Introduction to Turbulence & Turbulence Modeling Video Lecture | Fluid Mechanics for Mechanical Engineering

hi friends in this video lecture we
learn how to predict and quantify a
vector turbulence in engineering point
of view most of the flow products
occurring in engineering life are
turbulent in nature so knowledge in
turbulence is imperative for an engineer
so let's start the million-dollar
question why turbulence happens what's
the reason behind it well there is no
exact answer for this question how you
look at a famous statement made by Hazen
bird so in this lecture we won't discuss
white turbulence instead we will discuss
how turbulence what's the nature of
turbulence how we can predict and count
of a so the first step how I can log on
is whether a flow is turbulent or not
there are three characteristics for a
turbulent flow here they are turbulent
flows are always three dimensional in
nature it is always fluctuating and it
is always chaotic means it is full of
Eddie's and wakes and in this lecture we
will understand nature of turbulence by
examining a simple daily life problem so
let's get into it here it is a simple
tap water problem here in each case you
are increasing the flow rate so you can
observe in first case where Florida's
minimum flow is laminar in nature there
is no projection to the flow there's no
chaos is a pure Lemire case in other two
cases you can see a vector turbulence
increases flow is becoming more chaotic
it is becoming unsteady or fluctuating
in nature
so finding number one affected
turbulence increases as you increase
velocity of flow now let's do one more
experiment here you use water as your
working fluid now let us take some other
fluid more viscous fluid let's take oil
and this is a result here your flow rate
is high almost similar to second case
even then the flow is not turbulent in
nature rather it is laminar ocu's the
working fluid which is more viscous in
nature the chance of turbulence
decreases so finding number two as
viscosity of the
it increases effecter turbulence
decreases now let's summarize this to
fine is together turbulence increases
with increase in fluid flow velocity
first case and it again increases with
decreasing viscosity of fluid and
velocity of the fluid increases with
increase in inertial force the force
which is responsible to accelerate the
fluid so it is equal to say turbulence
increases with increasing inertial force
it is clear that if viscosity of the
fluid is low viscous force in the fluid
is also low so you could also say
turbulence increases with decreasing
viscous force so it is obvious from this
conclusions that when ratio of these two
forces are increasing turbulence
increases and this ratio will call us
pry nodes number or when Reynolds number
of the flow increases turbulence
increases and for this particular
problem you can simplify this equation
and you can express rhino's number like
this where D is diameter of the pipe so
RINO symbol is a criterion which defines
whether a flow is turbulent or laminar
so when Ryan assembly is greater than a
critical value you can say flows
turbulent and when it is less than a
critical value you can say flow is
laminar in nature now we will analyze
the same by problem in more detailed way
in order to gain more insight about
nature of turbulence here we have taken
a case which is turbulent in nature and
assume we are giving a constant flow
rate input here so we expect velocity at
the outlet of the flow is also a
constant with respect to time so let's
put I Peter to in the flow and measure
the velocity and here is a velocity
result a surprising result we expected
the velocity to be constant with respect
to time but is rather unsteady is highly
fluctuating
this is one big property of turbulent
flow flow is always unsteady but if you
do something called averaging on this
flow our regime means you take a time
interval delta T and you take average of
the values in between if you do so you
can see that the value is steady in
nature blue line represents average
divided
you and this averaging is a big concept
in turbulence so strictly speaking nor
turbine flow is steady and you could say
a turbine flows in steady state
only if average value of flow variable
is in steady state and in this section
we will see more on averaging consider
this graph velocity variation of a
highly fluctuating turbulent flow so
without any doubt we can say that such a
graph is of too much accuracy for an
engineer instead something like this
will be enough for him an average graph
so we will take a close look at this on
this algorithm we are examining this
small portion the red curve represents
the average value and the blue line
represents the actual value so you could
split the actual velocity into two
components one average component u bar
and s is a fluctuating component and if
you add these two components you will
get the actual value again and the
average value can be defined over a time
interval delta-t like this as an average
of integration and you should be careful
about the value of delta T you should be
big enough to consider any fluctuations
due to turbulence in the mean time it
should be small enough to consider any
unsteadiness in the flow so you could
memorize any value say other components
of velocity or pressure temperature etc
and an engineer always speaks in terms
of average quantities if we encounter a
turbulent flow in next section we will
move into more microscopic analysis of
turbulent flow here will unless shear
stress during a turbulent flow consider
this flow region and velocity profile in
this region could be plotted like this
and remember this is average velocity
profile since the flow is turbulent in
nature now let's put this profile like
this in order to make the analysis easy
and what we need here shear stress
inside these layers and if we say shear
stress in this case or base Newton's law
it is like this this answer would be
completely wrong
the reason is process so
this it is which transport must between
the layers since the flow is turbulent
and more detailed analysis shows that
the actual shear stress equation would
be something like this there should be
one more time to incorporate a vector
turbulence or effective fluctuations and
this dam is often known as turbulent
shear stress or Rhino stress physically
you can represent this equation like
this the actual shear stress is a sum of
laminar shear stress and turbulent shear
stress the shear stress which arises due
to a fitter turbulence or duty
fluctuation and this temprano stress is
a complicated one determination of this
Rhino stress in terms of known
quantities is considered to be one of
the most complicated problem in fluid
mechanics and that will be known as
turbulence modeling before winding up
the lecture will have look at effect of
turbulence in actual engineering device
most of the time turbulence is favorable
eating Reese's convective heat transfer
by a huge amount due to a fatty mixing
of different fluid layers it will
basically increases mass transfer and
mixing because there are lot of Eddie's
and vortices inside the flow another
finding is it reduces the drag around a
body and this is the reason why they
have put lot of dimples on a golf ball
this is to translate laminar flow into
turbulent flow that's where it is in
drug and thus by giving more range to
the ball hope you got a pretty good
introduction to the world of turbulence
and always remember turbulence is a vast
area