## 4 Model Application to Thermal Regenerator with WGR System  
The unsteady regenerator model is applied to the analysis of the WGR system. The WGR system is a low NOx strategy where a portion of exhaust gas is recirculated at the base of the RC in the air phase. The experimental tests on pilot furnaces performed in the PrimeGlass project [19] have confirmed that the WGR system does have an impact on the thermal balance of the regenerative chambers due to the increase of the mass flow rate and the increase in heat exchange caused by the introduction of radiant chemical species into the combustion air. In previous studies [16; 18], the WGR system was studied using CFD models in order to optimize the distribution of the waste gas in the stacker and the port to CC of the Cold RC. The CFD domain included the complete 3D geometry of the Cold RC [17], and the WGR ports were added at the bottom of the chamber. Multiblock structured meshes were generated, and the CFD solutions were obtained using the Ansys CFX CFD platform. The CFD model solved the Reynolds Averaged Navier-Stokes  
Figure 8: Capacitance of utilization variation for different RC sizing and inversion time. Figure 7: Thermal efficiency variation for different RC sizing and inversion time. (RANS) governing equations (continuity, momentum, energy) for the gas mixture using the second order upwind numerical scheme with the shear stress tensor (SST) turbulence closure added to model the effects of turbulence [15; 16; 17; 18]. The WGR system is investigated using CFD by changing the waste gas mass flow rate and the layout of the inlet ports. The following typical post-processing of the CFD solution is performed to understand the WGR system performance. The numerical CFD results are post-processed in order to track the waste gas flow inside the RC by detecting of the O2 concentration. The resulting O2 patterns in the case of waste gas/air mass flow ratio of 20% are reported in Figures 9-11. In Figure 9, the isosurface at 16% of oxygen concentration is highlighted in order to show the waste gas tracked across the Cold chamber. Figure 10 shows the oxygen concentration pattern in the stacker cross section at the stacking top. In Figure 11, the previous control surface of Figure 10 is discretized into twelve rectangular sections where the O2 and the mass flow distributions are plotted. From these analyses, it is clear that the waste gas flow fills only the first part of the chamber. The above experience gained from the application of 3D CFD has been used to inspire the WGR effects modeling into the present lower order code. The Cold RC is cut across its symmetry axis into three geometrical identical sub-sections in order to simulate the thermal effects from the WGR system. At each subsection, the mass flow, the fluid temperature, and the chemicals mass fraction are specified as boundary conditions (see Table 3). The above values can be obtained from a reference CFD solution (as in the present example) or taken from a range based on the experience gained using CFD on similar configurations. The profiles of the heat exchange coefficient for the Cold RC are obtained by adding to the reference linearized profiles [17] (valid for a standard regenerative system) the radiant effect introduced by the gas emission model presented in [20]. Figure 12 shows the heat transfer coefficient profile for each Cold RC sub-section. The first section is not fed with the waste gas (no radiant effect added), while the second and third sections have significant waste gas fraction; this explains the important heat transfer coefficient increase due to the radiant effect. Figure 11: Oxygen mass fraction and waste gas mass fraction distribution in the Cold phase chamber stacking (20% average waste gas fraction) [20].