Numerical investigation of the discharging process in a latent cold storage unit

In this study, a latent cold storage unit using vertical cylindrical structure coupled with a concentric air duct is proposed. The cold discharging process of the unit is simulated by computational fluid dynamics (CFD) based on the enthalpy-porosity method. The temperature distribution and liquid fraction distribution of the latent cold storage unit are analyzed. In addition, thermal performance including the average temperature of phase change material, outlet air temperature, the liquid fraction and the cold discharging power are analyzed in detail.


Introduction
Compared to the sensible cold storage, latent cold storage with phase change material (PCM) offers a higher energy storage density, nearly constant energy storage temperature as well as lower requirements of space and weight, which thereby has attracted great research attention in recent years [1][2][3][4].Thermal performance of the latent cold storage system is studied numerically and experimentally from different angles [5][6][7][8][9], which provides a useful reference for the progress of the technology.For summer air conditioning system in office buildings, the fresh air cooling occupies a considerable proportion of building energy consumption.Latent cold storage technology can provide an effectively way to solve this problem, which storages the cold from air source heat pump driven by valley electricity in the nighttime and precools the hot fresh air in the daytime.As the nighttime ambient temperature is lower, COP of the air source heat pump is effectively improved to realize the system energy saving.Meanwhile, the peak-valley electricity imbalance problem can be alleviated.
In this paper, a latent cold storage unit using vertical cylindrical structure coupled with a concentric air duct is proposed.The cold discharging process of the unit is simulated by CFD based on the enthalpyporosity method.Thermal performance of the unit is analyzed in detail.

Physical model
Figure 1 shows the schematic of a latent cold storage unit.The unit is in cylindrical shape, consisting of a concentric tube as air duct and a spiral coil as water-PCM heat exchanger, and the rest of the cylinder volume is full of PCM.The unit consists of the water-PCM cold charging process during the nighttime and the air-PCM cold discharging process during the daytime.For the charging process (solidification of PCM), the PCM is cooled by the cold water from the air source heat pump and the cold is stored.For the discharging process (melting of PCM), the PCM is heated by the hot fresh air and the cold is released.In this paper, the cold discharging process (melting of PCM) in the daytime is investigated.As water-PCM heat exchanger occupies only a small part of the cylinder space, in order to simplify the air-PCM heat transfer process, this part of the volume is ignored.In another word, the cylinder space is full of PCM during the air-PCM heat transfer process.As shown in Figure 2, the inner diameter, outer diameter and height of the unit are 150mm, 250mm and 1000 mm, respectively.

Numerical model
As shown in Figure 2, the air-PCM heat transfer process can be simplified to a 2D (two-dimensional) model along the vertical and radial directions.The enthalpy-porosity method is applied to describe the dynamic melting process of PCM.To build the CFD model, several assumptions are made as follows: (1) The outer surface of the latent cold storage unit is adiabatic.
(2) The air and PCM are considered incompressible fluids.
(3) Thermal properties of the air and PCM are temperature independent.
The FLUENT is used for simulation.2600 grid elements and 10s are chosen based on the independency test.To describe the air flow inside the air duct, the standard k-ε model and standard wall function approach are used.SIMPLE algorithm and PRESTO scheme are chosen for the pressure velocity coupling and pressure correction, respectively.During the cold discharging process, the inlet air temperature is 37℃ and the velocity is 0.2m/s.The initial temperature of unit is at a uniform temperature of 7℃.

Results and discussion
Temperature and liquid fraction distribution of the latent cold storage unit are shown in Figure 3 and Figure 4, respectively.The temperature and liquid fraction distribution show that the melting process of PCM starts at the top and then expands gradually upward from the bottom.The boundary conditions of the air inlet and air outlet are set as velocity inlet and outflow, respectively.With continuous thickening of the wall boundary layer in the direction of flow, the velocity distribution on the cross section will increase in the center and decrease at edges, meanwhile, the static pressure along the flow direction will continuously decrease in the boundary layer due to the friction.Therefore, negative pressure appears at the outlet and brings the back flow.The back flow strengthens the heat transfer process in the wall boundary layer and leads a faster melting rate at the top zone.Except for the outlet, the air temperature as well as temperature difference between the hot air and PCM are decreasing along the flow direction.As a result, the melting rate is also decreasing along the flow direction.
As shown in Figure 5(a) and (b), both the average temperature of PCM and the air outlet temperature maintain a relatively stable value after a rapid rise.This is because in the beginning of cold discharging process, the PCM does not melt and the energy is stored in the form of sensible heat.The temperature of PCM around the air duct increases rapidly from the initial value to the melting temperature, which reduces the heat transfer rate between the hot air and PCM and brings a rapid rise of the air outlet temperature.With the heat transfer process going on, the temperature of PCM around the air duct quickly reaches the melting temperature, the PCM starts to melt and the latent heat is stored in PCM with a small variation.Therefore, the heat transfer rate between the hot air and PCM is more stable than the initial period, which leads to a small variation of the air outlet temperature.As shown in Figure 5(c), the PCM liquid fraction keeps increasing linearly from the beginning to the end due to the stable heat transfer rate after the initial period.However, the final liquid fraction is 0.42 which indicates that the PCM is not completely melted.On one hand, this is because the amount of PCM is too large relative to the heat transfer area.In order to improve the utilization efficiency of PCM, the heat transfer area can be increased or the amount of PCM can be reduced.On the other hand, as volume of the water-PCM heat exchanger is ignored during the cold discharging process for simplification, the volume of PCM is equivalent to an increase, which reduces the actual liquid fraction.As shown in Figure 5(d), the cold discharging power drops rapidly and remains at a relatively stable value.This is because the cold discharging power is proportional to the temperature difference between the air inlet and outlet.The inlet air temperature is constant and the outlet air temperature is shown in Figure 5(b), which leads to the variation tendency of the cold discharging power.

Conclusion
In this study, a latent cold storage unit using vertical cylindrical structure coupled with a concentric air duct is proposed.The cold discharging process of the unit is simulated by CFD based on the enthalpyporosity method and thermal performance of the latent cold storage unit is analyzed.The results show that the melting process starts at the top and then expands gradually upward from the bottom.Both the average temperature of PCM and the air outlet temperature remain a relatively stable value after a rapid increase.The PCM liquid fraction keeps increasing linearly from the beginning to the end.The cold discharging power drops rapidly and remains at a relatively stable value after the initial period.

Figure 1 .
Figure 1.Schematic diagram of the latent cold storage unit.

Figure 2 .
Figure 2. Size of the latent cold storage unit.

Figure 3 .
Figure 3. Temperature distribution of the latent cold storage unit.

Figure 4 .
Figure 4. Liquid fraction distribution of the latent cold storage unit.