2.1 The certainties
2.2 The models
2.3 The properties of the materials
2.4 The initial and boundary conditions
2.5 The mathematical techniques
CFD rests on the sure foundation of the scientific laws of:
However, because the rigorous working out of the implications of all
these laws would vastly over-stretch modern computational power,
SHORT-CUTS are used. These are usually called "models".
CFD therefore rests also on the less-secure foundation of models of:
So the same guess-what's-important-and-ignore-the-rest process as
underlies empirical models is in operation here, but it a deeper
(and less damaging) level.
The turbulence models in current use derive mainly from researches
at Imperial College in the 1970's, with additions, in respect of
combustion, from the University of Trondheim.
Recently, after many years, new advances have been made at CHAM, and
have resulted in the LVEL and Multi-Fluid Models of Turbulence, both
of which can be activated by EXPLOITS.
The new approach allows quantitative computation of what had
previously to be guessed, namely the probability-density-function
which describes the fluctuations of temperature, concentration, etc.
The next few panels indicate what is entailed.
They show computed "fluid-population distributions" (a) in a gas-
mixing process, and (b) in a steadily-propagating flame
The displays on the left will show the population distributions
in a mixing layer, the leaner mixtures being on the left and the
richer on the right.
The displays on the right are reminders of how the population
of fluids might be distributed in a single computational cell,
namely at random.
A series of FPDs will now be shown, for a succession of
six different locations across the layer.
Such copious and detailed information about what happens in gas-
mixing and combustion processes has never been available before; and
its full implications will take some years to work out.
The important point to note is that the "strangle-hold" of the
so-called "k-epsilon model" has been broken, and research can at
last advance again.
The next sequence relates to one-dimensional steady turbulent flame
propagation.
It shows how, with the multi-fluid model, "population-grid-
refinement" studies can be carried out, so that it can be determined
how many fluids are needed for the desired accuracy.
This indicates how much expense is actually worth incurring; and it
shows that the necessary number of fluids may be quite small.
Aggregate-reaction-rate profiles for the 10-fluid model
Aggregate-reaction-rate profiles for the 20-fluid model
Aggregate-reaction-rate profiles for the 100-fluid model
The small essential differences brought about by population-grid
refinement beyond 20 fluids are confirmed by inspection of the
fluid-population distributions at a fixed point in the flame.
These will now be shown.
Fluid-population distributions at a fixed point in the flame for the 10-fluid model; IX/NX = 1/4
Fluid-population distributions at a fixed point in the flame for the 20-fluid model; IX/NX = 1/4
Fluid-population distributions at a fixed point in the flame for the 100-fluid model; IX/NX = 1/4
Even coarser sub-division of the fluids may be tolerable. Thus
the first computations presented by CHAM regarding the Spadeadam
experiments used a four-fluid model.
The two-fluid models ("eddy-break-up" or "eddy-dissipation concept")
used in earlier versions of PHOENICS, and in other computer codes,
now appear to be far too crude.
Regrettably, to discuss the matter in more detail here would
unbalance the lecture.
However, it is hoped that enough has been presented to make it
seem probable that turbulence research is again on the move.
Although explosion processes occur too rapidly for radiative
transfer of heat to exert much influence, quite the opposite is true
of the spread-of-fire process which may take place subsequently.
Radiation is a complex expensive-to-compute-exactly process. The
challenge has therefore been to invent a more economical (albeit
less rigorous) approximately-correct formulation.
The IMMERSOL technique (unique, so far, to PHOENICS but therefore
accessible to EXPLOITS) handles simultaneously radiation between
solid surfaces, heat conduction within those solids, and convective
and radiative interactions with the surrounding fluids.
Since this method is new (having been developed only in 1996) all
that can be asserted is that the method gives exactly correct
results in simple circumstances and plausible results otherwise.
It is also the only truly practicable method in existence.
Chemical reaction is also a complex expensive-to-compute-exactly
process; for what may be expressed simply as a single step, ie:
fuel + air ----> carbon dioxide + steam + heat
truly proceeds by way of hundreds of individual reactions involving
scores of distinct individual species, eg H, O, OH, CO, NO, etc.
Fortunately, in contrast to some other applications for which
PHOENICS is used (eg furnaces, gas-turbine combustors and
reciprocating engines), single-step models such as the above suffice
for explosion and fire-spread simulation.
It is far more important to represent the turbulence properly than
to refine the chemical-kinetic description.
EXPLOITS, like all flow-simulation software, must be supplied with
information about the properties of the fluid and solid materials
which are present and active.
Fortunately there is no difficulty about this; for EXPLOITS is
supplied with tables of properties of both solid and fluid
materials, which require simply to be selected by name.
A link also exists to the public-domain CHEMKIN data base.
Of course, in practice it may be hard to determine what particular
mixtures of hydrocarbons are involved in the leakage and explosion.
However, whatever the problem-specifier decides upon, EXPLOITS can
accept.
2.1 The certainties
2.2 The models
These models are embodied in sets of mathematical equations, similar
in form to those for the conservation of mass, momentum, etc, which
purport to describe the most significant aspects of the phenomena in
question.
Models of turbulence
First the mixing process
Turbulent flame propagation
Models of radiation
Models of chemical reaction
2.3 The properties of the materials