for the CH^-C^ system“ Most exhaust effluent matter is confined in a cone of full-apex angle of roughly 10 degrees. The effluents continually cool as they expand* Temperature falls roughly as inverse square-root of the distance from the engine exit, while density falls roughly as inverse-square. At a point where the cross section of the exhaust plume is about 3000 times that of the throat of the rocket engine, the local pressure and temperature are typically 1 torr and 250 K, respectively* This condition is the saturation point condition for the H2O molecules. For the first stage engines of the POTV, the saturation point occurs at about 140 meters behind the exit plane of the rocket engines, at which point the plume diameter is about 25 meters, number density about 4 x 10^ cm , mean-free-path about 0.004 cm, and collision frequency is of the order of 10 sec • For the second stage POTV engines, the same thermodynamic conditions occur at approximately 100 meters behind the engine where the plume diameter is about 18 meters. Beyond the saturation point, supersaturation conditions exist wherein condensation of H2O molecules is expected to occur. In all cases of interest, the condensation should lead directly to the solid state rather than the liquid state. Condensation could occur in both homogeneous and heterogeneous modes. Homogeneous condensation of water vapor is known to occur in the absence of high energy nucleation centers whenever the saturation ratio (the ratio of the local vapor pressure to the equilibrium vapor pressure) exceeds 6 (see Hill, 1966). Heterogeneous condensation occurs around the high energy nucleation centers, which in the case under consideration would consist of (1) atomic and molecular ions, (2) electronically or vibrationally excited atoms and molecules, and (3) metallic contaminants originating from the walls of rocket motors* When such nucleation centers are present, the heterogeneous nucleation can occur before the saturation ration reaches 6. As condensation progresses, heat is generated, which may lead to a pressure overshoot (Hill, 1966). Eventually, however, the heat released during condensation will be carried away by the effluent gas molecules that surround the particles that are undergoing cooling. Even when H90 molecules are completely removed by condensation, there will be the "inert" molecules such as H2 (in the system) or CO^ (in the CH^-C^ system) that could cool the particulates. There are two questions that need to be answered. They are: (1) What is the extent of condensation? l.e., What fraction of ^0 molecules convert to the condensed phase? and (2) What are the average sizes and size distributions of the particulates formed? Regardless of the actual mechanism of nucleation, the extent of condensation can be estimated by use of the homogeneous condensation theory, which is well developed. One can use the theory because the extent of condensation is independent of the nucleation mechanism. In the thermodynamic environments of concern, the speed of cooling and density change are sufficiently slow to cause almost complete condensation. Within about 50 meters behind the saturation point, most (i.e., at least 90%) of the ^0 molecules should be in the condensed phase. The question of particle size is more difficult to answer. If nucleation is homogeneous, one can calculate the final sizes, using the existing homogeneous condensation theory. A cursory examination indicates that the final particle sizes should be at most about 10 $ cm, if the nucleation process is heterogeneous, then it becomes virtually impossible to calculate the size distribution because the concentration and characteristics
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