Welcome to lecture number 38 of this lecture series on turbo machinery aerodynamics. We
have come towards the end of this particular lecture series, we have three more lectures
left and we have decided that as we promised in the first lecture that we are going devote
these three lectures towards discussion on some aspects of CFD or Computational Fluid
Dynamics specific towards turbo machine flows. We are assuming that you are aware of some
of the basics of CFD and that you have had a chance to understand the fundamental aspects
involved in CFD. So, we are assuming that this background information is available with
you and with that assumption we are going to discuss some of the aspects which hold
the key towards using CFD as tool for design as well as analysis of turbo machinery flows.
CFD as we know is relatively young compared to the other two methods of analysis which
have been existing for a very long time now. The other two methods being the theoretical
analysis, methodology as well as the experimental method which they of course, these have been
around for several years now, and therefore CFD in comparison to these methods have relatively
very short span I would say may be last 25 to 30 years also. So, it is in the last 25
to 30 years also, that there has been a tremendous development in techniques or design analysis
methods using a third approach which we now know as Computational Fluid Dynamics or CFD.
So, CFD is basically trying to solve the governing equations of a flow using a computing technique
using numerical techniques and that requires that we identify the domain of interest and
then decide which are the points on this flow that we would like to solve and then that
is considered to be taken as a representation of the flow field itself. So, depending upon
the number of points that we choose to analyze you can get better and better solutions depending
of course, upon a variety of other parameters like the solver being used and so on.
So, CFD though it is considered as a very powerful tool in the design analysis and optimization
loop which is a common loop that is used in any design exercise that it is taken up, that
there is a preliminary design then its goes to as 1-D analysis and then 2-D and 3-D analysis
and then it goes to an an optimization routine and then finally a CFD detail CFD analysis
and then this loop is kind of if required from the CFD analysis to be find that the
performance is not what we had intended then the designers have to come back to some of
the intermediate steps to correct those issues and try and achieve the performance that the
particular design exercise was intended for .
Traditionally these have always required the design analysis and optimization loop always
required an experimental validation of the design itself. This is partly being replaced
by Computational Fluid Dynamics, but as has been as was initially thought that CFD is
going to replace all numerical, all theoretical and experimental techniques that is quite
not true at least at that moment and few years from now that I can for see, that experimental
methods as well as analytical or theoretical methods will continue to guide us or be the
other two distinct analysis tool that will continue to exist along with CFD.
Of course, the importance and relevance of CFD is continuously growing with more and
more modifications and refinements that CFD tools have had in the last several years and
with the computing power that is available which is also increasing at an at a very fast
rate, CFD is definitely likely to be a very powerful tool which will be used and it is
continuously even now used and will continue to be used even more in design analysis in
general. But our interest as in this course is on turbo
machines and CFD of course, has been used in turbo machine design analysis and optimization
cycle, but there are certain very key challenges which are still which which still need to
be resolved. So, that CFD can be you know taken as a very standard technique of design.
Even though it is, but there are certain limitations which are which is what we shall be discussing
in today's lecture and possibly in next lecture as well.
We will continue with some of the issues associated with CFD and those which are currently under
revision in the sense that they need to be revised and better methods of estimation of
certain aspects need to be developed which hopefully will happen in the coming years.
Today's lecture we are going to devote towards basically three aspects. CFD I will give a
general introduction which I assume that you already have, but I will nevertheless give
you an introduction and overview of CFD then we shall talk about grid generation and boundary
conditions. Grid generation is is still an issue with
reference to CFD and of course, grid generation in general if you talk to people who work
in CFD they would admit that grid generation continuous to be relatively challenging aspect
because that something which is very much dependent on the geometry that we are trying
to solve. So, the more complex and intricate the geometry the more difficult it is to generate
grids for a particular geometry. In fact, considerable amount of time is usually required
for generating the grid for a very complex geometry. For example, if one has to generate
a geometry for a very complicated geometry let us say like combustion chamber including
all the holds and cooling holds which are present on the combustion chamber or for that
matter even a turbine blade which has all the cooling holds and which need to be simulated
using CFD. So, generating grids for such geometries is
extremely complicated and a tremendous amount of time is required for developing grids which
can accurately predict the performance and and people all over the world researches are
trying to develop automated tools which can be used for generating a grid which in some
form exist for relatively simpler geometries, but for very complex geometries like with
turbine blade cooling holds and combustion chambers and all that it becomes a later tricky
and we did not really have an automated grid generation tool which can faithfully grid
the such very intricate geometries and help us in the analysis.
