3.1. Validation
Water vapor is regarded as the primary phase (vapor), and liquid water as the secondary phase (liquid). As the relative vacuum is considered in TPCT at the initial state, for calculations of energy and mass transfer during the phase change, the boiling temperature of 348 K is applied. The length of the evaporator, adiabatic, and condenser parts is set to be 0.2, 0.1, and 0.2 m, respectively. Three different grid sizes, with 40,000, 80,000 and 120,000 (rounded figures) computational cells, are generated and evaluated to check the grid independency of the system. As a thin liquid film is formed near the wall, 12 mesh layers are used as the boundary layer to capture all changes near the inner wall. The static temperature distribution in the evaporator and condenser section of the TPCT are shown in
Table 2, when the input power is set to be 172.87 W. A slight difference can be seen in the prediction of the wall temperature of the TPCT between the 80,000 and 120,000 computational cells. Therefore, to reduce the calculation costs, the grid size with 80,000 cells is selected in the simulation (
Figure 1).
As reported in Ref. [
12], the wall temperature of the TPCT has been measured at eight points. In the evaporator, adiabatic and condensers, one, two, and five places are considered for temperature measurement, respectively.
Table 3 shows the position of the thermocouples, the experimental temperature values and the temperature value obtained from the current simulation. The relative error varies between 1.73 and 6.99%. Considering the error values, it found that the present numerical simulation is valid and can be used for other temperature ranges of thermosyphons.
The average temperature difference between the evaporator and condenser parts of the TPCT, divided by the input power, is known as the thermal resistance of TPCT. The thermal resistance, based on the current CFD compared with the existing experimental data [
12], is reported in
Table 4. As seen in this Table, the thermal resistance, according to the CFD analysis conducted by Fadhl et al. [
12], has a significant difference from their experimental results. However, in the present simulation, by modifying the input parameters in the Fluent software, somewhat more acceptable results have been obtained. The efficiency of TPCTs, which is regarded as the ratio of the energy given to the heat sink in the condenser to the input power from the heat source in the evaporator [
7], is calculated to be 84%.
The volume fraction of the liquid and vapor phase for pool boiling in the evaporator section of the TPCT is depicted in
Figure 2. The red and blue color is related to the vapor and liquid phase, respectively. The number one in the color map represents the pure vapor phase and the number zero represents the pure liquid phase. In the boundaries between the two phases, which is shown with green colors, there is a combination of liquid and vapor states. In a TPCT, heat is transferred through a phase change. The energy that is transferred from the TPCT wall in the evaporator section to the fluid inside the thermosyphon causes its phase to change. The liquid pool in the TPCT boils quickly due to the low pressure inside the thermosyphon, and this means that tiny bubbles are formed near the wall, which move upwards and can join with others and create more giant bubbles.
3.2. Simulation of TPCT at Moderate Temperature
The simulation process of the thermosyphon in an unsteady state is a very complicated and time-consuming process, even with the use of high-speed computers. Relative vacuum (15 kPa absolute) is applied inside the TPCT, at the initial state, for calculations of energy and mass transfer during the phase change. The value of latent heat in the UDF code is considered to be approximately 2648.9 kJ/kg. The constant temperatures of 493 K and 298 K are applied as boundary conditions on the evaporator and condenser walls, respectively. An appropriate working fluid must not be decomposed at those temperatures, and the boiling and condensation process should occur at higher temperatures than conventional TPCT. A specific high-temperature oil has been selected as the working fluid for this simulation, which has the same thermophysical properties as C
15H
32 (
Table 5).
The current research is the first part of a multi-year comprehensive program. The main purpose of this program is to investigate and evaluate the feasibility of replacing the Ljungstrom air preheater, used in steam power plants, with heat pipe heat exchangers. In the first step, which is also the main goal of this study, the simulation of the single heat pipe heat exchanger is conducted to measure the ability of the proposed working fluid in the system. In future stages, the pilot scale of the system will be built. Therefore, the dimensions of the heat pipe in the current simulation are selected according to the laboratory set-up in which the next stages of the comprehensive program will be built. The geometric characteristics of the studied TPCT are shown in
Table 6 and
Figure 3. A copper pipe with an inner and outer diameter of 28 and 32 mm, respectively, is considered. The total length of this TPCT is considered to be 1.1 m. The length of the evaporator section is considered larger than the other sections, because in real situations in the power plant, when the hot gases flow in this section, the maximum possible thermal power can be absorbed. The length of the adiabatic section is also considered to be 30 cm to ensure the separation of hot flow (smoke) and cold flow (air) and their non-mixing in real situations.
In this CFD study, 55,000, 110,000 and 180,000 (rounded figures) computational cells are considered to test the independence of the solution from the computational grid. The temperature distribution of the condenser and evaporator wall, at 20 s after the start of the process, is used to test the grid independency.
Table 7 shows the average temperature of the evaporator and condenser section. It is evident that the temperature difference between the 110,000 and 180,000 mesh sizes is not significant. Therefore, in this CFD research, the 110,000 computing-cell is selected and used non-uniformly to reduce the computing time, as depicted in
Figure 4. The compression of the mesh grid near the walls and their greater distance at points far from the walls are visible in this figure.
