1. Knut Vaagsaether, Vegeir Knudsen and Dag Bjerketvedt
Simulation of flame acceleration and DDT in H2-air mixture with a flux limiter centred method
Knut Vaagsaether, Vegeir Knudsen and Dag Bjerketvedt
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2. Outline Introduction Models and numerics Physical experiments
Numerical experiments
Conclusion
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3. The goal of this work is to simulate the explosion process from a weak ignition source through flame acceleration and DDT to a detonation
The simulation tool is based on large eddy simulation (LES) of the filtered conservation equations with a 2. order centred TVD method
Numerical results are compared to experimental results with pressure records
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4. Filtered conservation equations of mass, momentum and energy
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5. Turbulence model, by Menon et.al.
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6. In addition to the mass, momentum, energy and k, two other variables are conserved
Two reaction variables, α and z
α is a variable for the production of radicals where no energy is released
z is a variable for the consumption of radicals (exothermal reactions)
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7. α is only solved for the unreacted gas
α keeps track of the induction time
If α is below 1, no exothermal reaction is taking place
If α reaches 1 an exothermal reaction occurs
The production term of α is an Arrhenius function and can be assumed to be 1/τ
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8. The exothermal reactions are handeled in two ways
If the flame is a deflagration wave, a Riemann solver is used to calculate the states at each side of the flame
The Riemann solver use the burning velocity as the reaction rate
If the flame is a detonation wave or α reaches 1, another reaction model is used, presented by Korobeinikov (1972)
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9. Burning velocity as a function of velocity fluctuations, presented by Flohr and Pitsch (2000)
This model is developed for lean premixed combustion in gas turbine combustors
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10. Flame tracking with the G-equation
Where vf is the local particle velocity in front of the flame
G is negative in the unburned gas
The G0 surface is set to be immediately in front of the flame
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11. Solvers
A flux limiter centered method (FLIC) to solve the hyperbolic part of the equations, an explicit 2nd order TVD method
Central differencing for the diffusion terms
Godunov splitting for dimensions, diffusion terms and sub-models
4. order RK for ODEs
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12. Experimental setup Spark plug ignition at p0 30% hydrogen in air
1 atm, 20°C
Closed tube
10.7 cm ID
Spark plug ignition at p0
0.5 m between sensors
1.5 between p0 and p1
3 cm orifice in obstacle
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13. Experimental results, pressure records
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14. Numerical setup Same conditions as physical experiments
Assume cylindrical coordinates 2D
Axis-symmetric
Carthesian, homogeneous grid
CV length 2 mm (~ CV)
CFL number 0.9
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15. Comparison of pressure history at sensor p0
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16. Comparison of pressure history at p2
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17. DDT occurs between image 1 and 2
Density in a 240 mm X 107 mm area
Time difference is ms
DDT occurs between image 1 and 2
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18. Mach number at center line behind the obstacle as the flame reaches the opening
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19. Discussion and conclusion
The pressure in the ignition end of the tube is simulated with some accuracy, even with these assumtions
The detonation wave is simulated very accurate compared to the experiments which means that the Korobeinikov model is good enough for this work
A DDT is simulated
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20. Discussion and conclusion
Some discrepancies between numerical and physical results in the ignition part (deflagration) 2D
Boundary conditions for the G-equation
Burning velocity model
The DDT is simulated too late
Induction time
Errors in pressure from the ignition part
Is it possible with LES?
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21. Further work 3D simulation should be performed
Boundary conditions for the G-equation?
Burning velocity model
Adaptive mesh refinement
A new model for the induction time
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