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Appendix D Self-pressurisation and venting effects in liquid hydrogen tanks: an investigation, using the homogeneous and surface evaporation models Three models have been used previously for calculating the rate of pressure increase from self-pressurisation in a cryogenic container. These are a homogeneous model, a surface evaporation model, and a thermal stratification model. The first two are isothermal models, based on the assumption that no temperature gradient exists in the vapour and liquid regions. The homogeneous model assumes that the temperature of the entire tank is uniform at all times, whereas the surface evaporation model assumes that all the heat entering the vessel is used to vaporise the liquid cryogen. The thermal stratification model is based on the assumption that the heat leak is too small to cause nucleate boiling and that the heat is absorbed by liquid in proximity of the walls setting up convection currents·which carry the warmed liquid to the surface where surface evaporation occurs. The homogeneous model typically gives lower rates of pressure rise than those measured because in the real case only part of the liquid is heated. The surface evaporation model typically gives rates of pressure rise greater than those measured because in the real case not all the heat is used for vaporisation. All three methods have been reviewed by Gursu et al.[108,109]. Aydelott and Spuckler[110] reiterate that a majority of the work available on measuring and modelling self-pressurisation in stored liquid hydrogen is based on large vertical cylinders with heating, only on the side walls. The thermal stratification model developed by Arnett and Voth[111] uses natural convection theory for vertical plates to predict heat and mass transfer. Tatom et al.[112] found that bottom heating caused more heat from the side walls to be transferred to the bulk liquid and reduced the extent of thermal stratification. Vibration considerably enhances boil-off. An increase of up to 12 times is reported by Rotenburg[113]. It is interesting that at low levels of vibration excitation, the pressure rise is actually lower. This is thought to be due to the energy being absorbed in causing a mixing of the fluid and preventing thermal stratification. The same result is obtained by stirring[30], which is reported to reduce the boil-off rate by up to a factor of three. Most of the liquid hydrogen tanks built and used in automobiles in the recent past have been horizontal cylinders with hemispherical ends, and are small in size. Convection currents in these tanks may have effects similar to stirring. The application ofthe thermal stratification model, in particular, considering the development of a boundary layer along the vertical tank walls, is difficult for small vehicular tanks. Rotenburg[114] developed a numerical model based on the homogeneous model for self-pressurisation in small cryogenic tanks. Experimental correlation was done against the tank used by Stewart[115]. His results predicted the rate of pressure rise, 1.3 times lower than measured for nearly empty tanks, and 1.6 times lower for nearly full tanks. Aydelott and Spuckler[110] show that heat flux per unit volume may be used as a scaling parameter. In order to understand the effects of venting on cryogenic storage, the homogeneous and surface evaporation models used for self-pressurisation, were extended into the venting process. From the steady flow energy equation, for mass leaving thePDF Image | CO2 removal from air for alkaline fuel cells operating with liquid H2
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