**2.1. Computational domain and mesh of the original design**

The natural gas heat exchanger has a nominal power of 390 KW, and the effective length of its heavy-duty vessel is 3785 mm with an outside diameter of 457.2 mm. As a sketch shown in **Figure 2**, it accommodates 138 (276 rods) heating elements. The diameter of these elements is 10.9 mm, and the length is 3277 mm for 64 long elements and 3252 mm for 74 short elements.

**Figure 2.** The computational domain of the original design.

Five keepers are inserted inside the vessel to maintain the proper radial positions of these elements. The nominal diameter of the inlet and exit pipes is 80 mm. The computational domain covers the whole flow field of the heater from the inlet to the exit, including heat elements and five keepers. It is important to mention that the whole natural gas heat exchanger assembly was mounted horizontally.

The mesh for one section of the heat exchanger vessel is shown in **Figure 3(a)**, and the mesh at a cross section cutting through heating elements is illustrated in **Figure 3(b)**. In these two plots, the meshed areas are where the natural gas flows, and the unmeshed hollow regions or circles are where the heating elements are located. **Figure 3(c)** is the mesh cutting through one keeper. As shown in **Figure 3(c)**, there are hundreds of small holes (11.5 mm in diameter) on the perforated plate of the keeper, 276 holes are considered blocked by the heating elements, and the rest meshed are flow passages. A narrow annular flow channel surrounding the keeper is used to keep the heating elements away from the vessel inner surfaces. Adjacent to the annular flow channel, parts of full circles are cut out by a flat bar of the keeper. The mesh size is ~4.0 million in the number of cells.
