WEBVTT
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We have come to the last lecture of this lecture
series on Turbo machinery Aerodynamics. We
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have gone through all the components of machines
that are called Turbo machineries, and the
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aerodynamic principles of those components,
and in the last few lectures, we have been
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taking about application of Computational
Flow Dynamics-CFD in this exciting field of
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Turbo machinery Aerodynamics.
So, in the last lecture today, I will be again
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talking about CFD, and its application to
Turbo machinery. And will end up with some
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idea about how to apply CFD in turbo machinery
blade design. We have talked about blade design
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earlier of the compressors of the turbines,
and will have a quick look at how CFD is used
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in Turbo machinery blade design. You have
already had a couple of lectures in which
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CFD has been introduced to you, these lectures
which were done earlier, and today's lecturer
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essentially, introduction to CFD in the field
of Turbo machinery.
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If you do wish to actually, become an expert
in the field of CFD of Turbo machinery. It
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is necessary that you go through a full course
in CFD - a separate course. And then possibly
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learn various techniques that are required
for application of CFD to Turbo machinery.
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As you have already seen in the last couple
of lectures, application of CFD in Turbo machinery
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is some more different from application of
CFD in many other areas. So, Turbo machinery
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has its own aerodynamic issues, problems,
challenges and some of the problems are not
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yet properly resolved. So, we are looking
at issues that probably have some futuristic
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implications. In the sense, that CFD is still
a very challenging and open field of research
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in the field of Turbo machinery.
In today's lecture we will take a look at
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some of the fundamental issues of CFD. A bit
of through back in to the fundamentals, and
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then we will move into how to apply CFD, a
little bit of which you have done in the last
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couple of lecturers, and then apply try to
apply that to what we have done earlier in
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the field of blade design. So, let us first
start of with the fundamental issues of CFD,
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which you probably would learn much more in
much greater detail, if you get in to a full-fledged
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course of CFD. Let us, take the fundamentals
today first.
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The fundamentals of CFD are have been around
for quite some time, almost twenty five 30
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years actually, a little more if you would
like to think of right from the beginning.
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And some of these are based on fundamental
mathematical principles. Now, these mathematical
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principles have been around much longer, and
for a long time people were trying to figure
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out, how to find solutions to those mathematical
equations, which try to capture some of the
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aerodynamic issues or the physics of the aerodynamics
under certain given circumstances.
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The problem was that many of these mathematical
equations, which are let us see in the form
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of ordinary differential equations-OD is.
The analytical solutions to those often are
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simplistic; and not necessarily very useful
especially in the field of Turbo machinery;
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a little more comprehensive one, which are
captured in Partial Differential Equations
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or PDE. These have some problems, in the sense
that straight forward analytical solution
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is often not possible. And hence, one resorts
to various numerical methods. Now, this numerical
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method is what finally constitutes computational
fluid dynamics. In this numerical method essentially,
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the Partial Differential Equations are converted
to algebraic form, and then simultaneous solution
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of these algebraic equations quite often number
of equations, for example, as you know in
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flow dynamics, you have the energy equation,
you have the moment equation and the continuity
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equation. So, you try to solve number of these
which are applicable to your field of application,
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of the physics, of aerodynamics, as you are
doing now, and when you apply these you try
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to resort to numerical solution which is essentially
as I mentioned, involve converting you have
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PDE to algebraic form, and trying to find
solution to this algebraic equations.
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So, we will take a look at some of these fundamental
issues very quickly, very briefly, because
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it is a very big field, indeed very exciting
field, and we can only take a very quick look
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into some of the fundamental principles that
covered CFD. Let us take a look at some of
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these fundamentals.
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So, as I mention the physics of fluid mechanics
are often captured in Partial Differential
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Equations, and most of the useful ones are
in second order Partial Differential Equations.
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Now, the generally the governing equations,
as I was just mentioning few minutes back,
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a set of coupled non-linear Partial Differential
Equations valid in an arbitrary or irregular.
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Let us say, undefined domain, and subject
to various initial and boundary conditions.
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We will be talking about these initial boundary
conditions little, in a little while, so some
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of these definitions need to be understood
in proper context. Now, as I mentioned the
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purely analytical solutions of many fluids
mechanic equations are limited due to imposition
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of various boundary conditions of typical
fluid flow problems.
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So, very simplistic solutions are available
analytically, and they give you what can be
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called very simple handy solutions, and beyond
a certain level those handy solutions have
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very limited utility value. On the other hand,
there is reason to believe that experimental
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data are often used, because it is there is
reason to believe that CFD is not here in
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a position to capture everything that is happening
inside, especially in Turbo machinery. So,
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quite often at the end of the day, you probably
need to have some experimental data also,
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and together they form that so called analytical
drop back drop, which the designer could use
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for finally designing a product in our case
Turbo machinery.
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So, experimental data definitely is required.
It is simply called validation. You need to
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have validation of CFD three experimental
work. And once they are validated or they
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are matched, then you can say that you have
a data that is reliable, and the data can
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be used for design purposes. So, CFD alone
often does not quite produce sufficient information,
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it needs to be back tap, because it is known
that under certain circumstances the solutions
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or the results or the output that is available
from CFD solutions are not necessarily the
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correct solutions. So, some of these things
would need to be understood depending on the
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circumstances, and then the CFD data would
have to be as I mentioned validated and coupled
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or complimented with experimental data, and
then you have a certain set of data that are
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said to be useful for design or final analysis
purposes. So, let us take a look at the fundamental
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issues of Computational Flow Dynamics.
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Now, as I mentioned the they are often the
flow dynamics is often captured in Partial
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Differential Equations. Now, they are two
kinds really; the Linear and the Non-linear.
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Once the Linear one that is shown in over
here is a 1-d - one-dimensional Wave Equation,
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very well known. And that is del u del t equal
to minus a del u del x, where a is normally
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greater than 0.It is a non 0 quantity. On
the other hand, a Non-Linear Equation of the
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would be del u del t equal to minus u del
u del x; this is often the barges equation,
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and is a often apply to inviscid flow that
means there is no viscosity in that flow,
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what one sometimes is also called ideal flow.
