort of angle measured with
respect to the incipient flow.
Now let us try to make a sketch say from theta=0
to theta=pi, the variation of the coefficient
of pressure which is basically a non-dimensional
variation of pressure as a function of theta.
First of all, let us plot it for a potential
flow.
So for the potential flow if you recall that
it was 1-4 sin square theta for flow past
a circular cylinder without any rotation.
So if you want to make a plot of this say
this is pi/2 and this is pi.
So when theta=0, this is=1.
So let us say this one when theta=pi/2, it
is -3 so let us say may be this one, so if
you make a sketch of it like this and then
when theta=pi 1 again so something like this
okay.
So this is potential flow solution when will
the potential flow solution be valid in terms
of pressure distribution?
If there was no boundary layer separation
then it would have closely followed this because
whatever is the pressure that is imposed from
outside the boundary layer same pressure distribution
the boundary layer is supposed to feel so
long as the boundary layer theory itself is
valid that is so long as there is no boundary
layer separation but if the boundary layer
separation has occurred.
Then so if the boundary layer separation has
occurred so it all depends on whether the
separation is early or late and for that let
us consider say two Reynolds number one is
Reynolds number, these Reynolds number are
based on the diameter D of the cylinder.
So Re D. Let us say one value we take as say
2*10 to the power 5, another Reynolds number
we take as say 7*10 to the power 5.
And let us say in between there was a transition,
so let us consider that 2*10 to the power
5 is the laminar case.
So if it is a laminar case let us try to make
a plot of that so if you compare these two
in which case there will be earlier boundary
layer separation, in the first case right
because the turbulent boundary layer has a
greater momentum to sustain the adverse pressure
gradient so its separation will be delayed.
So we expect usually that the separation will
be there in the region where the adverse pressure
gradient is failed.
In reality in the region where there is an
adverse pressure gradient that is failed there
occurs a back flow and the effect of the back
flow is propagated even a bit in the upstream
direction.
So that the separation in the practical case
for a flow of this Reynolds number regime
occurs at roughly theta=82 degree.
That is the practical observation.
So till the separation has occurred maybe
it will not show a lot of deviation from the
potential flow theory but as it comes to a
separation it will show some sort of deviation
from the potential flow theory.
So this is Reynolds number=2*10 to the power
5.
See after the separation has occurred, the
Cp is roughly a constant.
That means the pressure in the low pressure
region or the wake region after which the
boundary layer separation has occurred is
almost like a uniform pressure which does
not change further with theta and it is typically
a low pressure region.
When it is 7*10 to the power 5 say it is beyond
the critical limit or the threshold limit.
So then the separation will be what?
It will be further delayed and typically these
separation may occur close to 120 degree or
something like that maybe 118 degree this
type of angle and till that limit so if you
draw that line so till that limit it will
follow very closely 
the line, which was there for the potential
flow solution and then when there is a flow
separation, it will come to a constant Cp
which is independent of the angle theta.
That is the constant pressure in the wake
region is almost like a constant.
So this is Reynolds number=2*10 to the power
7 and these angles are like roughly for the
angle from which this change of behavior is
observed depends on the separation for laminar
close to 80, 82 degree maybe for turbulent
close to 120 degree something like that.
So you can clearly see that depending on whether
the boundary layer is laminar or turbulent
you have a different pressure distribution
right.
And this all is because of the different points
of separation, so that means if you have on
one side of the cylinder a laminar boundary
layer, on another side of the cylinder a turbulent
boundary layer because of their difference
in the point of separation, you might have
different pressure distribution on the two
sides and that is what is the very important
understanding that we get out of that.
It is not only true for a cylinder, the similar
behavior is also true for a sphere and because
of this difference in pressure distribution
maybe around the two sides of a sphere because
of maybe the boundary layer is laminar in
one side or turbulent in another side.
It is possible that this sphere experiences
a lateral force.
So if it is a ball it starts swinging because
of that and we will try to now see that how
the dynamics of the sports balls are associated
with these sort of observations that we had
till this time.
So let us look into some examples related
to sports ball dynamics.
So we start with an example of a tennis ball.
So let us say that there is a tennis ball
which is being tested in a wind tunnel.
See if you want to test the behavior of say
pressure distribution around a ball you may
have the ball stationary and the air flowing
past it because what is important is the relative
velocity between the ball and the air.
In reality, the actual motion is the other
way because you throw the ball and the ball
is moving in the air but here you are keeping
the ball stationary and blowing air past it.
