# Design and Additive Manufacturing of TPMS Heat Exchangers
## 2 Design and Modeling of TPMS HXs  
### Design Procedures of TPMS HXs  
As shown in Table 1, the SplitP lattice has the highest surface area-to-volume ratio and Schwarz has the lowest surface-to-volume ratio at the same lattice unit length. The surface-to-volume ratio of different lattices increases linearly when the lattice unit length decreases. A conjugate heat transfer (CHT) model HX-40 in ANSYS Fluent was built in order to compare the performances of heat exchangers with different types of TPMS lattice. The steady state 3D flow field, including pressure, velocity and temperature, was calculated. The viscous model used in the analysis was an SST k-\(\omega\) model. The energy equations were included in the simulation in order to calculate the heat transfer in the heat exchanger. The inlet boundary condition was a mass flow inlet, and the outlet boundary condition was a pressure outlet. The pressure of the outlet was 0 Pa. Two interfaces between the solid wall and fluid were created in order to transfer heat between the solid and the fluid. As shown in Figure 2, the core of the heat exchanger in the CHT model was cube shaped, with an edge length of 40 mm. The temperature field and velocity field were the simulation results that shown in Figure 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Lattice Type** & **Lattice Unit Length** & **Surface Area-to-Volume Ratio** \\  & **mm** & **mm\({}^{-1}\)** \\ \hline Gyroid & \(10\times 10\times 10\) & 0.62 \\ \hline Diamond & \(10\times 10\times 10\) & 0.78 \\ \hline Schwarz & \(10\times 10\times 10\) & 0.48 \\ \hline SplitP & \(10\times 10\times 10\) & 1.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the different types of TPMS lattice. Figure 3: The simulation results for model HX-40. Figure 2: The CHT model HX-40, used to simulate different types of lattices. Grey color indicates the solid structure. Pink color indicates high temperature water. Light blue indicates the cold water. The hot inlet temperature of the water was 348 K and the cold inlet temperature was 288 K. The flow rate range was 0.05-2 kg/s. In Figure 4, for the HX-40 model, three different types of lattices were infilled in the HX core. As the volume of the core was the same, the unit lengths of different lattices were changed in order to keep the surface areas in the HX-40 the same as each other. In Figure 5, the heat transfer coefficient (HTC) multiplied by the surface area A represents the heat transfer capacity of the HX-40. The HTC\(\times\)A was used to evaluate the capacity of the HX. In Figure 5, the horizontal axis is the pressure drop of the HX-40. The vertical axis is the HTC\(\times\)A. The horizontal axis and vertical axis are both in logarithmic scales. For different lattices, the results were almost the same. For example, for the HTC\(\times\)A and pressure drop, the Diamond, SplitP, and Gyroid lattices have almost the same performance results. In this paper, the gyroid structure was used as an example to illustrate the design and modeling method. Figure 6 shows a single gyroid cell unit with definitions for modeling. A large gyroid structure was assembled with copies of itself by using commercial software such as Solidworks 2016\(\times\)64 Edition and nTopology 4.23.2. Figure 7 shows the flow chart to design and model the HX. Several iterations were needed to optimize the HX's performance.