DELITOS CONTRA LAS INSTITUCIONES DEL ESTADO

Figure 4-18 shows 3D geometry of concentric pipe heat exchange where the two pipes are made of copper with outer diameters of 6 mm and 15 mm respectively for the inner and outer tubes. The length of the heat exchanger was 500 mm and LN2 flows inside the inner while the secondary warmer fluid flows in the annular gap between the two tubes. The heat exchanger has a symmetrical geometry so only half of the geometry was modelled to reduce the computational time. Figure 4-19 shows the flow direction in the heat exchanger where both fluids have the same flow direction from the right hand side to the left hand side ( parallel flow) in order to reduce the risk of freezing the secondary fluid.

The secondary fluid was carefully selected considering the possibility of freezing around the LN2 carrier tube (in the annular space) which can restrict the flow. An investigation of substances that have low melting/freezing temperature and are in liquid form at room

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temperature was carried out and the results summarized in Table 4-1. Ethanol with melting temperature of -114 °C and boiling temperature of 78.5 °C was used in this work.

Figure 4-18: Heat exchanger geometry

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Table 4-1 Substances have low boiling temperature

Common Name IUPAC Name Melting Point (°C) Boiling Point

(°C)

Refrigerant 123 - -107.2 27.82

Refrigerant 11 - -111.1 23.8

Refrigerant 611 - -98.9 31.7

Methyl alcohol Methanol -97.8 65.0

Ethyl alcohol Ethanol -114.7 78.5

Ethyl chloride Chloroethane -136.4 12.3

Propyl alcohol 1-Propanol -126.5 97.4

Butyl alcohol 1-Butanol -89.5 117.3

Pentyl alcohol 1-Pentanol -79 138

Figure 4-20 shows the mesh where a high quality mesh with a total number of 532258 elements were used.

Figure 4-20: Heat exchanger mesh

Regarding the model setup, a steady state, pressure-based solver was used, and for the multiphase model Mixture Model was used due to the difficulties of using Eulerian Model with multi domains. Energy solver and turbulence viscous (k-ɛ) were also enabled for Nitrogen and Ethanol domains. To consider the LN2 mass transfer, Condensation- Evaporation model was used and the evaporating temperature was set as 77.35 K. In the heat exchange there were three phases LN2, N2 and Ethanol. In the model, LN2 was set as the

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primary phase while the nitrogen gas and ethanol were set as secondary phases. The model solves Continuity, Momentum, Energy, the Secondary Phases Volume Fraction and Mass Transfer equations which are briefly described in the following section. The properties of the liquid phase were assumed as function of temperature only, while the properties of nitrogen gas were varied with pressure and temperature according to ASHERA hand book (see appendix A, C) [87].

Regarding the boundary conditions, velocity inlet with different values (0.1-0.4 m/s) was applied at inlets of LN2 and ethanol fluids. This range was carefully selected reducing the LN2 inlet velocity below the value of 0.1 m/s will reduce the LN2 mass flow rate as result the cooling rate will be too small and hard to compare the cases. Increasing the inlet velocity higher than 0.4 leads to reduce the LN2 vapour volume fraction at the outlet indicating there is a limitation of increasing the inlet velocity with the current inner tube length. Several cases were simulated to investigate the effect of inlet mass flow rates on the LN2 outlet conditions (temperature, liquid volume fraction and vapour volume fraction), the ethanol outlet temperature, and the temperature of the outer surface of the inner tube. Table 4-2 shows the inlet condition (velocity and temperature) of each case, while the outlet pressure with a value of 1 atm was set for LN2 and ethanol outlets.

Table 4-2 Inlet condition of each case Case No LN2 Ethanol Velocity [m/s] Temperature [K] Velocity [m/s] Temperature [K] Case 1 0.1 77.3 0.1 323 Case 2 0.2 0.1 Case 3 0.3 0.1 Case 4 0.4 0.1 Case 5 0.1 0.2 Case 6 0.1 0.3 Case 7 0.1 0.4

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A high performance central computing in University of Birmingham (BlueBear) was used and each case took about 7 days to converge. The convergence criteria was based on monitoring different parameters including; the energy balance between the two fluids (i.e. comparing the absorbed energy by LN2 to the energy loss by ethanol), inlet/outlet mass flow rate of each fluid and outlet temperature of each fluid. Figure 4-21 shows LN2 and ethanol outlet temperature at the convergence time where it is clear that the outlet temperature of both fluids is no longer changed and this happen after a number of iteration of 1.5 million.

Figure 4-21: LN2 and ethanol outlet temperature at the convergence time

Figure 4-22 shows the nitrogen outlet temperature where it is clearly seen that, as the LN2 inlet velocity increases (cases 1-4) the outlet temperature decreases, however, when the ethanol inlet velocity increases there is no significant change in the nitrogen outlet temperature (cases 5-7). Figure 4-23 shows similar trend of the outlet vapour volume fraction where it decreases with increasing the LN2 inlet velocity however there is no significant change where the ethanol inlet velocity changes. The figure also presents the nitrogen liquid volume fraction which increases with increasing the LN2 inlet velocity indicating the LN2 did

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not fully evaporate. The first column in this figure shows the inlet liquid volume fraction LVF where it is equal to 1 indicating LN2 entered to the domain as single phase. Figure 4-24 shows the variation of the LN2 vapour volume fraction along the tube and near to the wall for cases 5-7, with higher ethanol inlet velocity, where a high vapour volume fraction ( ≈ 1) indicating full evaporation of LN2. Figure 4-25 shows the LN2 vapour volume fraction contours.

Figure 4-22: Nitrogen outlet temperatures

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Figure 4-24: Variation of the LN2 vapour volume fraction along the tube

Regarding the ethanol side Figure 4-26 shows the outlet temperature where it decreases with increasing the LN2 inlet velocity (cases 1-4), however, increasing the ethanol inlet velocity (cases 5-7) shows no significant change in the ethanol outlet temperature. This indicates that increasing the ethanol mass flow rate has no significant change on the outlet condition. This is due to the low heat transfer coefficient of N2 gas.

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Figure 4-26: Ethanol outlet temperatures

Figure 4-27 shows the temperature distribution along the outer surface of the LN2 carrier tube, and the dash line in the figure refers to the freezing temperature of ethanol. At the highest LN2 flow rate only about 5 cm shows the possibility of the ethanol freezing around the inner tube. Figure 4-28 shows the whole heat exchanger temperature contours.

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Figure 4-28: Temperature contours of whole heat exchanger