The boiling process in the TPCT, for filling ratios of 50, 70 and 90%, are shown in
Figure 5,
Figure 6 and
Figure 7, respectively. At the start of the process, the liquid pool at the bottom of the TPCT is heated; when the temperature of the pool reaches to saturation temperature, the liquid to vapor phase change occurs. The vapor is transferred to the condenser section, where condensation occurs along the cold walls, and a thin liquid layer is formed on the inner wall of the thermosyphon pipe. Due to the energy transfer to the working fluid from the walls, the boiling and phase change begins, and bubbles are generated. Then, the number of bubbles and their size increase. It can be seen that as the filling ratio increases, more bubbles are seen in the liquid phase, which is due to the enhancement of the heat transfer surface between the wall and the oil. The main reason for the thermal resistance against heat transfer in a TPCT is the generation of these bubbles in the liquid pool of the evaporator section. As liquid has a considerably higher convective heat transfer coefficient than vapor, more heat is transferred from the evaporator to the liquid phase. As a result, it is expected that the amount of boiling and bubble formations increases with the increase of the filling ratio. More giant bubbles lead to more thermal resistance, preventing the energy exchange between the TPCT wall’s solid and liquid phase. Therefore, at the lower filling ratio, the thermal resistance is less.
To obtain a better comparison between the formation and growth of bubbles in different filling ratios, the contour of the liquid volume fraction in the evaporator part, for two times of 0.7 and 2 s, are presented in
Figure 8. Relatively tiny bubbles are observed for the filling ratio of 50%, while more and more giant bubbles are generated at higher filling ratios. When the FR is equal to 90%, the interconnectedness of the bubbles in the areas near the border of the adiabatic part can also confirm the higher thermal resistance of the TPCT at higher filling ratios.
The temperature distribution for the studied filling ratio at 0.7 and 2 s in the evaporator section of the TPCT is illustrated in
Figure 9. Through the vaporization of the liquid, the produced vapor moves upwards due to the buoyancy effect. At FR = 50% and time = 0.7 s, the movement of vapor in the form of a jet from the interface of the liquid and vapor towards the condenser section of the TPCT is noticeable and the differentiation of its temperature contours compared to its surrounding points is also evident in this figure. At time = 2 s, the movement of the vapor towards the condenser part is similar to turbulent flow. It covers a larger part of the cross-section, which shows that the vapor occupies a larger volume of the space above the liquid with the higher temperature.
It is worth mentioning that the volume of the boiling liquid pool in the evaporator part of the TPCT increases when more time passes. Therefore, the interface between the liquid and the vapor advances towards the condenser section.
The contours of the liquid volume fraction, from 0 to 2 s, for the studied TPCT at FR = 30% is shown in
Figure 10. In this figure, the process of boiling and bubble formation can be seen. When time passes, more energy is transferred to the liquid phase through the wall in the evaporator section, and more phase changes in the bubbles’ shapes are observed. The thermal resistance of the TPCT has been checked in the initial stages of the process and it has been determined that at FR = 30%, the system has the lowest thermal resistance.
Figure 11 shows the liquid volume fraction and the static temperature distribution contours in a steady state for a filling ratio of 30%. From the moment that the process begins, the system is in a relative vacuum state. The thermal energy applied to the evaporator section of the TPCT leads to the evaporation of the working fluid, the fluid particles enter the vapor phase from the surface of the boiling pool, and the pressure of the system increases. The vapor phase is condensed on the condenser wall and a film of liquid is formed. As a result of gravity, the liquid film moves downward. With the passage of time, the pressure inside the TPCT increases and, accordingly, the temperature of the working fluid throughout the pipe is affected and changes. This change in the system’s temperature profile and mass contours continues until the system reaches its saturation state.
The simulation results show the behavior of both the rising hot vapor and the condensed liquid stream flowing down in the TPCT. Near the wall, the liquid and vapor phases collide, but the higher momentum phase keeps moving and pushes the other phase away from the wall. This flow characteristic causes the condensed liquid and vapor to move in an upward and downward flow, respectively. The average temperature of the inner wall of the TPCT in the evaporator, adiabatic, and condenser section was monitored systematically with the passage of time. After 84 s from the start of the process, no significant change was observed in these average temperatures, and it can be concluded that the system has reached its steady state. In other words, in a steady state, there is a balance between the evaporation and condensation processes. As much as the liquid evaporates, the same amount of vapor condenses, and this cycle repeats. As clearly shown in
Figure 11, the oil as the working fluid approaches the temperature of the evaporator and condenser wall at the lower and upper sections of the TPCT, respectively. The efficiency of this thermosyphon, which is charged with oil, is approximately 96%. As a result of the high computational cost of the simulation, the simulation is conducted for the optimal filling ratio of the system (FR = 30%) until reaching the steady state of the system. For other filling ratios, it is enough to check the process and compare them up to limited seconds after the start of the process, as described in
Figure 5,
Figure 6,
Figure 7,
Figure 8 and
Figure 9. It should be noted that obtaining the steady state results in TPCT requires approximately a month of time with our available high-speed computers.
The liquid film formation is directly dependent on the cooling rate; in other words, the amount of heat taken from the TPCT in the condenser section. As mentioned in
Table 1, a constant temperature of 298 K has been applied as a boundary condition on the pipe wall in the condenser section. In the upper part of the tube, no liquid film appears to have formed, or liquid droplets have formed but have not appeared as a film layer. It seems that by increasing the cooling rate in the condenser part of the system, the formation rate of the liquid film layer in the upper part of the TPCT can also be intensified. As it is not possible to create a full vacuum using conventional vacuum pumps in heat pipes, in the industrial applications of heat pipes, some non-condensable gases, such as air, always remain in the upper part of the system, which can affect the liquid film generation in that part as well.
The wall temperature distribution along the thermosyphon at 0.1, 0.5, 1 and 2 s after the start of the process for a filling ratio of 30% is illustrated in
Figure 12. It is evident that the temperature of the thermosyphon decreases from the evaporator to the condenser. The thermal resistance of the thermosyphon for the time of 0.1, 0.5, 1 and 2 s is obtained to be 0.59, 0.59, 0.58 and 0.58, respectively.
Figure 13 shows the steady state temperature of different points on the TPCT wall when FR = 30%. According to this figure, the thermal resistance of the TPCT is calculated to be 0.54 W/K.