Hydrogen combustion pressures and

interactions with the structure in an enclosure

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

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

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

Table 1. Peak detonation pressures and impulses on the containment wall

Initiation at mid-height Location on wall Initiation at the base Q/RTo=17 a/RT=17 Q/RTo=23

(sec)Impulse

oP (sec)

Impulse

oP (sec)

Impulse

oP

Radius (m)

Elevation (m)

oP

Pmax At 85

msec*

At 140

msec*

oP

Pmax At 85

msec*

At 140

msec*

oP

Pmax At 85

msec*

At 140

msec* 20.6 20.6 20.6 20.6 20.6 20.6 20.6 20.6 20.5 14.7 17.5 13.1 9.3 5.3

0

0.0 6.0

12.0 18.0 94.0 30.0 36.0 42.0 47.0 51.0 56.0 61.0 63.5 65.0 65.7

77.0 72.0 51.0 48.0 37.0 30.0 48.0 42.0 43.0 42.0 71.0 65.0 71.0 68.0 65.0

0.56 0.82 0.74 0.72 0.65 0.62 0.63 0.52 0.37 0.90 0.58 0.64 0.49 0.50 0.76

1.18 1.35 1.24 0.97 0.85 0.88 0.81 0.73 0.56 1.24 0.75 0.79 0.63 0.66 1.11

72.0 75.0 51.0 55.0 70.0 58.0 49.0 21.0 34.0 27.0 41.0 25.0 59.0 23.0 69.0

0.75 0.70 0.67 0.61 0.37 0.39 0.35 0.25 0.25 0.22 0.19 0.26 0.40 0.42 0.46

0.81 0.78 0.73 0.68 0.46 0.45 0.40 0.25 0.25 0.22 0.19 0.26 0.41 0.44 0.55

76.0 78.0 80.0 46.0 66.0 68.0 48.0 26.0 41.0 30.0 48.0 34.0 71.0 32.0 53.0

0.63 0.51 0.59 0.40 0.51 0.50 0.41 0.38 0.35 0.31 0.19 0.21 0.33 0.31 0.44

0.63 0.51 0.59 0.40 0.51 0.50 0.41 0.38 0.38 0.33 0.19 0.22 0.33 0.31 0.46

17oRT

q17

oRT

q

17oRT

q

Dome apex

Stress histories

Approximate solution is not conservative

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

The Riemann problem:right and left states define states at the next time step through

a simple algebraic relation

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

Detonation wave

u2/1

cjcjbbuucj /))/p(u(U

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)

Simple procedure for Glimm’s method

Sequence of Riemann Problems on Grid

Two dimensional case is handled by operator

splitting in space

Numerical conditions

• No numerical diffusion i.e. sharp discontinuities are reproduced

• CFL conditions must be satisfied

• Error is proportional to grid spacing

Error bound

• If h is the grid spacing, Dt is the time step , T is the final time of calculation , and uo the initial value the error is given by

o2/12/1N u))hT()

t

h(

3

2h()T(.,u)T(.,u

One dimensional spherical

Two dimensional axisymmetric

Pressure profile evolution Planar geometry

Pressure at the wall Planar geometry

Pressure profile evolution Spherical geometry (2m radius)

Pressure at the wall Spherical geometry

rtCo /

rtCo /

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.

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 validityC.K.Chu , 1978