1. Experimental and numerical research on interaction between gaseous detonation and solid explosive 1 Piotr Wolanski, Arkadiusz Kobiera Warsaw University of Technology Institute of Heat Engineering Nowowiejska Str. 21/25, 00-665 Warsaw, Poland e-mail: wolanski@itc.pw.edu.pl

2. Experimental and numerical research on interaction between gaseous detonation and solid explosive 2 The purpose of the research Presented research are focused on interaction between detonation wave and layer of high explosive materials. The detonation wave propagating over the layer causes the ignition of high explosive. The combustion of high explosive also influences the pressure and temperature behind front of gaseous detonation. The basic parameters describing the process are: ignition delay increase of average pressure behind detonation wave.

3. Experimental and numerical research on interaction between gaseous detonation and solid explosive 3 Test stand Ignition of the explosive layer was investigated by means of a shock tube which consisted of: driven section was filled with stoichiometric mixtures of oxygen and hydrogen with addition of helium. driven section 3.5 m long and 35x35 mm square cross- section, the section was filled with oxygen-hydrogen mixtures at low pressures (0.2 bar). the visualization section with optical quality window with the layer of the solid explosive placed on bottom wall of the section. pressure measuring system with three gauges: in front of layer (P1), over the layer (P2) and under the layer (P3). The process was recorded by drum camera with use of Schlieren system

4. Experimental and numerical research on interaction between gaseous detonation and solid explosive 4 The visualisation section

5. Experimental and numerical research on interaction between gaseous detonation and solid explosive 5 Materials A hydrogen-oxygen mixture was used as detonating mixture of different composition –30% H 2 –40% H 2 –50% H 2 –67% H 2 –75% H 2 As the explosive layer were used: –PETN powder, –PETN mixed with methyl methacrylate (plexi) –HNM mixed with methyl methacrylate (plexi). Weight ratio of methyl methacrylate was 10%. The layer dimension was: –190 mm length –5 ÷ 20 mm wildness –0.25 ÷ 5 mm thickness

6. Experimental and numerical research on interaction between gaseous detonation and solid explosive 6 Measured ignition delay The ignition delay was measured by means of streak photos. As an ignition delay the time was taken between passing of detonation wave front and light generated by combustion of high explosive layer.

7. Experimental and numerical research on interaction between gaseous detonation and solid explosive 7 Ignition delay - analysis Ignition delay for solid explosives are very similar i the range from 30-100  s. The most sensitive material is liquid nitroglycerine. The correlation between ignition delay and temperature behind detonation front is in good agreement with Arrhenius equation. The exception is HMN which seems to be sensitive to oxygen concentration in gases behind the detonation.

8. Experimental and numerical research on interaction between gaseous detonation and solid explosive 8 Kinetics of PETN ignition There was carried out simplified one-dimensinal calculation of heating and ignition of PETN-PLEX layer. It was assumed that: heat transfer (conduction) is one dimensional heat flux from the hot gases behind detonation front is described by Siechel at al. theory bottom side of layer has constant temperature the chemical kinetics of PETN decomposition is described by Arrhenius equation: the influence of 10% of PLEX was neglected It was assumed that kinetics of PETN decomposition is described by Arrhenius equation. The preexpnential constant and activation energy was determined on the base of experimental data. Obtained preexponential constant and activation energy for solid layer of PETN: A = 1.276*10 21 [1/s] E a = 110.56 [MJ/kmolK]

9. Experimental and numerical research on interaction between gaseous detonation and solid explosive 9 Pressure profiles Typical pressure profiles for mixture with 40% of H 2, with PETN layer and without layer are presented. Basic features are: First period after passing of detonation does not show any important changes in pressure. The combustion of the layer causes pressure increase after about 150  s.

10. Experimental and numerical research on interaction between gaseous detonation and solid explosive 10 Average pressure behind the detonation front Ratio of average pressure measured under the layer of different thickness to pressure measured in detonation without layer. Average pressure is calculated for 400  s. There is observed increase of average pressure with increase of thickness for dust layers of PETN. It can be explained by bigger number of grains taking part in combustion process of thicker layers. Average pressure for solid PETN (PETN +PLEXI) layers does not increase for thicker layers. It results from combustion of thin layer on the top of explosive. Lower parts do not burn and overall thickness does not play important role if it is bigger than 0.2-0.3 mm.

11. Experimental and numerical research on interaction between gaseous detonation and solid explosive 11 Numerical simulation Configuration Detonation propagates in H 2 -O 2 mixture Solid PETN is material of the layer The size of the layer (length-190 mm, thickness 0.25-1mm) is the same as in experiments Height of channel (35 mm) is equal to cross-section of the shock tube, the length 1.4 m is shorter than tube length 3.5 m.