The other form of Non-Linear Equation is other
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well known equations - the Laplace's Equation
del square phi del x square plus del square
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phi del y square is equal to 0, where x and
y are independent variables, and phi is a
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dependent variable of in the potential. And
then of course, the Poisson's Equations which
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is del square phi del x square plus del square
phi del y square is equal to function of x
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and y. So, these two are very well known equations
quite often used to capture somewhat simpler
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versions of fluid mechanic a problems, and
often give handy quick solutions to simple
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fluid mechanic issues.
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Now, if we move on to a little more generalized
form of the Non-Linear Equation; and if we
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just write down that the whole equation in
the form of A into del square phi del x square
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plus B into del square phi del x del y plus
C into del square phi del x square plus D
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into del square phi del y square plus E into
del phi del y plus F into phi plus G equal
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to 0. In this generalized form of Non-Linear
Equation A,B,C,D,E,F,G which are written down
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here are essentially functions of X and Y,
which are independent variables, and phi which
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was a dependent variable.
Now, if we assume that f equal to f X,Y that
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is function of X Y is a solution of the above
differential equation. This solution would
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typically be is would be a surface in a space,
and the solutions produce space curves which
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are called characteristics. So, quite often
you get characteristics as a solutions, which
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essentially come out of above a Non-Linear
Equation. Now, the second order derivatives
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along the characteristics are often indeterminate.
And they may even be discontinuous across
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the characteristics. On the other hand, the
first order derivatives are continuous. So,
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these are some of the simple solutions that
you can get out of Non-Linear Equation.
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Now, a simpler version of the second order
equation may be written down as A into dy
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square by dy dx square minus B into dy dx
plus C equal to 0. Now, solution of this second
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order equations yields the equations of the
characteristics, in the physical space, the
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characteristics we are talking about in the
last slide, and that would be dy dx equal
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to B plus minus root over B square minus 4AC
by twice A. Now, this is of course the standard
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solution of a second order equation, many
of you might recognize this standard solution
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of an algebraic equation of second order,
so it is something of the same order.
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Now, this gives us the characteristics. Now,
these characteristic curves can be real or
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imaginary. As we saw in the solution depending
on the values of B square minus 4AC. A second
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order Partial Differential Equation is normally
classified according to the sign of B square
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minus 4AC. Now, these are conventions. So,
the classification is that if B square minus
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4AC is negative that is less than 0. This
is an Elliptic form of Partial Differential
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Equation which is normally applied for Subsonic
flow that is Mach number less than 1. So,
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when the Mach number is clearly less than
1, and which in Aerodynamics, we simply say
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that there are no shocks anywhere around.
The Elliptic form of the equation is often
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applied for finding solution to those Aerodynamic
problems or Aerodynamic issues.
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On the other hand, when B square minus 4AC
is equal to 0, we call the Partial Differential
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form of the equation as Parabolic form and
it is applied for Sonic flow, where Mach number
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is exactly equal to 1. And then, when B square
minus 4AC is greater than 0 that is its positive,
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the Partial Differential Equation is referred
to as Hyperbolic equationm, and it is applied
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to Supersonic flow, where Mach number is clearly
more than 1. So, you have different forms
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of Partial Differential Equations to be used
for Subsonic flow, Sonic flow, and then Supersonic
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flow. It is stands to reason that when you
have both kinds of flow, Subsonic and Supersonic
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existing in a particular flow domain of interest,
you would probably need to apply both the
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forms in these two different zones in a judicious
manner to get you a correct solution.
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Now, this Partial Differential Equations,
as I was stating a while back are to be converted
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to algebraic equations, which then of course,
are converted to Finite Difference Equations
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and then Various Finite Difference Techniques,
the forward difference, the backward difference,
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ectera are often use to find solutions to
the Algebraic equations. So, what you are
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finally solving are a set of up algebraic
equations, which have been evolved from the
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set of Partial Differential Equations. So,
that is the procedure that computational flow
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dynamic people are often adopt.
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So, the Elliptic Partial Differential Equation
has no real characteristics. We were talking
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about the characteristics. A disturbance if
it is propagated in the domain, it it propagates
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instantly in all directions. Otherwise, if
you have characteristics, it disturbance propagate
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along the characteristics. A domain solution
of an Elliptic PDE is a closed region. And
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normally, you get a closed solution. And the
providing the boundary conditions uniquely
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yields the solution within the domain. So,
it it is easier to get the solutions in the
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Elliptic domain in a very well understood
form.
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The solution domain for a parabolic PDE is
open region, parabolic we saw was applicable
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to Sonic conditions. For a parabolic PDE one
characteristic line exists, which would essentially
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proper get the Sonic condition. On the other
hand, hyperbolic PDE has two characteristic
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lines, and a complete description of second
order Hyperbolic PDE requires two sets of
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initial conditions and two sets of boundary
conditions. Hyperbolic as we saw was applicable
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for Supersonic flow, which normally is characterized
by shocks, so, essentially the characteristic
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lines would be characterized by the shock
lines, the lines along which the shocks are
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present. So, that is one of the ways of looking
at the characteristics.
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And then of course, it needs two sets of initial
conditions, and two sets of boundary conditions.
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So that, you need to probably impose where
the shocks are going, where the shocks are
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anchored, so, many such issues need to be
clearly defined, and of course, the initial
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conditions must give the Mach number - the
supersonic Mach number that needs to be impose
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as the inflow condition. So, many of these
issues need to be looked into before one,
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applies the appropriate PDE for finding solution
to your Aerodynamic problems. We shall see
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later on that when it comes to Turbomachinery,
the issues there are many other issues that
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need to be also looked into.
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We were talking about the Initial and Boundary
conditions. The Let us take a quick look at
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what these things really are, the initial
condition is a dependent variable its prescribed
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at some initial condition, which may be at
the inlet to the flow into the particular
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domain of interest. So, you need to prescribe
whether the flow is uniform or whether it
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has a variable in terms of it is it is varying
in a particular cross-section, whether the
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velocity, the temperature, the pressure, the
density or the energy or enthalpy or variables
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or whether they are uniform that is constant
at the inlet from one end of the inlet to
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the other. Depending on, whether you are taking
a two-dimensional flow or a three-dimensional
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flow.
