Study on hydro-thermal coupling heat transfer performance of flue gas-water heat exchanger

The finned tube heat exchanger is the core component of the flue gas waste heat utilization system. In order to optimize and control the heat transfer efficiency of the heat exchanger in real time under smart heating conditions, we use the entransy dissipation thermal resistance as a kernel index to assess its heat exchange performance, and Trnsys simulation software is employed to figure out the influence of heat exchanger operating parameters (flue gas inlet velocity) and fin structure parameters (fin height, fin pitch) on heat exchanger heat transfer characteristics. The results show that in a reasonable range, increasing the flue gas inlet velocity can decrease the irreversible loss of heat transfer, obviously improving the heat transfer effect. The pitch and height of the fin also have a large impact on the performance of heat transfer. To significantly promote the performance of the heat exchanger, it is useful to reduce the pitch of the fin and increase the fin height within a reasonable range.


Introduction
The heat exchanger is a key piece of equipment for waste heat recovery.Many researchers have carried out extensive research and analysis on improving its heat exchange performance.Kang et al. [1][2] only rely on experimental means to investigate the performance of heat exchange, as science and technology continued to advance.Later, many scholars adopted the method of combining numerical simulation and experiment [3][4][5][6][7] to carry out systematic and comprehensive comparative analysis on various design schemes that affect the performance of heat transfer, and the results of the study were more accurate.Some scholars only studied the effect of heat transfer based on its own arrangement [8].
The above studies on finned tube heat exchangers mainly focus on strengthening the heat exchanger performance through changes in structural parameters, and most of them use the method of combining heat exchange and resistance loss to evaluate and optimize the heat exchanger performance.In recent years, Guo [9] introduced a new physical quantity representing the capacity for heat transfer "entransy", by the comparison of the thermal and electrical conductivity processes, its physical meaning of which is the total capability of the object to transfer heat, and the dissipation of entransy reflexes the lose of heat transfer ability result from irreversibility of heat transfer.Therefore, the equivalent thermal resistance of heat exchangers is defined to describe the irreversible dissipation caused by heat transfer.[10] In this paper, the fin-and-tube heat exchanger with waste heat utilization of flue gas is simulated based on TRNSYS software, compare and analyze the simulation results with the theoretical calculation results to verify the feasibility of simulation calculation.On this basis, taking the thermal resistance to entransy dissipation as the main performance target for evaluating the heat exchanger, the influences of fin height, fin spacing, and flue gas inlet velocity on the performance of the heat exchanger are studied and analyzed, which provides a benchmark for finned-tube heat exchanger optimization and future real-time operation.

Design calculation
This paper describes the design of a finned-tube heat exchanger for a biomass combustion boiler to retrieve its afterheat.Circulating water is heated by high-temperature flue gas so as to decrease the exhaust gas temperature and meet the requirements of heating water.According to the initial parameters of design: the flue gas volume is 1450 m 3 /h, the inlet temperature of flue gas t1' is 650℃, the water flow is 7000 kg/h, the water supply temperature t2' is 50℃, the design outlet temperature t2" is 75℃ and other related data, the overall heat transfer coefficient is 146.44 W/(m 2 •K) by thermodynamic calculation.The total heat transfer is 731498 KJ/h, and the results of the initial parameters of the finned tube obtained from design calculation are shown in Table 1.A carbon steel-aluminum composite annular finned tube is selected as the heat exchanger, and the form of a fork row-equilateral triangle arrangement is adopted.There are 20 drainage pipes located along the flow direction of the flue gas, there are 10 drainage pipes vertical to the flue gas flow direction, and the length of each water pipe is L = 1.1m.

Simulation model
This paper uses the Type 52 module in Trnsys to simulate finned tube heat exchangers, the module uses an effective model of counterflow geometry to simulate the heat exchanger performance.On the basis of the initial value obtained from the design calculation, set the heat exchanger property of the structure parameters and input fluid mass flow and temperature on both sides, so as to calculate the fluid outlet temperature on both sides and the total heat transfer.A detailed mathematical model description of the module can be found in [11].

Entransy dissipation thermal resistance
Entransy dissipation thermal resistance RE is a physical quantity that represents the wastage of heat transfer capacity of hot and cooled fluids corresponding to a unit of heat transfer, and its calculation for heat exchanger is as follows: where c is the specific heat capacity of fluid on both sides; m is the mass flow rate of the fluid; subscripts 1 and 2 are flue gas and cooling water respectively; K is the overall heat transfer coefficient; A is the overall heat transfer area, wherein the detailed calculation formula of K and A values is described in [12][13].

