Troels Dyhr Pedersen.indd - Solid Mechanics

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The mach number of the combustion products serves as a useful check of the model
validity. If all calculations are correct, M2 should be quite close to unity. M1 depends
strongly on the gas composition, but should be between 2 and 3.5 in atmospheric air.
M
M
12.3.9 Results for the stationary solution
The problem was solved in EES with initial conditions corresponding to adiabatic
compression at a compression ratio of 10. An equivalence ratio of 0.33 was used, since
this usually results in extensive knocking. The properties of ethanol were used for DME
in the calculation, since the properties of DME are not available in EES. The heating
values are comparable and the chemical composition identical.
1
2
u
=
c
1
1
u
=
c
The most important results from the calculation are listed in table 6 and 7.
Table 6: Comparison of properties after an explosion and a detonation
State Initial conditions Constant pressure
explosion
2
2
(CHEMKIN)
After detonation
(EES calculation)
Temperature 726 K 1800 K 1989 K
Pressure 2.4 MPa 6 MPa 12 MPa
Specific volume 0.086 m 3 /kg 0.086 m 3 /kg 0.048 m 3 /kg
Table 7: Calculated velocities and Mach numbers in a detonation
Velocities
Wave velocity, relative to chamber 1533 m/s
Mach number of wave, relative to chamber 2.92
Burned gas velocity, relative to wave 860 m/s
Mach number of burned gas, relative to wave 1.0004
The mach number of the burned gas is 1.0004 which is quite close to the desired value of
exactly 1. It is a very acceptable result which indicates that the equations are correctly
implemented.
The post detonation conditions indicate that the pressure wave should be clearly
discernible from an explosion. The highest pressure that may be developed by an
explosion is 60 Bar, whereas the pressure after a detonation will be twice that. Not
calculated here is the peak pressure of the shock front, which will be even higher than the
post shock pressure.