|M.Sc Student||Moshkovich Makarenko Irena|
|Subject||Study of the Physical Feasibility and Stability of the|
Chapman-Jouget Points in a Homogeneous Combustible
|Department||Department of Aerospace Engineering||Supervisors||Professor Beni Cukurel|
|Professor Eran Sher|
The progress of a flame wave in a quiescent flammable homogeneous medium under SSSF conditions may occur in two different discrete regimes; the deflagration (sub-sonic) regime and the detonation (above-sonic) regime. Since the Mallard and LeChateliet experiment in 1886 where a flammable gas/air mixture has been ignited at the open end of a long tube while the propagation of the flame front has been recorded, a large body of experimental observations has been collected during the last century for a number of fuels under a fair range of initial conditions. The two different regimes were clearly noted and many attempts were made to explain and predict them.
When the 3 basic conservation (continuity, momentum and energy) equations with a suitable equation of state are applied to a one-dimensional SSSF flame propagation process in a tube, one may soon realize that one more equation is needed to solve the 5 unknowns (inlet velocity, exit velocity, exit pressure, exit temperature and exit density). The inlet velocity is of particular interest to us since it defines the flame propagation velocity. It was shown by Rankine, Hugoniot and Rayleigh, that the 3 conservation equations may be combined with the equation of state into two simple equations (one quadratic and one linear) that customarily are plotted on a pressure density coordinates. The intersections of these two curves may define the different regimes. The slope of the linear equation (the Rankine-Rayleigh equation) however depends on the flame propagation velocity which is an unknown parameter. Chapman and Jouguet suggested that the two tangent points between these two curves represent the deflagration and the detonation conditions and the two different slopes of the linear equation represent the two propagation velocities. When comparing the results with the experimental observations, it is clear that while the predicted detonation propagation velocity fits well, the predicted deflagration propagation velocity if far higher; about one order of magnitude higher.
The thermal theory of combustion of Semenov and others, suggested that the critical mechanism of a deflagration propagation is the heat conducted from the exothermic front propagating layer to its successive layer. Introduction of the Fourier law to the 3 conservation equations provides the 5th equation that allows a closed solution. It however can be shown that this classic beautiful solution doesn’t conform to the momentum equation. It is true that the pressure difference across the flame front in deflagration regime is very small, but still, violating the momentum equation can hardly be accepted.
In the present work a new approach is suggested to bridge this classic gap. Instead of introducing the Fourier law, we suggest to introduce the Onsager relationship, which accounts for the entropy increase due to the heat transfer process from the front layer to its successive layer. Based on a few logical assumptions, a simplified Onsager relationship has been introduced to the set of the other conservation equations, and a closed solution that definitely conforms also the momentum equation has been obtained. A very good fitting has been obtained between the predicted and the experimentally observed values of the propagation flame deflagration speed.