# Design and Additive Manufacturing of TPMS Heat Exchangers
## 2 Design and Modeling of TPMS HXs
### Modeling and Simulation Results  
The conjugate heat transfer (CHT) model HX-70 in ANSYS Fluent was analyzed in order to calculate the performances of the heat exchangers infilled with gyroid lattice. The HTC and the pressure drop were calculated by the CHT model HX-70. The flow field and temperature field are shown in Figures 12 and 13.  
The impact of thickness and thermal conductivity on HTC and pressure drop were investigated by using the flow chart in Figure 7. Figure 14 shows the normalized HTC as a function of thermal conductivity for three different gyroid wall thicknesses: 0.32 mm, 0.64 mm, and 1.31 mm. In the simulation, all the data, with a variety of thicknesses, were normalized to the maximum HTC (W/K.m\({}^{2}\)) or thermal capacity (Watt) in the simulated range of thermal conductivity from 0.1 to 1000 W/m\(\cdot\)K. Obviously, the highest thermal conductivity and lowest wall thickness gives the maximum HTC or thermal capacity. This shows that the HTC or thermal capacity is less sensitive to the thickness change. A change of less than 5% occurs when the thickness changes from 0.32 mm to 1.31 mm. More interestingly, when the thermal conductivity is higher than 100 W/m\(\cdot\)K, less than a 10% change in HTC or thermal capacity occurs when varying thermal conductivity from 100 to 1000 W/m\(\cdot\)K. This is very important for cost and weight reduction of HXs, because Al alloys can be used to obtain comparable results with copper alloys.  
The pressure drop in the HX is shown in Table 3. The HX-70 performances were compared with the commercial HX, BT3\(\times\)8-20, as is shown in Figure 15. It shows that a two times reduction in size, a two-to-three times reduction in pressure drop, and a two-to-three times increase in heat transfer coefficient can be achieved for a 3 \(\times\) 3 \(\times\) 3 inch\({}^{3}\) gyroid HX (HX70-555, 0.3 mm wall thickness and 5 mm gyroid unit length) in comparison with a commercial 20 kW plate HX (model BT3\(\times\)8-20, dimension 3 \(\times\) 8 \(\times\) 2.2 inch\({}^{3}\)) at the same flow rate. These unprecedented features make the TPMS HX stand out, and deserves further intensive investigation.  
The temperature field of the HX-70 (capable of 20 kW thermal power management) is shown in Figure 16 (Left), which was calculated by the ANSYS Fluent. The mechanical stress of the HX70-101010\(-\)0.3 mm, made from aluminum under 2 MPa water pressure in one volume, was about 30 MPa.  
The distribution of the temperatures may result in thermal stress in the HX-70 during operation. The thermal stress of the HX-70 was calculated based on the temperature field. The temperature difference was 40 K for water fluid. The thermal stress of the HX-70 is  
Figure 14: Normalized HTC (**Left**) and thermal capacity (**Right**) as a function of thermal conductivity for three different gyroid wall thicknesses.  
Figure 15: Comparison between gyroid structure HXs and commercial plate type HX (BT3\(\times\)8-20) at various flow rates. (**Left**) Heat transfer coefficient (HTC), (**Right**) pressure drop.  
shown in Figure 16 (Middle). The maximum stress was about 47.5 MPa, much less than aluminum strength (240 MPa).  
The results under both thermal load and fluid operation pressure are shown in Figure 16 (Right). The water fluid pressure load was set at 2 MPa. The maximum stress of the HX-70 was about 72 MPa, which is still less than aluminum (240 MPa), and comparable with the strength of plastic PC.