Numerical Simulation of Heat Transfer Characteristics of Finned Tube Heat Exchanger at Different Flow Velocities

A heat exchanger is an important component where high-temperature hot air and normal-temperature water exchange heat. The heat exchange area of the finned tube heat exchanger is calculated by the rated working conditions. However, with the decrease of the heat storage temperature, the hot air temperature at the outlet of the thermodynamic energy storage device changes in a large range, directly affecting the heat exchange capacity and efficiency of the finned tube heat exchanger. This paper’s three-dimensional model is established. The heat exchanger of the finned tube is designed according to the temperature of the outlet section and the return section temperature of the heat storage system. The thermodynamic physical parameter property and characteristics of which heat exchanger’s finned tube in the air’s velocity range of 1∼10 m/s are simulated by fluent software. The velocity, temperature, pressure, and heat exchanger coefficient distribution characteristics at different positions along the airflow direction are obtained. The simulation results show that the mean flow velocity is 2.0 m/s and 5.0 m/s at the inlet cross-section. The average temperature difference between the inlet and outlet is 69.5 K and 100.5 K, respectively. The fin surface temperature difference between the first and eighth rows of finned tubes is 12.5 K and 14.4 K, respectively. The air pressure loss at the air channel inlet’s section and outlet’s section is 16.1 Pa and 69.4 Pa, respectively. When the inlet flow rate change from starting at 1.0 m/s and ending at 10.0 m/s, the tube’s wall coefficient of heat transfer, which is the second level of finned tubes, only increases by 1.8 times. The tube’s wall coefficient of heat transfer of the eighth level of finned tubes increases by the maximum, to 5 times the original, but the heat energy exchange capacity of which the second level of finned tubes is always the strongest.


Introduction
The finned tube heat exchanger is widely used in industry because of its compact structure and large heat exchange area.High-temperature solid heat storage and the heating system convert the electric energy at the low load of the power grid into heat energy for storage [1].Air is used as the heat transfer medium.The output hot air then provides users with hot air, hot water, saturated steam, etc., through heat exchange equipment.A heat exchanger with a fin is commonly used in thermal equipment for high-temperature solid heat storage and heating system.
At present, there have been many studies on the characteristics of heat exchangers with fins.Wang et al. [2] have studied the multilayer tubes, fin spacing, and other parameters, and when the number of tube rows is small, reducing fin spacing can help improve heat transfer performance.However, when the quantity of tube levels is more than 4, and the constant of Reynolds is greater than 2000, the influence of fin spacing's performance can be ignored.Syuhada et al. [3] tested the heat transfer characteristics of spiral finned tubes with different fin spacing (1 cm, 2 cm, 3 cm, 5 cm, and 7 cm).Their results showed that when the fin spacing was 2 cm, the maximum heat transfer rate, and coefficient were generated.Miansari et al. [4] showed that reasonable control of the flow rate of cold/hot fluid could optimize thermal efficiency.Yu et al. [5] showed that the tube spacing and fin spacing have an impact on the maximum temperature of the first two stages of finned tubes, and the temperature of the second stage of finned tubes is higher than that of the first stage.Qian et al. [6] simulated the plain tubes and streamlined tubes.They found that the wake area of streamlined tubes was smaller than that of circular tubes.The streamlined tube in finned is beneficial to optimize comprehensive performance.Chen et al. [7] used the experiments to study the characteristics of finned tube and primary heat exchanging equipment and gave the changes of friction factor 'f' and Colburn 'j', and the changes of 'Nu' with 'Re'.Some other researchers [8][9][10][11] paid attention to the form of fins and optimized the layout parameters of fins.
In this paper, the three-dimensional model of a finned tube heat exchanger used in a high-temperature solid heat storage system is established first.The change of trend in which the heat exchanger with a fin at an air velocity range of 1-10 m/s is simulated by fluent software.Besides, the distribution characteristics of velocity, temperature, pressure, and heat transfer coefficient of the finned tube at different positions along the airflow direction under different inlet velocities are compared.

