*2.5. Boundary Conditions and Simulations Settings*

Each of the computational domains corresponding to the geometric variants was given homogeneous boundary conditions. The zones defined are inlet, bypass inlet, outlet, wall and symmetry, marked in Figure 5. The inlet boundary condition corresponds to a flow of 90% of the main exhaust stream at a temperature lower than that required for the efficient operation of the SCR reactor. The design inlet type was defined as a mass flow inlet. The main inlet turbulence was specified with the intensity ratio and the hydraulic diameter. Immediately upstream of the design inlet, the boiler has a heat exchanger covering the entire cross-section of the flue gas duct. Therefore, the flue gas flow upstream of the inlet is

relatively uniform and regulated, making it possible to apply the uniform velocity field condition at the domain inlet.

The bypass inlet boundary condition corresponds to the higher temperature flue gases introduced into the main duct. These flue gases are led at 10% of the total amount from the higher temperature boiler part. Mixed with 90% of the flue gases from the main duct, they are supposed to ensure the safe operation of the SCR reactor in the appropriate temperature range. The design type of the bypass flue gas inlet is a mass flow inlet type with a uniform perpendicular velocity field. The uniform velocity field simplification was applied due to the relatively large dimensions of the duct, whose cross-section is almost four square meters. The flow is not laminar, and wall effects are negligible. The turbulence was specified with the intensity ratio and the inlet bypass duct hydraulic diameter.

The domain outlet located just upstream of the SCR reactor was defined as a pressure outlet. The appropriate conditions were applied, such as backflow temperature, exhaust composition and turbulence defined by the intensity and hydraulic outlet diameter.

The remaining boundary conditions are the symmetry condition and the wall condition. The symmetry condition was given on one surface, indicated in Figure 5, and it corresponds to the second, symmetrical part of the boiler, clearly visible in Figure 1. The wall condition was given on all other surfaces of the computational domain, i.e., the external surfaces of the duct as well as all surfaces corresponding to the flow control elements installed in the duct. All walls both inside and outside the channel were modeled as adiabatic. This approach was justified because the walls inside the duct, which are part of the flow control elements, are heated up to the temperature of the flue gases during the continuous boiler operation. Meanwhile, the external duct walls are well insulated, as indicated by modern temperature measurements installed within the examined boiler section.

The key chemical reactions affecting the flue gas composition no longer occur within the investigated boiler section, so the composition was assumed to be homogeneous for the inlets and the outlet. The flue gas composition and other boundary conditions are shown in Table 2. As symmetrical duct operation was simulated, the mass values refer to half of the flow.


**Table 2.** Flue gas composition and the main boundary conditions.

The key applied solver settings in ANSYS Fluent are coupled scheme with second order discretization for all parameters, pseudo-transient mode, convergence criteria: 10-4. In order to properly evaluate the simulation correctness, relevant parameters were monitored: outlet mass flow, mass-weighted outlet temperature, maximum and minimum temperature in the domain, pressure drop across the duct. The accuracy of the monitored parameters was obtained at a level below 0.1%. Simulations were carried out with a computing server and utilization of 60 cores. The time required to run a single simulation was approximately 8 h.

The numerical model was verified by comparing the current boiler geometry modeling results with the empirical values. The calculations were performed for several operational states of the boiler. The obtained results of temperatures, pressure drops and exhaust gas velocity distribution were compared with the current measurement data. The parameters calculated using the numerical model for the existing boiler structure were convergent with the measured parameters.

#### **3. Results and Discussion**

After calculating all geometric variants, and checking the results for correctness through appropriate monitors, the outcomes obtained were evaluated. The most important results testifying the effectiveness of mixing flue gas streams with different temperatures are the temperature fields generated by the calculations carried out. The flue gas temperature distribution for each geometric variant in the plane intersecting the design domain is shown in Figure 6. The right-hand side of Figure 6 also shows the temperature distribution on a plane perpendicular to the direction of flow, intersecting the mixing flap.

**Figure 6.** The flue gas temperature distribution for each geometric variant in the plane intersecting the computational domain (on the left) and in the plane perpendicular to the flow direction intersecting the mixing flap (on the right).

After analyzing the simulation results, it can be concluded that the most uniform temperature distribution was obtained for the G4 geometric variant. The simulation results of G1 variant indicate that the higher temperature exhaust gas is initially led to the lower part of the duct. However, immediately after the mixing flap, through buoyancy forces and the mass-dominant flow of the denser exhaust gas with a lower temperature, the hot exhaust gas is pushed to the upper part of the duct. They are then mixed to a small extent in the further duct section.

In variant G2, where U-profiles are used, mixing the flue gases is slightly better than in variant G1. In that case, however, most of the hot flue gases right after the bypass duct inlet are forced by the stream of denser and cooler flue gases into the spaces between the U-profiles and flush out the hot flue gases from further parts of the U-profiles. Therefore, the U-profiles installed in this way do not fulfill their intended role, not delivering the hot flue gases to the lower main duct section. Immediately after the mixing flap, the flue gases are directed upwards by buoyancy forces and mix to a small extent in the further section of the duct.

Variant G3 shows an improvement in the level of flue gas mixing compared to variants G1 and G2. The application of U-profiles with a flat section at the flap top allows for an appropriate hot flue gas distribution to the lower parts of the U-profiles. The initial flat section prevents hot flue gases from being washed out by the lower temperature main stream. However, as previously mentioned, the dimensions of each flap had to be adapted to the condition of maximum coverage of half the main duct cross-section. Therefore, U-profiles with a total width of two-thirds the width of the duct cannot be longer. Since the U-profile of variant G3 is wide but relatively short, the hot flue gases are not introduced deep enough to mix effectively with the cold flue gases.

