1. Hydrogen combustion pressures and interactions with the structure in an enclosure

2. Outline of the presentation Interaction of pressure waves with the structure Hydrogen combustion with emphasis on detonation A random choice method ( LES) for solving the compressible equations Conclusions

3. Relevant recent references S.B.Dorofeev ( and Russian Kuchatov institute) W. Breitung et.al. (Karlsruhe Forschungscentrum, OECD report) CFD codes: B02, DET3D, TONUS and others

4. Interaction with the structure The response of the walls is decoupled from the fluid dynamics because the characteristic times are vastly different The structure was Reinforced Concrete Approximate single degree of freedom system (SDOF) for the system represented by an infinite cylinder is not conservative. Therefore a complete FE solution is needed

8. Dome apex

9. Stress histories

10. Approximate solution is not conservative

11. The numerical method of solution Use the Riemann solution to solve the Euler equations i.e. viscosity and very small scale motions are neglected = LES (MILES) This solution is defined as if a dividing wall ( left and right side) separates two neighbouring uniform states Sharp discontinuities are reproduced

12. The Riemann problem:right and left states define states at the next time step through a simple algebraic relation

13. DETONATION STRUCTURE The ZND model applies i.e. a shock (Neumann conditions) is followed by expanding deflagration at CJ conditions Both the shock and reaction zones are thin so that the detonation is represented by a sharp discontinuity

14. Detonation wave

15. Advancing the solution to the next time step The dividing wall is assumed to be located at a random location between two neighbouring sates The solution is then advanced in time by sampling the exact solution at the mid- point (GLIMM-CHORIN)

16. Simple procedure for Glimm’s method

17. Sequence of Riemann Problems on Grid

18. Two dimensional case is handled by operator splitting in space

19. Numerical conditions No numerical diffusion i.e. sharp discontinuities are reproduced CFL conditions must be satisfied Error is proportional to grid spacing

20. Error bound If h is the grid spacing, Dt is the time step, T is the final time of calculation, and u o the initial value the error is given by

21. One dimensional spherical

22. Two dimensional axisymmetric

23. Pressure profile evolution Planar geometry

24. Pressure at the wall Planar geometry

25. Pressure profile evolution Spherical geometry (2m radius)

26. Pressure at the wall Spherical geometry

28. Discussion and Conclusions The RCM-Godunov method is an accurate LES and has been extended to 3-D calculations including reactions It can be used also for explosions with the reaction front represented as a discontinuity with a velocity equal to the maximum expected based on the turbulence level in a conservative sense.

29. Regarding computing as a straightforward routine, some theoreticians still tend to underestimate its intellectual value and challenge, while practitioners often ignore its accuracy and overrate its validity C.K.Chu, 1978