Fundamental study on cool thermal storage characteristics using trimethylolethane

3.1 Solidification point of TME hydrate

In general, when cooling a cool thermal storage material, a higher phase change temperature of the material results in a smaller energy required for cooling. Therefore, when developing a new latent heat storage material, it is necessary to seek a material with a higher phase change temperature than ice, which is currently used as a thermal storage medium. Therefore, the solidification point was measured according to the concentration of TME.

In this experiment, 300 ml of TME set to a certain concentration was injected into a beaker, and a T-type thermocouple was installed to monitor the temperature change while cooling up to the point of phase change. Subsequently, TME was heated until the solid phase disappeared. This process was performed repeatedly.

Figure 1 shows that the TME hydrate concentration is 20 - 30 wt % in the phase change temperature range of 0 – 15 °C, making it suitable for use in actual air-conditioning systems.

Figure 1:

Solidification temperature according to TME concentration

3.2 Specific gravity of TME hydrate

To determine the density of TME hydrates, their specific gravity was measured.

In this experiment, 500 ml of TME hydrates of any concentration was prepared in a beaker, and the hydrates were injected into a cylindrical container with an internal diameter of 40 mm and a height of 300 mm. The specific gravity was measured using a hydrometer. Meanwhile, the measurement temperature range was set from the solidification point of the TME hydrate with concentration between 5 – 50 wt % to 40 °C. The relationship between temperature and specific gravity is shown in Figure 2.

Figure 2:

Specific gravity of TME (5–50 wt %)

As shown in Figure 2, the specific gravity of TME hydrates is higher at any concentration compared with distilled water. In addition, the specific gravity increased with the concentration, but it decreased with increasing temperature.

3.3 Latent heat of TME hydrates

To use TME hydrates as a cool thermal storage material, it is necessary to measure the thermal storage calories, and the latent heat of TME hydrates was measured using differential scanning calorimetry (DSC).

Typically, DSC is used to measure the energy input difference between a sample and a reference as a function of temperature while changing it according to a program to control the temperature of a sample and a reference. The curve obtained from the function is called a DSC curve.

The measured results of a 30 wt% TME hydrate with 5 °C/min heating rate are shown in Figure 4 (see Figure 3 for reference).

Figure 3:

Schematics of DSC

Figure 4:

DSC result of TME 30 wt%

The DSC curve in Figure 4 shows a straight line parallel to the x-axis when the temperature difference between the TME hydrate and reference (alumina) is approximately zero. This line is called the base line. Furthermore, a curve that starts from the base line and returns to the base line is called a peak. At this time, with the base line as a center, when the curve moves upward, it corresponds to the heat dissipation, whereas a downward curve means heat absorption. Therefore, as shown in Figure 4, the area created by the connection between the points moving down from the base line, the peak point, and the point returning to the base line represent the latent heat of fusion.

As shown in Figure 4, the peak representing ice melting appears at approximately - 2 °C and the peak of TME hydrate melting is at approximately 17 °C.

In fact, the data used for cool thermal storage is the latent heat of TME hydrates; therefore, it is necessary to separate the latent heat of fusion of TME hydrates by subtracting the latent heat of fusion of ice from the total amount of latent heat of fusion. The latent heat of TME hydrates can be obtained from the total latent heat by determining the ratio of the TME hydrate to the remaining water molecules without undergoing hydration in 1 mol. Equation (1) calculates the TME latent heat from the measured total latent heat:

Here, L is the overall latent heat [kJ/kg], L_TME the latent heat of TME [kJ/kg], L_Water the water latent heat [kJ/kg], C the concentration of TME hydrate, n the hydration number, M_Water the water molecular weight, and M_TME the molecular weight of TME. In addition, because the TME hydration number can be 3 or 4, Figure 5 shows the result calculated with hydration numbers 3 and 4. As shown from the results, the latent heat increases in proportion to the increase in the concentration of TME hydrates, and we can deduce that the difference in hydration numbers 3 and 4 can be obtained from the difference in n, as shown in Equation (1).

Figure 5:

Latent heat of TME

3.4 Viscosity of TME hydrates

When transporting TME hydrates, their viscosity was measured to investigate the flow characteristics of the fluid. Figure 6 shows the schematics of the rotation viscometer used for the measurement in this study.

Figure 6:

Schematics of a rotation viscometer

The rotation viscometer is a measuring instrument that allows a rotor to be connected to a synchronous motor such that the rotor rotates through a spring in the sample and the viscous resistance torque can be measured by the rotating rotor. In addition, the relationship between shear speed and shear torque can be obtained by measuring the inner diameters of the rotor and the sleeve.

The rotation viscometer was used for measurements under the conditions of 5–50 wt % TME concentration and temperature range of 5–40 °C.

Figure 7 and Figure 8 show that the TME hydrates were a Newtonian fluid because the shear torque was proportional to the shear speed at any temperature range. The measured results were organized and summarized based on the relationship between temperature and viscosity, as shown in Figure 9.

Figure 7:

Shear torque according to shear speed for 20 wt % TME

Figure 8:

Shear torque according to shear speed for 40 wt % TME

Figure 9:

Viscosity according to the temperature of TME (5 –50 wt %)

4.1 Experimental apparatus

Figure 10 shows the schematics of a cool thermal storage experimental apparatus using TME hydrates.

Figure 10:

Schematics of experimental apparatus

The experimental apparatus comprised a double tube heat exchanger, which was a test section, a circulation system for TME hydrate slurries, a system for hot water, and a TME-hydrate-slurry generating section.

