Enfermedades Metabólicas

The pressure drops were measured for different strut shapes with a wide range of porosities (60% to 80%). Both aligned and staggered arrangements were considered in the simulations. The length-normalised pressure drops for the aligned struts were plotted against Darcian velocity and the results can be seen in Figure 3-13.

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Figure 3-13 Length-normalised pressure drop versus Darcian velocity for middle range porosities (60% to 80%) for (a) circular, (b) triangular, (c) squared, (d) rotated

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Figure 3-13 (Continuation) Length-normalised pressure drop versus Darcian velocity for middle range porosities (60% to 80%) for (a) circular, (b) triangular, (c) squared, (d)

rotated square and (e) hexagonal aligned struts

The numerical results showed that the pressure drop increased with increasing flow rate for all the aligned structures regardless of the strut shape. A quadratic trend is evident, indicating that the flow is in the Forchheimer regime. This quadratic behaviour is due to the inertial effects becoming more dominant (Yang et al. 2013, Kundu et al. 2014). Baǧci et al. (2014) reported that the Forchheimer regime starts at a flow velocity about 0.02m/s. The

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current study considered Darcian velocities from 0.03 to 0.27 m/s, so the pressure drop dependence on velocity is second order as shown in Figure 3-13.

The triangular and rotated square aligned patterns exhibited the highest pressure drops as shown in Figure 3-13 (b) and Figure 3-13 (d). The pressure drop values for the circular, squared and hexagonal struts are similar, although hexagonal struts showed slightly higher values than the other two. Baloyo (2016) also reported that pore structure has a significant effect on pressure drop and consequently affects the flow regime.

The structures with lower porosities, due to the reduction of strut spacing, have higher pressure drop as shown in Figure 3-13. Mancin et al. (2010a) reported a similar behaviour for high porosity aluminium foams. In their study, when the porosity was decreased the pressure gradient was increased. This is because lowering the porosity leads to a reduction in the void space inside the porous material due to an increase of solid material and thus higher pressure drops arise.

The length-normalised pressure drop was plotted against Darcian velocity for the staggered patterns and the resulting graphs are shown in Figure 3-14.

The pressure drop values for the staggered patterns also presented a quadratic trend. Once again the triangular and rotated square struts showed the highest pressure drops. The numerical pressure drop values for the staggered arrangements are somewhat higher than the pressure drop obtained for the aligned struts. Papathanasiou et al. (2001) observed when numerically studying fibrous media using 2D patterned circular struts that the staggered arrangements exhibited higher pressure drops and higher friction factors. They attributed the difference in pressure drop to more uniform distribution of the flow as the channels are more open, leading to a less contracting / expanding character. In addition, the tortuous paths created by staggering the struts inside the REVs, increasing mixing and wall friction (further analysis in section 3.10). The tortuous paths contrast with what could be called directional pores in the aligned struts structures.

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Figure 3-14 Length-normalised pressure drop versus Darcian velocity for middle range porosities (60% to 80%) for (a) circular, (b) triangular, (c) squared, (d) rotated

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Figure 3-14 (Continuation) Length-normalised pressure drop versus Darcian velocity for middle range porosities (60% to 80%) for (a) circular, (b) triangular, (c) squared, (d)

rotated square and (e) hexagonal staggered struts

In both the aligned and staggered arrangements, circular struts showed the lowest pressure drop for all the simulations. This can be explained by the smoothness of the perimeter of the circle where there are no sharp edges, in contrast with the other shapes that have sharp edges in the vertex. In addition, it is important to consider the frontal surface area facing the flow. For instance, squares and rotated squares have the same features and yet rotated squares showed pressure drops 6 to 10 times higher than the regular squares. The

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difference between the rotated squares and the other strut shapes can be explained in terms of the gap created amongst the struts. Because of the rotation, the projected area of the rotated square struts is much larger than those of other strut shapes. As a consequence the gap for the fluid flow is much smaller, leading to much higher pressure drops. Despois and Mortensen (2005) observed that for lower porosities, the bottleneck created between pores increases the pressure drop.

