**1. Introduction**

Stratification in cryogenic liquid storage systems is a complicated yet inexorable thermodynamic phenomenon involving a combination of heat and mass transfer. Owing to the very low boiling point, they are susceptible to heat ingress from the ambient. Cryogenic propellant tanks undergo typical operation sequences when preparing for launch, including tank filling, chilling, boil-off, level correction, tank pressure and hold until lift-off. The time duration between tank pressurization and lift-off is called ground parking period. During ground parking, the heat ingress is due to the large temperature gradient existing between the storage and atmospheric temperature. An overwhelming increase in heat ingress occurs due to aerodynamic heating (during flight) and space radiation, although not as significant as the former, during coast phase. The insulation provided to the propellant tanks is foam which is relatively less effective compared to vacuum or multi-layered insulation (MLI). This heat leakage raises the temperature of liquid adjacent to the walls inducing natural convection currents. The heated liquid starts flowing up due to buoyancy and accumulates at the liquid-vapor interface creating an axial temperature gradient called thermal stratification. The depth of this stratified layer increases with time.

Consequently, the tank pressure keeps increasing due to vaporization. This demands the proper design of venting devices and insulation system. Hence thermal stratification is a crucial design criterion for designing rocket fuel tanks. A schematic for thermal stratification is illustrated in **Figure 1**.

**Figure 1.** *Schematic of stratification phenomenon in a cylindrical tank.*

### **2. Literature review**

A wide variety of experimental and numerical studies have been conducted and reported by researchers across the globe on thermal stratification and selfpressurization of a cryogenic storage vessel. Tatom et al. [1] conducted an experimental investigation on a 500 - gal liquid hydrogen storage tank to provide stratification test data. The main objective of the study was to find out the effect of bottom

### *Effect of Roughness Elements on the Evolution of Thermal Stratification in a Cryogenic… DOI: http://dx.doi.org/10.5772/intechopen.98404*

heating on stratification. It was found that the controlled bottom heating can reduce the degree of stratification by transferring a large fraction of sidewall heat flux to bulk liquid. Schmidt et al. [2] conducted an experimental investigation to study pressurization and stratification of an LH2 tank and compared the results with the theoretical model. It is concluded that as interface temperature increases, the ullage pressure in the tank also increases, which results in more heat transfer to the stratified layer. The amount of additional heat transfer can be calculated using the theoretical model, which helps to optimize the pressure level within the storage tank. Ruder et al. [3] developed a mathematical method to determine the temperature profile inside a cryogenic storage tank under pressurized condition. They developed an empirical relation to represent the temperature profile which is similar in shape to a Gaussian probability distribution.

Several experimental kinds of researches on the evolution of thermal stratification and self-pressurization in a cryogenic storage tank have been reported in the literature. Aydelott et al. [4] developed a non-venting 9-inch diameter spherical container partially filled with liquid hydrogen for self-pressurization tests. The effects of filling per cent, heat flux, top heating, bottom and uniform heating were studied. It was found that the self-pressurization rate in the storage tank was mainly a function of the heating configuration with the per cent filling and heat-transfer rate playing a secondary role.

Ji et al. [5] conducted experiments on a heated container of liquid and developed various dimensionless parameters associated with thermal stratification. By comparing the dimensionless pressure and temperature, the quality of scaling was verified and concluded that parameters like tank pressure, bulk liquid temperature and the surface temperature could be scaled with dimensionless parameters. To study the self pressurization of a spherical liquid hydrogen tank, Hasan et al. [6] conducted an experimental investigation. The results showed that the initial conditions of the storage tank play a considerable role in self-pressurization. If the tank had previously experienced a steady boil-off rate due to long period venting, the self-pressurization rate seems to be lower and rapid pressurization rate was observed for the tank which is not at a steady venting condition. Yamaji et al. [7] conducted an experimental and numerical investigation of thermal stratification and plume mixing. Series of experiments were carried out using PIV and thermocouple measurements, and the developed CFX model reproduced the measured velocity distributions and temperature relatively well.

