Eli5: why is volcanic ash dangerous to aircraft, and yet they can fly through forest fire smoke?

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Volcanic ash includes silica, wood ash includes carbon.

The temperatures inside an engine after the combustion chamber are extremely high, so much so, that the used materials loose strength and could not withstand the centrifugal forces of the rotation. This is why the turbine blades are actively cooled.

Modern engines take “relatively” cool air (600°C) from the high pressure compressor just before the combustor and send it through thousands of tiny laser-drilled holes to apply a cooling and insulating film on the turbine blades.

If there is wooden ash particulate inside the air, it will have burnt off at those temperatures long before being ingested by the cooling system.
If there is silica particulate in the air, it will melt and plug up those tiny cooling holes. If your turbine blade cooling fails, your engine will very soon not have turbine blades any more and subsequently stop being an engine.

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