# Heat Transfer Performance and Flow Characteristics of Helical Baffle-Corrugated Tube Heat Exchanger
## 2 Numerical Simulation and Verification
### Numerical Simulation Theory
 \tag{5}\]  
where  
\[C_{1}\ =\ \max\bigg{[}0.43,\frac{\eta}{\eta+5}\bigg{]},\quad\eta\ =\ S\frac{k}{\epsilon},\quad S\ =\ \sqrt{2S_{ij}S_{ij}}\]  
In these equations, \(P_{k}\) represents the generation of turbulence kinetic energy due to the mean velocity gradients, and \(P_{b}\) is the generation of turbulence kinetic energy due to buoyancy. The structural parameters of the continuous helical baffle heat exchanger for the study are as follows: the inner diameter of the shell is 100 mm, the length of the shell is 1400 mm, and the diameters of the tube and shell course inlet and outlet are 40 mm. The tube form is a light tube, the number of heat exchanger tubes is 51, the center distance of the tube is 12.8 mm, the outer diameter of the tube is 10 mm, and the wall thickness is 1 mm. The tube layout is in the form of positive triangular tube distribution, and the helical baffle is used with a helical pitch of 100 mm and a thickness of 2 mm. The thickness is 2 mm. In order to ensure the accuracy and computational efficiency of the numerical simulation, the following simplifications are carried out in the establishment of the geometric overall model: (1) neglect the shell thickness; (2) neglect the bolts, nuts, and other connectors at the continuous helical baffle. ANSYS Meshing is used for meshing, and for the complex structure of the heat exchanger, the mesh is a composite mesh of hexahedral mesh combined with tetrahedral mesh. The 3D model and element model are shown in Figure 1.  
The mesh quality affects the accuracy of the numerical simulation results greatly, but too many mesh nodes will increase the computational volume, making the computational cycle much longer with limited improvement in accuracy. Therefore, it is necessary to verify the mesh independence of the finite volume model. Element sizes of 1, 3, and 5 mm (corresponding to the number of nodes 1,721,994, 2,828,456, and 5,958,327, respectively) are selected to verify the mesh independence by comparing the numerical simulation with the  
Figure 1: Continuous helical baffle heat exchanger: (**a**) model; (**b**) finite volume mesh model. experimental shell pressure drop and heat transfer coefficient, and the results are shown in Table 1. According to the results in Table 1, the element size in this study is 5 mm. The discrete partial differential equation method in the numerical calculation is the finite volume method, the solver adopts a pressure-based steady-state solver based on the pressure correction algorithm, and the turbulence model adopts the Realizable k-\(\varepsilon\) model, which is one of the most commonly used turbulence models in Fluent to simulate turbulence effects in turbulence by solving the turbulence kinetic energy equations and turbulence dissipation rate equations. The Realizable k-\(\varepsilon\) model has higher accuracy and reliability than the traditional k-\(\varepsilon\) model and performs better in dealing with high Reynolds number flow, reverse flow, and shear laminar turning [27]. The standard wall function is used to deal with the flow near the wall, the Coupled algorithm is used to carry out the coupling calculation of pressure and velocity, and the second-order windward format is used to calculate the pressure. The momentum, turbulent kinetic energy, turbulent dissipation rate, and energy equations are discretized using the second-order windward format. The convergence accuracy of the energy equation is \(1\times 10^{-6}\), and that of other equations, such as the continuity equation and the turbulent kinetic energy equation, is \(1\times 10^{-3}\). The flow model takes the effect of gravity into account, the exit temperatures of the shell and tube courses are set as the reference variables for convergence, and the calculations are stopped when the exit temperatures are stable and the residuals are less than \(1\times 10^{-3}\). The heat transfer medium of the heat exchanger tube and shell processes is saturated water, and the change in physical properties of water with temperature is ignored.