3.1. Helix Angle and Heat Transfer Performance
The structure of a continuous helical baffle plays a crucial role in strengthening the heat transfer performance of a heat exchanger. The continuous helical baffle has a helical surface, and the shell diameter determines the main structural parameters for the helix angle. Changing the same shell diameter under the pitch in essence is to change the helix angle. The definition of a helical angle is shown in Equation (6).
where
β is the helix angle,
Hs is the pitch of the helical baffle, and
ds is the helical diameter.
In this work, the pitches of the continuous helical baffle are 60 mm, 80 mm, 100 mm, 130 mm, and 170 mm, and the corresponding helix angles are 10.81°, 14.29°, 17.66°, 22.48°, and 28.42°, respectively. The change in helix angle corresponds to the change in baffle structure, which mainly affects the distribution of the heat exchanger shell flow field. The shell-stream volume flow rates of 3.5 m3/h, 4.5 m3/h, 5.5 m3/h, 6.5 m3/h, and 7.5 m3/h were selected, keeping the tube-stream volume flow rate of 4 m3/h unchanged.
Simulations were carried out for different shell volume flow rates, and the results for a shell volume flow rate of 7.5 m
3/h are shown in
Figure 5. From
Figure 5a, it can be seen that in the helical baffle heat exchanger with a larger helical angle, there is a phenomenon of sudden increase in the diagonal distribution velocity at the outlet position due to the sudden reduction in the fluid circulation area and change in the flow direction. While the helical angle is smaller, the axial velocity of the shell fluid in the direction of the extended center axis is smaller and closer to the transverse flow, so the smaller the helical angle of the helical baffle heat exchanger, the smaller the change of flow velocity at the exit. The pressure results of helical baffles with different helical angles are illustrated in
Figure 5b, and it can be seen that the smaller the helical angle, the greater the axial pressure drop of the helical baffle heat exchanger.
A comparison of the velocity streamline of helical baffle heat exchangers with different helical angles is shown in
Figure 6, and the results show that fluid stagnation zones exist in the inlet and outlet sections of helical baffle heat exchangers with different helical angles. In addition, clear vortices exist near the shell inlet when
β equals 17.66°, 22.48°. This is due to the fact that in the inlet section, the fluid flows vertically and axially from the shell process inlet and is affected by the disturbing effect of the tube bundles and the influence of the larger circulation area, which makes the flow velocity decrease rapidly, impacts the tube bundles and the shell process wall, and produces a reflux zone near the inlet area. In the exit section, the shell process fluid, due to the exit of the flow cross-sectional area and the reduction in the exit to produce acceleration, the vast majority of the fluid shows normal outflow. Due to the disturbing effect of the tube bundle, a small portion of the fluid will flow back in the exit section at the shell angle, forming a flow dead zone. Combined with
Figure 5a, it can be seen that with the reduction in the helical angle, the different helical angle of the helical baffle heat exchanger shell process fluid retention area is more obvious, but the smaller the helical angle, the smaller the shell process inlet and outlet section of the area, so that the inlet and outlet section of the fluid retention area is smaller.
The total heat transfer coefficient of the heat exchanger is an important evaluation indicator, and the total heat transfer coefficient
KC of the helical baffle heat exchanger can be calculated by Equation (7):
where
dh,
Dh are the inner and outer diameters of the heat exchanger tube,
Ks,
Kh are the heat transfer coefficients of the shell and tube,
Rw is the thermal resistance of the wall of the tube,
b is the thickness of the heat exchanger tube, and
λ is the thermal conductivity of the tube.
As can be seen in
Figure 7a, the total heat transfer coefficients of helical baffle heat exchangers with different helix angles all increase with the increase in the shell flow rate, and the improvement ranges from 30.80% to 38.91%. When the shell flow rate is the same, reducing the helix angle can effectively improve the total heat transfer coefficient of the heat exchanger. In this study, when the helix angle is reduced from 28.42° to 10.81°, the overall improvement is around 20%. The shell heat transfer coefficients per unit pressure drop corresponding to different helix angles are shown in
Figure 7b. The shell heat transfer coefficient per unit of pressure drop decreases with the decreasing helix angle. When the shell flow rate is small, i.e., there is a weaker degree of turbulence, the shell heat transfer coefficient per unit of pressure drop decreases significantly with the decreasing helix angle. In this study, when the shell volume flow rate is increased from 3.5 m
3/h to 7.5 m
3/h, comparing the helix angle of 28.42° with 10.81°, it is found that the percentage of reduction in the shell heat transfer coefficient per unit pressure drop decreases from 86% to 75%.
It is also found in
Figure 7 that when the total heat transfer coefficient is similar, the larger the helix angle is, the larger the shell heat transfer coefficient per unit of pressure drop is. This is because in the helical baffle heat exchanger, the fluid flows in the form of a helical plunger, and the smaller the helix angle is, i.e., the smaller the cross-sectional area of the fluid flow is, the smaller the axial component of its velocity, the larger the radial component, the larger the tangential component, and the stronger the effect of transverse flow. The helical flow of the bundle of the tube scouring is closer to the transverse scouring, which improves the overall turbulence level and achieves the purpose of destroying the boundary layer near the wall of the tube, thus increasing the convection heat transfer intensity of the shell process. However, at the same time, the disturbance of the flow field generated by the tube bundle and the resistance brought by the baffle will also be stronger, resulting in a larger pressure loss.
