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.
- UPDATE 2010-04-25 Following engine strip-downs, CAA establishes < 2mg/m3 as safe volcanic ash level. New Scientist 21 April 2010
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 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.
So, in dense parts of the plume:
- the air carries ~ 5 µg of ash per 1 g of oxygen.
Now we estimate how much air the engines take in. We approximate the combustion of aviation fuel as
- (CH2)2n + (O2)3n => (CO2)2n + (H2O)2n
- 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
- the air required to burn 1 tonne of fuel contains 70 g of ash.
An Airbus burns around 2 tonnes of fuel per hour. So 70 g of ash is an upper estimate 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.