So, that needs to be prescribed as an Initial
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Condition of the flow going into the domain
of interest. The Boundary Conditions on the
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other hand, are dependent variables or it
is derivatives that must satisfy on the boundary
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of the domain of PDE. Now, if you have a domain
in which the boundaries are defined. In such
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a case, the Boundary Conditions, some of the
Boundary Conditions need to be imposed. You
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could have if if it is let us say for example,
defining a solid wall, you may have to define
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that the what is the wall Boundary Condition,
that means the flow across through the wall
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would have to be say to be 0, because you
cannot have wall observing flow or flow coming
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out of the wall. So, that is one of the ways
of defining or what the flow velocity parallel
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to the wall which could be 0, if it is a viscous
flow that means the last layer of the flow
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is attach to the wall of the boundary. So,
these are some of the physical conditions
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that would have to be appropriately prescribed
as boundary condition, often the outlet flow
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condition may be one of the boundary conditions,
sometimes the flow quality of the flow or
21:40.210 --> 21:46.780
even the quantity of the flow, may be defined
in the outlet side as one of the prescribed
21:46.780 --> 21:50.390
boundary conditions.
Now, there are number of Boundary Condition
21:50.390 --> 21:57.390
that are fundamentally described, first one
is called Dirichlet Boundary Condition. An
21:57.799 --> 22:03.679
Dirichlet Boundary Condition essentially is
a Dependent Variable prescribed on at the
22:03.679 --> 22:10.679
boundary. For example, we have seen phi was
dependent variable a potential, so those are
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examples of dependent variable. And that needs
to be prescribed at the boundary. Neumann
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Boundary Condition is a Normal gradient of
the dependent variable. And as I was just
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mentioning, you could say the normal to the
velocity or the potential is specified at
22:29.280 --> 22:35.850
the certain boundary. And that needs to be
specified at certain boundary condition boundaries.
22:35.850 --> 22:41.880
The Robin Boundary Condition is a linear combination
of Dirichelt and Neumann Boundary Conditions.
22:41.880 --> 22:47.160
A Mixed Boundary Condition on the other hand
is not same as Neumann Boundary Condition,
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it is some part of the boundary has Dirichlet
Boundary Condition and some other part has
22:52.880 --> 22:58.490
Neumann Boundary Condition.
So, this is what sometimes you may have to
22:58.490 --> 23:05.490
consider the fact, that some part of the flow
has for example, Supersonic some other flow
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- part of the flow may be Subsonic. There
may be differences in terms of laminar flow,
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turbine flow, and of course many other issues
that are involved. So, you may have to impose
23:20.670 --> 23:27.670
different kind of Boundary Condition under
different circumstances, and you have then
23:27.740 --> 23:31.890
Mixed Boundary Condition.
Now, the boundary conditions are applied quite
23:31.890 --> 23:38.890
often on the Body Surface. For example, R
in the Far field, as I mention feel that is
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the Outlet flow station, let us to say let
us say from Turbo machinery that outlet of
23:46.530 --> 23:53.510
a compressor or turbine at some distance would
be consider the far field, then one would
23:53.510 --> 23:58.390
probably think of Symmetry as I was mentioning,
you may be talking about the uniformity of
23:58.390 --> 24:05.390
the flow or non uniformity of the flow. And
then you would need to probably apply exactly
24:05.510 --> 24:11.220
at the inlet flow condition or exactly at
the outlet flow condition of the domain that
24:11.220 --> 24:16.429
has been prescribed for computational understanding
or analysis.
24:16.429 --> 24:23.429
So, the boundary conditions are applied under
various various places, which could be a Body
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Surface of the body, which could be Far Field,
which could be related to the Symmetry or
24:31.650 --> 24:38.250
Uniformity of the flow field or it could be
related to the Inflow or Outflow condition
24:38.250 --> 24:44.450
of the domain that is been prescribed for
flow dynamic analysis. So, that those are
24:44.450 --> 24:47.690
the places, where you need to apply the boundary
conditions.
24:47.690 --> 24:54.690
Now, many of these boundary conditions would
have what you call physical domain. Now, physical
24:55.840 --> 25:00.610
domain is of course, the domain which you
are actually trying to understand, and an
25:00.610 --> 25:07.610
analyze from you understanding an application
of the Partial Differential Equations and
25:07.740 --> 25:14.740
the Aerodynamic principals. On the other hand,
the computation which often is done is done
25:15.020 --> 25:20.070
in a, what is known as computational domain.
So, the physical domain and computational
25:20.070 --> 25:26.540
domain may be slightly different from each
other, because the computational domain facilitates
25:26.540 --> 25:32.460
computation very fast and gives you solutions
at a very fast base.
25:32.460 --> 25:38.220
The physical domain of course, is what we
are indeed originally interested in. So, it
25:38.220 --> 25:44.400
becomes necessary often to transform the problem
from physical domain to the computational
25:44.400 --> 25:50.210
domain through a transformation technique
and such transformation techniques are been
25:50.210 --> 25:56.160
around for a long long time. And if you do
that, then you are facilitating the computation
25:56.160 --> 26:03.160
in a very simple as we said it is it is basically
solution of algebraic equations, and then
26:04.200 --> 26:08.330
you are computation can proceed very fast.
So let us take a look at what do you mean
26:08.330 --> 26:13.030
by Physical Domain and what do you mean by
Computational Domain.
26:13.030 --> 26:18.510
So, Physical Domain is where for example,
you having a flow over this surface, which
26:18.510 --> 26:24.250
is let us say, some you know, Elliptical Surface
or Pseudo Elliptical Surface. So, over this
26:24.250 --> 26:30.590
you have a flow and this flow you are trying
to analyze, and find out the details of what
26:30.590 --> 26:37.120
is happening to velocity, pressure, density,
etcetera, any or even temperature over this
26:37.120 --> 26:43.919
flow field; which may be let us say part of
an aerofoil or part of a blade. For example,
26:43.919 --> 26:49.840
of compressor or turbine you know you can
notice that it could be somewhere near by
26:49.840 --> 26:55.960
leading edge.
