# Heat Transfer Performance and Flow Characteristics of Helical Baffle-Corrugated Tube Heat Exchanger
## 3 Results and Discussion
### 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. [PERSON] 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 L9 (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 \({}^{\circ}\)C and the shell inlet temperature was 20 \({}^{\circ}\)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. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{3}{c}{**Factors**} \\ \cline{2-4}  & **A: Section Shape of** & **B: Helix Angle of** & **C: Helix Angle of** \\  & **Helical Groove** & **Corrugated Tube (\({}^{\circ}\))** & **Helical Baffle (\({}^{\circ}\))** \\ \hline
1 & Triangle & 37.07 & 18.10 \\
2 & Rectangle & 53.09 & 35.33 \\
3 & Semicircle & 67.69 & 51.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Factors and levels. Figure 8: Cross-sectional shape of corrugated tube. 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:  
\[\left\{ \begin{array}{l}\dfrac{\sum\limits_{j=1}^{n}S(i,j)}{n}\\ R_{i}=\max\overline{K}_{i}-\min\overline{K}_{i}\\ CR_{i}=\dfrac{R_{i}}{\sum_{i=1}^{n}R_{i}}\end{array} \right. \tag{8}\]  
where the average values of each level for each factor were named as \(\overline{K}_{i}\) ; the variances between each factor were defined as \(R_{i}\) to analyze the difference between the maximal and minimal value of the four levels for each factor; and \(CR_{i}\) indicates the influence of each factor.