# Computational ‘Fuel Cell’ Dynamics

**T**he story of Fluid Mechanics dates back to ancient Greece, to the time of King Hiero II who asked the mathematician, physicist, and engineer Archimedes of Syracuse to determine the purity of a golden crown he’d had made. As the famous story goes, the absent-minded genius took to the streets, naked, screaming “eureka! eureka!” once he realised that he could use the volume of water displaced to measure the crown’s density, and hence purity. He later published a book titled, “On Floating Bodies”, the first known work on hydrostatics, the part of fluid mechanics which deals with fluids at rest.

Later, with the development of calculus, giants like Euler, d’Aiembert, Lagrange, and Laplace – names familiar to anyone who has taken an advanced calculus course – unraveled the curtains of mystery to reveal that fluid flow was governed by partial differential equations. With the derivation of the Navier-Stokes equations, fluid mechanics reached a stage familiar to modern physicists today. It is revered as a holy equation in classical mechanics that could answer many questions in the world of fluids.

However, none have been able to arrive at a closed form theoretical solution due to its inherent non-linear character.

With the coming of the age of computers, fluid dynamics simulations could become more realistic – the immense number-crunching abilities of modern computers gave scientists the ability to model increasingly complex phenomena. As you read this line, thousands of processors around the world are inverting matrices and computing determinants, all with the aim of understanding the flows of fluids in various situations. It is a field which promises a lot more aerodynamic cars, more efficient engines, and better methods of refrigeration are just a few that one can recall. Because of the complexity of the calculations involved, CFD researchers are among the largest users of the High-Performance Computing Centre (HPCE) facility at IIT Madras. One of the main driving forces behind the evolution of Computational Fluid Dynamics is the speed at which simulations can be made – it is cost-effective to teach a computer physics and have it simulate air flow instead of building a large test chamber to figure out how air flows through the engine of an aeroplane.

Also, it ensures repeatability and can be performed at any location. It is interesting to note that the mathematical methods developed by these researchers can be applied in a number of fields which at first sight bear no relation to CFD whatsoever.

“Fuel cell” is one of the most bandied-about terms in the field of sustainable energy today. The promises of energy from water and of hydrogen-powered vehicles all rest upon the development of better, more efficient fuel cells. Structurally, fuel cells consist of arrays of square compartments in which the electricity-generating reactions occur. Each compartment has a size of about 1 cm by 1 cm, and as the fuel flows through them at speeds of around 10 cm/s, it may not stay long enough in the reaction chamber to be completely utilised. One way to get around this problem is to drill in small grooves in the reaction chambers, forcing the fuel to take a longer path, ensuring that it stays inside long enough to be completely consumed. But what is the best possible curve?

For a long time, people thought that it was the serpentine. The word serpentine, meaning ‘snake-like’ was f1rst used to describe a curve by Sir Isaac Newton. This shape, which resembles the letter S, was thought to provide the longest possible path between the opposite vertices of a square. However, scientists and engineers are not as sure of this as they once were, and are beginning to investigate other geometries which may be more efficient. At IIT Madras, S. Ravishankar’s work involves trying to find these geometries using computer simulations. “We propose new computational techniques to solve fuel cell problems,” he says.

The key to simulating fuel flow in a computer lies in making the computer understand the various geometries involved. “There are commercial simulation packages available, but many researchers prefer to write their own code so that they have complete knowledge and control over the simulation,” explains Ravishankar.

However, once we surmount the initial hurdles of coding the partial differential equations involved and making the computer understand the physical laws that come into play, the same code can be reused to study a wide range of problems from oil extraction in deep wells to the formation of galaxies in space. Biotechnologists, for example, use CFD engineers to study the diffusion of newly synthesized drugs in blocked arteries. So, once a model has been developed, it can be easily applied to various flows of matter and energy, with different geometries corresponding to each application.

Previously, Ravishankar had used similar programs to model heat transfer inside CPUs. The codes were tested well with a broad range of design parameters to obtain deeper physical insights of how the temperature on the electronic chips could be reduced. The model was enriched further with complex three-dimensional equations governing the deposition of hydrogen fuel and oxygen in a fuel cell catalyst. Currently, he is working on the principles of protonic and electronic charge creation and consumption in a fuel cell module. The models will be tested in a novel ‘flow field geometry’ which is aimed at improving the functioning in terms of even distribution of heat and fuel over long periods of operation without compromising on the electricity generated.

Ravishankar ends with a word of caution – although computational fluid dynamics simulations have revolutionised the design processes of modern machinery, a researcher is always skeptical about the validity of the simulated results. It always requires confirmation with experiments to a sufficient and satisfactory extent. Digital approximations are, however, extremely useful in design and optimisation, and that is something the march of technology will certainly require.

**S Ravishankar** is pursuing his MS in the Department of Applied Mechanics. He is a resident of Sindhu hostel.