So if you want to see that you now compare
the flow past similar tennis balls one with
the laminar boundary layer, another with a
turbulent boundary layer and you can clearly
see that in the laminar boundary layer because
of the early flow separation, there is a large
wake or the low pressure region that is formed
with a sort of rotating structure of flow
in the back.
In the turbulent boundary layer that separation
is somewhat delayed.
And you do not have such a large wake region
so that gives rise to a different kind of
pressure distribution in these two cases.
So these are examples with base balls and
even the similar types of phenomena they are
applicable.
Now if you see in terms of the rotation, now
rotation of a ball, it will depend on unlike
the lateral of the side force which depends
on the drag force I mean here it many times
may depend on a lift force, not always but
in certain cases because we have seen that
if you have a body of a given shape and if
you have a vortex which is one of the important
constituents that is generating flow past
a body of that shape, then that will create
a lift force.
And we could get an expression for the lift
force as a function of the circulation and
the free stream velocity and that applies
equally to the sports balls as well because
there is a lot of cricket that goes on in
our country maybe we will spend a bit more
time on how these cricket balls have different
types of motions.
So we will briefly look into the fluid mechanics
of cricket ball swing.
So the whole idea is not to like be very,
very detail in how a cricket ball should swing.
It is one of the very important and active
areas of research but what is more important
is to give a broad overview of whatever simple
things we have learnt in our boundary layer
theory and flow past bodies of different shapes.
Then how that maybe applicable to the movement
of the cricket balls that we very commonly
see in different matches.
So I mean everybody knows what is a swing
but let us just very briefly look into it.
So swing is a sort of lateral movement of
a ball right and this lateral movement is
influenced by many things and we will see
that what are the factors, which influence
the lateral movement but what is important
is to have a basic idea first of what is the
effect of the speed of the ball on this lateral
movement and that is very important.
Because we have intuitively seen that many
of these phenomena are strong functions of
Reynolds number and given the diameter of
the ball as fixed, so the velocity of the
ball relative to the fluid or in other words
velocity of the fluid or the air relative
to the ball is what is sort of important.
So I mean depending on the size of the ball
it may be different so for the size of the
cricket ball it is at speeds of around 80
miles per hour or roughly 130 kilometer per
hour, the usual transition to turbulence may
occur.
So at speeds of around say 90 miles per hour,
which is considered to be good speed of a
fast bowler or 145 kilometer per hour.
You will have the flow as turbulent.
Now the question is that if the flow is turbulent
and it is equal in all sides of the cricket
ball then it will generate and it is turbulent
in the same way in all the sides.
Then it will generate no resultant sidewise
thrust or sidewise movement.
So what may be important in one case say with
the brand new cricket ball is to have a turbulent
flow in one side and maybe a laminar flow
in another side and how that is possible it
depends on many factors.
We will come into those factors one by one
but just let us first for the sake of clarity
try to understand that we would be first talking
about a conventional swing in terms of outswingers
and inswingers.
So typically the outswingers as you know are
the swings where the ball deviates away from
the batsman and inswinger is it goes towards
the batsman.
So we will try to see that how these swing
balls are going to be affected in terms of
a scientific perspective, so the science of
swing the broad picture.
So as we have discussed earlier that the key
to have a cricket ball swing is to cause a
pressure difference between the two sides
of the ball.
It is not just true for a cricket ball, it
is true for any other ball that we may look
for.
And this pressure distribution depends on
the sort of local velocity of flow of air
on each side of the ball.
So the swing of course maybe some times generated
by which sometimes by accident also and we
will see that like accidentally even if you
are not gripping the ball for swing how it
may swing and we will see that but to have
an important effect what we can say is the
boundary layer sort of it may separate differently
on the two sides of the ball.
And that is what is the key thing.
So the boundary layer separation dictates
the pressure distribution.
The boundary layer separation may occur differently
on the two sides of the ball and the location
of this point of separation determines the
pressure distribution on the two sides of
the ball and because of the net differential
in pressure the side force is generated on
the ball because the ball moves from one side
to the other.
So now the question is that like as we first
were discussing that what should be the effect
of the speed of the ball say the speed of
the ball is 145 kilometer per hour and say
it is a new ball, it is equally turbulent
in all sides, so the resultant side force
is 0 so to say.
That means if you have a very fast bowler
and is holding a straight sort of seam or
maybe is not holding a straight seam but with
an inclined seam.
But is bowling in such a way that the flow
is equally turbulent in all sides, it will
not have any swing.
So it is not necessary that very fast bowlers
will be able to generate a swing.
So what is the key for generating a swing
that I mean it maybe a fast bowler but the
thing is that you have to have your speed
in such a way that one side of the ball the
flow will remain laminar and how that maybe
possible let me show that to you with a one
example of a cricket ball.
