Was the second - the big - explosion of the reactor core in the Chernobyl catastrophe a true nuclear explosion? There have been those who have said that it was ... but sayings to this effect do not gain much public traction. I think that explanations that invoke hydrogen production through the reaction of steam & zirconium are grossly implausible.
Any answer to this will necessarily import notions as to what constitutes a true nuclear explosion, and I am not stipulating any particuIar definition of one according to which this question 'is to be' answered. It could perhaps be said that the definition is one of the 'degrees of freedom' of it.
So the question really hinges, I think on whether the reactor was there, fatally damaged, and quite grossly overheating, with steam building up to high pressure, with free oxygen & hydrogen present, which at some point ignited explosively; or in a state in which essentially the same 'race' between escalation-of-nuclear-reaction & tendency to dissemble of the very reacting substance of the core was occuring as occurs in a nuclear bomb ... but obviously terminated very much sooner by reason of the very much lesser compaction of the core of a nuclear reactor compared to that of a nuclear bomb. Which latter compaction is in a bomb obviously contrived to be as extreme as is possible to be made with extant engineering resources.
It's quite reasonable also, I think, to consider whether the former of the two scenarios just adduced is 'worthy' of being deemed a true nuclear explosion as opposed to the latter not being. Certainly it is more similar than the latter to what occurs in a nuclear bomb, and is only really less in force than it by reason of the lesser degree of compaction of the reacting substance; whereas in the latter scenarion the nuclear reaction is indeed a copious source of heat, but the explosion is not one of the reacting substances per se.
And there is some concern amongst those who are appointed to search into these matters as to which of these two kinds of event the large explosion of the Chernobyl nuclear reactor was more nearly an instance of. I think the idea that it might have been more of a 'true nuclear explosion' according to the definition I have proposed is possibly one that has been somewhat suppressed ... not necessarily by force - I am not advancing a 'willful cover-up' theory - but more just through habits of public discussion having become settled in place.
So another way of framing the question might be this: I have seen, in the course of my 'trawling' for matter about the Chernobyl incident, matter in which the concern is with this very question; but not a very great deal & quite fragmentary; and I wonder whether anyone has seen anything really substantial about it; or what original thoughts there might be out there about it amongst folks who care about these kinds of thing.
Incidentally, I recall reading recently, in the course of the said 'trawling', that the last reading on the meter showing the heat output of the reactor core was 33GW.
Simple Mathematical Model for Exponential Growth with Two Widely Different Timescales.
This is not meant to be taken as any kind of actual engineering formula, however; it's merely a simple mathematical model for showing how it is thoroughly intrinsic to a positive feedback-system having two different timescales to flip precipitately from one to the other as a certain parameter passes from one range to another. It is expounded, & its relevance examined, more thoroughly, in the mathematics section. It shows just how imperative it is that the proportion excess of reactivity in the core be kept to substantially less than the delayed neutron fraction. It is my understanding that one of the reasons for there not being many plutonium reactors is that the delayed neutron fraction is significantly smaller for plutonium than it is for uranium, making this task much more difficult.
An expression giving the factor - say $1+\delta$ by which the activity of a reactor core increases over the mean duration of a neutron's being free in the core, according to a simple model, would be -
let $\alpha$ be the delayed neutron fraction;
let $1+\omega\alpha$ be the mean number of neutrons yielt by a neutron upon its reacting;
Let $\zeta$ be the ratio of the delay of the neutrons to the mean duration of a neutron's being free in the reactor core;
let $w()$ be $\operatorname{arcf}()$ where $\operatorname{f}(x)=x.e^x$ -
$$\delta = \frac{w(\zeta\alpha.\exp((1-\omega)\zeta\alpha))}{\zeta} - (1-\omega)\alpha .$$
The ratio $\zeta$ is a large number - a few thousand. So when $\omega$ is substantially less that 1, as it ought to be in proper operation, the argument to the lambert w function is large; and the approximation
$$w(z)≈\ln(z) - (1-\frac{1}{\ln(z)})\ln(\ln(z))$$
is valid, & the terms without $\zeta$ in the denominator vanish, leaving only (terms beyond $\ln(z)$ in the expansion of w(z))÷$\zeta$.
However, because the lambert w function tends to linearity as its argument becomes $<<1$, as soon as $\omega$ begins to exceed unity, the term without $\zeta$ in the denominator begins precipitately to preponderate.