So, CFD as I was saying is considered is now considered a standard third approach which
comes in the design analysis optimization cycle. The other two approaches as I mentioned
being the experimental approach as well as the theoretical approach. CFD definitely is
a third approach and is increasingly being used by designers in their design analysis
cycle. CFD has always been intended and will continue
to be intended to complement theory and experiments. It is not meant to replace either of them
will which is unfortunately very rather large misconception amongst people that CFD is something
which can replace experiments and theory and I do not think that is going to happen anywhere
in the future. CFD is going to compliment theory and experiments as third approach and
would of course, be increasingly used by designers all up the world.
And CFD is also very common research tool in the sense that there is lot of design exercises
which involve lot of research to be carried out on let us say optimization or a new design
to be developed through certain modifications of the shape or any other method that involves
a lot of research exercise to be carried out. CFD is definitely a very strong contender
for one of the research tools which can be used for such an analysis.
So, CFD is to summarize a few points and I was talking about CFD; obviously, is a very
powerful analytic tool and is a third approach for analysis besides experiments and theory.
CFD compliments very well theory and experiments and is primarily not intended to replace any
of these and off let CFD is very commonly used to research tool and it is definitely
recognized as a dependable research tool for a variety of flow applications accepting a
few cases where CFD is still struggling to kind of predict the performance very well.
For example, in compressor stall surge prediction that is something which CFD is not really
in a position to predict well and that is where some of these experimental or analytical
tools will still need to be used for such complex flow scenarios.
Now, let me quickly take you to the different methods or levels of CFD analysis that could
be carried out. So, one could carry out very simple fast simulations or one could carry
out very detailed and analysis of a particular flow field that it trying to simulate and
that depends upon the requirement, whether we really need it is very such high and computations
to be carried out which obviously requires a lot of time as well as effort and, and therefore
money or can simple calculations using CFD help us in understanding the the design methodology
and whether the basic design works or not. So, based on this one could either have very
simple Euler based solution which is a potential flow solution which could again be 2-D or
3-D or one could go for one level higher we could go to 2-Dimensional or axisymmetric
Navier-Stokes solution with of course, certain approximations or one could go for a 3-D Navier-Stokes
solution, one could either have a Reynolds Averaged Navier-Stokes - RANS as it is called
that is truncated form of Navier-Stokes equation using Reynolds Averaging or one could go for
an Unsteady RANS that is also called URANS - Unsteady Reynolds Averaged Navier-Stokes.
Another level higher is what is known as Large Eddy Simulation which is something which is
much more involved in complicated than URANS or RANS. Large Eddy Simulation involves simulating
the larger Eddies and computing the smaller Eddies directly. Larger Eddy Simulation; obviously,
requires much higher computational power as compare to RANS or for that matter any other
Navier any other form of solution and the ultimate aim of course, is to get what is
known as a direct numerical simulations or DNS. Direct Numerical Simulation is something
which is used well which could be eventually I would say few years from now may be could
be used for complex flow scenarios like the turbo machines. Currently this is simply being
respective to very simple flow fields like flow path circular cylinders and flow passes
an airfoil and so on. DNS involves use of the Navier-Stokes the
3-D Navier-Stokes equation in its original form without any approximations. Unlike in
RANS where there are certain approximations for example, turbulence is modeled in in RANS,
DNS does not require any turbulence modeling, and therefore that is considered to be the
most accurate most possible accurate numerical solution of a flow field, but; obviously,
this requires a huge amount of memory and also DNS is directly a function of the Reynolds
number. Higher the Reynolds number the more are the number of cells that will be required
for for us to develop a DNS solution. DNS in fact, is proportional to Reynolds number
square which means if we are looking at a Reynolds number, the number of nodes required
for DNS is square of the Reynolds number itself almost the square of the Reynolds number.
So, if you are looking at a Reynolds number which is let us say in typical turbo turbine
or compressor flows could be easily in ten to the power 5 or 6. So, square of that is
10 rise to 10 or 10 rise to 12. That is the amount of nodes or elements or discretized
elements which we will we required for us to develop DNS solutions.
