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The coaxial cylindrical chamber in an experiment consists of the primary core zone and the secondary annual jet zone. Diameters of the primary inject, annulus jet, and main outer chamber are 32.0, 64.0, and 194.0 mm, respectively. The total length test section that is oriented vertically with the gravity acting in the direction of the flow is 960.0 mm. Predictions are laden with the ultralight expanded graphite (EP) and the copper beads with a density of 21.9 and 8900.0 kg/m3 with each diameter of 45.0 and 1000.0 μm, respectively. Glass beads are used to verify the simulation result, which have 2500.0 kg/m3 density and are 45 μm in diameter with Stokes number St = 0.025. As for the gas phase, the initial primary central flow rate is 9.9 g/s, the initial annular flow rate is 38.3 g/s, and the inlet Reynolds number is 52,400. The particle mass flow rate is 0.34 g/s and the particle loading in the primary flow η is 0.034, which is defined as the ratio of the particle to gas phase mass flow rates in eq 1. The mass flow rates correspond to the particle inertia leading to the different effects on inlet flow structures. Larger inertia particles are easier to be entrained to the primary central regions instead of secondary flow regions.

The swirling number is set to 0.47 in this simulation (see eq 2). The date output positions are obtained at the length of 3.0, 52.0, 155.0, 195.0, and 315.0 mm along the streamwise directions. Detailed schematic diagrams are shown in Figure Figure11.

where s is the abbreviation of swirling number, a is the annular jet, r is the radius, da is the diameter of the annular jet, ug and wg are the axial and tangential gas velocity, respectively, and ρg is the density of gas phase. A dimensionless parameter, Stokes number St, is defined by St = τsf as eqs 3 and 4, which is used to classify the degree of the particle entrainment into the gas flow. τs is the particle relaxation time and τf is the fluid time scale, respectively.

Schematic diagram of a coaxial swirling chamber.

The experimental parameters and simulation settings are given as Table 2. Moreover, the interim value of St = 1.11 in between 43.6 and 0.002 using copper particles with diameter of 160.0 μm is also simulated to investigate the trend of the effect of Stokes number in-between on turbulence modulations.

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