So if you look into this as an example so
let us say that the bowler is bowling from
the side in which I am standing so let us
say that the bowler is trying to bowl an outswinger.
So the outswinger the typical grip is like
this.
So assume that I am releasing the ball from
this direction towards you so the seam will
be inclined or oriented towards the direction
in which the ball is expected to swing.
So typically in the direction of the slips
for a right-handed batsman.
So now you grip the ball in this way so this
is the typical way in which you grip the ball
for your outswinger.
Now consider that you have the ball moving
in the forward direction.
So if you look into it in the other way just
think that the ball is stationary and the
air is coming from the other side because
the aerodynamics is what which is governing
the behavior.
So when the air is coming from the other side,
see this seam is acting like a (()) or the
disturber on the flow.
So when the air is coming towards the ball
when this seam is present, so the seam will
disturb the flow and if it is close to the
critical Reynolds number because of this effect
of the seam the ball will have a transition
towards turbulence.
On the other hand, on the other side see because
you are oriented the seam in the other way
on the other side when the air is first coming
it is not encountering the seam.
So it is just falling on the surface of the
ball where the seam is not present.
So that means if it is a bit less or it is
close to the critical Reynolds number because
of a very smooth surface the disturbance will
be very less, so it will tend to be laminar.
So that means the seam here is a sort of actuator
of the turbulence in the flow.
So because of this one you may have a net
resultant force because now on this side of
the ball you have a turbulent boundary layer
on the other side you have a laminar boundary
layer, this we are talking about a brand new
cricket ball if an opening bowler is bowling
with this type of a ball.
So then because of the resultant force on
my left side, this ball after pitching it
will move in the air in that direction, so
that is the outswinger.
Now if you want to bowl an inswinger, it is
just the different, difference is just in
terms of the grip because the same policy
holds.
So wherever is the seam and the ball is coming
towards the seam, there it will try to have
the seam will create a disturbance and have
a transition towards turbulence.
So if you want to swing the ball in the other
way you have to just grip of the ball remains
the same but the seam is now pointed towards
the other end.
So when the ball comes like this it faces
now first the seam in the right side where
it becomes a sort of the turbulent flow on
the other side it still remains laminar.
Important thing is that you have to bowl it
close to the critical speed.
So if you bowl at a very high speed you cannot
get this effect because both sides it will
become turbulent and if you have very good
cricketing captains sometimes they make use
of these things in a very nice way.
One of the very classical examples that I
can remember is like it was 5 or 6 years back,
maybe 2001 or 2002, so it was Australia and
South Africa test match and in that match
what was happening is like I mean Australia
started bowling and they opened with Glenn
McGrath and Brett Lee and what was happening
is that Brett Lee was bowling from a direction
in which the wind was blowing.
And he was not getting any swing, the reason
is he was much faster than Glenn McGrath and
the air speed was helping the ball so that
it was always beyond the critical speed so
that it is turbulent in all the directions
and despite using the new ball it was generating
some pace but no movement and he is only base
bowler, base batsman will always be disturbed
more by movement and just by raw pace.
On the other hand, for Glenn McGrath he was
bowling against the wind, so his natural speed
is not that high and therefore he was not
able to disturb the batsman with a threshold
speed and when Steve Waugh realized it, he
quickly switched the ends of the two bowlers
and it was done in just two, three overs,
very quickly he did it and then Brett Lee
was bowling against the wind.
So when Brett Lee was bowling against the
wind what was happening is he no matter with
whatever speed he was releasing the ball because
of the air resistance, it came down lower
than the critical speed in one side and then
like it was possible to have laminar flow
in one side and the turbulent flow in the
other side and because of that sometimes he
was getting a late movement of a late swing.
Because it depends on the relative velocity
between the ball and the air and that was
being modulated by the air which was blowing
by itself.
So sometimes if one is bowling too fast then
it is not so good for a swing.
But this we are talking about a new ball and
for the new ball which is being used for a
swing it is important to see that it is not
just a new ball that one utilizes for a swing,
it is also important to have a swing even
with older ball and we will therefore talk
about 2 different or maybe 3 different types
of swings with the older ball.
So when you have older ball the thing is that
you are not solely relying on the seam.
Because with the older ball if you have one
side rough, the roughness of the ball may
itself trigger turbulence.
So then you are not depending on the effect
of the seam alone of course you grip in the
ball in the same way but no matter whatever
is your grip I mean say you are griping it
in a traditional way for a particular swing
say outswing but now this side of the ball
say is roughened.
So the contrast between the roughness between
the two sides of the ball is if it is very,
very strong because of the high smoothness
in one side it may be ensured in many ways.
