This paper presents a comprehensive analysis of the transport processes that control the self-pressurization of a cryogenic storage tank in normal gravity. A lumped thermodynamic model of the vapour region is coupled with the Navier-Stokes and energy equations governing heat, mass and momentum transport in the liquid. These equations are discretized using a Galerkin finite-element method with implicit time integration. Three case studies are considered based on three different heating configurations imposed on the tank wall: liquid heating, vapour heating and uniform heating. For each case, the pressure and temperature rise in the vapour and the flow and temperature distributions in the liquid are determined. Results are compared to a lumped thermodynamic model of the entire tank. It is shown that the final rate of pressure rise is about the same in each case and close to that predicted by thermodynamics even though the actual pressures are different because of varying degrees of thermal stratification. Finally, a subcooled liquid jet is used to mix the liquid and limit the pressure rise. Even so, there is still some thermal stratification in the liquid, and as a result the final vapour pressure depends on the particular heat distribution.

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Numerical results indicate that the model is successful in clearly distinguishing between 1-G normal and 1-G recurrent stone-former subjects based solely on their published 24-h urine biochemical profiles. Numerical case studies further show that the predicted renal calculi size distribution for a microgravity astronaut is closer to that of a recurrent stone former on Earth rather than to a normal subject in 1 G. This interestingly implies that the increase in renal stone risk level in microgravity is relatively more significant for a normal person than a stone former. However, numerical predictions still underscore that the stone-former subject carries by far the highest absolute risk of critical stone formation during space travel.

is used to assess the efficacy of citrate, pyrophosphate, and augmented fluid intake as dietary countermeasures aimed at reducing the risk of renal stone formation for astronauts. The model uses the measured biochemical profile of the astronauts as input and predicts the steady-state size distribution of the nucleating, growing, and agglomerating renal calculi subject to biochemical changes brought about by administration of these dietary countermeasures. Numerical predictions indicate that an increase in citrate levels beyond its average normal groundbased urinary values is beneficial but only to a limited extent. Unfortunately, results also indicate that any decline in the citrate levels during space travel below its normal urinary values on Earth can easily move the astronaut into the stone-forming risk category. Pyrophosphate is found to be an effective inhibitor since numerical predictions indicate that even at quite small urinary concentrations, it has the potential of shifting the maximum crystal aggregate size to a much smaller and plausibly safer range. Finally, our numerical results predict a decline in urinary volume below 1.5 liters/day can act as a dangerous promoter of renal stone development in microgravity while urinary volume levels of 2.5-3 liters/day can serve as effective space countermeasures.nephrolithiasis; gravity; weightlessness; crystal nucleation; crystal growth; agglomeration; inhibition; dietary countermeasures NEPHROLITHIASIS IS NOT ONLY a problem within the general population on Earth but is also a risk to the astronauts' health and survival during future long-duration missions where exposure to microgravity and other space conditions are likely to increase the risk of renal stone formation. The concern seems to be justified since a recent survey of renal stone formation in US astronauts has revealed 14 recorded postflight episodes (13, 26). Whether on Earth or in space, the development of calcium oxalate (CaOx) renal stones is initiated with nucleation of the sparingly soluble salt from a supersaturated urine as the necessary first step, followed by simultaneous growth and agglomeration of the crystals as two effective stone size-enhancing mechanisms. While the extent of urinary CaOx supersaturation in the nephron changes continuously depending on the level of hydration and the extent of other dietary intake, the urine of most individuals, healthy or stone former, remains supersaturated under normal everyday conditions.The progression from crystal nucleation and growth to a clinical colic situation is not yet well understood, but it is thought to occur by either free-or fixed-particle mechanisms (13, 32). Recent studies by Kim et al. (14) and Evan et al. (7) using advanced endoscopic imaging and comprehensive physiological biopsies suggest three possible free/fixed pathways to stone formation: 1) nucleation and growth on the Randall plaque deposits in the papillae; 2) growth after adherence to a possibly injured section of collecting or Bellini ducts; and 3) homogeneous nucleatio...

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