Now, one could also have CFD analysis which could be either steady or unsteady as I was
saying, one could have RANS solutions or one could have unsteady RANS solutions. One may
also have is the flow requirement is such that the Mach numbers are very low. One might
stick to an incompressible CFD analysis or if one is dealing with higher Mach numbers
then that is basically a compressible solution that we need to look at.
If the Reynolds numbers are very low it could be either laminar flow solution or if it is
high Reynolds numbers flow, then we need to go a turbulent flow simulation. One may be
also dealing with internal flow or external flow. In turbo machines, generally the flow
field that we are trying to simulate are internal flows, but if you looking at let us say a
simple airfoil or a blade shape without considering the casing and all that then that could be
considered like an external flow stimulation, but in general turbo machine flows are internal
flows simulations that we carrying out. So, these are different methodologies that
are available for a designer to choose from and try to apply some of these methods in
or incorporate these methods in his design exercise and depending upon the level of accuracy
that is required from the simulations the designer may choose for either a simple 2-D
Euler solution or a 2-D Navier-Stoke solution or one could go for a 3-D RANS solutions and
possibly when an LES depending upon the computer power that is available, but not a really
a DNS at this moment we are not really at a stage where we can use DNS for full a scale,
let us say compressor flow simulation or even a turbine flow simulation we are not really
up to that level, but hopefully in the next few years we should be able to develop techniques
which can be or develop computing power which can be used for using DNS for our numerical
simulations. So, DNS is likely to be depending upon other
developments which might take place and which probably requires much less computing power.
DNS could possibly be the ultimate aim of CFD user or a CFD researcher where one can
use DNS in flow field simulations and capture the entire range of scales that are there
in a turbulent flow. For example, if you are aware of turbulence and turbulent flow situations
then we know that in turbulent flow energy dissipation is taking place through Eddies
which are which which break down into smaller Eddies and eventually dissipates the energy
and the smallest scale through which energy is dissipated is known as the kolmogorov scale
and it has scales in length, time as well as velocity.
So, these are there are several ranges of these scales which are there through which
energy is dissipated and in large Eddy simulation, we try to compute this smaller Eddies properly
and simulate using certain approximation the larger Eddies and that is why it is called
large Eddy simulation and since we are simulating larger Eddies there is and there is scope
for some approximation that is coming in which is why earlier results though or much better
than RANS solutions, they are still not the final or the correct solutions.
Well it is correct in the sense, that it depends upon the level of accuracy are we looking
at where as if you look at DNS there are no such simulation or approximations that are
taking place it is computely it is completely simulating or calculating all these scales
present in a turbulent flow which means that to be able to capture the smallest scale from
smallest scale to the largest scale that many number of grids or nodes are required where
all the governing equations can be solved and that is why it is called direct numerical
simulations which does not involve any approximation. Currently the most commonly used 3-D analysis
tool is the RANS or Reynolds Averaged either in the steady mode or Unsteady RANS that is
URANS. But the only issue, one of the issues which
RANS or URANS has is in the computation of turbulence because we as such at the moment
do not really have turbulence model or a model which can simulate the turbulence in the right
way. There are several turbulence models which are available and designer has to choose among
these set of turbulence models which are available depending upon the applications. So, there
is no model which can be set to be universal and can be used in all applications their
application depended and that is one of the limitations that modern day CFD has when it
comes to computing turbulent flow. Now, I mentioned that the governing equations are
the once which are being computed or solved over a flow field.
Let us take a quick look at what are the different governing equations that are been solved in
a particular in a typical CFD simulation. I am sure you would be aware of this, but
this is just to recap fundamentals. So, CFD basically involves solving the governing
equations of fluid flow conservation of mass, conservation of momentum, conservation of
energy. One would also be using equation of state and the species conservation in case
it is a reacting flow. For example, in a turbine flow one as there are hot gases which are
present in a turbine flow and so, one may also be required to use the species conservation
equation because one would like to ensure that the species in terms of all the constituents
of the hot gases are conserved as it passes through the turbine.
