3.2.3. Present Model

The data yielded by the present, FEA-based model are listed in Table 6 together with the values provided by the operator of the boiler. Here, the accuracy was slightly lower than that of HTRI Xchanger Suite, but it still was acceptable. The computational time needed to automatically create the meshes, reached in 39 major iterations the solution, and export the necessary solution data into Kitware ParaView for visualization purposes was ca. 240 s on the same average desktop computer used in the previous example. The ranks of the matrices were ca. 9000 and ca. 18,500 in case of fluid flow and heat transfer, respectively.

As mentioned before, the present model uses a one-dimensional mesh to represent the shell side. This means that the predicted temperature distribution was, too, only one-dimensional, while flow distribution across the shell-side cannot be predicted at all. In the tube side, on the other hand, the mass flow rate was known for each individual tube, and the predicted temperature distribution was spatially as fine or as coarse as the utilized tube bundle mesh. Figure 13 shows the predicted shell-side temperature distribution along the portion of the flue gas duct enclosing the two bundles, which was obtained using the present model, and the corresponding temperatures provided by the operator of the boiler and yielded by HTRI Xchanger Suite. The temperature curve yielded by the model matches the

point values reasonably well with the discrepancies being most likely caused by the usage of different equations for the calculation of the necessary heat transfer coefficients.

**Table 6.** Results obtained using the present model and the corresponding errors compared to the data from the operator of the boiler. The accuracy was not as good as in the case of HTRI Xchanger Suite, but, in terms of fast, approximate analyses of process and power equipment, it was sufficient.


**Figure 13.** Comparison of the temperature distribution in the portion of the flue gas duct enclosing the two bundles, which was obtained using the present model, and the corresponding temperatures provided by the operator of the boiler and yielded by HTRI Xchanger Suite ("HTRI XS"). Vertical distance along the channel corresponds to the distance from the point denoted "y = 0 m" in Figure 9.

Similarly as before, a combined plot of water and flue gas temperatures was generated using Kitware ParaView. This is shown in Figure 14.

The obtained tube mass flow rates were distributed quite uniformly in both bundles. The actual relative standard deviations from uniform flow distribution computed using

$$\delta = \frac{100}{\dot{m}\_{\rm id}} \sqrt{\frac{1}{n} \sum\_{i=1}^{n} \left( \dot{m}\_i - \dot{m}\_{\rm id} \right)^2} \tag{15}$$

where . *m*id denotes the ideal mass flow rate through one tube of the bundle, *n* the number of tubes therein, and . *mi* the mass flow rate through the *i*th tube, were 0.3% and 0.4% in case of the top bundle and the bottom bundle, respectively.

**Figure 14.** Visualization generated in Kitware ParaView of the bundles and the surrounding portion of the flue gas duct (front faces are culled). These were colored by the tube-side (water) and the shell-side (flue gas) temperatures obtained using the FEA-based model.
