Encyclopaedia Index

4. CFD applied to explosions


    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

4.1 A typical scenario

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?

4.2 The physical and chemical processes considered

(a) Flame propagation in unconfined gas mixtures

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.

Sim 1

Sim 2

Sim 3

Sim 4

Sim 5

Sim 6

(b) Pressure rise in fully-confined gas mixtures

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.

(c) Pressure rise in partially-confined gas mixtures

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.




(d) The generation of turbulence by the flame

The effect of shear stresses

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:

        burning ----> gas expansion ----> increased velocity -->
          ^                                                     |
          |                                                     V
           <--- mixing <---- turbulence < velocity gradients <--

The effect of pressure gradients

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

4.3 How CFD codes simulate the processes

(a) Ignition

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.

(b) Laminar-flame propagation

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.

(c) Turbulence generation

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.

(d) Turbulence-controlled combustion

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.

4.4 Some typical findings

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.