**1. Introduction**

Petrochemical, cement, mineral, powder processing industries, use cyclone separators extensively for separating or filtering fine particles from the primary phase. They are also used in boilers for recovery of particulate fuel, in vacuum cleaners and in biomedical applications for filtering microscopic bacteria from the air. In industries all over the world, cyclone separators are subjected to a variety of operating conditions at which they need to work efficiently. Therefore developing an understanding of the relation between performance and the operating conditions is important. The operating conditions mentioned here refer to the velocity, temperature of the incoming dust-laden air and the size distribution, the concentration of the particulate matter suspended in the air stream. The performance of the cyclone separator is represented by two parameters, firstly the pressure loss across the cyclone, (its dimensionless form being the Euler number) and secondly its collection efficiency over the range of particle diameters (dimensionless form being the Stokes number), fed into the cyclone. This is presented in the form of a curve plotted between the particle diameter (Stokes number) and its collection efficiency known as the grade efficiency curve. This curve brings into the picture a new parameter known as the cut-size diameter Stk50 which has been used extensively to provide a sense of the collection efficiency of a cyclone separator. The cut-size

diameter is the particle diameter that corresponds to 50% collection efficiency on the grade efficiency curve. Physically it means that for the given operating conditions and the particular cyclone separator, particle diameters lesser than the cut-size will have less than 50% of the incoming solids getting collected in the dustbin. Whereas more than 50% of the larger particle diameters will be collected in the dust bin. This is observed in cyclone separators as the heavier particles have greater inertia and are more prone to separate from the swirling flow in the cyclone separator and move towards the walls. But the lesser diameter particles tend to move with the flow and are hence very difficult to separate. This behavior which determines whether a particle will be heavy enough to separate from the flow or be light enough to follow the flow depends on the drag exerted on the particle by the airflow and the Reynolds number of the flow. As the Reynolds number of the flow is same for all the particle sizes, the drag emerges as an important factor and is dependent on the diameter and roughness of the particle as suggested earlier that the grade efficiency curve is a function of the particle size.

Research suggests that apart from particle size, the grade efficiency curve or simply the collection efficiency for different particle sizes also shows a variation with the particle concentration inside the cyclone separator. Hoffmann et al. [1] experimented three cyclone models with different vortex finder diameters at three different inlet velocities and presented the variation of the two performance parameters with respect to solids loadings (0–0.04 kg/m3 ). The relation between separation efficiency and vortex finder diameter was found to be inversely proportional as reported by Brar et al. [2]. The separation efficiency improved with inlet velocity but only up to a certain solid loading, after which the reverse was seen. They concluded that an increase in solid loadings reduced the pressure drop slightly and increased the overall collection efficiency. An interesting point observed was that at lower inlet velocity (10 m/s) the improvement in efficiency due to an increase in solid loadings was higher than that at higher inlet velocity (20 m/s). The curves crossed at a solid loading of 0.02 kg/m3 . A similar observation of obtaining a higher collection efficiency at 18 m/s than at 27 m/s was reported by Fassani and Goldstein [3] who conducted experiments at solid loadings as high as 20 kg of solids/kg of gas. They further reported that dust-laden air showed lower pressure drop values than that of dust-free air, collection efficiency improved with solid loadings up to 12 kg of solids/kg of gas, after which reduction in efficiency was seen.

It has been reported that two-way coupling simulations are necessary beyond a certain solid loading threshold to capture the reductions in the swirl [4]. It has also been reported that if the cyclone separator load exceeded the critical load [1], improvements in separation performance would be seen. The present paper performance analysis of the Stairmand High-Efficiency Cyclone (SHEC) at four different solid loadings with the help of one way and two-way coupled Large-eddy Simulations. Both one way and two-way coupled simulations are performed to enquire if they can capture the reduction in swirl and the improvements in separation performance at solid loadings of 0.05, 0.1, 0.2 and 0.3 (kg of dust per kg of air). Many studies on the effect of mass loadings on the efficiency of cyclone separators are available in literature such as [1, 4–6]. But the upper limit of the range studied in most of them is only 0.1 kg of dust per kg of air, whereas Derksen et al. [7] investigated the effects on the flow up to the range of 0.2. Although the solids loading of 0.2 has been investigated by Derksen et al. [7] the authors stated that as the simulations were computationally expensive, they could not perform extended simulations to get quantitative results on various quantities. The present paper extends the upper limit of solid loadings to 0.3 and performs a comparison of one way and two-way coupled simulation strategies. The validation of the clean gas flow pattern with experimental data [8] has been done, this helps emphasize the particle modeling approach and its accuracy.
