Multiphase Detonations

The discussion above has focused on gaseous fuels. However, for most volume-limited applications, liquid fuels will have to be used. The primary fuel of interest to the Navy is JP-10. Detailed simulations of PDEs operating on JP-10 have been hampered by the lack of information on the chemistry as well as the multiphase properties of this fuel. 

A numerical simulation tool has been developed that is capable of accounting for radial and axial variations in liquid-fuel distribution. In the absence of definite information on the chemistry of JP-10, a two-step global model analogous to that used in the gas-phase detonation simulations has been constructed. In this model, the residence time of the fuel vapor is tracked, and energy releaise is allowed to occur only after the elapse of a specified induction time. The amount of energy release is based on the lower heating value of the fuel and is calibrated to result in the CJ-detonation velocity for a fully vaporized fuel. 

For effective use of the developed model, information on the induction time and droplet evaporation rates, as a function of the local conditions in the shock-heated mixture, is needed. Currently, in the absence of such information, parametric studies with various constant induction times and droplet evaporation rates have been carried out. The predicted detonation velocity as a function of the initial droplet size is shown in Fig. 11.6 for a nominalJP-lO-oxygen mixture with an equivalence ratio of 0.12. A d -law evaporation with a rate of 0.1 cm /s and an induction time for the fuel-vapor of 1 //s was used for this series of simulations. The velocity deficit observed previously in many experimental studies of multiphase detonations is predicted by the numerical model. In the absence 

The authors wish to thank Dr. Gopal Patnaik of the NRL for previous help with the development and improvement of the codes used in the computations presented here. The work vias performed under ONR contract N0001402WX20595 and the NRL Computational Physics Task Area. 

Proceedings. Salt Lake City, UT University of Utah 1998. 11th ONR Propulsion Meeting Proceedings. West Palm Beach, FL.) 

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Retcher, D. F. Thyagaraja, A. Multiphase detonation modelling using the CULDESAC code. Presented at 12th ICDERS, Univ. Michigan (1989). 

If the reaction order does not change, reactions with n < 1 wiU go to completion in finite time. This is sometimes observed. Solid rocket propellants or fuses used to detonate explosives can bum at an essentially constant rate (a zero-order reaction) until all reactants are consumed. These are multiphase reactions limited by heat transfer and are discussed in Chapter 11. For single phase systems, a zero-order reaction can be expected to slow and become first or second order in the limit of low concentration. 

There are several reasons for investigating PDEs, such as simplicity of the device, ability to operate over a range of speeds from zero to hypersonic, and overall performance. As part of the U.S. Office of Naval Research (ONR) program, computational tools are being developed and applied to gain a better understanding of the operation and performance of PDEs. The basic technical issues to be addressed and the various computational tools needed have already been discussed in previous years reports [1]. Some of the key issues that remain unresolved are the ideal performance estimate of the PDE, rapid initiation of detonations with minimum oxygen, and operation with multiphase fuels. Here, the last accomplishments are presented, and their implications are discussed. 

Fletcher, D.F. and Thyagaraja, A., Multiphase Flow Simulations of Shocks and Detonations, Part I Mathematical Formulation and Shocks , Culham Lab. Kept. CLM-R279, Abingdon, U.K., 1987. 

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