Encyclopaedia Index

2. The scientific basis of computational fluid dynamics


    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

2.1 The certainties

CFD rests on the sure foundation of the scientific laws of:

2.2 The models

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:

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.

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.

Models of turbulence

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

First the mixing process

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.

Location 1

Location 2

Location 3

Location 4

Location 5

Location 6

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.

Turbulent flame propagation

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.

Models of radiation

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.

Models of chemical reaction

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.

2.3 The properties of the materials

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.

2.4 The initial and boundary conditions

It is the problem-specifier's task also to define where the materials are located at the start of the process to be simulated, both in respect of:-

The task of the designers of EXPLOITS has been to make it easy for its user to introduce this information, and to see what he or she has done.

How this is achieved will be described below, in section 6.

2.5 The mathematical techniques

For those who are interested, there is much to be said (elsewhere) about the ways in which PHOENICS solves the equations which express the problem which the user of EXPLOITS has set.

For the user himself, however, all that is necessary is to state that he does not need to concern himself with such matters.

He should know that:

However, although the EXPLOITS user can "take over the controls" himself, he is advised to leave procurement of convergence to the built-in "auto-pilot", or to an expert human assistant such as is provided for by MICANET.