Modeling
The design conditions of a finned tube heat exchanger for a high-temperature solid heat storage system are as follows: hot air on the air side is 523.15K at the inlet, and 423.15K at the outlet, respectively, and waterside is 333.15K at the inlet and 343.15K at the outlet, respectively.The fins are flat and straight, and the finned tubes are arranged in a triangular manner.There are 8 rows of finned tubes, which are displayed in Figure 1, and finned tube geometric parameters are shown in Table 1.Due to the constant fin spacing and its periodic arrangement, the two columns of fin spacing were selected as the calculation domain.Considering the reflux during model calculation, the calculation domain at the inlet and outlet were extended by 3 to 5 times the inner diameter of the finned tube, as shown in Figure 2.

Governing equations
According to the characteristics of fluid between finned bundles, the simplified assumptions were made in the calculation of the research model, and it was assumed as follows: (1) The flow and heat transfer state is stable, and the fluid is incompressible.
(2) The physical parameters of hot air, pipe, and fin are constant.
(3) The flow state of hot air in the calculation domain is turbulent.
(4) The effects of gravity and radiation heat transfer are ignored.On the premise of the above assumptions, calculating the regional mathematical model is displayed as follows.
Continuity equation: Momentum equation: Energy equation: Standard k-epsilon equation: ( ) where k is the turbulent kinetic energy, ε is the turbulent dissipation rate, t μ is the coefficient τ is the viscous vortex term of Reynolds stress, f2 is the near wall attenuation function, and σ is the Prandtl number.

Mesh and boundary conditions
The geometric models are as follows: fluid region, finned solid region, and tube solid region.For optimizing the calculation accuracy, the influence of the boundary layer is fully considered, and local mesh encryption is carried out on the solid area of the fin and its surrounding area.The grid model is shown in Figure 3.

Equation solving and grid independence
Fluent software is used to solve and calculate the governing equation.A simple iterative algorithm is selected.When the residual of the energy equation is below 10 -6 , and the residual of other equations is below 10 -4 , the calculation is considered convergent.This study compares the simulation results of three sets of grids, as displayed in Table 3.The D-value between 125, 764 and 198, 766 grid cells in heat transfer factor j and resistance factor f is only 2.5% and 2.9%.Therefore, 198, 766 grid models are used for numerical simulation.

Velocity distribution
The staggered finned tube is conducive to generating turbulence in the process of hot air flow, thus enhancing heat transfer.The flow field distribution netrophs of different inlet velocities at the middle height section of the model (z=4 mm) are selected for comparison.The flow field velocity distribution is shown in Figure 4  The cloud image results show that, except for the first and second finned tubes, the flow near the windward heat exchange surface of the subsequent finned tubes will be affected by the wake of the front finned tubes in the direction of the wind heat exchange surface to varying degrees.However, increasing the velocity does not significantly reduce this situation.The hot air near the windward heat exchange surface of the second-stage finned tube is affected by the first-stage finned tube.The flow normal sectional area decreases, resulting in a shrinking nozzle effect, which increases the flow velocity compared with that at the same position of the first stage finned tube.In addition, the calculation results show that the maximum velocity within the section reaches 6.2 m/s and 14.8 m/s, respectively.In the model, the staggered finned tube speeds up the hot air by about 3 times, and the high-speed area starts at the side area of the fourth and subsequent finned tubes.

Temperature distribution
The temperature distribution of the surface is displayed in Figure 5  The image results show that after hot air flows through the finned tube every time, the high temperature wake produces a certain angle deflection.After passing through the finned tube at all levels, the high-temperature area of the wake becomes narrow obviously.Raising initial velocity can extend the high-temperature wake area.The calculated results show that different initial air velocities with different temperature drops, such as from 2.0 to 5.0 m/s and the drop from 69.5 to 100.5 K, respectively.
The first-row finned tube temperature distribution of the surface is displayed in Figure 7   The distribution results show that there are differences in the surface temperature of finned tubes, and superficial temperature with initial velocity is linear.In addition, the first and second finned tubes' high-value temperature zone appears in the middle of the windward heat exchange surface.The flow near the windward heat exchange surface of the subsequent finned tubes is affected by the wake of the front finned tubes in the direction with wind flowing surface, and the high-value temperature zone of the finned tubes appears at a certain Angle away from the middle.The calculation results show different initial air velocities with different average temperature differences in which first and eighth-stage finned tubes, such as from 2.0 to 5.0 m/s and the difference from 12.5 to 14.4 K, respectively.The data at other flow rates also display that raising the initial velocity will increase the average temperature difference between the finned tubes at all levels to some extent.