So, these are the governing equations that I am sure you are aware of and depending upon
the application some of them may or may not be use. For example, species conservation
may not really be used for a compressor flow at least the initial stages of a compressor
flow where the temperatures are not very high, one would not expect any combustion or any
reaction taking place. So, in non-reacting flows the use of species
conservation does not make any sense. So, one need not use species conservation. So,
these are the governing equations that have been solved in CFD analysis and then how do
you solve these governing equations. So, there are S series of steps of which are followed
in typical CFD analysis and basically the step begins with identification of what you
need to simulate. For example, if you need to simulate a compressor flow or flow field
around a compressor blade, one needs to define the domains or boundaries of this particular
flow field that you are simulating. So, in a compressor blade let us say we are
simulating only one blade of a compressor, then one needs to define what are the bounds
or limits around the compressor blade where we need to compute we also need to keep in
mind a few things that the domains are not too close to the surface because that would
not hel[p]- give us the chance to compute all the flow physics present. It cannot be
too far away because that will increase your computing time. So, one needs to have an optimum
domain and that is the first step of any simulation to identify the domain or boundaries of the
simulation. The second step is to discretize the domain
itself that is you would need to determine the number of points in the domain at which
the solutions or or the governing equations are solved. So, all these discretisation is
probably the second step after defining the geometry and the domain, one would need to
discretize the domain.
Discretisation would involved basically a machine or gridding the geometry by defining
points various points on the geometry and then the those points are where the governing
equation would be solved and so, discretisation could be either in the space domain or even
in the time domain. One could discretize in one definitely needs to discretize in time
well in space, one may also need to discretize in time if you are looking at unsteady solution
that is if it is a time marching solution there is also a discretisation in time domain
that is after how many times steps that we need to proceed and find out the solutions
for the next time step. Once you discretize the domain, the next step
is to define the boundary conditions that is you need to define the conditions at the
boundary because that is there the simulations would begin and then and the simulations or
the solver would maintain the boundary conditions that one is defining. Subsequently we solve
the appropriate governing equations at these discretize points and once the solving is
done through a series of iterations and once the iterations have converged as per the convergence
criteria that is been specified, one can post process and analyze the converge solution.
So, these are the series of steps that one would follow in a standard CFD solution this
is of course, independent of what you are trying to simulate whether it is flow pass
cylinder whether it is flow passed an aircraft or flow passed in airfoil or flow passed a
compressor blade, the steps that are required to be followed are identical in all these
cases. The governing equations are more or less identical, boundary conditions are different,
the geometry is of course, different. So, as we are discussing about turbo machinery
flows why is it that turbo machinery is very difficult to simulate as I have mentioned
in the beginning there are lot of challenges associated with simulating turbo machinery
flows. So, there are a few issues which are associated
with turbo machinery flows and probably specific primarily turbo machinery flows which makes
simulating turbo machine flow quite complicated and challenging task.
Now turbo machinery involves; obviously, very complex shear flows which involves shear layers
on rotating surfaces on the blades. Shear layers on which are developing on the curved
surfaces again on the blades, one may have separated flows which could be because of
shock and boundary layer interaction or corner separation or during stall. Shock boundary
layer interaction being when it is transonic case.
Turbo machinery flows also involves swirling flows, because the flow exiting a set of rotor
rotor blades are swirling and there are vortices involved in such flows and you also have interacting
boundary layers between the blade surface and the casing or blade surface and the and
the hub surface and end wall boundary layers and so on. So, all these put together make
turbo machinery flows extremely complicated and it is not possible to simplify this problem
one can of course, simplify, but with the loss of accuracy.
For example, if you have to really simulate a turbo machinery flow let us say compressor
flow, one cannot simply do a two dimensional Euler analysis and estimate the performance.
One could at a as a starting point, but it will no no way give us the exact performance
because Euler of course, solution does not give you the losses and if you go for a 2-D
NS solution Navier- Stoke solution, one would miss out on a variety of losses like the 3-D
losses which are involved. So, one needs to do a 3-D Navier-Stoke solution to be able
to estimate the performance in the right way, and therefore to be able to generate a 3-D
Navier-Stoke solution one needs to understand the complexities that are involved in this
solution. Now there are a lot of challenges as I have mentioned in turbo machinery CFD
starting from grid generation. So, grid generation itself is a challenge
because the geometry can be quite complex we have blades which could be twisted and
which could have different curvatures has lot of radii at the leading edge and trailing
edge and at the junction between the blade and the hub surface all these make the geometry
extremely complicated.
