4.1 A typical scenario
4.2 The physical and chemical processes considered
4.3 How PHOENICS takes these into account
4.4 Some typical findings
What if there does indeed exist an ignition source within the region
in which EXPLOITS predicts that a flammable mixture will form?
Will the flame be extinguished before spreading?
Or will it propagate with increasing speed and violence, leading to
fully-developed explosion?
Such are the questions to which the EXPLOITS-PHOENICS conbination
seeks to supply probably-correct answers, subject of course always
to the NOKFOS proviso.
Of especial interest are the additional questions: what will be the
pressure differences across damage-prone confining walls? and how
will these vary with time?
When a spark ignites a flammable mixture which is initially at rest,
a thin spherical flame spreads from it at a speed, relative to the
unburned gas, of between 0.1 and 1.0 metres per second, depending
upon the fuel and its concentration.
Such flames, although they might have bad thermal effects by reason
of their high temperature, can scarcely damage structures, because
pressure differences are of the order of: density * velocity ** 2.
So, unburned-gas density being of the order of 1 kg/m ** 3, and
velocity of the order of (at most) 10 m/s, no pressure differences
in excess of 100 Newtons/m**2 are likely to arise, ie of 0.1 % of an
atmosphere.
A PHOENICS simulation of such a flame now follows.
To consider the other extreme, let it be supposed that the
combustible mixture is completely confined within a fixed-volume
enclosure, raising the gas temperature therein from, say, 300 deg K
to 2100 deg K.
Then, no matter how rapidly the flame propagates, the pressure rise
will be of the order of 2100/300 - 1 , ie 6 atmospheres.
This is enough to fracture many structural elements.
Unfortunately, this is not even the worst case, as will be discussed
below.
In offshore-platform modules, the gas mixtures, if they burn, must
be regarded as partially-confined; for they are present in spaces
between solid obstacles, both large (such as compressor housings)
and small (such as tubes within a tube bank).
The influence of these restrictions to flow is to distort the shape
of the flame in such a way as to promote the mixing of hot burned
gas and cold still-to-be-burned gas.
This increases the volumetric burning rate, and so the "flame speed"
(the quotes providing the qualification "in so far as this concept
has any clear meaning") by one or two orders of magnitude.
The following PHOENICS-created simulation indicates how this comes
about.
The predictions agree fairly well with the experimental data.
The motion of gas through the succession of restrictions and
enlargements represented by the solid objects in an oil-platform
module creates "shear layers" ie regions exhibiting steep variations
of velocity.
Turbulence is created in these layers; and this promotes the further
mixing between burned and unburned gases which leads to further
combustion.
The "flame-acceleration cycle" can therefore be represented as:
It is not only velocity gradients which lead to flame acceleration;
for pressure gradients can do so as well.
They act by accelerating the less-dense hot-gas fragments more
easily than the more-dense unburned fragments. The former are
therefore thrust vigorously into the latter, forming new sources of
ignition.
This process can lead to detonations, ie explosive waves in which
the pressure exceeds even the constant-volume-burning pressure
calculated in sub-section (b) above.
This mechanism can be predicted by the two-fluid model of turbulence
which is a feature of PHOENICS; and it is illustrated by the
following pictures which show how a modest pressure wave can develop
detonation-like behaviour.
Velocity vectors of the cooler gas Time increases from left to right
Velocity vectors of the hotter gas, which has been more greatly accelerated
The contours of pressure At later times much higher pressures develop
It is usual to represent the ignition proces by the sudden raising
of the temperature of a small body of gas, for example that in a
single computational cell.
Until the flame meets the first obstacle, it is represented as
progressing as a thin front at the speed which is known from
laboratory experiments.
Differential equations are usually solved for the energy and the
length scale of the subsequently-generated turbulence. These may
contain special empirically-derived terms for the effect of
(restricted kinds of) obstacles.
The rate of burning of the gas is then taken as proportional to the
rate of energy dissipation, ie to the square-root of the energy
divided by the length scale.
This practice was first advocated in 1971 (Ref. 4), when it acquired
the name "eddy-break-up" model. A modification called the "eddy-
dissipation concept" was proposed in 1976 (Ref. 5). Most CFD codes
seeking to simulate explosions employ variants of one of these
models.
All such practices rely on the notion that there are two
distinguishable gases at each location, one significantly hotter
than the other. They can be classified as "two-fluid" models.
PHOENICS, and therefore EXPLOITS also, embody the recently-made
generalisation, ie the "multi-fluid" model.
The next picture, extracted from CHAM's contribution to the SCI
Spadeadam project, indicates the nature of the predictions made by
PHOENICS.
the nature of the predictions made by PHOENICS.
wbs
4.1 A typical scenario
4.2 The physical and chemical processes considered
(a) Flame propagation in unconfined gas mixtures
(b) Pressure rise in fully-confined gas mixtures
(c) Pressure rise in partially-confined gas mixtures
(d) The generation of turbulence by the flame
The effect of shear stresses
burning ----> gas expansion ----> increased velocity -->
^ |
| V
<--- mixing <---- turbulence < velocity gradients <--
The effect of pressure gradients
4.3 How CFD codes simulate the processes
(a) Ignition
(b) Laminar-flame propagation
(c) Turbulence generation
(d) Turbulence-controlled combustion
4.4 Some typical findings