3.2. Optimization of Helical Baffle–Corrugated Tube Heat Exchanger
There is no heat exchanger constructed from a helical corrugated tube and a continuous helical baffle, and its flow characteristics and heat transfer performance have not been studied yet. In order to expand the application of the continuous helical baffle and develop a new type of high-efficiency heat exchanger, this study constructs a helical baffle–corrugated tube heat exchanger, and numerical simulation methods are used to study the flow and heat transfer performance of the heat exchanger.
The main structural factors of a helical baffle–corrugated tube heat exchanger are the helical angle of the helical baffle, the cross-section shape of the helical groove, and the helical angle of the corrugated tube. Liu et al. [
28] investigated a corrugated tube with an inner diameter of 20 mm and corrugated tube pitches of 15 mm, 20 mm, and 25 mm, as well as corrugated tubes with triangular, rectangular, and semicircular cross-sections. In this study, the simulated single-tube heat exchanger shell has an inner diameter of 40 mm, corrugated tube pitches of 20 mm, 30 mm, and 40 mm, and helical baffle pitches of 20 mm, 40 mm, and 60 mm. The shell length and tube length are 200 mm, the diameter of the inlet and outlet of the tubular process is 15 mm, the outer diameter is 19 mm, and the thickness of the baffle is 0.5 mm. The cross-sectional shape of the corrugated tube shown in
Figure 8. The orthogonal tables L
9 (3
3) are used to arrange the experiments. As shown in
Table 2, three factors are evaluated each time and each factor takes three levels, and the detailed experimental programs are presented in
Table 3. Simulations were carried out under different conditions for different heat exchanger structures, in which the tube inlet temperature was 60 °C and the shell inlet temperature was 20 °C. The specific condition parameters are shown in
Table 4.
The total heat transfer coefficient and pressure drop for the nine programs under the five operating conditions designed are shown in
Table 5.
Due to the orthogonal features, the importance order of each factor could be found through the analysis. These nine test sets have tested all of the pairwise combinations of the independent variables. This demonstrates significant savings in testing efforts over the all-combinations approach. The variance analysis method (i.e., range analysis method) was used to clarify the significance levels of different influencing factors, and the most significant factors could be disclosed based on the result of the range analysis. The range analysis method mainly includes the following factors:
where the average values of each level for each factor were named as
; the variances between each factor were defined as
Ri to analyze the difference between the maximal and minimal value of the four levels for each factor; and
CRi indicates the influence of each factor.
The analysis results for the total heat transfer coefficient and pressure drop are shown in
Table 6 and
Figure 9. As seen from
Table 6, the factor influence of the total heat transfer coefficient decreases in the order
A >
B >
C according to the
R values; the pressure drop decreases in the order
C >
B >
A.
Figure 9 indicates that the semicircle cross-section helical groove has a significant advantage over other shapes for enhancing the heat transfer coefficient. Moreover, the best program of the optimized total heat transfer coefficient is
A3,
B1, and
C1 for the low tube flow rate, low shell flow rate condition (Condition I). With the increase in the tube flow rate and shell flow rate (Conditions II, IV, and V), the best optimization scheme of the total heat transfer coefficient is
A3,
B1, and
C2. It should be noted that when the tube flow rate is much higher than the shell flow rate (Case III), the best optimized solutions for the total heat transfer coefficient are
A3,
B2, and
C1.
Figure 9 also shows that it is always impossible to achieve the optimal flow resistance characteristic optimization at the same time as the optimal heat transfer performance optimization. Therefore, in this paper, the effectiveness evaluation parameter
EEC proposed by Liu et al. [
28] for the complex flow of heat exchangers is used for the evaluation, and the calculation method is shown in Equation (9):
where
Q is the heat transfer,
is the pump power, and
qv is the volume flow rate. The numerator represents the heat transfer benefit; the denominator represents the pump power loss. Equation (9) directly represents the ratio of heat transfer gain to flow cost.
The analysis results for the
EEC are shown in
Table 7 and
Figure 10. As seen from
Table 7, the factor influence of the
EEC decreases in the order
C >
A >
B according to the
R values. Furthermore, the contribution of
C,
B, and
A based on the
CR values to the
EEC influence range are from 74.51% to 80.33%, around 15%, and between 2.95% and 9.73%, respectively.
Figure 10 presents the level of influence of each factor for the
EEC. In the case of a low pipe flow rate (Conditions I, IV, and V), the optimum level of the helical baffle–corrugated tube heat exchanger is
A3,
B1, and
C3 in terms of heat exchanger efficiency evaluation coefficients; in the case of large pipe flow rates (Condition II and III), the optimum level of the helical baffle–corrugated tube heat exchanger is
A3,
B3, and
C3.
Heat exchanger research aims to improve equipment performance, but achieving an optimal balance between the heat transfer coefficient and pressure drop is challenging in production. The EEC index can help address this issue by evaluating comprehensive performance. In this study, the EEC index is used to optimize structural parameters, offering practical ideas for production.