So, grid generation is an extremely involved process in turbomachinery flows plus the fact
that we also have a rotating domain. The rotor blades are rotating and the rotating flow
goes into the stator and which is stationary. So, how do how do you actually take this into
account how do factor the fact that there is a rotating domain which is present in turbo
machinery flows. Besides this the flow in turbo machine is
three-dimensional, it is highly unsteady, it is turbulent, extremely complex shear flows
as I have mentioned in previous class a previous slide. Capturing all these different effects
and and also viscous effects and put together how do you actually simulate all these using
let us say Reynolds Averaged Navier-Stoke equation, because there is certain as I mentioned
the flow is also turbulent higher turbulent. In fact so, turbulence modeling becomes a
very challenging task in most of these turbo machineries CFD's. So, how do how does a designer
or an analyst who is trying to work out performance of a turbo machine take these factors into
account because the flow is extremely a complex. And if you also look at the performance of
some of the components like let us say the fan of turbo fan engine. The fan blades tends
to deflect and vibrate under the loads the aero dynamic loads and that vibration can
also induce an effect on the flow and then there is a back effect on the structure itself.
So, there is a very strong fluid-structure coupling and it is also referred to as aero
elasticity. So, that is yet another aspect that is quite challenging to simulate and
how do you simulate aero elastic effects in some these components like a fan blade. So,
fluid-structure interaction is also important which means that CFD also needs to be complimenting
other analytical tools like finite element methods which are used for structural analysis.
So, if you look at turbo machinery CFD we have a few options available, we could go
for 2D analysis as I said 2D or you could for a quasi 3D or even a full 3D analysis.
A two dimensional analysis could be used on a conceptual design phase where one does not
want to spend lot of time on 3 analysis because he would like to first freeze your design
and look at whether the design is is conceptually feasible. Well these have been used in in
a reasonably reasonably accurate way for let us say long blades where in two dimensional
effects can be fairly well simulated. For example, in the LP turbines the last stages
of a turbine. If you are not really looking at a very simplistic solution, one can go
for a quasi 3D analysis where in the area of the flow path changes which means it is
not necessarily 3D, but it is no longer 2D as well and one can add an extra source terms
for acceleration or deceleration or the boundary layer growth as a result of area change.
One could actually go for a 3D simulation which is of late being very commonly used
where of course, one requires to simulate the true geometry, it can simulate secondary
flows shock locations and interactions of end wall boundary layers and so on and so,
3D simulations are usually used towards the end of the design face where we have sort
of arrived at reasonably good design geometry. One could also go for a transient or stationary
simulations. Stationary simulations are usually or steady simulations usually are more common.
Transient simulations, one can interact one can actually compute the flow unsteadiness
vortex shedding interaction of wake with rotors and so on. So, these are simulations which
will require a transient CFD run to be carried out. So, these are the different options that
a designer has when it comes to trying to simulate a CFD solution. One could also use
different types of solvers as I mentioned, one could go for an Euler solver or one could
go with a RANS or URANS, LES or probably DNS sometime in the future.
So, what I will take up now are 2 distinct aspects of the solution procedure which are
very important aspects of the whole CFD simulation itself. So, we will begin witH-grid generation
or mesh generation we will discuss different types of grids or meshes which are used in
CFD simulations applied for turbo machinery blades. We will then discuss about boundary
conditions in some detail.
Now grid is the discretisation or grids are used for basically discretizing the domain
and there are different types of grids or meshes which are available and which can be
used. These can basically be classified as structured grids, unstructured grids and hybrid
grids. For a structure grids are primarily more suited
for relatively well-defined geometries, but they are more difficult to generate, but it
is possible for us to control the near-wall clustering of the cells very well. That is
because, one can change the near-wall number of cells very close to the wall in a much
better way using near-wall clustering and it is possible it is gives us more flexibility
and control over the size of grids. At the same time, structured grids require less number
of well less memory power. The only issue is that it is more difficult to generate and
when the geometry is very complex, structured grids may not be very easy to generate.
Unstructured girds on the other hand are intended primarily for complex geometries, they are
easier to generate it and very easy to automate as well, but the major disadvantage is we
do not really have a control over the near-wall clustering, we do have some control, but not
as much as control as we have in the case of structured grids. So, a designer would
often want to use structured grids for his analysis.
Let us take a look at both of one example of both of these different types of grids.
So, this is a typical structured grid and as you can see there is a certain amount of
structuring and you can define the grids in certain manner and it is not random. Structured
girds are usually used with multiple blocks and I will explain what is blocks and topology
little later, but you can see they are distinct where is one block here around the blade,
there is another block here, there are blocks here as well. So, this is what is known as
a multi block structured grid.