Now, this physical domain would need to be
26:55.960 --> 27:02.960
transform into this computational domain which
is straight forward domain. In which each
27:03.850 --> 27:10.850
of these, you know, grids or or domains, the
small part of the domain let us say, would
27:11.570 --> 27:18.570
have to be transform into this straight forward
rectangular domains. And as a result of this,
27:20.470 --> 27:26.919
the computational solution in this computational
space would proceed very fast. So, there are
27:26.919 --> 27:33.919
transformation techniques by which this transformation
is often done from physical domain to a computational
27:34.980 --> 27:40.730
space to facilitate computational to proceed
with the computation.
27:40.730 --> 27:45.950
There is an other kind of domain transformation
again; where let us say, this is the physical
27:45.950 --> 27:52.950
domain physical domain. In which, you have
a flow around this which could be a part of
27:53.600 --> 28:00.600
a sphere or circle or cylinder, and then the
flow is having this kind of a characteristic.
28:05.240 --> 28:12.240
This needs to be then converted to this computational
space in which the characteristics can then
28:14.530 --> 28:20.460
be found, and then again from point to point
basis they have to be transformed back or
28:20.460 --> 28:26.750
transform back into the physical domain to
get you a physical solution. So, you can get
28:26.750 --> 28:33.750
your computational done in the computational
space, you still need to transform it back
28:35.730 --> 28:41.900
into the physical domain to get your physical
solution. So, quite often, in in terms of
28:41.900 --> 28:47.460
computational polence, the computational may
converge or may give you good solution in
28:47.460 --> 28:53.549
the physical domain, but you may have difficulty
converting back into the physical domain,
28:53.549 --> 28:58.950
and then the computational would have to be
considered has not fully converged that means
28:58.950 --> 29:05.610
a full solution has not been obtained.
So, there are certain some issues where transforming
29:05.610 --> 29:11.400
it back could be a little problem. Of course,
transforming it forward from physical to computational
29:11.400 --> 29:18.400
domain is indeed and issue or a little problem
which needs to be solved through certain transformation
29:19.169 --> 29:25.130
techniques. So, both forward and backward
transformation needs to be completed before
29:25.130 --> 29:32.130
you can complain, before you can claim that
you have a solution that is applicable to
29:32.150 --> 29:33.910
the physical domain.
29:33.910 --> 29:40.910
Now, to create this computational space quite
often, you need to create as you have seen
29:41.020 --> 29:48.020
measures are what is simply call grid. Now,
there are essentially two kinds of grid that
29:48.130 --> 29:53.429
are you being use these days; one is called
the Structured Grid and other we will see
29:53.429 --> 29:58.530
in a little while which is called Unstructured
Grid. Now, the Structured Grid has you may
29:58.530 --> 30:05.530
have added some already introduction in the
earlier lectures. Essentially, has very simple,
30:07.160 --> 30:14.160
you know, Grid Structure in which one way
of doing the Structured Grid is to have Orthogonal
30:14.360 --> 30:20.760
Grid. So, if you look at this domain over
here which is been broken up into so many,
30:20.760 --> 30:27.760
you know grids, and each of this junctions
is of course called the node. And at the node
30:29.260 --> 30:36.260
in this Orthogonal Grid, the two surfaces
or two lines are essentially almost parallel
30:38.210 --> 30:43.160
to perpendicular to each other.
So, this perpendicularity or orthogonality
30:43.160 --> 30:50.130
makes it an orthogonal grid. So, even when
you are creating these grids; one has to be
30:50.130 --> 30:57.130
careful that at each of these points you have
maintained orthogonality. The other way of
30:58.600 --> 31:04.200
doing it is where grid is created without
orthogonality, which means these lines are
31:04.200 --> 31:11.200
actually non orthogonal to each other, and
they can indeed then be retained as some kind
31:11.350 --> 31:18.350
of a curve line. So, orthogonality is something,
which can be maintain which is orthogonal
31:19.650 --> 31:26.650
grid or grid. The modern way doing it could
be where you have grid without orthogonality
31:27.620 --> 31:34.620
and those are sometimes referd to as quasi
orthogonal grids. We shall have an example
31:35.360 --> 31:42.360
of this, when we can get into solution of
Turbo machinery in the blades in a little
31:43.070 --> 31:44.340
while from now.
31:44.340 --> 31:49.320
The Unstructured Grid, on the other hands,
starts off with certain identification of
31:49.320 --> 31:56.220
the boundary, and then the inside space which
you need to have solution to, and then you
31:56.220 --> 32:02.179
identify the nodes on which at the solution
need to be definitely found in terms of let
32:02.179 --> 32:09.179
us say velocity and pressure and other flow
parameters. You need though solutions at those
32:10.840 --> 32:16.390
points, and of course, what probablic are
known on the boundary. On the other hand,
32:16.390 --> 32:21.250
what needs to be done is this Domain Nodalization
which has been done.
32:21.250 --> 32:27.659
So, you need to first nodalize them create
the nodes at which you want the solutions
32:27.659 --> 32:34.240
definitely. And then you resort to what is
known as triangulation. So, if you connect
32:34.240 --> 32:41.240
these nodes, you start getting triangles.
So, once you start getting triangles, the
32:41.770 --> 32:48.770
solution or the computation can proceed from
one node two another. And as a result of which
32:50.309 --> 32:53.710
all of them now are sort of connected through
triangles.
32:53.710 --> 33:00.710
So, this triangulation then becomes necessary
step to all grid generation. And has we see
33:02.570 --> 33:07.470
more, and more and as we have done in the
earlier two lectures grid generation is an
33:07.470 --> 33:14.470
important, and very crucial and critical step
in the process of Computational Flow Dynamics.
33:15.340 --> 33:22.340
You need to create grid that appropriate to
your physical problem, and that is the first
33:22.429 --> 33:29.429
problem or the first issue that CFD people
would have to sort out, what kind of grid
33:29.919 --> 33:36.919
needs to be created to find a solution. So,
grid is essentially towards finding a solution,
33:37.100 --> 33:43.179
towards finding the solution to the Partial
Differential Equations. So, creating grid-appropriate
33:43.179 --> 33:48.340
grid is an important issue in finding CFD
solutions.