Gursu et al. [8] developed three different pressure rise models to predict thermal stratification and self-pressurization performance in cryogenic storage tanks; a homogeneous model, a surface evaporation model and a thermal stratification model. The thermal stratification model succeeds in predicting self-pressurization, whereas the other two models which are collectively the isothermal models could not predict the tank pressurization accurately enough. The flow pattern and thermal stratification of a cryogenic cylindrical tank were numerically studied by Chin-Shun Lin et al. [9]. The tank sidewall was subjected to either a uniform heat-flux or two discrete levels of uniform heat-flux at the upper and lower halves of the tank wall. The tank bottom was kept at a constant temperature controlled by the heat exchanger of a thermodynamic vent system. They successfully solved dimensionless steady-state conservation equations by a finite-difference method. Li et al. [10] developed a numerical model to study the thermodynamic effect of heat in-leak into a cryogenic tank and validated the model with experimentation. In the upper part of the liquid, a steady vortex-like region is developed as the heat inleak starts. A large temperature difference in the vertical direction was visible but little temperature difference in radial direction because the radial flow is predominant in that region. It was concluded that thermal stratification exists only in sub-cooled liquid and heat in-leak depends on the void fraction of fluid close to the tank wall. A calculation model is developed by Liu et al. [11] to predict self-pressurization and thermal stratification phenomenon of a liquid hydrogen storage tank. The effect of gravity level, fill level and temperature of the wall on the development of stratification were analyzed using the developed model. The effect of thermal aspect ratio on the self-pressurization is studied experimentally by Kang et al. [12]. A double wall vacuum insulated liquid nitrogen storage tank is developed for experimental investigation and the results were validated with the homogeneous model. Because of the thermal stratification, the experimental results slightly differ from that predicted by homogeneous model. The results indicate that the thermal stratification is highly correlated with the thermal aspect ratio.

The effect of rib shape and material thermal conductivity on the development of stratification was numerically studied by Fu et al. [13]. They considered cylindrical ribbed tank with 50% fill volume and rib shapes of rectangular and semi-circular. Tank pressurization rate was found to be lower for rib materials of low thermal conductivity. Semi-circular ribbed tank underwent lesser self-pressurization in comparison with the rectangular ribbed case for same rib cross-sectional area and locations.

Khurana et al. [14] carried out numerical investigations to minimize the thermal stratification in LH2 tanks. By providing transverse wall ribs on the inner surface of the cylindrical tank, they succeeded in achieving a 30% reduction in the stratification parameter. A delayed stratification, as well as lesser natural heat transfer coefficient, is observed for the tank with the ribbed inner surface than smooth wall tank. Polideri et al. [15] conducted an experimental investigation to study transient natural convection on a vertical ribbed wall. They reported a reduction in convective heat transfer coefficient below the initial rib and enhancement past the last one. A reduction in heat transfer performance was reported by Tanda et al. [16] for a case of natural convective air flow over a heated ribbed plate. To obtain the distribution of heat transfer coefficient, Schlieren optical technique was used to reproduce thermal field, and it was found that the induced flow creates thermally inactive regions just upstream and downstream of each protruding element.

Experimental and numerical studies were conducted by Shakerin et al. [17] to find out the flow behavior of air over a heated wall with single and repeated, twodimensional, rectangular roughness elements. The flow visualization studies confirm the formation of nearly stagnant regions between the ribs and surface heat flux in these regions was very low. So the presence of wall ribs did not contribute to heat transfer enhancement. Zhongqi et al. [18] used Volume of Fluid (VOF) method to investigate the depressurization and thermal stratification behavior of a liquid nitrogen tank with different baffle structures under microgravity conditions. By optimizing the baffle setting, a reduction of up to 54% in pressurization rate was achieved, which is an eye-catching improvement for extended duration missions. Justin Oliveira et al. [19] investigated the effect of isogrid on thermal stratification inside propellant tanks. Studies showed that the boundary layer thickness on the wall in a forced free stream flow was distinctly thicker (150–700%) than the equivalent flat plate boundary layer thickness. Isogrids can either enhance or suppress stratification rate compared to smooth tanks depending upon roughness size and tank conditions. Experimental and numerical studies were carried out by Faure et al. [20] to assess the boundary layer behavior over the propellant tank with mass saving isogrid structures. They revealed that more than 200% thicker velocity boundary layer is developed over isogrid wall than a smooth wall. It leads to rapid self-pressurization and enhanced fluid mixing.

The presence of roughness elements has been found to reduce thermal stratification. The effect of spacing to height ratios of transverse ribs, protrusion length, the conductivity of ribs on heat transfer performance has been studied extensively, but for flat

*Effect of Roughness Elements on the Evolution of Thermal Stratification in a Cryogenic… DOI: http://dx.doi.org/10.5772/intechopen.98404*

vertical and horizontal heated plates. Influence of ribs and grid structure on the reduction of stratification on a cryogenic cylindrical tank demand more detailed investigation.