And this is a typical unstructured gird and you can see that the grids are not in a particular
fashion. And they are relatively random and this is a typical example of an unstructured
grid. These are unstructured grids you can see that immediately that not very easy to
control the clustering around the blades where you would like to simulate the boundary layers
as well.
So, let us start with the structured grid multi-block and these are multi-blocks are
used if we need to simulate curved surfaces. So, generating a structured grid without multiple
on a single block is very difficult it is not really possible without having multiple
blocks around the curved surface and the in order to define multiple blocks on the curved
surface one needs to define what is known as a grid topology and grid topology also
is to it is should ensure that the grid topology will basically remain the same from the hub
to tip and so, that grid topology should be able to account for the variations in the
blade shape from all the way from hub to tip. So in a multi block structured grid, one needs
to first identify and develop the topology of the grid on the surface and then generate
the grids within each of these blocks and at the interface of these topologies or interface
of these different blocks the number of cells will have to be the same usually the same
and of course, in some solvers they dO-grid generators, they also give us a provision
for having variable number of mesh points at the interface. So, then adjacent blocks
need not necessarily have the same number of cells, but usually it is a practice used
to maintain the same number of cells across the blocks adjacent blocks.
So, when you develop these number of discrete number of blocks of around a surface, one
can actually control the number of elements in each of these blocks and that is the main
flexibility which a structured grid provides over an unstructured grid.
So, if you look at grid topology it is basically a structure of blocks that axis a frame work
for for measuring the mesh elements. So, you have to generate mesh, one needs a structure
into which the meshes can be placed or grids can be placed. The blocks are basically laid
out without any gaps so; obviously, and shared edges are and corners are possible blocks
contain primarily the same number of elements along each side. Topology usually does not
change from hub to tip as I mentioned one needs to maintain the same topology from hub
to tip and one can edit the topology on 2-D layers from hub to tip which means that if
you change it on any of these surface it will basically be applied all over from hub to
the tip section. The number of blocks will also determine the
skewness of the grid elements that is if you use lesser number of blocks, if you do not
have any blocks at all and try to generate a structured grid then what would happen is
the regions with where there is a very sharp change in the slope or curvatures the mesh
or the grid becomes extremely skewed and such a skewness can lead to lot of issues in convergence
of the solution or accuracy of the solution itself and that is why multiple block are
anyway required for curved surfaces and use of multiple blocks will give us a lot more
flexibility in terms of the mesh or grid management around the surface.
So, let us look at what are the different types of topology schemes that one can use
let us start with the O-grid. O-grid is usually used around the blade by forming a continuous
loop around a surface and it gives us very good boundary layer resolution because it
is around the blade surface that we would really be like interested in capturing the
boundary layer and the viscous loss effects. O-grid gives good control over y plus values
that needs to be tightly monitored as you are aware, y plus refers to the nearest element
to the surface and to be able to simulate the boundary layers very well one needs to
have very low values of y plus. O-grid gives us a very good control over the y plus and
O- grid also provides near orthogonal elements of the blades.
Now, let us look at a one of the O-grid topology. So, this is an O-grid that you can see around
the blade all along the blade there is a set of elements which have been demarcated as
you can see the close up of this leading edge of the blade, you can see that this is basically
the O-grid which demarcates the grid around the blade from rest of the blades.
So, there is clear cut demarcation here and that is possible because of the O-grid that
is usually developed around the blade surface. So, this is the basic O-grid topology.
Now there are other forms of topologies which I have shall discuss now there are J-grid,
H-grid, C-grid and L-grid. J-grid is usually used near the leading and trailing edges and
it usually wraps up in opposite directions at leading and trailing edges. On the other
hand, H-grid tends to complete the meshing by adding some blocks in an unstructured manner
that is towards the leading or trailing edge one may have some elements of unstructured
blocks. The structured blocks usually extend from upstream of the leading edge, downstream
of the trailing edge and between blades and periodic surfaces and you may have certain
elements of unstructured blocks which the H-grid will develop for us.
These are two examples of typical J-grid and H-grid topologies and why is it called J-grid
because you can see that this resembles a J and that is why there is a set of elements
which are resembling the symbol J. So, you can see a J here, this way and the J as I
mentioned would be in opposite orientation. So, at the trailing edge it is in this direction.
