Hello. Well, here we are,
we're at the last video. And I don't know about you but
I'm quite excited about this. I've been working on this for months, and
I'm really ready to be done with it and look forward to posting it so
that you folks can look at it. And I hope you've found it
an enjoyable experience or a youthful experience in any event. So what this last video is about as
a little bit about numerical methods for chemical kinetics. So as we discussed earlier, detailed
kinetic behaviors described by a set of read rate equations,
sometimes a very many rate equations. And to solve these equations requires
that all the rate coefficients and initial conditions be known. Since thermodynamic state makes, since
the thermodynamic state maybe changing one must solve the appropriate
conservation equations as well. And therefore, depending on
the physical system being considered, a large number of differential equations
must be solved and support for calculating rate constants and
thermodynamic properties. And transport, etc., must be provided. There is however, a big problem,
and that is the stiffness problem. So the characteristic times for
reactions can vary quite a lot. If you have a simple dissociation reaction
and unimolecular dissociation reaction, you can write the rate equation as
da DT is equal to minus K over A. And the simple solution of that
equation is an exponential. A at some time is equal to
the initial value of A, and when I say I mean concentration of A,
e to the minus kt, so the characteristic 1 over e time for
that reaction is 1 over K. Now for
real kinetic mechanisms its usual for the characteristic reaction times to
vary over many orders of magnitude, sometimes as many as ten to the nine or
ten to the ten order of magnitude. And this leads to the so-called
stiffness problem. So if a system of equation is stiff then
the step size needed to solve the system numerically is driven by the dependent
variables that are changing the fastest and this leads to extremely slow
solution times to overcome this problem. A number of methods have been
developed most notably ones that go into the- Pac package
of solvers and the gear method, and these are these are methods
that are typically used in both open source, and
open source and commercial codes. So this is a little bit
about to such codes. Chemkin is a commercial code, Cantera is
an open code, and they're designed for solving model problems of chemical
kinetics chemical kinetic model problems. Chemkin was originally developed at
the combustion research facility at Sandia National Laboratories in Livermore,
California. Commercial Code, it's now distributed
by ANSYS, and it's expensive. Cantera is an open source
code written in C++ and it's run via Python or Mac Matlab,
and you can get it for free. It doesn't cost anything. As I mentioned very early,
probably in one of the first videos in the whole series of courses is
that the advantage of commercial codes is that they generally have
a much easier to use interface. On the other hand,
they cost a lot of money, and the open source codes
are sometimes a little, you know, you have to run them a command line or
you can run them in Matlab. Or Cantera in any event you can run
in Matlab, and sometimes the physics in them are actually more up-to-date
than the commercial codes. But Chemkin's a fine, fine program and Cantera is a fine program, so
it's kind of depending on what you need. They do come with some different,
different features. So both Chemkin and Cantera are not full
CFD solvers, they solve model problems. And here are some example model problems,
a stabilized flame. So there are class of burners
called flat flame burners, and generally they are for
pre-mixed conditions. And the the fuel and oxidizer flow
through some kind of centered material that's temperature is controlled,
and that tends to stabilize a flame
that forms on the downstream side. There are opposed jet flows
where you have an oxidizer coming in one side and
a fuel coming in the other. You could have potentially have
a free-standing flame or you could have a what's called a plug flow reactor where
it's uniform in the radial direction. There's no diffusion in
the radial direction. You can have what they're called boundary
layer flows where you have a pipe or say two plates where there is
diffusion in the cross in that radial direction or cross flow direction. And that leads to a velocity
temperature profiles and so on. You can have just a reactor, can be
a well -stirred reactor, so-called well- stirred reactor or just a constant
pressure or constant volume reactor. You can analyze shock waves,
you can have what's called a stabilized burner flow where you have
a flat flame burner, but the flow impinges on a plate and
you can have various rotating designs. Those are used for
chemical vapor deposition problems. What all these model problems have in
common is they have a very simplified form and so their conservation equations
take on pretty simple forms and are therefore easier to solve numerically. So here's an example,
this is a stagnation flame example. And so what is plotted here is a mole
fraction of several species and the temperature versus
the height above the burner. So in this case zero means the surface
coming out of the porous plate, and the other end is the stagnation plate. And typically you would specify the
temperature at the centered surface and you specify the temperature of the wall,
the stagnation wall. And so the black line here
is the temperature, and it goes up because of heat release, but it
is it is fixed at the stagnation plate and it's a fairly high
temperature in this case. And then you can CO2 H2O Co CO2 and
methane. And this is actually an ethylene or H2H4. I'm sorry a C2H4 is ethylene, and its combustion of ethylene in oxygen. So this is the kind of problem you can do,
and of course a whole variety
of problems you can do. So finally, if you have a more complex problem you
have to use full CFD with reactions. And this is example example of
some work that's gone on in our group our combustion group,
and its flow in a wind tunnel. We study wildland fire, and
we have a wind tunnel, it can be tilted. And this is the calculation of
combustion up an inclined surface and there's a video that goes with this, and can you can can watch as
the combustion begins to occur, and the wood surface, Begins to burn. But this is a pretty complex problem. It takes a long time to run and
it's a full CFD solution. But many, many other kinds of
combustion problems are solved in this fashion using
full CFD simulations. So that's this video and
it's the end of the entire set of courses, the entire program. And I thank you for
your attention during all of this, and I hope wish you a great day and
a great career. And thanks very much for listening.