12. Experimental and numerical research on interaction between gaseous detonation and solid explosive 12 Basic assumptions and simplifications 2-D model is used. Interaction between layer and gas flow is simulated as boundary conditions. The flow of gas is described by Euler equations Layer is uniform and its properties do not change with temperature. The heating of the layer is described by heat conduction equation with heat source (decomposition of explosive). The combustion of the explosive is described by Arrhenius equation.

13. Experimental and numerical research on interaction between gaseous detonation and solid explosive 13 Mathematical model of gas flow Conservation form of Euler equation Where: State Fluxes Chemical reaction Axisymetric variables sources term (not used)

14. Experimental and numerical research on interaction between gaseous detonation and solid explosive 14 State equation Energy equation

15. Experimental and numerical research on interaction between gaseous detonation and solid explosive 15 Chemical reaction model Where:  =  C j  j,k – third body coefficient Chemical kinetics Forward reaction Backward reaction

16. Experimental and numerical research on interaction between gaseous detonation and solid explosive 16 Model of layer heating The layer is described by heat conduction equation with internal heat sources. To the top of layer the heat flux from hot gases is transferred. The bottom side has constatnt temperature Heat generation is described by Arrhenius equation

17. Experimental and numerical research on interaction between gaseous detonation and solid explosive 17 Boundary condition at interface of gas and layer Mass flux Momentum flux LAYER GAS Energy flux

18. Experimental and numerical research on interaction between gaseous detonation and solid explosive 18 Heat transfer between hot gases and the layer –Reynolds’ analogy Where: h r – stagnation enthalpy u e – gas velocity in reference to walls, u s – velocity of detonation front, u e – gas velocity at C-J plane, h e – enthalpy at C-J plane, h w – enthalpy at walls, Pr – Prandtl number in boundary layer for temperature T=0.5(T e +T w ) (or for Eckert’s conditions).

19. Experimental and numerical research on interaction between gaseous detonation and solid explosive 19 Heat flux to layer Using Blassius’ relation for turbulent boundary layer and Mirles’ profile of boundary layer (M>5) is is obtained

20. Experimental and numerical research on interaction between gaseous detonation and solid explosive 20 Chemical reactions set Hydrogen combustion A [cm,mol] n E a [cal/molK] 1. H 2 + O 2  HO 2 + H 5.4954E13 0.0 58200.0 2. H + O 2  OH + O 2.1878E14 0.0 16800.0 3. O + H 2  OH + H 1.8197E10 1.0 8900.0 4. OH +H 2  H + H 2 O 2.1878E13 0.0 5100.0 5. H + O 2  HO 2 + M 1.5136E15 0.0 -1000.0 Dysociation of CO 2 CO + O  CO 2 + M 6.1700E14 0.0 3000.0 CO + OH  CO 2 + H 3.5100E07 1.3 -758.0 CO + O 2  CO 2 + O 1.6000E13 0.0 41000.0 CO + HO 2  CO 2 + OH 5.8000E13 0.0 22930.0 C 5 H 8 O 12 N 4  0.4H2 + 0.4O2 + 3.6H2O + 2.4CO + 2.6CO2 + 2.0N2 1.276E21 0.0 26392.0 Decomposition of PETN

21. Experimental and numerical research on interaction between gaseous detonation and solid explosive 21 Modified kinetics of decomposition of PETN First simulation showed that activation energy of PETN obtained from experiments gave proper ignition delays but further decomposition of PETN was too fast and generated pressure peak not observed in experiments. Therefore in next simulations the activation energy was a function of temperature. The activation energy rise with temperature. It allowed to obtaining good agreement between experimental results and numerical calculation of pressure increase generated by combustion of explosive layer. The basic features of the function are: initial value for initial temperature of layer T 0 =300K is equal to value obtained from presented experiments E 0 = 110.56 [MJ/kmol], for higher temperature activation energy rises slowly, the asymptotic value is E 1 =196.7 MJ/kmol (Andriejew’s results for slow decomposition of PETN).

22. Experimental and numerical research on interaction between gaseous detonation and solid explosive 22 Numerical scheme Main features: 2-D ( with possibility of axi-symmetric calculation) TVD (time variety diminishing) semi-implicit up-winding FORTRAN Presented program is a modified version of program created at Nagoya University by T. Fujiwara, M.H. Lefebvre, J. Leblanc. It was originally for simulation of detonation and ram- accelerators.