33:48.340 --> 33:55.340
Here, you can see little more involved three-dimensional
Unstructured Grid Generation. In which triangulation
33:57.520 --> 34:04.520
has been completed and now you can see, you
have triangles on the boundary. So you have
34:05.240 --> 34:11.460
the shaded ones which are triangles on the
boundary; and these white triangles are the
34:11.460 --> 34:16.679
interior triangles in the interior of the
body. So, we are talking about a three-dimensional
34:16.679 --> 34:23.679
body, inside of which, we have the triangles
and outside on the surface we have the boundary
34:24.429 --> 34:30.690
triangles. So, when you have a three -dimensional
space or three-dimensional body, over which,
34:30.690 --> 34:37.690
let us say flow needs to be captured through
various CFD techniques, you need to resort
34:38.469 --> 34:44.099
to this kind of Grid Generation.
So, Grid Generation as I mentioned and as
34:44.099 --> 34:49.119
you have done in the earlier lectures, is
an important issue, that needs to be sorted
34:49.119 --> 34:56.119
out, many of the CFD packages that are available
these days, do have certain some time they
34:56.700 --> 35:03.619
have certain automatic grid generation facilitated,
but sometimes you have to really set down,
35:03.619 --> 35:08.890
and create a grid appropriate, and which is
not easy, which often takes quite a lot of
35:08.890 --> 35:15.670
time, before you have a grid that gives you;
a good solution that is useful to you. So,
35:15.670 --> 35:20.670
grid generation through some of the things
that we have been talking about; actually,
35:20.670 --> 35:27.229
is a it is a time consuming issue, some of
the packages facilitated automatic grid generation,
35:27.229 --> 35:34.229
but then you are then you are using something
that is automated and develops, and you have
35:34.690 --> 35:41.200
no control over it. So, many of the CFD people
would like to have control over the grid generation,
35:41.200 --> 35:45.499
and they like to create grid of their own,
in which case, some of things that we are
35:45.499 --> 35:52.499
talking about would indeed need to be done
in a more elaborate and very deliberate manner.
35:53.009 --> 36:00.009
So that, you have compressive grid, which
in compressors you entire flow domain, in
36:00.509 --> 36:06.849
which you would need to have your solution
of your flow dynamic problems; so, let us
36:06.849 --> 36:10.569
take a look at some of the issues related
to Turbo machinery.
36:10.569 --> 36:17.569
Now, CFD in blade design essentially proceeds
through number of steps. The Blade Design
36:18.710 --> 36:25.710
System actually, as we have done earlier,
you have a Through Flow technique; and then
36:26.069 --> 36:31.969
you resort to the Blade Section Designs, so
section by section, that is aerofoil by aerofoil,
36:31.969 --> 36:38.249
you need to develop Blade Sections, which
are indeed aerofoils; and then you resort
36:38.249 --> 36:43.549
to Blade-to-Blade design or Blade-to-Blade
Analysis. We will talk about what is this
36:43.549 --> 36:50.549
Blade-to-Blade Analysis? And then you have
Blade sections stacking. So, all these section
36:51.549 --> 36:56.549
that you have created need to be stacked in
a certain manner; and some of the stacking
36:56.549 --> 37:02.450
techniques are changing in the process of
stacking, people are applying sweep and dihedral
37:02.450 --> 37:08.469
to blade shapes, so some of those things we
have talked about earlier, and that is what
37:08.469 --> 37:13.839
stacking essentially means; and then finally,
the stacked full-fledged blade would have
37:13.839 --> 37:20.569
to be subject to three-dimensional flow analysis.
We will simply try to show you today, what
37:20.569 --> 37:25.950
the three-dimensional flow analysis would
indeed, mean or the beginning of the three-dimensional
37:25.950 --> 37:32.950
flow analysis, which would need to be later
on supplemented with Full fledged Blade Structural
37:33.109 --> 37:40.109
Analysis and Aero-elastic analysis, which
is be outside the preview of this course,
37:40.269 --> 37:46.690
on this lecture series, and but only after
all that is done, you go for Blade Making
37:46.690 --> 37:52.239
or Blade Construction. So, Blade Design is
something, in which lot of things need to
37:52.239 --> 37:59.239
be done in a very step by step manner, very
patiently, and you need to go step by step,
37:59.979 --> 38:06.900
so you need to create Blade Sections to begin
with. So, let us take a look at, what it means
38:06.900 --> 38:12.729
to create a blade using CFD along the way.
38:12.729 --> 38:19.339
Now Through Flow Program, which is what you
would probably need to look at first, to know,
38:19.339 --> 38:25.130
what kind of flow that you are creating, you
need to have the Annulus Information that
38:25.130 --> 38:31.450
means to need to have the tip diameter, the
hub diameter decided already, and that decision
38:31.450 --> 38:37.039
has to come from various design parameters
that we have talked about earlier. And then
38:37.039 --> 38:43.589
you need to a probably put in the Blade row
exit information, sometime this exit information
38:43.589 --> 38:49.339
are imposed on the Blade Design that means,
the exit would have to be axial or the exit
38:49.339 --> 38:53.200
would have to be at a certain angle or the
exit would have to be certain angle have to
38:53.200 --> 38:59.680
be turbine, for example, at a certain temperature
or the exit would have to be under certain
38:59.680 --> 39:05.729
flow uniformity condition, those things would
need to been imposed, and as you can as you
39:05.729 --> 39:12.729
know input dynamics, they would be the outflow
conditions or essentially boundary conditions
39:13.829 --> 39:19.920
at the exit flow field; then of course, you
need to provide the Inlet profiles of pressure
39:19.920 --> 39:26.809
temperature, and the flow condition in terms
of what should be the sonic velocity; So,
39:26.809 --> 39:32.910
those need to be supplied to the designer.
And then, the Inlet Mass flow; now, Turbo
39:32.910 --> 39:39.910
machinery is always, as we have seen design
for a specific mass flow. If it is air as
39:41.940 --> 39:48.940
the flow medium, then the air mass flow has
to be very accurately determined apriori,
39:49.940 --> 39:55.599
before that the design is initiated. So, mass
flow of the air or any flow it through the
39:55.599 --> 40:02.349
Turbo machinery needs to be decided apriori
before the design is on, and then you need
40:02.349 --> 40:07.489
to decide the Rotational speeds of the rotors;
this needs to be decided apriori, otherwise
40:07.489 --> 40:12.700
of course, you cannot have a design, and then
the blade geometry the loss distributions
40:12.700 --> 40:19.309
would need to be created through some loss
models, which are sometimes empirical, some
40:19.309 --> 40:24.690
empirical loss models; the blade geometry
needs to be created with the help of the design
40:24.690 --> 40:27.789
methodology that we have done in the earlier
lectures.
