Numerical calculation of the performance of cyclones for gas-particle separation is becoming a popular tool for cyclone analysis and design. A traditionally accepted way to treat these problems is by solving the flow field and particle transport equations in the spatial domain (C1) limited by the inlet and overflow outlet cross-sections, where the flow is usually assumed fully developed, and the dust outlet cross-section. Formulation of the boundary conditions for the flow and particles' transport at the dust outlet cross-section remains an open question. We address this problem numerically by comparing results of calculations performed by the above traditional approach, i.e., treating the problem in configuration C1, as well as in extended domains, namely those including a dust collecting bin (configuration C2) and a downcomer tubular outlet (configuration C3). Two boundary conditions at the downflow outlet were checked for each configuration, namely, a blocked outlet (zero velocity) and an open outlet (zero gas flow rate). Toward this goal, an efficient computational fluid dynamic (CFD) model of turbulent flow based on the Reynolds Stress turbulent closure scheme was developed, validated, and used to calculate velocity field and the pressure drop as well as particle cut size and separation efficiency in several Stairmand-type tangential flow cyclones. The results were tested and corroborated against the experimental data reported in the literature, including careful measurements performed by Gottschalk and Bohnet (1995, 1998) for a 225 mm tangential flow cyclone, with downflow outlet connected to a tubular extension. Particle separation in the traditional C1 cyclone configuration was shown to be most sensitive with respect to the choice of the boundary conditions at the downflow outlet, whereas with the dust outlet connected to a bin (C3 configuration) this condition has a much weaker effect on the fractional efficiency. Solutions for the C1 and C2 configurations, both combined with the blocked downflow outlet boundary condition yielded the cyclone's pressure drop in agreement with the Gottschalk and Bohnet's data. However, C2 configuration which contained a downcomer tubular extension was found preferable for correlating the measured fractional efficiency.