**4.3 Thermal stratification in a cryogenic storage tank with isogrid surface**

To study the impact on thermal stratification due to the presence of grids on tank wall, three cases were simulated. The roughness elements number varies such as 25, 30 and 35 corresponds to case 1, 2 and 3 respectively. For smooth wall case, the total volume of the tank is 196349.54 cm3 , the heated surface area is 15707 cm<sup>2</sup> and hence the volume to surface area ratio is 12.499. For tank with grids (case 1), the heated surface area increased to 17105.008 cm2 and volume reduced to 196286.87 cm<sup>2</sup> . So, the volume to surface area ratio reduces to 11.4754 which is 8.189%. Similarly, there is a reduction in volume to surface area ratio of 9.667% and 11.112% corresponds to case 2 and 3.

The evolution of pressure under three different cases is shown in **Figure 9**. As the number of elements increases, the value of pressure inside the tank also increases. The rise in pressure is noticeable after a time period of 60 seconds. It may due to the initial transient boundary layer formation process. As the number of roughness elements increases from 25 to 35, the heated surface area increases by 8.89% and 11.11%. It causes an increase in self-pressurization rate of 1.88 Pa/s (smooth wall) to 2.21 Pa/s (case 3). The case 3 with 35 number of obstruction elements have a selfpressurization rate which is 17.31% more than that of smooth wall case. The increase in self-pressurization rate due to presence of grids is shown in **Table 3**.

## **4.4 Thermal stratification in a cryogenic storage tank with rib surface**

A similar kind of analysis is done incorporating ribs instead of grids on the tank wall. The rib geometry used in the analysis is having height 'h', spacing 's' and

**Figure 9.** *Comparison of pressure evolution of a tank with different number of isogrids.*

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


**Table 3.**

*Influence of grid structure on the evolution of self-pressurization.*

#### **Figure 10.**

*Geometrical parameters of cylindrical tank with rib structure.*

thickness 't' with rectangular cross section. The ribs were provided in the liquid side only. To study the effect of ribs on the evolution of stratification, three cases were considered; case 4, 5 and 6. Keeping the rib geometry and dimensions same, the distance between them is varied. So, the number of ribs corresponds to the cases 4 to 6 will be 3, 5 and 7 respectively. The tank geometry and rib layout are shown in **Figure 10**. The geometrical parameters are shown in **Table 4**.


**Table 4.** *Geometrical parameters of ribs corresponds to cases 4–6.*

For smooth wall case, the volume of the tank is 196349.54 cm3 the heated surface area is 15707 cm2 and hence the volume to surface area ratio is 12.499. For tank with 3 ribs (case 4), the volume reduces to 188809.7 cm3 and heated surface area increases to 19476.91 cm<sup>2</sup> . So, the volume to surface area ratio reduces to 9.694 which is 22.411%. Similarly, there is a reduction in volume to surface area ratio of 33.13% and 41.63% corresponds to case 5 and 6. Apart from these statistics, there is more increase in run length due to the presence of ribs. For case 4, the run length increases by 30%, 50% and 70% corresponds to case 5 and 6.
