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 ICHS Pisa 2005

Outline Introduction Models and numerics Physical experiments Numerical experiments Conclusion ICHS Pisa 2005

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 ICHS Pisa 2005

Filtered conservation equations of mass, momentum and energy ICHS Pisa 2005

Turbulence model, by Menon et.al. ICHS Pisa 2005

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) ICHS Pisa 2005

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 ICHS Pisa 2005

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) ICHS Pisa 2005

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 ICHS Pisa 2005

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 ICHS Pisa 2005

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 ICHS Pisa 2005

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 ICHS Pisa 2005

Experimental results, pressure records ICHS Pisa 2005

Numerical setup Same conditions as physical experiments Assume cylindrical coordinates 2D Axis-symmetric Carthesian, homogeneous grid CV length 2 mm (~50 000 CV) CFL number 0.9 ICHS Pisa 2005

Comparison of pressure history at sensor p0 ICHS Pisa 2005

Comparison of pressure history at p2 ICHS Pisa 2005

DDT occurs between image 1 and 2 Density in a 240 mm X 107 mm area Time difference is 0.025 ms DDT occurs between image 1 and 2 ICHS Pisa 2005

Mach number at center line behind the obstacle as the flame reaches the opening ICHS Pisa 2005

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 ICHS Pisa 2005

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? ICHS Pisa 2005

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 ICHS Pisa 2005