We have seen many illegal ways in which many
of the teams have tried to do it.
So the key is in one side you keep it very
smooth, another side you keep it very rough
and then the rough side will have an automatic
triggering to turbulence and using that even
with the older ball, you may be able to swing.
And of course again it will matter that what
is the relative speed between the ball and
the air.
Now there are many factors which might affect
the swing, one of the important factors people
believe is the humidity and we have always
heard that in a highly humid condition, the
ball is expected to swing much more but there
has been no evidence of that from a fluid
mechanics perspective.
Because the density change or viscosity change
with the relative humidity change is so small
that the Reynolds number change is not sufficient
and from the fluid mechanics perspective Reynolds
number should have been the dictating factor.
So perhaps something else happens in that
situation and still it is an unresolved question
in fluid mechanics.
Now if you consider something called as a
reverse swing.
So the reverse swing the whole idea is that
the ball will now swing in the direction not
in the traditional way but in the other way
and the whole idea is that if you now see
that you grip the ball in the same way say
as an outswinger like this but now you make
this side of the ball rough, so you grip the
ball like a outswing delivery.
But you make this side rough and the other
side smooth just the opposite to the normal
swing case and then what will happen is if
you consider the flow that is there on the
ball then you will have so in the side where
you are making it rough, it will become turbulent,
on the side in which you have kept it smooth
because of the effect of the seam it will
become turbulent but the triggering of turbulence
is different in the two sides.
So the flow will not separate in the same
symmetric position in the two sides.
So in two sides the flow will be turbulent
but there will be a difference in the point
of separation and that will generate a net
sidewise force which is just opposite to the
way you are showing it by your grip.
So good batsman will know by looking into
the side which side is rough and which side
is polished that like what should be the nature
of the swing.
Now of course the reverse swing one of the
things is that it is also a strong function
of the condition of the ball and therefore
like issues of tempering of the ball and roughening
of the ball using illegal means have come
into the play.
A third type of swing which has not come into
the picture till very recently is known as
contrast swing.
So contrast swing is such a swing which is
not so much dependent on the seam of the ball,
so unlike the traditional swings where the
seam is held in a inclined direction I mean
where you want to move it.
In the contrast swing, the ball is held with
the seam straight.
So the seam is held perfectly straight and
for a novice bowler it is much easier to hold
a seam straight rather than holding it in
an appropriate direction for the swing.
So what happens in a contrast swing, if you
see that just look into this visual where
you have in the left side a ball with a contrasting
surface roughness flying through the air and
the seam is straight up.
So the name contrast comes from the contrasting
roughness on the two sides of the ball.
So in this case the boundary layer over the
upper surface separates relatively early in
the laminar state.
Because the upper surface is smooth whereas
on the bottom surface it separates later this
asymmetry results in a side force and it moves
in the direction which is facing in the other
way.
On the other hand if you just reverse the
roughness and the smoothness you may make
it move in this way and since the effect of
the seam is not there even in a torn out or
a ball which has got a lot of wear and tear
and the seam is not very prominent you can
have this type of swing.
And this is known as contrast swing but like
before closing our discussion let us just
look into some of the very good swing bowling’s,
great bowlers who perhaps never knew what
is the fluid mechanics of swing.
But could produce the swing in a much better
manner than anybody else in that would perhaps
do.
So let us look into this like Sarfraz Nawaz
was considered to be the inventor of reverse
swing.
So we will just slowly see some of the examples
like you can see before this we saw Imran
Khan, then Wasim Akram and like these were
great exponents Waqar Younis, these were obviously
great exponents of reverse swing bowling.
And like this is a typical inswing yorker
and you can see that what were the conditions
of the batsman during that time.
Aqib Javed was also one of the very good bowlers
and of course you can see Shoaib Akhtar one
of the devastating bowlers of the modern times.
Now just finally we will see one clip like
it was 2005 Ashes series which was known for
the series where you had reverse swing, contrast
swing and all these things.
So you can see this like one of the balls
delivered by Flintoff and another ball in
the same clip delivered by Simon Jones and
these balls will illustrate that how these
types of swings are there.
So the second ball will illustrate in a bit
more interesting way so just look into it.
So like these are typical cases of reverse
swing bowling and perhaps this is the first
time that English men could find out that
how to bowl good reverse swings and it was
good enough for them.
So look at the deviation in the ball and it
was the ball was gripped entirely in the opposite
direction, it was gripped as if it was going
to move in other direction.
So maybe we just stop here today in this lecture
and from the next class we will continue with
the new chapter that is pipe flow.
