Paper boats and Nuclear reactors

Dipin, a fourth year Ph.D. student in the Chemical Engineering department, points out to me something very mundane yet incredible. While chatting over tea, he pours the liquid from one glass to another and points out the way in which the stream of hot tea periodically twitches as it flows down. He explains to me how pressure imbalance within the stream causes this motion of the fluid jet.

Sensing my awe, he goes on, “Do you think there would be any fundamental similarity between inkjet printing and a nuclear reactor accident?” Although seemingly unrelated, the same science, he states, underlies the flows of ink and molten nuclear fuel – the science of fluid jets and their instabilities. If you have ever wondered why it rains in drops and not as streams of water, you’d have probably stumbled across this concept of jet instability. When the surface of a falling stream of fluid is slightly disturbed by, say, minute air currents, the disturbance can grow and cause the jet to split at the point of disturbance. The split portion of the jet then takes on the spherical shape of drop to minimize the total surface area.

You can also notice this in water-flow from a leaky tap, or when you shake paint off a brush. Known as Plateau-Rayleigh instability, this is exploited in inkjet printers to control the size of the ink drops that finally hit the paper and produce the print.

Although the context is different, a somewhat similar phenomenon is expected to take place in a pool-typed fast breeder nuclear reactor in the event of a nuclear meltdown accident.In particular, a fast breeder reactor like the one being set up at Kalpakkam, Tamil Nadu by the Indira Gandhi Center for Atomic Research (IGCAR). The core of the reactor comprises rods of radioactive fuel, such as uranium or thorium (or their oxides), cladded in stainless steel and surrounded by molten sodium coolant and isotopes – variants of the same element with different number of neutrons – of the fuel element that are non-fissile.

Fissile elements, like the nuclear fuel, are those that can be split by neutrons in a self-sustaining chain-reaction to release enormous amounts of energy. The atoms of the radioactive fuel, upon encountering neutrons, undergo fission to produce smaller non-radioactive atoms, and more neutrons and energy. The surrounding non-fissile isotopes absorb some of these resulting neutrons and transform to fissile isotopes which then act as radioactive fuel. This chain reaction goes on until all the fissionable material inside the reactor is exhausted. In the process, the coolant absorbs the energy released from fission and generates power.

The cooling mechanism is crucial to control the temperatures inside. If this mechanism goes awry, the tremendous amount of energy released can cause steep temperature increase, and the fuel and its steel cladding may melt and flow down through the coolant. This situation is termed a nuclear meltdown or a core disruptive accident (CDA).

A schematic of the Core Disruptive Accident-When the fuel melts, it passes as jets of fluid through the surrounding coolant. Courtesy: Prof.Pushpavanam
A schematic of the Core Disruptive Accident-When the fuel melts, it passes as jets of fluid through the surrounding coolant. Courtesy: Prof.Pushpavanam

One of the containment strategies when this happens is to make the molten fuel solidify as it passes through the coolant. Physical catcher plates are put up beneath the grid-like structure holding the fuel rods. As the fuel melts and passes through the grid, it comes out as fine jets and, ideally, breaks into smaller droplets which solidify when they lose heat to the coolant and settle on the plate. However, if solidification does not happen, and the jet/droplets settle on the plate as a liquid, the fuel material and steel separate, or stratify, and the steel tends to solidify around the fuel. Such an encapsulation is a dangerous state, as it traps the radioactive atoms and emitted neutrons. This can lead to another uncontrolled reaction and a secondary meltdown. This time, however, being close to the reactor wall, the melt may breach the reactor itself and enter the environment.

To prevent all this happening when there’s a CDA, the design of the reactor should incorporate the elements that lead to breakage and solidification of the jets before the molten fuel hits the core catcher plate.

Prof. Pushpavanam of the Chemical Engineering and Prof. Sundararajan of the Mechanical Engineering departments, in collaboration with IGCAR, undertook a study with the aim of identifying whether core disruption in a nuclear reactor with liquid sodium as poolcoolant would lead to stratification on the core catcher plate, or if the jets would just fragment and solidify. By mathematical modeling as well as experimentation, the research team, of which Dipin was a member, proved that pool-coolant reactors always almost result in solidification. Hence, they are inherently safer than, say, light water reactors, for which stratification has been reported.

Compared to the above examples of liquid instability in tap water or rain drops, there’s one fundamental difference in which the nuclear reactor accident situation differs. While the other examples are constant temperature phenomena, the temperature of the nuclear jet varies rapidly as it passes through the liquid sodium coolant.

Now, if you were the sort of kid who played with paper boats in rain, you might have tried putting camphor on the water and seen the boat self-propel away from camphor’s direction. This happens because wherever camphor dissolves locally, the surface tension of water lowers and the boat is pulled to neighbouring areas with higher surface tension. This liquid movement is called Marangoni effect and arises whenever there is a variation of surface tension on a liquid surface.

The same effect is seen when there is temperature variance on the jet stream. Wherever temperature is lower, the surface tension tends to be higher. As the jet travels through the coolant, the temperature along the surface of the jet stream decreases and the jet is further disturbed by the Marangoni effect produced on the surface. Early breakup of jets was predicted in such a case, and experimentally noticed also. As early breakup means faster solidification, the presence of Marangoni effect favours the safety of this pool type reactor. Another factor causing early breakup was that of increased viscosity due to liquid sodium. The latter is an intuitive result, considering a water jet would break earlier in, say, oil than in air.

Results from commonplace effects like jet instability were extended to analyzing operation hazards of nuclear reactors

Overall, the safety of pool type reactor in the event of a Core Disruptive Accident was favoured not just in theory, but was also substantiated by experiments and numerical simulations. Since experimentation in a nuclear reactor is not feasible, the group chose to work with a simple system substituting glycerol for liquid sodium, aluminium for steel cladding and lead for nuclear fuel. The fundamental equations governing the physics of the process were also established.

Prof. Pushpavanam, the lead researcher in this project, says, that the “theoretical or fundamental research helps one obtain scientific relations than just live with empirical observations. For example, with a theory, you would know the effect of varying the coolant or increasing the size of the nuclear reactor beforehand, and do not have to experiment each time a parameter of the system is changed. This knowledge is crucial as it saves experimentation time and effort. Often, modeling a system mathematically also throws up new insights and gives deeper understanding of the system. Indeed, there’s nothing more beautiful than a simple mathematical model explaining the rich physics of a bunch of phenomena! Here too, equations for jet instability were extended admirably to the operation hazards of nuclear reactors”

The results of this project, which is now in its final stages, will aid IGCAR in designing fast breeder reactors, strategized to be set up to utilize the existing nuclear ore reserves of the country and increase energy generation.