40:27.789 --> 40:34.209
So, you need to have a blade geometry to go
into CFD; this is something we have mentioned
40:34.209 --> 40:39.829
when we were discussing blade design that
blade design essentially creates a first cut
40:39.829 --> 40:46.829
geometry, as good as possible a first cut
geometry, which is then subject to CFD analysis;
40:47.849 --> 40:53.329
and then the Passage averaged perturbation
terms, there are all lot of many other issues
40:53.329 --> 40:59.039
here, the perturbation terms, the periodicity,
many of these issues would have to be defined,
40:59.039 --> 41:05.809
before you get into the through flow program.
The output from this would be in the form
41:05.809 --> 41:11.660
of a Blade row inlet and exit conditions,
you get the details of those things, and then
41:11.660 --> 41:18.660
the Streamlines are well defined, and the
stream tubes are created, and all the details
41:18.729 --> 41:25.729
of the stream path are captured through the
CFD solutions. So, these are the input and
41:27.039 --> 41:32.509
output of typical through flow program that
you would need to have with you, when you
41:32.509 --> 41:34.279
get into to the design mode.
41:34.279 --> 41:40.130
Now, we will take a look at, what is meant
by Blade-to-blade flow program? See, you can
41:40.130 --> 41:45.229
see here, there are two blades: one over here,
and other over here, and what it means is
41:45.229 --> 41:51.219
that you need to capture the entire flow domain
from this blade to that blade, and which essentially
41:51.219 --> 41:57.690
means that also of course, you have a hub
and you have the shroud or casing. So, this
41:57.690 --> 42:03.499
is your flow domain and on one side, you have
one blade and other side you exactly a similar
42:03.499 --> 42:08.539
blade; they are same shape. On one side, you
have the hub; on the upper side, you have
42:08.539 --> 42:14.279
the shroud or the casing. So, this is your
captured flow domain, in which you need to
42:14.279 --> 42:20.619
find your detail aero dynamic solutions.
So, Blade-to-blade flow program essentially,
42:20.619 --> 42:27.099
tries to move from one blade surface to the
other; that is one way, that is one may call
42:27.099 --> 42:33.049
them is one surface and then of course, you
are S 2 surfaces, which move you from hub
42:33.049 --> 42:40.049
to the tip of the blade. So, you can traverse
cross section by cross section from one blade
42:40.749 --> 42:47.259
to the other; and then, you can traverse from
hub to tip again cross section by cross section,
42:47.259 --> 42:53.640
each cross section is from one blade to other,
here, each cross section is from hub to casing.
42:53.640 --> 42:59.289
So, this is one cross section from hub to
casing; and this is another cross section
42:59.289 --> 43:03.680
from hub to casing; the third cross section
from hub to casing. So, you are moving from
43:03.680 --> 43:09.339
one blade to another, you have to remember
of course, that this surface of this blade;
43:09.339 --> 43:15.029
and the phasing surface of this blade are
dissimilar. So, when you move from this surface,
43:15.029 --> 43:21.349
finally approach the other surface. The surface
shape would be changing all the time similarly,
43:21.349 --> 43:27.109
when you move from hub to the casing, the
hub has one curvature the casing of course,
43:27.109 --> 43:32.559
has another curvature. So, as you move from
hub to the casing cross section by cross section,
43:32.559 --> 43:38.749
the curvature, the radius of curvature would
indeed change. So, this is the Blade-to-blade
43:38.749 --> 43:45.349
flow programs that quiet often, the CFD people
use in Turbo machinery.
43:45.349 --> 43:52.349
This is the space, which we are talking about
the typical space within two blades, and you
43:54.489 --> 44:01.469
have the two surfaces defined over here the
q 1 and q 2 are the quasi orthogonal stream
44:01.469 --> 44:07.729
surfaces; and this is what you can see that
the two surfaces are not orthogonal, they
44:07.729 --> 44:14.049
are quasi orthogonal; this is something which
we indicated a little while back. So, one
44:14.049 --> 44:21.049
is the hub to shroud stream surface. All the
way from here to here, the one which is hatched;
44:22.059 --> 44:29.059
and then it has a certain adjacent stream
surfaces within, which a flow solution is
44:29.140 --> 44:34.989
to be found; and then doing that you move
from all the way from this surface to that
44:34.989 --> 44:41.989
surface from one blade to the other; other
way is you have this surface, which is quasi
44:43.829 --> 44:50.829
orthogonal; and that has certain adjacent
stream surfaces, and within that flow domain
44:50.950 --> 44:57.950
you move from hub to the tip. So, these are
the methods by which you can capture all that
44:58.900 --> 45:05.049
is happening inside this that means all that
is happening inside the blades or blade passage
45:05.049 --> 45:10.670
between two blades of compressor or turbine.
45:10.670 --> 45:17.670
This is another Blade-to-blade flow program,
in which you can capture flow domain, again
45:17.819 --> 45:24.400
from this surface to that surface; this is
a surface, in which again you have the quasi
45:24.400 --> 45:30.910
orthogonal, and the the middle of which is
the stream surface, and then this is a Hub-to-shroud
45:30.910 --> 45:36.709
stream surface. So, this is near the hub;
that is near the shroud; and as you can very
45:36.709 --> 45:42.709
well might have already guessed, this is a
flow domain that is typical of a centrifugal
45:42.709 --> 45:47.660
machine, the earlier one you were looking
at typical of actual flow machine compressors;
45:47.660 --> 45:53.099
the actual flow compressors and turbines;
this is typical of centrifugal machine that
45:53.099 --> 45:59.609
we have done the compressors; and the turbines.