So, this is a typical J-grid topology and on the right hand side you have an H-grid
topology. So, H is resembling the letter H and so, this
is basically an H-grid topology and as I mentioned H-grid topology may lead to some amount of
unstructured elements towards the leading edge and trailing edges on account of the
topology itself. So, if you had introduced yet another block here that would become a
J-grid and then you may not require this unstructured block which are present here and all these
are in conjunction with an O-grid, you can see the O-grid right around the blade in both
J-grid as well as H-grid topology, one can see the O-grid right along the blade surface.
So, most these topologies are usually used in conjunction with an O-grid topology because
O-grid is some which gives you control over the boundary layer resolution or the grids
around blade surface which is where the boundary layer is one would like to capture that to
the best possible extent and so, O-grid gives you the flexibility.
There are other forms of grids which are also sometimes used the C-grid or the L-grid and
irrespective of what gird is been used whether it is J-grid, O-gird, C-grid or L-grid. There
are all used in conjunction with an O-grid for good resolution of the boundary layer
and it is also necessary that resolve the leading and trailing edges very well, because
the leading and trailing edges one has a very sharp in a let us say high speed compressor
blades the leading and trailing edges can be relatively quite sharp at a radius radii
at leading and trailing edges could be very small resolving these edges are very important
because performance of the whole compressor is a function also a function of the leading
and trailing edge radii. Now, irrespective of what kind of grid we
use or which application is to be used for one needs to establish that the grids or the
solutions that you get from the computations are independent of the grid sizes that is
if you use 1 million cells or 10 million cells is there is a difference in solutions then
which one do you believe one would want to believe which has more number of cells. So,
it is a common practice now standard practice now to establish the grid-insensitivity or
grid-independence of any simulation. So, one needs to demonstrate that as you change
the number of grids from certain number to the double that number or half the number,
the number of the depending upon how many numbers you have changed the solution should
not be dependent on the number of grids that you are using, and therefore one would of
course, like to optimize between number of cells used and the best possible solution
and that is where one would want to do a grid sensitivity analysis and establish that the
number of grids you are using for analysis is optimum and the solution for that particular
number of grids and anything above that would remain the same. So, one needs to establish
grid-independence irrespective of what kind of topology are you using.
And let us take a look at 2 other grid topologies the L-grid and C-grid. This is the L-grid
topology very similar to a J-grid, but just that in a J-grid one had a section here and
this is basically the L-grid topology that you can see and this is a typical C-grid topology
you can see that unlike the multi-block here multiple number of blocks here you have only
2 blocks which have been provided and this is the typical C shape that you get and that
is why it is called a C-grid topology. So, which topology to use basically depends
upon the application and there are certain standard thumb rules which are available which
can help an analyst making a decision on which kind of topology that he needs to use for
his application. So, I did not understood some elements of grid and grid generation.
Let us look at the other aspect of starting the simulation that is basically the boundary
conditions. Boundary conditions are; obviously, extremely important for a particular solution
and its accuracy because the solution primarily depends upon what kind of boundary conditions
you are setting. So, depending upon a different set of boundary
conditions the solutions can entirely be different. For example, if you look at a compressor operation,
if you set the design boundary conditions right one can get the design operating conditions
or simulations for that operating conditions, but if you get the design operating or the
boundary conditions which lead towards compressors. So, as then the solutions are entirely different
from what it should have been, and therefore to get the correct flow physics and to be
able to make sense out of the simulations one needs to ensure that the boundary conditions
are set correctly.
So, basically boundary conditions are essential in capturing the flow physics correctly and
appropriately and; obviously, the quality of the solution that you get is a very strong
function of the boundary condition itself. In a turbo machinery flow, there are of the
4 distinct types of boundaries that one would encounter. The inlet boundary from which the
flow begins or initiates, the exit boundary that is at the outlet of the flow domain,
periodic boundary on 2 sides of the domain and walls or surfaces which could be the blades
could be the hub or the casing.
So, this is the typical flow domain with the boundaries I have shown. This is compressor
blade here we have a low speed compressor blade the flow enters through the blade domain
and here we have seen relating only one blade and since all the blades are identical we
will have to set what are known as the periodic boundary conditions.