In general, the highest pressure drop was obtained at the lowest porosity in the middle porosity range (60% to 80%) for all strut shapes. Further reduction in porosity is expected to result in larger pressure drops. In order to corroborate this, a lower range of porosities, 40% and 50%, were also considered in the present study. However, only certain strut shapes can be considered due to the overlapping effect explained in section 3.1.1.4. The length- normalised pressure drops for circular, squared and hexagonal struts with low porosity are shown in Figure 3-15.

In the middle range porosity (60% to 80%), the pressure drops for circular, squared and hexagonal aligned struts are very similar. For example, the difference in the normalised- pressure drop between the squared struts and the circular struts is from 1% to 45%, depending on the flow rate and porosity. In the porosity range of 40% to 60%, however, the difference in pressure drop amongst the strut shapes becomes more evident. This can be explained by the different gaps. For instance, the gap for the squared struts is almost twice the gap for the circular struts, leading to pressure drop values of the circular struts being three times larger.

The length – normalised pressure drops for staggered patterns in the low porosity range are shown in Figure 3-16. The pressure drop increased in all cases when compared with their aligned counterparts. The pressure drop for the staggered struts increased about 25% at low flow rates and almost 125% at higher flow rates, compared with the aligned struts. This difference in pressure drop can be explained by the change in flow direction.

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Figure 3-15 Length-normalised pressure drop versus Darcian velocity for low range porosities (40% to 60%) for (a) circular, (b) squared and (c) hexagonal aligned struts

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Figure 3-16 Length-normalised pressure drop versus Darcian velocity for low range porosities (40% to 60%) for (a) circular, (b) squared and (c) hexagonal staggered

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In order to fully compare the pressure drops between the aligned and staggered arrangements, a dimensionless pressure drop ratio is defined as follows:

∏ = ∆𝑃𝑠 ∆𝑃𝑎

(3.10)

where ∆Ps and ∆Pa are the pressure drops for the staggered and aligned structures

respectively. The pressure drop ratios for different porosities are shown in Figure 3-17. It can be seen that ∏> 1 as the pressure drop for the staggered structures is always higher for all strut shapes.

Figure 3-17 Pressure ratios between aligned and staggered patterns versus flow rate of circular, squared and hexagonal struts at different porosities: (a) 40%, (b) 50% (c)

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Figure 3-17 (Continuation) Pressure ratios between aligned and staggered patterns versus flow rate of circular, squared and hexagonal struts at different porosities: (a)

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Figure 3-17 (Continuation) Pressure ratios between aligned and staggered patterns versus flow rate of circular, squared and hexagonal struts at different porosities: (a)

40%, (b) 50% (c) 60%, (d) 65%, (e) 70%, (f) 75% and (g) 80%

Figure 3-17 shows that the pressure drop ratio increases with flow rate. At low flow rate, the pressure ratio is between 1.1 and 1.5 for all strut shapes regardless porosity and for higher flow rates, the pressure ratio is increased between 1.4 and 3.4. In most of the cases the pressure ratio stabilises at higher flow rates (Q > 1.2 l/min).

It can also be seen that the pressure ratio was highly affected by the strut shape. The strut shape with the lowest pressure ratio was the rotated squares, followed by triangles, circles, hexagons and squares. The squared struts displayed the highest pressure drop ratio with

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1.4 for the lowest flow rate and up to 3.4 for the highest flow rate. Except for the squared struts, the pressure ratio remained between 1.1 and 1.4 at low flow rate and increased to 1.2 to 2 for the higher flow rates. The difference in pressure ratio between the strut shape is due to the different effects on the flow path.

Porosity also affects the pressure ratio for the 2D patterned structures. It is shown that pressure ratio increases when porosity is increased, especially at higher flow rates. Increasing porosity leads to less tortuous paths in the aligned arrangements compared with a low porosity structure.