Bubble Point Model Derivation

There is a sign convention that must be taken into account. Therefore, using assumption 2 for a smooth surface and smooth pressure jump. 

FIGURE 3.2 The Liquid/Vapor Interface of a Patch in the Dutch Twill Screen to Show the Geometry of the Curved Interface. 

FIGURE 3.3 Approximating a Dutch Twill Pore as an Inverted Vertical Capillary Tube. The normal is taken as pointing into the liquid phase. 

Note that the mean radius P of the pore forms a perfect spherical meniscus and that this radius will depend on the radius of the tube, and contact angle between liquid and solid tube through the following relation  

Assumption 4 is invoked to relate the pressure jump across the spherical interface with the actual bubble point pressure of the LAD screens. Therefore, the equivalent radius, flpore. of the vertical capillary tube that is isomorphic with the mean curvature, Hm, can be approximated using a hydraulic diameter of a circle inscribed within the complex triangular pore shape such that Equation (3.13) becomes  

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The following assumptions are required to derive the simplified bubble point model ... 

The current bubble point model, which is a simplification of the 3D YLE that was derived in Chapter 3, predicts bubble point pressures accurately for storable propellants and room temperature liquids. Effective pore diameters of a particular screen mesh must either be... 

The set of primary and secondary factors which influence LAD design were formulated, and a suite of physics-based models for the influential factors were developed and validated both in storable and cryogenic propellants. While the models agreed well with historical room temperature data, all LAD models validated by cryogenic data, including bubble point pressure, reseal pressure, FTS pressure drop, TVS cooling efficiency, and full-scale LAD channel pressure drop show strong temperature dependence and deviation from the room temperature behavior. The models derived here and validated both by the... 

The huhble point model has been derived in a way to make it facile for a system designer to predict performance for any screen in any fluid at any thermodynamic state. From Chapter 10, the updated cryogenic bubble point equation is expressed as ... 

In a similar manner, thickness distributions can be derived in other relatively simple but more realistic molds, such as truncated cones. In such cases, the above model holds until the bubble comes in contact with the bottom of the mold at its center. From that point on, new balance equations must be derived. 

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