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Amplification of pressure effect due to pre-compression (Mache effect)

The temperature gradient exists in the gas burnt in a closed vessel, rising from the gas burnt last to the gas burnt first (B.Lewis, 1961). The temperature gradient is known as “Mache effect” (Ya.Zeldovich, 1985) and was theoretically estimated in a paper (L.Flamm, 1917).

In a closed vessel combustion the gas temperature changes due to the heat release and due to adiabatic compression. Generally, an intermediate portion of unburnt gas in a closed vessel may be pre-compressed due to combustion of initial portions of gas, then it burns, producing burnt mixture with a higher temperature, and then these combustion products are compressed again due to combustion of following portions of gas.

At initial stage of process (close to ignition point) combustion occurs at initial pressure and temperature and then the combustion products undergo adiabatic compression with corresponding temperature rise. A volume of gas, which burns last, has been pre-compressed initially, and doesn’t undergo future compression and temperature rise after burning. Thus, these gas portions will have different initial conditions, different combustion products temperature and different composition. The Mache effect is known to reduce the explosion pressure below the one for uniform temperature distribution. The Mache effect is strongly pronounced for combustion in a closed spherical vessel with a central ignition, where the gas motion doesn’t cause mixing (Ya.Zeldovich, 1985).

Lewis B., von Elbe G. Combustion, Flames and Explosion of Gases. Academic Press, London, 1961.
Zeldovich Ya.B., Barenblatt G.I., Librovich V.B., Makhviladze G.M. The mathematical theory of combustion and explosions. Consultants Bureau, New-York, 1985.
Flamm L., Mache H. Combustion of an explosive gas mixture within a closed vessel. Wien: Ber.Akad.,Wiss., 126:9., 1917.

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