(584s) Study on Solidification Rate during the Phase Transformation Process of Pure Ethanol in the Annular Channel

There is a variety of latent heat thermal
energy storage systems researches focusing on phase change materials (PCMs) in
recent years. The most commonly used is paraffin wax, which can be used to
store waste heat. As for cool storage system, water is most suitable and
practical. However, these researches on phase change problems has been carried
out within the temperature range 273 K to 373 K. It is of great necessity to
find proper PCMs on cryogenic regions (< 173K).

Choosing a suitable material is one of the
most critical aspects for designing a thermal energy storage system. Comparing
with n-propanol, n-butane, and taking into consideration of density specific
heat, phase transition temperature and Std enthalpy change of fusion, ethanol (C2H6O)
is regarded as the most suitable material under such a low temperature. The freezing
point is 159K and melting point is the same.

A typical heat exchange system containing a
hollow cylinder of PCM with a heat transfer fluid (HTF) flowing inside the
inner tube is depicted as the figure 1. Inner circle diameter is 20 mm, and outer
circle diameter is 90 mm with a length of 1000 mm.

Figure 1 A typical heat exchange system

Based on the system above, this paper
conducts the numerical study to simulate different conditions via ANSYS Fluent and
redesigns a special visualized phase change experimental channel to observe
ethanol solidification process. Physical properties of PCM are related to the
temperature, pressure, especially temperature. Changes of some parameters are negligible,
but others cannot be ignored. Hence, the following assumptions are made for the
numerical analysis for the convenience of calculation.

(1)  Ignore the effect of PCM volume expansion from solid to liquid.

(2)  Physical properties of PCM are kept constant over small temperature
ranges.

Those factors affecting the solidification
rate during the phase transformation process of the pure ethanol at really low temperature,
including the initial temperature of the PCM, the wall temperature, and
temperature and velocity of HTF, are investigated to identify the primary one.

For numerical study, two simplified
physical model are used to figure out the main reasons. First, to treat the
inner wall temperature as constant, thus, the model is more simplified. In this
case, there is only PCM, which releases heat and gradually freeze. The outer
wall is regarded as adiabatic boundary, but the inner wall temperature is set
119 K, 124 K or 129 K, and the initial PCM temperature (in the solid phase) is
set 164K
or 169k, respectively. HTF flows into the inner tube with different velocities
and different temperatures to absorb heat from the PCM in the other model. Here,
the initial PCM temperature is also set 164K or 169k. Propane is used as HTF. And
inlet velocity of HTF are 0.1 m/s, 1.0 m/s, and Reynolds Number are around 900,
9000, which indicate that the flow states are laminar, turbulent, respectively.
This model is much closer to the experiment. Non-steady calculation method is
used for the both cases to acquire the liquid fraction of computational domain
over time, whose initial value is 1. Proportion of liquid PCM is tracked every 10
minute.

Another model similar to the literature
(Yoshihiro, 1986) is built to validate the accuracy of numerical
simulation. By comparing the Nusselt numbers along the axis in the condition of
the same Reynolds number, the results agree well with the literature. The dimensionless
temperature ¦È is defined as

where:

T₀is the initial temperature of PCM

T_fis the freeing point

T_w is the wall temperature

In the case 1, the conclusions
are as follows:

(1)  it takes almost the same time for the liquid fraction of PCM to fall
to just over half, at the different ¦È,

(2)  The time when the liquid fraction reduces to the same low level
(<5%) monotonically increases with the ¦È.

As there is great deviation to regard the
wall temperature T_w as
constant in the case 1, the boundary conditions do not conform to the reality.
Therefore, the case 2 is built to simulate the actual situation, where HTF takes
away the heat from PCM. It is also concluded that time for the liquid fraction
of PCM reduces to half are the same when considering the different wall temperature
and initial temperature. Another significant finding is that inlet velocity of
HTF makes little difference on solidification rate of PCM. This can be explained
that primary thermal resistance of heat transfer process is from PCM side. The
effects from the thermal conductivity of PCM far overweigh the convective heat
transfer coefficient. Both cases prove that in the early stage, boundary temperature
has little influence on the solidification rate in a certain range. However, considering
the flow of HTF, the inlet velocity does not contribute to solidification, but
inlet temperature has an accelerating effect on it.

A special experimental pipeline consists of
20 mm diameter stainless steel tube and 90 mm diameter PMMA (Polymethylmethacrylate)
tube, with a length of 1000 mm, is designed to visually present the
solidification process of ethanol. The whole circulatory system uses liquid
nitrogen to provide cold energy and uses propane as HTF to carry it, while the PMMA
tube is filled with pure ethanol. The experimental conditions are controlled as
close to the simulation conditions as possible. For numerical study, it is easy
to gain the percentage of liquid PCM over time, while it is difficult to figure
out how much liquid PCM is left in the tube. To overcome this problem, it
records the time when half and ninety-five percent of PCM freezes. The most
results are accordant with the numerical predictions.