So, again this is another kind of surface,
45:59.609 --> 46:06.609
which is Blade-to-blade, so that is the surface
is from one vane to the another in centrifugal
46:06.680 --> 46:12.019
machines we called them vanes, so this is
from one vanes to another; and so you move
46:12.019 --> 46:19.019
from hub to shroud surface by surface and
of course, you have the surface defined which
46:19.609 --> 46:26.609
is quasi orthogonal to the other surface.
So, you can again cover the entire space between
46:26.789 --> 46:33.660
two vanes, all the way from hub to shroud
by moving either along this surface or moving
46:33.660 --> 46:40.660
along that surface; and as result you captured
the entire flow domain inside two vanes. So,
46:40.749 --> 46:45.749
this is what is simply referred to as Blade-to-blade
flow program.
46:45.749 --> 46:51.150
So, here what what all the things, you need
the Blade geometry; you need the Inlet and
46:51.150 --> 46:57.519
Exit flow distribution, and you need the Streamline
definitions. The Output of which of course,
46:57.519 --> 47:03.440
would give you the Surface Velocity Distribution,
the pressure, and the loss distribution. These
47:03.440 --> 47:08.799
are the things of course, which you need,
the section stacking, which is very important
47:08.799 --> 47:15.799
in actual flow machine, you need to define
or have decided upon the aerofoils, the Blade
47:15.910 --> 47:21.579
Sections - the blade section Geometry, which
are as I mentioned aerofoils, then the Stacking
47:21.579 --> 47:27.849
points and the Stacking line. Most of the
conventional design has been whether stacking
47:27.849 --> 47:34.849
line is radial. So, all the blades are aerofoils
are stack radially, as we have discussed before,
47:35.420 --> 47:41.729
but many of the modern blades are being stacked
non radially; in an attempt to give Sweep
47:41.729 --> 47:48.170
or Dihedral to the blade shape, we had a few
look at few of these blade shapes. So, that
47:48.170 --> 47:55.170
is how stacking is being done in some of the
modern blades. And then these non-linear stacking
47:55.709 --> 48:02.709
lines then provide Sweep and Dihedral. So,
the exact amount of Axial and Tangential leans
48:04.410 --> 48:11.410
would have to be appropriately decided and
prescribed to apply certain amount of Sweep
48:13.529 --> 48:20.529
or certain amount of Dihedral, what you get
out of these is three-dimensional blade geometry.
48:21.319 --> 48:28.319
So, the Section Stacking Program, which essentially
is a geometric modeling, gives you the three-dimensional
48:28.959 --> 48:35.529
blade geometry. So, the Blade-to-blade flow
program gives you the Surface velocity distributions,
48:35.529 --> 48:42.529
the C p distributions, for example, on an
aerofoil and the profile and the loss distributions
48:42.559 --> 48:49.559
over these various blade shapes; two-dimensional
or three-dimensional loss distributions which
48:50.299 --> 48:57.299
would go into finally, finding the compressor
or turbine efficiency and their exact performance
48:59.529 --> 49:00.940
parameters.
49:00.940 --> 49:06.309
Let us take a look at, some of the solution
that you can get typically get out of dimensional
49:06.309 --> 49:11.299
solution of a Blade-to-blade program. Here,
the domain was all the way from here, all
49:11.299 --> 49:17.900
the way this is the whole domain inside, which
you have two blades in a cascade formation,
49:17.900 --> 49:24.829
such that the flow goes in in a prescribe
manner; and then those over this through this
49:24.829 --> 49:31.829
two passages subtended between three blades,
one, two, three; and you can see the one surface
49:31.940 --> 49:37.799
of one of the blades. So, two passages what
is being analyzed, and these two passages
49:37.799 --> 49:44.799
identical to each other; and you have to maintain
periodicity of the flow both in front, as
49:45.150 --> 49:51.619
well as at the exit. If you can do that you
get a solution of as we just stayed at what
49:51.619 --> 49:56.729
is happening over the blade surface in terms
of velocity; and pressure; and you can get
49:56.729 --> 50:02.430
the C p distribution this is a close up of,
what is happening the grid generation, the
50:02.430 --> 50:08.799
grid that have been created to capture exactly,
what is happening in front of leading edge
50:08.799 --> 50:15.559
of an aerofoil; you need very fine grids around
here near the surface, to capture all the
50:15.559 --> 50:21.549
things that are happening around the blade
surface, around the leading edge. So, this
50:21.549 --> 50:28.549
grid generation as I mentioned earlier, is
something that needs to be understood; and
50:29.219 --> 50:35.170
applied very judiciously to capture all the
details that you need to know to get on with
50:35.170 --> 50:37.009
your blade design.
50:37.009 --> 50:43.539
This is an typical output which you finally
get of that particular analysis, and here
50:43.539 --> 50:50.209
you can see the C p control in terms of the
color code that is available; and you can
50:50.209 --> 50:56.390
see the pressure of the C p distribution over
the entire flow domain, as was described in
50:56.390 --> 51:01.699
the last slide. So, this is the out kind of
output, you would get, if you do everything
51:01.699 --> 51:08.699
properly in a described or prescribed flow
domain. This was a two-dimensional cascade
51:09.699 --> 51:12.150
flow analysis.
51:12.150 --> 51:18.269
If on the other hand, you want to do a three-dimensional
flow analysis, this is what you would probably
51:18.269 --> 51:24.449
need to do, you would of course, be trying
to solve the continuity equation, the momentum
51:24.449 --> 51:30.249
equation, the energy equation, and in turbo
machinery; this is very important, you need
51:30.249 --> 51:37.190
to also bring in radial equilibrium equation
or the radial balance of forces that we have
51:37.190 --> 51:42.729
done earlier in the earlier lectures. So,
this is the flow kind of domain, he would
51:42.729 --> 51:48.829
have for the three-dimensional flow analysis,
in which you would need to solve all these
51:48.829 --> 51:53.949
equations; and find out what is happening
this is the meridianal plane that we have
51:53.949 --> 52:00.949
described before consisting of the actual
direction, and the radial direction at any
52:01.249 --> 52:07.199
given cross sections. So, it consist of the
actual and the radial access and this is where
52:07.199 --> 52:14.199
you have all the velocities that we have described
before the whirl component C w; the radial
52:15.410 --> 52:21.440
component, which the flow often acquires as
it gets inside the Turbo machinery C r, the
52:21.440 --> 52:28.440
actual velocity C a, and the meridianal components
C m, which is the combination of or vector
52:29.349 --> 52:36.349
product of C a and C r. So, that is a meridianal
velocity, so this is in rotation with angle
52:37.930 --> 52:44.930
of velocity omega; and C is the three-dimensional
result in velocity; this flow is experiencing
52:46.400 --> 52:52.099
phi is the meridianal flow angle.