A stainless steel tube with full length L = 2000 mm, inner tube inner diameter d_i = 14 mm, inner tube thickness t_i = 1.2 mm, outer tube inner diameter d_o = 37.1 mm, and outer tube thickness t_o = 2.8 mm was used for the double tube heat exchanger. In addition, to measure the temperature T_w of the tube outer wall surface in the test section, a T-type thermocouple (thickness of 0.3 mm) was installed in seven points in the horizontal direction of the test section and four points in the upper, lower, left, and right directions along the inner tube circumferential direction.

The circulation system of the TME hydrate slurry comprises a hydrate slurry storage tank, which is a TME hydrate slurry generator, a solution tank to store TME hydrates and control the solid phase ratio of the hydrates, a vortex pump, and stainless steel test section piping.

In the hydrate slurry storage tank, a propeller mixer with three blades was installed, and mixing was performed in the tank during hydrate slurry generation and supply.

The hot water circulation system comprises a thermostat, magnetic pump, float-type flow meter, and flow control bypass.

4.2 Reliability of experimental apparatus

To confirm the reliability of the experimental apparatus, the pressure loss was measured by flowing water at 5 °C in the test section. Figure 11 shows the relationship between flow rate and pressure loss, and Figure 12 shows the relationship between Reynolds number and pipe friction factor. A comparison between the theoretical equation and Blasius’ empirical equations for the laminar flow of water represented by the solid lines in the graphs of Figure 11 and Figure 12 shows an average difference of 1.5% in the relationship between flow rate and pressure loss and 3.8% for the relationship between Reynolds number and pipe friction factor. The difference can be considered to indicate that this experimental apparatus is reliable.

Figure 11:

Relation between ΔP/L and ufi

Figure 12:

Relation between λ and Re

4.3 Calculation of local heat transfer coefficient

Figure 13 shows a heat transfer model to calculate the local heat transfer coefficient. For the double tube test section used in this experiment, the pipe used as an actual heat exchange was estimated, and the value of d_i = 14 mm was set for the pipe inside the test section. However, as it was difficult to measure the inner wall surface temperature T_Wi directly by setting the local heat transfer coefficient α_Wi as the value at the inner wall surface Wi of the inner tube owing to the structure of the experimental apparatus, the inner wall surface temperature T_Wi and local heat transfer coefficient α_Wi were obtained by measuring the outer wall surface temperature T_Wo from the inner tube outer wall surface temperature Wo, as follows.

Figure 13:

Schematics of the overall heat transmission model

4.3.1 Local heat transfer coefficient α_Wo on the outer wall surface

It can be considered that the local heat transfer coefficient α_Wo on the outer wall surface does not change regardless of the local heat transfer coefficient α_Wi on the inner wall surface if the outer pipe (annulus) flow rate u_Fo is constant. Here, the local heat transfer coefficient on the inner wall surface was first calculated by introducing the previous empirical equation (Dittus–Boelter's equation) to calculate the local heat transfer coefficient α_Wo at the outer wall surface. Subsequently, the local heat transfer coefficient α_Wi at the inner wall surface was calculated using the calculated local heat transfer coefficient α_Wo on the outer wall surface.

In addition, the local heat transfer coefficient α_Wi on the inner wall surface can be regarded as exhibiting conditions close to the isothermal heating condition when the outer pipe (annulus) flow rate u_Fo is sufficiently high, with the temperature difference ΔT_Fo between the inlet and outlet of the annulus approximately 0.5–1 K and inner wall surface temperature T_Wi indicating an almost constant value in the horizontal direction of the test section. Therefore, the empirical equation for turbulent flow heat transfer under isothermal heating conditions was used to calculate the local heat transfer coefficient α_Wi. α_Wi can be calculated from Equation (3) by applying the Dittus–Boelter equation, which is a turbulent flow heat transfer equation in a circular tube, as shown below (Equation (2)), as the heat transfer coefficient on the inner wall surface when cold water flows in the inner tube.

$\[ Nu=0.023{Re}^{0.8}{Pr}^{0.4} \]$

(2)

$\[ a_{wi}=\frac{Nu{k}_f}{d_i} \]$

(3)

Here, Nu is the Nusselt number, Re the Reynolds number, Pr the Prandtl number, and k_f the heat transfer coefficient of water.

Next, assuming that the heat flux q_Wo at the outer wall is generated only in the radial direction, the heat flux q_Wo can be calculated from Equation (4):

$\[ q_{wo}=\frac{T_{wo}-T_{Fi}}{r_o\left(\frac{1}{r_i{a}_{wi}}+\frac{1}{k_p}ln\frac{r_o}{r_i}\right)} \]$

(4)

Here, k_p is the heat transfer coefficient of a circular tube. Therefore, the local heat transfer coefficient α_Wo on the outer wall can be calculated by Equation (5):

$\[ a_{wo}=\frac{q_{wo}}{T_{Fo}-T_{wo}} \]$

(5)

Figure 14 shows the change in the local heat transfer coefficient α_Wo in the horizontal direction of the test section on the outer wall surface, with the inner tube flow rate u_Fi calculated by the method above as a parameter. In this case, the measurement was performed under constant conditions of annulus flow rate u_Fo = 0.52 m/s and annulus inlet hot water temperature T_{Fo_in} = 293 K. As shown in Figure 14, even if the inner tube flow rate u_Fi was changed, similar values of local heat transfer coefficient α_Wo were obtained. From these results, the local heat transfer coefficient α_Wo, which can be calculated in the same manner, was considered to have provided valid results. Therefore, the local heat transfer coefficient α_Wi on the inner wall surface was calculated using the calculated local heat transfer coefficient α_Wo on the outer wall surface and the outer wall surface temperature T_Wo measured at the time of the heat transfer coefficient experiment.

Figure 14:

Overall coefficient of heat transfer at the outer wall surface of the inner tube