23. Experimental and numerical research on interaction between gaseous detonation and solid explosive 23 Results of simulation – parameters profiles

24. Experimental and numerical research on interaction between gaseous detonation and solid explosive 24 Comparison between experiments and simulation –pressure profile Simulation gives lower pressure behind detonation front (this could be improved by finer grid and better model of chemical kinetics of gaseous detonation) Influence of PETN combustion on pressure profile is qualitively similar in experiment and simulation. Influence of PETN combustion on pressure profile occur after about 100  s. Increase of pressure after 400  s is similar in both case

25. Experimental and numerical research on interaction between gaseous detonation and solid explosive 25 Comparison between experiments and simulation – average pressure When parameters of kinetics of decomposition of PETN are properly set for single case (40% H 2 0.5 mm PETN) the results of simulations are in very good agreement with experimental ones for different layers of PETN. Simulation proves that increase of solid explosive layer thickness does not influence the pressure. P av – average pressure with explosive layer P av0 – average pressure without layer

26. Experimental and numerical research on interaction between gaseous detonation and solid explosive 26 Influence of PETN combustion on increase of average pressure for different mixtures

27. Experimental and numerical research on interaction between gaseous detonation and solid explosive 27 Influence of PETN combustion on pressure profile (CFD)

28. Experimental and numerical research on interaction between gaseous detonation and solid explosive 28 Influence of PETN combustion on temperatures profile (CFD)

29. Experimental and numerical research on interaction between gaseous detonation and solid explosive 29 Calculated fields of pressure and temperature

30. Experimental and numerical research on interaction between gaseous detonation and solid explosive 30 Calculated temperature and ratio of decomposed PETN in the layer

31. Experimental and numerical research on interaction between gaseous detonation and solid explosive 31 Cross-section of flow area

32. Experimental and numerical research on interaction between gaseous detonation and solid explosive 32 Cross-section of layer The depth of heated layer is very small, less than 0.1 mm. It is the reason that layers of different thickness (0.25-1mm) behave very similar and pressure profile does not depends on layer thickness. Only 3% of PETN is decomposed in first 400  s.

33. Experimental and numerical research on interaction between gaseous detonation and solid explosive 33 Conclusion Presented experimental and numerical research allowed developing first simplified model of ignition and decomposition of PETN layer caused by gaseous detonation. The process of PETN combustion is quite complicated thus it was necessary to include some experimental parameters in theoretical model e.g. E a =f(T). Obtained numerical results are in qualitative agreement with experimental observations and it is possible to get information about parameters which were not measured: temperature of gas, temperature of layer, decomposition ratio of PETN. Both experimental and numerical results shows that combustion of PETN causes increase of pressure behind detonation wave. The average pressure increases about 15%. Combustion of PETN causes also increase of temperature of gas for about 700K Only very thin layer of PETN is heated and decomposed by interaction with gaseous detonation. Therefore the ignition and decomposition process is not sensitive on layer thickness.

34. Experimental and numerical research on interaction between gaseous detonation and solid explosive 34 Acknowledgements Presented work was supported by The State Committee for Scientific Research and The Foundation for Polish Science. We also thank Professor Toshi Fujiwara and Dr Joseph Leblanc from Nagoya University for help in developing of the program.

35. Experimental and numerical research on interaction between gaseous detonation and solid explosive 35 Appendix A: Algorithm of determination of chemical kinetics constants for PETN ignition Results for solid layer of PETN: A = 1.276*10 21 [1/s] E a = 110.56 [MJ/kmolK]

36. Experimental and numerical research on interaction between gaseous detonation and solid explosive 36 Appendix B: Modified kinetics of decomposition of PETN First simulation showed that activation energy of PETN obtained from experiments gave proper ignition delays but further decomposition of PETN was too fast and generated pressure peak not observed in experiments. Therefore in next simulations the activation energy was a function of temperature. It allowed to obtaining good agreement between experimental results and numerical calculation of pressure increase generated by combustion of explosive layer. The basic features of the function are: initial value for initial temperature T 0 is equal to value obtained from presented experiments E 0 = 110.56 [MJ/kmol], for temperature below T 2 activation energy rises slowly, the asymptotic value is E 1 =196.7 MJ/kmol (Andriejew’s results for slow decomposition of PETN), the slope of the function is controlled by parameter T 1, for temperature over T 2 the rate of decomposition is constant

37. Experimental and numerical research on interaction between gaseous detonation and solid explosive 37 Appendix B: Modified kinetics of decomposition of PETN The activation energy can be described by equation shown below. Temperature T 1 and T 2, was chosen in this way that ratio of average pressure in case with PETN decomposition and average pressure without PETN was the same in experiments and simulation. The average pressure was calculated for period of 400  s after detonation front passing. Ignition of 0.5 mm layer by detonation in 40% H 2 mixture was the reference case. E 0 = 110.5 MJ/kmol, E 1 = 196.7 MJ/kmol T 0 = 300 K T 1 = 950 K T 2 = 365 K

38. Experimental and numerical research on interaction between gaseous detonation and solid explosive 38 Appendix C: Heat transfer to wet walls in case of nitroglycerine layer where: Mass blockage effect occurs when walls are wet.

39. Experimental and numerical research on interaction between gaseous detonation and solid explosive 39 Calculated fields of pressure and temperature  t=75  s

40. Experimental and numerical research on interaction between gaseous detonation and solid explosive 40 Calculated temperature and ratio of decomposed PETN in the layer  t=37.5  s

41. Experimental and numerical research on interaction between gaseous detonation and solid explosive 41 Calculated temperature and ratio of decomposed PETN in the layer  t=37.5  s