Pressure distribution
The pressure distribution of the middle height section is displayed in Figure 9  The calculation results show different initial air velocities with different highest static pressure, such as from 2.0 to 5.0 m/s, and the highest static pressure difference in the section is 21.9 Pa and 453.7 Pa, respectively.The results of other flow velocity data show that increasing the flow velocity will produce a significant static pressure drop.

Heat-transfer coefficient
Average heat-transfer coefficients (α) of the fin's inner surface at different flow rates were selected for statistical comparison, and their distribution and variation trends were shown in Figure 10.Combined with the data of α on the inner wall of each finned tube, the results show that there are differences in α of each finned tube.α is positively correlated with the flow rate, but the growth trend of the heat transfer coefficient slows down with the raising of the flow rate.However, α of the wall surface of the second-stage finned tube is the highest, and its heat transfer capacity is the strongest.This is because the hot air near the windward surface of the second-stage finned tube is affected by the first-stage finned tube.The area of the normal flowing section decreases, causing a shrinking nozzle effect that makes the flow velocity increase compared with the same position of the first stage finned tube, resulting in the enhancement of heat transfer.The α of the wall inside the eighth finned tube is the lowest.In addition, the change in inlet velocity has a great influence on the α.Different initial air velocity has different α, such as from 1.0 to 10.0 m/s and α of the wall inside each fin tube increases from 1.8 to 5.0 times.

Conclusion
For this study, it can be concluded that: (1) The hot air near the windward heat exchange surface of the second-stage finned tube is affected by the first-stage finned tube, and the area of the normal direction of flowing decreases, causing a shrinking nozzle effect.It increases the flow velocity compared with the same position of the first-stage finned tube, resulting in the strongest convective heat transfer ability compared with other finned tubes.
(2) The staggered finned tubes make the high-temperature wake of hot air flowing through the tubes produce a certain angle deflection.After passing through all levels of finned tubes, the high-temperature area of the wake becomes significantly narrower.Raising the initial velocity is helpful to significantly extend the extension area of the high-temperature wake, which is conducive to improving the overall heat transfer effect.It also improves the difference in the average temperature on the surface of all levels of finned tubes to some extent.
(3) Raising the initial velocity will not only better the overall heat transfer capacity of the heat exchanger but also cause obvious pressure loss.Therefore, the supply wind speed should be controlled reasonably according to the actual energy consumption efficiency of the fan and the power requirements of the thermal equipment to achieve the optimal value of the overall efficiency.

Figure 1 .
Figure 1.Heat exchanger structure schematic diagram of main and top view.

Figure 3 .
Figure 3. Grid model.All boundary conditions are set as follows: the inlet side is set as the speed inlet boundary, u=1~10 m/s, T=523.15K; the outlet side's gauge pressure is 0; the inner wall of the tube is constant temperature wall, T=340.65 K; the top/bottom surfaces are symmetric surfaces; the front and rear planes are symmetric surfaces.Specific physical property parameters of materials in each computing domain are displayed in Table2.Table2.Physical parameter.

Figure 4 .
(a) with 2.0 m/s inlet velocity and Figure 4 (b) with 5.0 m/s inlet velocity.Velocity distribution.

Figure 6 .
(a) with 2.0 m/s initial velocity and Figure 5 (b) with 5.0 m/s initial velocity.The temperature distribution of intermediate height is displayed in Figure 6 (a) with 2.0 m/s initial velocity and Figure 6 (b) with 5.0 m/s initial velocity.Temperature distribution at intermediate height.
(a) with 2.0 m/s initial velocity and Figure 7 (b) with 5.0 m/s initial velocity.The eighth-row finned tube temperature distribution of the surface is displayed in Figure 8 (a) with 2.0 m/s initial velocity and Figure 8 (b) with 5.0 m/s initial velocity.

Figure 7 .Figure 8 .
First row finned tube temperature distribution.Eighth row finned tube temperature distribution.

Figure 9 .
(a) with 2.0 m/s initial velocity and Figure 9 (b) with 5.0 m/s initial velocity.Pressure distribution at middle height section.

Figure 10 .
Figure 10.α of finned tube surface at different inlet velocities.

Table 3 .
Grid independence verification results.