So these are the prescriptions with which
52:52.099 --> 52:59.099
you proceed with your three-dimensional flow
analysis. So, it is a long drawn out process
52:59.529 --> 53:05.039
quite often in in we have seen you may have
a single stage, you have a multi stage, and
53:05.039 --> 53:11.849
then the flow solution proceeds through rotor
stator rotor stator, and it is a multi stage
53:11.849 --> 53:18.849
flow solution which often is a very as I mentioned
long drawn out affair. So, many of these things
53:20.119 --> 53:26.789
require a lot of time, lot of computation
time, so computation in Turbo machinery is
53:26.789 --> 53:32.949
a very time consuming affair compare to simple
solution over an aerofoil.
53:32.949 --> 53:38.839
So, some of these things need to be done in
a step by step manner; and of course, more
53:38.839 --> 53:45.609
you know about it you can do it appropriately,
correctly right from the beginning for example,
53:45.609 --> 53:50.969
the grid generation the choice of the grids
and many other issues that have been talked
53:50.969 --> 53:57.969
about in your last two lecturers on CFD. So,
all that needs to put together to find a good
53:58.089 --> 54:05.089
solution for a particular Turbo machinery.
In Turbo machinery everything is case by case
54:05.190 --> 54:11.160
you have to solve every there is nothing like
a general solution, every compressor; every
54:11.160 --> 54:18.160
turbine centrifugal radial would have to be
solved on a case by case basis. If the flow
54:18.339 --> 54:22.729
conditions change you have to find another
solution; if the inlet flow condition of change
54:22.729 --> 54:28.329
you have to find another solution; if the
outlet outflow condition is changed the pressure
54:28.329 --> 54:34.839
field or temperature field is change you have
to find another solution. So, many of these
54:34.839 --> 54:41.839
issues require fresh computation and you have
to get in to another round of computational
54:43.199 --> 54:50.199
exercise, to get a find another solution.
Some, of these are related to fine tuning
54:50.219 --> 54:55.769
if you change the blade geometry just a little
you think it is just a little but, it requires
54:55.769 --> 55:02.199
a full pressure computation all over again.
So, many of these things would have to be
55:02.199 --> 55:07.999
understood, as you go along apply the principles
of Turbo machinery that we have done, and
55:07.999 --> 55:13.319
apply the principles of CFD that we have just
introduce to you and you would be able to
55:13.319 --> 55:20.319
then get together solution and a blade design
that is good efficient design; and gives the
55:21.309 --> 55:28.309
performance that is wanted by the Turbo machinery
engineer in the first place, which can be
55:28.459 --> 55:34.239
then be send for fabrication and construction.
So, these are the issues that are related
55:34.239 --> 55:36.410
to CFD.
55:36.410 --> 55:43.410
At the end of CFD, he would for example, in
a compressor he would need to produce a compressor
55:43.459 --> 55:50.329
characteristic map like this out of CFD. So,
CFD would give you a compressor map, which
55:50.329 --> 55:57.029
is delta P 0 verses mass flow typical compressor
map that you have done before and such a map
55:57.029 --> 56:04.029
can be produced by CFD before you go for rig
testing. So, these are the speed lines and
56:04.369 --> 56:09.859
at various speed lines, you get various maps,
various characteristic lines of the compressor,
56:09.859 --> 56:15.519
to tell you how good this compressor is, for
example, where the stall is going to occur
56:15.519 --> 56:21.019
it gives you an indication that this is where
the stall is going occur at this mass flow;
56:21.019 --> 56:26.509
and at at which this is the kind of pressure
after which the compressor is stalled, so
56:26.509 --> 56:33.130
this is something which you can get out of
a through flow CFD program; and it tells you
56:33.130 --> 56:40.130
the characteristics of the compressor as a
first cut output of your CFD analysis; and
56:40.779 --> 56:46.209
then you can decide whether this design is
good or bad or whether you like to do differently
56:46.209 --> 56:51.180
before you go for a very costly business of
making the compressor or turbine and going
56:51.180 --> 56:57.539
for rig testing, because those are very costly
things of course, the computation of Turbo
56:57.539 --> 57:03.779
machinery also as I mentioned in terms of
computational cost is also quite often quite
57:03.779 --> 57:10.180
costly but, it is much faster than going for
very time consuming and laborious rig testing.
57:10.180 --> 57:17.180
So, this is how you you CFD in making Turbo
machinery blades, which are modern compressor;
57:19.430 --> 57:24.900
and turbine blades; many of the modern turbine
compressor blades have indeed been produced
57:24.900 --> 57:31.900
with the help of CFD, we have tried to bring
to you a number of issues related to Turbo
57:32.140 --> 57:38.459
machinery, the compressors, the turbines,
the centrifugal, the axials and we have tried
57:38.459 --> 57:43.920
to give you some idea about the fundamental
principles of aerodynamics. We have not got
57:43.920 --> 57:48.719
into the structural issues; that is a separate
issue all together, you probably have to deal
57:48.719 --> 57:53.799
with it in a separate course.
We have deal with only the aerodynamics issues
57:53.799 --> 57:59.709
in this course of Turbo machinery aerodynamics;
and at the end we have try to bring together
57:59.709 --> 58:06.709
into your attention the use of Computational
Fluid Dynamics in design and analysis of Turbo
58:08.719 --> 58:15.719
machinery. On behalf of professor A.M Pradeep
and myself, I would like to thank you for
58:16.650 --> 58:23.299
participating in this course, I hope that
we have been able to bring to you the joys
58:23.299 --> 58:30.299
and the challenges of this course, and hope
that some of you would spend some time learning
58:30.749 --> 58:37.749
it more, and may be choosing it as your carrier,
in your future carrier after the your programs
58:39.949 --> 58:44.959
are over. Thank you very much again on behalf
of professor Pradeep and myself.