10.1 Estimating the numerical error

A well-known but often neglected fact about CFD calculations is that, unless the number of space and time intervals is sufficiently numerous, numerical errors render their results dubious.

How numerous is "sufficiently"? There is no way of finding out for certain other than repeating the calculations with a greater number of intervals, so as to determine whether the physically-significant results are appreciably altered.

This is an accepted rule; but it is rarely observed, because the expense of finer-grid calculations may be hard to tolerate.

EXPLOITS is not different from other codes in this repect. However, because it can run on parallel machines, the cost of the finer-grid runs may not be excessive.

By "science-based uncertainty" is meant that doubt which should properly attach to the use of "models" of turbulence, chemical reaction and radiation.

This doubt is quantitatively substantial; and may entail that one cannot be sure whether the predicted peak pressure, for example, is correct within plus or minus 50 %.

This is regrettable; but it is not the fault of the computer-code vendors, who can do no more than incorporate in their software the best that science has so far brought to light.

[Only those are at fault fail to emphasise their limitations]

How large may the errors be? Only extensive comparisons between predictions and experiments can reveal this.

The expense of these experiments entails that it may be many years before the question is adequately answered.

Before too much blame is heaped on the heads of the code vendors for not making fine-grid computations cheap enough, or of the scientists for not providing 100 % reliable models, it should be remembered that the questions that the predictions are intended to answer are not always posed with sufficient realism.

Thus, a uniform stoichiometric mixture of gas and air may be postulated as prevailing throughout the module in which the explosion is to be simulated; yet this is an initial condition which could never be attained in practice.

Or wind conditions external to the module may be supposed irrelevant and therefore inserted with little thought, whereas in fact a cross- wind may influence gas mixing within a module greatly.

Finally, the making of initial-condition postulates about the locations of gas leaks and ignition sources involves much guess-work; so it may well be argued that, with so much uncertain, some numerical or scientific deficiencies can be tolerated.

What CFD models are good at is revealing trends, which is to say the directions, and approximate magnitudes, of changes in the effects which will result from changes in the postulated causes.

Examples of conclusions of a believable kind are:-

"A 50 % increase in the spacing between the heat exchangers produces a 30 % reduction in the peak explosion pressure."

"Replacement of module-wall A, by one which will break at a pressure differential of ...., will reduce to maximum pressure on wall B by only 20 %".

"The introduction of a grating, in place of a solid floor, will make it impossible for a vapour/air mixture of flammable ratio to collect in the under-floor space, provided that the cross-sectional area of the passage between ... and ... is not reduced by more than 75 % ."

Other statements in which it may be safe to put some trust are of the following form:

"A water spray of ... kg/s m**2 may is much more than enough to extinguish a fire in ..... fed by oil supplied at the rate of ...."

"Fragments from the wall between Modules B and C, which is expected to break when the B-side pressure reaches .... , will probably hit the side of the .... tank with velocities of up to ..... m/s ."

"Should a fire break out in module D, ventilation-inhibiting and fir resistant screens, dropped across the windward end, will greatly reduce the rate of heat production; but it will be advantageous to provide a special stack though which the combustible gases can escape harmlessly to the atmosphere"

Experimental validation of predictions is, of course, the best basis for belief in them. However, it is necessary to be cautious even when a hundred or a thousand not-too-bad comparisons can be claimed for a particular code.

Thus, if all the cited cases concern small-scale experiments and none relate to large-scale ones of the kind currently of interest, the relevance of the claim is much reduced.

Or, the cited tests may have been made with uniform-composition gases, whereas in the circumstances of concern (as is usually the case) a variation of mixture ratio from below the lower flammability limit to above the upper one.

It is certainly safest to start from the assumption that NO computer code has been adequately validated; and thereafter to look at the inherent plausibiity, and the sensitivity to assumptions, of the results which are presented.

wbs