Influence of flue gas inlet velocity on heat transfer performance
Keep other parameters unchanged, fin height is 12.5 mm, fin pitch is 6 mm, flue gas inlet velocity is varied from 0.5 m/s to 2.5 m/s with 0.25 m/s step length, heat exchanger heat transfer characteristics with its 8 groups variation trend is shown in Figure 1.It can be seen from Figure 1 (a) that the RE value decreases gradually with the improvement of flue gas velocity, and the growth of velocity can reduce the heat loss in the heat exchange process and enhance the heat transfer efficiency.From Figure 1 (b), it can be plainly seen with the flue gas inlet flow rate increases, the flue gas side of the fluid flow perturbation is enhanced, and the heat transfer effect is enhanced, so the heat transfer coefficient gradually increases, from 129.06 W/(m 2 •K) to 398.85 W/(m 2 •K).It can be seen that the increase of flue gas velocity has a significant influence on the heat transfer coefficient, its conducive to strengthening the process of heat transfer.
From Figure 2, it can be seen that when the flow rate on the flue gas side increases, the resistance loss caused by the flow also improves significantly, and more energy needs to be consumed during the working process, so the power consumption of the fan will also increase, increasing the operating cost of the waste heat in flue gas recovery system.Therefore, when choosing to enhance the flue gas inlet velocity to strengthen heat transfer, its also essential to consider economic benefits under the condition of hydro-thermal coupling.Selecting the appropriate inlet velocity is not only conducive to the improvement of the performance of heat exchange equipment, but also it can ensure that the flow resistance is within a reasonable range and save costs.

Influence of the height of the fin on heat transfer performance
As the fin height increases, the distance of heat conduction increases.The heat from high temperature to low temperature takes a longer time, and the heat exchanger coefficient unit area will decline, which leads to a decrease in the amount of heat transfer per area of the fins, making the fin efficiency decrease, as shown in Figure 3, fin efficiency basically linearly decreases with the fin height changes.In this text, by changing the fin height, the change range is 8~22 mm, the step length is 2mm, a total of 8 groups, other parameters remain unchanged, and the features of the fin-tube heat transfer under different heights are obtained.From Figure 4 (a), it can be perceived that when the fin pitch is 6mm, the flue gas inlet velocity becomes 0.6m/s.As the fin height increases, the RE of the flue gas side (fire) is decreasing continuously.The heat dissipation accompanying the heat exchange process is smaller, the irreversible loss is reduced, and heat transfer efficiency is improved.The heat transfer coefficient in Figure 4 (b) improves gradually resulting from the height increases.Since the fin height increases, the fin surface area increases, i.e., the heat transfer area increases, thus the contact area increases so that the heat transfer coefficient is improved.Increasing the height helps to improve the performance of the heat exchanger.However, in general, with the increase in fin height, fin efficiency will continue to reduce the adverse effects, and the fin height should be set in a reasonable range, generally not more than the radius of the base tube as appropriate.
(a) (b) Figure 4. Effect of fin height on RE and heat transfer coefficient

Influence of the pitch of the fin on heat transfer performance
Changing the pitch of the fin in the range of 1~8 mm, the step size of 1mm, a total of 8 groups, the rest of the parameters remain unchanged, and the heat exchanger characteristics with the change law of the fin pitch are simulated.As can be seen from Figure 5 (a), as the fin pitch increases, the RE decreases gradually.The addition of fin pitch makes the area of flue gas flow larger, resulting in the decline of the temperature vary gradient in the basin, heat transfer obstruction decreases, the less irreversible dissipation in the process, the heat resistance decreases accordingly.However, as can find out from Figure 5 (b), the coefficient of heat transfer decreases due to the increase of fin pitch, which is due to the fact that there will be more fins on the unit length of the smaller fin pitch, so that the heat transfer area unit length increases, making the heat exchanger effect enhanced, while increasing the pitch of fin, the fin tube contact area per unit length decreases accordingly, and the total heat transfer coefficient also decreases.Reducing the fin pitch is beneficial to enhance the heat exchanger's characteristics, but it will cause a growth in thermal resistance and a greater irreversible loss.In addition, the choice of spacing should also take into account factors such as the nature of the circumfluent gas and the possibility of ash accumulation.Therefore, the actual selection should be considered comprehensively according to the system's performance.
(a) (b) Figure 5.Effect of fin pitch on RE and heat transfer coefficient

Conclusion
In this text, the Trnsys software is used to simulate the effect of finned-tube heat exchanger heat exchange performance with the change of parameters, and the following points are summarized: 1) Based on the analysis of influence design parameters on the heat transfer capacity, RE is used as the index to estimate the performance of the heat transfer.The smaller RE is, the smaller the corresponding heat transfer capacity loss is, and the even better the performance of the heat exchanger is.The analysis of the heat exchanger bottom on the RE provides another way of thinking for the heat exchanger optimization operation in the future.
2) The heat exchanger for waste heat recovery utilization of flue gas is calculated theoretically, and the heat transfer and flow features of the heat exchanger are simulated on the Trnsys platform, and both are consistent.
3) Increasing the flue gas inlet velocity and fin height are helpful to improve the heat transfer coefficient, strengthen the effect of the heat transfer, and reduce the heat dissipation in the heat exchange process; however, in practical application, it is obliged to take into account consider the impact of the increase of resistance value brought by the flow velocity increases and the reduce of efficiency accompanied by the fin height growths on system economy; its could also need to consider that the influence of fin height on exchanger performance is less than fin pitch.In general, when optimizing the design of finned tube heat exchangers, factors such as system heat exchange, thermal resistance, economy and other factors should be considered comprehensively, and the corresponding parameters should be selected within a reasonable range to improve the performance of the heat exchanger.

Figure 1 .
Effect of flue gas inlet velocity on RE and heat transfer coefficient

Figure 2 .
Figure 2. Effect of flue gas inlet velocity on resistance Figure 3.Effect of fin height on fin efficiency

Table 1
Specific parameters of finned tube heat exchanger