**4.2 Comparison of flow through a smooth and rough surface tank**

To study the effect of presence of obstruction elements on the natural convection flow, two cases were simulated. Flow through a smooth wall tank and flow through a storage tank with roughness elements at the inner wall surface. **Figure 4**


#### **Table 2.**

*Geometrical parameters of tank.*

**Figure 3.** *Geometrical parameters of grids in a storage tank.*

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

shows the development of velocity boundary layer in a smooth tank wall due to natural convection flow. We can identify the development of laminar boundary layer and its magnitude keeps on increasing along the run length. The maximum velocity value of 0.038 m/s is obtained near to tank wall which is indicated as red color zone. Comparatively stagnant or undisturbed zones were developed at the bottom part of the bulk liquid zone.

**Figure 5** shows the development of laminar boundary layer over a rough surface tank. Due to the presence of obstruction elements, we can see that the velocity near the tank wall is zero which is indicated by blue color zone. Also, stagnant regions are developed around the obstruction elements which causes further hindrance to the flow. Compared with smooth wall case, the bulk liquid seems undisturbed and flow due to natural convection takes place through the top face of the obstruction elements.

For the better understanding of the flow behavior over a tank surface with obstruction elements, stream line diagram can be used. The **Figure 6** shows the stream lines over a rough surface tank. It is clear that the flow gets obstructed with roughness elements. Stream line deflection also takes place due to the presence of obstruction elements. Apart from velocity distribution, the development of stratified layer greatly depends on the mechanism of heat transfer to the interface and bulk liquid.

**Figure 7** shows the comparison of temperature contour over tank with smooth and roughness elements after 150 seconds of flow. The development of stratification and degree of stratification is higher for tank with obstruction elements. The presence of roughness elements causes the formation of stagnant regions near the wall but the increase in heat transfer area leads to better heat transfer to the fluid.

**Figure 8** shows a detailed view of the development of thermal boundary layer over a tank with roughness elements. It can be seen that the boundary layer formed is almost uniform throughout the run length. It does not thicken monotonically along the wall. Due to increased surface area, there will be evident additional heating. So the temperature of liquid will be higher for rough wall case. The thermal

**Figure 6.** *Contour of stream lines over a tank with obstruction elements.*

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

**Figure 7.**

*Comparison of temperature contour over (a) smooth wall and (b) rough surface tank.*

boundary layer developed is also thicker for rough wall case which further results in increased rate of thermal stratification and self-pressurization rate.
