3.4.1. Simulation of the Tracer Concentration Profile

By using CFD simulation, the time profiles of the concentration of the tracer were calculated at any point along the stack, in order to make a comparison with experimental data and to select the best method to calculate the gas velocity during TT measurements. The simulated concentration profile varies along the vertical axis, as a consequence of the progressive mixing of the tracer. This makes the curves, at the two measuring planes, not perfectly overlapping and a specific criterion has to be defined in order to select the two reference timestamps (one for each curve) to be compared to measure the time delay for velocity calculation. Different choices, for these points, produce slightly different outcomes in terms of velocities, which means that this choice is an essential aspect of the method. The expected profiles of the concentration of the tracer, along the vertical axis of the stack, as calculated through CFD simulations, are reported in Figure 10, for an average gas velocity of 6 m/s and a temperature of 105 ◦C, as well as the corresponding bi-dimensional distributions, on a vertical plane, at 0.75, 1.25 and 1.75 s, as explained in the caption.

**Figure 10.** Computational fluid dynamic (CFD) tracer concentration profile along the stack axis (average velocity 6 m/s, T = 105 ◦C). Time origin is the transit time of the tracer at the upper junction (grey in the figures). (**a**) 0.75 s; (**b**) 1.25 s; (**c**) 1.75 s.

It can be observed that the increase/decay curve spans for a long distance along the vertical axis; from this point of view, these conditions are quite different from an ideal plug flow. The shape of the curve actually changes along the axis: its slope decreases and the peak broadens, as expected. In Figure 11 experimental and model results are compared: the signals of TT measurements collected at the lower and upper measuring planes are plotted together with the results of CFD simulation (circles) at the same test conditions. The broadening effect is produced by the combination of the bulk velocity of the flow and the diffusion velocity of the tracer molecules. The second peak in the simulation shows a larger broadening effect compared to the experimental results. It can be assumed that the adopted model of turbulence overestimated the turbulent diffusivity of the system. More advanced modeling, for instance including Large Eddy Simulation (LES) could have produced a better matching, but a fully detailed simulation is outside the scope of this work.

Molecular and turbulent diffusion produces an apparent velocity, which gives incorrect results if the reference timestamps of each curve are not selected properly. As far as an isotropic diffusivity is assumed, each molecule diffuses randomly in any direction: molecules mainly diffusing in the flow direction move faster than average fluid-dynamic velocity, while molecules diffusing mainly against the flow direction move slower than average fluid-dynamic velocity. Consequently, these points are not suitable for measuring the bulk velocity of the flow. The centroid of the tracer spike should be identified in order to get a correct result from the TT technique; EN ISO 16911-1 states that the best choice is the median of the concentration distribution. A specific analysis has been carried out to compare different possible criteria. The simulated concentration distributions can be used to compare the results one can

expect by applying different approaches of calculation on the same data. In Figure 12 the average gas velocity was estimated from three different sets of points, on the simulated curves: the peak of the curve, the median, and the mid-point between the maximum slope at both sides of the peak (the inset shows the location of these points). These calculations have been repeated for several axial distances, in order to evaluate the effect of the separation between the two measuring points. The best matching with the known average actual velocity is produced using the peaks. The velocities calculated based on the median are equally in good agreement with the expected result, except for very short distances when velocities would be overestimated. The sloping approach produces more erratic results, probably due to the fluctuations produced by the numerical derivation of the curves. It is noteworthy, anyway, that the three points, selected on each curve, are quite close to each other, because of the symmetry of these curves, while many different results may be expected in more asymmetric conditions.

**Figure 11.** Comparison between simulation and experimental data for concentration profiles at the average velocity 6 m/s, T = 105 ◦C).

**Figure 12.** Calculated velocities using different points on the simulated tracer concentration curves at different times (average velocity 6 m/s, T = 105 ◦C).

3.4.2. Simulation of Velocity Field Inside the Stack

A simulation of the velocity field inside the stack was carried out in order to understand how critical is the positioning of the Pitot tube, due to the fact that the flow field inside the stack does not feature a cylindrical symmetry, but a complex behavior, as reported in literature [3,21]. Figure 13

shows the calculated components of the gas velocity along the stack. The velocity vectors on the horizontal section where the Pitot probe was installed are shown in detail in Figure 14: the flow field is strongly asymmetric and the vectors are inclined in a quite complex configuration. As a consequence, the location of the Pitot probe can critically affect the velocity measurements and deserves further investigation.

**Figure 13.** Simulated velocity field inside the stack simulator in all its components: (**a**) total, (**b**) axial, (**c**) radial and (**d**) tangential velocity. Units are m/s.

**Figure 14.** Simulation of the flow field along a horizontal section of the duct, corresponding to the Pitot port position. Units are m/s.
