Ensuring order from chaos

Tom Shelley reports on recent applications that either prevent or make use of chaotic behaviour

Chaotic and other potentially damaging oscillations in systems can be modeled, their onset can be detected before they get nasty, and they can and are counteracted and suppressed, or in other cases, made use of.

Understanding and making use of them allows machines to be driven harder, particularly certain military jet engines, and even allows the detection of the onset of potentially fatal heart attacks, up to two hours before crisis.

Chaos is ubiquitous. By chaos, we do not mean random, but oscillations and movements that are highly complex, such as in turbulent flow, which can be modeled and predicted in detail if the model is fine grained enough, and sufficient computing power is applied to the problem.

As Professor Mohammed Sohby of the University of Kent school of engineering explained and demonstrated in a lecture earlier this year, the mathematics of chaos is now quite well understood, thanks to the work of the late US meteorologist, Professor Edward Lorenz. A simple example of mechanical chaos is a pendulum whose bob is attracted to four magnets on a surface, or a pendulum with a joint in the middle. The motion is complicated – it never goes back to exactly the same configuration – but it is not random. He demonstrated chaos in an electronic system, and showed how it could be modelled on a computer, and how the transition from harmonic oscillation to chaotic motion occurs when more energy is put in, and how the input of still more energy can lead to the system moving into a completely new area of states.

As energy is input, the beginning of the transition to chaotic behaviour is marked by the appearance of oscillations with double the natural frequency time interval called "Alternans". If the oscillation is initially harmonic oscillation, the alternans act as a warning that full chaos is liable to follow. Professor Sohby commented that he was particularly interested in the fact that, when this effect appears in the human heartbeat, the patient is, "About two hours away from fibrillation", when the heart beats in a completely chaotic manner and fails to pump blood. If alternans have been detected however, it is possibly to have a paramedic with a defibrillator standing by ready, who can then save the life of the patient.

We knew that chaotic behaviour and its control is well known in power electronics, but asked Professor Sohby if it was relevant to aerodynamics and jet engines. Professor Sohby replied strongly in the affirmative but declined to go into details, so we asked a researcher at Rolls Royce. They replied that the company had been involved in research into a strategy to control chaotic mechanical vibrations in rotors which involved, "Semi active control, as it is not necessary to control it with full cancelling energy, but only to feed in enough to re-stabilise the motion." They then referred us to the Whittle Laboratory in Cambridge.

Senior research fellow Dr Ivor Day told us that they had indeed looked at a strategy where a "Small spike" in the pressure distribution in a compressor was found to tip it into chaos under extreme conditions and a strategy had been devised to open valves round the compressor to "Blow it away". The strategy worked, but was not found to be cost effective.

However, Dr Robert Miller, reader in energy technology told us that there was a strategy that can and is used in jet engine combustors and afterburners. If an oscillation is detected, fuel input can be modulated to either decrease or increase heat. If fuel injection is modulated so that peaks correspond with combustor pressure troughs and vice versa, turbulence and heat is reduced, but if peaks are made to correspond with combustor pressure peaks, turbulence is increased and combustion temperature rises by, "150ºC plus", "Supercharging" the afterburner and increasing thrust.


* Chaotic as opposed to random motion can occur in many kinds of mechanical system and is the basis of turbulent flow

* It can be computer modelled, provided the model is either simple or sufficiently fine grained and computing power is large enough

Tom Shelley

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