The G4 variant represents the final concept developed, which represents a modification of the G3 variant. Similar to variant G3, a flat section is used in the upper flap section followed by three U-profiles. Variant G4 uses U-profiles that are narrower and longer than the profiles used in variant G3. As with G3, the flat section of the flap prevents the hot flue gases from being washed out in the upper duct section and ensures adequate hot flue gas distribution to the U-profiles. Suitably long profiles transport the hot flue gases to the lower part of the main duct. Then, due to the buoyancy forces, the hot flue gases are mixed with the main flue gas stream of higher density and lower temperature. Further downstream, the flue gas temperature is homogenized. Since the plane on which the temperature is displayed follows the curvature of the flue gas duct, clearly visible in Figure 1, the hot flue gas portion in the U-profile is cut off, so the observer cannot see the hot flue gas entering the end of the profile.

Figure 7 shows the temperature distributions at the computational domain outlet, corresponding to the SCR reactor exhaust inlet. The temperature scale has been narrowed to 100 K (from 570 to 670 K). The target temperature of the perfectly mixed exhaust gas is 597 K. The best degree of mixing of flue gases was obtained in the geometrical variant G4, as can be seen in Figure 7. In this case, the maximum flue gas temperature was 616 K, which is only 2.18% of the percentage deviation from the perfectly mixed flue gas temperature of 597 K. The minimum flue gas temperature, in this case, was 573.6, which is a deviation of 3.91% from the target temperature. In the cases G1–G3, the temperature amplitudes are considerably larger. All exceed values of 100 K. Simultaneously, in the lower section of the duct, flue gases with a low temperature (close to the initial temperature of the main stream) are observed, which indicates a complete lack of mixing of the lower layers of flue gases.

**Figure 7.** The temperature distributions at the computational domain outlet for each geometric variant.

Figure 8 shows a plot of the minimum and maximum temperatures found for each geometric variant at the outlet of the computational domain representing the inlet to the SCR reactor. The graph also shows the temperature amplitudes at the domain outlet, indicating the degree of exhaust gas stream mixing.

**Figure 8.** Plot of temperature and amplitude of flue gas temperature at duct outlet for each geometric variant.

The velocity vectors determined on the plane intersecting the computational domain are shown in Figure 9. It can be seen that for variant G1, the velocity of the main flue gas stream increases significantly in the area under the turbulizing flap. Meanwhile, a low-pressure field and backflows are created in the upper part behind the flap. In the G2 variant, the flue gases flow freely through the spaces between the turbulence flap's U-profiles, creating a slight swirl of gas behind the flap. The flow is then stabilized. As in the geometrical variant G1, in the variant G3 with its wide U-profile, the main exhaust flow velocity increases significantly in the area below the flap. Above the flap, a low-pressure field is created together with the backflow. The most uniform velocity field was obtained for variant G4, which is also the most effective in mixing the exhaust gas streams. The main exhaust stream flows gently through the relatively wide spaces between the flap U-profiles. Slight turbulence is created in the upper duct behind the flat part of the turbulence flap.

**Figure 9.** The flue gas velocity distribution for each geometric variant in the plane intersecting the computational domain.

#### **4. Conclusions**

This article presents an innovative method of mixing flue gas streams in a coal boiler using the designed mixing flap. The presented work is concerned with supporting the SCR system operation under low-load conditions of coal-fired boilers, contributing to the flexibility of the operation of these devices. The developed solution was exposed to CFD calculations, in which the distributions of temperature, velocity, density and other key thermodynamic parameters were examined. The results indicate that the invented flap works as intended, causing an adequate mixing of the exhaust gas streams. It results in a uniform gas temperature field before the inlet to the SCR system. The analyses showed that the mixing flap developed by the authors could lower the flue gas amplitude in the desired cross-section from 298 K to 43 K. In the intermediate solutions, amplitudes of 144, 125 and 106 K were obtained. By appropriate mixing, the maximum flue gas temperature was reduced by 251 K. In addition, the developed solution was subjected to computational analyses with regard to its functioning in the case of boiler operation with nominal load. The flap, as previously mentioned, can be folded towards the upper wall of the duct. It allows safe boiler operation in nominal conditions without significant pressure losses in the flue gas duct.

The developed solution entails investment costs and operating costs. However, due to the current energy policy and the need for coexistence of coal-fired boilers with renewable energy sources, such solutions are necessary for these facilities to function. As in the flue gas treatment installation, this type of modernization does not provide direct profits from the implementation but allows the facility to operate in new conditions of the energy system.

It is planned to create a construction design and then install the device on the OP-650 boiler in the longer term. Work will then be carried out to optimize the method. The next steps will involve the application of the method in coal boilers with different power ranges. Although the solution is dedicated to power boilers, it is possible to use the developed concept in other systems requiring mixing gases with different temperatures.

**Author Contributions:** Conceptualization, P.K., M.K.-G. and J.L.; final geometrical concept, P.K.; methodology, P.K. and M.K.-G.; numerical simulation, M.K.-G.; writing—original draft preparation, M.K.-G.; writing—review and editing, M.K.-G.; visualization, M.K.-G.; supervision, P.K. and J.L.; project administration, P.K. and J.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** This research is supported by the National Centre for Research and Development which is co-financed by the European Union in the framework of the Smart Growth Operational Programme and the Power Units 200+ Program. Innovative technology of changing the operating regime of 200 MWe power units.

**Conflicts of Interest:** The authors declare no conflict of interest.
