The D2 variation for isolated LOX drops and polydisperse clusters in hydrogen at high temperature and pressures

A study of the d2 variation for isolated fluid drops and for fluid drops belonging to polydisperse clusters has been conducted at a high temperature and elevated pressures. The mathematical formulation is based on a previously validated model of subcritical/supercritical isolated fluid drop behavior. Coupled with the isolated drop equations, a set of conservation equations has been developed to describe the global cluster behavior. All these equations are based on the general transport matrix including Soret and Dufour terms and they are consistent with nonequilibrium thermodynamics and at low pressure with kinetic theory. Moreover, the model also accounts for real gas effects through accurate equations of state and for correct values of the transport properties in the high pressure, high temperature regime. The model has been first exercised for isolated LOX drops in H2 at pressures ranging from 1.5 MPa (subcritical pressure for O2) to 20 MPa (supercritical pressure for O2). The results show that while at subcritical pressures the d2 variation is nearly linear, with increasing pressure it departs considerably from the linear behavior; the largest departure occurs in the vicinity of the oxygen critical point. The slope of d2(t) was fitted using both a constant and a linear fit, and it was shown that the linear fit provides a better alternative for correlation purposes. Simulations were also conducted for clusters of LOX drops in H2 in the range 6 to 40 MPa (reduced pressures of 1.2-8 with respect to pure O2). Parametric studies of the effect of the thermal diffusion factor value reveal that it is minor at 10 MPa and moderate at 40 MPa, and that although the Soret term is dominated by the Pick, Dufour, and Fourier terms, it is not negligible. The influence of a cluster Nusselt number is also shown to be relatively small in the range 103 to 104, consistent with the supercritical behavior being essentially a diffusive one. All of the results show a nonlinear d2 variation with curves having a positive curvature independent of the values of the thermal diffusion factor, the Nusselt number or the LOX/H2 mass ratio. The approximation of a binary size cluster containing relatively a much larger number of small drops by a monodisperse cluster with a drop size based upon the surface average of the drops in the polydisperse cluster yields a good evaluation of the thermodynamic quantities in the interstitial drop region but an underestimate of the lifetime of the drops in the cluster.