## Wednesday, April 21, 2010

### How much ash enters the jet engines?

I looked for some calculations like this on the net – but found none.

Please comment with corrections if these are wrong.

Maximum concentrations of ash (mainly finely shattered volcanic glasses) in the plume of ash over Europe are of the order of 300 µg/m3.

So how much ash does the engine turbines encounter? We have to calculate the volume of air passing through the engines.

A few facts: In the standard atmosphere, at 11,000 m the pressure is approx. 1/5 of standard pressure (1 atm and the absolute temperature is approximately 4/5 of standard temperature. At standard temperature and pressure, 1 mole of a gas occupies a volume of approx. 25 l. So at 11,000 m 1 mole of a gas occupies four times as much volume: approx. 100 l. Thus each m3 of the standard atmosphere at 11,000 m contains 10 moles of gas. Approximately 20% of this is oxygen – so we have 2 moles of oxygen (~ 60 g) per cubic metre, and 300 µg of ash.

Thus this air in these dense parts of the plume carries ~ 5 µg of ash per 1 g of oxygen.

We approximate the combustion of aviation fuel as (CH2)2n + (O2)3n => (CO2)2n + (H2O)2n

So each 28 g of fuel requires ~ 96 g of oxygen for combustion.

In addition, only about 25% of the oxygen entering the engine is used in combustion – so for every 1 g of fuel burned, the engine must take in ~ 14 g of oxygen, which brings with it 70 µg of ash. Thus, in burning 1 Kg of fuel we bring 70 mg of ash into the engine, and for 1 tonne of fuel, 70 g of ash.

An Airbus burns around 2 tonnes of fuel per hour. So 70 g of ash is an upper limit for a half-hour encounter with a plume containing 300 µg of ash per m3.

This may not seem much. But imagine taking a can of epoxy to gum up the works of a delicate jet engine – 70 g of epoxy, a yoghurt carton-full, seems like enough to do plenty of damage to a couple of engines. Molten glass is probably more effective.

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