Subcooled liquid bubble point model

Table 10.4 Complete Coefficient Matrix for Subcooled Liquid Bubble Point Model... 

To model this gain, the bubble point formula for saturated cryogenic liquid states can be modified to incorporate subcooled liquid states. Examination of subcooled data indicates that the gain in bubble point pressure is approximately linearly proportional to the degree of subcooling, or distance away from the saturation curve, on a temperature/pressure plot. Therefore, the proposed subcooled bubble point model takes the following form ... 

Upon computing the bubble point of the overhead product, we find that the measured reflux temperature is well below the estimated boiling point. Thus, we choose the subcooled condenser model. The steady-state concept of the subcooled condenser often does not exist in practice. Instead, the condenser is in vapor-liquid equilibrium with the vapor augmented by a blanket of noncondensable gas (that has the effect of lowering the dew point of the overhead vapor). The subcooled condenser is a convenient work-around for steady-state models (as is needed here), but not for dynamic models. We assume a partial reboiler. 

The seven known parameters that affect the bubble point pressure include the surface tension (liquid type), contact angle, effective pore diameter (which takes into account screen style, mesh, and metal type), liquid temperature, degree of subcooling (pressure), and pressurant gas type and temperature. The model will be validated through data collected over the past half-decade, as well as with data from the current work, which spans the space of these seven parameters. Ultimately, to be of topmost relevance for all future cryogenic propulsion missions, the model will be formulated in such a way that typical mission parameters like screen mesh, liquid properties, and pressurant gas properties can be input into the equation to obtain bubble point pressure easily and quickly at any desired condition. 

The heated gas coefficients were determined in the same manner as the subcooled liquid coefficients. For each heated gas data point, a corresponding model generated saturated bubble point was calculated at each liquid temperature. For a given screen, pressurant gas, and cryogenic liquid, the heated gas loss, defined as the ratio of bubble point pressures ... 

If reseal diameter is known, the reseal pressure equation can theoretically be used to determine the reseal point of any fluid with a known surface tension. However, the same problem arises with cryogenic reseal data as with the cryogenic bubble point data. The room temperature prediction value matches neither the non-condensable or autogenous pressurant gas case. In addition, the room temperature model cannot be used to predict reseal pressures of subcooled cryogenic liquid states or elevated pressurant gases. Therefore, the new model must therefore address the following three discrepancies that exist between cryogenic reseal pressure data and simplified room temperature model. These are ... 

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