So, this is the inlet domain that you can see here as the inlet, this is the hub surface
of the of the blade and this is the shroud of the tip. The flow enters through the domain
here and then it exits through the outlet which is shown here in an orange and this
is known as the outlet domain and on the sides of the blade we have what is known as periodic
boundary conditions which means that whatever happens here will be a reflection of what
should he happening even if they work in number of other blades it around it and the periodic
boundary walls will depend upon the number of blades basically depending upon the solidity
itself, if you have more number of blades then these boundaries would come closure.
In this particular domain, this is the domain which rotates and these are the 2 domain that
is the inlet and outlet domains are the one which are stationary. The rotor domain is
the one which rotates.
So, if you have to set inlet boundary conditions it; obviously, depend upon the application
itself which depends upon the flow conditions whether it is incompressible or compressible,
the most commonly used boundary condition for the inlet is this a set of predefined
total pressure at the inlet, total temperature and the velocity components or profile at
the inlet. So, this is most commonly used form of inlet
boundary conditions which are applied in a standard CFD solution for compressor or turbine
flows. There are other forms of specifying boundary conditions it could be velocity inlet
which if it is very low speed in compressible flow, one might even want to specify just
velocity inlets or a mass flow inlet and there are these are not generally used because there
are lot of limitations with specifying this as compared to the total pressure, total temperature
velocity components because that is specifying velocity or mass flow rate alone is too simplistic
boundary condition to be applied which probably is or simple two-dimensional analysis if you
one would carrying out that, but not generally used for series serious high and CFD dissimulations.
Similarly at the exit, one needs to specify a set of boundary conditions.
Now here again there are different ways of specifying boundary conditions, most commonly
used are either static pressure which can for a given inlet pressure give you a certain
amount of mass flow rate. The other boundary condition that one could use is mass flow
rate itself and for low speed incompressible flows whether you specify a static pressure
or mass flow rate the results are not going to be highly different and they are not very
sensitive to this boundary condition, but for high speed compressible flows specifying
static pressure at the exit is the standard practice and one would and also it this is
a common practice even now used for low speeds simulations it has been sort of establish
that a specifying static pressure is probably a better way of defining mass flow rate at
the exit of the domain. So, one could specify either static pressure at the exit or just
the mass flow rate itself
and but I say I mentioned for low speed incompressible flow it should not really matter whether you
are specifying static pressure or mass flow rate and it is also possible that one can
specify a static pressure distribution at the exit rather than just an average static
pressure, one may also want to be a little more accurate, one can simulate a static pressure
distribution as well at the exit.
Now, for single passage simulation like the one I have just showed periodic boundaries
are used for simulating the effect of a blade row and it is necessary that one appropriately
chooses this domain, so that periodic or periodicity is indeed valid. And on the surfaces like
the blade or the hub or the shroud it the standard boundary conditions like no-slip
and adiabatic conditions are used. But if you look at a turbine flow which has
hot gases present if you are also simulating the hot gases effect in a turbine flow instead
of adiabatic condition one may replace that with a constant heat flux condition . So,
these are the two periodic conditions that I mentioned and selecting this is very important
because this basically represents the solidity of the compressor itself and it simulates
the curvature on either sides of the blades. So, these are the different types of boundary
conditions that one can simulate, one can actually one needs to specify at the inlet
exit and the side walls and surfaces to be able to simulate the performance and flow
conditions and flow physics run correctly. So, let me now quickly recap our discussion
in today's lecture and we had a very quick discussion on CFD in general, this is as I
mentioned in the beginning this assuming that you have some knowledge of CFD already and
so, we are trying to look at CFD in general, but we are trying to understand aspects of
CFD in in the context of turbo machine flows and in that context I mentioned about two
distinct aspects today that is the challenges involved in grid generation to which I also
explained the different types of grids that are possible for a turbomachinery blade simulation
and the key challenges involved in grid generation. Subsequently we also discussed about boundary
conditions and the right way of setting boundary condition for turbo machinery flow simulations.
So, we will continue discussion on some of these aspects in next the couple of lectures
as well in the next lecture I intend to introduce a few other challenges which are involved
in turbo machinery flow simulation to do with basically the turbulence modeling and associated
problems are shown with turbulence modeling and why is it necessary that we use the right
model for a set of problems that we are trying to analyze. So, we will take up a few of these
aspects in the next two lectures that we would going to have on CFD as applied for turbo
machinery flows and next lecture we will take up some more challenges which are specific
for turbo machinery CFD. So, we will take up some of these topics for discussion in
the next lecture which would be lecture number 39.