nnl7-9310’9356,00+0.00 t lY97 Perg;tmon Press Lid Numerical study of the transient vaporization of an oxygen droplet at sub- and super-critical conditions J.-P. DELPLANQUE and W. A. SIRIGNANO Department of Mechanical and Aerospace Engineering. University or California. Irvine. CA 92717. U.S.A. Abstract-Unstsady vaporization of a droplet in a high-pressure quiescent environment has been studied. With spherical symmetry and constant pressure. the process is difusion controlled. At low pressures droplet heating is significant for mosl orthc droplet lifctimc, and an unsteady analysis oPthe gas phase is required. Then. the vaporization or a liquid oxygen droplet in gaseous hydrogen at moderate and high pressures is considered. At super-critical pressures. the surface temperature rcachcs the computed critical mixture value where a model For super-critical combustion is nceded. The details or the ditTusion layer of dissolved hydrogen do no1 significantly alTcct the results. Various methods are explored LO compute the gas-phase density. Under the model’s asstimptions. homogeneous nucleation is not likely to occur. 1. INTRODUCTION TI-IERE is renewed interest in investigating liquid rocket combustion instabilities and. more precisely. their interaction with droplet vaporization and combustion processes. Conscqucntly, a better description of these phenomena at the high-pressure, high-temperature conditions, prevalent in liquid rockets, is needed. However, a meaningful model to describe liquid- rocket engine combustion instability should include at least hundreds of droplets that each represent the average droplet in a small region of space. Therefore, the droplet model must be simple enough not to entail unrealistic computation times while still retaining the salient features of droplet combustion at high pres- surcs and temperatures. Usually, when the ‘film’ theory is used to model droplet combustion, the film surrounding the droplet is assumed to be quasi-steady. To a large extent, this assumption is legitimate, since the characteristic time for heat diffusion through the film, TV,, is typically two orders of magnitude smaller than the droplet lifetime. Nevcrthelcss, Williams [I] proved that this assump- tion may lcad to a 20% error in the evaluation of the total vaporization time. Many investigators [2-61 studied transient effects on droplet vaporization and burning. The main conclusion is that while the quasi- steady theory gives a good estimate of droplet burn- ing rates, it fails to predict correctly the evolution of the edme-to-droplet diameter ratio. Meanwhile, the unsteady theory predicts that the flame radius increases first and then decreases to zero [2], thus corroborating experimental observations [4]. Furthermore, a high pressure and temperature, pro- perties in the gas film are significantly modified, and tH is comparable with the droplet lifetime which rein- forces the intrinsic unsteadiness. Droplet vaporization and combustion under these conditions cannot be treated as quasi-steady [7]. Some investigators indi- cate that the quasi-steady theory is not valid for reduced pressure above 0. I [S]. On the other hand. the very high pressures and temperatures encountered in a liquid-rocket com- bustion chamber imply that both gas and liquid phases may deviate substantially from their usual behavior. Specifically, the ideal gdS assumption is not valid under these conditions, and the liquid-vapor equilibrium is not correctly represented by the classi- cal laws and approximations. These phenomena com- plicate significantly the modelling of droplet vapor- ization and burning in such regimes, but may have a critical importance in the liquid-rocket combustion instability phenomenon. As shown by Wieber [9] almost 30 years ago, near the critical point a small change in pressure could lead to violent boiling and possibly microexplosion of the oxygen droplet, there- by supporting the combustion instability. Wiebel also noticed that if the chamber pressure is so high that the droplet reaches a super-critical state and becomes a vapor puff, the rate-controlling mechanism for combustion instability might be the vapor diffusion into the gaseous environment. Therefore, determining accurately whether the liquid drop will get close enough to the critical state to exhibit such behavior is primordial and a large amount of work was devoted during the past two decades by the com- bustion community to investigate the vaporization of a spherically symmetric drop in a quiescent environ- ment under high pressure and temperature. Manrique and Borman [IO] first noted that Wieber did not account for high-pressure phase equilibrium, non- ideal gas effects, effects of pressure on physical prop- 303