The study of instabilities in natural circulation circuits are important precisely because such systems should operate only by the gravitational effect.

In a nuclear reactor last generation, for example, one of the security systems to ensure cooling of the reactor core in the event of a power outage due to the failure of diesel generators is the natural circulation circuit.

This system should always operate in accordance with the conditions under which it was designed. The system should ensure a flow of liquid which is able to cool the reactor core for a certain period.

A stable natural circulation circuit ensures the flow of liquid circulating through the reactor core, and removing the generated heat flow.

An unstable natural circulation circuit does not ensures that liquid flow into the core and, in turn, does not guarantee  heat flow removal, reducing the efficiency of the entire security system.

The study of the instability of the natural circulation circuits is of great importance in many areas of engineering.

Thankyou Marcelo S. Rocha 

In addition to what Marcelo said, in a very general way you have to check your reactor is able to withstand nearly any situation without risks. So if natural circulation is a problem, you have to study it.

Thanks@ Ludovic, As most of the reactors are forced circulation and in that there is an instability, but very few literature are available on that, in addition to this, why we study natural circulation in reactors, is it used practically for power generation?

No it's a question of safety.

If you have natural circulation in your reactor, your pump are OFF (either because you stopped them, or because of a problem). You have to ensure that in these difficult condition your reactor is still stable.

Why we study instability generally in natural circulation instead of force circulation reactor?

Instability has more effect on flow characteristic instead of force circulation reactor.

Concerns the safe operation of the reactors has led to use the natural circulation systems as a way to remove heat of the advance reactors core. Natural circulation circuits have many applications in nuclear industry because of their advantages such as elimination of pumps, safety aspects and simplicity